Nannan Zong B.E.(Hons), M.E.eprints.qut.edu.au/61125/1/Nannan_Zong_Thesis.pdf · DEVELOPMENT OF...
Transcript of Nannan Zong B.E.(Hons), M.E.eprints.qut.edu.au/61125/1/Nannan_Zong_Thesis.pdf · DEVELOPMENT OF...
DEVELOPMENT OF OPTIMAL DESIGNS OF
INSULATED RAIL JOINTS
By
Nannan Zong B.E.(Hons), M.E.
Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
School of Civil Engineering and Built Environment
Science and Engineering Faculty
Queensland University of Technology
2013
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Development of Optimal Designs of Insulated Rail Joints i
Abstract
Proper functioning of Insulated Rail Joints (IRJs) is essential for the safe operation of the
railway signalling systems and broken rail identification circuitries. The Conventional IRJ
(CIRJ) resembles structural butt joints consisting of two pieces of rails connected together
through two joint bars on either side of their web and the assembly is held together through
pre-tensioned bolts. As the IRJs should maintain electrical insulation between the two rails,
a gap between the rail ends must be retained at all times and all metal contacting surfaces
should be electrically isolated from each other using non-conductive material. At the gap,
the rail ends lose longitudinal continuity and hence the vertical sections of the rail ends are
often severely damaged, especially at the railhead, due to the passage of wheels compared
to other continuously welded rail sections.
Fundamentally, the reason for the severe damage can be related to the singularities of the
wheel-rail contact pressure and the railhead stress. No new generation designs that have
emerged in the market to date have focussed on this fundamental; they only have provided
attention to either the higher strength materials or the thickness of the sections of various
components of the IRJs. In this thesis a novel method of shape optimisation of the railhead
is developed to eliminate the pressure and stress singularities through changes to the
original sharp corner shaped railhead into an arc profile in the longitudinal direction. The
optimal shape of the longitudinal railhead profile has been determined using three non-
gradient methods in search of accuracy and efficiency: (1) Grid Search Method; (2)
Genetic Algorithm Method and (3) Hybrid Genetic Algorithm Method. All these methods
have been coupled with a parametric finite element formulation for the evaluation of the
objective function for each iteration or generation depending on the search algorithm
employed.
The optimal shape derived from these optimisation methods is termed as Stress Minimised
Railhead (SMRH) in this thesis. This optimal SMRH design has exhibited significantly
reduced stress concentration that remains well below the yield strength of the head
hardened rail steels and has shifted the stress concentration location away from the critical
zone of the railhead end. The reduction in the magnitude and the relocation of the stress
concentration in the SMRH design has been validated through a full scale wheel – railhead
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interaction test rig; Railhead strains under the loaded wheels have been recorded using a
non-contact digital image correlation method. Experimental study has confirmed the
accuracy of the numerical predications.
Although the SMRH shaped IRJs eliminate stress singularities, they can still fail due to
joint bar or bolt hole cracking; therefore, another conceptual design, termed as Embedded
IRJ (EIRJ) in this thesis, with no joint bars and pre-tensioned bolts has been developed
using a multi-objective optimisation formulation based on the coupled genetic algorithm –
parametric finite element method. To achieve the required structural stiffness for the safe
passage of the loaded wheels, the rails were embedded into the concrete of the post
tensioned sleepers; the optimal solutions for the design of the EIRJ is shown to simplify
the design through the elimination of the complex interactions and failure modes of the
various structural components of the CIRJ.
The practical applicability of the optimal shapes SMRH and EIRJ is demonstrated through
two illustrative examples, termed as improved designs (IMD1 & IMD2) in this thesis;
IMD1 is a combination of the CIRJ and the SMRH designs, whilst IMD2 is a combination
of the EIRJ and SMRH designs. These two improved designs have been simulated for two
key operating (speed and wagon load) and design (wheel diameter) parameters that affect
the wheel-rail contact; the effect of these parameters has been found to be negligible to the
performance of the two improved designs and the improved designs are in turn found far
superior to the current designs of the CIRJs in terms of stress singularities and deformation
under the passage of the loaded wheels. Therefore, these improved designs are expected to
provide longer service life in relation to the CIRJs.
Keywords: Insulated rail joint, Stress minimisation, Multi-objective optimisation, Edge
effect, Shape optimisation, Wheel-rail contact, Parametric finite element method
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Development of Optimal Designs of Insulated Rail Joints iii
List of Publications
From the research carried out, the following publications have emerged:
Journal Papers:
Zong, N, & Dhanasekar, M. (2012). Minimisation of Railhead Edge Stresses through
Shape Optimisation. Engineering Optimization
(DOI:10.1080/0305215X.2012.717075)
Zong, N. & Dhanasekar, M. (2012). Analysis of Rail Ends under Wheel Contact
Loading. International Journal of Aerospace and Mechanical Engineering, 6, 452-
460.
Zong, N., Askarinejad, T., Bandula Heva, T. & Dhanasekar, M. (2012). Service Condition
of Railroad Corridors around the Insulated Rail Joints. Journal of Transportation
Engineering, ASCE. (Accepted-In press)
Zong, N. & Dhanasekar, M. (2012). Shape optimisation of gap-joints subject to rigid
cylinder contact. Journal of Structural Engineering & Mechanics. (Under review)
Zong, N. & Dhanasekar, M. (2012). Experimental studies on the performance of rail joints
with modified wheel-railhead contact. Proceedings of the Institution of Mechanical
Engineers, Part F. Journal of Rail and Rapid Transit. (Under Review).
Conference Papers:
Zong, N., Dhanasekar, M., Bayissa, W. & Boyd, P. (2010). Study of wheel-rail impact at
insulated rail joint through experimental and numerical methods. In Key
Technologies of Railway Engineering-High-speed Railway, Heavy Haul Railway
and Urban Rail Transit, China Railway Publishing House, Beijing Jiao Tong
University, Beijing, pp. 356-360.
Boyd, P., Mandal, N., Thaminda Bandula Heva, T., Zong, N & Dhanasekar, M. (2012).
Experimental Investigation into the Failure Behaviour of Insulated Rail Joints.
Conference on Railway Engineering, Brisbane, 53-60.
CRC reports:
Zong, N. & Dhanasekar, M. (2011). Shape optimisation of gap-jointed elastic bodies
subjected to the passage of rigid cylinders. CRC for Rail Innovation. Project
research report for ―R3.100 Longer life for Insulated Rail Joints‖.
Zong, N., Bandula Heva, T., Askarinejad, H. & Dhanasekar, M. (2011). Analysis of field
data for service condition assessment of insulated rail joints. CRC for Rail
Innovation. Projected research report for ―R3.100 Longer life for Insulated Rail
Joints‖.
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Table of Contents
Abstract............................................................................................................................................. i
List of Publications .......................................................................................................................... iii
Table of Contents .............................................................................................................................iv
List of Figures ................................................................................................................................ vii
List of Tables ...................................................................................................................................xi
List of Symbols .............................................................................................................................. xii
List of Abbreviations ....................................................................................................................... xv
Acknowledgments .........................................................................................................................xvii
Preface .........................................................................................................................................xviii
CHAPTER 1: INTRODUCTION ...................................................................................................1
1.1 Introduction ............................................................................................................................1
1.2 Aims and Objectives ...............................................................................................................3
1.3 Scope and Limitations.............................................................................................................3
1.4 Thesis Structure ......................................................................................................................4
CHAPTER 2: LITERATURE REVIEW .......................................................................................7
2.1 Introduction ............................................................................................................................7
2.2 Design of IRJ ..........................................................................................................................7
2.3 Failure Mechanism of IRJs: Local and Global Perspectives ................................................... 11 2.3.1 Local failure .............................................................................................................. 11 2.3.2 Global failure ............................................................................................................. 12
2.4 Review of the Mechanics of Wheel-Railhead Edge Contact ................................................... 14 2.4.1 Classical wheel-rail contact mechanics ....................................................................... 14
2.4.1.1 Normal wheel-rail contact-Hertz Contact Theory (HCT)............................ 14 2.4.1.2 Normal wheel-rail contact-semi-Hertzian contact model ............................ 18
2.4.2 Advanced contact mechanics associated with the geometry edge effect ....................... 22 2.4.2.1 Edge effect ............................................................................................... 22 2.4.2.2 Indentation of body with free edge into half space ..................................... 23 2.4.2.3 Indentation of body into quarter space ....................................................... 24
2.5 Performance Study of the IRJs .............................................................................................. 29 2.5.1 Static wheel-rail contact analysis ................................................................................ 29 2.5.2 Dynamic wheel/rail contact simulations using rigid multibody dynamics .................... 31 2.5.3 Dynamic wheel/rail contact simulations using finite element method .......................... 34
2.6 Some Modified Novel Designs of IRJ ................................................................................... 36
2.7 Summary .............................................................................................................................. 38
CHAPTER 3: CONCEPTUAL DESIGNS OF IRJ FOR IMPROVED PERFORMANCE ........ 41
3.1 Introduction .......................................................................................................................... 41
3.2 Conceptual Design Principles ................................................................................................ 41
3.3 A Conceptual Design of Stress Minimised Railhead (SMRH) ................................................ 43
3.4 A Conceptual Design of Embedded IRJ................................................................................. 45
3.5 Summary .............................................................................................................................. 49
CHAPTER 4: DEVELOPMENT OF STRESS MINIMISED RAILHEAD (SMRH) ................. 51
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4.1 Introduction .......................................................................................................................... 51
4.2 Problem Definition for Stress Minimisation........................................................................... 51 4.2.1 Optimisation formulation ........................................................................................... 52 4.2.2 Scope of the optimisation formulation ........................................................................ 53
4.3 Modelling of Simulation-based Optimisation......................................................................... 54 4.3.1 FE modelling using Python ........................................................................................ 54 4.3.2 Implementation of optimisation algorithms ................................................................. 61 4.3.3 Optimisation framework............................................................................................. 65
4.4 Application to the Development of SMRH ............................................................................ 66 4.4.1 Comparison of optimal result from GSM and GA ....................................................... 67 4.4.2 Effect of wheel loads to optimal shape ........................................................................ 70 4.4.3 Effect of SMRH to contact pressure............................................................................ 73 4.4.4 Effect of SMRH to stress distribution ......................................................................... 75 4.4.5 Sensitivity of GA parameters ...................................................................................... 77
4.5 Hybrid GA for Development of SMRH ................................................................................. 79 4.5.1 Hybrid genetic algorithms .......................................................................................... 79 4.5.2 Hybridisation of GA with heuristic pattern move ........................................................ 81 4.5.3 Performance in stress minimisation of railhead end ..................................................... 84
