Queensland University of Technology School of Engineering Systems
DEVELOPMENT OF AN INTEGRATED MODEL FOR
ASSESSMENT OF OPERATIONAL RISKS IN
RAIL TRACK
Venkatarami Reddy
Master of Applied Science (Research and Thesis)
Master of Information Technology
Principal supervisor:
A/Prof. Gopinath Chattopadhyay
Associate Supervisor:
Prof. Doug Hargreaves
Submitted to
Queensland University of Technology for the degree of
DOCTOR OF PHILOSOPHY
2007
2
ABSTRACT In recent years there has been continuous increase of axle loads, tonnage, train speed,
and train length which has increased both the productivity in the rail sector and the
risk of rail breaks and derailments. Rail operating risks have been increasing due to
the increased number of axle passes, sharper curves, wear-out of rails and wheels,
inadequate rail-wheel grinding and poor lubrication and maintenance. Rolling contact
fatigue (RCF) and wear are significant problems for railway companies. In 2000, the
Hatfield accident in the UK killed 4 people, injured 34 people and led to the cost of £
733 million (AUD$ 1.73 billion) for repairs and compensation. In 1977, the Granville
train disaster in Australia killed 83 people and injured 213 people. These accidents
were related to rolling contact fatigue, wear and poor maintenance.
Studies on rail wear and lubrication, rolling contact fatigue and inspection and rail
grinding analyse and assess the asset condition to take corrective and preventive
measures for maintaining reliability and safety of rail track. Such measures can reduce
the operational risks and the costs by early detection and prevention of rail failures,
rail breaks and derailments. Studies have so far been carried out in isolation and have
failed to provide a practical solution to a complex problem such as rail-wheel wear-
fatigue-lubrication-grinding-inspection for cost effective maintenance decisions.
Therefore, there is a need to develop integrated economic models to predict expected
total cost and operational risks and to make informed decisions on rail track
maintenance.
The major challenges to rail infrastructure and rolling stock operators are to:
1. keep rolling contact fatigue and rail-wheel wear under controllable limits,
2. strike a balance between rail grinding and rail lubrication, and
3. take commercial decisions on grinding intervals, inspection intervals, lubrication
placements, preventive maintenance and rail replacements.
This research addresses the development and analysis of an integrated model for
assessment of operational risks in rail track. Most significantly, it deals with problems
associated with higher axle loads; wear; rolling contact fatigue; rail defects leading to
early rail replacements; and rail breaks and derailments. The contribution of this
research includes the development of:
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� failure models with non-homogenous Poisson process and estimation of
parameters.
� economic models and analysis of costs due to grinding, risks, downtime,
inspection and replacement of rails for 23, 12, 18 and 9 Million Gross Tonnes
(MGT) of traffic through curve radius 0-300, 300-450, 450-600 and 600-800 m;
and application of results from this investigation to maintenance and replacement
decisions of rails. Cost savings per meter per year are:
• 4.58% with 12 MGT intervals compared to 23 MGT intervals for 0-300 m
• 9.63% with 12 MGT intervals compared to 23 MGT intervals for 300-450 m
• 15.80% with 12 MGT intervals compared to 23 MGT intervals for 450-600 m
• 12.29% with 12 MGT intervals compared to 23 MGT intervals for 600-800 m.
� a lubrication model for optimal lubrication strategies. It includes modelling and
economic analysis of rail wear, rail-wheel lubrication for various types of
lubricators. Cost effectiveness of the lubricator is modelled, considering the
number of curves and the total length of curves it lubricates. Cost saving per
lubricator per year for the same curve length and under the same curve radius is:
• 17% for solar wayside lubricators compared to standard wayside lubricators.
� simulation model for analysis of lubrication effectiveness. Cost savings per meter
per year for:
• 12 MGT grinding interval is 3 times for 0-450 m and 2 times for 450-600 m
curve radius with lubrication compared to without lubrication.
• 23 MGT grinding interval is 7 times for 0-450 m and 4 times for 450-600 m
curve radius with lubrication compared to without lubrication.
� a relative performance model, total curve and segment model.
� an inspection model for cost effective rail inspection intervals. Cost savings per
year for same track length, curves and MGT of traffic:
• 27% of total maintenance costs with two inspections, compared to one
inspection considering risk due to rail breaks and derailments.
� a risk priority number by combining probability of occurrence, probability of
detection and consequences due to rail defects, rail breaks and derailments.
� integrated model combining decisions on grinding interval, lubrication strategies,
inspection intervals, rectification strategies and replacement of rails.
Cost saving per meter per year for 12 MGT is:
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• 5.41% of total maintenance costs with two inspections, compared to one
inspection considering risk due to rail breaks and derailments.
• 45.06% of total maintenance costs with lubrication for two inspections,
compared to without lubrication.
Cost saving per meter per year for 23 MGT is:
• 5.61% of total maintenance costs with two inspections, compared to one
inspection considering risk due to rail breaks and derailments.
• 68.68% of total maintenance costs with lubrication for two inspections, per
year compared to no lubrication.
The thesis concludes with a brief summary of the contributions that it makes to this
field and the scope for future research in wear-fatigue-lubrication-grinding-inspection
for maintenance of rail infrastructure.
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ACKNOWLEDGEMENT The preparation of a substantial piece of work such as this thesis is not possible
without the assistance and support of a large number of people. I would like to take
this opportunity to acknowledge all those people who have contributed to the
completion of this project.
• My principal supervisor, A/Prof. Gopinath Chattopadhyay for his sincere
constant and determined support, encouragement, and guidance throughout
this research project. He spent his valuable time in discussing various
solutions related to the problems of the research project. I am indebted to him
for his patience during discussions and detailed examination of this
manuscript. His critical insight and valuable suggestions have contributed to a
great extent to the final form of this dissertation.
• My associate supervisor, Professor Doug John Hargreaves, Head of School,
School of Engineering Systems, for his valuable assistance, direction and
support for my research work and for providing valuable financial support,
without which it would have been impossible for me to continue this research.
• Dr. Per-Olof Larsson, Banverket, Swedish National Rail Administration, for
providing his support and valuable time for providing data and for helping me
in analysing the data.
• Professor Joseph Mathew, Chief Executive Officer, CIEAM and Associate
Professor Lin Ma, Faculty of Built Environment of Engineering for providing
financial support.
• Professor John Bell, Director and Assistant Dean of Research, for giving me
this opportunity and providing financial support.
• Mr. John Powell and Mr. Nicholas Wheatley, Queensland Rail, for their
support in providing data and analysis of models.
• Dr. Lance Wilson, Research Assistant for providing his support in analysing
data and analysis of the integrated model.
• Professor Uday Kumar, Head of Division of Operation and Maintenance
Engineering, Lulea University of Technology, Lulea, Sweden for providing
financial support during research in Sweden and presentation at the
COMADEM 2006 Conference.
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• Prof. Dinesh Kumar, Indian Institute of Management, Bangalore, India, for
proving his support in analysis of models during my candidature.
• Dr. Aditya Parida, Lecturer, Division of Operation and Maintenance
Engineering, Lulea University of Technology, Lulea, Sweden for providing
support during the exchange programme in 2006.
• Mr. Anisur Rahman, Mr. Praveen Posinaseeti and Mr. Ajay Desai, Mr.
Saurabh Kumar, Mr. Ambika Patra for helping me from time to time in
preparation of this thesis and in analysis of models.
• Finally, I express my heart felt appreciation to my wife Suneetha and my
Parents (Samba Shiva Reddy and Subbalaxmamma) and my sister’s family
(Sri Laxmi, Ramasubba Reddy, Surendranath Reddy and Sumathnath Reddy)
for their love, support, sacrifice and continuous encouragement throughout
this doctoral program.
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STATEMENT OF ORIGINALITY
I declare that to the best of my knowledge the work presented in this thesis is original
except as acknowledged in the text, and that the material has not been submitted,
either in whole or in part, for another degree at this or any other university.
Signed:………………………………Venkatarami Reddy
Date:
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LIST OF RESEARCH PUBLICATIONS PUBLICATIONS RESULTING FROM THIS THESIS Refereed international journal Papers (Published):
1. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson P. O. (2007) “Modelling and Analysis of Rail Maintenance Cost”, International Journal of Production Economics, 105, 475-482, Feb 2007 (Chapter 4).
2. Chattopadhyay G., Reddy V. and Larsson P. O. (2005) “Decision on
Economical Rail Grinding Interval for Controlling Rolling Contact Fatigue”, International Transactions in Operational Research, 12.6, 545-558, Nov 2005 (Chapter 4).
3. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004)
“Assessment of Risks and Cost Benefit Analysis of Various Lubrication Strategies for Rail Tracks Under Different Operating Conditions”, Published in TRIBOLOGIA – Finnish Journal of Tribology, 1 – 2 Vol. 23/2004, Norway, 32-40, ISSN 0780-2285 (Chapter 5).
Refereed international Conference and Journal Papers (under review/in process):
4. Reddy V. Chattopadhyay G., Hargreaves D. (2007). “Modelling & Analysis of Operational Risks due to Rail defects”, in process for IEEE Transactions on Reliability (Chapter 6).
5. Reddy V., Chattopadhyay G., Hargreaves D., (2007). “Analysis of
Lubrication Effectiveness for Different Rail Materials”, in process for International Journal of Tribology (Chapter 5).
6. Reddy V., Chattopadhyay G., Hargreaves D. (2007). “Rail-Wheel
Lubrication: An Overview”, in process for International Journal of Wear (Chapter 5).
Refereed international conference papers (Published):
7. Chattopadhyay G., Reddy V. (2007) “Cost-Benefit Model for Rail Inspection Decision Using Limited and Incomplete Data”, 20th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2007), 13th – 15th June, 2007, Faro, Portugal (Chapter 6).
8. Reddy V., Chattopadhyay G., Hargreaves D. (2006) “Analysis of Rail Wear
Data For Evaluation of Lubrication Performance”, 7th International Tribology Conference to be held in Australia and the 3rd in Brisbane AUSTRIB 2006 (Chapter 5).
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9. Chattopadhyay G., Reddy V., Hargreaves D. (2006) “Development of Framework for Benchmarking Rail-Wheel Lubrication”, 7th International Tribology Conference to be held in Australia and the 3rd in Brisbane AUSTRIB 2006 (Chapter 5).
10. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O. (2006)
“Techniques in Developing Economic Decision Model Combining Above Rail and Below Rail Assets”, 1st World Congress on Engineering Asset Management (WCEAM 2006), Gold Coast, Australia, Paper 58, ISBN 1-84628-583-6.
11. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O. (2006)
“Development of Wear-Fatigue-Lubrication-Interaction Model for Cost Effective Rail Maintenance Decisions”, 1st World Congress on Engineering Asset Management (WCEAM 2006), Gold Coast, Australia, Paper 59, ISBN 1-84628-583-6 (Chapter 7).
12. Reddy V., Chattopadhyay G., Larsson-Kråik P. O. and Hargreaves D. (2006)
“Analysis of field data to develop rail wear prediction model”, 19th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2006), Lulea, Sweden, 585-594, ISBN 978-91-631-8806-0 (Chapter 5).
13. Chattopadhyay G., Reddy V., Larsson-Kråik P. O., Hargreaves D. (2006)
“Rail-wheel lubrication practice: framework for lubrication effectiveness”, 19th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2006), Lulea, Sweden, 595-604, ISBN 978-91-631-8806-0 (Chapter 5).
14. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O.
(ICORAID-2005-ORSI) “Analysis of Lubrication Effectiveness For Different Rail Materials”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operation Research Society of India (ORSI) 27 - 29, December 2005 NSSC Auditorium, IISc, Bangalore, India (Chapter 5).
15. Chattopadhyay G., Reddy V., Pannu H. S. and Dinesh Kumar U. (ICORAID-
2005-ORSI) “Modelling and Analysis of Wear limit for Economic Rail Replacements”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operation Research Society of India (ORSI) 27 - 29, December 2005 NSSC Auditorium, IISc, Bangalore, India.
16. Larsson-Kråik P. O., Chattopadhyay G., Powell J., Wheatley N., Hargreaves
D., and Reddy V. (ICORAID-2005-ORSI) “Rail-Wheel Lubrication: A Conceptual Decision Model”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operational Research Society of India (ORSI) 27 - 29, December 2005, NSSC Auditorium, IISc, Bangalore, India.
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17. Larsson P. O., Chattopadhyay G., Reddy V. and Hargreaves D. (2005) “Effectiveness of Rail-Wheel Lubrication in Practice”, 18th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2005) Cranfield University, UK, 453-462, ISBN 1871315913.
18. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004)
“Comparative Evaluation of Various Rail-Wheel Lubrication Strategies”, 17th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2004) The Robinson College, Cambridge, UK, 52-61, ISBN 0-954 1307-1-5.
19. Reddy V., Chattopadhyay, G. and Larsson, P. O. (2004) “Technical vs.
Economical decisions: A case study on preventive rail grinding”. The Fifth Asia-Pacific Industrial Engineering And Management Systems Conference 2004 (APIEMS 2004). 12-15 December 2004, Gold coast, Australia, ISBN 0-9596291-8-1 (Chapter 4).
20. Reddy V., Chattopadhyay G. and Ong P. K. (2004) “Modelling & analysis of
risks due to broken rails & rail defects”. VETOMAC-3 & ACSIM-2004 Conference, 6th – 9th December 2004, New Delhi, India (Chapter 6).
Refereed international symposium
21. Reddy V. (ISRS 2004) “Development of Framework for Integrated Prediction Models for Analysis of Operational Risks due to Rolling Contact Fatigue (RCF) and Rail/Wheel Wear”, International Symposium for Research Students on Materials Science and Engineering, December 20th - 22nd, 2004, IIT Madras, India.
OTHER PUBLICATIONS
22. Chattopadhyay G., Soenarjo M., Powell J. and Reddy V. (2007) “Study and Analysis of Risks at Railway Level Crossings”, Second World Congress on Engineering Asset Management and the Fourth International Conference on Condition Monitoring (WCEAM CM 2007), 11-14th June, 2007, Harrogate, UK.
23. Kumar S, Chattopadhyay G., Reddy V. and Kumar U. (2006) “Issues and
Challenges with Logistics of rail Maintenance”, International Intelligent Logistics Systems Conference 2006 (IILS 2006), Brisbane, Australia, 16.1-16.9, ISBN 0-9596291-9-X.
24. Chattopadhyay G., Reddy V., Ong T. K. and Hayne M. (COMADEM 2004)
“Development of a Low Cost Data Acquisition System for Condition Monitoring of Rail Tracks”, 17th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2004) The Robinson College, Cambridge, UK, 62-69, ISBN 0-954 1307-1-5.
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25. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004) “Integrated Rail & Wheel Maintenance Model for Cost sharing by Rail Players”, VETOMAC-3 & ACSIM-2004 Conference, 6th – 9th December 2004, New Delhi, India.
26. Chattopadhyay G., Reddy V. and Larsson P. O. (2003) “Integrated Model for
Assessment of Risks in Rail Tracks under Various Operating Conditions”, International Journal of Reliability and Applications, 4.3, 113-120.
27. Chattopadhyay G., Reddy V. and Larsson P. O. (2003) “Mathematical
Modelling for Optimal Rail Grinding Decisions in Maintenance of Rails”, 16th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2003), Växjö, Sweden, Pg 565-572, ISBN 91-7636-376-7.
28. Chattopadhyay G., Reddy V., Larsson P. O. and Hargreaves D. (2003)
“Development of Optimal Rail Track Maintenance Strategies based on Rolling Contact Fatigue (RCF), Traffic Wear, Lubrication and Weather Condition”, 5th Operations Research Conference on Operation Research in the 21st Century, the Australian Society of Operations Research ASOR (Qld), Sunshine coast, Australia, 9-10 May, 2003, 54-66.
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NOMENCLATURE
a Expected cost per derailment [AUD]
Ac Critical railhead area when rail replacement is recommended [mm2]
Ai Cross sectional rail profile area ith interval [mm2]
AGWj Cross sectional area loss due to grinding in period j [mm2]
ATWj Cross sectional area loss due to traffic wear in period j [mm2]
A0 Cross sectional profile area of a new rail [mm2]
AH Hertzian contact area [m2]
AGWq Cross sectional area loss due to grinding in period [mm2]
ATWq Cross sectional area losses due to traffic wear in period q [mm2]
Alub Area below lubricated wear rate for high rail [mm2]
Anon-lub Area above non-lubricated wear rate for high rail [mm2]
% AHL percentage of reduction in area head loss [mm2/MGT]
A Dimension of table wear [mm2/MGT]
B Dimension of side wear [mm2/MGT]
Cr Cost per rectification of rail breaks on emergency basis [AUD]
cs Particular curve section under consideration [m]
c Expected cost of each rail break repair on emergency basis [AUD]
cd Down time cost [AUD/year]
cg Grinding cost [AUD/year]
ci Inspection cost [AUD/year]
cr Risk cost [AUD]
cre Replacement cost [AUD/year]
lc Lubrication cost [AUD/year]
totc Total cost [AUD/year]
mirsC Cost of maintenance during the failure of ith lubricator [AUD/year]
'mirsC Cost of emergency repair during the failure of ith lubricator [AUD/year]
'pirsC Cost of personnel involved in maintenance of ith lubricator [AUD/year]
rmC Cost of rail material per kg [AUD]
C0 Cost of each service on site [AUD]
Cdl Cost of each service pf lubricator in depot [AUD]
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0C Expected cost of each service on site [AUD]
dlC Expected Cost of each service pf lubricator in depot [AUD]
EC Total cost for electric lubricators [AUD]
mtC Maintenance cost for each lubricator in time t. [AUD]
reC Cost to replace rail [AUD]
trebC Benefit due difference between lubricated and non-lubricated rail [AUD]
CNDT Total expected cost for NDT inspection interval [AUD]
wC Total cost for wayside lubricators [AUD]
sC Total cost for solar wayside lubricators [AUD]
scC Setup cost for each lubricator lubricator [AUD]
jC Cost per unit time for running each train in period j [AUD]
d Expected cost of down time due to traffic loss [AUD/h]
da/dN Crack propagation rate [ - ]
da/dn Crack propagation rate [ - ]
D Sliding distance [m]
E Energy dissipation [J/m]
E [Mi+1, Mi] Expected number of failures over Mi and Mi+1 [ - ]
Ej [Mi+1, Mi] Expected number of failures over Mi and Mi+1 for jth strategy [ - ]
tE Electric consumption cost in time t [kWh]
Fx ,Fy Creep forces in x and y direction [N]
Fn(m) [fn(m)] Rail failure distribution [density] function [ - ]
Fj(m) [fj(m)] Rail failure distribution [density] function for jth strategy [ - ]
f2 = f(rlub) = f2(R) is the function of curve radius for the lubricated curve [mm2]
f2(R) = ( ) 1=Rφ , this is the traffic wear rate for Lubricated high rails [MGT/mm2]
f1 = f(rnon-lub) = f1 (R) the function of curve radius for the non-lubricated curve [mm2]
f1 (R) = ( ) 0=Rφ , the traffic wear rate for non-lubricated high rail [MGT/mm2]
f tangential friction force [ - ]
G Cost of grinding per pass per m [AUD/pass/m]
G(c) Distribution function of cost of each rail break repair [ - ]
jGD Wear Depth due to rail grinding after period j [mm]
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GDq Grinding Depth due to grinding after period q [mm]
GW Rail side (gauge) wear [mm2]
h Vertical central wear on the railhead [mm]
hDT Expected downtime due to each grinding pass [h]
H Material hardness [Pa]
H Weighted side- and height wear [mm]
Hlimit Critical H when the rail must be replaced [mm]
I Cost in investment of rail for segment L [AUD]
If Inspection frequency in Millions of Gross Tonnes (MGT) [ - ]
I Index [ - ]
ic Cost of each inspection [AUD]
j Index [ - ]
j Lubrication strategy [ - ]
k Cost of rectification of potential rail breaks based on NDT [AUD]
K wear coefficient of Archard equation [-]
∆K the range of the stress intensity factor [-]
L Length of rail segment under consideration [m]
L% Percent rail length under consideration [ - ]
m Millions of Gross Tonnes [kg.106]
mj MGT in period j [ - ]
mq MGT in period q [kg.106]
Mi Total accumulated MGT of the section studied up to decision I [kg.106]
jM Total accumulated MGT for the section studied up to decision j [kg.106]
MN Total accumulated MGT for rail life up to end of period N [kg.106]
MΦ Spin moment [Nm]
n The number of failures [ - ]
nw total number of wheels passing through the curve section [ - ]
nAj Number of accidents in period j [ - ]
nGPi Number of grinding passes for ith grinding [ - ]
nNDTj Number of detected potential rail breaks using NDT [ - ]
nRBj Number of rail brakes in between two NDT inspections [ - ]
nAq Number of accidents in period q [ - ]
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nGPij Number of grinding pass for ith grinding in jth strategy [ - ]
nNDTq Number of NDT detected potential rail breaks in period q [ - ]
nRBq Number of rail breaks in between two NDT inspections in period q [ - ]
N Normal load [N]
N(Mi+1,Mi) Number of failures over Mi and Mi+1 [ - ]
NI Number of inspection over rail life [ - ]
Nj Total number of periods up to safety limit for renewal for strategy j [ - ]
Nj(Mi+1,Mi) Number of failures over Mi and Mi+1 as per strategy j [ - ]
P[.] Probability [ - ]
Pi(A) Probability of undetected potential rail breaks leading to derailment [ - ]
Pi(B) Probability of detecting potential rail breaks using NDT [ - ]
EP Purchase price of electric lubricator [AUD]
wP Purchase price of wayside lubricator [AUD]
sP Purchase price of solar wayside lubricator [AUD]
spP Purchase price of the solar panel and its maintenance [AUD]
Rev Revenue per MGT [AUD]
q Index [ - ]
r Discounting rate between preventive rail grindings [%]
ri Discounting rate between inspections using NDT [%]
ry Annual discounting factor [ - ]
R Track circular curve radii [m]
RCw Estimated Rail Crown wear width [mm]
RGw Estimated Rail Gauge wear width [mm]
s Flange wear [mm]
S Speed of train [km/h]
Suj Supply of the year j [ - ]
T Tangential force [N]
icslTC Total cost of differential wear loss for particular curve section [AUD]
icsWTC Total cost of differential wear loss for particular curve section [AUD]
TDj Wear Depth due to traffic after period j [mm]
TDq Traffic Depth due to wear after period q [mm]
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TW Table (crown) wear [mm2]
VW Wear volume [m3]
WOLi Worn out level of rail after ith grinding [%]
wz Normal applied load [ - ]
Wt Weighted wear rate [ - ]
icsW Differential wear loss [mm2/MGT]
Wagonv Wagon capacity [ - ]
x the inspection intervals per year for a rail corridor under consideration [ - ]
γ Creepage [m/m]
γ’ slide/roll ratio [ - ]
γx , γy Creepage in x and y direction [ - ]
Φ Spin [-]
jY = Decision variable for lubrication strategy [ - ]
= 0 for no or continuous lubrication [ - ]
= 1 for stop/start lubrication [ - ]
y rail life in years [ - ]
α Miniprof degrees [o]
β, ( Weibull parameters [ - ]
Λ(m) Failure intensity function associated with m [ - ]
βj, λj Weibull parameters for failures in jth strategy [ - ]
Λj(m) Failure intensity function associated with m in jth strategy [ - ]
µ Coefficient of friction with film parameter Λ [ - ]
φ = Traffic wear rate [MGT/mm2]
Twear = Total wear rate between lubricated and non-lubricated curves [MGT/mm2]
17
CONTENTS
ABSTRACT…………………………………………………………………………..2
ACKNOWLEDGEMENT ………………………………………………..…………..5
Statement of Originality……………………………………………………..….……..7
LIST OF PUBLICATIONS……………………………………………..………….....8
NOMENCLATURE………………………………………………………………….12
LIST OF TABLES.......................................................................................................21
LIST OF FIGURES .....................................................................................................24
CHAPTER 1
SCOPE AND OUTLINE OF THESIS ........................................................................29
1.1 Introduction.........................................................................................................29 1.2 Scope of the research study.................................................................................31 1.3 Aims and Objectives ...........................................................................................31 1.4 Thesis Outline .....................................................................................................32
CHAPTER 2
OVERVIEW OF RAIL TRACK STRUCTURE, DEFECTS AND
MAINTENANCE STRATEGIES ...............................................................................34
2.1 Introduction.........................................................................................................34 2.2 Railway Track Structure .....................................................................................34 2.3 Rails ....................................................................................................................35 2.4 Fastening System ................................................................................................35 2.5 Sleeper (Tie)........................................................................................................36 2.6 Ballast..................................................................................................................37 2.7 Subballast ............................................................................................................38 2.8 Subgrade..............................................................................................................38 2.9 Track Component Characteristics .......................................................................38 2.10 Rail Degradation ...............................................................................................38 2.11 Rolling Contact Fatigue (RCF) and Grinding Strategies ..................................39 2.12 Rail Wear and Lubrication Strategies ...............................................................45 2.13 Inspection Frequency and Techniques ..............................................................50 2.14 Maintenance Strategies .....................................................................................54 2.15 Rail transposition ..............................................................................................55 2.16 Rail straightening ..............................................................................................55 2.17 Rail replacement ...............................................................................................55 2.18 Sleeper replacement ..........................................................................................55 2.19 Ballast maintenance ..........................................................................................56 2.20 Tamping ............................................................................................................56 2.21 Subgrade stabilisation .......................................................................................56 2.22 Operational Conditions .....................................................................................56 2.23 Summary ...........................................................................................................57
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CHAPTER 3
STUDY OF RAIL WEAR, ROLLING CONTACT FATIGUE AND RAIL MAINTENANCE MODELS.......................................................................................58
3.1. Introduction........................................................................................................58 3.2 Rail Wear and Rolling Contact Fatigue Models .................................................58 3.3 Rail Maintenance Models ...................................................................................70 3.4 NSW State Railway Authority’s Wheel-Rail Management Model ....................70 3.5 Railways of Australia (ROA) Rail Selection Module.........................................71 3.6 Railways of Australia (ROA) Rail Grinding Model ...........................................71 3.7 Railways of Australia (ROA) Wheel/Rail Management Model .........................71 3.8 ECOTRACK .......................................................................................................71 3.9 TOSMA...............................................................................................................72 3.10 Mini-MARPAS .................................................................................................73 3.11 AMP98 Cost Model ..........................................................................................73 3.12 Track Maintenance Cost Models (TMCOST) ..................................................73 3.13 Swedish Track Degradation Cost Model ..........................................................73 3.14 An Austrian Track Maintenance Cost Model ...................................................74 3.15 The UNIFE Life Cycle Costing ........................................................................74 3.16 Track Degradation Model .................................................................................74 3.17 Track Maintenance Planning Model (TMPM)..................................................75 3.18 Survey of Lubrication Practice .........................................................................75 3.19 Summary ...........................................................................................................85
CHAPTER 4
MODELLING AND ANALYSIS OF RAIL DEGRADATION AND RAIL GRINDING DECISIONS............................................................................................86
4.1 Introduction.........................................................................................................86 4.2. System Approach and Modelling.......................................................................86 4.3 Modelling Rail Breaks ........................................................................................87 4.4 Modelling Rail Degradation (Rail Section Loss)................................................90 4.5 Economic Grinding Model for Optimal Grinding Decisions..............................94
4.5.1 Modelling preventive rail grinding cost ....................................................98 4.5.2 Modelling down time cost due to rail grinding (loss of traffic) ................99 4.5.3 Modelling inspection cost..........................................................................99 4.5.4 Modelling risk cost of rail breaks and derailment ..................................100 4.5.5 Modelling Replacement Costs of Worn-Out Unreliable Rails ................101 4.5.6 Modelling Total Cost of Rail Maintenance .............................................101
4.6 Estimation of cost and life data.........................................................................102 4.6.1 Analysis of results....................................................................................102 4.6.2 Grinding cost ...........................................................................................102 4.6.3 Grinding cost/m.......................................................................................103 4.6.4 Grinding cost/MGT/m .............................................................................104 4.6.5 Risk cost/m...............................................................................................105 4.6.6 Risk cost/MGT/m .....................................................................................105 4.6.7 Down time cost/m ....................................................................................105 4.6.8 Down time cost/MGT/m...........................................................................106
4.7 Annuity Cost/m .................................................................................................107 4.7.1 Annuity cost/m for grinding.....................................................................107 4.7.2 Annuity cost/m for risk.............................................................................108
19
4.7.3 Annuity cost/m for down time..................................................................108 4.7.4 Annuity cost/m for inspection ..................................................................109 4.7.5 Annuity cost/m for replacement...............................................................110 4.7.6 Total annuity cost/m ................................................................................111
4.8 Annuity cost/m assessment for each MGT .......................................................111 4.8.1 Annuity cost/m for 23 MGT .....................................................................111 4.8.2 Annuity cost/m for 12 MGT .....................................................................112 4.8.3 Annuity cost/m for 18 MGT .....................................................................113 4.8.4 Annuity cost/m for 9 MGT .......................................................................114
4.9 Summary ...........................................................................................................115
CHAPTER 5
MODELLING AND ANALYSIS OF WEAR AND LUBRICATION DECISIONS………………………………………………………………………...117
5.1 Introduction.......................................................................................................117 5.2 Assessment of lubricator’s performance...........................................................119 5.3 Lubrication decision model...............................................................................122 5.4 Modelling rail wear ...........................................................................................127
5.4.1 Modelling Rail Wear Limits ....................................................................131 5.4.2 Modelling Rail Lubrication .....................................................................136 5.4.3 Modelling Repair Cost of Applicator due to Breakdowns.......................138 5.4.4 Modelling Replacement Cost of Applicator ............................................138 5.4.5 Cost for various Lubricator Maintenance Strategies..............................138 5.4.6 Modelling Lubricant Cost........................................................................139 5.4.7 Modelling Benefits of Lubricators by Reducing Rail Wear Cost ............139 5.4.8 COST-BENEFIT Analysis of Applicators and Various Lubricants.........140 5.4.9 Failure of Lubricators .............................................................................141 5.4.10 Cost for Fixing Breakdowns..................................................................141 5.4.11 Cost to Maintain Lubricators ................................................................141 5.4.12 Cost-Benefit Analysis of Lubricators.....................................................141 5.4.13 Cost of Lubricants .................................................................................142
5.5 Modelling Failures ............................................................................................142 Renewal Process...............................................................................................144
5.6 Framework for Benchmarking Lubrication ......................................................147 5.7 Modelling Annuity Cost of Lubricators............................................................148 5.8 Collection and Analysis of Data .......................................................................150
5.8.1 Estimation of Area Head Loss (AHL)......................................................151 5.8.2 Analysis of Wear for Curves radii 0-300 m.............................................152 5.8.3 Analysis of Wear for Curves radii 301-450 m.........................................159 5.8.4 Analysis of Wear for Curves radii 451-600 m.........................................164
5.9 Analysis of Annuity Costs ................................................................................170 5.9.1 Numerical Example .................................................................................173
5.10 Summary .........................................................................................................177
CHAPTER 6
MODELLING AND ANALYSIS OF INSPECTION FOR INSPECTION DECISIONS...............................................................................................................179
6.1 Introduction.......................................................................................................179 6.2 Modelling Inspection ........................................................................................179
20
6.2.1 Modelling Rail Breaks.............................................................................180 6.2.2 Modelling Replacement Costs of Worn-out Unreliable Rails .................181 6.2.3 Modelling Cost Benefit Analysis .............................................................181
6.3 Failure Mode and Effect Analysis (FMEA)......................................................182 6.3.1 Occurrence of Failure .............................................................................183 6.3.2 Detectability of Failure ...........................................................................184 6.3.3 Severity of Failure ...................................................................................186 6.3.4 Risk Priority Number Ranking (RPN) .....................................................188
6.4 Collection and Analysis of Rail Failure Data ...................................................190 6.4.1 Rail Defect Initiation ...............................................................................190 6.4.2 Rail Failures from Defect Initiation ........................................................192 6.4.3 Cost-Benefit Analysis of Inspection Frequency.......................................193 6.4.4 Analysis of cost data................................................................................195 6.4.5 Analysis of selected defect, rail break and derailment............................196 6.4.6 Limitations of data...................................................................................198
6.5 Total cost of rail inspection and rectification....................................................199 6.6 Limitations of Detecting Rail Breaks................................................................201 6.7 Effect of Seasonal Conditions on Rail Defect Initiation...................................202 6.8 Summary ...........................................................................................................203
CHAPTER 7
DEVELOPMENT OF AN INTEGRATED MODEL FOR ESTIMATION OF EXPECTED TOTAL COSTS ...................................................................................204
7.1 Introduction.......................................................................................................204 7.2 Development of the Integrated Model ..............................................................204 7.3 Analysis of Results............................................................................................207
7.3.1 Annuity costs/m for 12 MGT....................................................................209 7.3.2 Annuity costs/m for 23 MGT....................................................................210 7.3.3 Annuity costs/m for 12 MGT & 23 MGT.................................................212 7.3.4 Estimation of Annuity costs/m .................................................................214
7.4. Summary ..........................................................................................................229
CHAPTER 8
CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH ..................231
8.1 Introduction.......................................................................................................231 8.2 Contribution of This Thesis ..............................................................................231 8.3 Scope for Future Research ................................................................................234
REFERENCES ..........................................................................................................235
APPENDICES ...........................................................................................................250
Appendix - A .....................................................................................................250 Appendix – B.....................................................................................................258 Mechanism of Way-side Lubricators (Mechanical) .........................................276 Mechanism of Hydraulic Lubricators ..............................................................277 Visual Inspection ..............................................................................................278 Rail head temperature rise method ..................................................................278 Tribometer ........................................................................................................279
21
LIST OF TABLES
Table 3.1: Cost of Lubrication strategies.....................................................................77
Table 3.2: Lubrication costs to rail players..................................................................77
Table 3.3: Lubricators used in Sweden, 2004..............................................................80
Table 3.4: Lubricators used in UK...............................................................................81
Table 3.5: Lubricators used in Spoornet ......................................................................81
Table 4.1: Measurements of grinding ..........................................................................92
Table 4.2: Safety limit for Malmbanan........................................................................94
Table 4.3: The ideal grinding for heavy-haul ..............................................................95
Table 4.4: Track path divided into sections .................................................................97
Table 4.5: Estimated costs and area safety limits ......................................................102
Table 4.6: Grinding cost/m for 0 to 800 m curves .....................................................103
Table 4.7: Grinding cost/MGT/m for 0 to 800 m curves ...........................................104
Table 4.8: Risk cost/m for 0 to 800 m curves ............................................................105
Table 4.9: Risk cost/MGT/m for 0 to 800 m curves ..................................................105
Table 4.10: Down time cost/m for 0 to 800 m curves ...............................................106
Table 4.11: Down time cost/MGT/m for 0 to 800 m curves .....................................106
Table 4.12: Annuity cost/m for grinding 0 to 800 m curves......................................107
Table 4.13: Annuity cost/m for risk in 0 to 800 m curves .........................................108
Table 4.14: Annuity cost/m for down time in 0 to 800 m curves ..............................109
Table 4.15: Annuity cost/m for inspection in 0 to 800 m curves...............................109
Table 4.16: Annuity cost/m for replacement in 0 to 800 m curves............................110
Table 4.17: Total annuity cost/m for 0 to 800 m curves ............................................111
Table 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves .................................112
Table 4.19: Annuity cost/m for 12 MGT in 0 to 800 m curves .................................112
Table 4.20: Annuity cost/m for 18 MGT in 0 to 800 m curves .................................113
22
Table 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves ...................................114
Table 5.1: Cost of Trackside Lubrication ..................................................................120
Table 5.2: ‘Where to lubricate’ and ‘not to lubricate’ ...............................................124
Table 5.3: Expert Chart of Lubrication Effectiveness ...............................................125
Table 5.4 Traffic for Section A to B during period from 1998 to 2004 ....................150
Table 5.5: Area head loss (mm2/MGT) for 300 m curve...........................................153
Table 5.6: Costs of Wayside Lubricator ....................................................................171
Table 5.7: Estimated rail lives in heavy-haul track....................................................172
Table 5.8: Savings achieved ......................................................................................177
Table 6.1: Causes of Defective Rails.........................................................................183
Table 6.2: Causes of Broken Rails.............................................................................183
Table 6.3: Ranking of Failure Occurrence.................................................................184
Table 6.4: Ranking of Detectability...........................................................................185
Table 6.5: Train Accidents Jan 2000 - Dec 2003.......................................................186
Table 6.6: Severity Ranking of Failure......................................................................187
Table 6.7: Risk Priority Number (RPN) ratings ........................................................188
Table 6.8: Cost Benefit Analysis ...............................................................................200
Table 7.1: Examined cases with the integrated model...............................................208
Table 7.2: Annuity costs/m for 12 MGT with lubrication .........................................209
Table 7.3: Annuity costs/m for 12 MGT without lubrication....................................210
Table 7.4: Annuity costs/m for 23 MGT with lubrication .........................................211
Table 7.5: Annuity costs/m for 23 MGT without lubrication....................................212
Table 7.6: Analysis of total annuity costs/m for 12 MGT .........................................213
Table 7.7: Analysis of total annuity costs/m for 23 MGT .........................................213
Table 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection ...........214
Table 7.9: Annuity costs/m for 12 MGT without lubrication, one inspection...........215
23
Table 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection .........216
Table 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection ....217
Table 7.12: Annuity costs/m for 12 MGT with lubrication for two inspections .......218
Table 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections ..219
Table 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections .......220
Table 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections ..221
Table 7.15: Annuity costs/m for 12 MGT with lubrication for three inspections .....222
Table 7.17: Annuity costs/m for 12 MGT without lubrication for three inspections 223
Table 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections .....224
Table 7.19: Annuity costs/m for 23 MGT without lubrication for three inspections 225
Table 7.20: Total annuity costs/m for 12 and 23 MGT with lubrication...................226
Table 7.21: Total annuity costs/m for 12 and 23 MGT without lubrication..............227
Table 7.22: Findings from examined cases................................................................230
Table B1: Mean temperature rise...............................................................................278
Table B2: Friction Coefficients based on Tribometer ...............................................279
24
LIST OF FIGURES
Figure 1.1: Factors behind the problems......................................................................30
Figure 2.1: Cross sectional view of rail track structure ...............................................34
Figure 2.2: Profile of rail head.....................................................................................35
Figure 2.3: Spikes, Rail Anchors and Elastic Fastening System .................................35
Figure 2.4: Concrete and Wooden Sleepers and Fasteners..........................................36
Figure 2.5: RCF, Shelling and Gauge Corner Cracking ..............................................39
Figure 2.6: Flaking problems.......................................................................................41
Figure 2.7: Influence of rail wear from lubrication .....................................................47
Figure 2.8: Rail area worn off with and without lubrication .......................................47
Figure 2.9: Ultrasonic and induction techniques .........................................................51
Figure 2.10: Improved ultrasonic test vehicle system .................................................53
Figure 2.11: Automated re-railing machine.................................................................55
Figure 3.1: Synergy of rail metallurgy & track engineering........................................61
Figure 3.2 Phases of crack life using curve of da/dn and length .................................62
Figure 3.3 Truncation of a shallow angled crack.........................................................63
Figure 3.4 Life line due to wear and fatigue................................................................63
Figure 3.5: Head check (HC) and transverse rail fracture ...........................................66
Figure 3.6: Factors influencing rail/wheel degradation ...............................................69
Figure 3.7: Lubrication systems...................................................................................75
Figure 3.8: Lubricators are full of ice and snow in track.............................................79
Figure 3.9: Rail and wheel lubricators.........................................................................82
Figure 3.10: Bleeding from the blade ..........................................................................83
Figure 3.11: Short wave corrugation ...........................................................................84
Figure 3.12: Grease leakage and environmental hazard ..............................................84
Figure 4.1: Integrated system approach for modelling and analysis ...........................87
25
Figure 4.2: Rail profile measurement using MINIPROF.............................................91
Figure 4.3: Central vertical wear and side wear ..........................................................92
Figure 4.4: Measurement of rail wear..........................................................................93
Figure 4.5: Flow chart of the track monitored base model ..........................................96
Figure 4.6: Probabilities of failures ...........................................................................101
Figure 4.7: Grinding cost estimation method ............................................................103
Figure 4.8: Grinding cost/m for 0 to 800 m curves....................................................104
Figure 4.9: Grinding cost/MGT/m for 0 to 800 m curves..........................................104
Figure 4.10: Down time cost/m for 0 to 800 m curves ..............................................106
Figure 4.11: Down time cost/MGT/m for 0 to 800 m curves ....................................107
Figure 4.12: Annuity cost/m for grinding 0 to 800 m curves ....................................107
Figure 4.13: Annuity cost/m for risk in 0 to 800 m curves........................................108
Figure 4.14: Annuity cost/m for down time in 0 to 800 m curves.............................109
Figure 4.15: Annuity cost/m for inspection in 0 to 800 m curves .............................110
Figure 4.16: Annuity cost/m for replacement in 0 to 800 m curves ..........................110
Figure 4.17: Total annuity cost/m for replacement of 0 to 800 m curves..................111
Figure 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves................................112
Figure 4.19: Annuity cost/m for 12 MGT in 0 to 800 m curves................................113
Figure 4.20: Annuity cost/m for 18 MGT in 0 to 800 m curves................................113
Figure 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves..................................114
Figure 5.1: Flowchart for the modelling and analysis of lubrication decisions.........118
Figure 5.2: A well lubricated rail wear face in a Spoornet curve ..............................119
Figure 5.3: Lubrication decision model .....................................................................123
Figure 5.4: Coefficient of friction..............................................................................124
Figure 5.5: Dry rail condition ....................................................................................125
Figure 5.6: Aggressive wear ......................................................................................126
26
Figure 5.7: Lubricated rail-wheel interface ...............................................................126
Figure 5.8: Rail with minimal wear ...........................................................................126
Figure 5.9: Simulation model to estimate total costs due to wear .............................130
Figure 5.10: Wear limit for rail head cross sectional area .........................................131
Figure 5.11: Traffic wear rates for high rail ..............................................................134
Figure 5.12: Rail wear limits for mainline, rail type 20 kg/m ...................................135
Figure 5.13: Lubrication influencing rail life ............................................................140
Figure 5.14: Wayside lubrication...............................................................................142
Figure 5.15: Framework for benchmarking lubrication.............................................147
Figure 5.16 Curve distribution for A-B corridor .......................................................150
Figure 5.17: Table wear and side wear measurements ..............................................151
Figure 5.18: Wear for curves radii 0-300 m from 1998-2001 ...................................153
Figure 5.19: Wear for curves radii 0-300 m from 2001-2004 ...................................154
Figure 5.20: Rail wear for four different curves ........................................................154
Figure 5.21: Curve fitting analysis for curve radius 300 m .......................................155
Figure 5.22: Gaussian distribution of the RMSE for 0-300 m curves .......................156
Figure 5.23: Area head loss comparison for 47 kg rail..............................................157
Figure 5.24: Area head loss comparison for 50 kg ....................................................158
Figure 5.25: Wear for curve radius 300 m.................................................................158
Figure 5.26: Wear for curve radius 245 m.................................................................159
Figure 5.27: Wear for curves radii 301-450 m from 1998-2001 ...............................159
Figure 5.28: Wear for curves radii 301-450 m from 2001-2004 ...............................160
Figure 5.29: Rail wear for different radii for accumulated MGT..............................160
Figure 5.30: Curve fitting for curve radius 415 m.....................................................161
Figure 5.31: Gaussian distribution of the RMSE for curve radii 301-450 m ............162
Figure 5.32: Area head loss for 50 kg rail .................................................................163
27
Figure 5.33: Area head loss for 47 kg rail .................................................................163
Figure 5.34: Wear data for curves radii 451-600 m from 1998-2001........................164
Figure 5.35: Wear data for curves radii 451-600 m from 2001-2004........................165
Figure 5.36: Rail wear for curves with different radii ...............................................165
Figure 5.37: Curve fitting for curve radius 500 m.....................................................166
Figure 5.38: Gaussian distribution of the RMSE for curves radii 451-600 m...........167
Figure 5.39: Area head loss for 47 kg........................................................................168
Figure 5.40: Area head loss for 50 kg rail .................................................................169
Figure 5.41: Area head loss curve radius 500 m........................................................169
Figure 5.42: Analysis of lubrication costs .................................................................174
Figure 5.43: Wear progression for curve radius 236.7 m from 1997-2004 ...............176
Figure 6.1: Rail defects occurrence ...........................................................................188
Figure 6.2: Rail defects detectability .........................................................................189
Figure 6.3: Rail defects severity ................................................................................189
Figure 6.4: Proposed model for risk mitigation of rail defects ..................................189
Figure 6.5: Rolling contact fatigue defects ................................................................191
Figure 6.6: Error in ultrasonic (NDT) inspection ......................................................192
Figure 6.7: Analysis of NDT and visual inspection of rail ........................................193
Figure 6.8: Process map of rail inspection................................................................195
Figure 6.9: Block diagram of inspection and detection .............................................197
Figure 6.10: Venn diagram of inspection ..................................................................198
Figure 6.11: Pie chart for preventive, corrective (rail breaks) ...................................199
Figure 6.12: Pie chart for detected rail breaks and derailment ..................................199
Figure 6.13: Detecting rail breaks using signalling system .......................................202
Figure 7.1: Integrated model for rail grinding-lubrication-inspection.......................205
Figure 7.2: Annuity costs/m for 12 MGT with lubrication........................................209
28
Figure 7.3: Annuity costs/m for 12 MGT without lubrication...................................210
Figure 7.4: Annuity costs/m for 23 MGT with lubrication........................................211
Figure 7.5: Annuity costs/m for 23 MGT without lubrication...................................212
Figure 7.6: Total annuity costs/m for 12 MGT..........................................................213
Figure 7.7: Total annuity costs/m for 23 MGT..........................................................214
Figure 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection..........215
Figure 7.9: Annuity costs/m for 12 MGT without lubrication for one inspection.....216
Figure 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection........217
Figure 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection...218
Figure 7.12: Annuity cost/m for 12 MGT with lubrication for two inspections........219
Figure 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections.220
Figure 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections ......221
Figure 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections.222
Figure 7.16: Annuity costs/m for 12 MGT with lubrication for three inspections ....223
Figure 7.17: Annuity costs/m for 12 MGT without lubrication for three inspection 224
Figure 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections ....225
Figure 7.19: Annuity costs/m for 23 MGT without lubrication for three inspection 226
Figure 7.20: Total annuity costs/m for 12 & 23 MGT with lubrication ....................227
Figure 7.21: Total annuity costs/m for 12 & 23 MGT without lubrication ...............228
Figure B1: Mechanical lubricators.............................................................................276
Figure B2: Plunger mechanism..................................................................................277
Figure B3: Smear Test ...............................................................................................278
Figure B4: Tribometer at the gauge face ...................................................................279
29
CHAPTER 1
SCOPE AND OUTLINE OF THESIS
1.1 Introduction
Rails play a significant role in transport of passengers and freight movements. In 2003
the rail industry contributed AUD $ 5.3 billion in value to the Australian economy
(Australasian Railway Association Inc, 2004). In the past five years, railroads have
purchased approximately 500,000 tonnes of replacement rails per year at an estimated
total cost of US $1.25 billion (AUD $ 1.37 billion). Even a small improvement in rail
performance has significant economical benefits to rail industry (Kristan, 2004). In
2000, the Hatfield accident in UK was caused due to rolling contact fatigue. It killed 4
people and injured 34 people and led to the cost of £ 733 million (AUD $ 1.73 billion)
for repairs and compensation payments. In 1977, the Granville train disaster in
Australia killed 83 people and injured 213 people. These accidents were mainly due to
wear, rolling contact fatigue (RCF) and poor maintenance.
Increasing traffic density, axle loads, accumulated tonnages (Million Gross Tonnes
(MGT)), train speed and longer trains have increased productivity but with an
increased risk of rail breaks and derailments. Rail wear and rolling contact fatigue
(RCF) are inevitable due to rail wheel interaction. These problems have increased the
maintenance and replacement costs. If undetected, these problems can cause
derailment causing huge loss of revenue, disruption of service, resulting damage of
assets, and loss of lives. RCF alone costs European railways around € 300 million
(AUD$ 485 million) per year and these defects account for about 15% of the total
costs. The total costs of all defects are about € 2 billion (AUD$ 3.23 billion) per year
(Cannon et al., 2003). The American Association of Railroads (AAR) estimated that
the wear and friction occurring at the wheel/rail interface of trains due to ineffective
lubrication, costs American Railways in excess of US $ 2 billion each year (Sid and
Wolf, 2002). The Office for Research and Experiments (ORE) of the International
Union of Railways (UIC) has noted that maintenance costs increases directly (60–65
per cent) with increase in traffic, train speed and axle load. These costs are greater
when the quality of the track is poor (ORR, 1999).
30
In rail transport, operational risks are defined as risks of rail breaks and derailments
that occur during the rail-wheel interaction. During the rail-wheel interaction, some of
these unwanted events occur due to lack of maintenance, rail-wheel wear and rolling
contact fatigue (RCF) cracks. These are influenced by various operating conditions
such as traffic density, freight, rail material type, size, hardness, bogie type, speed
limit, temperature, curve radius and environmental factors. Risks have been
increasing due to increased number of axle passes, steeper curve radius, worn-out rail-
wheel profile in the system and inadequate material hardness, unfavourable rail/wheel
interaction, inappropriate rail-wheel grinding, poor lubrication and poor maintenance.