4.6 Summary .............................................................................................................................. 90
CHAPTER 5: EXPERIMENTAL VALIDATION OF THE STRESS MINIMISED RAILHEAD
(SMRH) ………………………………………………………………………………………...93
5.1 Introduction .......................................................................................................................... 93
5.2 Preparation of Test Specimens for Strain Measurement ......................................................... 93 5.2.1 Manufacturing of test specimens ................................................................................ 93 5.2.2 Strategy for measuring rail end strain ......................................................................... 96
5.3 Loading Program in Experimental Study ............................................................................. 102
5.4 Experimental Test Setup ..................................................................................................... 103
5.5 Summary ............................................................................................................................ 112
CHAPTER 6: PERFORMANCE OF THE STRESS MINIMISED RAILHEAD (SMRH) ...... 113
6.1 Introduction ........................................................................................................................ 113
6.2 Strain Gauge Data ............................................................................................................... 113 6.2.1 Data from static wheel load ...................................................................................... 113 6.2.2 Typical data from repetitive rolling wheel load program ........................................... 117
6.3 Feasibility of PIV ............................................................................................................... 121 6.3.1 Static load experiments ............................................................................................ 121 6.3.2 Repetitive rolling wheel load .................................................................................... 124
6.4 Performance Examination of the SMRH .............................................................................. 125 6.4.1 Distribution of strain components ............................................................................. 126 6.4.2 Contact-stress response of the SMRH ....................................................................... 134 6.4.3 Behaviour of the SMRH under repetitive rolling wheel ............................................. 137
6.5 Summary ............................................................................................................................ 139
CHAPTER 7: DEVELOPMENT OF EMBEDDED IRJ (EIRJ) ............................................... 141
7.1 Introduction ........................................................................................................................ 141
7.2 Formulation of the Optimisation Model for EIRJ ................................................................. 141 7.2.1 Functions of the EIRJ ............................................................................................... 141 7.2.2 Formulation of optimisation problem ........................................................................ 142
7.3 Multi-objective Optimisation Modelling .............................................................................. 145 7.3.1 Finite element modelling of the EIRJ ........................................................................ 145 7.3.2 Multi-objective optimisation—NSGA-II................................................................... 151
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7.3.3 Coupling of FEM and NSGA-II................................................................................ 154
7.4 Optimisation Result and Discussion .................................................................................... 156 7.4.1 Evolution of pareto-optimal solutions ....................................................................... 157 7.4.2 Discussion of practical feasibility for the optimal solutions ....................................... 159
7.5 Summary ............................................................................................................................ 162
CHAPTER 8: SIMULATION OF FIELD APPLICATION OF THE OPTIMAL IRJ DESIGNS165
8.1 Introduction ........................................................................................................................ 165
8.2 Improved Designs of IRJ .................................................................................................... 165
8.3 Dynamic FE Modelling ....................................................................................................... 167 8.3.1 Idealisation of geometry ........................................................................................... 168 8.3.2 Idealisation of support system .................................................................................. 169 8.3.3 Implicit to explicit wheel-rail contact........................................................................ 170
8.4 Dynamic Responses of IRJ at Wheel Contact-Impact .......................................................... 173 8.4.1 Contact impact force at IRJ ...................................................................................... 173 8.4.2 Contact pressure at IRJ ............................................................................................. 175 8.4.3 Von Mises stress distribution at IRJ .......................................................................... 177 8.4.4 Deflections of railhead ends ..................................................................................... 178
8.5 Field Applications of the Improved Designs ........................................................................ 180
8.6 Sensitivity Study ................................................................................................................. 183 8.6.1 Effect of load magnitude .......................................................................................... 184 8.6.2 Effect of travelling speed.......................................................................................... 185 8.6.3 Effect of wheel radius .............................................................................................. 188
8.7 Summary ............................................................................................................................ 189
CHAPTER 9: SUMMARY & CONCLUSIONS ........................................................................ 191
9.1 Conclusions ........................................................................................................................ 193 9.1.1 General conclusions ................................................................................................. 193 9.1.2 Specific conclusions ................................................................................................. 194
9.2 Recommendation & Future Work ........................................................................................ 195
REFERENCES ............................................................................................................................ 197
APPENDICES ............................................................................................................................. 205
Appendix A: EXAMPLE of PARAMETRIC FE MODELING USING PYTHON .......................... 205
Appendix B: DATA OF STRAIN GAUGES 5, 6, 7 & 8 AT STATIC WHEEL LOAD .................. 209
Appendix C: DATA OF STRAIN GAUGES 5, 6, 7 & 8 AT REPETITIVE LOADED WHEEL ..... 213
Appendix D: COMPARISON OF VERTICAL STRAIN AT POINTS OF GAUGES 2, 3 & 4. 214
Appendix E: SENSITIVITY OF DESIGN AND OPERATIONAL DESIGN PARAMETERS ........ 215
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List of Figures
Figure 1-1: A block diagram of a rail break/vehicle detection system ..................................................1
Figure 1-2: Typical design of IRJ in rail track system .........................................................................2
Figure 2-1: Typical insulated joint assembly (AS1085.12, 2002) ........................................................8
Figure 2-2: An insulated rail joint with 6-bolt joint bars in Australia ...................................................8
Figure 2-3: Suspended IRJ .................................................................................................................9
Figure 2-4: Supported IRJ ..................................................................................................................9
Figure 2-5: Various cross-sectional shapes of joint bar ..................................................................... 10
Figure 2-6: Different shapes of joint gap .......................................................................................... 10
Figure 2-7: Configuration of a gap-jointed rail ends subject to wheel contact loading ........................ 11
Figure 2-8: Two local failure modes in Australian heavy haul networks ............................................ 12
Figure 2-9: ―Step‖ mechanism at insulated rail joint ......................................................................... 13
Figure 2-10: Various global failure modes of IRJs ............................................................................ 13
Figure 2-11: Contact between two non-conformal bodies ................................................................. 15
Figure 2-12: Wheel-rail contact configuration .................................................................................. 17
Figure 2-13: Geometrical penetration of contact bodies .................................................................... 19
Figure 2-14: Schematic procedure of discretisation in semi-Hertzian contact solution ....................... 21
Figure 2-15: Rigid punch contacting with half plane......................................................................... 23
Figure 2-16: Contact problem and contact result............................................................................... 24
Figure 2-17: Frictionless indentation of quarter plane by a rigid cylindrical punch ............................ 25
Figure 2-18: Sketch of the contact characteristics as cylindrical axis over free edge .......................... 26
Figure 2-19: Frictionless indentation of quarter plane by a rigid cylindrical punch ............................ 27
Figure 2-20: Distribution of contact pressure at different contact distance ...................................... 28
Figure 2-21: Static analytical model for insulated rail joint (Kerr and Cox 1999) .............................. 29
Figure 2-22: 2D wheel-rail contact at unsupported rail end (Chen (2003))......................................... 30
Figure 2-23: 3D wheel rail contact at IRJ (Zong and Dhanasekar (2012)) ......................................... 31
Figure 2-24: History of contact force over the rail joint (Jenkins et al. 1974) ..................................... 32
Figure 2-25: Multi-body dynamic model (Sun and Dhanasekar, 2002) .............................................. 33
Figure 2-26: Contact impact force at different settlement around IRJ ................................................ 34
Figure 2-27: 3D dynamic FE analysis (Wen et al. (2005)) ................................................................ 35
Figure 2-28: Dynmic FE analysis of whee contact-impact at IRJ ...................................................... 35
Figure 2-29: Cross section and plan view of tapered insulated rail joint (Plaut et al. 2007) ................ 37
Figure 2-30: New design of IRJ with a joint saddle .......................................................................... 37
Figure 3-1: Overall schematic conceptual design principles .............................................................. 42
Figure 3-2: Conceptual design of local railhead shape for stress minimisation................................... 44
Figure 3-3: Definition of design problem for eliminating the local failure modes .............................. 45
Figure 3-4: Assembly of conceptual design of EIRJ ......................................................................... 46
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Figure 3-5: Insulating material between the embedded steel rail and the concrete sleeper .................. 46
Figure 3-6: Design requirements for the EIRJ................................................................................... 48
Figure 4-1: Design parameters defining arc shape at rail end corner .................................................. 52
Figure 4-2: Python script interacting with Abaqus ............................................................................ 55
Figure 4-3: Sketch of wheel rail contact model at free end ................................................................ 56
Figure 4-4: Arc surface modelling using Python programming ......................................................... 57
Figure 4-5: Wheel coupling strategy ................................................................................................ 59
Figure 4-6: Finite element model ..................................................................................................... 60
Figure 4-7: Result of mesh sensitivity study ..................................................................................... 61
Figure 4-8: Scheme of grid search method ....................................................................................... 62
Figure 4-9: Binary coding of design parameters in GA ..................................................................... 63
Figure 4-10: Genetic operators ......................................................................................................... 64
Figure 4-11: Schematic diagram for the proposed optimisation model .............................................. 66
Figure 4-12: Profile of optimal result using GSM ............................................................................. 68
Figure 4-13: Evolution of optimal maximum von Mises stress at load ........................................... 70
Figure 4-14: Evolution of optimal von Mises stress at unloaded 0.2 ............................................... 71
Figure 4-15: Optimal shape at the symmetrical plane of the rail edge ................................................ 72
Figure 4-16: Distribution of contact pressure at railhead surface ....................................................... 73
Figure 4-17: Contact pressure and deflection of the contact surface along the rail symmetric plane
(z=0) ............................................................................................................................... 74
Figure 4-18: Distribution of von Mises stress in the SMRH and SCRH ............................................. 75
Figure 4-19: GA evolution using larger mutation rate 0.05 instead of 0.005 ...................................... 78
Figure 4-20: GA evolution using larger crossover rate 0.9 instead of 0.7 ........................................... 78
Figure 4-21: GA evolution using larger population size 40 instead of 20 ........................................... 79
Figure 4-22: Flow chart of hybrid GA based on heuristic pattern move ............................................. 83
Figure 4-23: Evolution of optimal solution at wheel load F .............................................................. 87
Figure 4-24: Effect of local parameter on the genetic evolution ( =0.5) ........................................ 89
Figure 4-25: Effect of local parameter on the genetic evolution ( =0.5) ........................................ 89
Figure 5-1: Manufacture of optimal arc shape in SMRH ................................................................... 94
Figure 5-2: Reinforced cage welded with rail bottom and base plate ................................................. 95
Figure 5-3: Setup for concreting and the final product ...................................................................... 95
Figure 5-4: Principles of PIV analysis .............................................................................................. 97
Figure 5-5: Calculation of lateral strain using two patches ......................................................... 98
Figure 5-6: Calculation of vertical strain using two patches in (a) Image 1 (b) Image 2 .............. 99
Figure 5-7: Calculation of shear strain using two patches in (a) Image 1 (b) Image 2.................. 99
Figure 5-8: Camera body and long-distance microscope ................................................................. 100
Figure 5-9: Location of four strain gauges at railhead end ............................................................... 101
Figure 5-10: Location of strain gauges along the depth of rail end .................................................. 101
Figure 5-11: Static wheel loading positions .................................................................................... 102
Figure 5-12: Repetitive rolling of loaded and unloaded wheel ......................................................... 103
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Development of Optimal Designs of Insulated Rail Joints ix
Figure 5-13: Design of load rig ...................................................................................................... 105
Figure 5-14: Installation of rail specimen onto the load rig ............................................................. 105
Figure 5-15: Trajectories of vertical and horizontal actuators at static load 130kN .......................... 106
Figure 5-16: Typical one time moving load procedure .................................................................... 107
Figure 5-17: Camera installation for PIV photographing................................................................. 109
Figure 5-18: Typical image at railhead end surface ......................................................................... 110
Figure 5-19: Strain gauge recording ............................................................................................... 110
Figure 5-20: Flowchart of the overall control during the lab test ..................................................... 111
Figure 6-1: Gauge-1 data ............................................................................................................... 114
Figure 6-2: Gauge-2 data ............................................................................................................... 115
Figure 6-3: Gauge-3 data ............................................................................................................... 115
Figure 6-4: Gauge-4 data ............................................................................................................... 116
Figure 6-5: Distribution of vertical strain along depth of rail end .............................................. 116
Figure 6-6: Strain gauge signature from Gauge-1 to Gauge-4 ......................................................... 118
Figure 6-7: Enlarged view of vertical strain history of Guage-1 at 130kN ....................................... 119
Figure 6-8: Typical strain signature in one time rolling wheel load at gauge-1 ................................ 120
Figure 6-9: Test patches generated surrounding the point of Gauge-1 ............................................. 122
Figure 6-10: Comparison of vertical strain at point of Gauge-1 in the SCRH ............................ 122
Figure 6-11: Comparison of vertical strain at point of Gauge-1 in the SMRH ........................... 123
Figure 6-12: Comparison of vertical strain in the SCRH ........................................................... 124
Figure 6-13: Comparison of vertical strain in the SMRH .......................................................... 125
Figure 6-14: Vertical strain variation at 130kN in the SCRH .......................................................... 127
Figure 6-15: Vertical strain variation at 130kN in the SMRH.......................................................... 128
Figure 6-16: Shear strain variation at 130kN in the SCRH .............................................................. 130
Figure 6-17: Shear strain variation at 130kN in the SMRH ............................................................. 131
Figure 6-18: Lateral strain variation at 130kN in the SCRH ............................................................ 132
Figure 6-19: Lateral strain variation at 130kN in the SMRH ........................................................... 133
Figure 6-20: Vertical strain in symmetric plane of the rail ........................................................ 136
Figure 6-21: Vertical strain history under the repetitive moving load in the SCRH .......................... 138
Figure 6-22: Vertical strain history under the repetitive moving load in SMRH ............................... 138
Figure 6-23: Contact patch after repetitive rolling of loaded wheel ................................................. 139
Figure 7-1: Design parameters of half of EIRJ ................................................................................ 143
Figure 7-2: Schematic diagram for the simplified model of the EIRJ............................................... 146
Figure 7-3: One single part with different material regions ............................................................. 147
Figure 7-4: Simplification of wheel contact load to concentrated load ............................................. 148
Figure 7-5: Idealisation of normal ballasted sleeper support ............................................................ 149
Figure 7-6: Finite element model of EIRJ ....................................................................................... 150
Figure 7-7: Procedure of non-dominated sorting and crowding distance sorting .............................. 152
Figure 7-8: Integrated optimisation procedure coupled with FEM and NSGA-II ............................. 155
Figure 7-9: Static wheel load at railhead ends in CIRJ .................................................................... 156
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Figure 7-10: Evolution of pareto-optimal solutions ......................................................................... 157
Figure 7-11: Details of design Solution 1 ....................................................................................... 160
Figure 7-12: Details of design Solution 2 ....................................................................................... 161
Figure 7-13: Details of design Solution 3 ....................................................................................... 162
Figure 8-1: Two improved designs of IRJ ...................................................................................... 166
Figure 8-2: Simplification of contact interaction amongst various components................................ 168
Figure 8-3: IRJ model consisting of solid rail and beam rail............................................................ 169
Figure 8-4: Simplified supporting system different designs of IRJ .................................................. 170
Figure 8-5: Wheel loading and boundary condition in implicit and explicit analysis ........................ 171
Figure 8-6: Finite element model of three chosen designs of IRJ ..................................................... 172
Figure 8-7: Contact force histories for the three chosen designs ...................................................... 174
Figure 8-8: Contact pressure distribution at wheel crossing the joint gap ......................................... 176
Figure 8-9: Von Mises distribution at wheel crossing the joint gap ................................................. 177
Figure 8-10: Deflections as wheel passing over joint gap ................................................................ 179
Figure 8-11: Manufacturing procedure of improved designs of the IRJs .......................................... 181
Figure 8-12: Field installation of the improved designs................................................................... 182
Figure 8-13: Grinding process in the vicinity of the SMRH ............................................................ 183
Figure 8-14: Contact impact facotr and impact rate with different travelling speed .......................... 186
Figure 8-15: Maximum contact pressure at different travelling speed .............................................. 187
Figure 8-16: Vertical deflection at different travelling speed ........................................................... 188
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List of Tables
Table 2-1: Relations of non-dimensional coefficients , and (Iwnicki, 2006) ............................. 18
Table 4-1: Elastic property of wheel rail steel and end post ............................................................... 58
Table 4-2: GA parameter values used in optimisation ....................................................................... 67
Table 4-3: Comparison of optimal design parameters at wheel load and 0.2 ............................... 71
Table 4-4: Comparison of SCRH and SMRH at different wheel positions ......................................... 76
Table 4-5: Hybrid GA parameter values used in optimisation ........................................................... 84
Table 4-6: Optimal stress from hybrid GA ....................................................................................... 85
Table 4-7: Optimal design parameters from hybrid GA .................................................................... 86
Table 4-8: Comparison of converging runs from simple GA and hybrid GA ..................................... 88
Table 5-1: Selected PIV photographing cycles ............................................................................... 108
Table 5-2: Selected wheel positions at moving load cycle .............................................................. 108
Table 5-3: Example of control program .......................................................................................... 112
Table 7-1: Genetic operators in NSGA-II ....................................................................................... 155
Table 7-2: Objective values and structural displacements for the selected three solutions ................ 158
Table 7-3: Optimal design parameters for the selected three optimal solutions ................................ 159
Table 8-1: Effect of load magnitude on maximum von Mises stress at speed of 80km/h .................. 185
Table 8-2: Effect of load magnitude on vertical deflection at speed of 80km/h ................................ 185
Table 8-3: Effect of wheel radius on the maximum von Mises stress ............................................... 188
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List of Symbols
Latin Symbols
-- relative curvature about axis,
-- relative curvature about axis,
-- elastic modulus,
-- vertical load,
-- elastic shear modulus,
-- generalized Cauchy kernel (Hanson and Keer 1989),
-- lower limit vectors of design parameters,
-- jth
generation,
-- upper limit vectors of design parameters,
-- vector of design parameters,
-- corrected relative curvature about direction in semi-Hertzian contact,
-- corrected relative curvature about direction in semi-Hertzian contact,
-- first newly generated two individual in hybrid GA,
-- second newly generated two individual in hybrid GA,
--damping coefficient for the normal prestress concrete sleeper support,
--damping coefficient of the modified embedding sleeper,
-- normal contact force of strip at point in semi-Hertzian contact,
--spring stiffness of the modified embedding sleeper,
--spring stiffness of the normal prestress concrete sleeper support,
-- lower limit of design parameter ,
-- lower limit of design parameter ,
-- first impact peak during the contact impact at IRJ,
-- second impact peak during the contact impact at IRJ,
-- crossover rate in GA,
-- individual with the best fitness value in the previous generation,
-- individual with the best fitness value in the current generation,
-- mutation rate in GA,
--parent population in NSGA-II,
--newly generated population in NSGA-II,
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-- principle radius of Body-1 about direction,
-- principle radius of Body-1 about direction,
-- principle radius of Body-2 about direction,
-- principle radius of Body-2 about direction,
-- principle radius of the rail about axis,
-- principle radius of the rail about axis,
-- principle radius of the wheel about axis,
-- principle radius of the wheel about axis,
--a set of individuals that the individual dominates in NSGA-II.