Modelling and analysis of operating risks require failure time data, probability of
detection and consequences of failures. Interpretation of various rail defects and
broken rails and their consequences is extremely important for developing these
models. Preventive rail grinding and lubrication is used to control surface fatigue
defects and to reduce wear and noise. However, knowledge of surface fatigue cracks,
rail-wheel wear, rail grinding and lubrication is limited.
Figure 1.1: Factors behind the problems
Some of the factors behind the problems are shown in Figure 1.1. It is important to
study the interaction of rail-wheel degradation and influencing factors, monitor those
factors and find cost effective technological solutions to eliminate or reduce those
problems. Therefore, there is a need to develop an integrated model to predict
operational risks, and take appropriate economic decisions to reduce maintenance
costs and improve reliability and safety of rail operation.
31
This chapter begins with a brief introduction of the research problem in Section 1.1.
This is followed by the scope of this research work in Section 1.2. Aims and
objectives are presented in Section 1.3. Finally an outline of the thesis is presented in
Section 1.4.
1.2 Scope of the research study
Research shows that most of the existing models for predicting rail degradation and
operational risks are based on Million Gross tonnes (MGT). They have not considered
other possible influential factors. This research is a comprehensive study of rail wear,
rolling contact fatigue (RCF), lubrication, rail grinding, inspection, rectification and
rail replacements. It develops stochastic models and economic models, and integrate
those models for grinding, lubrication, inspection, rail maintenance and replacement
decisions. These models will be useful for informed strategic decisions based on
operating conditions.
1.3 Aims and Objectives
This research addresses the development and analysis of an integrated model for
assessment of operational risks in rail track. The main focus of this research is
problems associated with higher axle loads, wear, early rail replacements, rail defects
leading to rail breaks and derailments.
The specific aims of this research project are to develop:
• Knowledge based models for analysis and assessment of operational risks
associated with rail-wheel degradation due to wear, lubrication, rolling contact
fatigue (RCF), rail grinding, inspection, replacement and operating conditions.
• Integrated economic models for decision support systems that investigate risk
and economical impact analysis with “what if” scenarios for maintenance
strategies.
The main objectives of this research are:
• Collection and analysis of data on rail failures, rail breaks and related costs of
lubrication, grinding, inspection, rectification and replacement of rails.
• Development of failure models and estimation of parameters, considering
operational and environmental conditions.
• Development of grinding models for optimal grinding decisions, linking
cumulative MGT, axle load, curve radius and operating conditions.
32
• Development of lubrication models for optimal lubrication strategies.
• Development of inspection models for optimal inspection decisions, considering
detected and undetected defects, using non destructive ultrasonic testing methods.
• Development of an integrated model for managerial decisions based on costs and
risks.
1.4 Thesis Outline
Outline of the thesis is as follows:
Chapter 1 defines the scope and outline of this research. It clearly defines the
background of the problem and the need for the development of an integrated model
to predict operational risks and maintenance costs.
Chapter 2 provides a brief overview of the literature on rail track structure, rail
defects, rail wear, rail-wheel lubrication, rail grinding, inspection, replacement of rails
and maintenance strategies.
Chapter 3 provides models for rail wear, rolling contact fatigue (RCF), and rail
maintenance. It analyses the gaps in the existing models and proposed solutions to
eliminate/ reduce these gaps for increased safety and reliability of rail operation.
Chapter 4 deals with modelling and analysis of rail degradation and rail grinding
costs. Real life data are collected and analysed for developing these models.
Economic models are developed and analysed. Illustrative numerical examples are
used for application to industry.
Chapter 5 deals with the development of lubrication models for optimal lubrication
strategies. It includes modelling and economic analysis of rail wear and rail-wheel
lubrication, based on various types of lubricators and curve radius.
Chapter 6 deals with development of inspection models for optimal inspection
decisions, considering detected and undetected defects, using non destructive
ultrasonic testing.
33
Chapter 7 deals with development of an integrated model for managerial decisions
related to lubrication, grinding, inspection and replacements, based on costs and risks.
It includes development of decision support systems and user friendly software.
Finally, Chapter 8 provides a summary of this thesis, the contribution of the thesis to
this field of research, and a discussion of the potential extensions and topics for future
research.
34
CHAPTER 2
OVERVIEW OF RAIL TRACK STRUCTURE, DEFECTS AND
MAINTENANCE STRATEGIES
2.1 Introduction
Rail transport makes a significant contribution to the Australian economy,
representing a sizeable gross domestic product (GDP) and providing passenger,
freight, and heavy haul services. However, rail infrastructure owners are lagging
behind best practice in monitoring, controlling and predicting rail defects and
maintenance strategies to reduce operational risks. Railways have a history of two
hundred years of steel wheels on steel rails, still there are more unknown than known
features of their interaction. Rail degradation depends on rail track structure, rail
condition and maintenance strategies for reliable and safe operation.
This chapter provides an overview of rail structure, rail defects and existing models
for predicting wear, rolling contact fatigue, inspection, lubrication and grinding
decisions for rail maintenance strategies.
2.2 Railway Track Structure
Rail tracks are important for carrying passengers and moving freight. The main
components of rail track structure (Esveld, 2001) are shown in Figure 2.1.
Figure 2.1: Cross sectional view of rail track structure (Esveld, 2001)
35
2.3 Rails
Rails operate under harsh environment, heavy axle loads, accumulated tonnage,
million gross tonnes (MGT), longer trains, increased traffic density and increased
train speeds. As a part of track structure, they have no redundancy, thus their defects
and failures can lead to rail breaks and result in derailments causing huge loss of
property, revenue and lives. Rails are major capital investments and incur a huge
amount of maintenance cost for infrastructure owners. Rail steels are usually joined
together, either bolted or welded. There are complexities in the replacement of
defective and broken rails due to temperature changes, cost of materials, transposing
decisions and laying techniques (Cope, 1993). A profile of rail head is as shown in
Figure 2.2.
Figure 2.2: Profile of rail head
2.4 Fastening System
The purpose of the fastening system is to retain the rails against the sleepers and resist
vertical, lateral, longitudinal and overturning movements of the rail.
Figure 2.3: Spikes, Rail Anchors and Elastic Fastening System (PANDROL)
Gauge Corner
Rail Head
Web
Foot
Gauge Corner
Rail Head
Web
Foot
36
These movements are caused by force systems from the wheels and temperature
changes in the rails. Various types of fasteners used in railtrack systems are shown in
Figure 2.3:
(a) Spikes
(b) Rail anchors
(c) Elastic fastening system
The selection of appropriate fasteners depends on railtrack structure (rail type and
size, sleeper type and size, track curvature and superelevation), traffic conditions (axle
loads, train speeds and annual tonnage), maintenance requirements and economic
restraints (Zhang, 2000).
2.5 Sleeper (Tie)
Sleepers hold the rails to the correct the gauge and transmit loads on the rails to the
ballast. Sleepers or ties have several important functions (Esveld, 2001). These are to:
1. receive the load from the rail and distribute it over the supporting ballast at an
acceptable ballast pressure level;
2. hold the fastening system to maintain the proper track gauge;
3. restrain the lateral, longitudinal and vertical rail movement by anchorage of
the superstructure in the ballast; and
4. provide support to the rails to help develop proper rail/wheel contact.
Various types of sleepers used in the railtrack system are: timber, concrete and steel.
Timber sleepers are the most commonly used in the railway system. The reasons for
choosing timber are its cost effectiveness, resilience, corrosion resistance,
workability, ease of handling, potential re-use and insulation. The life of timber
sleepers can vary from 8 to 30 years depending on quality and density of traffic,
position in the track, climate and maintenance. Some species may even have a life of
50 years (McAlpine, 1991). Figure 2.4 shows concrete and wooden sleepers and
fasteners.
Figure 2.4: Concrete and Wooden Sleepers and Fasteners (PANDROL)
37
Concrete sleepers are generally considered more economical than timber sleepers for
heavy haul tracks. Concrete sleepers have much longer life than timber sleepers, with
an anticipated life of 50 years. Prestressed concrete sleepers were first used in
Australia in 1940 and are now widely used since the 1980s (Muller, 1985). Tracks
constructed with concrete sleepers also have higher buckling resistance, lower
maintenance requirements and uniform specifications. However, due to heavy weight
of more than 300 kg each, they need special laying machines for installation. They
also need special considerations in specifying design loads to prevent cracking, and
need rail pads to reduce vibrations (McAlpine, 1991). Concrete sleepers are very
sensitive to impact loads (Riessberger, 1984). Therefore, rail top irregularities need to
be controlled to avoid impact loads.
Steel sleepers are used because of sleeper life advantages over timber sleepers and
resistance to insect attack (Brodie et al., 1977). They also provide greater lateral and
longitudinal track resistance than timber sleepers (Birks et al., 1989). However, due to
their special cross shape, they require more tamping after initial installation. Special
attention must also be paid to rail fastening selection and insulation. Steel sleepers
have been used for many years, particularly in countries where termites are a problem.
Research is being undertaken in this area by British Steel Corporation for techno-
economic evaluation (BSC) (Cope, 1993).
2.6 Ballast
Ballast is the selected, crushed granular material placed as the top layer of the
substructure in which the sleepers are embedded. The functions of ballast are to:
• resist vertical, uplift lateral and longitudinal forces applied to the sleepers to
retain track in its required position;
• provide some of the resiliency and energy absorption for the track;
• provide large voids for storage of fouling material in the ballast, and
movements of particles through the ballast;
• facilitate maintenance surfacing and lining operations (to adjust track
geometry) by the ability to rearrange ballast particles with tamping;
• provide immediate drainage of water falling onto the track; and
• reduce pressures from the sleeper bearing area to acceptable stress levels for
the underlying material (Esveld, 2001).
38
2.7 Subballast
The layer between the ballast and the subgrade is the subballast. The functions of
subballast are to:
• prevent upward migration of fine material emanating from the subgrade;
• prevent interpenetration of the subgrade and the ballast; and
• prevent subgrade attribution by the ballast, which in the presence of water,
leads to slurry formation. [This is a particular problem if subgrade is hard
(Ernest and John, 1994)].
2.8 Subgrade
The subgrade is the platform upon which the track structure is mounted. It is also
referred to as formation (Zhang, 2000). Its main function is to provide a stable
foundation for the subballast and ballast layers. The subgrade is an important
substructure component which can have a significant influence on track performance
and maintenance. It acts as superstructure support resiliency, and contributes
substantially to the elastic deflection of the rail under wheel loading. Its stiffness
magnitude influences ballast, rail and sleeper deterioration (Esveld, 2001).
2.9 Track Component Characteristics
The railtrack is composed of several components with specific functions. The rail
tracks experience vertical, horizontal and longitudinal forces that can be static,
dynamic and thermodynamic (Zhang, 2000). These forces influence the functions of
the basic components in the track which, in turn, affect degradation and the failure
process. The failure of each component has an effect on the function of other
components in the rail track system. It is, therefore, important to analyse the
characteristics of each component to be able to measure the defects and failures to
prevent catastrophic failures. This research focuses mainly on the rails.
2.10 Rail Degradation
Rail degradation is a major economic burden for rail infrastructure owners around the
world. It costs approximately € 2 billion per year in the European Union alone
(Cannon et al., 2003). Failures include:
� rail manufacturing defects
� defects or damage caused by inappropriate handling, installation and use
39
� exhaustion of rail steel’s inherent resistance to the fatigue damage.
2.11 Rolling Contact Fatigue (RCF) and Grinding Strategies
Head checks, gauge-corner cracks, squats and shelling (as shown in Figure 2.5) are
forms of rolling contact fatigue. They are caused by a combination of high, normal
and tangential forces between rail and wheel.
Figure 2.5: RCF, Shelling and Gauge Corner Cracking (QR, 2005)
The initiation of crack occurs due to accumulation of shear deformation due to
repeated rolling-sliding contact loading. The plastic deformation caused by large
contact stresses has a great influence on crack initiation. The microscopic crack
produced, propagates through the heavily deformed material until it reaches a depth
where the steel fails to retain its original isotropic properties. At this stage the crack is
a few millimetres deep and may lead to spalling of material from the rail surface
(Ishida et al., 2003). However, isolated cracks can turn down into the rail and, if not
detected, can cause the rail to break. These events appear to be rare, but are highly
dangerous since RCF cracks tend to grow almost continuously at a given site. Fracture
at one crack increases stress in the nearby rail, increasing the risk of further breaks
and disintegration of the rail Cannon et al., (2003). Bower and Johnson (1991) and
Bogdanski et al., (1997) found that shallow angle crack propagation, is encouraged by
fluid entrapment that leads to crack pressurization. To reduce crack face friction, it
allows relative shear of the crack faces. The direction of growth of the crack beneath
the rail surface and the direction of the crack mouth on the rail surface, are both a
guide to the predominant direction of traction causing the crack. Generally, large
numbers of head checks can form on high rail (especially on steep curves) and deep
transverse head checks may be developed from some of them. The squat defect is a
similar form of fatigue damage that tends to occur more randomly on very shallow
curves and tangent track. These forms of surface-initiated RCF pose special
40
inspection problems. For both head checks and squats, the development of a
downward-turning fatigue crack leads to final rail failure.
This research found that limitations exist in accurately predicting rolling contact
fatigue (RCF) and initiation of cracks which lead to rail breaks. The stages of fatigue
crack as outlined by Milker (1997) are follows:
• Stage 1: shear stress driven initiation at the surface
• Stage 2: transient crack growth behaviour
• Stage 3: subsequent tensile and/or shear driven crack growth
Bannantine et al., (1991) and Suresh (1998) identified two types of approaches that
may be used to analyse crack initiation. They are:
• The defect-tolerant approaches
• The total-life approaches
The defect-tolerant approaches rely on the resistance to crack growth in materials that
are inherently flawed by small cracks. These approaches use fracture mechanics to
calculate the number of cycles required to propagate a crack to a critical size. There
are, however, some disadvantages related to these approaches: (a) it is difficult to
establish by tests the material parameters and crack growth data mechanically for
small cracks, (b) the results are sensitive to the choice of initial crack and defect size
and (c) it is has been difficult to establish approaches that are applicable to
engineering calculations, in particular, for elastic–plastic conditions (Ringsberg,
2001).
The total-life approaches estimate the resistance to fatigue crack initiation based on
nominally defect-free materials and components. These approaches attempt to analyse
the total fatigue life to failure (initiation); they are divided into stress-based and
strain-based approaches. The stress-based approach is characterised in terms of low
cyclic stress ranges that are designed against fatigue crack initiation (high-cycle
fatigue failures). The strain-based approach (also called the strain-life approach)
involves the fatigue life prediction of crack initiation according to which the strain
range characterises the fatigue life. The stresses in this approach are high enough to
cause plastic deformations that govern fatigue failure (low-cycle fatigue failures). A
drawback to the total-life approaches is that the definition of fatigue failure (or
41
initiation) is ambiguous. Tests should therefore be carried out to define fatigue failure
and the size of the initiated crack at this point (Ringsberg, 2001).
Yokoyama et al., (2002) investigated rolling contact behaviour for the materials of
standard carbon rail steel with Vickers hardness of 270 (270 HV), a head hardened
premium pearlitic rail steel with 390 HV, a bainitic rail steel of 270 HV and a high
strength bainitic rail steel of 420 HV. The carbon contents of pearlitic steels are in the
range from 0.65 to 0.80 mass %, which are almost double those of the bainitic steels.
Bainitic steels contain large amounts of chromium, molybdenum, niobium and
vanadium to obtain the desired strength using less carbon.
Figure 2.6: Flaking problems (Yokoyama et al., 2002)
Results show that bainitic steel has much better flaking (as shown in Figure 2.6)
resistance than pearlitic rail steels of the same tensile strength level. The initiation
time for RCF damage decreases with an increase in the angle of attack for all the
steels tested. Bainitic rail steels showed better RCF damage resistance than pearlitic
rail steels at any angle of attack.
Sawley and Kristan (2003) conducted small and full scale tests to investigate potential
resistance of rolling contact fatigue damage. They found that wear performance of
bainitic rail steel depends considerably on test conditions; however, the indication was
that bainitic steel rails can have significantly better rolling contact fatigue
performance compared to pearlitic rails. There is a need for better understanding of
fatigue performance.
Garnham and Beynon (1991) analysed rolling-sliding contact fatigue behaviour of rail
steels. They described a new wear machine which is capable of testing large, standard
cyclic discs at high contact with accurate control of low creepages. An eddy current
method is used for the detection of the initiation and propagation of cracks during
42
RCF test. They examined the relationship between rolling-sliding contact fatigue,
contact stress, creepage, microstructure and surface events for a range of pearlitic rail
steels. Magel and Kalousek (2002) examined the influence of rail wheel profiles.
Performance of profile for a given application is measured in terms of:
• resistance to wear
• resistance to fatigue
• resistance to corrugation development
• minimisation of lateral and truck forces
• maximisation of stability
• minimisation of noise
Rail grinding is used for removing the surface defects due to RCF and maintaining
favourable rail profiles. The appropriate rail-grinding interval depends on the rail
metallurgy, track curvature, axle loads and fasteners. Magel and Kalousek (2002)
recommended an interval of 8-12 MGT (280-300 BHN standard carbon rail) and 12-
25 MGT (360-380 BHN premium rail) for sharp curves (<500 m). Rail players around
the world take grinding decisions based on Visual Qualitative Checks (VQC), Non
Destructive Testing (NDT) report, assumed Million Gross Tonnes (MGT) and Traffic
Density (TD). This is a slow, time consuming and costly process for decision making,
leading to a risky operating condition between inspections.
Kalousek and Magel (1997) introduced the concept of a magic wear based on
boundary between sufficient and insufficient wear – the optimal, or “magic”, wear
rate –a trade-off in which the development of fatigue is arrested by wear/ metal
removal. The magic wear rate is achieved when the surface material wears just
enough to prevent surface fatigue cracks from propagating. A combination of
lubrication and light, but frequent profile grinding is recommended. Every wheel/rail
system has a magic wear rate. It changes with the hardness of the materials, the
average contact stress, the wheelset-steering performance, coefficient of friction and
the effectiveness of the lubrication. Ishida et al., (2003) carried out a detailed study on
rail grinding. He recommended a scientific determination of grinding interval (how
frequently the grinding should be conducted) and grinding depth (how much surface
material should be removed) based on rail signature. This knowledge is important for
improving the efficiency of grinding work and reducing the track maintenance cost
and risk.
43
Kapoor et al., (2002) studied plastic deformation at asperities (unevenness of surface)
between wheel and rail and its effect on the shakedown process. Shakedown process
is used as a basis for design of railway track and bearings. When the load increases
above the ‘elastic limit’, the contact stresses exceed the yield and the rail material
flows plastically. Upon unloading, material develops residual stresses. These stresses
reduce the tendency of plastic flow in the subsequent passes of the wheel. This,
together with any effect of strain hardening, enables the rail material to support loads
which are much higher than its elastic limit. This is called the shakedown process.
The maximum contact pressure which is carried purely elastically in the steady state
is known as ‘shakedown limit’. For frictionless rolling/sliding, this shakedown limit is
four times the shear yield stress of the rail material. With increasing friction the limit
drops, initially gently and then rapidly, at a friction coefficient of about 1/3. It is
found in the observations that substantial plastic deformation in a sub-surface layer of
thickness 15-20 µm, is generally found in cross sections of rails. Ishida et al., (1998)
confirm that the plastic flow is confined to a thin surface layer where material fails
and leads to initiation of squat cracks. Removing this layer by preventive grinding,
reduces the chances of cracks initiating and developing squats. Magel et al., (2003)
examined rail grinding, corrugations and lubrication from theoretical modelling based
on lab based experiments and field trails.
Johnson (1989) studied plastic deformation due to repeated transmission of wheel
load to the rail through a tiny contact area under high contact stresses. He found that
the depth of the plastic flow depends on the hardness of rail and sharpness of curves.
Due to sliding in the contact area, significant wear occurs for poorly lubricated
conditions of wheel-rail contact (Olofsson et al., 2000). The wear affects the form of
contacting surfaces of a rolling-sliding contact. Contact pressure, the size of the
sliding component, lubrication, microstructure and hardness are influencing factors
behind the wear rate (Garnham and Beynon, (1992), and Muster et al., (1996).
Ishida et al., (2003) studied wheel rail interface problems resulting from rolling
contact fatigue (RCF), squat defects and corrugations. The study covers grinding and
lubrication of Japanese Railways (JR). In Japan, grinding started in the 1970s with
100 km of track per year. Since 1995 more than 1000 km of track per year is subject
to grinding (Tada, 1999). It is found that the number of squats has been steadily
44
decreasing as a result of grinding. The target has been a grinding thickness of 0.08
mm/pass and a grinding interval of 40 MGT.
Grohmann and Schoech (2002) studied contact geometry for minimising the risk of
head check formation. German Railways (DBAG) experimented with target profile
for appropriate tolerances in rail grinding to limit or prevent head checks. This
research revealed that optimal grinding strategies should aim at correct profiling and
minimal metal removal.
The potential failures of a single component or multi-component system indicates that
complacency must not set in because an accident has not occurred in the past, / its
probability of occurrence is low, or its past consequences were not severe. Rail Track
was blamed for the train accident at Ladbroke Grove, Paddington, UK (1999) because
Rail Track had taken inadequate action following earlier incidents at the same site.
There was inadequate analysis of what else might happen and, equally importantly, of
potential rather than actual consequences. When resources needed to be added for
thousands of locations across a complex network, the choices become more complex.
The solution was automatic train protection (ATP). Four years earlier, when Rail
Track was government owned, the government decided not to proceed with ATP, as it
was too costly compared to safety priorities. The Ladbroke Grove accident led to 31
fatalities and many serious injuries. Safety decisions, taking into account technical,
political and economic aspects, become more complex.
Ringsberg (2001) developed a strategy for life prediction of rolling contact fatigue
and crack initiation. It comprises elastic-plastic finite element analysis, multiaxial
fatigue assessment of life to fatigue initiation, and comparison of results with lab tests
and field observations.
Field data showed that at loads of 10 tons per wheel and at 200 km/h speed, the
dynamic load increases the static load per wheel by 6 tons. This means that the rail
deteriorates at a faster rate with the combination of higher axle loads and train speeds.
After the Hatfield accident, extensive investigation was carried out all over Britain’s
rail network. The number of broken rails on the network increased sharply from 656
in 1995-96, to 949 in 1999-2000. Larsson et al., (2003) developed an integrated
approach to modelling rail track degradation for deciding optimal maintenance
45
strategies. Chattopadhyay et al., (2003) developed an integrated model for assessment
of risk in rail tracks under various operating conditions.
Besuner et al., (1978) revealed limitations of rail life prediction models using MGT
because they do not differentiate between the following cases:
1. a certain number (say m) of heavy wheel loads of magnitude P and
2. twice this number (2m) of smaller wheel loads of magnitude P/2.
For fatigue crack initiation and propagation, the heavier wheel load of Case 1 is more
damaging to the rail compared to the larger number of lighter loads of Case 2.
Johnson and Besuner (1977) proposed that the crack propagation rate da/dN is
proportional approximately to the 4th power of stress, leading to an effective usage
parameter, MGT-Effective given by
4/1
1
4)(
=− ∑
=
n
i
MGTEffectiveMGT (2.1)
where n = total number of wheels passing through the curve section.
The usage for an accurate prediction model should consider axle load, gross tonnage,
speed and curvature such that the damage level is estimated based on wear, RCF,
defects, failure rate, rail grinding and maintenance including lubrication, rectification
and replacements.
2.12 Rail Wear and Lubrication Strategies
Wear is the loss of material from the contacting surface due to rail-wheel interaction.
Rail operators currently use executive judgement and take decisions based on
experience and historical data to mitigate wear. Rail area head loss and rail wear
depend on train speed, axle load, rail-wheel material type, size and profile, track
construction, characteristics of bogie type, Million Gross Tonnes (MGT), curvature,
traffic type, lubrication, rail grinding, weather and environmental conditions. There is
no international standard available for rail-wheel lubrication and grinding, capable of
accurately predicting rail-wheel wear for monitoring and control. It is important to
study the factors behind these and develop a model for predicting rail area loss under
wear-lubrication-fatigue-grinding interaction.
Dearden (1954) found that wear on the top of running surface of rail in straight track
is predominantly a corrosion problem. Clayton and Allery (1982) found, from the
46
very different rail surface appearance and lower wear rates of modern rails, that the
situation had changed. It was described as severe metallic wear, following the
terminology of Archard and Hirst (1956). Beagley (1976) used an Amsler machine to
determine patterns of wear. He found that, at a certain contact pressure, wear changed
from mild wear to severe wear. Under severe wear conditions the wear rate was found
to be a function of contact pressure. The experimental approach of Beagley was
criticized by Bolton et al. (1982) on the basis that, even in the severe wear regime,
copious quantities of oxide were produced. This problem was overcome, in a practical
sense, by continually brushing the roller surfaces with a wire brush. The second
feature of the experimental technique to come under scrutiny was the very short time
intervals over which the wear loss was measured for a given set of operating
conditions. It was noted that this approach could lead to much of the wear data
representing break-in rather than steady state conditions. In the rail-wheel contact,
three wear regimes are defined by Nilsson (2005). They are mild, severe and
catastrophic wear. The mild and severe wear was studied by Jendel, (1999). The
changeover from mild to severe wear is found to be governed by a combination of
sliding velocity, contact pressure and temperature in the contact region. In the mild
wear it was observed that the wear process is slow, similar to oxidation. In the severe
wear it occurs much faster, similar to adhesive wear, as observed in curves under dry
conditions. Mild wear is observed at the wheel tread and rail crown. Severe wear is
observed at the wheel flange and gauge face. The catastrophic wear is one in which
the wear rate is extremely high and is unacceptable due to safety requirements (Bolton
and Clayton, 1984).
The Stockholm local network studied the lubricated and non-lubricated rails for UIC
900A and UIC 1100 grade rail steel under various seasons. The study found that the
contact situation in terms of pressure and sliding between rail and wheel, strongly
influences the wear. When the surfaces are worn, the contact situation changes due to
changed geometries. The changed geometries can lead to altered conditions regarding
sliding and pressure distribution between the surfaces. The curve radius of the track
has significant influence on wear behaviour. It is found that the wear rate increases
exponentially for decreasing curve radius. Sharper curves lead to increased track
guiding forces on the wheels, leading to increased creep and increased wear. The
study shows that new rails have higher wear rate than old rails. It was also found that
47
the wear rate is approximately four times higher for new rails compared to the rails
that already had been in the system (Nilsson, 2005). Track side lubrication reduces
rail wear significantly. Figure 2.7 shows the lubrication benefit as a factor of 9 for
small radius curves (300 m). For 600 - 800 m radius curve the lubrication benefit
varied from 2 to 4 compared to non-lubricated curves. An increase in the temperature
of the rail leads to increased rate of wear. This may be because of the high
temperatures causing the lubricant to become more liquefied, thus resulting in
inadequate lubrication at the wheel-rail contact area. It can also be due to the fact that
the oil in the grease evaporates, which results in reduced effect of the lubricant.
Figure 2.7: Influence of rail wear from lubrication (Nilsson, 2005)
The properties of steel and surface treatment can have a significant impact on the
behaviour of wear. The effect is shown in Figure 2.8 for high rails with steel grade
900A and UIC 1100, compared to non-lubricated surface in 300 m curve.
Figure 2.8: Rail area worn off with and without lubrication (Nilsson, 2005)
For the non-lubricated curve, the ratio of rail wear rate for the 900A grade rail
compared to that of 1100 grade rail, is approximately 2. This ratio for lubricated
conditions is approximately 9 (Nilsson, 2005).
48
The wear is proportional to the normal load and inversely proportional to hardness of
the softer material. In the wheel/rail interaction, the coefficient of friction and the
degree of lubrication greatly influence the size of creep forces in the contact area and
therefore influence wear. Increase of train speeds has a significant impact on wear
rate. Archard’s wear model (1953) for sliding adhesive wear is as follows:
H
NK
D
Vw •= (2.2)
Where WV = Wear volume [m3]
D = Sliding distance [m]
N = Normal load [N]
H = Material hardness [Pa]
K = Wear coefficient of Archard’s equation that can be interpreted as the probability
that a wear particle is formed due to shear effect when a local contact is broken.
The energy dissipation model indicates that wear is proportional to the work done by
forces in sliding contact. Jendel (1999) expressed the wear coefficient with sliding
velocity on the horizontal axis and contact pressure on the vertical axis. Wear model,
using energy dissipation per running distance, can be expressed as wear index, as
follows:
φγγ φMFFE yyxx ++= (2.3)
Where xxF γ = Product of creep forces and creepages in x direction, yyF γ = Product of
creep forces and creepages in y direction, φ = Spin and φM = Spin moment. The
energy dissipation E is defined as the product of the creep forces and creepages, spin
moment and spin, and is proportional to the amount of wear. Relations between the
energy dissipation and material worn off are used for prediction of absolute wear.
Step-like behaviour of the wear rate is modelled by assigning different constants for
different levels of energy dissipation.
The energy approach is adopted in the rail/wheel analysis to study the relationship
between wear rate and contact conditions. This is done to comply with a wear model
from the non-linear curving (Elkins and Gostling, 1977). Bolton and Clayton (1984)
modelled wear rate as a linear function of tangential force (T) times slide/roll ratio (γ),
divided by Hertzian contact area (AH) for a narrow range of materials. McEwen and
49
Harvey (1988) applied this to a full-scale laboratory test. Tγ/AH parameter (wear
parameter) calculated from the curving model was used to predict wear performance
as a function of suspension characteristics and wheel-rail profiles. Martland and
Auzmendi (1990) modified wear parameter to fit railroad practice. It is difficult to
accurately describe wear using existing predictive models because of the stochastic
process involved in rail wear. Therefore, there is a need for an integrated approach
where a wear model, combined with updated track field measurement, is able to
predict rail wear based on rail signature. The complexity of the problem indicates that
empirical models, combined with continuously updated field test data, might be a
realistic way of predicting and controlling the wear at different parts of the track. This
would be useful to railway players in planning cost effective maintenance of rail
infrastructure.
A survey of heavy haul railways in the mid 1990s indicated rail lives varying between
about 1500 million gross tonnes (MGT) of traffic in straight track and about 300
MGT in highly curved track. This life also depends on axle load, traffic density, track
formation, bogie type and railway track maintenance practices. Rail area loss includes
the material removed by wear, grinding to maintain the rail profile to remove surface
cracks, and spalls caused by rolling contact fatigue (RCF). It is found in one set of
Association of American Railroads studies that rail material removed by grinding
exceeded that removed by natural wear. The ratio of ground/worn rail material
removed varied from 1.4 to 3.1 for high rails and from 2.1 to 9.8 for low rails, in
curves varying from 240 to 540 m in radius (Sawley and Kristan, 2003).
Fletcher and Beynon (2000) conducted twin-disc simulation tests to investigate the
influence of contact pressure variation on rail steel fatigue life using colloidal
suspension of molybdenum disulphide in an oil carrier fluid (similar to commercial
flange lubrication product) and water as lubricants. It was found that the reduction of
1500 to 900 MPa of the maximum Hertzian contact pressure (at which a
molybdenum-disulphide-lubricated and previously worn rail sample was tested)
extended the fatigue life of the rail steel by over five times. Water lubrication
produced only a marginal increase in fatigue life.
50
Reiff and Gage (1999) found lubrication increases wheel and rail life; reduces energy
consumption of trains; and reduces lateral curving loads and noise emissions.
However, improper application of lubrication may have a negative impact on truck
curving, train handling, and rail fatigue.
Franklin et al., (2005) conducted twin-disc tests (using two laser-cladded coated rails
numbered 222 and 508) to determine rolling contact fatigue (RCF) performance in the
laboratory. The result showed that 222 had high fatigue resistance at the lower
pressure, but that 508 was found to be susceptible to surface crack initiation during
prolonged (15000 cycles) unlubricated testing. They found that lubrication after a
long period of dry testing had accelerated crack propagation.
2.13 Inspection Frequency and Techniques
Inspection methods commonly used are (Cope, 1993).
1. Visual inspection
2. Dye penetrant inspection and magnetic particle inspection
3. Eddy current testing
4. Radiography
5. Ultrasonic
Visual inspection is often carried out by track maintenance staff and pedestrian
operators of ultrasonic equipment.
Dye penetrant inspection works on the principle that liquid is drawn into a “clean”
crack due to a capillary action. After a certain dwell time, the excess penetrant is
removed. A developer is then applied which acts like a “blotter” and draws the
penetrant from within the cracks. This method, however, relies on a clean surface and
thorough removal of the excess penetrant so as not to yield misleading indications and
can only be used on non ferro-magnetic materials. The magnetic particle inspection
technique is used on ferro-magnetic materials. Contrast paint is applied to the rail,
followed by the magnetic particle coating. The inspection is carried out in two
directions at very slow speed. This technique uses the principle that a flaw is detected
by the distorted flux. If a surface defect (or one that is close to the surface) is present
within the magnetic field when a magnet is applied to a ferro-magnetic material, the
location of the flaw can be determined from “flux leakage”. The effectiveness of the
51
method depends on flaw depth and type of flaw. Surface irregularities and scratches
can give misleading indications and, therefore, extensive surface preparation is
required before testing.
The eddy current testing method uses electromagnetic technique. This technique uses
an energised coil in close proximity to the surface, which induces eddy currents in the
specimen. These eddy currents create a magnetic field opposite to that which caused it
and, therefore, affect the impedance of the coil. This change in impedance is
measured to detect flaws.
Rail Testing really became a regular inspection activity entity in the late 1920s when
Dr Elmer Sperry, driven by the needs of the US railroad industry, developed the
induction method for testing railroad rail (Allison, 1968). Over the years, this
technique was refined in the US and then, in the 1950s, ultrasonic testing emerged and
started to become the method for rail testing. Some exceptions to this have been
Sperry in the US, where the idea of ‘complementary testing techniques’ has been
developed, and in Russia where the magnetic induction technique is used.
Figure 2.9: Ultrasonic and induction techniques (Clark, 2004)
The report prepared by the Transportation Technology Center, Inc. (TTCI) for the
Office of the Rail Regulator in October 2000 provides much useful background on the
global rail testing industry (Sawley and Reiff, 2000). Figure 2.9 shows the technology
deployed on the US railroads. The system brings together the complementary
ultrasonic and induction testing techniques on a hi-rail platform. This provides the
railroad with high quality testing and increased flexibility of deployment. In the past,
induction was not possible on a rail bound vehicle because of the large size of the
plant needed to generate the high currents injected into the rails. With developments
in power supply technology, the production of a hi-rail based vehicle has become
feasible (Clark et al., 2000). These vehicles operate at speeds of up to 32 km/h,
52
although with the ‘stop and confirm’ testing requirements in North America, there is
always an operational trade-off between going forward faster and the risk of longer
reversing moves when a confirmation is required.
In North America, the most common and problematical defects are transverse defects,
weld defects and vertical split head defects. These defects constitute around 55% of
the yearly detected defects. They also constitute 75% of the notified failures. A
notified failure is an instance where a rail has broken and the company has been
informed of the occurrence. In many cases, an investigation is performed to identify
the cause of the failure. The possible causes are many—each situation presenting a
source of further learning. On many occasions the defect is classified as undetectable
at the time of test because it has been too small or the surface condition of the rail
may have presented additional ‘noise’ that masked the defect. The cause of the broken
rail can also be a wheel flat. In these instances, a latent defect likely to be found at the
next test may become a catastrophic failure due to the impact of a wheel flat. Sawley
and Reiff (2000) found that broken rails are the result of the following major factors:
• Poor inspection procedures (This may be due to poor operator training, out-of
calibration equipment.)
• Surface conditions interfering with the ultrasonic signal (It is known that
surface damage, such as cracks, spalls, and flakes can hinder ultrasonic
inspection by affecting transmission of ultrasound signals.)
• Defects that are inherently difficult to detect using existing technologies
(Ultrasonic signals enter the head of rail and, though they travel down the web
section, they are not able to find defects in the outer edges of the foot. Cracks
towards the outer edges of the head are difficult to locate, similar to
vertical/transverse cracks found in thermite welds.)
• Inspection intervals that are longer than optimum (If the inspection interval is
too long, defects can grow from non-detectable to critical sizes between
inspections.)
There are three aspects to rail inspection: (1) technology used, (2) frequency of
inspection, and (3) actions specified when a defect is detected. Inspection is important
for reducing rail breaks. Inspection is generally based on line speed, track conditions,
traffic tonnage, axle load and traffic type. German Railways uses intervals from 4 to
24 months; Japanese Railways uses frequency from once in every year to once in 5
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years depending on the MGT per year in the route; SNFC rail uses frequency from 3
times a year to once in 5 years depending on the track classification. Most of the
large freight railways in North America now use risk management to schedule
ultrasonic inspections. A 40 million gross tonnes (MGT) per year freight line is
inspected two or three times annually, and lines over 140 million tones per year are
inspected every 30 days. Inspection intervals can be as frequent as every 7 days, as in
Australia on 37 tonnes axle load lines (Cannon et al., 2003).
In railway applications, the rails are regularly inspected by ultrasonic techniques using
inspection vehicles followed by manual walking stick for verification. Inspection
vehicles operate up to speed of 40 - 50 km per hour and have a much higher number
of ultrasonic transducers than manual systems. Manual systems are more sensitive to
defects than test vehicles but the results are influenced by the sensitivity of the
operator.
The detection vehicle shown in Figure 2.10 was tested on special test track (the Rail
Detection Test Facility – RDTF) at the Transportation Technology Centre (TTCI),
Pueblo, Colorado. It indicates a possible false alarm rate of 2.4% and a missed defect
rate of 3.6%. The vehicle was also able to detect head checks in gauge corners
previously not possible to detect with conventional systems. Small defects in welds
are also detectable with a false alarm rate of 16.7% and a missed defect rate of 6.3%.
Figure 2.10: Improved ultrasonic test vehicle system (Cannon et al., 2003)
Cannon at el., (2003) noted that, although the NDT techniques mentioned above have
been able to detect defects, there is a need to improve current techniques for
consistent and accurate detection. Some of the techniques currently being evaluated
are:
� Inspection using ultrasonic waves generated by electromagnetic acoustic
transducers (EMAT)
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� Low-frequency eddy-current sensors to locate deeply buried defects
� Neural network analysis of signals to improve defect detection and
identification
� Longitudinal guided waves (for example, to potentially allow locomotives to
scan the track head)
� Laser generation and reception of ultrasonic waves to enable non-contacting
inspection
� Improved ultrasonic probe combinations and arrangements in vehicle-based
systems
� Higher speed ultrasonic testing
� Non-destructive measurements of residual stresses and rail neutral temperature
Granström and Kumar., (2004) studied the punctuality of the transportation system
that can be improved by applying condition monitoring technology. This
methodology was identified to evaluate different condition monitoring applications in
relation to punctuality problems.
2.14 Maintenance Strategies
Maintenance is one of the major issues in a railway track system. It is very important
to detect the possible problems in advance and to find cost effective solutions to
prevent them (Simson, 1999).
The majority of Amtrak railway train accidents since 1993 have been found to be due
to train de-railing. Proper maintenance of railway tracks can prevent similar accidents.
Exceeding the life spans and limits of rail track components can result in failure to
perform the intended function, thereby affecting the rail operation. Various types of
maintenance methods currently used are (Cope, 1993):
• Rail grinding
• Lubrication of rails
• Rail transposition
• Rail straightening
• Rail replacement
• Sleeper replacement
• Ballast maintenance
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• Tamping
• Subgrade stabilization
2.15 Rail transposition
Transposition is carried out on tight curves where wear on the high rail is the main
cause of rail replacement. Rail from the high rail is changed to the low rail of the
curve. Rail transposition requires rail grinding of the rail profile to reduce problems of
tight contacts, high contact stresses and poor lubrication. Otherwise, it is likely to
have higher wear rates, high wheel squeal noise and gauge corner shelling.
2.16 Rail straightening
Welded rail joints are straightened by stretching the joint. Rail straightening is
performed on previously mechanically jointed track that has been upgraded by rail
welding. Even though the rail ends of mechanical joints are cropped before rail
welding, a certain amount of rail misalignment can occur.
2.17 Rail replacement
Rail replacement is often done in conjunction with other major maintenance activities
such as sleeper replacements (Figure 2.11). Rail and the rail fasteners are replaced to
fix problems of rail wear, fatigue defects or derailment damage causing notches or
bends.
Figure 2.11: Automated re-railing machine (Simson, 1999)
2.18 Sleeper replacement
Sleeper replacement is done either mechanically or manually. The need and
productivity of re-sleepering is greatly influenced by the density of the defective
sleepers to be replaced.
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2.19 Ballast maintenance
Ballast rehabilitation or stone blowing cleans the fines from the ballast with high-
pressure air. Ballast rehabilitation or undercutting involves automated machinery that
uses chains or mechanical arms to pull through the ballast bed for removing ballast
fines (Wenty, 1996). Ballast undercutters scoop up the ballast and pass it over the
strainer. The fines are removed and the rest of the ballast is returned to the track. At
least 30% of the ballast bed is removed by a ballast rehabilitator/undercutter. As a
result, extra ballast is added to maintain the depth of the ballast after undercutting.
2.20 Tamping
Tamping is used for correcting the rail-sleeper geometry faults. The tampers used by
British Rail (BR) typically combine the functions of correcting top, cross level and
line on the one machine and all corrections are carried out during one pass. Chirsmer
and Clark (1998) discuss the economics of continuous tamping over spot tamping,
along with lift tamping compared to conventional tamping. In conventional tamping,
the track is lifted to return it to the design track profile and alignment. In design lift
tamping, the track is lifted to a mirror image to allow for the rapid settling of the track
profile following tamping. This means the track has a much flatter profile after
stabilising than it would have with conventional tamping.
2.21 Subgrade stabilisation
Reactive soils or clay patches are major problems in track maintenance, causing a
whole range of defects. Lime slurry injection stabilises reactive soils that harden to
cement for filling soil voids. Lime slurry is injected into the sub-grade through a
nozzle lowered through the ballast. Slurry injection will only affect the upper layers of
the subgrade and sometimes several applications may be required to stabilise the
subgrade.
2.22 Operational Conditions
Operational conditions are influenced by train speed, track construction,
characteristics of bogie type, the available adhesion between the wheel and the rail
(based on environmental conditions), tonnage, axle load, curvature and traffic type.
Other factors include rail material and rail type and size, sleepers and fasteners.
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Operating conditions have significant influence on reliability and safety of rail
operation.
Weather (precipitation) creates a natural lubricating layer of water in the wheel/rail
contact. It is found that the decreased wear rate at low temperatures (below 00 C) can
occur due to the condensation on the rail surface. Lower bulk temperature can reduce
the temperature in the contact area and hence reduce the wear rate. Water, snow or
ice, alters the friction coefficient of wheel and rail. Other elements such as organic
debris from trees and fields, and non-organic debris in contact with water/moisture,
worn metallic debris from rails and silicon debris from the concrete sleepers/ballast
can also influence contact conditions. Air temperature and exposure to sun are other
factors influencing evaporation and condensation to the rail surface (Nilsson, 2002).
Track and wheel discontinuities can cause high dynamic forces depending on the
speed and geometry. Rail stresses depend on the amount of wear and the track
structure (including sleeper, ballast and subgrade condition).
2.23 Summary
In this chapter, an overview of rail track structure, defects and maintenance strategies
is presented. It explores the principle structure of rail track, and the functions of its
components, to establish a comprehensive background understanding of the whole
track system. Rolling contact fatigue, rail wear, rail grinding, rail-wheel lubrication,
inspection techniques, and maintenance strategies are also discussed. The major issues
arising from these influencing factors and models will be addressed in Chapter 3. The
major focus of this research will be maintenance of rails. Cost and risk models will be
developed in this thesis for managerial decisions. Development of economic models
on rolling contact fatigue and rail grinding, lubrication and inspection, for optimal
maintenance decisions will be presented the Chapters 4, 5 and 6.
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CHAPTER 3
STUDY OF RAIL WEAR, ROLLING CONTACT FATIGUE AND RAIL
MAINTENANCE MODELS
3.1. Introduction
An overview of rail track structure, defects and maintenance strategies are discussed
in Chapter 2. Grounded theories on rail wear, rolling contact fatigue (RCF) and rail
maintenance models will be discussed in this chapter. The gaps in the existing models
are analysed. Risk based economic models for grinding, lubrication and inspection are
proposed and the need for an integrated model is assessed.
The outline of this chapter is as follows: a review of existing rail wear and rolling
contact fatigue models is carried out in Section 3.2; Section 3.3 presents existing rail
maintenance models; a survey of lubrication practice in Australia and around the
world is discussed in Section 3.4; finally, a summary of this chapter is presented in
Section 3.5.
3.2 Rail Wear and Rolling Contact Fatigue Models
Elkins and Gostling (1977) studied a general quasi-static curving theory for railway
vehicles. They developed a non-linear and vehicle curving model which can be used
to analyse wear behaviour and estimate wear rate. An energy approach is developed to
analyse the relationship between wear rate and contact conditions. That is, wear rate
(expressed as weight loss per meter per rolling per unit of Hertzian contact area) is a
linear function of (tangential force T × slide/roll ratio γ’)/hertzian contact area AH,
considering different relationships for each case. Subsequent work by McEwen and
Harvey (1985) showed that this approach was equally applicable to full-scale
laboratory tests and field. Lyon and Weeks (1983) used this approach to estimate
anticipated improvements in wear by changing the suspension design of confined
rolling stock. Danks and Clayton (1987) studied the wear process for eutectoid rail
steels, using field and laboratory tests. The results are compared with those from a
similar study of the wear surfaces of rail steel specimens, tested in both a pin-on-disk
and a twin-disk rolling contact wear testing device. It is found that, provided the test
conditions are chosen carefully, an adequate simulation can be produced.
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Devanathan and Clayton (1991) conducted rolling-sliding wear tests on three bainitic
steels with 0.04, 0.10 and 0.52 wt% C. The contact conditions employed simulate the
most severe wear situation encountered by wheels and rails in curved track. The
results confirm the potential of bainitic steels for wear resistance, particularly at high
contact pressures. The wear behavior of the bainitic steels has been examined in
relation to microstructure and the surface damage experienced by the worn rollers.
Tyfour and Beynon (1994) studied the effect of different single and multiple rolling
direction reversal (RDR) regimes on wear rate and mechanism. Changes in structure
deformation morphology and accumulated plastic strain are analysed. Results
obtained under the test conditions used show that RDR has a beneficial effect on the
wear rate of pearlitic rail steel. Multiple short RDR resulted in the lowest wear rate,
less than half the unidirectional value.
Clayton (1995) analysed the existing academic models (described as general wear
models) developed by Archard (1953), Quinn (1967), Sub (1973) and Zum Gahr
(1987). The approaches used for these models to predict wear over a wide range of
operating conditions for any material, have small practical significance. Rail
infrastructure owners raised questions about the applicability of the Martland and
Auzmendi (1990) model to heavy haul rail road applications. Bolton and Clayton
(1984) investigated wear behaviour of several rail steels in rolling-sliding contact with
a wheel steel in the laboratory, using an Amsler wear testing machine. Three wear
regimes were identified and metallurgical examinations to determine the characteristic
wear modes within these regimes are described. These were defined as Type I, II and
III, and occur in ascending order of contact pressure and slide/roll ratio. Type I
involves a combination of two modes of wear, resulting in debris containing oxide
and metal particles leading to oxidative wear. Type II involves complete metallic
wear debris, the occurrence of ripples on the roller surface and some metal transfer.
Type III involves an initial break-in period that leads to the production of large pieces
of wear debris. Laboratory work by Danks and Clayton (1987) suggests that Type III
wear simulates unlubricated gauge face wear. Although Type I relations are used to
model wear on the top of the rail, there has been no research to justify this. Finally,
Clayton et al., (1988), Devanathan and Clayton (1991), suggested that specific
relation between wear rate and contact parameters is a function of material properties;
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this model is based on work with relatively soft rail steel. Martland and Auzmendi
(1990) selected the work of Bolton and Clayton (1984) to develop a simplified model
for rail wear for use in track maintenance planning. The wear parameters were
modified to make them fit better with those normally used in rail road operations.
They retained the relations between wear rate and contact parameters derived from the
small scale tests (Clayton, 1995). Clayton (1995) conducted a study on rail and wheel
wear over many years and had concluded that general wear models are unlikely to
yield any real practical benefits. The number of operating variables is overwhelmingly
large and the basic understanding of wear phenomena still limited. The use of models
with very restricted application can prove more useful. The relationships derived from
laboratory tests have been successfully applied to developing new materials and
assessing the benefits of vehicle suspension changes. Such an approach is particularly
applicable to the railroad situation because the cost of access, downtime and materials
for replacement are relatively low. While the general model approach (favoured by
academics) has had little practical impact, it serves to keep in focus the limitations of
existing knowledge and understanding.
Tyfour et al., (1995) conducted a study on the steady state wear behaviour of pearlitic
rail steel. The results show that steady state wear rate prevails after a certain number
of rolling-sliding cycles. It was found that the start of the steady state wear rate
coincides with the termination of plastic strain accumulation and additional strain
hardening.