-- upper limit of design parameter ,
-- upper limit of design parameter ,
-- major half axis of contact ellipse in HCT,
-- minor half axis of contact ellipse in HCT,
-- contact distance between cylindrical axis and free edge of quarter space,
-- depth of arc surface at the railhead end,
-- design objective function,
-- geometric separation between Body-1 and 2,
-- length of arc surface at the railhead end,
-- non-dimensional coefficients in HCT,
-- non-dimensional coefficients in HCT,
-- contact pressure,
-- Hertzian coefficient,
-- Poisson‘s ratio.
-- major half axis of geometric ellipse in semi-Hertzian contact,
-- contact length for strip at point in semi-Hertzian contact,
-- minor half axis of geometric ellipse in semi-Hertzian contact,
-- first order derivative of geometric separation between Body-1 and 2,
-- second order derivative of geometric separation between Body-1 and 2.
-- jth
digit of design variable ,
--domination count in NSGA-II,
-- maximum contact pressure in HCT,
-- longitudinal displacement at rail end,
-- design limit of longitudinal displacement at rail end,
xiv
xiv Development of Optimal Designs of Insulated Rail Joints
-- lateral displacement at rail end,
-- design limit of lateral displacement at rail end,
-- vertical displacement at rail end,
-- vertical deformation at contact point of Body-1,
-- vertical deformation at contact point of Body-2,
-- design limit of vertical displacement at rail end,
-- ith
design parameters,
-- contact surface profile of Body-1,
-- contact surface profile of Body-2,
--the increase in the volume of the modified rail,
the increase in the volume of the modified sleeper,
-- width of trip at point in semi-Hertzian contact,
Greek Symbols
-- corrected vertical interpenetration in semi-Hertzian contact,
-- maximum vertical deformation of Body-1,
-- maximum vertical deformation of Body-2,
-- interpenetration for strip at point in semi-Hertzian contact,
-- lateral strain at rail end,
-- in plane shear strain at rail end,
-- vertical strain at rail end,
-- maximum von Mises stress at railhead end,
-- local control parameter for heuristic pattern move,
-- local control parameter for heuristic pattern move,
-- vertical interpenetration of Body-1 and 2,
-- angle of coefficient in HCT.
Subscript
, , , -- counter,
-- along the direction,
-- along the direction,
-- along the direction.
xv
Development of Optimal Designs of Insulated Rail Joints xv
List of Abbreviations
2D Two-Dimensional,
3D Three-Dimensional,
CIRJ Conventional Insulated Rail Joint,
CRC Cooperative Research Centre,
CRE Centre for Railway Engineering,
CWR Continuously Welded Rail,
DIC Digital Image Correlation,
DOF Degree of Freedom,
EIRJ Embedded Insulated Rail Joint,
ERS Embedded Rail Structure,
FE Finite Element,
FEA Finite Element Analysis,
FEM Finite Element Method,
GA Genetic Algorithm,
GSM Grid search method,
GUI Graphical User Interface,
HCT Hertz Contact Theory,
HPC High Performance Computing,
IRJ Insulated Rail Joint,
NSGA Non-dominated Sorting Genetic Algorithm,
IMD1 Improved Design 1 (CIRJ+SMRH),
IMD2 Improved Design 2 (EIRJ+SMRH),
PIV Particle Image Velocity,
QUT Queensland University of Technology,
RMD Rigid Multi-Body Dynamics,
SCRH Sharp Cornered Railhead,
SMRH Stress Minimised Railhead
xvii
Development of Optimal Designs of Insulated Rail Joints xvii
Acknowledgments
I would like to thank all those people who have given me generous help and support during
the past three and half years.
Many thanks to my principal supervisor, Prof. Manicka Dhanasekar; I sincerely appreciate
his sustained guidance and support in both academic and personal way from the
commencement to the completion of my PhD study. Without the assistance and
encouragement from him, I could not have achieved such a milestone in my life.
I wish to thank associate supervisors A/Prof. Yuantong Gu and Dr. David Wexler (UoW)
for their valuable advice and assistance in Stage 2, Confirmation and Final Seminar.
I also would like to express my appreciation to the research staff in Centre for Railway
Engineering, Mr. Paul Boyd and Prof. Colin Cole who have made major contribution to the
important and interesting experiment in this research.
Thanks to Mr. Armin Liebhardt and many technicians in Design & Manufacturing Centre,
QUT, for their generous help and support for preparing the test specimens for this research.
Thanks to Mr. Mark Barry, Dr. Joe Young and other research staff in High Performance
Computing, QUT, for their precious advice and contributions to the numerical optimisation
framework in this research.
The thesis was possible thanks to the scholarship awarded by CRC for Rail Innovation and
tuition fee waiver by QUT. With their generous support, I could concentrate on my PhD
study without any financial distractions.
Special thanks to my parents Lianyin Zong and Feng Fan and my beautiful wife, Jia Lu
who are a source of strength and encouragement at all times during my PhD candidature. I
am also grateful to Bandula Heva Thaminda, Hossein Askarinejad, Fengfeng Li and Ruizi
Wang for inspiring me through fruitful discussions and making my candidature so much
fun. Thanks to Qi Liu who made my life in Australia more memorable.
xviii
xviii Development of Optimal Designs of Insulated Rail Joints
Preface
This PhD thesis (#3 in the list below) is part of a large project funded by two generations
of the Cooperative Research Centre for Rail Innovations (Rail CRC). Several PhD and a
master theses have emerged as parts of the project; those theses supervised by Professor
Manicka Dhanasekar are listed below:
1. Tao Pang, ―Studies on Wheel/Rail Contact –Impact Forces at insulated Rail Joints‖,
Master of Engineering Research Thesis, Central Queensland Australia, 2007. This
thesis has proposed that reducing the size of the end post gap from the then 8.5mm to
5.0mm would significantly reduce impact loads due to passage of loaded wheels across
the gap. The rail industry in Australia adopted this finding in 2008.
2. Nirmal Mandal, ―Failure of the Railhead Material of the Insulated Rail Joints‖, Thesis
for the award of the degree of Doctor of Philosophy, Central Queensland Australia,
2011.This thesis identified the vulnerable location of the railhead of the insulated rail
joint.
3. Nannan Zong, ―Development of the Optimal Designs of the Insulated Rail Joints‖,
Thesis for the award of the degree of Doctor of Philosophy, Queensland University of
Technology, Australia, 2012. This thesis has developed innovative designs through
optimisation framework to eliminate/ minimise the railhead vulnerability due to the
passage of loaded wheels across the end post gap.
4. Thaminda Bandula Heva, ―Ratchetting of Railhead in the Vicinity of the Gap of the
Insulated Rail Joints‖, Thesis for the award of the degree of Doctor of Philosophy,
Queensland University of Technology, Australia, 2012. This thesis has developed a life
prediction model for those insulated rail joints that fail due to ratchetting of railhead
steel.
5. Hossein, Askarinejad, ―Track Input into the Failure of Insulated Rail Joints‖, Thesis
for the award of the degree of Doctor of Philosophy, Central Queensland Australia,
(expected - March 2013). This thesis identifies the contribution of track support to the
failure of the gapped insulated rail joints.
Chapter 1: Introduction 1
Chapter 1: Introduction
1.1 INTRODUCTION
Insulated Rail Joint (IRJ) is a safety critical device in the signalling system of the rail track
network intended for the detection of rail break or train location. The signalling function is
realised by employing a current delivered to an isolated block of a rail track through two
pairs of IRJs (Figure 1-1). A control unit is adapted to receive input from the voltage
sensor and the shunt current sensor to monitor the variation of the shunt current with
respect to the voltage to detect the rail break or train occupancy. The two pairs of IRJs at
two ends of a block are said to define a track circuit.
Figure 1-1: A block diagram of a rail break/vehicle detection system
To realise the electrical isolation function, IRJs use insulation materials inserted between
rail ends secured by the joint bars and the bolts as shown in Figure 1-2. IRJ is also required
to possess adequate structural strength to enable safe passage of wheels across the section
of the joint. As such, bonded IRJs are safety critical components that should satisfy both
the requirements of the structural integrity as well as signalling function for the railway
systems.
2
2 Chapter 1: Introduction
Figure 1-2: Typical design of IRJ in rail track system
Unfortunately, IRJ is regarded as a weak section of the track structure as they exhibit short
service life. Due to the lower stiffness at the joint gap and the complexity of the assembly
of various structural components, IRJs are susceptible to accelerated mechanical failure
under various failure modes. This is particularly so in heavy haul corridors where the axle
load and annual gross haulage are on the rise. Consequently, the average life of the IRJs (as
little as 200 million gross tonnes (MGT) or 1-2 years) is reported to about 20% of the
continuously welded rails (CWR) and the number of replacements about 20–50% of the
total replacements of rail track components, leading to significant maintenance costs to the
rail industry. This situation stimulates high demand from the rail companies to improve the
performance of IRJs.