Alp et al., (1996) developed a standardised method to measure the railroad gauge side
lubricant performance. This method correlates the amount of energy saved to
lubricant breakdown and stabilisation points, and lubricant breakdown duration to
lubricant performance. A vertical pin-on-disk system was modified and used as a
bench-top friction and wear test machine, available at Argonne National Laboratory.
A series of experiments were conducted to evaluate the effectiveness of each
lubricant, in terms of friction, wear and amount of energy saved. It is observed that
lubricants which provided a considerable amount of reduction friction energy
dissipation, resulted in a greater savings in energy. This can be considered as a
measure of effectiveness of lubricant. Hiensch and Smulders (1999) studied rolling
contact fatigue propagation after initiation. The study shows that head checks are a
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potential hazard and can cause rail failure. A critical limit value at which vertical
propagation suddenly occurs was identified. Lubrication of rails appears to encourage
vertical propagation.
Magel and Kalousek (2002) developed a pummelling model at The NRC Center for
Surface Technology to quantify the performance of rail profiles when loaded with a
large number of measured new and worn wheels. Contact mechanics principles are
further discussed on several aspects of rail grinding, including surface roughness, rail
gauge width and rail grinding interval. The IRSID group developed an analytical
model to examine the life of rails experiencing rolling contact fatigue. Corus (2004)
has further developed this model in combination with other analytical techniques to
form the Corus Track System Suite of Model (TSM). This model consist of
� a vehicle dynamics model using Adams Rail Software
� a global track model using Abaqus FE software
� a detailed wheel-rail contact model using Abaqus FE software
� analytical fatigue and fracture models, and
� a detailed component model, including the pad and fastening system
The model produces a “time to crack” initiation which enables the high speed grinder,
or other preventive maintenance procedures, to run over the line to prevent the
development of cracks. This process of fatigue management allows the track engineer
to carry out predictive maintenance well in advance (Jaiswal, 2004).
Figure 3.1: Synergy of rail metallurgy & track engineering (Jaiswal, 2005)
Jaiswal (2005) mentions that appropriate and timely maintenance is an integral part of
the system approach that needs to be adopted by railways if they are to meet the
demanding challenges they face. The synergy of optimum rail metallurgy, good track
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engineering and non-destructive high-speed grinding is explained in Figure 3.1. On
17th October 2000 an inter-city train was derailed at 188 km/h by a broken rail near
Hatfield on Britain’s East Cost main line. The cause was gauge corner cracking
(GCC) or head checking, which are forms of rolling contact fatigue (RCF), and the
rail broke into many small pieces. This is not only confined to Britain; it caused a
collision in Switzerland in 1998 and SNCF views surface defects resulting from RCF
as a serious concern. Substantial problems have also been reported from Germany and
Queensland. Kapoor et al., (2002) indicate that interaction between wear and rolling
contact fatigue is the key issue in managing the wheel/rail interface for optimum rail
life. Four main phases in crack life using curve of (da/dn) against crack length are
discussed and shown in Figure 3.2. They are:
� Crack initiated and driven by ratchetting in the plastically deformed layer
(Curve R)
� Contact stress greatly influencing on the crack as it becomes longer and deeper
(the propagation rate increases because the stress intensity rises with
increasing crack length [Curve Ss]
� Decrease in the crack propagation rate as it becomes longer still and a critical
crack length has been reached. (At this point, the crack tip moves away from
the region with high contact stress and the stress intensity drops. In the
descending part of the curve SL, (da/dn) changes are determined by the shape
of the ∆K curve for long cracks and the crack growth.)
Figure 3.2 Phases of crack life using curve of da/dn and length (Kapoor, 2002)
� The effect of the contact stresses diminishing at certain crack depth, and the
crack driven by the bending, residual and continuously-welded rail stresses in
the rail (Curve B).
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Kapoor et al., (2002) modelled wear using several different approaches. They used
experimentally determined Archard wear and coefficient to link the wear process with
all phases of crack propagation.
Figure 3.3 Truncation of a shallow angled crack (Kapoor et al., 2002)
Figure 3.3 illustrates the effect of wear on crack propagation. As the running surface
wears, the crack mouth is truncated. The effect is most rapid for shallow crack angles.
From the results of this model it is possible to identify strategies for maintaining the
rail/wheel interface to a better standard, and for optimising rail life and safety. Kapoor
et al., (2002) developed a whole life model in a collaborative project with AEAT Rail.
Statistical variations in traffic, axle loads, and vehicle and traffic dynamic
characteristics, determine crack initiation, propagation and wear. To correct crack
growth at the marginal and high risk sites, rail track has reintroduced preventive
grinding and has ordered new rail grinding trains to cope with the workloads, but the
rail life remains a balance between wear and fatigue. Figure 3.4 shows rail life line
due to wear and fatigue.
Figure 3.4 Life line due to wear and fatigue (Kapoor et al., 2002)
If total rail head wear is limited to T, and the rate of removal is ∆T per million gross
tonnes, both by grinding and traffic wear, then the life is T/∆T. At higher wear rates,
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rail must be replaced frequently. For fatigue crack growth, increasing the material
removal rate increases rail life because cracks are truncated before they can move
deep into the rail head. Maximum rail life occurs where two life curves intersect. A
successful strategy (employed by North American and Australian railways) is to use
grinding in conjunction with low wear rate rail steel, to achieve an appropriate
material removal rate to ensure the operation in the region of controlled by wear
Kapoor et al., (2002).
Ekberg et al., (2002) developed an engineering model for prediction of rolling contact
fatigue of railway wheels. Three well-known types of fatigue in wheels considered for
this model are: surface-initiated fatigue, subsurface-initiated fatigue and fatigue
initiated at deep material defects. The model can be integrated in a multibody
dynamics code without significantly increasing computational demands.
Jendel (2002) developed a wheel profile wear prediction tool and applied it to a
vehicle operating the commuter rail network in Stockholm. The methodology is based
on a load collective concept where time-domain simulations are performed, based on
actual track data, measured rail profiles, and pertinent operating conditions. The
vehicle model is built in the GENSYS MBS software utilising validated suspension
models. The contact between wheel and rail is modelled with Hertzian theory and
Kalker’s simplified theory (FASTSIM). The wear modelling is based on Archard’s
wear model and the implementation, including laboratory measurements, is performed
in cooperation with tribology experts at KTH Machine Elements. Comparisons
between simulated and measured wheel profiles, including four scalar wear measures
(flange thickness, flange height, flange inclination and area worn off), are explained.
Yoshida et al., (2002) discussed the influence of elastic modulus of a plated layer on
the contact pressure and the subsurface stresses. It is found that the failure mode of all
metal to metal contact surfaces (spalling/flaking) was caused by subsurface cracking.
The rolling contact fatigue strength of soft surface modified metals is higher than that
of non-coated ones. This is due to smaller contact pressure and smaller subsurface
stresses by the small elasticity, as well as the conformity of the surface modified
elements.
65
Magel et al., (2003) discussed modern rail grinding practices, but these discussions
were largely based on a combination of field experience and intuitive speculation.
Many theories related to crack initiation and growth have been proposed through the
decades, and those concepts have been cleverly extended to the field of rail grinding
to form the basis of the practice known as 'preventive grinding'. However, only
recently have practical models emerged from the laboratory and theoretical
environment and been applied to the process of rail grinding. These models are
substantiating the past practices and providing a pathway towards the development of
improved predictive tools for rail fatigue and profile deterioration. While there have
been many advances in rail grinding over the last four decades, there is still much
work to do. The practical importance of surface roughness is still not well understood.
Franklin et al., (2003) developed a computer model which simulates the ratchetting
wear of a ductile material subject to repeated loading. Variation of material properties
is a feature of the model, failure by ductility exhaustion occurring at isolated points or
extending regions of failure. Such regions form crack-like features. Mechanisms for
removal of weakened material from the surface as wear debris, are described. The
wear process causes a degree of surface roughness. The simplicity of the model
enables simulation of millions of load cycles in only a few hours' computer time. The
computer model is used to study the effect of partial slip on wear rate. When creepage
is relatively low, the wear rate increases sharply with creepage. When creepage is
relatively high, the wear rate is largely insensitive to the creepage.
Cannon et al., (2003) studied an overview of rail defects. This review covers many
topics relating to railway rail failures. The emergence of surface-initiated rail RCF as
a major cause of premature rail removal is of great concern as it indicates that
operating conditions are taking the rail to and beyond its natural endurance limit. This
review indicates that current research and modelling activity are very much focussed
on this issue, but the problem is complex and much still must be done. It is likely that
a major step in rail/wheel technology will be required to solve the RCF problem.
Figure 3.5 shows some forms of RCF defects.
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Figure 3.5: Head check (HC) and transverse rail fracture (Railtrack plc., 2001)
Despite major improvements in rail making and inspection, rail breaks still occur: for
example, in the UK the annual number of broken rails remained almost constant at
about 770 per year between 1969 and 2000. The costs of reducing rail failures have to
be balanced against reduced costs from death and injury, penalty payments, train
disruption, increased customer satisfaction, and better planning of track maintenance
and renewal.
Ringsberg and Bergkvist (2003) developed a finite element model to predict short
crack growth conditions for rolling contact fatigue (RCF) loading. This model is used
for linear-elastic and elastic–plastic FE calculations of short crack propagation,
together with fracture mechanics theory. The crack length and orientation, crack face
friction, and coefficient of surface friction near the contact load are varied.
Comparison of results from linear-elastic and elastic–plastic FE calculations, shows
that the former cannot describe short RCF crack behaviour properly, in particular,
0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is
required instead.
Fletcher et al., (2003) conducted image analysis to reveal crack development, using a
computer simulation of wear and rolling contact fatigue. The simulation allows
simultaneous investigation of wear, crack initiation and propagation. The model
reveals the interaction of wear with crack development, processes which are linked
because wear truncates surface-breaking cracks, and can completely remove small
surface-breaking cracks.
Andersson (2003) developed modelling and simulation of train-track interaction,
including wear prediction. The proposed train-track interaction model, together with a
wear model, constitutes a frame within which the effects of the compound
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longitudinal, lateral and vertical dynamics on rail corrugation growth can be
investigated.
Olofsson and Telliskivi (2003) conducted full-scale tests and laboratory study for
wear, plastic deformation and friction of two rail steels. This investigation was to
study the development of these damage mechanisms on new and 3-year-old rails in a
commuter track over a period of 2 years. The experimental results from the
measurements show that there was a significant change in rail profile due to wear, as
well as to plastic deformation. Plastic deformation and wear was a continuing process,
even for rail that had been in service for 5 years. The plastic deformation mechanism
was plastic ratchetting. Material tests were performed on two different testing
machines: a two-roller and a pin-on-disk machine. On the basis of results from the
material testing, a simple wear map was constructed. In the wear map, the wear
coefficient is presented as a function of sliding velocity and contact pressure. The
results from laboratory tests showed that wear coefficient depended strongly on
sliding velocity. The increase in the wear coefficient when increasing sliding velocity,
was due to a change of wear mechanism from mild wear to severe wear.
Telliskivi and Olofsson (2004) developed a wheel–rail wear simulation. The normal
load was validated for two cases by comparison with results obtained from FEM
analysis. The result show that the wear expressed, as mass loss per distance slid, can
be up to 2.5 times higher when using an elastic–plastic material model compared with
a linear-elastic material model. Also, the form change for a typical two-point contact
in a low radius curve was analysed and discussed.
Chattopadhyay et al., (2005) studied decisions on economical rail grinding intervals
for controlling rolling contact fatigue. The complexity of deciding the optimal rail
grinding intervals for improving the reliability and safety of rails is due to insufficient
understanding of the various factors involved in the crack initiation and propagation
process. They identified the factors influencing rail degradation, analysing the costs of
various grinding intervals for economic decision making. They developed a total cost
model for rail maintenance considering rail grinding, downtime, inspection, rail
failures and derailment, and replacement of worn-out rails.
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Nolsson (2005) studied wear in sliding and rolling contacts such as the wheel-rail
contact for rail roads and the roller-washer contact for roller bearings. Wear and
surface cracks on rails have been observed for a period of three years. They compared
the wear depth with the crack length and equilibrium between these two damage
mechanisms was found for lubricated rail. They found that, by using lubricant with
friction modifiers, the stresses were low enough to prevent crack propagation; also,
rail was hard enough to reduce wear rate.
Lee and Polycarpou (2005) studied wear of conventional pearlitic and improved
bainitic rail steels that were tested in an actual wheel/rail track. Micro-Vickers and
Rockwell C hardness measurements at different length scales were conducted to
investigate the cause of their wear behavior. It was found that the initially softer
pearlitic rail steel was work hardened more than the initially harder bainitic rail steel
as in-service stresses accumulated on the rails, and thus the better wear performance.
Pure sliding laboratory experiments were performed, using both pearlitic and bainitic
samples. These simpler laboratory experiments confirmed that, indeed, pearlitic steel
work hardens more with tribological contact testing and exhibits less wear compared
to J6 bainitic steel, and supported the rail track findings. It is, therefore, important to
consider the in-service work microhardening behavior of rail steels as the initial
hardness cannot reliably predict rail wear and rail life.
Viáfara et al., (2005) conducted sliding wear tests, in a pin-on-disk device to study the
behavior of AISI 1070 pearlitic and AISI 15B30 bainitic pins sliding against AISI
1085 pearlitic disks. The sliding speed was 1 ms−1 for all the tests, and normal loads
of 10, 30 and 50 N were used. The wear resistance was related to the mass loss
measured after the tests and the worn surfaces - as well as particle debris - were
analyzed by optical and scanning electron microscopy. Micro-hardness profiles were
also obtained to analyze strain hardening effects beneath the contact surfaces. The
pearlitic steel showed higher sliding wear resistance than bainitic steel, due to the
excellent strain hardening of pearlite compared to bainite. Oxidative wear regimes
were observed in the pearlitic steel, while in the bainitic one, adhesive wear was the
main removal mechanism, leading to a much more accentuated damage of the surface.
In fact, the wear regime for bainitic samples was always severe, even for the lower
loads applied.
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Franklin et al., (2005) conducted twin disc tests using specimens claded with the same
coatings to determine rolling contact performance in the laboratory. The effects of
lubrication, applied load and coating thickness were studied. An eddy current probe
was used for crack detection. Both materials survived 200,000 cycles of water-
lubricated twin-disc testing without crack formation, in contrast to UIC (260 grade)
900A base material which showed severe cracking after only 4000 cycles.
Metallurgical investigations show excellent RCF resistance, although one coating
developed cracks quickly during water-lubricated testing (after 15,000 dry cycles) and
bonding of the tested coatings (delamination occurred at the bonding interface of one
coating during high-pressure tests). Donzella et al., (2005) developed a model to study
the competitive role of wear and surface origin RCF, predicting their occurrence in
rolling contact as a function of material properties and working conditions. The
presence of the quiescent zone and the exceeding of the elastic shakedown limit were
evaluated in order to predict crack initiation. In rolling/sliding tests, wear is important,
producing large thin metallic flakes and removing surface micro-cracks. From the
preliminary results on wear behaviour under very low creepage conditions, wear rate
seems to be almost constant up to a high number of cycles and dependent on contact
pressure. Figure 3.6 shows the number of factors influencing rail-wheel degradation.
Figure 3.6: Factors influencing rail/wheel degradation
Lewis and Dwyer-Joyce, (2006) studied wear rates and mechanisms of rail and wheel
wear as a result of sand application. This research found that sand causes severe
surface damage. A semi-empirical model has been developed to predict wear of rail
steel caused by sand.
70
Jiang and Dwight (2006) conducted a study to investigate the possibility of using
wheel-rail noise as a real-time indicator of wheel-rail lubrication condition. It has
been found that both wheel flanging noise level and the flanging distance increase as
the interface lubrication deteriorates.
Kumar et al., (2006) studied issues and challenges with logistics of rail maintenance
to reduce costs and risk related to rail operations. It is found that rail operation is
influenced by effective logistics decisions related to rail inspection, grinding,
lubrications, rectifications and rail replacements.
The study demonstrated an extensive literature of existing models of wear and rolling
contact fatigue defects. Gaps were identified and it was found that existing models
related to wear and fatigue are not satisfactory for rail infrastructure owners. This is
mainly due to limited knowledge of the consequences of various influencing factors
between rail-wheel interactions under different operating conditions. There is more
work needed to better understand and to increase safety and reliability of rail
operation and reduce maintenance costs. Concerns are growing for rail owners due to
increasing demand for axle loads, traffic, freight and heavy haul services. Therefore, it
is important to develop an integrated economic model for maintenance decisions
considering rail wear, lubrication, rolling contact fatigue, rail grinding, and inspection
and replacement strategies.
3.3 Rail Maintenance Models
A considerable number of different maintenance planning systems have been
developed by American and European railways. Different approaches and methods
have been used on these systems. But these systems face challenges due to increase of
axle loads, high speed and growing traffic densities. To overcome these problems, rail
players have changed the intervals of inspection and maintenance.
3.4 NSW State Railway Authority’s Wheel-Rail Management Model
A wheel/rail management computer model has been developed for the State Rail
Authority of New South Wales, Hunter Valley Coal Operations. The model can be
used to determine cost effective procedures for wheel machining, rail grinding and
lubrication (Soeleiman et al., 1991). This model focuses on wear related rail failure.
71
This allows large amounts of condition data pertaining to alignment. Non-rail
components are ignored and a more detailed examination of wear data is carried out.
3.5 Railways of Australia (ROA) Rail Selection Module
A technical and economic Rail Selection Module covering 31, 41, 47, 50, 53, 60
kg/m, and 60 lbs /yd rail sections has been developed for the Railway of Australia
(ROA), (Twiddle et al., 1991). The model utilises system specific operating
conditions such as axle load, gauge, track stiffness, annual tonnage, curve radius,
wheel/rail contact position, vehicle speed and superelevation. The model provides an
output which indicates allowable head wear limits, rail life, rail costs, corrugation and
defect warnings for various rail sections. It aids the design of new railway track and
the selection of rails for replacement of worn and damaged rails.
3.6 Railways of Australia (ROA) Rail Grinding Model
Rail profile grinding can result in improved curving performance (wheel/rail
interaction) and reduced propagation of surface cracks due to RCF. It is necessary to
quantify the major cost factors influenced by the engineering phenomena associated
with wheel rail interaction. The rail-grinding model can be used to determine an
optimal grinding cycle, together with the cost sensitivity to variations (Soeleiman and
Rucinski, 1991).
3.7 Railways of Australia (ROA) Wheel/Rail Management Model
This is a wheel and rail deterioration computer model (WRDM) for the railways of
Australia (ROA), using a quasi-expert systems approach. It is a simple model that
uses general track link data to determine what maintenance practices should be
applied and what upgrading of track structure can minimise on going track
maintenance costs (Soeleiman and Mutton, 1993).
3.8 ECOTRACK
European Railway Research Institute (ERRI) has developed ECOTRACK.
ECOTRACK plans track maintenance based on forecasts of track conditions for the
next five years. It enables track maintenance to be optimised in terms of cost, time
scale and maintenance crew resources, or consumable resources. The most important
use is a decision support tool. Savings of up to 5% ~ 10% on track maintenance are
expected following evaluation trials (Leeuwen, 1997; Korpanec, 1998).
72
ECOTRACK assesses homogeneous track sections as small as 200 meters at a time. It
considers rail replacement, tamping, rail grinding and ballast rehabilitation, and
sleeper and fastener renewal maintenance activities. The system relies on user input to
select the best maintenance activity and an expert system to select the timing of
maintenance scheduling. ECOTRACK is designed as a modular system with an
interface to use the existing database of the individual railway. ECOTRACK is
dependent on the accuracy and extent of an existing track condition database. The
database required to achieve the full potential of ECOTRACK is well beyond that
which is available within the majority of railway systems (Leeuwen, 1997; Korpanec,
1998).
The ECOTRACK system has already been implemented by European railway for
(SNCB) 5000-km of track. The prototype of the system was tested on 10 European
railways since 1995. The system is highly complicated and requires expert staff to
run. ECOTRACK is the leading technology in the field of railway maintenance
planning. It is flexible and can be modified to suit any railway operation, having an
existing, detailed, historical track condition database (Leeuwen, 1997; Korpanec,
1998).
3.9 TOSMA
TOSMA is the new track maintenance system of Central Japanese Railways (JR).
This is a highly specialised system that has been developed for a high speed rail
operation, specifically, the Tokyo to Osaka route, with 11 passenger trains an hour
operating at speeds of up to 270 km/hr (Ohtake and Sato, 1998). Such operating
conditions clearly require more care than typical freight operations.
The key to the TOSMA is the data collection from JR Central’s high speed track
recording car that records track geometry every 10 days on the entire high speed
system. Geometry data is for a 10 m versine and is recorded at every track meter. Any
irregularities showing rapid growth are identified immediately. The work priorities
and volumes in track sections are calculated and interpolated into the feature for the
whole line. TOSMA allows the planner to identify problem locations that may require
sub-grade or formation work. It identifies any rapid deterioration problems before
they become a hazard to traffic. It also allows the track engineer to program work
73
volumes into the feature for tamping and ballast renewal operations (Ohtake and Sato,
1998).
3.10 Mini-MARPAS
Mini-MARPAS is a Maintenance and Renewal Planning Aid System which was
developed by BR Research (Grimes and Kay, 2002). There are seven basic track
damage sub-models (Booz-Allen & Hamilton, 1999):
� Rail Maintenance
� Rail Life
� Sleeper Life
� Track Geometry Maintenance
� Ballast Life
� Switch & Crossing Model
� Track Inspection Model
Mini-MARPAS has also been further developed to a Track Usage Cost Model which
is used by Railtrack to establish track usage charge. However, there are a number of
limitations in both the Mini-MARPAS and the Track Usage Cost Model (Booz-Allen
& Hamilton, 1999; Railtrack, 2001; Thanh, 2003).
3.11 AMP98 Cost Model
Asset Management Plan 98 (AMP 98) is a cost model developed to estimate the cost
of rail track maintenance and renewal for a 10 year planning cycle with different
scenarios of traffic (passenger and freight) growth (Sultan, 1999; Atkins, 1999;
Thanh, 2003).
3.12 Track Maintenance Cost Models (TMCOST)
Hargrove (1985) developed an aggregate model to estimate maintenance costs for
given standards of track components (Andersson, 2002). The model uses separate
deterioration models for rail wear as a function of traffic load, rail fatigue as a
function of repeated loading cycles, and ballast and sleepers as a function of loading
(Thanh, 2003).
3.13 Swedish Track Degradation Cost Model
Swedish Railway developed an economic model for track degradation to estimate
maintenance costs due to increasing axle loads from 25 to 30 tonnes (on heavy haul
74
lines) and from 22.5 to 25 tonnes (on normal lines). This model considers track
length, quality, friction and superelevation; axle loads; coefficients for wear and
fatigue; speed profile as function of curvature and height to centre of gravity; and
traffic (annual MGT per vehicle set) (Paulsson, 1998; Andersson, 2002; Thanh,
2003).
Patra and Kumar (2006) studied methods to determine life period of the track, proper
scheduling of preventive maintenance/overhauling, man power allocation for
maintenance and spare parts quantity determination for all the major parts of the
railway track system.
3.14 An Austrian Track Maintenance Cost Model
To achieve an economic track strategy in Austria, a model was developed for
evaluating track maintenance (Veit, 1997). This model considers track type
(continuous welded or bolted track), type of rails, sleeper fastening and ballast,
subgrade condition and traffic density. It also covers investment and operation costs
of machinery and equipment and materials used for maintenance of track. The model
is based on life cycle costing and calculates the cash flow (NPV, IRR) and the annuity
(Thanh, 2003).
3.15 The UNIFE Life Cycle Costing
The Union of the European Railway Industries Life Cycle Cost (LCC) Working
Group (UNIFE LCC) has developed software for collection and exchange of LCC
data. The main focus of this model is on rolling stock and train operation and
maintenance. Economic analysis of the whole system is not covered in this model
(Thanh, 2003).
3.16 Track Degradation Model
Zhang (2000) has developed the integrated track degradation model (ITDM) to
predict future track condition. This model contains four interrelated sub models for
rails, sleepers, ballast and subgrade, and track modulus. The rail sub model is for rail
wear analysis and the sleeper sub model is for timber sleeper damage prediction.
75
3.17 Track Maintenance Planning Model (TMPM)
Simson et al., (1999) hava developed the Track Maintenance Planning Model
(TMPM) to simulate the costs of maintaining rail track. This model is capable of
calculating the costs of track maintenance and train operations when traffic or track
conditions are changed. The model links track condition obtained from the ITDM
(Zhang, 2000) track degradation model, to train delays and other operating costs. The
TMPM model did not include rail grinding, ballast undercutting and ballast blowing
maintenance activities.
The above literature shows that, even though there are a number of existing rail
maintenance models, most of them are generic and not specific. None of these models
has considered the integration of rail grinding, lubrication, inspection, rectification
and rail replacement maintenance activities. This research developed an integrated
approach for the assessment of operational risks in rail track. Models for rail grinding,
lubrication, inspection, rectification and replacement of rails are developed in this
research thesis to evaluate risks and costs.
3.18 Survey of Lubrication Practice
Lubrication at the wheel flange and rail gauge face on sharp curves has been accepted
as an effective solution to reduce rail and wheel wear and noise. Three methods of
lubrication are used: Track-side (way-side), Onboard and Hi-rail (shown in Figure
3.7).
Figure 3.7: Lubrication systems (Chattopadhyay et al., 2004)
76
In the wayside lubrication system, grease is applied to track when the lubricator is
activated either mechanically or electronically by passing wheels. For the on board
lubrication system, the lubricator is mounted on the locomotive and the lubricant is
applied using a spray system to the locomotive wheel flanges. Hi-rail lubrication
systems use a specially designed mobile truck for grease application from the nozzle,
as a thin bead along the rail gauge face. By using one or a combination of the above
systems, railroads can achieve significant savings in fuel and cost of wheel/track
maintenance. However, there are some harmful effects of using excessive lubricant.
These are wastage, loss of locomotive traction due to presence of lubricant on the top
of rail, and environmental concerns of underground water contamination (Pandey et.
al., 2000).
Railway flange lubrication is used to reduce wear of the rail and wheel which is
particularly severe at curves. However, fluid lubricants may contribute to the
development of rolling contact fatigue (RCF) cracks by mechanisms; for example,
crack face friction modification and fluid entrapment. The possibility therefore exists
that, while application of a fluid lubricant may reduce rail and wheel wear, the
lubricant may contribute to rail RCF failures. Dry, solid lubricants have some
advantage in avoiding this problem (Fletcher and Beynon, 2000). The American
Association of Railroads (AAR) estimated that the wear and friction occurring at the
wheel/rail interface of trains due to ineffective lubrication, costs American Railways
in excess of US $ 2 billion each year. Currently, the largest expenditure faced by the
railroad industry is rail maintenance and replacement. Application of lubricants at the
wheel rail interface dramatically reduces the rail track degradation and fuel
consumption (Sid and Wolf, 2002). Rail life has been increased by a factor of two and
wheel life by a factor of five (Queensland Rail, Australia), using appropriate
lubrication. Spoornet (South Africa) has reported that rail life was increased from 27
MGT to up to 350 MGT, depending on curve radius. Canadian Pacific (CP) rail
indicated that rail life improved by 110%, using effective lubrication. Experiments on
the Olympic Park loop, NSW (Australia) on a 200 m radius curve, indicated that
flange wear rate is reduced from 0.36 mm/day (life of 0.2 year) to 0.006 mm/day (life
3.5 years). HKMTRC (Hong Kong) reported a cost saving of £ 783,000 per year on
wheel and rail maintenance on the solid lubricant lines. Eurostar conservatively
estimates that effective lubrication saves £ 1,000,000 per year on maintenance and
77
wheel replacement costs (Larke, 2002). ERL/Malaysia has recorded data on
lubrication shown in Table 3.1.
Table 3.1: Cost of Lubrication strategies (Larke, 2002)
Track/Vehicle
condition
Wheel life in km Wheel life in weeks
Typical lubricant costs in the UK are between £ 2.50/kg to £ 6/kg. In the field
measurement, Norfolk Southern, the electric lubricators achieved 107% improvement
in lubricant dispersion along the track, a 67% reduction in lubricant usage and a 57%
reduction in wastage (Larke, 2002). Typical grease usage data, lubricant costs and
maintenance costs are shown in Table 3.2.
Table 3.2: Lubrication costs to rail players (Larke, 2002)
Railway Quantity
(tonnes/yr)
Lubricator
(AUD$/yr)
Three types of lubrication strategies are considered in this research:
• No lubrication: Cost of lubricant is zero. Rail wear increases for sharp curves and
the replacement of rails occurs more frequently. Wheel wear is rapid and causes
damage to rail and wheels and increases wheel replacement costs.
• Continuous lubrication: Lubrication is applied over rail and wheel throughout
the year (especially in dry areas where temperature is between 20 to 40 degrees
78
0C) and lubrication cost per MGT is reasonably high. However, research shows
that continuous lubrication extends rail and wheel life; improves vehicle/track
interaction and reduces wear in rail and wheel; reduces fuel costs and also
prevents derailments to some extent.
• Stop/Start lubrication: This lubrication strategy is applied in cold countries
where temperature is below 4 degrees 0C. In the cold countries like Europe, North
America and Scandinavia, lubrication is stopped in the winter and starts operating
again in spring and dry seasons. In this strategy, lubrication cost is less compared
to continuous lubrication. However, there is the cost of switching stop/start
mechanisms and increased wear during winter compared to lubrication periods.
For “no lubrication”, the cost of lubrication is nil. However, field experiments in
Scandinavia show that the wear rate at non-lubricated sharp curves for 300 to 400 m
radius is ten times higher than for lubricated curves. For curve radius 600 m and
above, the wear rate is about two to five times higher than lubricated curves (Jendel,
2002). In start/stop lubrication, lubrication is activated periodically according to need.
Field experiments show that the wear rate during the autumn, winter and spring is
higher than the wear rate during the fall. This has aesthetic (and possibly economic)
appeal but it is not a common option by rail players in the world (Nilsson, 2002). In
continuous lubrication, lubricant between wheel and rail reduces (i) squeal, (ii) wheel
flange vertical wear and (iii) rail gauge face wear. It is also used to prevent low rail
corrugations at sharp curves (Ishida et al., 2003). On the other hand, lubrication of the
rail crown has some risk of wheel sliding. Therefore, advantages and risks need to be
balanced by choosing reliable lubrication methods and a lubricant with a suitable
friction coefficient. Railway companies are looking for the appropriate lubricant that
can enhance the efficiency of operation, along with reliability and safety.
Transportation Test Centre (TTC) in Pueblo Colorado USA recommends that research
efforts should be aimed at developing and testing lubricants to meet the different
needs that the railroads have in different countries. There is a need to work towards
an international standard.
Nilsson (2002) discusses important factors influencing rail wear such as friction
coefficient (based on humidity, temperature, surface texture); type of lubrication
equipment (on board or wayside); grease contamination from dust, leaves, worn away
metal particles, water and rail and wheel profile rectification. Other influential factors
79
are track irregularities (vertical, lateral, cant, gauge), curve radius, magnitude of creep
in wheel/rail contact, traction braking and acceleration. Rail players in Canada have
found that lubrication is effective in some areas and inadequate in others. The reason
for this is not clear, but lubrication may not be working effectively. Reasons might be
that they are running out of lubricant or that they need to monitor the method of
lubrication and improve standard maintenance activities (Judge, 2000). The trackside
lubrication system in Spoornet had problems of labour intensive maintenance and hi-
rail lubrication was substituted. The subsequent investigation found that some curves
were poorly lubricated and the schedule of hi-rail lubrication operation was increased,
with resultant increased maintenance costs (Koker, 2003). In Sweden, curves with
radius less than 600 m are routinely lubricated with stationary (wayside, Clicomatic)
applicators. Around 3000 such units are currently in use in Sweden. Figure 3.8 shows
the conditions in winter.
Figure 3.8: Lubricators are full of ice and snow in track (Larsson et al., 2005)
In the 1970s Swedish State Railways (SJ) experienced a heavy increase in wear on
rail curves and wheel flanges. Conventional lubricators did not work satisfactorily.
Clicomatic LP has been developed by SRS in cooperation with SJ Track division to
address this problem. In 1995 the SRS Clicomatic EC was designed and developed
out of LP-version. Clicomatic FC operates under to 220V/50Hz (alt, 110V/60Hz) and
has a transparent, exchangeable grease container. SJ Track division observed that rail
wear in steep curves has been reduced by up to 98% with a small amount of grease
(17 grams (0.06 oz.)/1000 wheels). It also showed that the wear on wheel flanges
decreased up to 50% after installation of lubricators. From 1978 to 1996 more than
2500 lubricators of the Clicomatic type were placed in Scandinavian rail track. Trains
create vibrations in the track which are detected by the vibratory sensor in the grease
gun housing. The electronic control unit receives a signal from the vibratory sensor
and opens the solenoid valve at preset intervals, activating the grease gun. The grease
is then ejected through a four-hole nozzle, hitting the rail flange with four spots of
80
grease; the intervals between the impulses can be preset for different time intervals.
This means that, while the sensor is registering vibrations, either one or several grease
shots can be released during a train passage, depending on the preset time interval.
Table 3.3: Lubricators used in Sweden, 2004 (Larsson et al., 2005)
Type
Installation and
setup cost (AUD
$)
Maintenance cost
per annum (AUD $)
All costs (in Table 3.3) are determined in a yearly agreement with the subcontractor.
Field measurements in the USA have shown that rail and wheel flange lubrication
reduces rolling resistance of up to 50% around curves and up to 30% on straight and
tangent track compared to the unlubricated track. The efficiency of the lubricant film
between the rail and wheel greatly affects the improvement of rail and wheel life.
In the UK a number of QHi Rail lubricators are used to lubricate the track. Both
mechanical and electric powered rail lubricators are used to cater for high/low speed
lines, low and high radius curves and running /check rail. There are upgrade kits for
QHi and Portec units. The system is a simple mechanical design that is easy to install
and suits all rail types (Network Rail approved Cert. No. PA05/459). The pump is a
positive displacement pump that produces a consistent volume of grease flow. The
plunger only requires minimal movement to apply the amount of grease on to the rail.
Grease used is standard grease and it is suitable for high and low speed traffic. The
modular distribution blade applicator (GDU) has a controller for grease flow. The
grease reservoir is a robust durable aluminium construction that can contain 35 or 70
kg. Network rail has 8 000-10 000 mechanical QHi units and London Underground
Ltd has 200 units (figures updated up to 2001). Lubricators that are mounted directly
on rail need to be dismounted and remounted when rail grinding or other work (such
as tamping) is performed. Network Rail also has 20 top of rail lubricators (Portec
protector IV). Uneven rail wear and very high rail wear rate was found in certain
sections at sharp curves at London Underground, even though the line had been fitted
81
with a number of lubricators. A special team investigated the lubricators at the
London Underground in December 2000 and found that not all the lubricators were
working properly (they were not dispensing sufficient grease). In some cases this
resulted in the replacement of rail every 18 months instead of 18 years. Consequently,
this has increased maintenance costs. It is also important to achieve the critical
balance between over-greasing and under-greasing – a bit of black art (Briginshaw,
2004). All costs (in Table 3.4) are estimated in SEK and maintenance cost is from
yearly agreement with the subcontractor.
Table 3.4: Lubricators used in UK (Larsson et al., 2005)
Type
Installation
and setup
cost (AUD $)
Maintenance cost
(AUD $) per annum
Locomotive wheel life of 35000 km and less, and rail life of less than 25 million gross
tonnes have been recorded on unlubricated Spoornet track (South Africa). The
economic implications of these high wear rates are exorbitant, as the cost of new rail
is more than $AUD 65.20 per m, excluding replacement costs. Spoornet has achieved
a seven to tenfold increase in rail life with rail and flange lubrication. On the Richards
Bay Coal line (South Africa), high-tensile rail under high axle-loading conditions has
provided an expected life of more than 1500 million gross tonnes (MGT) with
lubrication (Koker, 2003), compared to rail life of 25 million gross tonnes without
lubrication.
Spoornet has 3 000 lubricators manufactured by RailQuip and another 500 (reservoir
of 120 kg capacity) hydraulic lubricators manufactured by Moore & Steel. There is
maintenance cost data but no technical data available. All costs (in Table 3.5) are
estimated in SEK and maintenance cost is from yearly agreement with the
subcontractor.
Table 3.5: Lubricators used in Spoornet (Larsson et al., 2005)
Type
Installation
and setup
cost
Maintenance cost
(AUD $) per annum
82
In the Canadian rail track, the Top-of-rail coefficient of friction was difficult to
achieve with wayside lubricators. Running trains in the westbound direction, then in
the eastbound direction, leads to drying of the top of the rail a few miles from
lubricators, and iron oxide particles from the top of the rail begin to accumulate on the
ties. Lubricators were turned to pump more grease to wheels, leading to wastage,
environmental problems, high maintenance (filling of grease) and potential slips for
locomotives (Judge, 2000). Other types of lubricators are widely used by rail players
around the world. Figure 3.9 illustrate examples from Protec and Lubritech.
In Australia, a self-contained, stand-up unit with choice of AC or DC (with/without
solar panel) power supply, as well as sensor or adjustable pre-set timing for lubricant
flow to suit varied traffic patterns, is used by rail players. These are designed for train
and tramway systems for rail and wheel lubrication. Top of rail Lubricators and
Gauge Face Lubricators:
• Increase rail and wheel life and reduce fuel consumption
• Minimize derailment potential, abate noise and reduce lateral forces in track
Figure 3.9: Rail and wheel lubricators (Chattopadhyay et al., 2004)
83
These are central lubrication systems operated by compressed air, which
intermittently spray the minimum possible amount of lubricant in exact quantities on
to the friction points.
The problems associated with wheel and track lubrication in the Australian system are
different from those of the Scandinavian system in many ways: clogging; cleaning
intervals; temperature; pumpability problems in hot seasons; placing the lubricant in
the correct position on the rail head for a mixed traffic line; and oil/thickener
separation problems. However, most of the rail players have common problems in
planning and maintaining way-side lubricators. Such problems could include: long
distances between lubricators, environmental problems, cleaning the ballast of grease,
and unpleasant working conditions (with potential health risks of maintenance crews
in handling grease and lubricants).
Figure 3.10: Bleeding from the blade (QR, 2005)
Wayside lubricators are found to be highly reliable with low maintenance cost.
However, Piston is heavy (a mechanical/hydraulic device to pull the plunger could be
helpful) and actuating block clamp screw is not user friendly. Grease contamination
(as shown in Figure 3.10) has been observed on lubricated sites due to dust, leaves,
worn metal particles, water, and rail and wheel profile rectification. Corrosion found
on the rail head due to the oxidation of metals results in vibration, noise and uneven
wear of rail. Field tests and literature show that preventive rail grinding and top of
rail lubrication and friction modifiers can be used to overcome corrugation.
84
Figure 3.11: Short wave corrugation (QR, 2005)
It was found that (as shown in Figure 3.11) insufficient lubrication at curve sections
results in higher flanging noise. This may be due to improper application of lubricant
from blades across the curves. This also has a negative effect on truck curving and
train handling, rail fatigue and energy savings. Excessive amounts of lubrication can
cause numerous problems ranging from operating conditions to environmental impact.
Too much lubrication (as shown in Figure 3.12) causes wheel slippage and increases
the train braking distance. This is an important safety issue for the rail administrators.
Excessive lubrication can also cause locomotive adhesion problems that may result in
increased wheel and rail wear.
Figure 3.12: Grease leakage and environmental hazard (QR, 2005)
Lubricants spread easily and have a tendency to migrate to the top-of-rail even if
applied at the gauge face of rail. However, from the literature and observation, it is
found that there are a limited number of lubrication programs to accurately and
effectively measure and maintain the effectiveness of lubrication on the rail. Routine
maintenance of lubricators and tolerable numbers of lubricant application can be
achieved only if adequate monitoring methods are available.
Questions have been recently raised by rail players as to how much lubricant is
appropriate and effective for a particular curve section under various operating
Shortwave Corrugation
85
conditions. Research is being carried out to investigate the amount of lubricant and
its effectiveness for a particular curve. There is a need to develop a performance
evaluator of lubricators for achieving desirable benefits and savings.
3.19 Summary
Extensive literature on existing models of rail wear and rolling contact fatigue, rail
grinding and lubrication are discussed in this chapter. A survey of lubrication practice
in Australia and around the world is presented. It is found that there are several
existing models available to predict rail wear, rolling contact fatigue and rail track
maintenance. However, there is a need for an integrated model to predict and assess
operational risks and costs. The model includes rail grinding, lubrication, inspection
for grinding, NDT inspection, rectification and replacement of worn-out rails and
risks due to rail breaks and derailments. These models are discussed in subsequent
chapters. Failure and cost models will be developed for optimal grinding decisions in
Chapter 4.
86
CHAPTER 4
MODELLING AND ANALYSIS OF RAIL DEGRADATION AND RAIL
GRINDING DECISIONS
4.1 Introduction
Grounded theory of rail wear, rolling contact fatigue (RCF), rail track maintenance
models and survey of rail lubrications were discussed in Chapter 3. This chapter will
focus on modelling and analysis of rail degradation and rail grinding costs. Real life
data is collected and analysed for developing these models. Economic models are
developed, analysed for the risks and costs due to rolling contact fatigue and optimal
rail grinding. Illustrative numerical examples are used to assist industry with informed
strategic decisions in rail grinding.
The outline of this Chapter is as follows: In Section 4.2, a system approach to
modelling is discussed; in Section 4.3, modelling rail breaks and rail degradation are
explained; Section 4.3 deals with economic models for optimal grinding decisions;
numerical examples are provided in Section 4.4; simulation results are analysed and
interpreted in Section 4.5, and an analysis of annuity cost/m per MGT is discussed in
Section 4.6; in the concluding section, results are summarised and contributions are
discussed.
4.2. System Approach and Modelling
Rail failures can be modelled using a system approach, as shown in Figure 4.1.
87
Figure 4.1: Integrated system approach for modelling and analysis
Rail defects and rail wear occur due to accumulated tonnage (Million Gross Tonnage)
on rail track from traffic and freight movements and heavy haul services. In real life,
the asset life is at risk due to continuous usage, initiation and propagation of defects,
loss of material due to rail-wheel interaction and increased axle loads and train
speeds.
4.3 Modelling Rail Breaks
Chattopadhyay et al. (2002) developed models for optimal maintenance of high
volume infrastructure components. Kalousek and Magel (1997) proposed a ‘magic’
Collection and analysis of rail wear, rail breaks, derailments, lubrication, inspection, grinding data from the rail industry and lab experiments
Identification of causes and characterisation of problems
System characterisation depending on operating conditions
Stochastic modelling and development of integrated models
Risk (cost-benefit) analysis to minimise the probability of occurrence, detectability and severity of rail defects.
Parameter estimation of developed models
Testing and validation of these models using real life data
Application and implementation of these models in real life industry
Optimisation of model
Collection and analysis of rail wear, rail breaks, derailments, lubrication, inspection, grinding data from the rail industry and lab experiments
Identification of causes and characterisation of problems
System characterisation depending on operating conditions
Stochastic modelling and development of integrated models
Risk (cost-benefit) analysis to minimise the probability of occurrence, detectability and severity of rail defects.
Parameter estimation of developed models
Testing and validation of these models using real life data
Application and implementation of these models in real life industry
Optimisation of model
88
wear rate in the maintenance of railway tracks. They applied contact mechanics to rail
profile design and rail grinding. Ringsberg (2001) developed models of life prediction
in rolling contact fatigue crack initiation. Jendel (2002) developed prediction models
for wheel profile wear and compared the predictions with field measurements.
Kalousek et al., (1989) proposed the use of Preventive Rail Grinding Strategy. This
process is applicable to both standard and head hardened rails. Grinding cycles are
used to remove small initiating surface cracks early and frequently with light
grinding, rather than applying heavy grinding based on the surface appearance of the
rail. It was argued that longer rail grinding intervals require a disproportionately
greater amount of metal removal, since it is necessary to remove longer cracks that
are propagating more rapidly than short cracks. [Also, continuously restoring
favourable profiles to control the rail stress, creepage and rail surface roughness
minimises both the rates of initiation and propagation]. Canadian Pacific Railway
(CPR) experimented with the idea, grinding up to 6 times per year (i.e. 10-MGT
intervals) on 'typical rail with cracks'. Field tests on Canadian Pacific Railway (CPR)
and British Columbia Rail (BCR) proved that this method would control cracks and
was, in fact, a considerably more economical technique for grinding rail, permitting
single pass grinding where multiple passes had been required before. Canadian
National and Burlington Northern had similar findings and adopted a frequent
grinding cycle in their high tonnage regions.
In the preventive mode, rail grinding is a process of controlled artificial wear and,
through fine-tuning, can be applied to restore the desired profiles and achieve the
required depth of metal removal, with minimal grinding effort and steel wastage.
'Fine-tuning' means both determining and applying the 'Magic Wear Rate'– that is, the
combined amount of natural and artificial wear required to just remove the existing
and incipient cracks that are contained within a thin skin of metal at the surface.
CPR's Magic Wear Rate in sharp curves has, over time, evolved to be about 0.025
mm (0.001 in) per MGT of traffic, providing approximately 750 MGT wear life,
based on 19 mm (0.75 in) of allowable wear. At a 25 MGT grinding interval, this
translates into about 0.6 mm of vertical wear each cycle, of which about 0.2–0.3 mm
is typically removed during grinding – the rest being natural wear.
89
The model proposed here is based on a total cost of rail maintenance. Cost data
collected from infrastructure players are: inspection cost, grinding cost, down time
cost due to rail grinding (loss of traffic), replacement of worn-out rails, rectification,
and associated cost of rail breaks and derailment.
Counting Process
In the integrated approach, failures can be modelled as a point process. A point
process { }0),( ≥ttN is a counting process where N(t) represents the total number of
failures that have occurred up to time t. It must satisfy:
1. 0)( ≥tN
2. N (s, t] is integer valued random variable, counting the number of failures that
occur in the time interval (s, t]. It includes both the number of failures
occurring in (s, t] and the times when they occur.
3. If s < t, then )()( tNsN ≤
4. For s < t, { })()( sNtN − equals the number of events that have occurred in the
interval (s, t].
Λ(m) is an intensity function, where m represents Millions of Gross Tonnes (MGT)
and Λ(m) is increasing function of m, indicating that the number of failures in a
statistical sense increases with MGT. Fn(m) denotes the cumulative rail failure
distribution, modelled as Weibull distribution (Crowder et al., 1995) given by:
))(exp(1)( βλmmFn −−= (4.1)
)(1)( mFmS n−= (4.2)
where S(m) is survivor function.
Then the density function is expressed as:
dt
mdS
dt
mdFmf n
)()()( −== (4.3)
Then intensity function, Λ(m) is given by:
)(1
)()(
mF
mfm
n
n
−=Λ (4.4)
11
)())(exp(1(1
))(exp()(
)(1
)()( −
−
=−−−
−=
−=Λ β
β
ββ
λλβλ
λλλβm
m
mm
mF
mfm
n
n (4.5)
1)()( −=Λ βλλβ mm (4.6)
90
with the parameters β > 1 (shape parameter) and λ > 0 (scale parameter [characteristic
life]). This is an increasing function of m. The probability of failure rate is higher in
case of aged (old) rails with the increase of accumulated MGT passed through this
section. Note that this corresponds to the failure rate of two-parameter Weibull
distribution. As a result, ),( 1 ii MMN + the number of failures over 1+iM and iM are a
function of MGT and random variable. With condition on N(Mi+1, Mi) = n, the
probability is given by:
∫
∫Λ−
Λ==++
+
1
1
!/
)(
})({});1
({i
M
iM
iM
iM
n
dmm
endmmni
Mi
MNP (4.7)
This type of characterisation is considered appropriate because rail track is made
operational through repair or replacement of the failed segment and no action is taken
with regards to the remaining length. Since the length of failed segment replaced at
each failure is very small relative to the whole track, the rectification action can be
viewed as having negligible impact on the failure rate of the track as a whole. Then
the expected number of failures over 1+iM and iM is given by:
))()(()],([ 11βββλ iiii MMMMNE −= ++ (4.8)
where the total accumulated MGT, Mi, is given by:
∑=
=i
i
ii mM0
(4.9)
where im is MGT in period i.
4.4 Modelling Rail Degradation (Rail Section Loss)
MINIPROF (Greenwood Engineering) is a standard system used for the determination
of rail profiles in the field. The sensing element consists of a magnetic wheel 12 mm
in diameter, attached to two joint extensions. When the magnetic wheel is moved
manually over the rail surface, two angles are measured and stored in a computer. The
profile is then transformed to Cartesian co-ordinates. Marks on the edge of the rail are
used to ensure that the measurements were performed at the same location each time.
The accuracy of the MINIPROF system is of the order ± 0.015 mm for similar
profiles. Figure 4.2 shows rail profile measurement using MINIPROF.
91
Figure 4.2: Rail profile measurement using MINIPROF (Greenwood, Denmark)
From profile measurement data, a stochastic rail model is developed, using effect of
traffic wear and grinding wear. The area after ith period is modelled as:
( )∑=
+++−=i
oj
jwwjwwi GDRGRCTDRGRCAA )()(0 [TD0, GD0 = i] (4.10)
where A0 is the cross sectional profile area of a new rail, RCw is Rail Crown wear
width, RGw is Rail Gauge wear width, TD is the wear Depth from Traffic, GD is the
Grinding Depth due to grinding. It can be expressed as:
∑=
+−=i
j
GWTWi jjAAAA
00 ][ ci AA ≥ (4.11)
where jTW
A is the cross-sectional area loss due to traffic wear in period j and jGW
A is
the cross-sectional area loss due to grinding wear in period j.
( ) jWwTW TDRGRCAJ
+= (4.12)
( ) jWWGW GDRGRCAi
+= (4.13)
The % worn out level of rail after ith period is given by:
c
ii
AA
AAWOL
−
−∗=
0
0100 (4.14)
where Ac is the critical railhead for rail replacement, based on safety
recommendations. Ai is the cross sectional rail profile area at ith interval. The rail
industry from Scandinavia used the MINIPROF Rail profile system to measure the
profiles just before and after rail grindings (Åhrén et al. 2003). Transverse profiles are
measured for outer and inner rails at 60 positions on Malmbanan line in Sweden. The
rate of metal removal by rail grinding is about 0.2 mm across the railhead for every 23
MGT. It considers two measurements for railhead wear (Regulations BVF 524.1,
92
1998). The vertical wear on the railhead h and the flange wear s, 14 mm down from
the top of a new rail profile (Figure 4.3) is explained in Equation 4.15.
Figure 4.3: Central vertical wear and side wear (Chattopadhyay et al., 2005)
2BV
BVBV
ShH += (4.15)
The mean wear per year and amount of material removal per year due to grinding is
presented in Table 4.1.
Table 4.1: Measurements of grinding (Chattopadhyay et al., 2005)
12 months of traffic, (MGT) 23 [106 kg]
93
Figure 4.4: Measurement of rail wear (Åhrén et al. 2003)
Figure 4.4 shows measurement of wear for 23 MGT Malmbanan. Using the relation
between measured s and h, one can determine Ac, the critical railhead area. The
Malmbanan line shows the annual h/s from traffic wear 0.16/0.24 mm and that from
grinding wear 0.48/0.42 mm per year for 23 MGT intervals at curve radii R<800 m.
The relation between s and h to H (equation 4.15) is as follows:
For traffic wear: TBVTBVTBVTraffic hhhH 75.1*2*16.0
24.0=+= (4.16)
For grinding wear: GBVGBVGBVGrinding hhhhH 44.116
23*
2*48.0
42.0≈=+= (4.17)
Total wear: )()()( 1.52*2*64.0
66.0GBVTBVGBVTBVGBVTBVTotal hhhH +++ ≈+= (4.18)
The safety wear limit Hlimit is set to 11 mm for the 50-kg/m BV50-rail profiles in
Malmbanan line. Ac can be calculated as function of hBV and is given by:
WWc RGsRChA ** += (4.19)
where RCw is the estimated Rail Crown wear width and RGw is the estimated Rail
Gauge wear width. Results are shown in Table 4.2.
94
Table 4.2: Safety limit for Malmbanan (Åhrén et al. 2003)
s Traffic
The critical area that corresponds to the safety limit of 11 mm (BV50) is 440 mm2 and
for UIC 60 is estimated to be 560 mm2. For a theoretical 80 kg/m rail, 1000 mm2 wear
area is used (Åhrén et al. 2003).
4.5 Economic Grinding Model for Optimal Grinding Decisions
A huge share of the operational budget is spent on maintenance and replacement of
rails and wheels. Although many factors contribute to degradation, the influence of
wheel/rail contact conditions, the magnitude of friction coefficient and the rail wheel
condition are extremely important. The possible reasons for the increase in broken
rails through the 1990s include:
• Falling levels of rail renewals over the last 30 years
• Increased reliance on manual ultrasonic rail inspection
• A worsening of track quality and a possible increase in wheel irregularities
and higher dynamic forces
• Increased traffic which has not been followed up by increased inspections, and
revised minimum action criteria for defect removal, and
• Acceleration of rolling contact fatigue as a result of the introduction of bogies
with higher wheelset yaw stiffness.
Burlington Northern Santa Fe (BNSF) followed hybrid grinding procedure with a
corrective grinding practice, and faced poor surface condition and increasing defect
counts and was seeking a method to get back to the preventive grinding practice from
which they had regressed several years earlier. Canadian Pacific Railway (CPR)
successfully extended their previous 18 MGT to 25 MGT intervals on their timber-
sleepered track while retaining the single pass grinding strategy. This step removed
full grinding cycle, saving 440 000 US dollars annually in rail grinding costs without
compromising rail life.
95
Table 4.3: The ideal grinding for heavy-haul (Magel & Kalousek, 2002)
Grinding depth [mm]
Magel and Kalousek (2002) identified the favourable “wear rate”, as shown in Table
4.3. The vertical crack rate is estimated to be 0.05 to 0.15 mm/ 10 MGT. The
preventive rail grinding is used to control the vertical crack propagation rate with
removal of railhead material as proposed in Figure 4.5.
96
Figure 4.5: Flow chart of the track monitored base model
It is important to develop effective maintenance strategies combining technology and
safety methods for optimal rail grinding in controlling RCF and wear. Some of the
associated costs are:
START
Track segment and inspection
input: initial track data; wear
from grinding and traffic data,
lubrication data and period of
analysis (MGT -step)
Statistical Input Data
Distribution of: rail break,
derailment, detected cracks,
grinding passes, traffic wear,
grinding “wear”
Calculate wear
rate distribution
due to Traffic
Calculate wear
rate distribution
due to Grinding
Calculate
distribution of No. of
Grinding passes
Current values of
track costs and
track conditionsCalculate distribution of
rail breaks, detected
cracks and derailments
UpdateNext increment
in traffic MGT
Generate a new
expected value of
rail profile
Calculate total
cost to reach
optimal safety life
Is safety limit
reached?
Display total
cost/MGT
Economic Input Data
Cost for inspection, rail
breaks, derailment, down
time (loss of traffic),
grinding cost, lubrication
cost and replacement of
worn-out rails
Yes
No
START
Track segment and inspection
input: initial track data; wear
from grinding and traffic data,
lubrication data and period of
analysis (MGT -step)
Statistical Input Data
Distribution of: rail break,
derailment, detected cracks,
grinding passes, traffic wear,
grinding “wear”
Calculate wear
rate distribution
due to traffic
Calculate wear
rate distribution
due to grinding
Calculate
distribution of No. of
grinding passes
Current values of
track costs and
track conditionsCalculate distribution of
rail breaks, detected
cracks and derailments
UpdateNext increment
in traffic MGT
Generate a new
expected value of
rail profile
Calculate total
cost to reach
optimal safety life
Is safety limit
reached?
Display total
cost/MGT
Economic Input Data
Cost for inspection, rail
breaks, derailment, down
time (loss of traffic),
grinding cost, lubrication
cost and replacement of
worn-out rails
Yes
No
START
Track segment and inspection
input: initial track data; wear
from grinding and traffic data,
lubrication data and period of
analysis (MGT -step)
Statistical Input Data
Distribution of: rail break,
derailment, detected cracks,
grinding passes, traffic wear,
grinding “wear”
Calculate wear
rate distribution
due to Traffic
Calculate wear
rate distribution
due to Grinding
Calculate
distribution of No. of
Grinding passes
Current values of
track costs and
track conditionsCalculate distribution of
rail breaks, detected
cracks and derailments
UpdateNext increment
in traffic MGT
Generate a new
expected value of
rail profile
Calculate total
cost to reach
optimal safety life
Is safety limit
reached?
Display total
cost/MGT
Economic Input Data
Cost for inspection, rail
breaks, derailment, down
time (loss of traffic),
grinding cost, lubrication
cost and replacement of
worn-out rails
Yes
No
START
Track segment and inspection
input: initial track data; wear
from grinding and traffic data,
lubrication data and period of
analysis (MGT -step)
Statistical Input Data
Distribution of: rail break,
derailment, detected cracks,
grinding passes, traffic wear,
grinding “wear”
Calculate wear
rate distribution
due to traffic
Calculate wear
rate distribution
due to grinding
Calculate
distribution of No. of
grinding passes
Current values of
track costs and
track conditionsCalculate distribution of
rail breaks, detected
cracks and derailments
UpdateNext increment
in traffic MGT
Generate a new
expected value of
rail profile
Calculate total
cost to reach
optimal safety life
Is safety limit
reached?
Display total
cost/MGT
Economic Input Data
Cost for inspection, rail
breaks, derailment, down
time (loss of traffic),
grinding cost, lubrication
cost and replacement of
worn-out rails
Yes
No
97
• Restricted track access while grinding
• Rail grinding cost per m
• Replacement of worn-out rails
• Derailment and damage of track, train, property, life and down time
• Repairing rail breaks in terms of material, labour, equipment and down time
• Inspecting rail tracks in terms of material, labour, equipment and down time.
The grinding at Malmbanan has been an increasing problem. In 2001 a new ore
carrier was introduced with 30 tonne axle loads. This rise in axle load from 25 tonnes
resulted in RCF damage. Scandinavian rail industry carried out rail profile
measurements before and after grinding activities for analysis of its effectiveness in
controlling rolling contact fatigue (RCF) (Åhrén et al., 2003). The grinding campaign
is analysed in Table 4.4.
Table 4.4: Track path divided into sections (Larsson et al., 2003)
Sections
In spite of aggressive grinding programs and frequent, onboard, non-destructive
measurements, rail breaks happen. Other factors such as weld joints, rail geometry
and corrugation contribute to the risk. The cost of these unplanned replacements is
treated as risk cost. For an infrastructure player, it is essential to measure and manage
these risks by implementing cost effective traffic and maintenance management
strategies (Larsson et al., 2003). Questions commonly posed are:
• How much is the current risk of derailment on a specific track section?
• Will the current risk change with changed maintenance strategies in the
future? and
• What is the cost/benefit ratio of various strategies in terms of maintenance
costs and risk costs?
The total cost of maintaining any segment of rail is modelled as the sum of costs for:
rail grinding; down time due to rail grinding (loss of traffic); rectification and
associated costs of rail breaks and derailment; and inspection and replacement of
worn-out rails. The present value of rail maintenance associated costs is discounted at
98
annuity rate. (For example, the present value of $1 to be received t periods in the
future at a discount rate of r, (PV = $1 × [1/(1+r)t)] = $1/(1+r)t), where r is discount
rate and t is number of periods.)
Results from the analysis show that different sections have different technical life for
high rail and low rail. This analysis did not consider changes in the technology of
steel making for rail material. Using the statistical data on derailments, rail breaks and
rectifications initiated by routine inspections, the expected costs are estimated.
Finally, the total costs for different traffic situations and grinding strategies are
analysed using an annuity method.
4.5.1 Modelling preventive rail grinding cost
Let G be the cost of grinding per pass per m and ni be the number of grinding pass for
ith grinding; L be the length of rail segments (0-300, 300-450, 450-600, 600-800 m of
curve radius sections) under consideration; N be the total number of periods up to
safety limit for renewal; and r be the discounting rate per period. It is assumed that
payments are made to subcontractors after each of the (N-1) grinding.
Then, total grinding cost in present value =
( )∑
−
= +
1
1 1
N
ii
i
r
G (4.20)
The total present value of grinding cost is spread in equal amounts each year of those
N periods. Then the annuity cost is (G) for each period and total annual grinding cost
can be given by:
( )∑= +
y
ii
yrG
1 1
1 (4.21)
where y is expected life in years and ry is yearly discounting factor. Discounting
factor for grinding interval, r, is given by (ry*i/12) where i is months interval between
grindings.
Results of 4.20 and 4.21 equation are the same.
( )∑= +
Y
ii
yrG
1 1
1 =
( )∑−
= +
1
1 1
N
ii
i
r
G (4.22)
Then annuity cost can be derived from equation 4.22:
99
Annuity cost G = ( )
( )∑
∑
=
−
=
+
+Y
ii
y
N
ii
i
r
r
G
1
1
1
1
1
1 (4.23)
Equation 4.21 can also be expressed as:
Total cost = ( ) ( ) ( ) ( )Yyyyy r
G
r
G
r
G
r
G
+++
++
++
+ 1...............
111 321 (4.24)
After simplification,
Annuity cost G = ( )
( )
+−
+∑
−
=
Y
Y
yN
ii
i
r
r
r
G
1
11
*1
1
1
(4.25)
Therefore, the annuity cost for rail grinding is given by:
)))1/(1(1/(*})1/()**({1
1
y
yy
iN
i
ig rrrLnGc +−+= ∑−
=
(4.26)
4.5.2 Modelling down time cost due to rail grinding (loss of traffic)
Let hDT be the expected downtime due to each grinding pass, nGPi be the number of
grinding pass for ith grinding and d be the expected cost of down time per hour. Then
down time cost due to rail grinding leading to loss of traffic is given by:
)))1/(1(1/(*})1/({1
1
y
yy
iN
i
DTGPd rrrdhnci
+−+∗∗= ∑−
=
(4.27)
Congestion costs and delay costs are not considered in this research.
4.5.3 Modelling inspection cost
Let If be the inspection per MGT and ic be the cost of one inspection. Then annual
spread, over inspection cost, over the rail life, is given by:
)))1/(1(1/(*})1/(({1
y
yy
j
i
N
j
ci rrricI
+−+= ∑=
(4.28)
where
][f
N
II
MIntegerN = (4.29)
and ri is discounting rate associated with interval of Non Destructive Testing (NDT).
100
4.5.4 Modelling risk cost of rail breaks and derailment
Let cost per rectification of rail breaks on emergency basis, Cr be modelled through
G(c), and is given by
][)( cCPcG r ≤= (4.30)
For example, if G(c) follows exponential distribution (Crowder et al, 1995), then it is
given by
cecG ρ−−= 1)( (4.31)
where c denotes the expected cost of each rail break repair on emergency basis and is
given by:
]/1[ ρ=c (4.32)
Let k be the expected cost of repairing potential rail breaks based on NDT in a
planned way and a be the expected cost per derailment; then k and a could be
modelled in a similar manner.
The risk cost associated with rail break and derailment is based on the probability of
NDT detecting potential rail breaks, rail breaks not detected by NDT, derailments and
associated costs.
Let Pi(B) be the probability of detecting potential rail break in NDT; Pi(A) be the
probability of undetected potential rail breaks leading to derailments; nNDTj be the
number of NDT detected potential rail breaks; nRBj be the number of rail breakes in
between two NDT inspections and nAj be the number of accidents in a period. Then
the risk cost is given by:
)))1/(1(1/()1(*)))1/(1(1(*})1(
/]*))(1(*)((*))(1(*)([)],([{0
1
y
yyy
i
N
i
iiiiiir
rrrr
cAPaAPBPkBPMMNEc
+−++−+
−+−+∗= ∑=
+(4.33)
where Pi(B) and Pi(A) could be estimated based on nNDTj the number of NDT detected
potential rail breaks; nRBj the number of rail breakes in between two NDT inspections;
and nAj be the number of accidents in between two NDT inspections over j periods.
Figure 4.6 shows probability of failures.
101
Probability of failures
Pi(A),
2%
Pi(B),
92%
1-Pi(A),
6%
Figure 4.6: Probabilities of failures
4.5.5 Modelling Replacement Costs of Worn-Out Unreliable Rails
Let cre be the expected cost of replacement for segment L and consist of labour,
material, and equipment, consumable and down time cost for rail replacement. Let I
be the cost of current investment in new rail. In this model, the cost of replacement is
assumed to be occurring at the beginning of each year and is simplified as the annual
spread over of investment of new rail. Then cre is given by:
)))1/(1(1/()))1/(1(1(* y
yre rrIc +−+−= (4.34)
4.5.6 Modelling Total Cost of Rail Maintenance
Costs associated with rail maintenance are estimated separately for low rail, high rail
and curve radius and added up to obtain total cost of maintenance. Therefore, the total
cost of maintaining a segment of rail is equal to the sum of cost for: Preventive rail
grinding cost (cg); down time cost due to rail grinding (loss of traffic) (cd); inspection
costs (NDT) (ci); risk cost of rectification based on NDT, rail breaks and derailment
(cr) and replacement cost of worn-out unreliable rails (cre). It is the given by:
reridgtot cccccC ++++= (4.35)
This is analytically intractable and so a simulation needs to be used to arrive at train
speed, inspection frequency and MGT interval for preventive rail grinding. Rail
breaks generally occur from fatigue initiated surface cracks (shells/squats/head
checks) and transverse defects. Other rail defects can be due to manufacturing
problems, wear, welding problems (Railtrack plc. 2001) and other factors such as
heavy axle loads, high speed and many other factors such as wheel burn. There is risk
involved due to these undetected defects that lead to rail breaks, rail failures and
102
derailments, loss of lives, revenue and property. This, in turn, increases maintenance
costs and risks to safety and reliability.
4.6 Estimation of cost and life data
Data was collected from field observations and, in these calculations, Weibull
distribution is used with the parameters β = 3.6 and 1250/12350 << λ (Besuner et
al., 1978), to estimate the rail breaks and derailments. In this case, the grinding speed
is set to 10 km/h with 3 passes (Table 4.1) to a total cost of 2 AUD/ m/pass. Other
costs are given in Table 4.5. Discounting factor is used, assuming 10% per year.
Table 4.5: Estimated costs and area safety limits (Chattopadhyay et al., 2005)
Cost of grinding per pass per m 2.00 [AUD/pass/m]
(For detailed data, see Appendix B.)
4.6.1 Analysis of results
Data is used in simulation model developed and analysed using Mat lab and Microsoft
Excel, and results are shown in sections 4.6.2 to 4.8.
4.6.2 Grinding cost
Grinding cost is estimated using the grinding cost/m/pass data ($AUD 2.00/m/pass)
and the average number of passes per section (minimum 2 and maximum 5 passes per
section). Grinding cost estimation method is shown in Figure 4.7.
103
Figure 4.7: Grinding cost estimation method (Chattopadhyay et al., 2005)
4.6.3 Grinding cost/m
Analysis of grinding cost/m for 23, 12, 18 and 9 MGT intervals are compared for
curve radius from 0 to 800 m. Results are given in Table 4.6.
Table 4.6: Grinding cost/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (m) Radius (ms) Grinding cost/m ($AUD) 1318 0-300 10 20 18 36
1384 300-450 16 12 22 40 36524 450-600 16 16 26 30 33235 600-800 6 8 32 22
104
Grinding cost/meter
0
10
20
30
40
50
0-300 300-450 450-600 600-800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18 MGT
9 MGT
Figure 4.8: Grinding cost/m for 0 to 800 m curves
Figure 4.8 shows the analysis of grinding cost/m for 23, 12, 18, and 9 MGT intervals
of curve radius from 0 to 800 m. It is observed that cost is higher for smaller grinding
intervals. The costs for lower curve radius 0-300 m are in general more compared to
higher curve (300-450 or more) sections of rail segment. This indicates more rolling
contact fatigue (RCF) in tighter curves.
4.6.4 Grinding cost/MGT/m
Analysis of grinding cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared
for curve radius from 0 to 800 m. Results are given in Table 4.7.
Table 4.7: Grinding cost/MGT/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Grinding cost/MGT/m ($AUD) 1318 0-300 0.43 1.67 1 4
1384 300-450 0.7 1 1.22 4.44 36524 450-600 0.7 1.33 1.44 3.33 33235 600-800 0.26 0.67 1.78 2.44
Grinding cost/MGT/meter
0
1
2
3
4
5
0-300 300-450 450-600 600-800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18 MGT
9 MGT
Figure 4.9: Grinding cost/MGT/m for 0 to 800 m curves
105
Figure 4.9 shows the analysis of grinding cost/MGT/m for 23, 12, 18, and 9 MGT
intervals of curve radius from 0 to 800 m. It is observed that cost/MGT/m trend is
similar to per m costs.
4.6.5 Risk cost/m
Analysis of risk cost/m for 23, 12, 18 and 9 MGT intervals are compared for curve
radius from 0 to 800 m. Results are given in Table 4.8.
Table 4.8: Risk cost/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Risk cost/m ($AUD) 1318 0-300 0.00004 0.0000076 0.00002 0.0000013 1384 300-450 0.00003 0.0000080 0.00001 0.0000012 36524 450-600 0.00000 0.0000003 0.00000 0.0000000
33235 600-800 0.00000 0.0000003 0.00000 0.0000000
4.6.6 Risk cost/MGT/m
Analysis of risk cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared for
curve radius from 0 to 800 m. Results are given in Table 4.9.
Table 4.9: Risk cost/MGT/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Risk cost/MGT/m ($AUD) 1318 0-300 0.000002 0.000001 0.000001 0.000000
1384 300-450 0.000002 0.000001 0.000001 0.000000 36524 450-600 0.000000 0.000000 0.000000 0.000000 33235 600-800 0.000000 0.000000 0.000000 0.000000
From the above Tables 4.8 and 4.9, it is observed that risk cost is negligible in these
sections. This is due to the fact that rail operators work in a conservative manner
related to rail replacements and rail repairs. It may be also due to the fact that many of
the failure and accident data are not reported so as to avoid public criticism.
4.6.7 Down time cost/m
Analysis of down time cost/m for 23, 12, 18 and 9 MGT intervals are compared for
curve radius from 0 to 800 m. Results are given in Table 4.10.
106
Table 4.10: Down time cost/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Down time cost/m ($AUD) 1318 0-300 1.57 3.14 2.82 5.64 1384 300-450 2.51 1.88 3.45 6.27 36524 450-600 2.51 2.51 4.08 4.7
33235 600-800 0.94 1.25 5.02 3.45
Down time cost/meter
0
2
4
6
8
0-300 300-450 450-600 600-800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18 MGT
9 MGT
Figure 4.10: Down time cost/m for 0 to 800 m curves
Figure 4.10 shows the analysis of down time cost/m for 23, 12, 18, and 9 MGT
intervals of curve radius from 0 to 800 m. It is observed that cost is higher for 9 MGT
interval, compared to 23, 12 and 18 MGT intervals. This is due to increased number
of set ups for lower MGT intervals. Costs are higher for steeper curves, compared to
other sections of rail segment. This may be due to increase in grinding passes due to
more rolling contact fatigue (RCF) in sharper curves.
4.6.8 Down time cost/MGT/m
Analysis of down time cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared
for curve radius from 0 to 800 m. Results are given in Table 4.11.
Table 4.11: Down time cost/MGT/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Down time cost/MGT/m ($AUD) 1318 0-300 1.57 3.14 2.82 5.64 1384 300-450 2.51 1.88 3.45 6.27
36524 450-600 2.51 2.51 4.08 4.7 33235 600-800 0.94 1.25 5.02 3.45
Figure 4.11 shows the analysis of down time cost/MGT/m for 23, 12, 18, and 9 MGT
intervals of curve radius from 0 to 800 m. It is observed that cost/MGT/m trends are
similar to per m costs.
107
Down time cost/MGT/meter
0
0.2
0.4
0.6
0.8
0-300 300-450 450-600 600-800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18 MGT
9 MGT
Figure 4.11: Down time cost/MGT/m for 0 to 800 m curves
4.7 Annuity Cost/m
Annuity cost/m for 23, 12, 18 and 9 MGT intervals are estimated. Results are
compared for each MGT and for different curves. Annuity costs/m for grinding, risk,
down time, inspection and replacement are estimated using the mathematical model.
4.7.1 Annuity cost/m for grinding
Analysis of annuity cost/m for grinding 23, 12, 18 and 9 MGT intervals are compared
for curve radius from 0 to 800 m. Results are shown in Table 4.12.
Table 4.12: Annuity cost/m for grinding 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Annuity cost/m for grinding ($AUD) 1318 0-300 5.42 6.82 11.41 14.00 1384 300-450 5.95 6.08 11.00 12.00
36524 450-600 6.00 7.12 11.00 10.00 33235 600-800 5.88 6.86 12.00 11.00
Annuity cost/meter for Grinding
0.00
4.00
8.00
12.00
16.00
0<R<300 300<R<450 450<R<600 600<R<800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18MGT
9 MGT
Figure 4.12: Annuity cost/m for grinding 0 to 800 m curves
108
Figure 4.12 shows the analysis of annuity cost/m for grinding 23, 12, 18, and 9 MGT
intervals of curve radius 0 to 800 m. It is observed that annuity cost/m for grinding is
higher for 9 and 18 MGT. This is due to excessive grinding in these intervals.
4.7.2 Annuity cost/m for risk
Analysis of annuity cost/m for risk 23, 12, 18 and 9 MGT intervals are compared for
curve radius from 0 to 800 m. Results are shown in Table 4.13.
Table 4.13: Annuity cost/m for risk in 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Annuity cost/m for risk ($AUD) 1318 0-300 0.0016 0.0002 0.0011 0.0000 1384 300-450 0.0018 0.0004 0.0002 0.0000 36524 450-600 0.0001 0.0000 0.0000 0.0000
33235 600-800 0.0001 0.0000 0.0000 0.0000
Annuity cost/meter for Risk
0.0000
0.0005
0.0010
0.0015
0.0020
0<R<300 300<R<450 450<R<600 600<R<800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18MGT
9 MGT
Figure 4.13: Annuity cost/m for risk in 0 to 800 m curves
Figure 4.13 shows the analysis of annuity cost/m for risk 23, 12, 18 and 9 MGT
intervals of curve radius from 0 to 800 m. It is observed that annuity cost/m for risk
trend is similar to cost/MGT/m of grinding. The data on risk cost is based on a very
small number of derailment incidents and there is enough scope for estimating actual
risk cost based on real life derailment data.
4.7.3 Annuity cost/m for down time
Analysis of annuity cost/m for down time 23, 12, 18 and 9 MGT intervals are
compared for curve radius from 0 to 800 m. Results are shown in Table 4.14.
109
Table 4.14: Annuity cost/m for down time in 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Annuity cost/m for down time ($AUD) 1318 0-300 0.85 1.07 1.79 2.14 1384 300-450 0.93 0.95 1.56 1.85 36524 450-600 0.94 1.12 1.77 1.57
33235 600-800 0.92 1.08 1.83 1.74
Annuity cost/meter for Down time
0
1
2
3
0<R<300 300<R<450 450<R<600 600<R<800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18MGT
9 MGT
Figure 4.14: Annuity cost/m for down time in 0 to 800 m curves
Figure 4.14 shows the analysis of annuity cost/m for down time 23, 12, 18 and 9
MGT intervals of curve radius from 0 to 800 m. It is observed that annuity cost/m for
down time trend is similar to annuity cost/m of grinding.
4.7.4 Annuity cost/m for inspection
Analysis of annuity cost/m for inspection 23, 12, 18 and 9 MGT intervals are
compared for curve radius from 0 to 800 m. Results are shown in Table 4.15.
Table 4.15: Annuity cost/m for inspection in 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Annuity cost/m for inspection ($AUD) 1318 0-300 0.044 0.023 0.035 0.017
1384 300-450 0.044 0.023 0.033 0.017 36524 450-600 0.044 0.023 0.030 0.016 33235 600-800 0.044 0.023 0.031 0.018
110
Annuity cost/meter for Inspection
0.00
0.01
0.02
0.03
0.04
0.05
0<R<300 300<R<450 450<R<600 600<R<800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18MGT
9 MGT
Figure 4.15: Annuity cost/m for inspection in 0 to 800 m curves
Figure 4.15 shows the analysis of annuity cost/m for inspection 23, 12, 18 and 23
MGT intervals for curve radius 0 to 800 m. It is observed that the cost for inspection
is slightly higher for 23 and 18 MGT intervals compared to 9 and 12 MGT intervals.
This is due to increased life and number of inspections.
4.7.5 Annuity cost/m for replacement
Analysis of annuity cost/m for replacement 23, 12, 18 and 9 MGT intervals are
compared for curve radius from 0 to 800 m. Results are shown in Table 4.16.
Table 4.16: Annuity cost/m for replacement in 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Annuity cost/m for replacement ($AUD) 1318 0-300 17.65 15.00 16.00 20.62 1384 300-450 15.17 13.10 24.00 25.00 36524 450-600 16.06 11.63 32.00 28.00 33235 600-800 15.00 11.49 21.00 28.00
Annuity cost/meter for Replacement
0
10
20
30
40
0<R<300 300<R<450 450<R<600 600<R<800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18MGT
9 MGT
Figure 4.16: Annuity cost/m for replacement in 0 to 800 m curves
Figure 4.16 shows the analysis of annuity cost/m for replacement 23, 12, 18 and 9
MGT intervals of curve radius from 0 to 800 m. It is observed that cost for
111
replacement is higher for 9 and 18 MGT intervals compared to 23 and 12 MGT
intervals. This may be due to more replacements and excessive grinding in higher
MGT intervals.
4.7.6 Total annuity cost/m
Analysis of total annuity cost/m for 23, 12, 18 and 9 MGT is compared for curve
radius 0 to 800 m. Results are shown in Table 4.17.
Table 4.17: Total annuity cost/m for 0 to 800 m curves
MGT Interval 23 12 18 9
Length (ms) Radius (ms) Total annuity cost/m ($AUD) 1318 0-300 23.96 22.91 29.24 36.78 1384 300-450 22.09 20.15 36.59 38.87 36524 450-600 23.04 19.89 44.80 39.59
33235 600-800 21.84 19.45 37.86 40.76
Total annuity cost/meter
0.00
10.00
20.00
30.00
40.00
50.00
0-300 300-450 450-600 600-800
Curve radius (meters)
Cost ($AUD)
23 MGT
12 MGT
18 MGT
9 MGT
Figure 4.17: Total annuity cost/m for replacement of 0 to 800 m curves
Figure 4.17 shows the analysis of total annuity cost/m for 23, 12, 18 and 9 MGT
intervals of curve radius from 0 to 800 m. From the analysis, it is observed that cost is
higher for 18 and 9 MGT intervals. This may be mainly due to more rail replacements
due to excessive grinding for lower MGT intervals.
4.8 Annuity cost/m assessment for each MGT
4.8.1 Annuity cost/m for 23 MGT
Analysis of annuity cost/m of grinding, risk, down time, inspection and replacement
for 23 MGT interval of curve radius from 0 to 800 m is compared. Results are shown
in Table 4.18.
112
Table 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves
Radius (m) 0-300 300-450 450-600 600-800
Length (m) 1318 1384 36524 33235 Maintenance costs Annuity cost/m ($AUD)
Grinding 5.42 5.95 6.00 5.88
Risk 0.00 0.00 0.00 0.00 Down time 0.85 0.93 0.94 0.92 Inspection 0.04 0.04 0.04 0.04
Replacement 17.65 15.17 16.06 15.00 Total cost 23.96 22.09 23.04 21.84
Annuity cost/meter for 23 MGT
Inspection0%
Risk0%
Down time4%
Grinding23%
Replacement73%
Figure 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves
Figure 4.18 shows the analysis of annuity cost/m for 23 MGT of curve radius from 0
to 800 m. It is observed that replacement and grinding costs are higher compared to
other costs. It is found that total costs for tighter curves (radii 0-300 m) are higher
compared to radii of 301 - 800 m curves.
4.8.2 Annuity cost/m for 12 MGT
Analysis of annuity cost/m of grinding, risk, down time, inspection and replacement
for 12 MGT of curve radius from 0 to 800 m is compared. Results are shown in Table
4.19.
Table 4.19: Annuity cost/m for 12 MGT in 0 to 800 m curves
Radius (m) 0-300 300-450 450-600 600-800
Length (m) 1318 1384 36524 33235
Maintenance costs Annuity cost/m ($AUD) Grinding 6.82 6.08 7.12 6.86 Risk 0.00 0.00 0.00 0.00
Down time 1.07 0.95 1.12 1.08 Inspection 0.02 0.02 0.02 0.02 Replacement 15.00 13.10 11.63 11.49
Total costs 22.91 20.15 19.89 19.45
113
Annuity cost/meter 12 MGT
Grinding30%
Risk0%
Down time5%
Inspection0%
Replacement65%
Figure 4.19: Annuity cost/m for 12 MGT in 0 to 800 m curves
Figure 4.19 shows the analysis of annuity cost/m for 12 MGT of curve radius from 0
to 800 m. It is observed that the cost is higher for replacement and grinding. It is
found that total costs for tighter curves (radii 0-300 m) are higher, compared to radii
of 301 - 800 m curves.
4.8.3 Annuity cost/m for 18 MGT
Analysis of annuity cost/m of grinding, risk, down time, inspection and replacement
for 18 MGT of curve radius from 0 to 800 m is compared. Results are shown in Table
4.20.
Table 4.20: Annuity cost/m for 18 MGT in 0 to 800 m curves
Radius (m) 0-300 300-450 450-600 600-800
Length (m) 1318 1384 36524 33235 Maintenance costs Annuity cost/m ($AUD)
Grinding 11.41 11.00 11.00 12.00
Risk 0.00 0.00 0.00 0.00 Down time 1.79 1.56 1.77 1.83 Inspection 0.03 0.03 0.03 0.03
Replacement 16.00 24.00 32.00 24.00 Total costs 29.23 36.59 44.8 37.86
Annuity cost/meter for 18 MGTGrinding39%
Risk
0% Down time
6%
Inspection0%
Replacement55%
Figure 4.20: Annuity cost/m for 18 MGT in 0 to 800 m curves
114
Figure 4.20 shows the analysis of annuity cost/m for 18 MGT of curve radius from 0
to 800 m. It is observed that the cost for replacement and grinding are higher
compared to other costs.
4.8.4 Annuity cost/m for 9 MGT
Analysis of annuity cost/m of grinding, risk, down time, inspection and replacement
for 9 MGT of curve radius from 0 to 800 m is compared. Results are shown in Table
4.21.
Table 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves
Radius (m) 0-300 300-450 450-600 600-800
Length (m) 1318 1384 36524 33235 Maintenance costs Annuity cost/m ($AUD)
Grinding 14.00 12.00 10.00 11.00
Risk 0.00 0.00 0.00 0.00 Down time 2.14 1.85 1.57 1.74 Inspection 0.02 0.02 0.02 0.02
Replacement 20.62 25.00 28.00 28.00 Total Costs 36.78 38.87 39.59 40.76
Annuity cost/meter for 9 MGT
Inspection
0%
Down time7%
Risk0%
Replacement
44%
Grinding49%
Figure 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves
Figure 4.21 shows the analysis of annuity cost/m for 9 MGT of curve radius from 0 to
800 m. It is observed that grinding cost is higher compared to other costs. In this
research, risk is defined as the percentage of defects occurrence, annual rate of
undetected defects, rail breaks and derailments. Track segments are used as per the
database of rail replacements and ageing is estimated by assuming 23 MGT per year
of traffic flow.
115
4.9 Summary
This chapter proposed a systematic approach to developing cost models for rail
grinding decisions. Field data from rail industry have been used for developing
models and estimation of parameters. In this research work failures are modelled with
non-homogenous Poisson process. Results from this investigation can be used for
maintenance and replacement decisions about rails. The annuity cost/m for grinding,
risk, down time, inspection and replacement are analysed. Results for 23, 12, 18 and 9
MGT of curve radius from 0 to 300, 300-450, 450-600 and 600-800 m are discussed.
Summary of the findings are:
• Analysis shows that total annuity cost/m for 0-300 ms for 23 MGT AUD $ is
23.96; for 12 MGT is AUD $ 22.91; for 18 MGT is AUD $ 29.24; for 9 MGT
is AUD $ 36.78. It shows that rail players can save 4.58% of costs with 12
MGT intervals, compared to 23 MGT intervals.
• Analysis shows that total annuity cost/m for 300-450 ms for 23 MGT AUD $
is 22.09; for 12 MGT is AUD $ 20.15; for 18 MGT is AUD $ 36.59; for 9
MGT is AUD $ 38.87. This shows that rail network providers can save 9.63%
of costs with 12 MGT intervals, compared to 23 MGT intervals.
• Analysis shows that total annuity cost/m for 450-600 ms for 23 MGT AUD $
is 23.04; for 12 MGT is AUD $ 19.89; for 18 MGT is AUD $ 44.80; for 9
MGT is AUD $ 39.59. This shows that rail players can save 15.80% of costs
with 12 MGT intervals, compared to 23 MGT intervals.
• Analysis shows that total annuity cost/m for 600-800 ms for 23 MGT AUD $
is 21.84; for 12 MGT is AUD $ 19.45; for 18 MGT is AUD $ 37.86; for 9
MGT is AUD $ 40.76. This shows that rail players can save 12.29% of costs
with 12 MGT intervals, compared to 23 MGT intervals.
In steep curves, rail replacement is more due to rolling contact fatigue (RCF),
compared to curves with higher radius. It is found that rail players can save with 12
MGT intervals compared to 23 MGT intervals. Analysis suggests that 23 MGT (or
longer) grinding intervals demand much heavier grinding each cycle, or the use of
heavy relief in curves to control fatigue. Both of these measures can result in large
wear rates, reduced rail life and ineffective use of the grinding budget. Therefore, it is
recommended that 12 MGT grinding interval is economical to achieve optimal wear
and to control surface fatigue cracks. There is enormous scope to extend these models
116
for optimal maintenance decisions concerning rail-wheel lubrication. Modelling and
analysis of lubrication strategies will be discussed in Chapter 5.
117
CHAPTER 5
MODELLING AND ANALYSIS OF WEAR AND LUBRICATION
DECISIONS
5.1 Introduction
Cost models on rail grinding for optimal rail grinding decisions are developed in
Chapter 4. The annuity cost/m for grinding, risks, down time, inspection, replacement
and lubrication are analysed. This chapter focuses on modelling and analysis of
lubrication strategies. Data collected from rail industry is used for illustration.
Rail wear is an important element for budgeting rail replacements and reducing
operational risks. It acts as a performance indicator for rail-wheel lubrication.
Currently, rail players are making executive decisions based on experience. There are
no international standards for rail lubrication. It is important to study the factors
behind wear and develop lubrication models for lubrication decisions.
The outline of this chapter is as follows: in Section 5.2, there is an assessment of
lubricators’ performance; modelling of rail wear and rail wear limits are discussed in
Section 5.3; modelling for rail lubrication decisions is explained in Section 5.4;
Section 5.5 deals with modelling failures of lubricators using renewal process;
framework for benchmarking lubrication is discussed in Section 5.6; in Section 5.7,
annuity costs of lubricators are modelled; collection and analysis of data is explained
in Section 5.8; cost-benefit analysis is discussed in Section 5.9; finally, the
conclusions, summary and contributions are discussed in Section 5.10.
Rail infrastructure owners have been working around the world to improve
performance of lubrication. Three types of lubrication (way-side lubricators, on-board
lubrication, and hi-rail lubrication) are generally used. It is a great challenge for rail
infrastructure owners to decide whether a lubrication system is economical under
different operating conditions. Wayside lubrication has problems of wastage of
lubricant, nozzle clogging, empty reservoirs and oil separation. For the Hi-rail
lubrication system, the track availability is a challenge to rail infrastructure owners.
On-board lubrication systems have problems of maintenance linked to reliability and
safety. It is important to analyse and identify the costs and benefits of these systems
118
and develop a model for comparison of performance. Variables affecting the lubricant
transfer at the wheel-rail interface can be grouped into the following categories:
� Application method that is wayside, on-board, hi-rail
� Parameters of the lubricant, such as viscosity and its variation with temperature,
separation rates and base oil attributes
� Geographic issues such as grade, curvature (expressed as degrees of central
angle), location of wayside lubricators (temperature difference), rail contour, and
wheel contour
� Operating issues such as train length, gross weight, and speed
� The initial state of the lubrication, including surface roughness
� Temperature generated due to rail-wheel interaction
Generally, the three types of track mounted lubricator systems used are:
� Hydraulic lubricator (eg. PORTEC M&S 761, HL1, PW Series, PORTEC MC3)
� Mechanical lubricator (eg. P&M – Model C4, M6, RTE 25)
� Electric lubricator (eg. SYSCOM)
It is important for track practitioners to identify the types of lubricator when
conducting maintenance activities, to record the condition of the lubricators, position
of the lubricator, identification of spare parts, and skills required to trouble shoot
different types of lubricators. (For more details, see Appendix B). Figure 5.1 shows
the flowchart for the modelling and analysis of lubrication decisions.
Figure 5.1: Flowchart for the modelling and analysis of lubrication decisions
Framework for Lubrication Effectiveness
Assessment of lubricators performance
Modelling
� rail wear, wear limit
� rail lubrication
� applicators
� lubricant
� benefits of lubricators
� failures
� cost-benefit analysis
� annuity cost of lubricators
Collection and analysis of data
Estimation of annuity costs
Numerical example
Evaluation of
Lubrication
Decisions
119
5.2 Assessment of lubricator’s performance
In the UK it has been estimated that only 25% of the 8000-10000 conventional
lubricators are adequately maintained. This is not only due to the requirement to refill
frequently (small capacity reservoirs) or frequent adjustment of wearing parts, but
also due to the lack of dedicated teams of experienced and trained personnel. Track
side lubricators can be effective only if they are positioned correctly and maintained
properly. Way-side lubrication is more effective in sharper curves (for example, 200
m).
Figure 5.2: A well lubricated rail wear face in a Spoornet curve (Koker, 2004)
Recent experience and measurements on Spoornet track suggests that the wear
induced in one month of poor or no lubrication on sharp curves (radius less than 300
m) is equal to that of sixty months (five years) of a well lubricated curve. For medium
curves between 300 and 800 m radius, the figure gradually reduces to 30 times. Figure
5.2 shows a well lubricated rail wear face in a Spoornet curve (Koker, 2004). Koker
(2004) has discussed the problems in track side lubrication systems on Richard Bay
Coal Line. The trackside lubrication system was labour intensive due to lower grease
capacity and inadequately trained maintenance staff. As an interim measure,
electronic, gas-operated lubricators, mounted on inspection trolleys, were used. This
system failed because of leakage in the gas lines and the mechanical unreliability of
the trolleys. A decision was taken to use trackside, small capacity lubricators. Table
5.1 shows the costs of track side lubrication on Richard Bay Coal Line. A monitoring
system was implemented for measuring the efficiency of the lubrication. The
positioning of the machines was optimized. Staff members were trained for
maintenance of lubricators. Grease consumption and availability data were recorded
and analysed.
120
Table 5.1: Cost of Trackside Lubrication Koker (2004)
Item Cost ($ AUD) Percentage of Total
Thelen and Lovette (1996) identified factors that can significantly affect the
effectiveness of wayside lubricator:
• The location of the lubricator in regard to the curve
• The viscosity of the grease at different temperatures
• The grease output adjustment
• The level of maintenance of lubricators
On-board lubrication systems mainly use a liquid or solid lubricant applied to the
wheel flange or directly to the rail. These systems are maintained in the depot during
routine maintenance operations. It was found that, due to negligible migration of the
lubricant to the top-of-rail in dry tunnels without natural lubrication, this type of
lubricant leaves the top-of-rail totally unlubricated, leading to excessive wheel wear
problems. Liquid spray systems that incorporate control systems to spray according to
various set parameters are more expensive to install compared to solid lubricant
systems, but lubricant costs are likely to be lower. Excessive dosage rates can cause
contamination problems. Solid lubricant systems are applied continuously, are
cheaper to install, and the system is less likely to produce contamination.
Hi-rail lubrication systems have been cost effective for many rail players around the
world. They can be controlled with a limited of application of lubricant through beads
directed to the rail gauge face on the track. The hi-rail equipment improves the
maintenance procedures as the equipment is regularly returned to workshops. It helps
in improved train handling, reduced train noise, bogie hunting and development of rail
corrugation. Koker (2003) found that, on Richards Bay Coal Line (South Africa), hi-
rail grease application on curves was sufficient and most curves were always well
lubricated. Some curves were poorly lubricated because they were situated at the
beginning of momentum gradients. Some of the problems with hi-rail lubrication
exposed by the study are:
121
� Increased risk of over-lubrication (This causes wastage, rail/wheel damage
through slippage, interference with ultrasonic testing, fouling of ballast, and
environmental pollution.)
� Increased risk of rail flaking (The pumping of lubricant into micro-cracks may
lead to fatigue cracking or flaking at the gauge corner.)
� Increased risk of rail damage if not correctly supervised (Lubrication on the rail
head, coupled with sanding for traction, may produce a grinding paste which
increases head wear.)
� Relatively high capital cost and
� Accumulation of lubricant on vehicle bogie and bodies.
Some of the factors influencing economic analysis are:
� resources to run and maintain lubricators
� reservoir capacity of lubricators
� location and position of the lubricator and grease coverage
� skilled personnel and their time for maintenance and repair of lubricators
� grease travel on rail track
� availability of spare parts
� replacement of aging lubricators and product support
� training in fitting, fault diagnosis and maintenance
� refilling interval of reservoirs
� inspection and maintenance intervals.
Assessment of lubricators and lubricants is important to examine overall
effectiveness. The configuration of lubrication systems may vary for the following
reasons (Tew and Mutton, 1991):
� Proportion of tangent and curved track
� Constraint introduced by track availability
� Maintenance requirements
Tew and Mutton (1991) found that effectiveness of lubrication depended on the
following factors:
� Application method
� Lubricants
� Frequency of application
� Rate of application (dose)
� Lubricator components (pump, container, nozzle and hose system)
122
� Grease consumption based on various axle loads (tonnes)
Performance of lubrication systems can be analysed based on visual inspection,
scientific method and readings from a tribometer.
5.3 Lubrication decision model
Determination of the effectiveness of a lubricator is possible by using finger testing at
the gauge face after a week or two of operation. The grease film should be seen on the
gauge face of the curve. Change of position of the lubricators can improve the
distance the lubricant is carried. Any visible, excessive grease on the top of the rail
indicates that the ramp or wiping bars should be lowered. Insufficient grease is
possible in some areas, even though the lubricators are functioning properly. The
insufficiency of the grease indicates that the ramp or wiping bars should be raised.
Temperature changes indicate requirements for adjusting the ramp settings to achieve
consistency and lubrication propagation (Larsson et al., 2005). At high temperature,
lower ramp allows the lubricant to stay at the same level on the gauge face. High
temperature reduces the grease viscosity and can cause problems due to grease
migrating on the top of the rail. Cold temperature increases the viscosity and can
cause clogging of the distribution hole. Therefore, higher ramp settings are
recommended during the cold season. Heeler (1979) suggested that rail lubricator
maintainers need to consider the following points before installation and maintenance
of lubricators:
� Positioning of the lubricator should be close to where the wheel flange intacts
with the high rail. Indication of improper installation of lubricator is evidenced by
thick beads of lubricant visible on distribution bars. The train passage can cause
fling off of the grease, leading to a messy environment. Positioning of the
lubricator should be near the curve. In addition, the pump should be set low on
fast lines and high on slow lines.
� Refilling activity should be scheduled frequently rather than waiting for the
lubricators to be empty.
� The number of lubricators and maintenance intervals should be determined by
lubricator effectiveness.
� Grease plates need to be adjusted to the desired height for an even distribution of
lubricant over the gauge face.
123
The key roles and responsibilities of the lubricator maintainer are to (QR, 2005):
� understand basic principles of tribology ( friction and wear)
� understand benefits of lubricating the rail/wheel
� understand rail/wheel interaction at various curves
� recognize usefulness of different types of lubricators
� adjust the position of the lubricator
� record important information related to improving lubricator performance and
lubricant effectiveness.
� conduct analysis for effectiveness of lubricants and lubricators
� address the environmental issues
Figure 5.3: Lubrication decision model
Figure 5.3 shows the lubrication decision model. Table 5.2 shows ‘Where to place’
and ‘Where not to place’.
Issues in lubrication decision� type of Lubricator� on-site or depot service� plan for maintenance activity� selection of resources and skilled personnel� type of inspection using lubricator manual
Inspection,Maintenance, Servicing
Checking during inspection� tank� plunger condition, air locks� leaks at hose connection � replace gaskets if necessary� check pumps are working properly� grease leaks and loose bolts� bent plungers must be replaced� position and location of lubricator
Measures of lubrication effectiveness� rail head temperature rise method� visual inspection� tribometer measurements
Analysis of data� estimation of energy dissipation� continuous and uniform lubrication� relative performance of different lubricants� relative performance for different curves� lubricant type� position, location and operation of lubricator
Maintenance/Service decision� minimal repair� overhaul� planned or preventive� corrective � condition based
Review of Lubrication Decision� Review of lubricator location and position� distance covered by each lubricator� type of application� type of lubricant� maintenance intervals
Issues in lubrication decision� type of Lubricator� on-site or depot service� plan for maintenance activity� selection of resources and skilled personnel� type of inspection using lubricator manual
Inspection,Maintenance, Servicing
Checking during inspection� tank� plunger condition, air locks� leaks at hose connection � replace gaskets if necessary� check pumps are working properly� grease leaks and loose bolts� bent plungers must be replaced� position and location of lubricator
Measures of lubrication effectiveness� rail head temperature rise method� visual inspection� tribometer measurements
Analysis of data� estimation of energy dissipation� continuous and uniform lubrication� relative performance of different lubricants� relative performance for different curves� lubricant type� position, location and operation of lubricator
Maintenance/Service decision� minimal repair� overhaul� planned or preventive� corrective � condition based
Review of Lubrication Decision� Review of lubricator location and position� distance covered by each lubricator� type of application� type of lubricant� maintenance intervals
124
Table 5.2: ‘Where to lubricate’ and ‘not to lubricate’ (CETS, 2004)
Position for placing lubricator Position for not placing lubricator
It is important to evaluate the gauge face friction before positioning the lubricators, in
order to determine the point of contact when physical interaction occurs between rail
and the wheel. Coefficient of friction means the classification of the surface
roughness. Smoothness of the surface means a reduction of wear. The coefficient of
friction µ as a function of film parameter λ is shown in Figure 5.4. The coefficient of
friction is defined as:
µ = f/w z (5.1)
where f is tangential friction force and w z is the normal applied load.