As part of the research project (R3.100 Longer life insulated rail joint), which aims to
investigate the failure mechanism of the IRJs and develop new designs that ensure longer
life and minimal maintenance interventions, this thesis has employed robust optimisation
models combined with a parametric finite elements method (FEM) and developed
innovative designs of IRJs from the first principles of mechanics satisfying the
fundamental functions of retaining electrical insulation at all times with the structural
deformation and stresses commensurate to the other continuous rail sections. The
developed new designs have been examined through laboratory experiments and FE
simulations; the results provide confidence that the designs will have longer service life.
Insulation
material
Joint bar
Rail ends Bolts
3
Chapter 1: Introduction 3
1.2 AIMS AND OBJECTIVES
The aim of this PhD research is to develop improved designs of IRJ for less failure modes
and longer service life. This aim is achieved through the following aspects:
1. Review the failure modes of the existing designs of the IRJs and define their failure
mechanisms.
2. Develop conceptual designs of IRJs to minimise/eliminate the failure mechanisms
commonly observed in the conventional IRJs.
3. Establish optimisation models using coupled parametric finite element modelling
method and search algorithms to determine the optimal shapes of the conceptual
designs.
4. Validate the optimal shapes through measurement of strains in the critical zones of the
railhead under the loaded wheels using full scale test rig.
5. Derive improved designs of IRJs based on the optimal shapes developed in 3 above,
and illustrate their applicability for field adoption through dynamic simulations of
rolling loaded wheels across the improved designs.
6. Carry out sensitivity studies of those critical design and operational parameters that
affect the contact characteristics near the critical zone of the IRJs‘ railhead.
1.3 SCOPE AND LIMITATIONS
The scope of this research is to develop improved designs of IRJs through the
investigations of the wheel-rail interaction in the vicinity of the gap. The contact, stress and
the structural deflections in the vicinity of the gap of the IRJs are of particular interest in
this thesis. The numerical methods and optimisation algorithms used for developing the
optimal shapes of the IRJ components are also examined for ensuring the efficiency and
accuracy of the design optimisation procedure. A sensitivity study of several key design
and operational parameters is also included to justify the suitability of the improved
designs in the field applications.
Due to the complexity of the numerical modelling of the wheel/railhead interaction in the
vicinity of the end post (or simply, the gap), the following aspects are considered as out of
scope of this research:
1. The wear and defects on either the railhead or the wheel tread.
4
4 Chapter 1: Introduction
2. Rail track misalignments
3. Curved track
4. Settlement of track support system
5. Rail longitudinal stress due to temperature alteration
6. Loosening of bolt
7. Wagon/bogie/wheelset dynamics
1.4 THESIS STRUCTURE
This thesis contains nine chapters presenting the development of improved designs of IRJ.
The content for each chapter is briefly outlined:
Chapter 2 presents the designs of the conventional insulated rail joints (CIRJs) and their
failure mechanisms, the mechanics of the wheel-rail contact and the computational method
for IRJ analysis. A review of various IRJ designs employed worldwide is reported. Failure
modes of the IRJs are described and their failures mechanism is reported. Wheel-rail
contact mechanics and the fundamentals of contact study of the unsupported free edge are
reviewed and the performance study of IRJ using the various numerical methods is also
included.
With a view to eliminating/ minimising the failure mechanisms described in Chapter 2, two
conceptual designs of the IRJs are presented in Chapter 3. The design principles for
developing the conceptual designs are discussed. A conceptual design of stress minimised
railhead is first proposed with a view of minimising the contact pressure /stress singularity
experienced by the CIRJ. A conceptual design of embedded IRJ (EIRJ) is reported with a
view of simplifying the design through elimination of the various components that exhibit
complex interactions and failure modes.
Chapter 4 presents the development of shape optimisation of the stress minimised railhead
(SMRH) in the proximity of the gap, aiming at minimising the high level of stress
concentration through parametric finite element and genetic algorithms framework.
Problem description and mathematical representation of the railhead shape optimisation is
outlined. A framework of coupling optimisation methods and numerical simulation is
presented. The application of optimisation model using two non-gradient based methods
5
Chapter 1: Introduction 5
(Grid Search Method and Genetic Algorithm) is presented. Hybrid GA with the view to
improving the efficiency of searching optimal solutions is also presented.
Chapter 5 reports a laboratory test on rail specimens for investigating the performance of
the SMRH developed in Chapter 4. The preparation of the test specimens and strain
measuring methods is presented, the experimental loading procedure is presented and the
overall experimental setup and data acquisition systems are presented.
Chapter 6 reports the analysis of the experimental datasets for characterising the SMRH
and the CIRJ. Analysis of the vertical strain collected from eight strain gauges along
the rail end depth is presented and the feasibility of a digital image correlation method,
known as the particle image velocimetry (PIV) for the strain measurement at localised
railhead end (critical zone) is validated through the comparison with the strain gauge data.
The strain components: vertical strain , lateral strain and in plane shear strain
are also presented for completeness.
Chapter 7 presents a multi-objective optimisation method using a second generation non-
dimensional sorting genetic algorithm (NSGA- II) and a parametric finite element model.
The formulation of the optimisation problem is described including the multiple design
objectives, design parameters and the design constraints. A parametric finite element
model for the evaluation of the critical deflections of the railhead is described. The
principles of the NSGA- II and the integration with the developed parametric finite
element model for the optimisation problem are also illustrated. The optimisation result is
discussed. Three optimal solutions of the EIRJs are particularly discussed with respective
to their practical implementation potential.
Two improved designs of practical implementation potential (IMD1 & IMD2) have been
derived from the developed SMRH (Chapter 4) and the EIRJ (Chapter 7); these improved
designs are reported in Chapter 8. These improved designs have been simulated for field
conditions using a dynamic wheel-rail contact impact modelling method of rolling of
loaded wheels across the gap. Details of the configuration of the improved designs are
presented. Dynamic modelling using implicit-explicit FE analysis is reported with several
idealisations for saving computational effort. Numerical results are presented in terms of
the impact load factor, impact rate, peak contact pressure, peak von Mises stress and
6
6 Chapter 1: Introduction
deflections as the wheel passing across the gap; the performance between the improved
designs and the CIRJ is compared and the superiority of the IMD1 and IMD2 designs over
the CIRJ is clearly established. The practical issues that might arise in the manufacturing,
installation and maintenance of the two improved designs are qualitatively described.
Finally, the sensitivity of several design and operational parameters is discussed.
The summary, conclusions and recommendations of this thesis are reported in Chapter 9.
Chapter 2: Literature Review 7
Chapter 2: Literature Review
2.1 INTRODUCTION
To gain substantial understanding of the current design of Insulated Rail Joints (IRJs) and
their failure mechanisms, the mechanics of the wheel-rail contact and the computational
and analytical methods of the analysis of the IRJs are reviewed. This chapter presents a
review of various IRJ designs employed worldwide in Section 2.2. Failure modes of the
IRJs are described in Section 2.3 and a hypothesis of categorising failures of the IRJs used
in the heavy haul network of the Australian railways is reported in Section 2.3. Wheel-rail
contact mechanics, a key factor of initiating various failure modes, is reviewed in Section
2.4; Section 2.5 reviews the performance study of IRJs from both the classical analytical
method and the computational finite element method. Section 2.6 reports some of the new
IRJ design emerged in the world market. The chapter review is summarised in Section 2.7.
2.2 DESIGN OF IRJ
IRJs are used in the rail industry to serve the following two main functions:
1. To prevent electrical current from flowing between the two rails with a view to
isolating sections of the track, allowing for identifying train locations and
controlling the signalling system;
2. To provide the rail joint with adequate strength and stiffness for supporting the
passage of the loaded wheels.
The most common design of IRJs contains two rails connected by two joint bars on either
side of the rail webs. Bolts, which are electrically insulated from the joint bars and the rails
by ferules, are used to mechanically fasten together the joint, while layers of insulating
fabric containing adhesive are inserted between the joint bars and rails. A section of
insulating material (end post) with the same cross sectional shape as that of the rail is
introduced between the rail ends. Figure 2-1 shows a typical IRJ assembly used in
Australia. In Australia 6-bolt joint bars and 4-bolt joint bars assemblies are the most widely
used designs; an example of a newly manufactured insulated rail joints with 6-bolt is
shown in Figure 2-2.
8
8 Chapter 2: Literature Review
(a) Cross section
(b) Exploded view
Figure 2-1: Typical insulated joint assembly (AS1085.12, 2002)
Figure 2-2: An insulated rail joint with 6-bolt joint bars in Australia
Several design practices of IRJs are reported in the literature. These designs vary in terms
of the parameters of the supporting systems, joint bars and insulation end posts. Two types
9
Chapter 2: Literature Review 9
of supporting systems of IRJs exist depending on the positioning of the sleepers with
reference to the end post:
Suspended IRJ
Supported IRJ
As shown in Figure 2-3, the suspended IRJ has the sleepers positioned symmetric to the
end post. In general, the distance between the adjacent sleepers at IRJ is between 600mm
and 700mm, depending on the length of the joint. On the other hand, in the supported IRJ,
the end post is placed directly on the supporting components. These supporting
components can be achieved by either directly positioning the sleeper underneath the end
post as shown in Figure 2-4(a) or using the specially designed joint bars known as
―abrasion plate‖ to continuously support in the vicinity of the two rail ends as shown in
Figure 2-4(b).
Figure 2-3: Suspended IRJ
(a) Continuously supporting (b) Sleeper supporting
Figure 2-4: Supported IRJ
4-bolt IRJ
Sleeper
Joint bars continuously
supporting the joint
Tie plate
Sleeper underthe end post
10
10 Chapter 2: Literature Review
The design of joint bar is characterised by various shapes of the joint bar cross-section and
the length of joint bar, normally 4-bolt joint bar and 6-bolt joint bar as mentioned above.
Various cross-section shapes have been adopted as shown in Figure 2-5. The main idea
behind these various joint bar designs is to provide better support to the railhead and
additional structural stiffness due to rail discontinuity.
Figure 2-5: Various cross-sectional shapes of joint bar
Joint gap, where the end post is inserted, also have different angle with either square (90º)
or inclined (75º) to the longitudinal axis of the rails. Figure 2-6 shows examples of these
types of joints.
(a) Square cut; (b) Inclined cut
Figure 2-6: Different shapes of joint gap
Joint bar
design No.1
Joint bar
design No.2
Joint bar
design No.3
Joint bar
design No.4
(c)
Sleepers
Inclined cut – top view
75°
(b) Square cut – top view
90°
11
Chapter 2: Literature Review 11
The properties of the end post materials play important role in the response of the IRJs.
Polymer, Nylon and Fibreglass are the commonly used IRJ insulation materials. The gap
size (thickness of end post material) is also varied from 4mm to 15mm and is also a key
parameter for the IRJ design. In addition, the design of IRJs also differs with the detailing
of end post fitting between the rails. Glued IRJ and inserted IRJ (non-glued) end posts are
two common forms employed. The glued IRJs use adhesive material such as the epoxy to
ensure full contact between the steel joint bars and the rail web whilst they remain
electrically insulated. The inserted IRJs are contains a simple insert of the insulated
materials into the end post gap with thermal treatment but without any adhesion material.
2.3 FAILURE MECHANISM OF IRJS: LOCAL AND GLOBAL PERSPECTIVES
2.3.1 LOCAL FAILURE
Although IRJs designs are constantly under improvement, with most designs increasing the
stiffness or using higher yield materials as described in Section 2.2, a purpose-made gap
with the insert of low-stiffness insulation material is always included between the two
lengths of the rails for maintaining the electrical insulation for signalling control. Such
basic design principle inevitably introduces the geometric discontinuities characterised by
two unsupported edges (rail ends) as shown in Figure 2-7.
Figure 2-7: Configuration of a gap-jointed rail ends subject to wheel contact loading
Unsupported or supported edges(Rail ends)
SharpCorners
Stress concentration
Contact pressure
Contact surface
RailheadRailhead
Wheel load Wheel load
A
B
12
12 Chapter 2: Literature Review
Under the wheel loading, localised stress concentration exists well below the contact
loading surface as long as the contact remains far away from the unsupported edges (Point
A in Figure 2-7). However, as the wheel approaches the gap (unsupported edge), the
elliptical contact pressure distribution modifies from elliptical shaped distribution into a
hyperbolic shaped one; and the stress concentration that has resided below the contact
surface (Point A) migrates upwards to the sharp corner (Point B) of the unsupported edges.
Due to the edge effect, the stresses at the corners of both of the rail ends often exceed
material yield limits and can cause severe early localised damages leading to low service
life.
In the Australian heavy haul networks, railhead metal flow/fatigue and delamination
/battering of the end post (Figure 2-8) are the mostly observed failure modes in the
localised interaction zone between the rail ends and the end post. The cyclic accumulation
of railhead material deformation under repeated wheel passages and the loss of the end
post material ultimately lead to railhead fatigue failure and possible short-circuiting
between the rail ends, resulting in electrical isolation failure.
(a) Metal flow (b) Delamination of end post
Figure 2-8: Two local failure modes in Australian heavy haul networks
2.3.2 GLOBAL FAILURE
Globally, due to the low bending stiffness of the joint-bars at the gap during the wheel
passage, the rail ends in the IRJs are subjected to wheel impact due to ‗step‘ mechanism
schematically illustrated in Figure 2-9 (Dhanasekar et al 2007 and Steenbergen, 2006).
With the uneven vertical deformation of the top rail surface at either side of the rail gap
shown as dotted profile, the wheel will momentarily experience double point contact whilst
Metal flow
End postdelamination
13
Chapter 2: Literature Review 13
crossing the rail gap. Subsequently it would hit the ―rise‖ of Rail-2 resulting in an impact
load.
Figure 2-9: ―Step‖ mechanism at insulated rail joint
The higher wheel-rail contact impact force adversely affects the integrity of the IRJ. Apart
from the localised railhead metal flow/failure, the other failure modes (Figure 2-10) from
the global perspective are: 1) Bolt loosening; 2) Broken rail end and joint bar; and 3)
Deterioration of sleeper, ballast and subballast supporting system in the vicinity of IRJs.
(a) Cracking of rail end (Wen et al., 2005) (b) Bolt loosening (Jeong, 2001)
(c) Degradation of supporting system
Figure 2-10: Various global failure modes of IRJs
Cracking of rail end
Bolt loosing
Loosing of tie plate
Crack of sleeper support
Gap
Rail-2 Rail-1 Step
Travel Direction
14
14 Chapter 2: Literature Review
Although IRJs used in Australia are assembled in factory with good quality control
procedure (AS1085.12, 2002), the current complex assembly of structural components
leads to the variety of the failure modes. More importantly, all failure modes, with one
aggravating to another, lead to a vicious circle of accelerating the overall failure of the
IRJs.
2.4 REVIEW OF THE MECHANICS OF WHEEL-RAILHEAD EDGE
CONTACT
Various failure modes are initiated from the wheel-rail contact interaction; therefore, it is
important and necessary to understand the characteristics of wheel-rail contact mechanics,
as the wheel passing over the joint gap (unsupported rail edges). This section reports the
mechanics of contact from the two perspectives:
Classical wheel-rail contact mechanics;
Advanced contact mechanics associated to the edge effect (unsupported rail end).
2.4.1 CLASSICAL WHEEL-RAIL CONTACT MECHANICS
2.4.1.1 Normal wheel-rail contact-Hertz Contact Theory (HCT)
The earliest theory of wheel-rail contact mechanics is due to the pioneering researcher
Heinrich Hertz, who published a classical paper on contact in 1882 (in German). The Hertz
Contact Theory (HCT) can be regarded as the foundation of contact mechanics. It has been
widely accepted and used for conducting stress analysis of contacting bodies with the
assumption that the solids in contact are limited to (Johnson 1985 and Knothe 2008):
Contact bodies must be semi-infinite (half-spaces);
Contact interaction must be frictionless;
Material of contact bodies is isotropic and homogeneous (perfectly elastic); and
Contact surfaces are regarded as second-order polynomials.
Figure 2-11 shows two solids bodies (Body-1 and Body-2) in contact at the origin of the
xyz coordinate system subjected to vertical load F. It is assumed that the contact point O
will spread into a region horizontally located within the xoy plane. Before the two bodies
15
Chapter 2: Literature Review 15
are forced into contact by F, the profiles of the contacting surfaces of the two bodies are
shown by the dotted lines (termed as and for simplicity) in Figure 2-11 and expressed
analytically in Eq. (2-1) and Eq. (2-2):
Figure 2-11: Contact between two non-conformal bodies
where and
are the principal radii of the Body-1, and and
are the principal
radii of the Body-2 within the contact zone. The separated distance between two surfaces
is given by;
and stand for the relative curvatures, obtained by averaging the bodies‘ curvatures
As the bodies are pressed into contact with the vertical displacement of , they form the
contact width of . and are the maximum vertical deformation of Body-1 and
z
Oxoy plane
1
2 1
2
F
FBody-1
Body-2
a a
16
16 Chapter 2: Literature Review
Body-2 respectively the vertical deformation and of Body-1 and Body-2 at any
point in the contact region can be obtained from:
If Eq. (2-6) is not satisfied, the bodies are separated with the following condition:
For both Eq. (2-6) and Eq. (2-7), and can be obtained by implementing the
elasticity theory with the contact pressure that is to be determined:
By inserting Eq. (2-8) and Eq. (2-9) into Eq. (2-6), an integral equation can be obtained by
employing the potential theory. The pressure distribution results as:
where and represent the major and minor axis of the elliptical contact region and can
be determined by resolving the following set of integral equations once the curvatures of
contact surfaces ,
, and
are determined:
The maximum contact pressure is given by:
As the above contact formulations are applied into the wheel-rail contact configuration as
shown in Figure 2-12, the principal curvatures and
of Body-1 become and
of the rail; and the principal curvatures and of the wheel. Because the rail is
17
Chapter 2: Literature Review 17
assumed straight and wheel contact surface is assumed flat along the lateral direction (y
axis). The and are infinite.
Figure 2-12: Wheel-rail contact configuration
Therefore, the vertical deformation and of the rail and the wheel at any point in the
contact region can be obtained from:
Based on the Hertzian contact theory (HCT), the contact region is assumed to be an elliptic
shape. By inserting Eq. (2-8) and Eq. (2-9) into Eq. (2-14) and assuming the wheel and rail
have the same Young‘s modulus and Poisson‘s ratio . The major and minor axis of the
elliptical contact region, and and the vertical displacement of are solved as:
z
yO
Rwx→∞
Rrx
z
xO
Rwy
Rry→∞
18
18 Chapter 2: Literature Review
where and are non-dimensional coefficients and is Hertzian coefficient. Their values
are related to , which is defined as:
The values of and can be obtained from Table 2-1 (Iwnicki, 2006).
Table 2-1: Relations of non-dimensional coefficients , and (Iwnicki, 2006)
(º) 90 80 70 60 50 40 30 20 10 0
1 0.7916 0.6225 0.4828 0.3652 0.2656 0.1806 0.1080 0.0470 0
1 1.128 1.285 1.486 1.754 2.136 2.731 3.816 6.612
1 0.8927 0.8000 0.7171 0.6407 0.5673 0.4931 0.4122 0.3110 0
1 0.9932 0.9726 0.9376 0.8867 0.8177 0.7263 0.6038 0.4280 0
2.4.1.2 Normal wheel-rail contact-semi-Hertzian contact model
The classical Hertz contact theory (HCT) presented in Section 2.4.1.1 only suppose that the
principle curvature of the wheel and the rail are constant in the contact region. Due to its
simplicity, it has been widely used in many software applications (VAMPIRE, SIMPACK,
GENSYS) for determining the wheel-rail contact interaction. However, in the real wheel-
rail situation, the geometrical curvatures are not constant, more precisely the relative
curvature and vary along the lateral direction (y axis) (Figure 12). Under this
circumstance, advanced method for efficient prediction of the contact region is needed.