Figure 5.4: Coefficient of friction (Hamrock and Dowson, 1981)
Wheel and rail interaction operates in various lubrication regimes. The film thickness
parameter λ, is related to the coefficient of the friction, µ and depends on the mode of
lubrication. International Heavy Haul Association (IHHA) recommends “Expert
Eyeball Chart” as replacement of tribometer to cut down the cost of labour and time
when assessing lubricated curves. Expert Eyeball Chart estimates the coefficient of
friction of the rail gauge surfaces. Table 5.3 shows expert chart of lubrication
effectiveness from International Heavy Haul Standards.
125
Table 5.3: Expert Chart of Lubrication Effectiveness (IHHA, 2001)
Observed Conditions of Rail Gauge Face Surface Evaluation of the Coefficient
of Friction
Figure 5.5: Dry rail condition
Figure 5.5 shows the microscopic view when rail/wheel interface without lubrication.
It is observed that wear rates increase dramatically. When two surface roughnesses
are in contact, abrasive wear occurs. This is also known as ‘Snowing’. If lubrication is
not taken seriously, coefficient of friction can reach up to 0.6, where it is considered
aggressive wear. Figure 5.6 shows the aggressive wear with coefficient of friction
approximately 0.6.
Unlubricated Wheel/Rail Interaction
� Dry Rail Condition Coefficient of friction, µ = 0.45 to 0.6
� Propagate wear at both wheel flange and rail gauge
Microscopic view of surface roughness if not separated by lubricant film thickness (boundary lubrication)
Steel particles known as ‘Snowing’ drops on the foot of the rail
126
Figure 5.6: Aggressive wear (Powell and Wheatley, 2004)
Figure 5.7: Lubricated rail-wheel interface
Figure 5.7 shows the effectiveness of lubrication at rail-wheel interface. It was
analysed earlier that 1 mm2 of material loss for rail 50 kg SC is AUD $ 6.93 and
increases the lifespan of rail from 30 years to 50 years, provided that proper
maintenance of lubricators are conducted. Coefficient of friction of 0.15 to 0.2 is
desirable, not only to reduce wear but also to obtain optimum wear rate which can
also solve defects issues as well. It is important to know that lubrication does not
mean 100% benefit.
Figure 5.8: Rail with minimal wear (Powell and Wheatley, 2004)
127
Figure 5.8 shows rail that has undergone minimal wear with effective lubrication and
coefficient of friction. Excessive lubrication can lead to other problems such as
lubricants wastage, environmental concern, wheel slip and traction problems.
5.4 Modelling rail wear
The rail life is determined by rail area head loss limit, which is a relative measure of
the ratio of a worn rail head to the area of a new rail head (Zhang, 2000). Clayton
(1996) concluded that general wear models are unlikely to produce the practical
benefits in the field. The existing models are restricted to particular application under
limited conditions.
Rail area head loss can be estimated using rail table (crown) wear (TW) and rail side
(gauge) wear (GW), based on current Civil Engineering Track Standards (CETS).
Then the % of reduction in area head loss (%AHL) is given by
+
=B
GW
A
TWAverageredAHL% (5.2)
where A and B are dimensions of table and side of rail. For example, wear loss for
period from j to j+1 can then be expressed as:
jj TWTW AAjjWearloss −=++1
)1,( (5.3)
Wear rate for period j due to traffic wear can be expressed as
( )j
j
jMGT
mmHLreductionAWearrate
2
= in MGTmm /2 (5.4)
It is assumed that the track is used by mixed traffic; for example, passenger, freight
and heavy hauls such as rock, ore and coal. It is also assumed that the pattern of
traffic distribution (% of each category) and the wear factor (wear rate conversion
compared to normal traffic category; for example, passenger traffic in city area) of
each category is known. Let At be the wear loss after tth period and modelled as:
ttt WNPA = (5.5)
where NPt is the total axle passes in tth period and Wt is the weighted wear rate (say
the average of 5% heavy haul, 10% freight and 85% passenger train mix) for the
period. Assuming the traffic, forecast up to the N period (which is the mean life of the
lubricator or the contract duration) is known by using forecasting techniques.
128
Lubrication cost can be estimated assuming cost of lubricant (Cl) selected for
application of particular curve section (cs) of rail segment under known weather and
environmental conditions. Let Cmirs be the cost of maintenance of each lubricator. It
includes lubricator servicing, checking and filling of lubricator tanks, evaluating the
performance of lubricators and checking the blades and plungers for each lubricator.
'micsC = cost of emergency repair during the failure of ith lubricator or lubricant leak
or spilling of lubricant.
Cpics = cost of the personnel involved in maintenance of ith lubricator.
The wear loss can be analysed as a differential wear loss and given by:
Differential Wear loss (Wics ) = Total rail wear before lubrication – Loss of material
after lubrication for ith lubricator of curve section r of rail segment s. (5.6)
Where i is the index.
Cr = Cost of rail material per m per kg
Therefore, the total cost of differential wear loss for a particular curve section (r) of
rail segment (s) can be expressed as
csicsW CWTCics
∗= (5.7)
Total cost of lubrication for ith lubricator at curve section (cs) and rail segment can be
expressed as
picsmicsmicsLicsl CCCCTC +++= ' (5.8)
IficsWicsl TCTC ≤ (5.9)
then the lubrication is effective.
This is a comparison of total cost of each lubricator and total wear cost for particular
curve section (cs) and rail segment. For some places, it is difficult to compare these
costs due to different curve radius and rail size, age and condition of rail. The results
will be more appropriate if we consider average total cost of n number of lubricators
for curve section for a rail segment. Therefore, the total average cost of n number of
lubricators for curve section (cs) and rail segment can be expressed as:
∑=
=n
iicslnlcs TCTC
1
(5.10)
The total average wear cost for n lubricators of curve section (cs) and rail segment can
be expressed as:
129
∑=
=n
iicsWwncs TCTC
1
(5.11)
The ratio of Equation (5.10) and (5.11) can be used to determine the percentage of
average costs of wear and lubrication for particular curve section at a rail segment
under consideration. Therefore, the ratio can be expressed as,
% of average costs = 100×wncs
nlcs
TC
TC (5.12)
The average costs can be compared to determine the effectiveness of lubrication and
differential wear costs. The ratio of these costs could be used to determine the
percentage of savings in terms of lubrication costs and also for evaluation of the
lubricator’s performance. Then the total cost of maintaining n lubricators for
particular curve section (csi) of rail segment per year can be shown as:
∑=
=n
iirsClc TT
1
(5.13)
Figure 5.9 shows the logic for a simulation model for statistical analysis, prediction,
estimation and evaluation of rail wear costs, with lubrication and without lubrication.
130
Figure 5.9: Simulation model to estimate total costs due to wear
Lubrication effectiveness can be analysed using a simulation model and identifying
the influencing factors such as
� Curve radius
� Curve length
� Number of curves lubricated
� Rail material, size, profile, and hardness
� Rail wear with and without lubrication
Measuring factors for effectiveness of lubrication
� Cost savings in rail wear
� Cost of lubricator maintenance
� Effectiveness of lubricator (performance)
� Financial model for the analysis of effectiveness of lubrication
�
131
5.4.1 Modelling Rail Wear Limits
Wear limit is considered as one of the main criteria for rail replacements. It monitors
and controls the risks associated with rail operation based on axle load, train speed,
rail type, Million Gross Tonne (MGT) and curve radius. Wear is the loss or
displacement of a material from a contacting surface. Material loss may be in the form
of debris. Material displacement may occur by transfer of material from one surface to
another by adhesion or by local plastic deformation.
The existing standards of wear limits are very generic and are conservative in many
situations. Conversely, in some cases, the existing limits may no longer be suitable
due to the increased traffic loads that have been introduced to existing lines. Most of
the rail wear limits specify side, table and combined wear for specific rail sizes.
However, they do not allow any significant differentiation between specific traffic and
track variables such as axle loads, track modulus and curve radii. Figure 5.10 shows
rail profile with wear limit for rail head cross sectional area section.
Figure 5.10: Wear limit for rail head cross sectional area (Larsson, 2003)
The Stockholm local network studied the lubricated and non-lubricated rails for two
different rail hardness grades (standard UIC 900A grade rail steel and the harder UIC
1100 grade rail steel) under various seasons. The study found that the contact
situation, in terms of pressure and sliding between rail and wheel, strongly influences
the wear. When the surfaces are worn, the contact situation changes due to changed
geometries. The changed geometries can lead to altered conditions regarding sliding
and pressure distribution between the surfaces. The curve radius of the track has a
strong influence on the vehicles and their behaviour. It is found that the wear rate
increases exponentially for decreasing curve radius. Sharper curves lead to increased
132
track guiding forces acting on the wheels, which can lead to increased creep and,
hence, increased wear. The study shows that new rails have higher wear rate than old
rails that already have been run in. In the test, it was found that the wear rate is
approximately four times higher for new rails compared to the rails that already had
been worn, for UIC 900A grade rails. This is mainly due to alteration in the contact
geometry (Nilsson, 2005).
The Volpe Center (USA) conducted research on estimation of wear limits based on
rail strength. Rail-wear limits were assumed based on fracture strength of the internal
transverse defect (detail fracture) of the existing rail (Jeong et al., 1998). The study
shows that, for safe operation on railroad tracks, allowable rail-wear limits should be
estimated on the basis of fracture strength. The research considered only lightest rail
sections and limits for allowable wear were estimated as 1.27 cm (0.5 inch) head-
height loss or 1.52 cm (0.6 inch) gauge-face loss, under the assumption that the rail is
inspected for internal defects every 20 million gross tons (MGT). This research has
limitations for estimation of wear limits, considering accumulated MGT and axle load
for different rail size and materials and also above rail parameters. There is huge
scope for research in this area to consider the above rail parameters and different
curve radii sections.
Setting a lower wear limit for rail replacements means throwing away effective use of
life before it should be replaced; this ultimately affects the cost of maintaining
infrastructure. On the other hand, higher wear limit means additional operating life of
the rail in the track which poses higher risk of accidents/derailments. Therefore, a
trade off is required, based on rail signature for reducing operating costs and risks of
accident/derailments. CN's (Canadian National) SPC 3200 (Standard Practice
Circular) indicates that, for 100-pound (45.45 kg) rail with standard joint bars, the
vertical rail wear limit is 7 mm (¼ inch), while the sum of vertical and gauge side
lateral wear limit is 3/8 inch (10 mm). The accident in 2002 at Dartmouth Yard, Nova
Scotia, Canada, found that the combined vertical and lateral rail wear measurements
were a maximum of 14 mm (9/16 inch). The maximum vertical wear was 10 mm (3/8
inch), and was found near the point of derailment. The measurements of both the
vertical wear and the combined vertical and lateral wear exceeded SPC 3200 limits.
133
When the rail wear exceeds these limits, the rail must be removed from the main
track.
The rail wear rate decreases with increase in curve radius for both high and low rails.
The wear rate ratio between non-lubricated and lubricated sites decreases for the
curves with higher radius. There is a need to analyse wear rate for the operating point
of a line to identify “good”, “acceptable with possible improvements”, or “poor”
lubrication segments. The area below (Alub) in the Figure 5.18 - the lubricated high
rail curve - is considered as a safe region where rail life is enhanced due to low wear
rate. The area above (Anon-lub) in the Figure 5.18 - the non-lubricated curve - is
considered as operating with high wear rates, where rail is required to be replaced
earlier than planned due to excessive wear. Each track segment - depending on traffic
type, tonnage, lubrication strategy, history of maintenance and weather conditions -
will operate with its own typical values. It is therefore essential to establish a finger
print and a status of the rail lubrication on each line segment. When that is done, it is
possible to compare each curve with itself or with other curves on that segment over
time. It is also possible to detect curves with a “good” lubrication and identify causes
when lubrication starts to fail. An operating value, or a Lubrication Key Performance
Indicator (LubKey), can be defined by assuming that the actual measured operating
point for a curve lies between the points A and B in the Figure 5.11, and is different
for different curves and curve radii. It varies with lubrication performance and
depends on curve radii and environmental and operating conditions.
134
Figure 5.11: Traffic wear rates for high rail (Reddy, 2004)
The wear rate [mm2]/MGT can be used to measure, indicate and determine if a track
is operated close to the upper curve, f1(R), - “poor”, non-lubricated high wear scenario
- or close to the lower curve, f2(R) - “good” effective lubrication, compared to the
actual operating point. If such value is more than 1, then the rail is operated with a
high wear rate.
Let ( ) ( )( )RfRf 21 ≥ and let α (R) be the range between 1f and 2f for curve radius
R=500 m between points A and B. The operating point range, from a non-lubricated
curve of rail, is given by:
( ) ( )( )
( )Rf
RfRfR
1
21 )(−=α
(5.14)
This α is a measure of how wide the range is between the best lubricated situation and
the poorly lubricated (non-lubricated) situation. High ranges between lubricated and
non-lubricated curves, with same radii, give high α value and indicate good
possibilities of improvements in lubrication. Low α value indicates low range
between lubricated and non-lubricated curves with same radii; that is, there is a small
operational difference. However, different α values for a specific line do not indicate
if the studied line is better or worse compared to other lines. The value is an
operational indicator for curves with high wear rates, compared to other curves on the
same line. α - value can pinpoint curves not operating, as well as other simular curves
on the same line. An example of defining a LubKey-Line-Performer value is given
below.
135
Let β(R) be the range between 1f and 2f for a specific curve radius R. The studied
track section or track lines operating mean point is expressed as:
( ) ( )( )2
)(21 RfRfR
+=β (5.15)
The β value is used for comparing the same type of lines with another line that
operates under similar conditions. The number of parameters involved and the
uncertainty and complexity of the wear problem, suggest that each infrastructure
player needs to develop their own best practice plots of “good” and “poor”
lubrication. Indicators such as β and α are useful tools for internal benchmarking and
continuous improvements.
A typical rail maintenance plan includes activities such as yearly preventive grinding,
rail head re-profiling and extensive rail lubrication. Maintenance supportability for
these activities can be different for different lines. For example, it can be achieved by
giving responsibility for the lubrication program to in-house or out-sourced
contractors.
There is a need to define drivers for lubrication improvements such as loss of
lubricants into the environment, long or short term asset costs, safety, noise reduction,
wear reduction and energy consumption. Figure 5.12 shows rail wear limits for
mainline track of rail type 20 kg/m.
Figure 5.12: Rail wear limits for mainline, rail type 20 kg/m (Larsson, 2005)
136
The rail wear limits are: Dimension A is the Table wear in mm: Dimension B is the
Side wear in mm; and Combined Wear Dimension A’ and B’ are shown in Figure
5.19. Dimensions B and B’ are to be measured 16 mm below the original top of the
rail. When any of the linear measurements A, B, A’ or B’, or the percentage reduction
in area are exceeded, the rail is ready for replacement. Four different examples of
measurements of A and B are plotted together with the limits for rail renewal and
shown in Figure 5.19. Knowing the average traffic tonnage per month, it is now
possible to estimate the average wear rate of A and B in mm /10 MGT/month. Hence,
it is possible to estimate when the wear rate line is expected to cross the maximum
wear limit.
The maintenance and strategic planner, together with the budget and economic
strategies for the company, need budget forecast and estimate of when, in the
planning period, these replacements might occur. Instead of using the outer limit of A
and B, it is possible to use plan and budget lines for A and B. For example, if the
planning period for rail renewal is two years, one needs to find a two year forecast
limit line for A and B. Those maintenance planning limit constraints are then plotted.
When the measurements of A and B crosses that planning line, it signals the need for
renewal of this section in the next plan.
5.4.2 Modelling Rail Lubrication
Investigations in Sweden using a tribometer (by measuring friction) found that a
single wayside lubricator can cover 1-1.5 km of track (say +/- 750 from the lubricator
for bidirectional traffic). It also found that the friction is reduced up to a distance +/-
100 m from the applicator.
The failure rate on the applicator, rail wear and consumption of lubricant, are
modelled, based on time of the year, traffic volume in terms of Million Gross Tonnes,
number of axle passes and weather conditions. In this model, applicator failures are
modelled as a point process with an intensity function Λ(p), where p represents the
number of axle pass. Λ(p) is an increasing function of p, indicating that the number of
failures in a statistical sense increases with the number of axle passes. Let Fi(p)
denote the cumulative rail failure distribution for ith type of applicator modelled as
Weibull distribution, given by:
137
))(exp(1)( βλppFi −−= (5.16)
with the parameters β > 1 and λ > 0.
Then the expected number of failures over period t and (t+1) can be obtained from
failure intensity, Λ(p). Then Λ(p) is given by:
11
)())(exp(1(1
))(exp()(
)(1
)()( −
−
=−−−
−=
−=Λ β
β
ββ
λλβλ
λλλβp
p
pp
pF
pfp
i
i (5.17)
with the parameters β > 1 and λ > 0. Then the expected number of failures over
period t and (t+1) is given by:
))()(()],([ 11βββλ tttt PPPPNE −= ++ (5.18)
where Pt is the total number of axle passes up to tth period.
Modelling lubrication can be based on lubricant, application equipment (whether
wayside or on board) and lubrication strategy whether it is continuous or stop/ start
lubrication based on weather condition. Therefore, if the applicator and lubricants are
selected, there are three possibilities:
• No lubrication: the wear occurs more in sharp curves and the replacement of
rails occurs too frequently.
• Lubrication is continuous: per MGT cost of lubrication in curves is more;
however, there is no cost of switching for stop/start mechanism. There may be
environmental cost due to lubrication contaminating ground water.
• Start/ Stop Lubrication: per MGT cost of lubrication is less; it can reduce RCF
to some extent. However, there is the cost of switching stop/start mechanism
and also some risk of spalling. There may be reduced impact on environmental
damage.
)))1/(1(1/(*})1/()({1
j
j
j
y
yy
N
i
i
sjjjl rrrcYMcc +−++= ∑=
(5.19)
As already mentioned
j = 1 means lubricated
= 0 means no lubrication
In no lubrication, cost of lubrication is nil. In this case, rail replacement cost may rise.
From the field experiments, it is found that the wear rate at non-lubricated sharp
curves for 300 to 400 meters radius is ten times higher than the lubricated curves. For
curve radius 600 meters and above, the wear rate is about two to five times higher
than lubricated curves (Jendel, 2002).
138
In start/stop lubrication, lubrication is effective periodically according to the
requirement. This method may have aesthetic and economic appeal but it is not a
valid option, particularly in areas with high moisture. From the field experiments, it is
found that the wear rate during the autumn, winter and spring is higher than the wear
rate during the fall. It is also found that, if the average daily precipitation is about 1.4
millimeters then the wear rate may reach to 35 - 50 mm2/MGT in dry conditions. With
the continuous lubrication it is possible to reach the wear rate between 7 to 10
mm2/MGT. Precipitation and air temperature are important parameters that influence
the rail wear rate under non-lubricated conditions. Increased precipitation reduces the
rail wear rate at non-lubricated conditions and increased air temperature increases the
wear rate. High rail temperature may cause lubrication to become more liquified and
vanish more easily from wheel-rail contact zone. It may also cause the lubrication to
dry up to reduce the effect of the lubrication.
5.4.3 Modelling Repair Cost of Applicator due to Breakdowns.
Let c be the expected cost of each repair, then cost of repair (Cs, t) for each year could
be obtained by multiplying c with the expected number of failures for any particular
year.
where Cs, t is given by:
))()(( 1,βββλ −−= ttts PPcC (5.20)
5.4.4 Modelling Replacement Cost of Applicator
Let I be the expected cost of replacement for applicator and consist of labour,
material, equipment, consumables and down time cost of replacement. This can be
estimated based on historical data.
5.4.5 Cost for various Lubricator Maintenance Strategies
• On site service: Extra time is taken due to train passing and lack of tools to
perform proper service quickly. However, there is no cost for keeping extra
lubricator. However, there is risk of down time of applicator and trains passing
during that time, causing additional wear and contamination of ballast and ground
water.
• In depot service: Efficiency and quality of service in depot reduces time and cost
of maintenance. This also reduces the risk of ballast and ground water
139
contamination. However, there is a need to keep spare units for quick
replacements in the track.
Let C0 be the cost of each service on site and Cd be the cost of each service in depot
which considers the elements as mentioned above. These are random variables. Let
0C and dC be the expected cost for service on site and in depot respectively. The
number of services required is based on service interval and is estimated by
combining failure intensity of applicators, capacity of tank for lubricant and traffic
flow. Let Cm,t be the cost for service for maintenance strategy m in period t, based on
number of services ns. Then the cost for each service for a particular maintenance
strategy can be estimated by using cost per service, based on servicing strategy and
number of services.
• m = 1 maintenance and service on site
• m = 0 replacement on site and maintenance of non-conforming lubricators in
depot
5.4.6 Modelling Lubricant Cost
Let Cl be the cost of lubricant per kg and q be the amount of lubricant used in kg per
axle pass. Then cost of lubricant for the period t can be obtained by using the number
of passes based on traffic flow, quantity per pass and cost per kg.
5.4.7 Modelling Benefits of Lubricators by Reducing Rail Wear Cost
Let Ac be the critical area for replacing rail. If A0 is the area for new rail, then the
allowable wear is (A0 -Ac). Let cost to replace rail be Cre, then cost in period t due to
rail wear can be obtained, based on pro-rata life loss of rail. The difference between
lubricated and non lubricated rail is the benefit of lubrication and is given bytrebC .
Figure 5.13 shows the lubrication effect over rail life for different curve radii.
140
Figure 5.13: Lubrication influencing rail life (Larsson et al., 2005)
This benefit in terms of rail life varies from lubricant to lubricant and type of
applicator.
5.4.8 COST-BENEFIT Analysis of Applicators and Various Lubricants
For no lubrication, the cost of lubrication is nil. In this case, rail replacement costs
may rise. The wear rate for non lubricated rail is higher than lubricated curves (Jendel,
2002). Wear rate for various lubricants can be estimated from laboratory tests and
field data. This can be used to calculate the cost due to rail wear.
Net Present Value (NPV) of lubrication decision in any particular curve can be given
by:
NPV = Ir
CCCCttltmts
N
ttreb −
+−−−∑
= )1(
1*)( ,,,
1
(5.21)
where r is the discounting rate.
This model is able to determine economic lubrication, lubricator and maintenance
policies based on the following variables:
i = curve segment for particular radius
j = lubrication strategy = 1 means lubricated and 0 means non-lubricated
curves
u = applicator type and make
l = lubricant type based on product and supplier
m = lubricator maintenance strategy= 1 means on site maintenance and 0
means replacement on site
141
5.4.9 Failure of Lubricators
The lubricators in Scandanavia generally fail due to nozzle clogging. Static pre
pressure of the grease container causes the oil to be separated from the grease. The
graphite and soap thickener clogs the nozzle and stops the system working properly. It
then needs to be cleaned thoroughly. In Australia, during summer seasons with high
temperature, if the applicator is not used for a long time, the nozzles start clogging.
This leads to improper functioning of the lubrication system.
5.4.10 Cost for Fixing Breakdowns
It takes two persons one and a half to two hours in the Scandinavian system to clean
up wayside applicators (Clicomatic). If it is done on site, it costs AUD $480 /service
(2 personnel x 2 hours and one car for transportation). If it is done at the depot, the
cost could be different.
5.4.11 Cost to Maintain Lubricators
The cost to maintain lubricator in Scandinavia is around AUD $1200 - $2000
/year/apparatus (only six months operation of applicators per year due to no
lubrication during winter) to fill up applicators and maintain the lubricators.
5.4.12 Cost-Benefit Analysis of Lubricators
Generally, to service a lubricator, the total number of hours used at lubrication site, is
approximately 2.5. The service cost includes total vehicle cost (Cv), total travelling
cost (Ct), total repair cost (Cr) and total labour cost (CL). The service cost also
depends on the number of services (n) per year, cost per service (Csi) and unplanned
maintenance cost (Cum) resulting from failures. Then, the expected total service cost
per year (Cs) is expressed as:
( )∑=
++++=n
i
umLrtvis CCCCCCsC
1
)(* (5.22)
where unplanned maintenance cost (UMc) is expressed as:
))((1
tNECCn
i
umium ∗= ∑=
(5.23)
where i is index for unplanned maintenance for each event
n is the number of unplanned maintenance per year
Cumi is unplanned maintenance cost for each maintenance
142
E(N(t)) is expected number of failures per each service of the lubricator
Cumi
∑=
+++=n
i
Lrtvumi CCCCC
1
)( (5.24)
Then expected total maintenance cost of each lubricator per year is expressed as
∑=
++=n
i
lumsmt CCCC
1
)( (5.25)
where Cl is the cost of lubricant per year.
5.4.13 Cost of Lubricants
Cost of lubricant varies in the range of AUD $ 3.20 to AUD $ 4.80 /kg and usage of
15 kg /year per applicator in Scandinavian rail, with no lubrication during winter.
Figure 5.14: Wayside lubrication (Larsson, 2004)
As can be seen in Figure 5.14, the lubricated area shows 30% less in terms of the
lateral wear of the rail head. This means that infrastructure owners can save at least
30% in wear losses by using an appropriate lubrication and maintenance strategy
(Larsson, 2004).
5.5 Modelling Failures
A system failure (either complete or partial) is due to the failure of one or more of its
components (Blischke and Murthy, 2000). Failures over the lifetime can be modelled
either at component level or at the system level. The component level models are
sometimes appropriate for certain policies but the difficulty with these models is that
they require data at component level. Often, companies do not keep records of those
143
data at component level, but system level models require aggregated data which are
usually available from the data base.
Age Policy can be followed in this case. Age Policy is used for components that
degrade with age. When the degradation is due to usage (rather than age), then this
policy is used with T representing a measure of usage.
We assume that T<t. The time required for a corrective maintenance action (replacing
a failed component by a new one) and preventive maintenance action (replacing a
non-failed component of age T by new one) are sufficiently small so that they can be
ignored. The costs of each corrective and preventive maintenance action are Cc and Cp
(<Cc), respectively.
Let iX~denote the age of Item I when it is replaced (either under preventive or
corrective maintenance). Then it is easily seen that
{ IX
TiX =~
TifX
TifX
i
i
≥
<
(5.26)
where iX is the time to failure.
Failure of each component can be modelled separately. The modelling of the first
failure needs to be treated differently from that of subsequent failures. It depends on
(i) whether the component is repairable or not, (ii) the type of rectification and (iii) the
type of component (new or used) used as replacement. MTTF of the first failure can
be modelled by a probability distribution function. Subsequent failure can be
modelled either by ordinary renewal process (when every failure results in a
replacement by a new product and the replacement times are negligible) or a delayed
renewal process or point process (when all failures are repaired with negligible repair
time and with a specified intensity function) (Blischke and Murthy, 1994). When the
rectification involves either repair or replacement by a used or cloned part, then the
modelling is more complex and can be formulated by the modified renewal process
(Kijima 1989).
Modelling first failure for one dimensional formulation – Black Box approach
Let X1 denote the usage of an item at its first failure. This is also called time to first
failure. Let F(m) and R(m) denote the cumulative distribution function and reliability
144
function (the probability that the first failure does not occur prior to x) for the first
time to failure respectively. Then f(x) is the density function for this case and is given
by
f(m) = dF(m)/dx. (5.27)
Here we have,
( ) { }mXPmF ≤= 1 and (5.28)
( ) ( ) { }mXPmFmR >=−= 11 (5.29)
The conditional probability of item failure in the interval [m, m + t], given that it has
not failed before m, is given by
( ) ( ) ( )[ ] ( )mRmFmtFmtF −+=
(5.30)
The failure rate associated with a distribution function F(m) is defined as
( )( ) ( )
( )mR
mf
t
mtFmr
t==
→0lim
(5.31)
For Exponential distribution, the density function, f(m), and failure rate, r(m), are given by
( ) ( )memf λλ −= , for 0 ≤ m < ∝, and λ > 0 (5.32)
( ) λ=mr (5.33)
where λ is the failure intensity.
For Gamma distribution, the density function and failure rate are given by
( )( )β
λ λββ
Γ=
−− memmf
1
, for 0 ≤ m < ∝, λ > 0 and β > 0 (5.34)
( ) ( )11 −
∞−−
−
= ∫m
mt dtem
tmr λ
β
(5.35)
For Weibull distribution, the distribution function and failure rate are given by
( ) ( )[ ]βλmemF −−= 1 , for 0 ≤ m < ∝, λ > 0, and β > 0 (5.36)
( ) ( ) 11
1
1 −−−
− =×
== ββ
ββ
β
ηβ
ηηβ
λβλ mxmmr
(5.37)
Renewal Process
Let us consider the renewal process for a lubricator whose lifetime is independent and
identically distributed. Generally, preventive maintenance is scheduled twice in every
145
month. For example, if there is a failure found in the lubricator, then as per the
renewal process Xi is the renewal at time i, let
S0 = 0, ∑=
=n
i
in XS1 , 1≥n
(5.38)
That is, S1 = X1 is the time of the first renewal; S2 = X1 + X2 is the renewal until the
first renewal, plus the time between the first and second renewal; that is, S2 is the time
of the second renewal. In general, Sn = denotes the time of the nth renewal. Under
these conditions, ( ){ }0,,, ≥tmtmN is a renewal process when N(m, t) represents the
number of items that failed by usage m and time t. The distribution of N(m, t) can be
obtained with the number of renewals by time t is greater than or equal to n if, and
only if, the nth renewal occurs before or at time t. That is,
( ) tSntN n ≤⇔≥ (5.39)
( ){ } ( ){ } ( ){ }1+≥−≥== ntNPntNPntNP
= { } { }tSPtSP nn ≤−≤ +1 (5.40)
We can apply an ordinary renewal process (Cox, 1962) as follows:
Let the number of renewals over the usage m [0, m), be M(m), and this is given by
( ) ( )[ ] ( ){ }∑
∞
=
==0n
mNnPmNEmM
(5.41)
where E[N(m)] is the expected number of renewals during the usage m of the item,
and n is the number of failures, and n =0, 1, 2, …….
Conditioned on X1(the time to first failure), M(m) can be expressed by
( ) ( )[ ] ( )xdFxXmNEmM ∫∞
==0 1 (5.42)
According to the renewal property, the following expression is valid:
( )[ ]( )
≤−+
⟨==
mxifxmM
mxifxXmNE
,1
,01
(5.43)
If the first failure occurs at x ≤ m, then the number of renewals over (m – x) occur
according to an identical renewal process, and hence, the expected number of
renewals over the period is M(m - x). Therefore, we have
146
( ) ( ) ( ) ( )dxxfxmMmFmML
∫ −+=0 (5.44)
where, F(m) and f(x) represent cumulative failures during usage period and
probability distribution function respectively. Therefore, the total cost over the usage
of the item is given by
( ) ( ) ( ) ( )
−+= ∫
L
ii dxxfxmMmFcmC0 (5.45)
where, ci is the cost of each failure replacement.
Let the new failure distribution be given by G(x), which is different from the failure
distribution of the new item F(x). This situation represents the delayed renewal
process (Cox, 1962).
A counting process {N(t), t ≥ 0} is a delayed renewal process if
1. N(0) = 0
2. X1, the time to first renewal, is a non negative random variable with
distribution function F(x).
3. Xj, j ≥ 2, the time interval between jth and (j-1)th repair, are independent and
identically distributed random variables with distribution function G(x), which
is different from F(x).
4. N(t) = sup{n; Sn ≤ t}, where S0 = 0 and, for n ≥ 1.
∑=
=n
j
jn XS1 (5.46)
Let Md(m) denote the expected number of renewals over the lifetime [0, m) for the
delayed renewal process. Then, in line with Ross (1970), we can rewrite the following
expressions for products sold with lifetime warranties:
( ) ( )[ ] ( )[ ] ( )xdFxXmNEmNEmML
d ∫ ===0 1 (5.47)
An expression for this can easily be obtained using the conditional expectation
approach used for obtaining M(m) for the ordinary renewal process. Conditioning on
T1, the time to first renewal, we have
( )[ ] ( )
≤−+
>==
mxifxmM
mxifxXmNE
g1
,01
(5.48)
147
where, Mg(m) is the renewal function associated with the distribution function G(m).
This follows from the fact that, if the first repair occurs at x ≤ m, then over the interval
(x, m), the repairs occur according to a renewal process with distribution G. Hence,
Md(m) is given by
( ) ( ) ( ) ( )dxxfxmMmFmML
gd −+= ∫0 (5.49) And the total cost is given by
( ) ( ) ( )
−+= ∫ dxxfxmMmFcC
L
gjj 0 (5.50) where cj is the average cost of all repairs.
5.6 Framework for Benchmarking Lubrication
The framework for benchmarking lubrication effectiveness with what-if scenario for
integrated economic lubrication strategies is shown in Figure 5.15. The model can be
used to analyse annuity costs of maintenance and replacement of different types of
lubricators.
Figure 5.15: Framework for benchmarking lubrication (Larsson, 2004)
148
The following measures are proposed for assessing lubrication effectiveness and
improving performance:
• Relative performance model: The absolute values of effectiveness of lubrication
may not provide accurate results for assessment of lubricator performance [for
example, if lubricator is placed near 300 m, 400 m and 2000 m curve radius for
three locations]. The assessment of lubrication effectiveness of three curves is
based on rail head temperature rise and acoustic emission and tribometer
measurements. The relative performance of these curves with the same application
strategy under different operating conditions can be an appropriate measure for
the assessment of lubrication effectiveness.
• Total curve and segment model: It is important to determine the length and
radius of curve to determine the plunger adjustment and to provide adequate
lubrication along the curve.
• Above rail and below rail model: This model is to consider known wear of
rolling stock related to rail head wear and uses head wear data for assessing the
effectiveness of lubrication, considering both above rail and below rail.
5.7 Modelling Annuity Cost of Lubricators
Let P be the purchase price of lubricator and Csc be the cost of investment for each
lubricator (it includes set up cost of each lubricator), r be the discount rate assumed
for the estimation of present value of each lubricator in use.
For electric lubricator, let
=EP Purchase price of electric lubricator
=tE Electric consumption cost in time t
=EC Total cost for electric lubricators
=mtC Maintenance cost for each lubricator in time t. This includes lubricant cost,
cost for purchasing and replacing spare parts, vehicle cost, labour cost for each
lubricator.
Total cost of each lubricator investment can be estimated using the following
equations.
Cost for one electric lubricator is given by
)( mttEscE CEPCC +++= (5.51)
Therefore, the annuity cost of electric lubricator is given by
149
( )∑= +−
×+
+++=
n
iy
y
y
imttEsc
Er
r
r
CEPCC
1 )))1/(1(1(1
)( (5.52)
where r is discount rate per year
i is number of years and
n is number of maintenance periods per year and
y is expected life of lubricator in number of years.
Cost for standard way-side lubricator is given by
Cw = purchase price of lubricator + setup cost + maintenance cost
mtscww CCPC ++= (5.53)
Therefore, the annuity cost of standard way-side lubricator is given by
( )( ) ( )( )( )y
y
yn
ii
mtscww
r
r
r
CCPC
+−×
+
++= ∑
= 1/1111
(5.54)
Cost for solar lubricator is given by
Cs = purchase price of lubricator + setup cost + maintenance cost + purchase price of
solar panel and its maintenance.
spmtsscs PCPCC +++= (5.55)
Therefore, annuity of solar lubricator is given by
( )( ) ( )( )( )y
y
yn
ii
mtspssc
sr
r
r
CPPCC
+−×
+
+++= ∑
= 1/1111 (5.56)
Failure of lubricator depends on various factors which include:
� poor maintenance
� poor support from lubricator’s manufacturer
� problems with lubricator’s service
� aging of lubricators
� inefficient delivery of grease
� problems in finding correct blade and pump
� inappropriate plungers
� clogging of grease
� distribution units and
� reliability and environmental conditions.
150
5.8 Collection and Analysis of Data
Data collected from rail industry is used to analyse lubrication effectiveness, to
estimate costs and predict risks due to rail wear and lubrication. Most rail
infrastructure owners are spending millions of dollars to control rail wear and to
achieve effective rail-wheel lubrication. This has been costly and ineffective due to a
lack of preventive maintenance of lubricators, lack of technology and ad-hoc
maintenance procedures. Therefore, it is important to analyse the field data and
estimate the costs involved to predict associated risks and achieve effective
lubrication maintenance to reduce costs and maximise savings, enhance rail-wheel life
and increase safety of rail operation.
Data for sections A and B was collected from 1998 to 2004 in Australia. The curve
distribution of the corridor is shown in Figure 5.16. Table 5.4 shows traffic for
Section A to B during the period 1998 to 2004.
Curve Distribution
17%
7%
18%
22%
8%
28%
0-300m
301-450m
451-600m
601-800m
801-1500m
1501-6000m
Figure 5.16 Curve distribution for A-B corridor
Table 5.4 Traffic for Section A to B during period from 1998 to 2004
Traffic from Year 1998-2004 in A to B Corridor
Year 1998 1999 2000 2001 2002 2003 2004
Traffic (MGT) 8.576 9.233 9.101 9.586 9.438 9.496 9.478
(For detailed data see Appendix B.) Rails are the most expensive component in the railway tracks and cost approximately
AUD $ 180 per m, accounting for millions of dollars annually in the rail industry
budget. It is advantageous for rail owners to be able to identify when to replace worn
rail, not only for budgeting purposes, but also for regular maintenance of rail for safe
and reliable rail operation with increased axle loads, speed and million gross tonnes
151
(MGT) which accelerate rail wear and rail degradation, leading to rail breaks and
derailments. In this research, rail table (head) wear and rail gauge side wear are
considered to estimate area head loss (AHL) in mm2, % area head loss and wear rate.
Due to inconsistency in data, statistical distribution was used to analyse the data and
results are presented in the following sections. Figure 5.17 shows rail table wear and
side wear measurements.
Figure 5.17: Table wear and side wear measurements (Grassie, 2005)
5.8.1 Estimation of Area Head Loss (AHL)
Let A be the total area head loss allowable, A0 be the rail new area and AL be the area
head limit for rail to renewal or replacement of rail. Therefore, the total allowable area
head loss is given by
A = (A0 - AL) MGT/Year (5.57)
If i is index, then area head loss for ith period for million gross tonnes (MGT) Mi is
given by
=i
i
M
A MGT/year (5.58)
AK is the critical area head loss for remaining life = (A0 – AK)
% of error = Actual area head loss – Predicted area head loss/Actual *100
% remaining life =
−
−
L
a
AA
AA
0
0 (5.59)
% per year difference from normal distribution = µ
152
No of years on average = µ
LK AA − (5.60)
According to international standards, rail wear can be predicted, based on statistical
studies of rail wear; that is, current wear level measured in the curve divided by the
accumulated tonnage since new.
The analysis of lubrication effectiveness performed for curve radius is in a scale of
� 0 – 300 m
� 301 – 450 m
� 451 – 600 m
� 601 – 800 m
� 801 – 1500 m
� 1501 – 6000 m
The main focus of the study is between 0-800 m curve radii. Curves below this radius
wear off significantly faster than curves with longer radii. A significant amount of
lubrication is used for these sections to control severe wear. Furthermore, this is the
main focus of rail players to reduce maintenance costs to control wear and enhance
rail life, with minimum maintenance of lubricators and rails.
5.8.2 Analysis of Wear for Curves radii 0-300 m
Data collected was investigated and extracted for analysis. Data was reliable and was
used for analysis since the results will help to predict the models and to make better
maintenance decisions which reduce costs. Data was collected between 0-6000 m
curve radius for different rail size (47, 50, 53 and 60 kg) during the years 1998 to
2004. The data is filtered with separation of curves that have no replacement over this
period. In this case, there was a reduction of 25% of overall data. This is considered
mainly due to the fact that new rail wears much less than old rails. Statistical
distribution is used to estimate area head loss for every year and wear rate, due to
inconsistency in the data. The amount of wear and rate indicated performance and
effectiveness of lubrication for particular curve in a particular period. Table 5.5 shows
a sample of the amount of area head loss per MGT for a curve radius 300 m of section
from 88.028 to 88.076.
153
Table 5.5: Area head loss (mm2/MGT) for 300 m curve (QR, 2005)
Area head loss (mm^2) for curve radius 300 m from 88.028 to 88.076 section
Wear can be estimated as follows:
� Wear (1998-1999) = (22.847 – 16.183) mm2/MGT = 6.665 mm2/MGT
� Wear (1999-2000) = (23.179 – 22.847) mm2/MGT = 0.331 mm2/MGT
� Wear (2000-2001) = (29.534 – 23.179) mm2/MGT = 6.356 mm2/MGT
� Wear (2001-2002) = (29.997 – 29.534) mm2/MGT = 0.463 mm2/MGT
� Wear (2002-2003) = (36.829 – 29.997) mm2/MGT = 6.832 mm2/MGT
� Wear (2003-2004) = (36.889 – 36.829) mm2/MGT = 0.070 mm2/MGT
Wear (mm^2/MGT) for curves radii 0-300 m
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30
Curve Section
Wear (m
m^2/MGT)
1998-99
1999-00
2000-01
Figure 5.18: Wear for curves radii 0-300 m from 1998-2001
Wear data collected and analysed as shown in Figure 5.18. The data lies between ± 30
mm^2/MGT. The positive (+ve) values show the rate of increase of wear every year,
with accumulated tonnage at different sections. The negative (-ve) values show the
rate of decrease of wear every year. Analysis found that:
� Decrease of wear is mainly due to better performance of lubricators at some
sections of curve radii
� Measurement error in estimation of area head loss has significant influence in
determining the wear rate and performance of lubricators
154
� Accurate results can be obtained by comparing analysis of data for mixed
traffic under various operating and environmental conditions
Figure 5.19 shows the wear data analysis for curve radii 0-300 m from year 2001 to
2004. The analysis shows the increase of area head loss in 2001 to 2004 compared to
area head loss during 1998-2001. However, there is only a small percentage of
increase of wear during this period. This may be due to the effectiveness of
lubrication or replacement of new rail.
Wear (mm^2/MGT) for curve radii 0-300 m
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30
Curve Section
Wear (m
m^2/MGT)
2001-02
2002-03
2003-04
Figure 5.19: Wear for curves radii 0-300 m from 2001-2004
Wear data for curve radius 0 to 300 m were further analysed. Figure 5.20 shows wear
for various curves radii between 0-300 m for accumulated MGT.
Rail Wear (mm^2/MGT)
0
20
40
60
80
100
8.576 9.233 9.101 9.586 9.438 9.496 9.478
MGT
Wear (m
m^2/MGT)
194.9
231
256
300
Figure 5.20: Rail wear for four different curves
155
It is observed that wear has increased constantly with accumulated MGT. It shows
that wear for curves radii 300 and 194.9 m is higher, compared to curves with radii
231 and 256 m. For curves 231 and 256 m, wear has increased for the first few years
and then stable for all other years; however, for curves 300 and 194.9 m, wear has
been increasing continuously. This shows that the effectiveness of lubrication is better
at curves radii 231 and 256 m, compared to curves with radii 300 and 194.9 m
respectively.
Data is analysed for the better prediction and estimation of wear rate for various
curves. Weibull and Gamma distributions have been explored for analysis and R-
square and Root mean square error (RMSE) were not acceptable. Due to the variation
in the data, curve fitting methods and Gaussian (Normal) distribution have been
applied for better accuracy of results. Figure 5.21 shows a sample of curve fitting of
actual and predicted data for accumulated MGT of a 300 m curve radius for a
particular location (Section 88.028 to 88.076).
0 20 40 60 80 100 1200
20
40
60
80
100
120
140
160
180
Fit w
ith 9
5%
pre
d b
ounds
Analysis of fit "fit 1" for dataset "ahl8 vs. mgt"
fit 1
95% prediction bounds
ahl8 vs. mgt
Figure 5.21: Curve fitting analysis for curve radius 300 m
The analysis found that general Gaussian (Normal) distribution is best suited to fit this
continuous data.
( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= (5.61)
where x is normalized by mean 44.47 and standard deviation 39.46
Coefficients (with 95% confidence bounds):
MGT
156
a1 = -7247 (-1.398e+009, 1.398e+009)
b1 = 1.602 (-1425, 1429)
c1 = 1.749 (-1489, 1492)
a2 = 7386 (-1.398e+009, 1.398e+009)
b2 = 1.617 (-1448, 1451)
c2 = 1.765 (-1498, 1501)
Goodness of fit: Sum of Squared Errors (SSE): 443.4, R-square: 0.9865 Adjusted R-
square: 0.9813, (Root Mean Square Error) RMSE: 5.84. Analysis found that R2 is
closer to 1 which indicates the best fit. These results were further analysed using a
distribution fitting tool to find out mean, variance and standard deviation for better
prediction of the wear rate. Data is best fitted with Gaussian (Normal) distribution and
results shown in Figure 5.22.
2 4 6 8 10 12 140
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Data
Density
ahl9 data
fit 1
Figure 5.22: Gaussian distribution of the RMSE for 0-300 m curves
Therefore Mean of RMSE = 6.58104, Variance: 8.56982, Standard Deviation =
2.92743. Analysis shows that Mean of RMSE is considered as wear rate for
estimation of rail life and to analyse lubrication effectiveness. For 0 to 300 m curve
radii for accumulated MGT is 6.58 mm2/ MGT.
Estimation of rail life is as follows: CETS limit for 47 kg rail size = 684 mm2
Measurement of area head loss for a curve section 63.920 to 63.945 for a radius 300
m in year 2004 = 390 mm2
Wear rate = 6.58 mm2/MGT
Estimated actual rail life = 684 mm2/ 6.58 mm2/MGT = 104 MGT
157
Estimated rail life left = (684-390) mm2/ 6.58 mm2/MGT = 45 MGT
The analysis of comparison of area head loss (mm2) for 47 kg rail is shown in Figure
5.23. The analysis shows that, continuous increase of wear for 220 m and 300 m.
Area Head Loss (mm^2) for 47 kg rail from 0-300 m
0
200
400
600
800
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
300 (RS1)
300 (RS2)
Wear Limit
220
Figure 5.23: Area head loss comparison for 47 kg rail
The wear rates for curves radii 300 m at different locations are analysed and
compared in the Figure 5.23. Wear is higher for curve radius 300 m of rail segment 1
(RS1), compared to that for curve radius 300 m of rail segment 2 (RS2) at different
locations. Analysis found that effective lubrication at the RS2 has significantly
reduced wear compared to RS1. This is due to poor performance and maintenance of
lubricators in the RS1 section.
The analysis shows that, according to the CETS standard, the estimated rail life for 47
kg size rail is approximately 104 MGT. Analysis shows that, for the section 63.920 to
63.945 of curve radius 300 m, the rail life left after 2004 is 45 MGT. It is found in the
investigation of actual data and predicted data, rail has 4 years life left, if on an
average 10 MGT every year. This may change with effectiveness of lubrication and
traffic density and operating conditions.
Measurement of area head loss for a curve section 87.641 to 88.020 for a radius 300
m in year 2004 = 733 mm2
Wear rate in 5 years from 2000 to 2004 is 31 mm2/ MGT.
CETS limit for 50 kg rail size = 866 mm2
Estimated actual rail life = 866 mm2/ 31 mm2/MGT = 28 MGT
Estimated rail life left = (866-733) mm2/ 31 mm2/MGT = 4 MGT
158
Area Head Loss (mm^2) for 50kg rail curves radii 0-300 m
0
150
300
450
600
750
900
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
195
241
300
300
Wear Limit
Figure 5.24: Area head loss comparison for 50 kg
The analysis of comparison of area head loss (mm2) for 50 kg rail is shown in Figure
5.24. This shows that, according to the CETS standard, estimated new rail life for 50
kg size rail is approximately 28 MGT. Analysis shows that, for the curve radius 300
m, the rail life left over after 2004 is 4 MGT. It is found in the investigation of actual
data and predicted data, that rail needs to be replaced immediately. It shows poor
performance of lubrication in this section. Rail condition may be improved with
improved effectiveness of lubrication and operating conditions (which are more
economical than replacing with new rail), but it has involved higher risk of rail breaks
or derailments. Figure 5.25 shows that the wear of section 87.641 to 88.020 is 5 times
higher, compared to the section 63.920 to 63.945 for same curve radius 300 m in the
last five years.
Wear (mm^2/MGT) for 300 m
0
10
20
30
40
1998-2002 1999-2003 2000-2004
Year
Wear (mm^2/MGT)
Wear at 63.920-63.945
Wear at 87.641-88.020
Figure 5.25: Wear for curve radius 300 m
159
The analysis of lubrication effectiveness needs to be carried out for accurate
prediction and estimation of rail life, to reduce and prevent risk of rail breaks and
derailments. Figure 5.26 shows the analysis of wear for a section from 93.341 to
93.596 of curve radius 245 m. A considerable decrease of wear is observed in this
section. For years 2000 to 2004, wear has decreased approximately at 15 (mm2/MGT)
per year. This shows that lubrication performance is effective and has extended rail
life in this section.