The semi-Hertzian contact solution has been widely used for calculating the contact region
under the geometrical condition described above. Semi-Hertzian contact solution was
firstly proposed by Pascal and Sauvage (1993) and Kik and Piotrowski (1996). The main
strategy is to use the geometric interpenetration of the contact solids to estimate the shape
of the contact region.
To explain the procedure of formulating the semi-Hertzian contact model, the Hertzian
problem with the simple elliptical contact region was initially illustrated. As shown in
19
Chapter 2: Literature Review 19
Figure 2-13, it is assumed that the wheel and the rail touch at point o and are just surfaces.
When one surface penetrates the other by the distance along the vertical direction (z), the
other surface penetrates and intersects the original surface along some line, but in the
opposite direction. The projection of the intersection of the contacting bodies is called an
interpenetration region as shown in Figure 2-13. The geometric intersection of the
contacting bodies is defined by a negative vertical separation :
The interpenetration region is also formed as an geometric ellipse with the major and
minor axis of and , which are defined as:
Figure 2-13: Geometrical penetration of contact bodies
However, in reality the wheel and the rail cannot interpenetrate due to the deformation of
the wheel and the rail due to the local contacting zone. It has been shown by Hashemi and
Paul (1979) that the geometric interpenetration region encloses the real contact region if
the influence function is unidirectional. Therefore, the shape ratio of the geometric
interpenetrating ellipse and the real contact region are different and are only determined by
the geometrical curvatures as shown:
z
o
F
F Body-1
Body-2
b’ b’
y
x
y
a’o
Geometrical
ellipse
20
20 Chapter 2: Literature Review
In the semi-Hertzian contact model, the geometrical ellipse ratio should have the same
characteristics as the contact region from the HCT ( = and = ). The relative
curvatures and should be changed to and respectively. Subsequently, the
geometric indentation is changed to . Two methods have been used for making the
change possible, namely the compensation of curvature (Quost et al. 2006) and the
compensation both and (Ayasse and Chollet, 2005). The compensation of curvature
has been more widely used due to the simplicity of its implementation. In this method,
and are considered equal ( = ). The resultant is given by and is obtained from:
This compensated the curvature together with the curvature are used for the
calculation of the axes of the contact ellipse and . In the Hertzian case, the ellipse will
be the same if the interpenetration value is changed into:
The above expressions are exact when the both curvatures of the contacting bodies are
constant within the potential contact zone. For the case of wheel-rail contact, the
curvatures of the wheel and the rail contact surface are not constant along the lateral
direction (y) (Figure 12). Therefore, semi-Hertzian is implemented through the
discretisation of the contacting surface along the lateral direction. Figure 2-14 presents the
schematic discretisation procedure. The contact region is divided into several strips with
the width of along the y direction. In each strip, the contact pressure is still in elliptical
shape in x direction and constant in y direction.
21
Chapter 2: Literature Review 21
Assuming the contact between the wheel and the rail is entering at the origin of the
coordinate system and before they are further penetrating into each other, the separate
distance is defined by the profile of the rail and the wheel as follow:
After they are penetrating against each other of , to determine the contact length at
point (0, ), the curvature is first calculated from:
where and are the first order and second order derivative at point along y
direction. The corrected curvature can be obtained from Eq. (2-25).
Figure 2-14: Schematic procedure of discretisation in semi-Hertzian contact solution
Thereafter, the contact length for the strip at point is determined by:
is the geometric interpenetration for the strip at point and is given as:
y
z
y
x
o
o
Rail contact surface
Wheel contact surface
Parallel strips along
later direction
22
22 Chapter 2: Literature Review
Because of the assumption that the contact pressure distribution along the x direction in
any strip is still elliptical shape, the normal contact force in the strip at point can be
expressed as:
The total force is obtained by:
From the descriptions of the HCT and semi-Hertzian contact mode reviewed in this
section, it can be seen that the determination of the normal wheel rail contact can be
expressed analytically and solved numerically. Other similar approximate methods based
on the geometric interpenetration strategy for solving the normal contact problem for
wheel and rail is proposed by Knothe and Le (1984) and Piotrowski and Kik (2008)).
However, the assumption of the infinite geometry (half-space) away from the contact
region is violated for the wheel-rail contact in the vicinity of gap in IRJs. The ensuing
section focuses on the review of the contact mechanics associated with the geometry edge
effect close to the contact region.
2.4.2 ADVANCED CONTACT MECHANICS ASSOCIATED WITH THE
GEOMETRY EDGE EFFECT
2.4.2.1 Edge effect
The classical wheel-rail contact mechanics is extensively applied for understanding the
normal wheel and rail contact problems. These theories are generally proved to be
satisfactory for wheels that run on the Continuously Welded Rail (CWR), because the
contact bodies can be assumed to be half spaces. However, in some contact mechanics
problems of practical interest, the contact region is not far away from other external
surfaces or boundaries. One such external surface is ―free edge‖ (see Figure 2-7), may
appear in close proximity to the contact region and thus violate one of the Hertz
assumptions.
23
Chapter 2: Literature Review 23
Free edge will affect the wheel-rail contact close to the gap perpendicular to the contacting
surface. Since the semi-infinite assumption of the Hertz theory is violated, the question
becomes that how inaccurate the Hertzian contact distribution are when applied to free
edge problems. In general, a high level of stress concentration would be expected close to
the free edge (Johnson, 1987). The answer to this expectation requires the careful
examination of concentrated contacts near free edges. The ensuing sections review the
edge effects.
2.4.2.2 Indentation of body with free edge into half space
The edge effect in contact problem was firstly examined through the contact of a rigid flat
punch with square corners (90°) over an elastic half plane (Figure 2-15) (Muskhelishvili
(1949) and Nadai (1963)). The form of the pressure distribution in the contact region of
is obtained:
The principal shear stress is given as:
where and are polar coordinates from an origin at = and limited to .
Figure 2-15: Rigid punch contacting with half plane
It can be seen that at the corner of the punch ( ), Eq. (2-33) shows that the contact
pressure reaches a theoretically infinite, resulting the contact singularity at the sharp
F
z
xO
a a
Half plane
Rigid punch
Sharp cornersθ
r
24
24 Chapter 2: Literature Review
corner. Subsequently, Eq. (2-34) demonstrates that the principal shear stress also exhibit an
infinite value at the sharp corner of the punch ( 0). Further study on the general edge
problem for the corner angle that were other than 90° was conducted by Dundurs & Lee
(1972) for frictionless contact and by Gdoutos &Theocaris (1975) and Comninou (1976)
for frictional contact and by Bogy (1971) for non-slip (tilted) contact. Their analysis result
show that the contact pressure/stress singularity occurs to the sharp corner of the free edge.
It is expected that in real situations, body at the sharp corner can easily yield plastically/
torn or damaged depending on the nature of the material.
Recently, similar contact problem was also investigated by Guilbault (2011), who studied a
cylindrical contact against a think rubber sheet (Figure 2-16(a)). The contact patch and
pressure distribution were obtained through an over-corrected contact model and compared
with experiment. In the experiment, the cylinder surface was initially covered with a very
thin layer of a coloured waxy solid. The waxy solid penetrated into the rubber surface and
resulting in the contact mark. Figure 2-16(b) presents the contact patch and contact
pressure distribution. It showed that at the free edged of the cylinder the contact width in
direction experienced an obvious increase. Furthermore, contact pressure singularities
occurred at the edges of the cylinder.
(a) Cylindrical contact into rubber sheet (b) Distribution of contact pressure
Figure 2-16: Contact problem and contact result
2.4.2.3 Indentation of body into quarter space
The contact problems examined in Section 2.4.2.2 illustrate the situation, in which the
bodies with the free edges are loaded and pressed into the half-space. These bodies are
usually assumed as rigid or have much higher elastic modulus compared to the half-space.
F
Thick rubber sheet
Cylinder
free edge
free
edge
E2 v2
E1 v1
x
z
Pressure (MPa)
x (mm)z (mm)
Contact concentration
at free edge
25
Chapter 2: Literature Review 25
Contrast to the above contact problem, in the wheel-rail contact in the vicinity of IRJ, the
wheel is loaded and tend to penetrating into the railhead, which possess the external free
edge. Depending on the wheel position, the contact region might or might not extend to the
free edge. This section reviews such contact problems.
A frictionless rigid cylindrical indentation into a quarter plane (Figure 2-17) was conducted
by Gerber (1968) and Hanson and Keer (1989) to investigate the effect of free edge on the
contact behaviour.