Wear (mm^2/MGT) for 245 m
-20
-10
0
10
20
1998-2002 1999-2003 2000-2004
Years
Wear (mm̂2/MGT)
Wear for 93.341-93.596
Figure 5.26: Wear for curve radius 245 m
5.8.3 Analysis of Wear for Curves radii 301-450 m
Collected data was analysed for curves radii 301-450 m for different locations. Figure
5.27 shows the wear for curves radii of 301-450 m. It is observed that scattered wear
data has fallen between ±30 mm2/MGT. Analysis shows that wear rate of increase
(that is, +ve values) is higher than the wear rate of decrease (that is, –ve values). This
may be an indication of poor performance and effectiveness of lubrication in these
sections.
Wear (mm^2/MGT) for curves radii 301-450 meters
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30 35 40
Curve Section
Wear (mm^2/MGT)
1998-99
1999-00
2000-01
Figure 5.27: Wear for curves radii 301-450 m from 1998-2001
160
Figure 5.28 shows the wear for curves radii of 301-450 m from year 2001-2004. It is
observed that scattered wear data has fallen between ±30 mm2/MGT. Analysis shows
that wear rate of increase (that is, +ve values) is higher than the wear rate of decrease
(that is, –ve values). It also shows that wear has increased at a slower rate and is close
to X-axis. This may indicate good performance and effectiveness of lubrication in
these sections.
Wear (mm^2/MGT) for curves radii 301-450 meters
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30 35 40
Curve Section
Wear (mm^2/MGT)
2001-02
2002-03
2003-04
Figure 5.28: Wear for curves radii 301-450 m from 2001-2004
Figure 5.29 shows that rail wear has increased constantly with accumulated MGT. It
shows that wear for curves radii 400 and 388 m is higher, compared to curves with
radii 320 and 425 m. Analysis shows that wear has decreased for both curves after
first 8.576 MGT, and then wear rate has increased constantly at a slower rate.
Rail Wear (mm^2/MGT)
0
20
40
60
80
8.576 9.233 9.101 9.586 9.438 9.496 9.478
MGT
Wear (m
m^2/M
GT)
320
388
400
425
Figure 5.29: Rail wear for different radii for accumulated MGT
161
Analysis shows the effectiveness of lubrication is better for curves with radii 320 and
425 m. Further data is analysed for all the section between curves of radius 301 to 450
m, using the Gaussian (Normal) distribution for better and accurate prediction of wear
rate and to estimate rail life. Curve fitting tools have been used to find R2 and RMSE
for curves radius 301 to 450 m. Figure 5.30 shows a sample of curve fitting for actual
and predicted data for accumulated MGT of a curve radius 415 m for a particular
location (Section 135.283 to 135.512).
0 20 40 60 80 100 12055
60
65
70
75
80
85
90
95
Fit w
ith 9
5%
pre
d b
ounds
Analysis of fit "fit 1" for dataset "ahl8 vs. mgt"
fit 1
95% prediction bounds
ahl8 vs. mgt
Figure 5.30: Curve fitting for curve radius 415 m
Data is best fitted with Normal (Gaussian) distribution
( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= where x is normalized by
mean 44.47 and standard deviation 39.46
Coefficients (with 95% confidence bounds):
a1 = 101.3 (-336.4, 539.1)
b1 = 4.594 (-65.05, 74.24)
c1 = 7.006 (-72.7, 86.71)
a2 = 9.834 (-121.8, 141.5)
b2 = -0.6955 (-4.211, 2.82)
c2 = 0.8351 (-4.239, 5.909)
Goodness of fit: Sum of Squared Errors (SSE): 104.1, R2: 0.9139, Adjusted R2:
0.8808, Root Mean Square Error (RMSE): 2.83.
MGT
162
These results were further analysed using the distribution fitting tool to find out mean,
variance and standard deviation for better prediction of the wear rate. Data is best
fitted with Gaussian (Normal) distribution and results shown in Figure 5.31.
0 5 10 15 20 25 300
0.05
0.1
0.15
Data
Density
q data
fit 1
Figure 5.31: Gaussian distribution of the RMSE for curve radii 301-450 m
Therefore Mean of RMSE 8.37691, Variance is 29.9521, Standard Deviation is
5.47285
Mean of RMSE is considered as wear rate for estimation of rail life and to analyse
lubrication effectiveness. For 301 to 450 m curve radii, accumulated MGT is 8.38
mm2/ MGT.
Estimation of rail life is as follows:
CETS limit for 50 kg rail size = 866 mm2
Measurement of area head loss for a particular curve section 101.424 to 101.671, for a
radius 410 m in year 2004 = 733 mm2
Wear rate = 8.38 mm2/ MGT
Estimated actual rail life = 866 mm2/ 8.38 mm2/MGT = 103 MGT
Estimated rail life left = (866-733) mm2/ 8.38 mm2/MGT = 16 MGT
The analysis of comparison of area head loss (mm2) for different rail curve sections is
shown in Figure 5.32.
163
Area Head Loss (mm^2) for 50kg Rail
0
150
300
450
600
750
900
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
301.3
345
400.2
410
Wear Limit
Figure 5.32: Area head loss for 50 kg rail
This shows that, according to the CETS standard, actual estimated rail life for 50 kg
size rail between 301-450 m curve radius is approximately 103 MGT. Analysis shows
that, for the section 101.424 to 101.671 of curve radius 410 m, the rail life left after
2004 is 16 MGT. It is found in the investigation of actual data and predicted data that
rail has only 2 years life left, if on an average 8 MGT every year. This may indicate
changes with effectiveness of lubrication and traffic density and operating conditions.
Measurement of area head loss for a curve section 98.555 to 98.775 for a radius 400
m in year 2004, is 693 mm2. From the actual data, wear rate in 5 years from 2000 to
2004, is 12 mm2/ MGT. CETS limit for 47 kg rail size = 684 mm2
Estimated actual rail life = 684 mm2/ 12 mm2/MGT = 57 MGT
Estimated rail life left = (684-693) mm2/ 12 mm2/MGT = -0.75 MGT
Results show that rail wear has reached critical wear limit. Immediate replacement or
repair of rail is essential to avoid rail break or derailment.
Area Head Loss (mm^2) for 47kg Rail
0
200
400
600
800
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
303
320
400
415
Wear Limit
Figure 5.33: Area head loss for 47 kg rail
164
The analysis of comparison of area head loss (mm2) for 47 kg rail is shown in Figure
5.33. This shows that, according to the CETS standard, estimated new rail life for 47
kg size rail is approximately 57 MGT. Analysis shows that, for the section 98.555 to
98.775 of curve radius 400 m, the rail should be replaced immediately. Figure 5.33
shows that it has crossed the wear limit and there is a high risk of rail break or
derailment involved. It shows poor performance of lubrication in this section. Rail
condition can be improved with effectiveness of lubrication and operating conditions.
It is more economical to replace with new rail, rather than overhauling old rail and
increasing risk of rail break and derailments.
5.8.4 Analysis of Wear for Curves radii 451-600 m
Collected data was analysed for curves radii 451 to 600 m in different locations.
Figure 5.34 shows the wear for curves radii of 451-600 m. It is observed that scattered
wear data has fallen between ±30 mm2/MGT. Analysis shows that wear rate of
increase (i.e. +ve values) is higher than the wear rate of decrease (i.e –ve values). This
may be an indication of poor performance and effectiveness of lubrication in these
sections.
Wear (mm^2/MGT) for 451-600 m from 1998-01
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30 35
Curve Section
Wear (m
m^2/M
GT)
1998-99
1999-00
2000-01
Figure 5.34: Wear data for curves radii 451-600 m from 1998-2001
Figure 5.35 shows the wear for curves radii of 301-450 m, from year 2001-2004. It is
observed that scattered wear data has fallen between +30 and -10 mm2/MGT.
Analysis shows that wear rate of increase (i.e. +ve values) is higher than the wear rate
of decrease (i.e –ve values).
165
Wear (mm^2/MGT) for 451-600 m from 2001-04
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30 35
Curve Section
Wear (m
m^2/M
GT)
2001-02
2002-03
2003-04
Figure 5.35: Wear data for curves radii 451-600 m from 2001-2004
It also shows that wear has increased at a slower rate and most of the data fell close to
X-axis. This may be an indication of good performance and effectiveness of
lubrication in these sections. Figure 5.36 shows that rail wear has increased constantly
with accumulated MGT. It shows that wear for curves radii 600.2 and 500 m is
higher, compared to curves with radii 465.5 and 550 m. Analysis shows that wear has
decreased for 465.5 m curve after the first 8.576 MGT, then increased constantly at a
slower rate, and suddenly increased in the last accumulated MGT. This shows the
effectiveness of lubrication is better for curves with radii 550 and 465.5 m
respectively.
Rail Wear (mm^2/MGT) for accumulated MGT
0
20
40
60
80
8.576 9.233 9.101 9.586 9.438 9.496 9.478
MGT
Wear (mm
2̂/MGT)
465.5
500
550
600.2
Figure 5.36: Rail wear for curves with different radii
Further data is analysed for all the section between curves of radius 451 to 600 m,
using the Gaussian (Normal) distribution for better and accurate prediction of wear
rate and to estimate rail life. Curve fitting tools have been used to find our R2 and
166
RMSE for curves radius 451 to 600 m. Figure 5.37 shows a sample of curve fitting
analysis of actual and predicted data for accumulated MGT of a curve radius 500 m
for a particular location.
0 20 40 60 80 100 1200
50
100
150
200
250
300
Fit w
ith 9
5%
pre
d b
ounds
Analysis of fit "fit 1" for dataset "ahl8 vs. mgt"
fit 1
95% prediction bounds
ahl8 vs. mgt
Figure 5.37: Curve fitting for curve radius 500 m
Data is best fitted with Normal (Gaussian) distribution (Gauss2)
( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= where x is normalized by
mean 44.47 and std 39.46, Coefficients (with 95% confidence bounds):
a1 = 391 (-2922, 3704)
b1 = 3.332 (-29.04, 35.7)
c1 = 2.213 (-32.5, 36.93)
a2 = 20.85 (-1591, 1632)
b2 = 0.2542 (-21.21, 21.72)
c2 = 1.265 (-20.41, 22.94)
Goodness of fit: SSE: 323.8, R2: 0.9971, Adjusted R2: 0.996, Root Mean Square Error
(RMSE) 4.991. These results were further analysed using the distribution fitting tool
to find mean, variance and standard deviation for better prediction of the wear rate.
Data is best fitted with Gaussian (Normal) distribution and results are shown in Figure
5.38.
MGT
167
0 2 4 6 8 10 12 14 16 180
0.02
0.04
0.06
0.08
0.1
0.12
Data
Density
q data
fit 1
Figure 5.38: Gaussian distribution of the RMSE for curves radii 451-600 m
Therefore Mean of RMSE = 5.49596, Variance = 9.58875, Standard Deviation =
3.09657
Mean of RMSE is considered as wear rate for estimation of rail life and to analyse
lubrication effectiveness. For 451-600 m curve radii for accumulated MGT is 5.50
mm2/ MGT.
Estimation of rail life is as follows:
CETS limit for 47 kg rail size = 684 mm2
Measurement of area head loss for a particular curve section 66.265 to 67.004 for a
radius 600.20 m in year 2004 = 693 mm2
Wear rate = 5.50 mm2/MGT
Estimated actual rail life = 684 mm2/ 5.50 mm2/MGT = 124 MGT
Estimated rail life left = (684-693) mm2/ 5.50 mm2/MGT = -1.63 MGT
168
Area Head Loss (mm^2) for 47 kg Rail
0
150
300
450
600
750
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
506.5
553.2
600.2
Wear Limit
Figure 5.39: Area head loss for 47 kg
The analysis of comparison of area head loss (mm2) for 47 kg rail is shown in Figure
5.39. This shows that, according to the CETS standard, estimated new rail life for 47
kg size rail is approximately 124 MGT. Analysis shows that, for the section 66.265 to
67.004 of curve radius 600.20 m, the rail should be replaced immediately. Figure 5.24
shows it has crossed the wear limit and there is a high risk of rail break and
derailment involved. It shows poor performance and effectiveness of lubrication in
this section. It is also found that wear rate is constant for curve radius 553.2 m. This
may be an indication of good performance of lubrication in this section. For the curve
radius 506.50 m, wear rate has been increasing constantly, but at slower rate. Rail
condition can be improved with effectiveness of lubrication and operating conditions.
It is more economical to replace with new rail rather than overhauling old rail and
increasing risk of rail break and derailments.
CETS limit for 50 kg rail size = 866 mm2
Measurement of area head loss for a particular curve section 89.648 to 89.819 for a
radius 500 m in year 2004 = 638 mm2
Wear rate for last five year (2001-2004) = 16.73 mm2/MGT
Estimated actual rail life = 866 mm2/ 16.73 mm2/MGT = 52 MGT
Estimated rail life left = (866-733) mm2/ 8.38 mm2/MGT = 14 MGT
Analysis shows that, for the section 89.648 to 89.819 of curve radius 500 m, the rail
should be replaced immediately. Figure 5.38 shows it is close to wear limit and can
tolerate one more year with an average of 10 MGT under effective lubrication
performance and suitable operating conditions. It is more economical to replace with
169
new rail rather than overhauling old rail and increasing risk of rail break and
derailments.
CETS limit for 50 kg rail size = 866 mm2
Estimated actual rail life for 50 kg rail = 866 mm2/ 5.50 mm2/MGT = 157 MGT
Area Head Loss (mm^2) for 50 kg Rail
0
150
300
450
600
750
900
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm̂
2)
500
550
597
Wear Limit
Figure 5.40: Area head loss for 50 kg rail
Figure 5.40 shows the analysis of comparison of area head loss (mm2) for 50 kg rail
of different rail curve sections. According to the CETS standard, actual estimated rail
life for 50 kg size rail between 451-600 m curve radius is approximately 157 MGT. It
was found in the investigation that wear of actual and predicted data of rail curve with
radius 597 m is constant for an accumulated MGT. This may be due to superior
performance and effectiveness of lubrication in this section. For the curves radii 500
and 550 m, wear has constantly increasing with accumulated MGT. This may be due
to poor performance and effectiveness of lubrication. Rail life improved in these
sections with continuous monitoring of lubricator performance and rail condition
under effective operating conditions.
Area Head Loss (mm^2) for 500 m Radius
0
150
300
450
600
750
900
1998(8.576)
1999(9.233)
2000(9.101)
2001(9.586)
2002(9.438)
2003(9.496)
2004(9.478)
Year(MGT)
Area Head Loss (mm^2)
47 kg rail
50 kg rail
Wear limit 47 kg rail
Wear limit 50 kg rail
Figure 5.41: Area head loss curve radius 500 m
170
Figure 5.41 shows the analysis of area head loss of 500 m curve radius for different
rail size of 47 and 50 kg. It is observed that, in both rail size 47 and 50 kg, rail wear
has been constantly increasing at a lower rate and is significantly below the wear
limit. This shows that there is high quality of lubrication performance in these
sections. It was found in the recent research that rail degradation or loss of rail
material increases risk of rail breaks and derailments. This, in turn, increases cost of
rail maintenance to rail infrastructure owners. However, it is important to study and
understand the severity of damage and measure the risk due to these defects before
planning maintenance schedules. These defects may lead to increased rail and wheel
repair costs and increased risk of rail breaks and derailments. Reduction of rail side
and table wear with effective performance of lubrication and preventive grinding
maintenance methods, extends rail life. It is found that, with proper lubrication, it
would take at least two years to remove the amount of rail material that is removed in
one week of dry running (Kalousek, 1997). Excessive grinding maintenance intervals
reduce rail life and increase rail maintenance costs. It is important to achieve proper
effective lubrication strategies with optimal grinding intervals to reduce maintenance
cost and annual rail replacement costs, to enhance rail and wheel life and increase
safety of rail operation.
5.9 Analysis of Annuity Costs
Data was collected from survey and field observations to estimate the maintenance
cost of lubricator and rail wear costs. In this case, the cost and analysis is calculated
for wayside lubricators. Discounting factor is used, assuming 10% per year. Table 5.6
shows the costs of wayside lubricator.
171
Table 5.6: Costs of Wayside Lubricator
Item Cost (AUD $)
Purchase cost of Standard Wayside
Lubricator (37.5 kg)
AUD $ 4200
Solar Lubricator (including the overhead
cost and installing, excluding 2 solar
panels)
AUD$ 15968.50
Standard setup cost (labour cost) per hour AUD $ 50
Standard hours to set up lubricator 2 hours
Personnel required to set up lubricator 2
Grease per drum (One drum of lubricant
for a month is expected to lubricate
approximately 1600 m of track length.)
AUD $ 132.85
Lubricant cost per m (AUD$ 132.85/1600
m)
AUD$ 0.08303
Lubricant cost for 313 m track curve
length
AUD$ 25.98
Lubricant cost for 313 m track curve
length per year
311.86/year
Lubricant cost per kg AUD $ 4.5
Labour cost per hour for unplanned
maintenance
AUD $ 50
Vehicle cost per hour for unplanned
maintenance of lubricator
AUD $ 45
(For detailed data see Appendix B.) Activities involved and approximate time required to maintain lubricators are:
� Adjusting plunger/remove plunger (0.6 hours)
� Removing or positioning lubricator (2 Hours)
� Filling (0.6 hours)
� Tightening & retightening plunger (0.6 hours – 0.75 hours )
� Removing servicing pump & cleaning filter, nozzles (2 Hours)
� Travelling (Average 0.3125 hours for single way; total time is 0.625)
172
Generally, rail life of up to 10 years can be expected with effective lubrication and
proper maintenance. Worn-out rails are replaced at shorter intervals - approximately 5
to 6 years in sharp curves - due to lack of proper lubrication and maintenance. For
example, some sections of London Underground Rail have been replaced every 18
months instead of 18 years, even though lubricators are working properly
(Briginshaw, 2004). Effective lubrication can extend rail life up to 50% under optimal
operating conditions (Tuzik, 1996). Effective wayside and/or hi-rail lubrication
reduces gauge face wear substantially. Table 5.7 gives estimated rail life in heavy
haul, straight, and curved track (Cannon et al., 2003).
Table 5.7: Estimated rail lives in heavy-haul track (Cannon et al., 2003)
Curve Radius
Estimated rail life (MGT traffic)
Generally removal and installation of rails is costly and influenced by:
� Rail cost escalation rate (% per annum)
� Maintenance cost escalation rate (% per annum)
� Non –inflated discount rate (% per annum)
� Inflation rate (% per annum)
� Track maintenance cost ($AUD per track km)
� Track Grinding Cost ($AUD per track km)
� Rail Installation Cost ($AUD per rail km)
� Risk Cost/MGT/m ($ AUD)
� Down time cost/m ($AUD)
Data from industry show that
60 kg Rail for 110 m (HH) -----------------------------------AUD $7805.40
50 kg Rail for 110 m (SC) ----------------------------------- AUD $6592.40
Cost for installing or removing rail is approximately = AUD $ 175 per m
173
5.9.1 Numerical Example
Analysis of Standard Wayside Lubricator
Time to travel from depot to site and time to service the wayside lubricator = 2.3
hours. Curve radius of 236.7 m of a 50 kg rail (SC) for curve length of 313 m for
passenger traffic is considered for estimation of rail costs and benefits, with
lubrication and without lubrication.
Costs with Lubrication
50 kg Rail (SC) for one m = (6592.40/110) = AUD $ 60 per m
Cost for 313 m curve length of rail = (60*313) = AUD $ 18780
To install or remove rail for 313 m of curve length of 50 kg SC rail = (175*313) =
AUD $ 54775. Therefore, total cost of rail for 313 m of rail curve length =
(18780+54775) = AUD $ 73555. Then, the annuity cost of rail for 313 m rail curve
length for 10 years = AUD $ 66868.18. The annuity cost per m for rail = AUD $
213.64
Generally, lubricator maintenance takes place twice a month. Then, the total cost per
service = AUD $ 267.
The total unplanned maintenance cost per each failure = AUD $ 190
Total expected cost of service per year Cs = AUD $ 3202
Total standard setup cost Csc = AUD $ 400
Estimation of total cost of lubrication for 7 years = Investment of a lubricator +
Maintenance cost of lubricator + Lubricant consumption
Using equation 5.55, the annuity cost of lubricator to lubricate 313 m of rail section =
AUD $ 5665
Then, the annuity cost per m for 313 m curve length = AUD $ 18.10
Then, total annuity cost of rail with lubrication per m = (213.64+18.10) = AUD $
231.74
Costs without Lubrication
It is assumed that rail life without lubrication is 5 years and needs immediate
replacement. Total cost to replace 313 m of curve length of 50 kg SC rail for 5 years =
(18780+54775) = AUD $ 73555. Figure 5.42 shows analysis of lubrication and rail
replacement costs.
174
Figure 5.42: Analysis of lubrication costs
The annuity of rail without lubrication for 313 m of curve length of 50 kg SC rail for
10 years = AUD $ 99240.34
The annuity cost rail per m without lubrication for 313 m curve length of 50 kg SC =
AUD $ 317.06
The savings per m for rail of curve length 313 m of curve radius 236.7 m of 50 kg SC
with and without lubrication = AUD $ ( 317.06 – 231.74) = AUD $ 85.32 per m.
There is a huge difference between the costs of rail with lubrication and without
lubrication. The analysis shows that lubricating rails below 500 m curve radius
throughout the year can reduce rail replacement costs. It is also found that rail
replacement cost is much higher without lubrication and it affects the total rail
maintenance costs and also wheel maintenance costs.
Analysis of Solar Wayside Lubricator
Time to travel from depot to site and time to service the solar lubricator = one hour.
Analysis of solar wayside lubricator for curve radius of 236.7 m of a 50 kg rail (SC)
for curve length of 313 m for passenger traffic is considered for estimation of rail
costs and benefits with lubrication and without lubrication.
Costs with Lubrication
50 kg Rail (SC) for one m = (6592.40/110) = AUD $ 60 per m
Cost for 313 m curve length of rail = (60*313) = AUD $ 18780
Wear rate [mm2/MGT]
300 600 900 1200
Bad lubrication, un-lubricated
Good lubrication, lubricated
Increased rail life – saving costs
Investm
ent in lubrication (AUD$)
73555
147110
220665
275831
Wear rate [mm2/MGT]
300 600 900 1200
Bad lubrication, un-lubricated
Good lubrication, lubricated
Increased rail life – saving costs
Investm
ent in lubrication (AUD$)
73555
147110
220665
275831
175
To install or remove rail for 313 m of curve length of 50 kg SC rail = (175*313) =
AUD $ 54775. Therefore, total cost of rail for 313 m of rail curve length =
(18780+54775) = AUD $ 73555. Then, the annuity cost of rail for 313 m rail curve
length for 10 years = AUD $ 66868.18. The annuity cost per m for rail = AUD $
213.64
Generally, lubricator maintenance takes place twice a month. Then, the total expected
cost of service = AUD $ 145
The total unplanned maintenance cost per each failure = AUD $ 190
Total expected cost of service per year Cs = AUD $ 1740
Total standard setup cost Csc = AUD $ 400
Estimation of total cost of lubrication for 7 years = Investment of a lubricator +
Maintenance cost of lubricator + Lubricant consumption
Using equation 5.55, the annuity cost of lubricator to lubricate 313 m of rail section =
AUD $ 3429.47
Then, the annuity cost per m for 313 m curve length = AUD $ 10.96
Then, total annuity cost of rail with lubrication per m = (213.64+10.96) = AUD $ 224.
60.
Costs without Lubrication
It is assumed that rail life without lubrication is 5 years and needs immediate
replacement. Total cost to replace 313 m of curve length of 50 kg SC rail for 5 years =
(18780+54775) = AUD $ 73555.
The annuity of rail without lubrication for 313 m of curve length of 50 kg SC rail for
10 years = AUD $ 9240.34
The annuity cost rail per m without lubrication for 313 m curve length of 50 kg SC =
AUD $ 317.06
The savings per m for rail of curve length 313 m of curve radius 236.7 m of 50 kg SC
with and without lubrication = AUD $ ( 317.06 – 224.60 ) = AUD $ 92.46 per m. The
analysis shows more savings with solar lubricator than standard wayside lubricator.
This may vary with number of failures and operating and environmental conditions.
Is lubrication cheaper than wear?
It is important to determine the cost of area head loss of the rail to assist the track
practitioner to measure annual budget costs.
176
For 50 kg rail SC, the percentage of area head loss allowable is 32 % (or 866
mm2)from the total area of head which is 2680 mm2. It is mentioned that the cost to
purchase 50 kg Standard Carbon rail of 110 m length is AUD $6592.40. In this case,
curve radius length and size affected the cost of area head wear. Figure 5.43 shows
wear progression for curve radius 236.7 m, from 1997 to 2004.
Area Head Loss for curve radius 236.7 meter (97 - 04)
0
150
300
450
600
750
900
1997 1998 1999 2000 2001 2002 2003 2004
Year (MGT)
Area Head Loss (mm^2)
Limit of Rail Head Wear 857.6 mm 2̂ 50 kg SC
Figure 5.43: Wear progression for curve radius 236.7 m from 1997-2004
Civil Engineering Track Standard (CETS) noted that 50 kg SC rail was allowed to
wear 32% of total area head (2680 mm2), which is 866 mm2. That is:
% Reduction Area Head Loss x Cost Rail Length = 32% x 18777.00 = AUD $6008.64
Total Area Head Loss for 50 kg SC rail (866 mm2) is AUD$ 6008.64
Cost of Area Loss per mm2 = AUD $ 6008.64 ÷ 866 mm2 = AUD $6.93/ mm2
Figure 5.50 shows that there is 2% of increment in area head loss for an average of
7.9 MGT per year. Then, 2% of total area head loss of 50 kg SC 313 m length = 0.02
x 2680 = 53.6 mm2
Therefore, the total cost of losing 53.6 mm2 = 53.6 mm2 x AUD $6.93/ mm2 = AUD
$371.448. The cost for accumulated area head loss for 7 years = AUD$ 371.448 x 7
= AUD $2600.136
Therefore, savings can be calculated by subtracting Total Area Head Loss for 50 kg
SC rail (866mm2) is AUD$ 6008.64 to Total Area Head Loss for 50 kg SC rail in 7
years (AUD $2600.136) which is AUD $ 3408.504. The analysis found that the
annuity cost of 37.5 kg standard wayside lubricator is AUD $ 10562.98 for the curve
radius of 236.7 m radius. According to the CETS standards, the curve is only allowed
to wear at 32% from the total area head which is 866 mm2. The total cost of 32% wear
177
limit is AUD $6008.64 for that curve length of 313m. However, questions arise from
this analysis:
� Can savings be made if the wayside lubricator could lubricate more than one
curve?
� What is the distance the grease travels and what is the cause of this mobility?
� How does the wheel profile affect the savings?
� Can maintenance of the lubricators ensure savings?
For solar lubricator, savings can be achieved if the lubricator can lubricate more than
3 curves. The annuity cost solar lubricator is AUD $ 6091.228 and to achieve savings,
it has to lubricate effectively at least 5 curves (of 313m length) because, for every 313
m length of curve, the limit rail cost AUD $ 6008.64.
This analysis shows that lubrication is cheaper than wear but it depends on the cost of
the lubricator, maintenance activity and number of curves requiring lubrication to
cover the purchase cost, setup cost and maintenance cost. Maintenance cost can be
reduced by using the solar lubricators. Table 5.8 shows savings that can be achieved.
Table 5.8: Savings achieved
Lubricator Type Radius Curve No of Curves to Achieve
Savings
Standard Wayside
lubricator (37.5 kg)
< 500 m 2
Solar Wayside lubricator <500 m More than 5
On Board <500 m Unknown
Hi Rail <500 m Unknown
Due to the limitation of the data, standard wayside lubricator and solar wayside
lubricator costs and benefits were analysed. It was found that solar lubricators are
more economical than standard wayside lubricators. These savings vary with
environmental and operating conditions.
5.10 Summary
Modelling and analysis of rail wear, rail wear limit and lubrication are discussed.
Economic models are developed for lubrication decisions. A framework for
benchmarking lubrication effectiveness is proposed in this chapter. Data collected
178
from rail industry is used for illustration. Modelling of failures and renewal of
lubricators is carried out. A simulation model for analysis of lubrication effectiveness
is developed. Cost-benefit analyses of lubricators and annuity costs of lubricators are
estimated for managerial decisions. The analysis shows that cost effectiveness of the
lubricator depends on the numbers of curves it lubricates and the length of curve. It
also provides guidelines for installation and maintenance of lubricators. Rail area head
loss and rail wear data are analysed to determine rail life and evaluate the
effectiveness of lubrication decisions. Real life rail wear data was collected from
industry for analysis of 0-600 m curves. For better prediction and estimation of wear
rate for various curves, Gaussian (Normal) distribution and curve fitting methods have
been used. Prediction of rail life and lubrication effectiveness is analysed. The
specific outcomes of this chapter are:
� Lubricator failures are modelled with non-homogenous Poisson process
� Data analysis found that higher wear in 50 kg rails for curve radii from 0 – 300
m and need immediate replacement or repair to avoid risk of rail break or
derailment
� Cost-benefit analysis of lubricators for standard wayside lubricator and solar
wayside lubricator were estimated. The analysis found that solar wayside
lubricators are economical and more effective than standard wayside
lubricators. It is found that solar lubricators save 17% more than standard
wayside lubricators.
� A simulation model for analysis of lubrication effectiveness estimation of
wear and lubrication costs is proposed
� A relative performance model, total curve segment model and above rail and
below rail model are proposed
Modelling of inspection intervals for rail testing methods are discussed in Chapter 6.
Integration of rail grinding, lubrication and inspection models considering operational
risks will be discussed in the subsequent chapters.
179
CHAPTER 6
MODELLING AND ANALYSIS OF INSPECTION FOR INSPECTION
DECISIONS
6.1 Introduction
Modelling and analysis of wear, lubrication decisions and a framework for
benchmarking lubrication effectiveness are discussed in Chapter 5. This chapter
focuses on the development of an inspection model, analysis of rail failure data and
reliability of inspection technology for optimal inspection decisions. Real life data are
collected from industry for analysis. Ultrasonic rail inspection including manual
verification, costs around € 70 million per year for 0.5 million kilometre track system
(Cannon et al., 2003). These costs do not include derailment costs. There is a need to
develop models and analyse costs for inspection to reduce economic pressure due to
the number of broken and defective rails and derailments.
The outline of this chapter is as follows: Modelling of inspection, rail breaks,
replacement costs of worn-out unreliable rails and cost benefit analysis are discussed
in Section 6.2; modelling and analysis of rail defects using failure mode and effect
analysis (FMEA) and risk priority number (RPN) are presented in Section 6.3;
collection and analysis of rail failure data, rail defect initiation, rail failures, cost-
benefit analysis of inspection and derailment are discussed in Section 6.4; Section 6.5
discusses the total cost of rail inspection and rectification; limitation of detecting rail
breaks by signalling system is discussed in Section 6.6; the effect of seasonal
conditions is discussed in Section 6.7; finally, summary, conclusion and results are
presented in Section 6.8
6.2 Modelling Inspection
Inspection is carried out at predetermined intervals. An inspection cost model is
developed using MGT interval. Let If be the inspection per MGT and ic be the cost of
each inspection. Then, annual inspection cost over the rail life is given by:
( )
+−
∗
+= ∑
=
N
N
j
j
i
c
i
r
r
r
iC
I
1
11
11
(6.1)
180
where
=
f
NI
I
MIntegerN and ri is discounting rate associated with interval of non
destructive testing (NDT).
Let c denote the expected cost of each rail break repair on an emergency basis. Let k
be the expected cost of repairing potential rail breaks based on railhead area, RCF and
speed of train. Let a be the expected cost per derailment. The risk cost associated with
rail break and derailment is based on railhead area, RCF and speed of train. Let Pi(A,
Fatigue, s) be the probability of undetected potential rail breaks leading to
derailments based on rail head area, RCF and speed of train. Pi(B) is the probability of
detecting potential rail breaks based on rail head area, fatigue and speed of train.
Rolling contact fatigue (RCF) is given by Million Gross Tonnes (MGT). Railhead
area is determined by wear and preventive rail grinding, based on MGT. When
expected number of failures are modelled as Non Homogeneous Poisson process and
is given by E[N(Mi+1, Mi), then the risk cost is given by:
( )[ ] ( ) ( )( ) ( ) ( )( )( )[ ]( )
( )
+−
∗
+
−+∗∗−+∗∗= ∑
=+
N
N
ii
iiii
iir
r
r
r
cSFatigueAPaSFatigueAPBPkBPMMNEC
1
11
1
,,1,,1,
01
(6.2)
6.2.1 Modelling Rail Breaks
In this study, failures are modelled as a point process with an intensity function Λ(m),
where m represents Millions of Gross Tonnes (MGT) and Λ(m) is an increasing
function of m, indicating that the number of failures in a statistical sense increases
with MGT. That means that older rails with higher cumulative MGT passed through
the section, are expected to have more probability of initiating defects and, if
undetected, then further passing of traffic can lead to rail failures. As a result, N(Mi+1,
Mi), the number of failures over Mi and Mi+1, is a function of MGT, m, and is a
random variable. Let cumulative MGT of rail till inspection by NDT car, m, be
known, and Fn(m) denote the cumulative rail failure distribution, modelled as Weibull
distribution given by:
))(exp(1)( βλmmFn −−= (6.3)
with the parameters β (known as shape parameter of the distribution) > 1 and λ
(known as inverse of characteristic function for the distribution)> 0
181
When β is greater that 1 it indicated that there is increasing failure rate of the item
under study and ageing is predominant in failure mechanism (Chattopadhyay et. al.,
2003). Then failure intensity function Λ(m) is derived from (1) and is given
by 1)( −βλλβ m . Rail track is normally made operational through repair or replacement
of the failed segment and no action is taken with regards to the remaining length of
the whole track in case of detected defects and rail breaks. Since the length of failed
segment replaced at each failure is very small relative to the whole track, the
rectification action can be viewed as having negligible impact on the failure rate of
the track as a whole. Then the expected number of failures over period i and (i+1) is
given by:
))()(()],([ 11βββλ iiii MMMMNE −= ++ (6.4)
where the total accumulated MGT up to ith inspection, Mi, is given by:
∑=
=i
j
ji mM0
(6.5)
6.2.2 Modelling Replacement Costs of Worn-out Unreliable Rails
Let cre be the expected cost of replacement for segment L and consist of labour,
material, equipment, consumables and down time cost for rail replacement. Let I be
the cost of current investment in new rail. Cost of replacement is assumed to be
occurring at the beginning of each year and is simplified as the annual cost of
investment for new rails. Then cre is given by:
( )
( )
+−
+∗
=
N
re
r
r
rI
C
1
11
1 (6.6)
6.2.3 Modelling Cost Benefit Analysis
Cost benefit analysis is modelled based on demand and supply for the year j. Revenue
of the organisation depends on supply Suj and the operating condition of the rail head
area, fatigue, and speed of the train. When travel time (t) is variable and based on
speed s, then t is given by t = L/s
Supply is given by Suj = min {Dj, (Fj/t) * Wagonv * n} (6.7)
Then, net present value (NPV) over rail life is given by
182
( ) tot
N
jj
jv
j Ci
Cs
L
nWagonv
SuNPV −
+
∗
∗
−
∗= ∑=1 1
.
1Re
(6.8)
6.3 Failure Mode and Effect Analysis (FMEA)
Failure mode and effect analysis (FMEA) enables the recording and monitoring of
information regarding actual and potential failures, failure causes and effects. A Risk
Priority Number (RPN) for each rail defect is analysed based on assessment of
severity of failures, frequency of occurrence, probability of detection of failures. A
higher RPN indicates that the defect is more critical. Data from Railtrack (UK), SNCF
(French Railways), HSPC (North American High Speed Passenger Corridor), NS
(Netherlands Railways), EJR (Japanese Railways), Banverket North Region
(Sweden), Spoornet (South Africa), HH1 and HH2 (North America Heavy Haul) are
analysed in this paper (Sawley and Reiff, 2000). Rolling Contact Fatigue defects
(squats, shells, head checks, horizontal and vertical head split, wheel burns)
associated with increased axle load (transverse defects and broken base) and defects
associated with welding (thermite weld and flash weld defects) are analysed. Some of
the limitations of the current data are:
1. Track mileage is not always known accurately.
2. Each railway track classification system and method of collecting traffic data is
different.
3. Railways may use different definitions for “defects” and “breaks” and reporting
may be more or less accurate. Railways have different types of traffic and thus
have different types of defects. This is especially the case for the heavy haul
railroads, which run more slowly (typically 30 to 60 mph) and much heavier
traffic (often 286,000-pound cars) compared to passenger lines.
4. Railways have many different populations of rail age (i.e. a newer railway with
higher renewal frequency ought to have fewer defects and breaks than an older
established railway).
Due to problems in comparing the performance of railways with different types of
traffic and methods of quantifying, the data is summarized largely on the basis of the
numbers of defects and rail breaks per track mile. Tables 6.1 & 6.2 explain the
183
common causes of rail defects and rail breaks of various railway networks around the
world.
Table 6.1: Causes of Defective Rails (Sawley and Reiff, 2000)
Railway First Second Third Fourth
Table 6.2: Causes of Broken Rails (Sawley and Reiff, 2000)
Railway First Second Third Fourth
6.3.1 Occurrence of Failure
The estimation of likelihood of occurrence of potential failure is graded on a scale of
“1-10”. The lowest number in the scale indicates the lowest probability of occurrence.
The analysis shows that RCF and Thermite weld problems are contributing at a higher
184
percentage, leading to the probability of a high risk of rail breaks and derailments.
The defects are ranked according to Hasting (2000), revised using executive
judgement, and presented in Table 6.3.
100*%soccurrenceofnumberTotal
defectforoccurrenceOccurrence=
(6.9)
Table 6.3: Ranking of Failure Occurrence (Reddy et al., 2004)
Probability of failure Defects Occurrence of
each defect
%
occurrence
Table 6.3 shows the analysis of rail defect occurrence. The ranking of these defects
can be used to estimate the likelihood of occurrence of those potential failures which
cause risk of rail breaks and derailments. The analysis enables the inspection crew to
estimate the frequency of occurrence of each failure and to decide upon the optimal
maintenance solution. The probable solution may be speed restriction, and temporary
or permanent repair to avoid the risk of heavy revenue losses.
6.3.2 Detectability of Failure
Detectability of failure establishes the cause/mechanism/weakness of actual or
potential failure which can be graded on a scale of “1-10”. The lowest number in the
scale indicates high probability of detecting a failure. The ratio of broken to defective
rails is a measure of the efficiency of ultrasonic inspection. A low ratio implies that
185
defects are being found and removed before rail breaks. The analysis shows that
thermite welds and broken base have a high ratio and are least able to be detected by
inspection. These defects are ranked according to detectability of the failure rating
table (Leitch, 1995), revised in line with the technique mentioned earlier in the
occurrence section, and shown in Table 6.3. Table 6.4 shows the detectability ranking
of failure, with broken base having the highest rank; this indicates least detectability
of defects by ultrasonic inspection. Rail players need to increase frequent visual
inspection to avoid undetected broken base defects.
100*det
%ratioectabilityTotal
defecteachofratioityDetectabilityDetectabil = (6.10)
Table 6.4: Ranking of Detectability (Reddy et al., 2004)
Detection Chance that failure mode will
be detected by control Defect
Detection
ratio Rank
Recent research in the UK shows that the current technology can detect rail defects of
20% to 25% size with high reliability. After a section of track has been inspected, it is
likely that some defects above the 25% size will remain undetected on the track and
continue to grow. If the next inspection does not occur in a reasonable time, the
186
likelihood of a break is high (Sawley and Reiff, 2000). The increase of inspection
frequency increases the likelihood of detection of undetected defects and can prevent
the risk of rail breaks and derailments.
6.3.3 Severity of Failure
The severity of failure is the assessment of the seriousness of the defect of the actual
and potential failure mode if it occurs. Severity is estimated on a “1-10” scale with the
lowest number of the scale indicating minor concerns. The classification of severity
level is a subjective value and it needs to take into account the system failure mode,
the possible degree of damage and financial loss, and the risk of injury or maybe even
death to the operator and other personnel (Leitch, 1995). Table 6.5 shows train
accident data from Federal Railroad Administration (FRA) (USA) from 2001 to 2003
and the number of derailment by each defect type. For the ranking of the severity
level, it is assumed that the casualty (people killed is ranked higher compared to
injured) has been caused by the defect derailment. If there is no casualty reported,
then the ranking is done based on the number of derailments caused by the defect
type.
Table 6.5: Train Accidents Jan 2000 - Dec 2003 (Orringer, et al., 1999)
Total Type of Accident Damage Casualty
187
Table 6.6: Severity Ranking of Failure (Reddy et al., 2004)
Total Type of accident Casualty
Table 6.6 shows the analysis of severity of failure ranking. Thermite fissure, RCF,
horizontal split head and weld defects and bolt holes are ranked with high severity. It
also indicates that severity of rail defects varies from location to location.
188
6.3.4 Risk Priority Number Ranking (RPN)
RPN is the product of severity, occurrence and detection, as shown in Table 6.7.
Analysis shows that thermite weld, transverse defects, shells/squats/head checks and
broken base are in the top four ranking for critical failures. Identification of critical
failures provides the probability of occurrence, detectability and severity to analyse
the consequences of each defect.
Table 6.7: Risk Priority Number (RPN) ratings
Rank Defects Occurrence Detectability Severity RPN (O x D x S)
1 Thermite weld 9 2 9 162
2 Transverse defects 8 2 10 160
3 Shells/Squats/Head Checks 8 2 9 144
4 Broken base 4 5 7 140
5 Bolt hole defects 6 2 9 108
6 Horizontal split head 8 1 9 72
7 Vertically split head 8 1 7 56
8 Head/web defects 6 1 9 54
9 Wheel burn 6 2 4 48
10 Flash weld 5 1 9 45
11 Rail manufacture 4 2 4 32
Total 1021
Figure 6.1: Rail defects occurrence
Figure 6.1 shows the analysis of rail defects occurrence. It indicates that 27% of risks
of occurrence of rail breaks or derailments are due to thermite welds, 25% due to
transverse defects, RCF, horizontal split head and vertical split head.
Rail defect occurrence using RPN
TW27%
TD, RCF, HSH, VSH25%
BH, WB, HWD19%
BB, RM13%
FW16%
189
Figure 6.2: Rail defects detectability
Figure 6.2 shows the analysis of rail defects detectability. It indicates the high
probability of risk due to undetected rail defects (such as broken base) during the
inspection. Figure 6.3 shows the analysis of severity of rail defects. It indicates the
high probability of risk due to severity of undetected defects such as thermite welds
and RCF during the inspection.
Figure 6.3: Rail defects severity
Figure 6.4: Proposed model for risk mitigation of rail defects
Reduce risk of rail breaks and derailments, downtimes, loss of lives, property and revenue
Reduce occurrence of rail defects
Increase of Detectability of rail defects
Reduce intensity of severity of rail defects
Detectability of rail defects using RPN
BB62%
HSH, VSH, HWD, FW13%
TW, TD, RCF, BH, WB, RM
25%
Severity of rail defects using RPN
TW34%
WB, RM13%
BB, VSH23%
TD, RCF, BH, HSH, HWD, FW30%
190
Figure 6.4 shows the proposed model for risk mitigation of rail defects. This method
can be used for corrective and preventive measures, based on continual analysis. The
magnitude of the defect, length of defect, time phase of defect propagation, and
mitigating factors (such as consequences of derailment/accident due to each defect)
need to be considered for detailed analysis.
6.4 Collection and Analysis of Rail Failure Data
Here we assume rails are inspected by means of non destructive testing. Data
collected from the industry is from NDT inspections and followed by handheld
inspection for validation. The probability of detectable defects developed in the rail
for known MGT at inspection and accumulated MGT before next inspection, is
determined and analysed. Rail breaks are detected by signalling system and inspection
and derailment data are analysed for known MGT.
In spite of preventive grinding programs and frequent onboard non-destructive
measurements, rail breaks happen. Factors such as weld joints, rail geometry, wheel
burns, and corrugation contribute to the risk. The cost of unplanned replacements due
to these problems is considered as a risk cost. For an infrastructure player, it is
essential to monitor and control these risks by implementing cost effective traffic and
maintenance management strategies. Questions commonly asked are:
• How much is the current risk of derailment in a specific track section?
• Will it change with changed operating, traffic and maintenance activities?
• What is the cost/benefit ratio of these factors?
6.4.1 Rail Defect Initiation
In last few years there has been a tremendous increase in annual traffic volumes. This
has influenced the significant increase in number of defects on existing railways.
Figure 6.5 shows the increase of rolling contact fatigue related defects (such as
horizontal head crack and tache ovale) due to the increase of traffic and axle loads and
million gross tonnes (MGT) (Marais and Mistry, 2003). Data analysis shows that
horizontal head crack defects are severe compared to tache ovale.
191
Figure 6.5: Rolling contact fatigue defects (Marais and Mistry, 2003)
Detectability of initiation, size and depth of sub surface initiated defects, depends on
the orientation and location of the defect, reliability of the inspection equipment and
processes and skill of the inspection personnel. The determination of crack length and
crack growth rate of defect depends on the ultrasonic testing method used, rail and
probe temperature, the efficiency of sound transmission of the couplant between the
ultrasonic probe and the rail, and even the stress level in the rail. Initiation of sub
surface defects depend on the rail degradation, rail material condition, age of the rail,
size of the rail, accumulated tonnage and axle loads passed though the rail
(Chattopadhyay and Reddy., 2007). The analysis includes:
� Initiation and occurrence of rail defect
� Progression to critical stage resulting in rail breaks due to traffic loading
� Expected number of critical defects between inspections
� Expected number of detections of probable defects using ultrasonic testing cars
and subsequent validation by hand held device
� Expected number of undetected defects for various inspection strategies
� Expected cost of rectifications, rail breaks and derailments for various alternative
strategies.
� Estimation of ageing in terms of MGT of traffic passed through the line
� Analysis of effect of grinding campaign by comparing the data before 1997 and
after 1997
It was found in the research that probable errors in ultrasonic detection are:
� Rail area scanned by 0º probe
192
� Rail area scanned by transverse 45º probe
� Rail area scanned by 70º probe
� Rail area scanned by 35 - 45º probe
(a) (b)
(c) (d)
Figure 6.6: Error in ultrasonic (NDT) inspection (Chattopadhyay et al., 2005)
Figure 6.6 shows error in ultrasonic non destructive (NDT) inspection. As ageing
takes place in the line, due to tonnage accumulation on track resulting from traffic
movement. Rail defects are developed due to the steel, axle load, maintenance of rail
and wheel and contact fatigue. The number of defects expected for a given rail and
MGT till inspection with a predictable MGT before next inspection due to traffic flow
is modelled using Weibull distribution.
6.4.2 Rail Failures from Defect Initiation
It is realistic to assume that initiated defect left in the system will continue to grow in
size with increase in cumulative MGT. This research estimates the expected number
of undetected defects in the system with probability for rail breaks. With increased
193
inspections per year, the expected number of undetected defects with high probability
of resulting failure leading to rail breaks and derailments, are reduced. A model for
cost benefit analysis is developed to examinine the effectiveness of various inspection
frequencies in reducing risk and cost. Figure 6.7 shows the analysis of NDT and
visual inspection of rail.
Figure 6.7: Analysis of NDT and visual inspection of rail
6.4.3 Cost-Benefit Analysis of Inspection Frequency
Currently, inspection is done annually by most rail owners. In cold countries such as
Scandinavia, inspection is carried out twice per year, especially in cold climatic
places. These tests do not take into account the ageing of rail, type of the rail and
defect history. The detectable defect data and rail failure data can be used for Weibull
parameter estimation. Data analysed from Scandinavian countries, showed that failure
rate is higher in winter compared to that in summer. Maximum allowable defect size
was analysed by experienced ultrasonic testing personnel for defect validation based
on test car data and, subsequently, by Hand Held ultrasonic equipment analysis of the
locations identified by test cars.
Rail defects�Shells/Squats/Head Checks
� Thermite weld
� Transverse defects (HSH, VSH)
� Broken base
� Bolt hole defects and Head/web defects
Inspection of Rail
-
Non destructive testing (NDT)
Handheld equipment
Defect is critical Defect is not critical Defect is minor
1 2 3
Either
rectify or
repair
Cost depends
repair and
operating
conditions
No need for immediate
replacement
Need to estimate the
time length for criticality
Rail break
Derailment
Risks
Minor break
Costs
Major break
Minimal Huge cost (millions)
Damage depend on
Speed axle load, MGT
Huge cost (in millions)
Loss of lives
Down time
Property Damage
Service DisruptionImmediate repair or
replacement
-
This involves huge cost
Ineffective
� Lubrication
� Grinding
� Inspection
� Maintenance
Strategies
� How to prevent rail breaks and derailments?
� How to reduce costs due to these defects?
Detected
Not detected
Rail defects�Shells/Squats/Head Checks
� Thermite weld
� Transverse defects (HSH, VSH)
� Broken base
� Bolt hole defects and Head/web defects
Inspection of Rail
-
Non destructive testing (NDT)
Handheld equipment
Defect is critical Defect is not critical Defect is minor
1 2 3
Either
rectify or
repair
Cost depends
repair and
operating
conditions
No need for immediate
replacement
Need to estimate the
time length for criticality
Rail break
Derailment
Risks
Minor break
Costs
Major break
Minimal Huge cost (millions)
Damage depend on
Speed axle load, MGT
Huge cost (in millions)
Loss of lives
Down time
Property Damage
Service DisruptionImmediate repair or
replacement
-
This involves huge cost
Ineffective
� Lubrication
� Grinding
� Inspection
� Maintenance
Strategies
� How to prevent rail breaks and derailments?
� How to reduce costs due to these defects?
Detected
Not detected
194
• Rail Defect History Data (NDT testing Car and Service Defects)
• Location
• Type
• Date Found
• Rail Replacement History
• Location
• Date Installed, date manufactured
• Size (Kilogram per Metre), Steel Grade
• Ageing in terms of MGT
• Annual MGT assumed is 23 on average and is multiplied by the number of
years that portion of rail is in operation since last replacement
• Number of NDT car inspections per year (1, 2 or 3)
Rail segments were based on rail replacement data from rail industry in Scandinavia.
The expected number of defect initiation and failures are estimated using the model.
Current practice is documented and a process map is developed after data collection
and interviews with inspection and maintenance personnel (Chattopadhyay et al.,
2005).
1. Measurement cars for rail geometry and surface quality
2. Non Destructive Testing (NDT) cars for ultrasound inspection, measuring
internal cracks and probable rail breaks
3. Hand held ultrasound testing to verify identified weak spots by NDT cars
4. Rectification of identified defects by cutting rail segment and welding a new
rail segment using a preventive maintenance programme. In winter, a
temporary rectification is carried out first, using fish plate concept and is
inspected every two weeks to monitor and control risk. The segment is
permanently welded at the end of the winter.
5. Undetected cracks and probable rail breaks can lead to rail breaks
6. Some of the railbreaks are detected through signalling systems. Emergency
rectification is carried out following the procedure explained in Step 4.
7. Some of the rail breaks undetected by signalling system, cracks and probable
rail breaks, are detected by visual inspection. These are picked up by drivers,
passers-by and rail inspectors.
195
8. Undetected rail breaks by NDT, visual and signalling systems, can lead to
derailments. Emergency rectification is carried out following the procedure
explained in Step 4.
Figure 6.8: Process map of rail inspection (Chattopadhyay et al., 2005)
Figure 6.8 shows the process map of rail inspection and rectification. PM=Preventive
Maintenance, CM=Corrective Maintenance, HH=Inspection using Hand Held
ultrasound testing device.
6.4.4 Analysis of cost data
Relevant costs for this analysis are taken from the rail industry in Scandinavia and
other published documents (Chattopadhyay et al., 2005):
• Cost of ultrasonic inspection (u): For 130 km = AUD $ 12,375
196
• Cost of hand held inspection (h) test to run is AUD $ 1320 /day. (Can inspect 7 to
10 detected cracks per day, depending on travel time and access to track)
• Cost of physical visual inspection (v) AUD $ 1320 /day
• Cost of planned repair (k) AUD $ 4,950 /break
• Cost of emergency unscheduled repair (b) is Subcontracting price - Emergency
rail break rectification is AUD $ 990 + permanent fixed cost AUD $ 4950 +
maintenance control of the emergency rectification AUD $ 743 in total AUD $
6683 /rail break
• Cost of regular inspection of temporary repairs (d) AUD $ 743 /break per site for
the winter
• Cost of temporary repair and full repair at convenient time (w), done in two stages
6683 + 743 for regular inspection = AUD $ 7,425 for emergency
• Cost of derailment (a); [The average cost is between AUD $ 428,980 to AUD $
577,472 depending on time of year (more expensive in winter) and how many
wheels and wagons are damaged. Need to estimate average and variance based on
historical data, including life loss and injuries. It could approximate AUD $
2,474,880, including human loss and injuries.]
6.4.5 Analysis of selected defect, rail break and derailment
Data on detection of rail defects using ultrasonic system, hand held device, signalling
system, visual inspection, rail breaks and derailments linked to cracks, are collected
for analysis. Data from detected defects using Hand Held Devices are analysed to
estimate the probability of detecting defect with potential for failure before next
inspection. Defect developed later, or undetected during inspection, can result in rail
break. Some rail breaks are detected by signalling system. Some undetected breaks
are detected by visual checks. Balance of undetected rail breaks can result in
derailment (Chattopadhyay et al., 2003). Probability of rail break between inspections
depends on the probability that the detectable defect was present at the time of
inspection but remained undetected; the developed defect then grows into rail break
before the next inspection. Expected detectable defects with potential for rail breaks
in between MGT for various inspection frequencies, are estimated. Cost Benefit
Analysis of those inspection frequencies for one, two and three per year is carried out
(Chattopadhyay et al., 2005).
197
Data for incidents (1999-2004)
Item Numbers
Derailments 2
Detected through Ultrasonic NDT inspection 27
Detected through signalling 23
Detected through NDT HH 474
Rail break data and detected defects (using NDT Hand Held for incidents with
information on last replacements) are used for MGT. Time between incidents and
year of last replacements is multiplied by 23 MGT per year for analysis. Figure 6.9
shows a block diagram of rail inspection and detection. Figure 6.10 is a Venn diagram
of inspection, rail breaks and derailment (For detailed data, see Appendix B).
Figure 6.9: Block diagram of inspection and detection (Chattopadhyay et al.,
2005)
198
Figure 6.10: Venn diagram of inspection (Chattopadhyay et al., 2005)
6.4.6 Limitations of data
Accurate data for NDT car, calibrations and confirmation by Hand Held, is used for
analysis (Chattopadhyay et al., 2005). Technology has limitations and some defects
remain undetected due to location and orientation in the rail. Estimation can be
possible by destructive testing of replaced rails.
α = error of NDT not detecting defects where there is a defect
NDefcal = Number of defects correctly picked up in calibration
NDeftot = Total number of defects in the test rail
−=
tot
cal
NDef
NDef1α = 11.5% to 19.2%
During the inspection, 3 out of 26 tests in calibration were not detected and 2 more
defects (close to other defects) were detected as one defect. Without considering the
second category, the total number of defects not detected accurately by NDT car in
calibration is 3 out of 26 known defects. Considering the second category, 5 out of 26
known defects were not picked up accurately.
Φ = error of NDT car finding defects where there is no defect
NDefHH = Number of defects verified by Hand Held
NDeftot (NDT car) = Number of Defects identified by NDT Car
( )
−=Φ
NDTcartot
HH
NDef
NDef1 = 30.2%
199
There is inconsistency in data of defects detected by NDT car and validated by Hand
Held NDT equipment for the years 1999 - 2004. However, 2002 data appears to be
reasonably consistent with other rails around the world and is considered for analysis.
It is found in the analysis that the total number of defects detected by NDT car is 119,
and the number of defects validated by NDT Hand Held equipment is 83
(Chattopadhyay et al., 2005).
6.5 Total cost of rail inspection and rectification
Costs associated with rail inspection and rectifications are estimated. The total cost of
inspection and rectification of rail is equal to the sum of costs for: ultrasonic
inspections using non destructive testing (NDT) cars; Hand Held NDT verification;
rectifications based on NDT (planned rectification cost); repair of rail breaks detected
by signalling and inspection; inspections detecting rail breaks undetected by
signalling system, inspection of temporary rectifications during winter; rectification of
defects temporarily in winter and finally in summer; and derailments. Figure 6.11
shows the pie-chart for preventive and corrective rail breaks. Figure 6.12 shows the
pie chart for detected rail breaks and derailment (Chattopadhyay et al., 2005).
Percentage of rectification (1999-2004)
Corrective Rail
break, 10.36%
Deraiment,
0.38%
Preventive,
89.27%
Figure 6.11: Pie chart for preventive, corrective (rail breaks)
Detection of rail breaks
Signaling
system
40%Visual
Inspection
56%
Deraiment
4%
Figure 6.12: Pie chart for detected rail breaks and derailment
200
Table 6.8: Cost Benefit Analysis (Chattopadhyay et al., 2005)
Inspection Frequency per year
201
Table 6.8 shows the cost benefit analysis for inspection intervals. Total risk costs
considering different derailment costs, and for one, two three inspection intervals, are
estimated. These costs include inspection of non destructive testing (NDT) by car and
inspection of non destructive (NDT) Hand Held (HH) equipment. Probability of
derailment, probability of detection by signalling and probability of visual inspection
are modelled with non homogenous poisons process. Failures are found with Weibull
distribution. The analysis shows that two NDT runs per year is cost effective and
economical for the rail segment under consideration. The difference of probability of
undetected defects with two inspection intervals, compared to the probability of
undetected defects with three inspection intervals, is negligible. There is a need to
integrate data management to extract more meaningful information about risk and
cost associated with inspection, maintenance and rail replacements. There is huge
scope to carry out this analysis for all other segments of rail track, to minimise risks
and costs associated with inspection, maintenance, and rail replacements
(Chattopadhyay et al., 2005).
6.6 Limitations of Detecting Rail Breaks
The purpose of a track signalling system is primarily to detect if there is a train
positioned on an isolated section of the track. One rail is labelled as S-rail and the
other rail is called I-rail. The I-rail is incoherent and is isolated in parts to ensure that
the section is divided into sub-sections along the track. S-rail is coherent and is acting
as the continuous rail for feeding back the power current from the electric
locomotives. The S-rail is a continuous welded rail with no isolation cuts for
sectioning, and the S-rail is also connected to the contact wire pole foundation and,
hence, connected to a zero electric potential regarding ground. The S-rial will then
close the electric current to the electric power for the locomotive engine. The I-rail
has also a 6 volt electric potential compared to the S-rail and hence, in each isolated
section of the track, there will be a 6 volt difference between rails. The two rails are
connected via an intermediate rely and the relay is then closes 6 volt circuit of two
rails. As long as the relay has a 6 volt potential difference, the adjoining section’s
signalling system is set to green (OK to pass) between the sections. If the circuit is
closed by a train, the adjoining section’s signalling system is set to red. This indicates
no passing between the sections. When the circuit is not completely closed, that is,
there exists a rail break on the I-rail, the relay changes its value and the signalling
202
system for the adjoining section is set to red. This indicates that you are not allowed
to pass on to the next adjoining section; the train then stops. However, if there exists a
rail break in S-rail, this rail is connected to ground, the circuit might be closed via the
ground and the rely will then "believe" that the circuit is not broken. Hence, the signal
is in green with a rail break in S-rail (Chattopadhyay et al., 2005). Figure 6.13 shows
detection of rail breaks using the signalling system.
Figure 6.13: Detecting rail breaks using signalling system (Chattopadhyay et al.,
2005)
6.7 Effect of Seasonal Conditions on Rail Defect Initiation
Failures and defect identifications can be analysed separately for estimating the effect
of seasonal conditions (summer and winter) on rail defect initiation and failures for a
known MGT of ageing and traffic movement before next inspection.
Rail Industry from Scandinavia believes that the number of detected failures in May
due to the impact of winter (when no lubrication and grinding campaign can operate),
is greater than that detected in September (when defects are generated by summer
traffic flow and both grinding and lubrication campaigns operate).
y
203
6.8 Summary
Modelling and analysis of inspection models and analysis of rail failure data for
optimal inspection decisions, are discussed in this chapter. Real life data was collected
from industry for analysis. Probability models are developed to reduce unplanned
maintenance due to rail breaks. The specific outcomes of this chapter are:
� Analysis found that two NDT inspections per year are more cost effective than
one and three inspections
� Rail owners can save 27% on total maintenance costs with two inspections per
year over one inspection per year
� Risk priority number is used to analyse risks due to rolling contact fatigue and
rail defects
� Analysis found that there is high probability of failure due to the severity of
undetected defects such as thermite welds and rolling contact fatigue related
defects
There is a need to integrate these models. Integration of grinding, lubrication,
inspection and rectification models will be discussed in Chapter 7. Results,
conclusions, contributions, and scope for future work will be presented in Chapter 8.
204
CHAPTER 7
DEVELOPMENT OF AN INTEGRATED MODEL FOR ESTIMATION OF
EXPECTED TOTAL COSTS
7.1 Introduction
Probabilistic models are developed for optimal inspections to reduce unplanned
maintenance due to rail breaks and undetected defects in Chapter 6. This chapter
focuses on development of an integrated model for estimating expected total cost of
grinding, lubrication, inspection, rectification and replacement decisions, and
associated risks of derailments.
The outline of this chapter is as follows: In Section 7.2 development of the integrated
model is presented. In Section 7.3, the integrated model is proposed for wear-fatigue-
lubrication interaction. It proposes a cost model for effective maintenance decisions.
The concluding section presents the summary and scope for future work.
7.2 Development of the Integrated Model
This research has focused on the development of economic models for rail grinding,
lubrication, inspection, rectification and replacement. A simulation model is
developed to integrate grinding, lubrication, inspection, rectification and replacement
models. The integrated model can be used:
� to predict and assess operational risks due to rail defects in the track for
informed managerial decisions to improve reliability and safety of rail
operation,
� to estimate the expected total annuity costs for grinding, lubrication,
inspection and replacement of rails,
� for cost-benefit analysis and making managerial decisions on risk based
approach on grinding, lubrication and inspection intervals,
� to estimate relative performance of lubricators, total curve and segment, above
rail and below rail for assessing effectiveness of lubrication strategies and
� to estimate the savings with grinding, inspection intervals, lubrication, rail
replacement and rectification decisions.
Figure 7.1 shows the proposed integrated model for economic evaluation, based on
cost-benefit analysis and risk based approach for managerial decisions.
205
Figure 7.1: Integrated model for rail grinding-lubrication-inspection
The Integrated Model consists of grinding, lubrication and inspection models to
estimate total annuity costs of maintenance of rail segment under consideration.
Therefore, the total cost of maintaining a segment of rail is equal to the sum of cost
for: Preventive rail grinding cost (cg); down time cost due to rail grinding (loss of
traffic) (cd); inspection costs for rail grinding (ci); risk cost of rectification based on
NDT; rail breaks and derailment (cr); and replacement cost of worn-out, unreliable
rails (cre); lubrication (cl); and NDT inspection cost (Ultrasonic NDT car, NDT hand
held equipment). Then the total annuity cost/m can be modelled as:
Start: InputExperimental dataRail and wheel discs, curve radius
steel grade, axle load, speed and lubricant
Integrated wear-fatigue-lubrication model
Lubrication model
(Chapter 5)
Change the conditions and variables
Industry dataRail data (year installed, material, size (kg), profile,
age), curve radius, MGT, rail grinding, wear and
lubrication, rail inspection, rail rectification and
replacement, weather and environmental conditions
Current condition and usage of rail
�Measurement of wear rate
�with and without lubrication
� Compare wear rate
with existing wear standards,
�experiment,
� field, environmental and
�weather conditions
� Inspection of rail for
� RCF defects by NDT
� Signaling system and
� Visual inspection
� Inspection of lubricators
Interpretation of RCF
defects, Wear and
Lubrication interaction
Grinding model
(Chapter 4)Inspection model
(Chapter 6)
� Rail lubricant
� Applicator performance
� Lubricator position
� Condition of lubricator,
� axle loads, traffic types and
speed
� curve length, radius and
number curves and
� Environmental conditions
Rectification and Replacement
(Chapter 4, 5, 6)
� Detection of RCF cracks
� Rail profile measurements,
� Rail grinding interval
� Selection of rail segment
� Grinding depth
� Rectification of RCF defects
� Determining wear limit
� Correction of rail profile
� Lubricator maintenance
� weather and environmental
conditions
Decisions on
Cost of replacing rail
segment
Maintenance of lubricators
Risk of rail breaksDecisions on
whether to grind or not?
what is grinding depth and frequency?
Operational risks and costs due to
undetected defects
Accuracy of detection technology
Appropriate maintenance activity
Decisions on lubricant
type, lubricator position,
and performance
risk of fluid entrapment
Start: InputExperimental dataRail and wheel discs, curve radius
steel grade, axle load, speed and lubricant
Integrated wear-fatigue-lubrication model
Lubrication model
(Chapter 5)
Change the conditions and variables
Industry dataRail data (year installed, material, size (kg), profile,
age), curve radius, MGT, rail grinding, wear and
lubrication, rail inspection, rail rectification and
replacement, weather and environmental conditions
Current condition and usage of rail
�Measurement of wear rate
�with and without lubrication
� Compare wear rate
with existing wear standards,
�experiment,
� field, environmental and
�weather conditions
� Inspection of rail for
� RCF defects by NDT
� Signaling system and
� Visual inspection
� Inspection of lubricators
Interpretation of RCF
defects, Wear and
Lubrication interaction
Grinding model
(Chapter 4)Inspection model
(Chapter 6)
� Rail lubricant
� Applicator performance
� Lubricator position
� Condition of lubricator,
� axle loads, traffic types and
speed
� curve length, radius and
number curves and
� Environmental conditions
Rectification and Replacement
(Chapter 4, 5, 6)
� Detection of RCF cracks
� Rail profile measurements,
� Rail grinding interval
� Selection of rail segment
� Grinding depth
� Rectification of RCF defects
� Determining wear limit
� Correction of rail profile
� Lubricator maintenance
� weather and environmental
conditions
Decisions on
Cost of replacing rail
segment
Maintenance of lubricators
Risk of rail breaks
Decisions on
Cost of replacing rail
segment
Maintenance of lubricators
Risk of rail breaksDecisions on
whether to grind or not?
what is grinding depth and frequency?
Operational risks and costs due to
undetected defects
Accuracy of detection technology
Appropriate maintenance activity
Decisions on
whether to grind or not?
what is grinding depth and frequency?
Operational risks and costs due to
undetected defects
Accuracy of detection technology
Appropriate maintenance activity
Decisions on lubricant
type, lubricator position,
and performance
risk of fluid entrapment
Decisions on lubricant
type, lubricator position,
and performance
risk of fluid entrapment
206
NDT
y
yy
N
i
i
sjjj
y
y
y
yyy
i
N
i
xixixixixixi
y
x
y
yy
j
i
N
j
c
y
yy
iN
i
DTGP
y
yy
iN
i
itot
xCrrrcYMc
rrI
rrrr
cAPaAPBPkBPMMNE
rrri
rrrdhn
rrrLnGC
j
j
I
i
++−++
++−+−
++−++−+
−+−+∗
++−+
++−+∗∗
++−+=
∑
∑∑
∑
∑
∑
=
=+++
=
=
−
=
−
=
))1/(1(1/(*})1/()({
)))1/(1(1/()))1/(1(1(*
)))1/(1(1/()1(*)))1/(1(1(*})1(
/]*))(1(*)((*))(1(*)([)],([{
)))1/(1(1/(*})1/(({
)))1/(1(1/(*})1/({
)))1/(1(1/(*})1/()**({
1
0,,,,1
0
1
1
1
1
1
(7.1)
where ( )BP xi, is probability of detecting potential rail breaks in non destructive
testing (NDT) for x number of inspections per year; ( )AP xi, is probability of
undetected potential rail breaks leading to derailments for x number of inspections per
year, in a planned way; and a is the expected cost per derailment. NDTxC is the cost
for non destructive testing for x number of inspections per year.
( ) α=BPi 1, (7.2)
where ( )BPi 1, is probability of detecting potential rail breaks in non destructive testing
(NDT) for one inspection per year, and α is % of defects detected in NDT.
( ) ( ){ }( )( )
+
−+−−=
==
==
2,1,
2,1,2,
111
xixi
xixi
iNN
NNBP
αα (7.3)
where ( )BPi 2, is probability of detecting potential rail breaks in non destructive
testing (NDT) for two inspections per year. The Ni is number of rail defects found
during x number of inspections per year.
( ) ( ){ }( )( ) ( )α
αα−
++
+−+−−=
===
=== 111
13,2,1,
3,2,1,3,
xixixi
xixixi
iNNN
NNNBP (7.4)
where ( )BPi 3, is probability of detecting potential rail breaks in non destructive
testing (NDT) for two inspections per year.
G is the cost of grinding cost per pass per m, ni number of grinding pass for ith
grinding and L is the length of rail segments under consideration; N be the total
207
number of periods up to safety limit for renewal, and r is the discounting rate per
period.
x is the inspection intervals per year for a rail corridor under consideration,
CNDT is total expected cost for NDT inspection interval,
hDT is the expected downtime due to each grinding pass and d is the expected cost of
down time per hour.
ci is the cost of inspection before and after rail grinding
c is the expected cost of each rail break repair on emergency basis
I is cost of investment in new rail
sc is switching cost for stop/start lubrication
jY is the decision variable for lubrication strategy (dimensionless), 0 for no or
continuous lubrication (dimensionless), and 1 for stop/start lubrication
(dimensionless).
The integrated model can be used for effective maintenance decisions on grinding
interval, application of lubrication and inspection intervals. It can also be used to
estimate the relative performance of lubricators, total curve and segment model,
above rail and below rail model for assessing effectiveness of lubrication strategies
and to evaluate the performance of lubricators.
7.3 Analysis of Results
Heavy haul data was used for analysis of the model, for prediction, and to estimate
total annuity costs. Table 7.1 shows all the cases examined with the integrated model.
208
Table 7.1: Examined cases with the integrated model
Case Studies Sections
Total annuity cost for 12 MGT with lubrication Section 7.3.1
Total annuity cost for 12 MGT without lubrication Section 7.3.1
Total annuity cost for 23 MGT with lubrication Section 7.3.2
Total annuity cost for 23 MGT without lubrication Section 7.3.2
Total annuity cost for 12 MGT with and without lubrication Section 7.3.3
Total annuity cost for 23 MGT with and without lubrication Section 7.3.3
EAC/m for 12 MGT with lubrication for one NDT inspection/year (Case 1) Section 7.3.4
EAC/m for 12 MGT without lubrication for one NDT inspection interval/
annum (Case 1)
Section 7.3.4
EAC/m for 23 MGT with lubrication for one NDT inspection
interval/annum (Case 1)
Section 7.3.4
EAC/m for 23 MGT without lubrication for one NDT inspection
interval/annum (Case 1)
Section 7.3.4
EAC/m for 12 MGT with lubrication for two NDT inspection/ annum
(Case 2)
Section 7.3.4
EAC/m for 12 MGT without lubrication for two NDT inspection/ annum
(Case 2)
Section 7.3.4
EAC/m for 23 MGT with lubrication for two NDT inspection/ annum
(Case 2)
Section 7.3.4
EAC/m for 23 MGT without lubrication for two NDT inspection/ annum
(Case 2)
Section 7.3.4
EAC/m for 12 MGT with lubrication for three NDT inspection/ annum
(Case 3)
Section 7.3.4
EAC/m for 12 MGT without lubrication for three NDT inspection/ annum
(Case 3)
Section 7.3.4
EAC/m for 23 MGT with lubrication for three NDT inspection/ annum
(Case 3)
Section 7.3.4
EAC/m for 23 MGT without lubrication for three NDT inspection/ annum
(Case 3)
Section 7.3.4
EAC/m for 12 & 23 MGT with and without lubrication Section 7.3.4
* EAC- Estimated Annuity Cost/m
209
7.3.1 Annuity costs/m for 12 MGT
Analysis of annuity costs/m of grinding, risk, down time, inspection and replacement
for 12 MGT of curve radius 0 to 600 m are compared. Results are shown in Table 7.2.
Table 7.2: Annuity costs/m for 12 MGT with lubrication
Radius (ms) 0-300 300-450 450-600 Length in ms (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)
Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 6.82 6.08 7.12 Risk 0.0002 0.0004 0.00011
Down time 1.07 0.95 1.12 Inspection 0.02 0.02 0.02 Replacement 15.48 13.10 11.63 Lubrication 0.67 0.46 0.34
Total Annuity Cost/m 24.06 20.02 20.23 Figure 7.2 shows the analysis of annuity costs/m for 12 MGT of curve radius 0 to 600
m with lubrication. It is observed that the replacement and grinding costs are higher
compared to risk, inspection and down time cost.
Annuity costs/meter for 12 MGT with Lub
0
5
10
15
20
Grinding Risk Downtime Inspection Replacement Lubrication
Maintenance Costs
Cost/meter ($ AUD)
0-300
300-450
450-600
Figure 7.2: Annuity costs/m for 12 MGT with lubrication
Table 7.3 shows the annuity costs/m for 12 MGT without lubrication.
210
Table 7.3: Annuity costs/m for 12 MGT without lubrication
Radius (m) 0-300 300-450 450-600 Length in m (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)
Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 6.12 6.12 5.70 Risk 0.000024 0.00004 0.00002
Down time 0.96 0.64 0.8936 Inspection 0.0232 0.02 0.0238 Replacement 66 53.16 46.99
Total Annuity Cost/m 73 60 54
Figure 7.3 shows the analysis of annuity costs/m for 12 MGT of curve radius 0 to 600
m without lubrication. It is observed that replacement and grinding costs are higher
compared to downtime, inspection and risk costs. This is mainly due to early
replacement of rails at steeper curves with no lubrication.
Annuity costs/meter for 12 MGT No Lub
0
20
40
60
80
Grinding Inspection Risk Downtime Replacement
Maintenance Costs
Cost/meter ($ AUD)
0-300
300-450
450-600
Figure 7.3: Annuity costs/m for 12 MGT without lubrication
7.3.2 Annuity costs/m for 23 MGT
Analysis of annuity costs/m of grinding, risk, down time, inspection and replacement
costs with lubrication for 23 MGT of curve radius 0 to 600 m are compared. Annuity
costs/m for 23 MGT are shown in Table 7.4.
211
Table 7.4: Annuity costs/m for 23 MGT with lubrication
Radius (m) 0-300 300-450 450-600 Length in m (Percentages) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)
Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 5.42 5.95 6.00 Risk 0.00 0.00 0.00
Down time 0.85 0.93 0.94 Inspection 0.04 0.04 0.04 Replacement 17.65 15.17 16.06 Lubrication 0.68 0.46 0.33
Total Annuity Cost/m 24.64 22.55 23.37 Figure 7.4 shows the analysis of annuity costs/m for 23 MGT of curve radius 0 to 600
m. It is observed that replacement and grinding costs are higher compared to other
maintenance costs.
Annuity costs/meter for 23 MGT with Lub
0
4
8
12
16
20
Grinding Inspection Risk Downtime Replacement Lubrication
Maintenance Costs
Cost/meter ($ AUD)
0-300
300-450
450-600
Figure 7.4: Annuity costs/m for 23 MGT with lubrication
Table 7.5 shows annuity costs/m for 23 MGT without lubrication. Annuity cost/m of
grinding, risk, down time, inspection and replacement costs without lubrication for 23
MGT of curve radius from 0 to 600 m are compared and estimated.
212
Table 7.5: Annuity costs/m for 23 MGT without lubrication
Radius (m) 0-300 300-450 450-600 Length in m (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)
Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 16.02 13.61 6.3074
Risk 0.044 0.04 0.04
Down time 0.0014 0.0018 0.0001
Inspection 2.51 2.13 0.99
Replacement 152 152 79.41
Total Annuity Cost/m 171 168 87
Figure 7.5 shows the analysis of annuity costs/m for 23 MGT of curve radius 0 to 600
m without lubrication. It is observed that the cost is higher for replacement compared
to other maintenance costs. Rails develop wear and rolling contact fatigue cracks in
between longer grinding and inspection intervals. In many heavy haul lines rails are
mainly removed due to rail wear and rolling contact fatigue cracks. The rate of
replacement of rails is much higher for curves without lubrication than with
lubrication.
Annuity costs/meter for 23 MGT No Lub
0
40
80
120
160
Grinding Inspectiont Risk Downtime Replacement
Maintenance Costs
Cost/meter ($ AUD)
0-300
300-450
450-600
Figure 7.5: Annuity costs/m for 23 MGT without lubrication
7.3.3 Annuity costs/m for 12 MGT & 23 MGT
Table 7.6 shows total annuity costs/m for 12 MGT with and without lubrication for
curve radius 0-600 m.
213
Table 7.6: Analysis of total annuity costs/m for 12 MGT
Radius (m) With Lubrication Without Lubrication Length in m (Percentage) Total Annuity costs/m ($AUD) for 12 MGT
0-300 24.06 73
301-450 20.62 60
451-600 20.23 54
Figure 7.6 shows the total annuity costs/m for 12 MGT with and without lubrication.
The analysis found that the total annuity costs/m for without lubrication is 3 times
higher compared to with lubrication for 0-600 m curve radius.
Total Annuity Costs for 12 MGT
0
20
40
60
80
0-300 301-450 451-600
Curve Radius (meters)
Costs/meter ($ AUD)
With Lubrication
Without Lubrication
Figure 7.6: Total annuity costs/m for 12 MGT
Table 7.7 shows total annuity costs/m for 23 MGT with and without lubrication for
curve radius 0-600 m.
Table 7.7: Analysis of total annuity costs/m for 23 MGT
Radius (m) With Lubrication Without Lubrication Length in m (Percentage) Total Annuity costs/m ($AUD) for 23 MGT
0-300 24.64 171
301-450 22.55 168
451-600 23.25 87 Figure 7.7 shows the total annuity costs/m for 23 MGT with and without lubrication.
The analysis found that the total annuity costs/m for without lubrication is 7 times
higher for 0-450 m curve radius and 4 times higher for curves 451-600 m curve radius
compared to with lubrication.
214
Total Annuity costs for 23 MGT
0
40
80
120
160
200
0-300 301-450 451-600
Curve Radius (meters)
Total Annuity Costs
($AUD)
With Lubrication
Without Lubrication
Figure 7.7: Total annuity costs/m for 23 MGT
7.3.4 Estimation of Annuity costs/m
The total annuity costs/m for risk and inspection are further analysed considering the
expected number of failures under various inspection scenarios.
Case 1 – One Inspection per year
Data collected from industry for one inspection interval using ultrasonic (non
destructive testing) NDT and verified with handheld equipment. Table 7.8 shows the
total annuity costs/m of rail grinding, inspection for grinding, risk, downtime and
replacement, lubrication and NDT inspection costs for 12 MGT with lubrication for
one inspection interval.
Table 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.82
Inspection for grinding 0.02
Risk 36.31
Down time 1.07
Replacement 15.48
Lubrication 0.67
NDT Inspection 1.60
Total Annuity cost 61.97
215
Annuity costs/m for 12 MGT with Lub, One Ins
Lubrication,
0.67, 1%
Replacement,
15.48, 25%
Inspection for
rail grinding,
0.02, 0%
Downtime,
1.07, 2%
Risk, 36.31,
58%
Grinding, 6.82,
11%
NDT Inspection
, 1.60, 3%
Figure 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection
Figure 7.8 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m with
lubrication for one inspection interval. It is found that risk cost is higher compared to
replacement and grinding costs. This is mainly due to higher number of detected
defects with NDT during the year. These failures have a significant influence on the
risk of rail breaks and derailments. The risk and inspection cost has a great influence
on total maintenance and it is much higher without lubrication. Table 7.9 shows the
total annuity costs/m for rail grinding, inspection, risk, downtime, replacement and
NDT inspection for 12 MGT without lubrication for one inspection interval.
Table 7.9: Annuity costs/m for 12 MGT without lubrication, one inspection
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.12 Inspection for grinding 0.000024
Risk 36.31
Down time 0.0232
Replacement 66
NDT Inspection 1.60
Total Annuity cost 110
216
Annuity costs/m for 12 MGT without Lub One Ins
Grinding, 6.12,
6%
Risk, 36.31,
33%
Downtime,
0.0232, 0%
Inspection for
rail grinding,
0.000024, 0%
Replacement,
66, 60%
NDT Inspection
, 1.60, 1%
Figure 7.9: Annuity costs/m for 12 MGT without lubrication for one inspection
Figure 7.9 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m without
lubrication for one inspection interval. It is observed that replacement cost is higher
compared to all other costs. This is mainly due to early replacement of rails and a
higher number of defects detected with NDT during the year with no lubrication.
Lubrication has significant influence on rail defects which increase risk of rail breaks
and derailments. Table 7.10 shows the total annuity costs/m for rail grinding,
inspection, risk, downtime, replacement, NDT inspection for 23 MGT with
lubrication for one inspection interval.
Table 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection
Radius (m) 0-300
Length in m (Percentages) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 5.42
Inspection for rail grinding 0.00
Risk 43.32
Down time 0.04
Replacement 14.03
Lubrication 0.68
NDT Inspection 3.82
Total Annuity Cost/m 70.93
Figure 7.10 shows annuity costs/m for 23 MGT of curve radius 0 to 300 m with
lubrication for one inspection interval. The analysis shows that the risk cost is higher
compared to other costs. This is mainly due to the higher number of failures found in
one inspection for 23 MGT. The analysis shows that higher MGT grinding intervals
have increased the risk of rail break and derailment costs.
217
Annuity costs/m for 23 MGT with Lub One Ins
Replacement,
17.65, 25%
Risk, 43.32, 61%Downtime, 0.04,
0%
Inspection for rail
grinding, 0, 0%
Lubrication,
0.68, 1%
NDT Inspection,
3.82, 5%Grinding, 5.42,
8%
Figure 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection
Table 7.11 shows the total annuity costs/m for rail grinding, inspection, risk,
downtime, replacement, NDT inspection for 23 MGT without lubrication for one
inspection interval.
Table 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection
Radius (m) 0-300
Length in m (Percentages) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 16.02
Inspection for rail grinding 0.044
Risk 43.32
Down time 2.51
Replacement 152
NDT Inspection 3.82
Total Annuity Cost/m 218
Figure 7.11 shows annuity costs/m for 23 MGT of curve radius 0 to 300 m without
lubrication for one inspection interval. The analysis shows that the replacement cost is
higher compared to other costs. This is mainly due to early replacement of rails and a
higher number of defects detected with NDT during the year with no lubrication.
218
Annuity costs/m for 23 MGT without Lub One Ins
Grinding,
16.02, 7%
NDT
Inspection,
3.82, 2%
Inspection for
rail grinding,
0.044, 0%
Downtime,
2.51, 1%
Risk, 43.32,
20%
Replacement,
152, 70%
Figure 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection
Case 2 – Two inspections per year
The expected number of failures estimated with stochastic models in two inspection
intervals per year is 55.79508. Table 7.12 shows the annuity costs/m of rail grinding,
inspection for grinding, risk, and downtime, replacement, lubrication and NDT
inspection for 12 MGT with two inspections intervals.
Table 7.12: Annuity costs/m for 12 MGT with lubrication for two inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.82
Inspection for rail grinding 0.02
Risk 32.93
Down time 1.07
Replacement 15.48
Lubrication 0.67
NDT inspection 1.63
Total Annuity cost 58.62
Figure 7.12 shows annuity costs/m for 12 MGT of curve radius from 0 to 600 m with
lubrication for two inspection intervals per year. The analysis shows that risk cost and
replacement costs are higher compared to other costs. It is observed that the NDT
inspection cost for two inspection intervals is higher compared to one inspection
interval per year.
219
Annuity costs/m for 12 MGT with Lub, Two Ins
Replacement,
15.48, 26%
NDT Inspection
, 1.63, 3%Grinding, 6.82,
12%
Lubrication,
0.67, 1%
Inspection for
rail grinding,
0.02, 0%
Downtime,
1.07, 2%
Risk, 32.93,
56%
Figure 7.12: Annuity cost/m for 12 MGT with lubrication for two inspections
Table 7.13 shows the annuity costs/m of rail grinding, inspection for grinding, risk,
and downtime, replacement and NDT inspection for 12 MGT without lubrication for
two inspection intervals per year.
Table 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.12
Inspection for rail grinding 0.000024
Risk 32.93
Down time 0.0232
Replacement 66
NDT inspection 1.63
Total Annuity cost 107
Figure 7.13 shows annuity costs/m for 12 MGT of curve radius from 0 to 600 m
without lubrication for two inspection intervals per year. The analysis shows that the
replacement cost is higher compared to other costs. This is mainly due to early
replacement of rails and a higher number of defects detected with NDT during the
year with no lubrication.
220
Annuity costs/m for 12 MGT without Lub Two Ins
NDT Inspection
, 1.63, 2%
Replacement,
66, 61% Inspection for
rail grinding,
0.000024, 0%
Downtime,
0.0232, 0%
Risk, 32.93,
31%
Grinding, 6.12,
6%
Figure 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections
Table 7.14 shows the annuity costs/m for rail grinding, inspection for rail grinding,
risk, downtime and replacement, lubrication and NDT inspection for 23 MGT with
lubrication for two inspection intervals per year.
Table 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 5.42
Inspection 0.00
Risk 39.29
Down time 0.04
Replacement 17.65
Lubrication 0.68
NDT inspection 3.87
Total Annuity cost 66.94
Figure 7.14 shows annuity costs/m for 23 MGT of curve radius from 0 to 300 m with
lubrication for two inspection intervals per year. The analysis shows that the risk and
replacement costs are higher, compared to other costs. Higher NDT inspection cost is
observed for two inspection intervals, compared to one inspection interval per year.
221
Annuity costs/m for 23 MGT with Lub Two Ins
Grinding,
5.42, 8%
NDT
Inspection,
3.87, 6%Lubrication,
0.68, 1%
Inspection for
rail grinding,
0, 0%
Downtime,
0.04, 0%
Risk, 39.29,
59%
Replacement,
17.65, 26%
Figure 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections
Table 7.15 shows the annuity costs/m for rail grinding, inspection for rail grinding,
risk, downtime and replacement and NDT inspection for 23 MGT without lubrication
for two inspection intervals per year.
Table 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 16.02
Inspection for rail grinding 0.044
Risk 39.29
Down time 2.51
Replacement 152
NDT inspection 3.87
Total Annuity cost 214
Figure 7.15 shows annuity costs/m for 23 MGT of curve radius from 0 to 300 m
without lubrication for two inspection intervals per year. The analysis shows that the
replacement and risk costs are higher compared to other costs.
222
Annuity costs/m for 23 MGT without Lub Two Ins
Replacement,
152, 72%
Risk,
39.28879671,
18%
Downtime,
2.51, 1%
Inspection for
rail grinding,
0.044, 0%
NDT
Inspection,
3.87, 2%
Grinding,
16.02, 7%
Figure 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections
Case 3 – Three inspections per year
The expected number of failures estimated with stochastic models in three inspection
intervals per year is 27.47331. Table 7.16 shows the annuity costs/m of rail grinding,
inspection for grinding, risk, downtime and replacement, lubrication and NDT
inspection for 12 MGT with lubrication for three inspection intervals per year.
Table 7.15: Annuity costs/m for 12 MGT with lubrication for three inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.82
Inspection for grinding 0.02
Risk 31.58
Down time 1.07
Replacement 15.48
Lubrication 0.67
NDT Inspection 1.68
Total Annuity cost 57.32
Figure 7.16 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m with
lubrication for three inspection intervals per year. The analysis shows that risk and
replacement costs are higher compared to other costs. It is observed that the NDT
inspection cost for three inspection intervals is higher compared to one and two
inspection intervals per year.
223
Annuity costs/m for 12 MGT with Lub, Three Ins
Replacement,
15.48, 27%
Risk, 31.58,
55%Downtime,
1.07, 2%
Inspection for
rail grinding,
0.02, 0%
Lubrication,
0.67, 1% Grinding, 6.82,
12%
NDT Inspection
, 1.68, 3%
Figure 7.16: Annuity costs/m for 12 MGT with lubrication for three inspections
Table 7.17 shows the annuity costs/m of rail grinding, inspection for grinding, risk,
downtime and replacement and NDT inspection for 12 MGT without lubrication for
three inspection intervals per year.
Table 7.17: Annuity costs/m for 12 MGT without lubrication for three
inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 6.12
Inspection for grinding 0.000024
Risk 31.58
Down time 0.232
Replacement 66
Lubrication 0.67
NDT Inspection 1.68
Total Annuity cost 105
Figure 7.17 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m without
lubrication for three inspection intervals per year. The analysis shows that
replacement and risk costs are higher compared to other costs. It is observed that the
NDT inspection cost for three inspection intervals is higher compared to one and two
inspection intervals per year.
224
Annuity costs/m for 12 MGT without Lub Three Ins
Grinding,
6.12, 6%
Risk, 31.58,
30%
Downtime,
0.0232, 0%
Inspection for
rail grinding,
0.000024, 0%
Replacement,
66, 62%
NDT
Inspection ,
1.68, 2%
Figure 7.17: Annuity costs/m for 12 MGT without lubrication for three inspections
Table 7.18 shows the annuity costs/m for rail grinding, inspection for grinding, risk,
downtime, replacement, lubrication and NDT inspection for 23 MGT with lubrication
for three inspection intervals per year.
Table 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 5.42
Inspection for grinding 0.00
Risk 37.68
Down time 0.04
Replacement 17.65
Lubrication 0.68
NDT inspection 4.00
Total Annuity cost 65.47
Figure 7.18 shows annuity costs/m for 23 MGT of curve radius from 0 to 300 m with
lubrication for three inspection intervals per year. The analysis shows that the risk and
replacement cost are higher compared to other costs. Higher NDT inspection cost is
observed for three inspection intervals, compared to one and two inspection intervals
per year.
225
Annuity costs/m for 23 MGT with Lub Three Ins
Replacement,
17.65, 27%
Risk,
37.68386716,
58%Downtime,
0.04, 0%
Inspection for
rail grinding, 0,
0%
Lubrication,
0.68, 1%
NDT
Inspection,
4.00, 6%Grinding, 5.42,
8%
Figure 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections
Table 7.19 shows the annuity costs/m for rail grinding, inspection for grinding, risk,
downtime, replacement, lubrication and NDT inspection for 23 MGT without
lubrication for three inspection intervals per year.
Table 7.19: Annuity costs/m for 23 MGT without lubrication for three
inspections
Radius (m) 0-300
Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)
Grinding 16.02
Inspection for grinding 0.044
Risk 37.68
Down time 2.51
Replacement 152
NDT inspection 4.00
Total Annuity cost 212
Figure 7.19 shows annuity costs/m for 23 MGT of curve radius from 0 to 300 m
without lubrication for three inspection intervals per year. The analysis shows that the
replacement and risk costs are higher compared to other costs.
226
Annuity costs/m for 23 MGT without Lub Three Ins
Grinding,
16.02, 8%NDT
Inspection,
4.00, 2%
Inspection for
rail grinding,
0.044, 0%
Downtime,
2.51, 1%
Risk, 37.68,
18%
Replacement,
152, 71%
Figure 7.19: Annuity costs/m for 23 MGT without lubrication for three inspections
The analysis shows that the annuity costs/m of inspection has been increased with
increase of inspection intervals per year. However, the risk cost and total cost are
lower for three inspection intervals, compared to two and one inspection intervals per
year. Three inspection intervals per year have a significant influence on the
probability of detecting a number of rail defects and rail breaks. This has significant
influence on risk and total maintenance cost. Table 7.20 shows the comparison of
total annuity costs/m of 0-300 m curve radius for 12 and 23 MGT with lubrication.
Table 7.20: Total annuity costs/m for 12 and 23 MGT with lubrication
Radius (m) 0-300
Length (m) (Percentage) Total annuity costs/m ($AUD) Rail maintenance 12 MGT 23 MGT One Inspection 61.97 70.93
Two Inspection 58.62 66.95
Three Inspection 57.32 65.47
Figure 7.20 shows total annuity costs/m for 12 and 23 MGT of curve radius 0 to 300
m with lubrication for one, two and three inspection intervals per year. The analysis
shows that total annuity costs/m for one inspection interval is 5.41% higher with
lubrication for 12 MGT and 5.61% higher with lubrication for 23 MGT, compared to
two inspection intervals per year. It is also observed that total costs/m for 23 MGT is
higher, compared to 12 MGT grinding interval.
227
Total Annuity Costs/m with Lubrication
0
20
40
60
80
One Two Three
Inspections/year
Costs/m ($ AUD)
12 MGT
23 MGT
Figure 7.20: Total annuity costs/m for 12 & 23 MGT with lubrication
Table 7.21 shows the comparison of total annuity costs/m of 0-300 m curve radius for
12 and 23 MGT without lubrication.
Table 7.21: Total annuity costs/m for 12 and 23 MGT without lubrication
Radius (m) 0-300
Length (m) (Percentage) Total annuity costs/m ($AUD) Rail maintenance 12 MGT 23 MGT One Inspection 110 218
Two Inspection 107 214
Three Inspection 105 212
Figure 7.21 shows total annuity costs/m for 12 and 23 MGT of curve radius 0 to 300
m without lubrication for one, two and three inspection intervals per year. The
analysis shows that total costs/m for one inspection interval is higher, compared to
two and three inspection intervals per year. It is also observed that total costs/m for 23
MGT is higher, compared to 12 MGT grinding interval. It is found that total costs/m
without lubrication inspection intervals are higher, compared to lubrication inspection
intervals.
228
Total Annuity Costs/m without Lubrication
0
40
80
120
160
200
240
One Two Three
Inspections/year
Costs/m
($ AUD)
12 MGT
23 MGT
Figure 7.21: Total annuity costs/m for 12 & 23 MGT without lubrication
Therefore, the analysis found that two inspection intervals with lubrication is
economical, compared to one inspection and three inspection intervals per year.
The existing models have not considered the integration of all the maintenance
activities to assess operational risks and to estimate total annuity costs. The integrated
model developed in this research considers:
� Rail grinding: Increase of axle loads, accumulated tonnage (Million Gross
Tonnes), axle passes, curve radius, grinding wear, traffic wear, detected cracks
and derailments
� Lubrication: Total annuity costs were estimated considering lubrication and non-
lubrication, wayside lubricators, lubricator maintenance, rail wear and area head
loss, and rail maintenance
� Inspection: Non destructive testing (NDT) ultrasonic, NDT hand held, signalling
and visual inspection.
� Rectification and replacement: Rectification of rails due to worn-out rails,
undetected rail defects, rail breaks and derailments.
The integrated model considered relative cost of maintenance for various curves. The
relative performance of these curves, with the same lubrication strategy under
different operating conditions, can provide accurate results for assessment of
lubrication effectiveness. The integrated model can be used for managerial decisions
on rail grinding, rail lubrication, rail inspection intervals and rectification and
replacement of rails. It is important to consider increase of axle load, gross tonnage,
and speed such that the damage level based is on wear, RCF, defects, failures. It also
229
includes rail grinding and maintenance including lubrication, inspection, rectification
and replacements for accurate prediction of risks due to rail breaks and derailments.
Currently, research is being carried out by Larsson D (2004), Lee and Chiu (2005)
and Leong (2006) in the area of increase of axle loads and their impact on existing rail
tracks. The difference of axle loads (including dynamic load) could be included in this
model for the analysis of risk and, therefore, the effect on total cost. The productivity
increase due to increased axle loads from 26 tonnes to 30 tonnes, is 15.5 %. The cost
effectiveness due to this increase can be based on increased damage. The Office for
Research and Experiments (ORE) of the Union International des Chemins de Fer
(UIC) has noted that maintenance costs vary directly (60–65 per cent) with change in
axle load. It is found from the failure data analysis that 25% of the total failures occur
as a result of rolling contact fatigue defects. The multiplying factor for 30 tonne axle
load compared to 26 tonne axle load for failures can be (0.25*0.60) - a 15% increase
in failures. This is around 25% of 60% increase in maintenance problems and a 15%
increase in costs.
7.4. Summary
An integrated model is developed for grinding interval, lubrication decisions,
inspection intervals, rectification and replacement decisions. Total annuity costs
(TAC) are estimated, using an integrated wear-fatigue-lubrication-grinding-
inspection-rectification and replacement decision model. The analysis also shows that
inspection cost is higher for three inspection intervals per year, but the total
maintenance cost is lower, compared to one inspection interval and two inspection
intervals per year. It is found that two inspection intervals are more economical and
can reduce risk of rail breaks and derailment costs. Table 7.22 shows all the cases
examined with the integrated model and their findings. The conclusion and summary
of this thesis and a outline of the scope for future research are included in Chapter 8.
230
Table 7.22: Findings from examined cases
Case Studies Sections Conclusions
TAC/m for 12 MGT with
and without lubrication
Section
7.3.1
TAC for 0-600 m is 3 times higher without
lubrication compared to with lubrication.
TAC/m for 23 MGT with
and without lubrication
Section
7.3.2
TAC for 0-450 m is 7 times and 450-600 m
is 4 times higher without lubrication
compared to with lubrication.
TAC/m for 12 MGT with
and without lubrication for
one NDT inspection/yr
Section
7.3.3
Case 1
TAC/m for 0-300 m without lubrication for
one inspection is 43.69% higher compared
to with lubrication for 12 MGT
TAC/m for 23 MGT with
and without lubrication for
one NDT inspection/ annum
Section
7.3.3
Case 1
TAC/m for 0-300 m without lubrication for
one inspection is 67.40% higher compared
to with lubrication for 23 MGT
TAC/m for 12 MGT with
and without lubrication for
two NDT inspection/ annum
Section
7.3.3
Case 2
TAC/m for 0-300 m without lubrication for
two inspection is 45.06% higher compared
to with lubrication for 12 MGT
TAC/m for 23 MGT with
and without lubrication for
two NDT inspection/ annum
Section
7.3.3
Case 2
TAC/m without lubrication for 0-300 m for
two inspection is 68.68% higher compared
to with lubrication for 23 MGT
TAC/m for 12 MGT with
and without lubrication, for
three NDT inspection/
annum
Section
7.3.3
Case 3
TAC/m for 0-300 m without lubrication for
three inspection is 45.62% higher compared
to with lubrication for 12 MGT
TAC/m for 23 MGT with
and without lubrication for
three NDT inspection/
annum
Section
7.3.3
Case 3
TAC/m for 0-300 m without lubrication for
three inspection is 69.15% higher compared
to with lubrication for 23 MGT
TAC/m for 12 MGT with
lubrication for one and two
NDT inspections/ annum
Section
7.3.3
Cost savings per meter for 12 MGT is
5.41% with two inspections compared to
one inspection
TAC/m for 23 MGT with
lubrication for one and two
NDT inspections/ annum
Section
7.3.3
Cost savings per meter per year for 23
MGT is 5.61% with two inspections
compared to one inspection
231
CHAPTER 8
CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH
8.1 Introduction
In recent years there has been a continuous increase of axle loads, tonnage, train
speed, and train length which has increased the productivity in the rail sector and
increased the risk of rail breaks and derailments. Rail operating risks have been
increasing due to increasing number of axle passes, steeper curves, wear-out of rails
and wheels, inadequate rail-wheel grinding, poor lubrication and reduced
maintenance. Rolling contact fatigue (RCF) and wear are significant problems for
railway companies. In 2000, the Hatfield accident in UK killed 4 people and injured
34 people and has lead to the cost of £ 733 million (AUD$ 1.73 billion) for repairs
and compensations. In 1977, the Granville train disaster in Australia killed 83 people
and injured 213 people. These accidents were related to rolling contact fatigue, wear
and poor maintenance.
The scope of this research was to develop models for rail grinding, wear and
lubrication, inspection and replacement of rails. Integration of these models is applied
for economic analysis of costs and operational risks. This chapter summarises the
contributions of this thesis and discusses scope for future research. The main
contributions of this thesis are development of (i) failure models and estimation of
parameters, considering operational and environmental conditions, (ii) grinding
models for optimal grinding decisions under various operating conditions, (iii)
lubrication models for optimal lubrication strategies, (iv) inspection models for
optimal inspection decisions, considering detected and undetected defects using non
destructive ultrasonic testing methods and (v) integrated models for estimating costs
and operating risks. A summary of the contributions are provided in Sections 8.2.
Scope for future research work is discussed in Section 8.3.
8.2 Contribution of This Thesis
Chapter 1 of this thesis provides the scope and outline of this research. It discusses the
background of the problems associated with rail degradation, influencing factors, and
the need for development of integrated models to predict and monitor maintenance
costs and operational risks.
232
In Chapter 2, a brief overview of the literature on rail track structure, rail defects, rail
wear, rail-wheel lubrication, rail grinding, inspection, replacement of rails and
maintenance strategies was provided as background for this research.
In Chapter 3, grounded theory of rail wear models, rolling contact fatigue (RCF) and
rail maintenance models are discussed. An extensive literature review identified the
gaps in the existing models and the approach needed to reduce the gaps for increased
safety and reliability of rail operation.
In Chapter 4, failure models are developed and parameters, considering operational
and environmental conditions, are estimated. Failures are modelled with non-
homogenous Poisson process and economic models are developed to analyse the
costs due to grinding, risks, downtime, inspection and replacement of rail. Costs for
23, 12, 18 and 9 MGT of curve radius from 0 to 300, 300-450, 450-600 and 600-800
m are estimated. Cost savings per meter per year are:
• 4.58% with 12 MGT intervals compared to 23 MGT intervals for 0-300 m
• 9.63% with 12 MGT intervals compared to 23 MGT intervals for 300-450 m
• 15.80% with 12 MGT intervals compared to 23 MGT intervals for 450-600 m
• 12.29% with 12 MGT intervals compared to 23 MGT intervals for 600-800 m
Analysis shows that rail players can save with 12 MGT intervals, compared to 23
MGT intervals under conditions outlined in this research.
In Chapter 5 a lubrication model is developed for optimal lubrication strategies. It
includes modelling and economic analysis of rail wear, rail-wheel lubrication, and
various types of lubricators. Cost-benefit analyses and annuity costs of lubricators are
estimated for managerial decisions. The analysis shows that cost effectiveness of
lubricator depends on the numbers of curves and length of curve it lubricates. The
Specific Outcomes of this chapter are:
Cost savings per lubricator per year for same curve length and under same curve
radius is:
• 17% for solar lubricators, compared to standard wayside lubricators.
Cost savings per meter per year are:
• 3 times for 0-450 m and 2 times for 450-600 m curve radius with lubrication
compared to without lubrication for 12 MGT grinding interval
233
• 7 times for 0-450 m and 4 times for 450-600 m curve radius with lubrication
compared to without lubrication for 23 MGT grinding interval
A relative performance model, a total curve and segment model and a simulation
model are developed for analysis of lubrication effectiveness.
In Chapter 6, a model is developed for rail inspection. Modelling and analysis
includes failure mode and effect analysis (FMEA) and risk priority number (RPN).
Collection and analysis of rail failure data, rail defect initiation and cost-benefit
analysis for inspection frequency are discussed. Probabilistic models are developed to
reduce unplanned maintenance due to rail breaks. The specific outcomes of this
chapter are the development of:
� an inspection model for cost effective rail inspection intervals
� a risk priority number by combining probability of occurrence, probability of
detection and consequences due to rail defects, rail breaks and derailments
Cost savings per year for same track length, curves and MGT of traffic:
• 27% on total maintenance costs with two inspections, compared to one
inspection considering risk due to rail breaks and derailments.
Analysis found:
• a high probability due to severity of undetected defects such as thermite welds
and rolling contact fatigue related defects
• that two NDT inspection intervals per year is cost effective, compared to one
inspection interval per year of the rail track under consideration
In Chapter 7 an integrated model is developed for costs and risks. It combines
decisions on grinding interval, lubrication strategies, inspection intervals, rectification
strategies and replacement of rails. Total annuity costs (TAC) are estimated using this
integrated wear-fatigue-lubrication-grinding-inspection-rectification and replacement
decision model.
Cost savings per meter per year for 12 MGT are:
• 5.41% on total maintenance costs with two inspections compared to one
inspection, considering risk due to rail breaks and derailment
• 45.06% on total maintenance costs with lubrication for two inspections,
compared to without lubrication
Cost savings per meter per year for 23 MGT are:
234
• 5.61% with two inspections, compared to one inspection, considering risk due
to rail breaks and derailments.
• 68.68% with lubrication for two inspections per year, compared to without
lubrication.
In summary, the main contributions of this research thesis include the development
of:
• failure models and estimation of parameters, considering operational and
environmental conditions
• economic models for rail grinding decisions linking cumulative MGT, axle load,
curve radius and operating conditions
• cost models for optimal lubrication strategies
• a risk based cost benefit model for optimal inspection decisions, considering
detected and undetected defects using non destructive ultrasonic testing
• integrated models for estimation of expected total cost and associated risks for
grinding, lubrication, inspection, rectification and replacement decisions.
8.3 Scope for Future Research
There is huge scope for future research in this area. Some suggestions are:
1. Assessment of operating risks due to rolling contact fatigue (RCF) and rail
grinding under various environmental conditions
2. Modelling and analysis of rolling contact fatigue crack initiation and growth rate,
considering passenger and mixed traffic under various operating conditions
3. Modelling and analysis of rail-wheel wear and rolling contact fatigue cracks for
higher axle loads and tonnage
4. Development of an international standard for rail-wheel lubrication
5. Development of an international standard for wear limit
6. Analysis of inspection technologies for better detection and to reduce undetected
defects leading to rail breaks and derailments
7. Development of extended models on rail grinding, lubrication and inspection
considering rail-wheel profile, material, hardness and size of rail under
deregulated environment
8. Development of a penalty pricing model, considering a deregulated environment
9. Detailed data collection for analysis to develop and predict more accurate and
appropriate models
235
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250
APPENDICES
Appendix - A
% This Simulation program is calculating the .... % clear % Clear the working memory % % Set number of data that you will study, in the DAT file there is 720 data that you can use % %ndata = 100; % ndata is set % %load Inputdata.dat; % This is to Import the wear data for different curve sections %Inputdata=10*Inputdata; %This is to convert to 10MGT for each wearrate step %dummy=Inputdata; %dummy(1:8,2)=(Inputdata(1:8,1)+Inputdata(1:8,3))/2;% Manipulate 900A-Hi Rail %dummy(1:8,8)=(Inputdata(1:8,7)+Inputdata(1:8,9))/2;% Manipulate 1100-Hi Rail %dummy(1:8,2)=Inputdata(1:8,2).*0.85; %dummy(1:8,3)=Inputdata(1:8,3).*0.80; % The column 3 is moved to Colum 2 due to wrong input file set up %dummy(1:8,3)=Inputdata(1:8,2); %Inputdata=dummy; % % Create a radius vector starting at R=150, with a step of 10 ends at 801 % R = 200:25:800; % % Indata for wear rates, two different values, max wear rate high rail and % min wear rate for high rail. Data from KTH and litterature findings. Data % from south of Stockholm. % % General equation is: Wear(R)=A^(B*R+C)+D , dim (mm2/MGT) % % High Rail no lubrication % Hinolub=[1.6 -0.01 8 0]; % Based on BV findings of wear rates % [1.6 -0.01 8 0] is the nominal values % High Rail with lubrication % Hilub=[1.2 -0.01 4 0]; % Based on BV findings of wear rates % [1.2 -0.01 4 0] is the nominal values % % HilubOpt=[1.4 -0.01 6 0]; % for i =1:max(size(R)); HinonlubWear(i)=Hinolub(1)^(Hinolub(2)*R(i)+Hinolub(3))+Hinolub(4); HilubWear(i)=Hilub(1)^(Hilub(2)*R(i)+Hilub(3))+Hilub(4); % HilubOptWear=HilubOpt(1)^(HilubOpt(2)*R(i)+HilubOpt(3))+HilubOpt(4); end; %
251
% rUIC60_900A = 800; % This is replacement [SEK] cost per meter of one Rail % for segment L due to worn out regulation (I AUD % = 5.21 SEK) %rUIC60_1100 = 900; % rBV50_900A = 800*49/60; % This is replacement cost [SEK] per meter of BV50 Rail for one rail % for segment L due to worn out regulation. %rBV50_1100 = 900*50/60; % % Calculation of the total life as function of curve radii for the two % different wear rate functions, Hinonlubwear and Hilubwear. % BV50arealoss = 585; % Total critical area that can be used before renewal for 50 kg/m rail UIC60arealoss = 745; % Total critical area that can be used before renewal for 60 kg/m rail % % % Calculate total no of MTG before renewal % for i =1:max(size(R)); TotalMGTBV50(i,1)=BV50arealoss./HinonlubWear(i); % Index 1 is for Non lubrication TotalMGTBV50(i,2)=BV50arealoss./HilubWear(i); % Index 2 is for lubrication TotalMGTUIC60(i,1)=UIC60arealoss./HinonlubWear(i); % Index 1 is for Non lubrication TotalMGTUIC60(i,2)=UIC60arealoss./HilubWear(i); % Index 2 is for lubrication end; % % Calculate the annuity cost for rail replacement per meter for the % four different scenarios, UIC, BV, Lub, NonLub % Discount = 0.04; % MGT = 24; % To get No years, set MGT to a value of 24 for studied track of Malmbanan at BV % % Calculate present value and life for the unlubricated and lubricated curves % sumation1 = 0.; clear m k; for m=1:max(size(R)); % Non lubrication curves BV 50 profile for k=1:(max(TotalMGTBV50(m,1)./MGT)) sumation1(k,m) = rBV50_900A./(1+Discount)^(k); end; end; % sumation2 = 0.; clear m k; for m=1:max(size(R)); % Lubricated curves BV 50 profile for k=1:(max(TotalMGTBV50(m,2)./MGT)) sumation2(k,m) = rBV50_900A./(1+Discount)^(k);
252
end; end; % dummy1=sum(sumation1); % sum up the total values for Non lubrication curves BV 50 profile dummy2=sum(sumation2); % sum up the total values for lubrication curves BV 50 profile % for i=1:max(size(R)); sumpv_RailBV50(i,1) = dummy1(i); % Transpose back sumpv_RailBV50(i,2) = dummy2(i); % Transpose back end; % % Calculate the sum pv values for UIC60 % % Totalpv = 0.; clear m k; for m=1:max(size(R)); % Non lubrication curves for k=1:(max(TotalMGTUIC60(m,1)./MGT)); Totalpv(k,m) = rUIC60_900A./(1+Discount)^(k); end; end; % sumation4 = 0.; clear m k; for m=1:max(size(R)); % Lubricated curves for k=1:(max(TotalMGTUIC60(m,2)./MGT)) sumation4(k,m) = rUIC60_900A./(1+Discount)^(k); end; end; % dummy3=sum(Totalpv); dummy4=sum(sumation4); % % for i=1:max(size(R)); sumpv_RailUIC60(i,1) = dummy3(i); % Transpose back sumpv_RailUIC60(i,2) = dummy4(i); % Transpose back end; % % % Calculare the annuity cost for lub and un-lub curves % % for p=1:max(size(R)); Noyears60(p,1) = (TotalMGTUIC60(p,1)./MGT); % Calculate the no years for different radii Noyears60(p,2) = (TotalMGTUIC60(p,2)./MGT); Noyears50(p,1) = (TotalMGTBV50(p,1)./MGT); % Calculate the no years for different radii Noyears50(p,2) = (TotalMGTBV50(p,2)./MGT); end; % for w=1:max(size(R));; % Calculate the annuity cost for # no years annuUIC60(w,1)= sumpv_RailUIC60(p,1).*Discount./(1-(1./(1+Discount))^Noyears60(w,1)); annuUIC60(w,2)= sumpv_RailUIC60(p,2).*Discount./(1-(1./(1+Discount))^Noyears60(w,2)); annuBV50(w,1)= sumpv_RailBV50(p,1).*Discount./(1-(1./(1+Discount))^Noyears50(w,1));
253
annuBV50(w,2)= sumpv_RailBV50(p,2).*Discount./(1-(1./(1+Discount))^Noyears50(w,2)); end; % % % Calculate the savings per meter rail, i.e. difference between the lubricated and the unlubricated case. % Saving = anuity_Rail???(i,1) - anuity_Rail???(i,2) % savingBV50 = annuBV50(1:max(size(R)),1)-annuBV50(1:max(size(R)),2); savingUIC60 = annuUIC60(1:max(size(R)),1) - annuUIC60(1:max(size(R)),2); % % % Calculate cost for one lubricator according to BV data findings % % Maintenance cost (Service, Inspection and repair costs) % MainCostLub=6000; % mc=5800 to 6300 (Sek) per lubricator per year (12 months) % Independent of Tonnage 30 MGT per year (12 months) % Technical life of lubricator is 15 years LifeLub=15; % Discount rate = 4% Discount=0.04; % The purchase price of lubricator=26600 Sek PurchpriceLub=26000; % Lubricator Setup cost at the site = 5000 Sek LubSetCost=5000; % There are three types of lubricators (Electric (A), Gas(B) and Solar cell(C)) % Additional purchase cost for A = (50000-26600)=23400 Sek PurchpriceLubElecA=PurchpriceLub+23400; % Additional maintenance cost for B = (5800+1360)=7160Sek MainCostLubGasB=MainCostLub+1360; % Additional Purchase cost for C = (5000+26600)=31600Sek (Cost is for ten years) PurchpriceLubSolarC=PurchpriceLub+5000; % % Cost_inv_Lub = Cost of investments of Lubricators % Cost_inv_Lub(1)=(LubSetCost+PurchpriceLub); %Investments cost for one standard Lubricator Cost_inv_Lub(2)=(LubSetCost+PurchpriceLubElecA); %Investments cost for a El lub Cost_inv_Lub(3)=(LubSetCost+PurchpriceLub); %Investments cost for Gas Lub Cost_inv_Lub(4)=(LubSetCost+PurchpriceLubSolarC); %Investments cost Solar Lube % % Cost_main_Lub = Cost of investments of Lubricators % Cost_main_Lub(1)=(MainCostLub);%Maintenance cost for standard lubricator Cost_main_Lub(2)=(MainCostLub);%Maintenance cost for Type A Elc lubricator Cost_main_Lub(3)=(MainCostLub+MainCostLubGasB);%Maintenance cost for Type B Gas lubricator Cost_main_Lub(4)=(MainCostLub);%Maintenance cost for Type C Solar lubricator
254
% pv_LubMaint(1) = (Cost_main_Lub(1));% Lubricator maintenance cost is assumed same every year. Discount rate is constant over % period of time. Standard pv_LubInv(1) = (Cost_inv_Lub(1)).*Discount./(1+Discount);% Standard pv_LubMaint(2) = (Cost_main_Lub(2)); % Electrical pv_LubInv(2) = (Cost_inv_Lub(2)).*Discount./(1+Discount)^(15);% Electrical pv_LubMaint(3) = Cost_main_Lub(3);% ./(1+Discount)^(15);% Gas pv_LubInv(3) = Cost_inv_Lub(3).*Discount./(1+Discount)^(15);% Gas pv_LubMaint(4) = Cost_main_Lub(4);% ./(1+Discount)^(15);% Maint + Standard inv + Solar for 10 years pv_LubInv(4) = Cost_inv_Lub(4).*Discount./(1+Discount);% PV of Solar Lub % pv_LubSolPanel = (Cost_inv_Lub(4)-LubSetCost).*Discount./(1+Discount);% Solar panel life % % % % Calculate the Annuity cot for the four differnt Lubricators. Lubricator 4 % has solar panel that have 10 y life % anuity_LubMaint=pv_LubMaint; % for i=1:3 anuity_LubInv(i)=pv_LubInv(i)./(1-(1/(1+Discount))^15); end; anuity_LubInv(4)=pv_LubInv(4)./(1-(1/(1+Discount))^15)+pv_LubSolPanel./(1-(1/(1+Discount))^10); % anuity_Lub=anuity_LubMaint+anuity_LubInv; % % MGTL is a dummy for making plots with MGT step on x-axis % MGTL = MGT:MGT:1500; length = 1:1:max(size(R)); % % Calculate the BEP for each lubricator, each curve radii for each profile % for j=1:max(size(R)); for k=1:max(size(R)); saveMGTBV50(j,k)=savingBV50(j).*length(k); saveMGTUIC60(j,k)=savingUIC60(j).*length(k); end; end; % % %if saveMGTBV50(j,k)<=anuity_Lub(1) % BEP(j)=K %elseif saveMGTBV50(j,k)>=anuity_Lub(1) % statements2 %else % statements3 %end; % % Plot the total accumulated MGT v.s. curve radii for the choosen wear rates
255
% for i=1:max(size(R)); output(i,1)=R(i); output(i,2)=TotalMGTUIC60(i,1); output(i,3)=TotalMGTUIC60(i,2); output(i,4)=TotalMGTBV50(i,1); output(i,5)=TotalMGTBV50(i,2); output(i,6)=sumpv_RailUIC60(i,1); output(i,7)=sumpv_RailUIC60(i,2); output(i,8)=sumpv_RailBV50(i,1); output(i,9)=sumpv_RailBV50(i,2); output(i,10)=annuUIC60(i,1); output(i,11)=annuUIC60(i,2); output(i,12)=annuBV50(i,1); output(i,13)=annuBV50(i,2); output(i,14)=savingUIC60(i); output(i,15)=savingBV50(i); end; % save Case1 -ascii -double output;
Hinolub=[1.6 -0.01 8 0] With Lub No Lub With Lub No Lub With Lub No Lub With Lub No Lub
Hilub=[1.2 -0.01 4 0] Case 1 Case 1 Case 2 Case 2 Case 3 Case 3 Case 4 Case 4
A 1.2 1.6 1.2 1.6 1.2 1.5 1.2 1.8
B -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01
C 4 8 4 8 4 8 4 8
D 0 0 0 2 0 0 0 0
Replacement [SEK] cost per m UIC60 800 SEK
Replacement [SEK] cost per m BV50 653 SEK
Total critical area loss UIC60 745 mm2
Total critical area loss BV50 585 mm2
Discount rate 0.04
MGT/year 24
Annuity cost for 4 lubricators 8.68E+
03 8.72E+03 1.49E+
04 1.28E+04
Output
TotalMGTBV50 v.s. Radii
TotalMGTUIC60 v.s. Radii
Failure data MGT Interval
13.13 13.16
17.28 17.72
17.72 18.29
29.05 29.73
30.25 31.00
31.68 32.46
32.46 32.49
256
257
10.00 100.00
1.00
5.00
10.00
50.00
90.00
99.00
ReliaSoft's Weibull++ 6.0 - www.Weibull.com
Probability - Weibull
Million Gross Tonnes (MGT)
Unre
liability, F(t)
2/03/2007 16:14LUTChattopa
WeibullData 1
W2 RRX - RRM MED
F=7 / S=0CB[FM]@95.00%2-Sided-B [T2]
β=3.0983, η=27.6176, ρ=0.9456
258
Appendix – B
Data for 23 MGT from curve radius 0 to 300 meters
5.74 27.57 7 67 1 0
Low Rail
MGT Traffic wear Grinding wear No of passes Detected cracks Rail brakes Derailments
23.00 5.43 21.10 4.00 62.00 0.00 0.00
46.00 5.93 23.15 2.00 48.00 3.00 0.00
69.00 6.66 25.47 3.00 52.00 1.00 0.00
92.00 6.79 29.43 7.00 48.00 3.00 0.00
115.00 6.77 23.02 4.00 60.00 2.00 1.00
138.00 6.96 23.04 2.00 59.00 3.00 0.00
161.00 5.83 21.20 5.00 51.00 1.00 0.00
184.00 5.77 25.69 4.00 50.00 2.00 0.00
207.00 5.40 26.88 7.00 50.00 3.00 0.00
230.00 6.38 16.84 3.00 50.00 2.00 0.00
253.00 6.00 24.92 3.00 61.00 2.00 0.00
276.00 6.70 25.94 4.00 50.00 1.00 0.00
299.00 7.24 22.56 2.00 63.00 0.00 1.00
322.00 6.66 17.63 5.00 49.00 2.00 0.00
345.00 5.64 16.71 2.00 66.00 3.00 0.00
368.00 7.29 23.04 4.00 53.00 0.00 0.00
391.00 5.45 19.46 2.00 49.00 0.00 0.00
414.00 6.65 29.65 3.00 59.00 3.00 0.00
437.00 6.91 22.13 4.00 64.00 3.00 0.00
460.00 6.80 27.21 2.00 51.00 0.00 0.00
7.31 33.19 5 80 3 0
High Rail
Traffic wear Grinding wear No of passes Detected cracks Rail brakes Derailments
6.87 27.42 2.00 84.00 1.00 0.00
8.75 31.40 1.00 79.00 3.00 1.00
8.35 26.87 1.00 83.00 3.00 0.00
9.08 33.25 5.00 83.00 0.00 0.00
8.53 23.48 2.00 82.00 3.00 0.00
7.24 33.28 1.00 89.00 3.00 0.00
8.36 20.91 3.00 80.00 3.00 0.00
8.42 32.04 2.00 80.00 1.00 0.00
7.41 19.11 5.00 90.00 3.00 0.00
7.83 24.91 1.00 78.00 1.00 0.00
8.47 25.27 2.00 80.00 3.00 0.00
8.77 29.96 2.00 86.00 2.00 0.00
8.96 29.56 1.00 89.00 3.00 0.00
9.16 26.72 2.00 83.00 1.00 0.00
6.97 27.28 1.00 79.00 2.00 0.00
7.71 18.02 2.00 82.00 2.00 1.00
7.47 19.03 1.00 82.00 2.00 0.00
7.21 33.48 2.00 81.00 3.00 0.00
8.52 26.75 2.00 79.00 3.00 0.00
8.23 18.82 1.00 83.00 2.00 0.00
259
Estimation of total annuity cost for grinding, inspection, risk, down time,
replacement
Cost ofgrinding per passper meter($AUD)
2 Section Curve radii [m]
Length [m] Percentage Length [m]
Grinding production speed
10 1 0<R<300
1318 1.01% 51791
Cost ofreplacement of one rail for segment Ldue toworn outregulation ($AUD)
152 2 300<R<450
1384 1.06% 30526
Expected costs ofrepairing rail brakes($AUD)
1700 3 450<R<600
36524 27.98% 48220
Expected cost perderailment (accident) ($AUD)
3000000 4 600<R<800
33235 25.46% 130537
Expected cost ofdown timeper hour($AUD)
3136 5 800<R<1500
4569 3.50%
Inspection cost ($AUD)
0.0043 6 1500<R<9 999
4569 3.50%
New railcross sectional area
2960 7 10 000<R 718 0.55%
Critical area forreplacement decision
2520 8 Tangential track
16073 36.94%
Discount rate
0.1 Total length
130537 100.00%
Weibull constants Beta
3.6
4.5$AUD per
Kg
Weibull constants Lambda
0.001
1.36Kg per MGT
Pi(A) Probability of failure to detect the undetected potential rail breaks leading to
derailment during the NDT
(1-Pi(A)) is the probability of detecting the undetected potential rail breaks during
the NDT leading to derailment are repaired in an emergency.
Lubrication consumption
Pi(B) is the probability of detecting potential rail breaks during the NDT and
repairing immediately
(1-Pi(B)) is the probability of undetected potential rail breaks during the NDT
leading to derailment
Lubrication Cost The costs vary with quality of the
lubrication oil.
Discount rate is 10% is taken as flatrate for 23 MGT
Radius<800
Radius>800
Tangential track
260
Data for 23 MGT of curve radius from 0 to 300 meters low rail
23 Low RailYear MGT Comment Traffic
wearGrinding wear
No of passes
Detected cracks
Rail brakes
Derailments
1 23 6 25.92 3 50 1 02 46 5.38 23.16 3 60 3 03 69 7.09 26.92 4 67 3 04 92 7.27 16.85 5 64 1 05 115 5.9 16.71 4 50 3 06 138 6.98 18.11 4 61 3 07 161 6.8 27.35 3 65 1 08 184 7.21 20.54 4 64 3 09 207 7.17 28.82 4 49 2 010 230 6.87 17.03 5 51 1 011 253 6.76 22.09 4 54 3 012 276 7.23 26.24 2 62 2 013 299 7.2 19.63 5 61 2 014 322 6.56 26.4 5 60 3 015 345 7.1 18.85 5 51 3 116 368 6.53 24.56 5 52 2 017 391 No
grinding6.79 26.62 2 52 1 0
18 414 Replaced 5.4 30.32 5 49 3 0 Estimation of annuity cost for grinding low rail Grinding cost
Present value
Total PV at
Replacement
Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
7910.54 7191.47910.54 6537.6410547.39 7924.4113184.24 9005.0110547.39 6549.110547.39 5953.737910.54 4059.3610547.39 4920.4410547.39 4473.1213184.24 5083.0910547.39 3696.85273.69 1680.3613184.24 381913184.24 3471.8213184.24 3156.213184.24 2869.27
80390.76 9110.77 6.91 396.12 0.3
261
Data for 23 MGT of curve radius from 0-300 meters high rail
23 High Rail
Year MGT Comment Traffic wear
Grinding wear
No of passes
Detected cracks
Rail brakes
Derailments
1 23 8.76 20.16 2 83 1 02 46 7.89 28.44 2 83 1 03 69 8.66 32.41 2 80 1 04 92 9.02 29.15 3 84 3 15 115 9.29 23.42 2 79 2 06 138 8.16 19.61 2 80 0 17 161 8.41 23.32 1 79 3 08 184 8.97 29.7 2 80 1 09 207 7.27 24.88 2 79 1 010 230 7.22 18.36 4 79 2 011 253 6.83 26.01 2 85 2 012 276 7.12 32.88 1 87 1 013 299 9.29 25.27 4 89 2 114 322 8.25 33.75 4 82 2 015 345 No
grinding7.71 23.49 4 79 3 0
16 368 Replaced 7.32 22.77 3 79 3 0 Estimation of annuity cost for grinding high rail Grinding cost
Present value
Total PV at
Replacement
Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
5273.69 4794.275273.69 4358.435273.69 3962.27910.54 5403.015273.69 3274.555273.69 2976.862636.85 1353.125273.69 2460.225273.69 2236.5610547.39 4066.485273.69 1848.42636.85 840.1810547.39 3055.210547.39 2777.46
43406.93 5188.07 3.94 225.57 0.17
262
Average annuity cost for grinding of high rail and low rail for practical purpose Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
Grinding cost/Meter
Grinding cost/MGT/Meter
10 0.4310 0.4312 0.5216 0.712 0.5212 0.528 0.3512 0.5212 0.5218 0.7812 0.526 0.2618 0.7818 0.7810 0.4310 0.43
7149.42 5.42 310.84 0.24 Data for accumulated area loss for low rail and high rail
Low Rail High Rail
Accumulated Area Loss [mm2]
Worn out level %
Area loss/MGT
Accumulated Grinding Passes
Accumulated Area Loss [mm2]
Worn out level %
Area loss/MGT
Accumulated Grinding Passes
E(M j+1 ; M j)
31.91 7.25% 1.39 3 28.92 6.57% 1.26 2 060.45 13.74% 1.31 3 65.25 14.83% 1.42 4 0.000194.46 21.47% 1.37 7 106.32 24.16% 1.54 6 0.0001118.58 26.95% 1.29 12 144.5 32.84% 1.57 9 0.0002141.18 32.09% 1.23 16 177.2 40.27% 1.54 11 0.0004166.27 37.79% 1.2 20 204.97 46.58% 1.49 13 0.0006200.41 45.55% 1.24 23 236.7 53.79% 1.47 14 0.0009228.17 51.86% 1.24 27 275.36 62.58% 1.5 16 0.0012264.16 60.04% 1.28 31 307.51 69.89% 1.49 18 0.0016288.05 65.47% 1.25 36 333.08 75.70% 1.45 22 0.0021316.91 72.03% 1.25 40 365.92 83.16% 1.45 24 0.0026350.38 79.63% 1.27 42 405.92 92.25% 1.47 25 0.0032377.2 85.73% 1.26 47 0 0.00% 0 0 0.004410.16 93.22% 1.27 52 42 9.55% 0.13 4 0.0048436.11 99.12% 1.26 57 73.21 16.64% 0.21 8 0.00570 0.00% 0 0 103.3 23.48% 0.28 11 0.0067
33.42 7.59% 0.09 2 137.56 31.26% 0.35 12 0.007869.14 15.71% 0.17 7 164.87 37.47% 0.4 15 0.00998.36 22.35% 0.23 10 199.87 45.42% 0.46 17 -0.0508
263
Estimation of probabilities and annuity cost for risk of low rail
Low rail
Pi(B) (1-Pi(B)) Pi(A) (1-Pi(A)) Risk cost PV Risk cost
Total present value
Annuity Risk cost
Annuity Risk
cost/Meter
Annuity Risk
cost/MGT
Annuity Risk
cost/MGT/Meter
0.9804 0.0196 0 0.0196 0.024 0.02180.9524 0.0476 0 0.0476 0.087 0.07190.9571 0.0429 0 0.0429 0.2058 0.15460.9846 0.0154 0 0.0154 0.3912 0.26720.9434 0.0566 0 0.0566 0.6627 0.41150.9531 0.0469 0 0.0469 1.0195 0.57550.9848 0.0152 0 0.0152 1.4682 0.75340.9552 0.0448 0 0.0448 2.0435 0.95330.9608 0.0392 0 0.0392 2.7245 1.15540.9808 0.0192 0 0.0192 3.519 1.35670.9474 0.0526 0 0.0526 4.4864 1.57250.9688 0.0313 0 0.0313 5.5479 1.76770.9683 0.0317 0 0.0317 6.7764 1.96290.9524 0.0476 0 0.0476 8.1847 2.15530.9273 0.0545 0.0182 0.0364 26.235 6.28040.963 0.037 0 0.037 11.4265 2.48670.9811 0.0189 0 0.0189 21.8531 2.4766 0.0019 0.1077 0.0001
Probabilities of Low rail Risk cost calculations for low rail
Estimation of probabilities and annuity cost for risk for high rail
Pi(B) (1-Pi(B)) Pi(A) (1-Pi(A)) Risk cost PV Risk cost
Total present value
Annuity Risk cost
Annuity Risk
cost/Meter
Annuity Risk
cost/MGT
Annuity Risk
cost/MGT/Meter
0.9881 0.0119 0 0.0119 0.024 0.02180.9881 0.0119 0 0.0119 0.0864 0.07140.9877 0.0123 0 0.0123 0.2045 0.15370.9545 0.0341 0.0114 0.0227 0.6495 0.44360.9753 0.0247 0 0.0247 0.6585 0.40890.9877 0 0.0123 -0.0123 0.9826 0.55460.9634 0.0366 0 0.0366 1.4745 0.75660.9877 0.0123 0 0.0123 2.0304 0.94720.9875 0.0125 0 0.0125 2.71 1.14930.9753 0.0247 0 0.0247 3.5228 1.35820.977 0.023 0 0.023 4.4601 1.56320.9886 0.0114 0 0.0114 5.5259 1.76070.9674 0.0217 0.0109 0.0109 9.4098 2.72570.9762 0.0238 0 0.0238 8.1461 2.14510.9634 0.0366 0 0.0366 14.06 1.6805 0.0013 0.0731 0.0001
Probability calculations for High rail Risk cost calculations for High rail
264
Average annuity cost for risk of high rail and low rail for practical purpose Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
Risk cost/Meter
Risk cost/MGT/Meter
0 00.0001 00.0003 00.0008 00.001 00.0015 0.00010.0022 0.00010.0031 0.00010.0041 0.00020.0053 0.00020.0068 0.00030.0084 0.00040.0123 0.00050.0124 0.00050.0199 0.00090.0087 0.0004
2.0786 0.0016 0.0904 0.0001 Estimation of annuity cost for down time of low rail Down time cost
PV of Down time cost
Total PV Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
1240 11281240 10251654 12432067 14121654 10271654 9341240 6371654 7721654 7012067 7971654 580827 2632067 5992067 5442067 4952067 450827 164 12605 1429 1.08 62.11 0.05
265
Estimation of annuity cost for down time of high rail Down time cost
PV of Down time cost
Total PV Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
827 752827 683827 6211240 847827 513827 467413 212827 386827 3511654 638827 290413 1321654 4791654 4361654 396 6806 813 1 35 0.03
Average annuity cost for down time of high rail and low rail for practical purpose Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
Down time cost/Meter
Down time cost/MGT/Meter
1.57 0.06821.57 0.06821.88 0.08182.51 0.10911.88 0.08181.88 0.08181.25 0.05451.88 0.08181.88 0.08182.82 0.12271.88 0.08180.94 0.04092.82 0.12272.82 0.12272.82 0.12272.51 0.1091
1121 0.85 48.74 0.04
266
Average annuity cost for inspection of High rail and low rail for practical purpose Inspection cost
PV of Inspection
Total PV Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
Inspection cost/Meter
65 59 0.04965 54 0.04965 49 0.04965 45 0.04965 40 0.04965 37 0.04965 33 0.04965 30 0.04965 28 0.04965 25 0.04965 23 0.04965 21 0.04965 19 0.04965 17 0.04965 16 0.04965 14 0.04965 13 510 58 0.04 2.51 0
Estimation of annuity cost for replacement of Low rail Replacement cost
PV Total PV Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
199873 1998730 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0 199873 22652 17 985 1
267
Estimation of annuity cost for replacement of High rail Replacement cost
PV Total PV Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
199873 19987300000000000000 199873 23889 18 1039 1
Average annuity cost for replacement of high rail and low rail for practical purpose
Annuity cost Annuity cost/Meter Annuity cost/MGT Annuity cost/MGT/Meter
23270 17.65 1011.76 0.77
268
Estimation of annuity cost for lubrication of high rail Lubrication cost
Present value
Total PV at Replacement
Annuity cost
Annuity cost/Meter
Annuity cost/MGT
Annuity cost/MGT/Meter
985 896985 814985 740985 673985 612985 556985 506985 460985 418985 380985 345985 314985 285985 259985 236
7494 896 0.68 39 0.0295 Estimation of average annuity cost for lubrication of low rail and high rail for practical purpose Lubricatio
n cost/Meter
Lubrication
cost/Meter/MGT
Total annuity cost/meter up to
replacement
Total annuity cost/meter with
lubrication
0.75 0.030.75 0.060.75 0.10.75 0.130.75 0.160.75 0.190.75 0.230.75 0.260.75 0.290.75 0.320.75 0.360.75 0.390.75 0.420.75 0.450.75 0.490.75 0
23.97 24.65
269
Inspection data Conversion rate (AUD) 6.0892
Total track length (m) considered for analysis 130537
Insp cost NDT Car 75000 150000 225000
NDT HH 76921.60 76005.99073 76660.955
Planned 2884560.00 2850224.65 2874785.8
Risk with 3500000 Derailment cost 35622036.21 31229236.78 29953537
Total Cost 38658517.81 34305467.43 33129983
Total NDT inspection cost 3036481.60 3076230.643 3176446.77
Risk cost/meter SEK 272.89 239.24 229.46
Total Insp cost /meter SEK 23.26 23.57 24.33
Risk cost/meter AUD 44.82 39.29 37.68
Total Insp cost /meter AUD 3.82 3.87 4.00
270
Lubrication Data Data to estimate total annuity cost for Way Lubricator COST
Item $ AUD Purchase cost of lubricator 4200
Standard set up (Installation cost) per hour is $AUD 50 (2 hours*2 personnel*$AUD 50)
400
Lubricant cost per meter (Club)(AUD$132.85/1600 m) 0.08303
Vehicle cost per hour is AUD $ 45 ( for example 2.3 hours) 104
Travelling cost AUD $ 35 (for example 2.3 hours) 0 Labour and repair cost (generally 2 people) per hour AUD $ 50 (for example 2.3 hours) 163
Number Services per month 2
Expected total cost of per service 267
Expected total cost of per service per month 534 Expected total number of failures per year (for example in year 2006 failures was 5) per each lubricator 2 Unplanned Maintenance cost per failure maintenance $ AUD 190 Expected total cost of unplanned maintenance per year $ AUD 380
Expected total cost of service per year $ AUD 6403
Expected life of Lubricator (y) on an average 30
Cost of lubricant for 313 meters 25.98839
Lubricant cost per year for 313 meter rail 311.86068
Expected total cost of maintenance activity per each lubricator (Cmt) $ AUD 6905
Discount rate 0.1
Inflation every year 0.025
271
Years
Traffic during the year (Million gross tonnes, MGT)
Total number of failures every year
Expected total Unplanned maintenace cost
Expected total cost of service per year
Cost of Lubricant per year pe meter
Expected total cost of lubricant per year
Total Maintenace cost
Present Value
1998 8.576 1.00 190 6403 0.08 0.9964 6905.06 6277.33
1999 9.233 1.00 190 6403 0.08 0.9964 6905.06 5706.66
2000 9.101 1.00 190 6403 0.08 0.9964 6905.06 5187.87
2001 9.586 1.00 190 6403 0.08 0.9964 6905.06 4716.25
2002 9.438 1.00 190 6403 0.08 0.9964 6905.06 4287.50
2003 9.496 1.00 190 6403 0.08 0.9964 6905.06 3897.73
2004 9.478 1.00 190 6403 0.08 0.9964 6905.06 3543.39
Total Present Value at replacement
Annuity cost for each lubricator
Annuity cost for each lubricator per meter
Rail material cost
Rail installation cost
Total cost of rail material and installation
PV Total PV Annuity cost
Annuity cost per meter
18780 54775 73555 66868.18
73555 60789.26
73555 55262.96
73555 50239.05
73555 45671.87
73555 41519.88
33616.73 10563 33.75 73555 37745.35
73555 34313.95
73555 31194.5
73555 28358.64 451963.6 66868 213.64
Total cost/m with lubrication 247.38
272
Rail material cost
Rail installation cost
Total cost of rail material and installation
PV Total PV
Annuity cost
Annuity cost per meter
18780 54775 73555 73555 66868.18
73555 60789.26
73555 55262.96
73555 50239.05
147110 91343.74
147110 83039.76
147110 75490.69
147110 68627.9
147110 62389
147110 56717.27 670767.
8 99240.34 317.0618
Savings/m 69.6779
Savings for 313 m per year 21809.18
Savings for 313 m for 10 years 347582.2
AA35*(1-1/(1+0.1)^10)/0.1*(1.1)^10
Curve length Cost of rail per meter
313 60 300 73555 6886
Rail installation cost 175 600 147110 6886
0.99636 311.86068 800 220665 6886
207 1000 294220 6886
273
Wear Data 47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
1998 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 57 6.65
163.146 163.296 231.00 No 47 500 58.28
97.312 97.394 256.00 No 47 360 41.92
100.386 100.522 295.00 No 47 193 22.50
63.920 63.945 300.00 No 47 250 29.14
64.673 64.698 300.00 No 47 219 25.56
160.626 160.651 300.00 No 47 136 15.85
177.792 177.813 300.00 No 47 0 0.00
192.327 192.352 300.00 No 47 136 15.85
193.100 193.125 300.00 No 47 26 3.07
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
1999 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 57 6.17
163.146 163.296 231.00 No 47 526 56.99
97.312 97.394 256.00 No 47 443 47.96
100.386 100.522 295.00 No 47 193 20.89
63.920 63.945 300.00 No 47 250 27.07
64.673 64.698 300.00 No 47 219 23.74
160.626 160.651 300.00 No 47 136 14.72
177.792 177.813 300.00 No 47 0 0.00
192.327 192.352 300.00 No 47 136 14.72
193.100 193.125 300.00 No 47 26 2.85
274
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
2000 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 228 25.05
163.146 163.296 231.00 No 47 552 60.70
97.312 97.394 256.00 No 47 640 70.34
100.386 100.522 295.00 No 47 224 24.57
63.920 63.945 300.00 No 47 307 33.72
64.673 64.698 300.00 No 47 0 0.00
160.626 160.651 300.00 No 47 136 14.93
177.792 177.813 300.00 No 47 83 9.15
192.327 192.352 300.00 No 47 0 0.00
193.100 193.125 300.00 No 47 0 0.00
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
2001 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 228 23.78
163.146 163.296 231.00 No 47 552 57.63
97.312 97.394 256.00 No 47 640 66.78
100.386 100.522 295.00 No 47 281 29.27
63.920 63.945 300.00 No 47 333 34.76
64.673 64.698 300.00 No 47 189 19.67
160.626 160.651 300.00 No 47 162 16.92
177.792 177.813 300.00 No 47 83 8.69
192.327 192.352 300.00 No 47 0 0.00
193.100 193.125 300.00 No 47 0 0.00
275
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
2002 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 228 24.16
163.146 163.296 231.00 No 47 609 64.58
97.312 97.394 256.00 No 47 666 70.61
100.386 100.522 295.00 No 47 281 29.73
63.920 63.945 300.00 No 47 333 35.31
64.673 64.698 300.00 No 47 189 19.98
160.626 160.651 300.00 No 47 162 17.19
177.792 177.813 300.00 No 47 83 8.83
192.327 192.352 300.00 No 47 0 0.00
193.100 193.125 300.00 No 47 0 0.00
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
2003 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 254 26.78
163.146 163.296 231.00 No 47 609 64.18
97.312 97.394 256.00 No 47 579 60.95
100.386 100.522 295.00 No 47 307 32.32
63.920 63.945 300.00 No 47 333 35.09
64.673 64.698 300.00 No 47 246 25.86
160.626 160.651 300.00 No 47 162 17.08
177.792 177.813 300.00 No 47 83 8.77
192.327 192.352 300.00 No 47 193 20.32
193.100 193.125 300.00 No 47 57 6.00
276
47 kg Rail
Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction
2004 Reduction in Reduction in
CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss
FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT
72.466 72.484 220.00 No 47 254 26.83
163.146 163.296 231.00 No 47 609 64.30
97.312 97.394 256.00 No 47 579 61.06
100.386 100.522 295.00 No 47 307 32.38
63.920 63.945 300.00 No 47 390 41.17
64.673 64.698 300.00 No 47 272 28.68
160.626 160.651 300.00 No 47 219 23.13
177.792 177.813 300.00 No 47 83 8.79
192.327 192.352 300.00 No 47 364 38.40
193.100 193.125 300.00 No 47 83 8.79
Mechanism of Way-side Lubricators (Mechanical)
Figure B1: Mechanical lubricators (QR, 2005)
Figure B1 shows an example of a mechanical lubricator. It was found that mechanical
lubricators have been widely used because of simple, effective mechanical design and
high performance in reducing wheel and rail wear. However, evolving cutting edge
technology such as hydraulic and electric lubricators have replaced mechanical
lubricators to adapt to changes in operating and environmental conditions.
The basic components of a Mechanical Lubricator are:
(A) Grease Container: Contains a piston attached to the springs which supplies the
energy to deliver the grease to the hose to be picked up by the wheel flange. In
addition, it contains a valve to ensure safe filling of the tank and provide
protection to the operation (as it is operating in high pressure). Selection of
the tank is based on the volume of traffic which passes the lubricator. The
lubricator comes with a range of tank capacity from 9 kg to 75 kg.
277
(B) Grease Pump: The grease pump is clamped or bolted outside of the rail for the
wheel tread to push the grease pump to create pressure in the grease container.
(C) Grease Distribution Unit: A pair of blades/wiping bars are clamped or bolted
at gauge face of the rail. Grease is distributed evenly on and along the length
of the wiping bars. The length of the wiping bars varies from 400 mm to 600
mm depending on the model.
(D) Grease Hose System: The larger diameter of the grease hose system enables
the grease to travel to the delivery hose and be distributed evenly on the
wiping bars. The position of the grease container on the ballast must be
carefully taken into consideration as the vibration from the traffic may
damage the mechanical operation of the lubricator.
(E) Grease Delivery Hose System: The hose acts as a transport medium between
the tank and the distribution unit. The hoses are long and smaller in diameter
than the feed hose. The grease travelling in the hose will be under high
internal pressure. The lubricator maintainer has to ensure that the hose does
not leak. In addition, the placement of the hose under the rail must be given
tolerance to avoid pressure drop (which can break the hose) and squashing.
Positive Displacement Pump
Displacement moves the liquid from one place to another place. As the plunger moves
toward the inside of the cylinder, liquid is displaced. The plunger displacement is
positive and the volume displaced is equal to the volume of the plunger in the
cylinder. Therefore, grease pump that displaces constant volume of grease is defined
as positive displacement pump (as shown in Figure B2).
Figure B2: Plunger mechanism (QR, 2005)
Mechanism of Hydraulic Lubricators
Hydraulic lubricators are widely used on track for rail flange lubrication. However,
maintenance of these lubricators shall not be neglected. These lubricators are designed
for:
278
� Effective lubrication
� Economic solution to lubrication
� Minimum maintenance
� Use under any operating condition (eg. Tracks, MGT, temperature etc)
� Improvement of grease distribution
� Ease and convenience (for example, simple operation and easy adjustments
when tank filling)
The lubricator is designed in 3 different sizes: 12.5 kg, 25 kg and 37.5kg.
Visual Inspection
Visual inspection is commonly used by rail players to assess the effectiveness of the
lubricators and lubricants. Finger or “smear test” on the gauge faces helps to assess
lubricant distribution (as shown in Figure B3). This is useful to understand the need
for adjusting plunger height and blade position (Reiff, 1991).
Figure B3: Smear Test (Powell and Wheatley, 2004)
Rail head temperature rise method
Rail head temperature rise method is used to indicate the effectiveness of lubrication.
For energy, a Type K thermocouple is placed at the lower corner of the gauge side. To
avoid/compensate for noise effects, another thermocouple is located on a dummy rail
section. In order to accommodate longer operations, photo – voltaic arrays is used to
maintain battery power in remote locations.
Table B1: Mean temperature rise (Tew and Mutton, 1991)
Condition Mean Temperature Rise (°C)
Fully Lubricated 0 – 0.5°C
Dry 2 – 3 °C
Non Lubricated 5°C
279
Table B1 shows mean temperature rise, indicating the condition of the lubricated rail
track under metropolitan transit conditions. Tew and Mutton (1991) found that this
method is applicable for heavy haul conditions where higher temperature rise occurs.
Tribometer
Use of the tribometer overcomes limitations of visual and scientific methods. It
provides data on limiting co-efficient of friction for both rail top and gauge faces. The
tribometer is able to measure friction as a function of distance from trackside
lubricator, lubricants and application rates (dose amount and frequency). Table B2
shows friction coefficients based on tribometer measurements.
Table B2: Friction Coefficients based on Tribometer (Tew and Mutton, 1991)
Condition Friction Coefficient
Fully Effective Lubrication 0.1 – 0.15
Dry 0.35 – 0.45
Unlubricated > 0.45
Advantages of The tribometer:
� accurate assessment of friction as an indicator of wear
� objective comparison over a wide range of track locations and conditions
� provision of friction data for service conditions and rail profiles
Figure B4: Tribometer at the gauge face (Powell and Wheatley, 2004)
Figure B4 shows the application of the tribometer for measuring friction. However,
the tribometer is not equipped with high storage facilities required for inspecting large
track section.
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