Figure 2-17: Frictionless indentation of quarter plane by a rigid cylindrical punch
As shown in Figure 2-17, this contact scenario can be regarded as a rigid cylindrical wheel
is loaded and pressed into the railhead with the unsupported free edge in 2D. By using
Hetenyi's superposition method of transferring the quarter plane into a half plane (Hetenyi,
1960, 1970), the contact pressure distribution in various proximities of the cylindrical
position to the free edge was examined and discussed. An integral equation for this contact
problem was depicted by Hanson and Keer (1990) in the form:
where is the displacement along the horizontal contact surface in the direction;
is the contact pressure within the contact region ; is a generalized
Cauchy kernel (Hanson and Keer 1989); is the shear modulus and ( is the
Poisson‘s ratio).
x
y
FRigid
cylinder
Quarter
plane
Vertical
free edge
Sharp
corner
Symmetric axis of
Rigid cylinder
x2x1
o
26
26 Chapter 2: Literature Review
Based on the above integral equation, as the contact extends to the sharp corner ( =0), a
bounded displacement gradient at the corner results in a bounded contact pressure at the
sharp corner (Hanson and Keer, 1990). The above integral equation at the sharp corner can
be simplified as:
Eq. (2-36) indicated an interesting phenomenon for the vertical frictionless indentation of
quarter plane by a rigid cylindrical. When the sharp corner is at the left side of the
symmetric axis of the cylinder, the displacement gradient at the corner is negative, which
means that it requires a tensile stress to maintain the contact between the cylinder and the
sharp corner. Because this is impossible practically, it can be seen that the contact will
never extend to the sharp corner until the lowest tip of the cylinder moves beyond the free
edge. As the wheel is symmetric to the axis right over the free edge as shown in Figure
2-18(a), the contact pressure at the corner becomes zero. The contact at this situation
was particularly discussed as explained in Figure 2-18(b).
(a) Cylinder axis over free edge (b) Contact pressure distribution
Figure 2-18: Sketch of the contact characteristics as cylindrical axis over free edge
As shown in Figure 2-18(b), the numerical analysis revealed a general property of
frictionless contact near a vertical free edge: the presence of the edge causes a loss in
stiffness as compared to a half plane. Therefore, under the same load subjected to the
cylinder, although the contact pressure distribution still exhibited the elliptic shape, the
contact length as the cylinder is over the free edge was less than the one as the cylinder is
x
y
FRigid
cylinder
Quarter
planeVertical
free edge
Sharp
corner
Symmetric axis of
Rigid cylinder
o
Pressure (MPa)
x (mm)0
pmax2
pmax1 pmax1>pmax2
2a1 2a2a1>a2
HCT
Contact at
free edge
27
Chapter 2: Literature Review 27
away based on HCT. As a result, to compensate the loss of the structural stiffness and
reduction of the contact region, maximum contact pressure increased, resulting in
increase of the deflection of the contact surface close to the free edge as well as the
increase of the stress concentration at localised corner of the quarter plane.
The edge effect on contact of quarter space was further investigated by Hanson and Keer
(1994), who examined the frictionless spherical contact of an elastic quarter plane (Figure
2-19) and provided a piecewise constant approximation to the contact pressure at the
vertical free edge. Under the same vertical indentation, the distribution of the contact
pressure at different contact distance was analysed and presented as shown in Figure
2-20.
Figure 2-19: Frictionless indentation of quarter plane by a rigid cylindrical punch
The contact result for a rigid spherical indentation was first presented as shown in Figure
2-20(a). When the contact is far away from the vertical free edge ( ), the contact
pressure approximated to the HCT prediction with the maximum pressure and the contact
region equal to and . As the sphere approached the free edge with the same
indentation, both the maximum contact pressure and the contact region decreased
significantly. It was also found that when the sphere axis was located at the free edge, the
contact pressure at the edge vanished, which was in agreement with the finding from Eq.
(2-36). Due to the loss of the stiffness close to the free edge, the same vertical indentation
of the sphere produced lower maximum contact pressure, thus lower contact force. In
contrast, the same loaded sphere would pronounce higher contact pressure at the small
contact region, similar to the explanation in Figure 2-18(b).
Quarter space
c
Elastic
sphere
E1, v1
E2, v2
28
28 Chapter 2: Literature Review
The contact result with a similar elastic modulus for the sphere and the quarter space is
shown in Figure 2-20(b). The edge effect was not as obvious as the rigid spherical contact,
when the sphere was approaching the free edge, such as at . However, as the contact
extended to the free edge, the contact characteristic changed entirely. The elliptical shape
of the contact pressure distribution at in Figure 2-20(a) could not be observed.
Instead, bounded maximum contact pressure occurred at the edge; and its magnitude was
found larger than the maximum contact pressure from the HCT. Subsequently, the
higher contact intensity with the decreased contact region could lead to a severe stress
concentration at the sharp edge of the quarter space.
(a) E2/E1=
(b) E2/E1=1
Figure 2-20: Distribution of contact pressure at different contact distance
The above study of the geometrical edge effect on various contact problems reveals an
important feature: The contact pressure singularity at the external free edge of the
contacting bodies is obvious, which often exceed the material yield strength and accelerate
the material failure in real situation. As for the IRJ, the rail ends at the gap works similarly
to those idealised as vertical free edge of the contact bodies. However, the wheel-rail
p/pmax
c/a0 1 2 3 4 5 6
1
0.8
0.6
0.4
0.2
c/a=5c/a=3c/a=0
p/pmax
c/a0 1 2 3 4 5 6
1
0.8
0.6
0.4
0.2
c/a=5c/a=3c/a=0
29
Chapter 2: Literature Review 29
contact in the vicinity of the joint gap are usually numerically solved since the contact
interaction and the contact geometry of the rail and the wheel are much more complex,
resulting in higher contact and geometrical nonlinearities. In the following sections,
numerical tools /methods are usually utilised for the understanding of the rail end effect
subjected the wheel contacting.
2.5 PERFORMANCE STUDY OF THE IRJS
Failure mechanism of the IRJs from the local and the global perspectives is presented in
Section 2.3. With a view to predicting these failure mechanisms, a number of modelling
methods are reported in the literature. IRJ is a complex system that involves various
structural components, interacting with each other; the modelling methods reviewed in this
section described the attempts of the authors to quantify such interactions.
2.5.1 STATIC WHEEL-RAIL CONTACT ANALYSIS
Kerr and Cox (1999) established an analytical static loading model of IRJ to examine the
deflection near the end post as shown in Figure 2-21. A modified beam model supported
on elastic foundation was used to model the IRJ system. The rail sections and joint bars
were modelled as linear elastic beams, and the epoxy-fiberglass insulation was simplified
as spring layers as shown in Figure 2-21. The model demonstrated that the deflection
around IRJ was generally larger than the continuously welded rail (CWR), due to the lower
bending stiffness of the joint bars.
Figure 2-21: Static analytical model for insulated rail joint (Kerr and Cox 1999)
F/2 F/2 Joint bar
Rail
Spring between
Joint bar and rail
Rail
support
30
30 Chapter 2: Literature Review
Chen (2003) investigated the effect of an unsupported rail end of IRJ under the static
loading using a 2D static wheel/rail contact finite element (FE) model. The contact
pressure, stress variation and deflection of the localised rail end were reported as the
cylinder in contacting at various proximities to the rail end. It was concluded that the Hertz
theory was violated near the gap (unsupported free edge) due to edge effects. Larger
deflection and higher stress concentration (Figure 2-22(b)) occurred as the wheel
approached to the end. The maximum stress was found be exceed the material yield
strength valued at the sharp corner of the rail end.
(a) 2D FE model; (b) stress concentration close to the rail end
Figure 2-22: 2D wheel-rail contact at unsupported rail end (Chen (2003))
Chen and Kuang (2002) carried out a static analysis of an IRJ subjected to vertical wheel
load by establishing an elastic 3D FE rail model. It was found that the traditional HCT was
not valid for predicting the contact pressure distribution near the joint. Recently, a similar
3D FE model was developed to further investigate the stress field in the vicinity of the gap
by Zong and Dhanasekar (2012) as shown in Figure 2-23. The result in the contact pressure
was found to be in good agreement with Chen and Kuang (2002). Furthermore, as the
wheel was located at the centre of the gap, due to the lower stiffness of the insulation
material, severe stress concentration was pronounced at the corners, which would lead to
the metal flow and delamination of end post.
Unsupported rail end
Unsupported
rail end
Wheel load
Stress concentration
exceed material
yield limit
Wheel
Rail
31
Chapter 2: Literature Review 31
(a) 3D FE model; (b) Stress field as wheel in centre of gap
Figure 2-23: 3D wheel rail contact at IRJ (Zong and Dhanasekar (2012))
Davis and Akhtar (2005) proposed a typical six-bolt insulated joint FE model and analysed
the stresses and strains in IRJ. Result showed that the stress levels in IRJ components were
well below the yield limits of material for load cases with firm support; however, under the
loading condition involving differential settlement, the joint-bars had a tendency to yield.
This high stress concentration at the bottom of the joint bar initiated the loosening of the
bolt connection and the ultimate joint bar cracking.
The papers reviewed in this section mainly have focused on the study of the structural
response and contact pressure subjected to static load near the end post. Although it is
important for the preliminary understanding of the contact mechanism of IRJ, these papers
have not reported any possible solution for reducing the contact/stress concentration or
enhancing the structural stiffness, which are the potential design objectives for the
optimisation design of insulated rail joint. Furthermore, due to their modelling limitation
and research scope, the dynamic behaviour of IRJ during the wheel passing over IRJ is not
included in the above papers; dynamic analysis of IRJs is reviewed in the subsequent
section.
2.5.2 DYNAMIC WHEEL/RAIL CONTACT SIMULATIONS USING RIGID
MULTIBODY DYNAMICS
As the wheel approaches the joint, the running surface discontinuity at the gap
momentarily generate a ―step‖ as shown in Figure 2-7. The wheel then crosses over the gap
and hit on the rail and generates the dynamic impact. For the dynamic analysis of the IRJs,
Rigid Multi-body Dynamics (RMD) is widely used by different researchers.
0 0.5 1 1.5 2 2.5 3-0.5-1-1.5-2-2.5-3
0
0.5
1
1.5
2
2.5
3
IRJ
Wheel Position
780
715650585
520
455
390
325
260
195
130
65
Rail-1Rail-2
Max:1676
130
65 195
260
325
390
455
520
715650
585
780
Max:1677
65
130
195
260
32
32 Chapter 2: Literature Review
Jenkins et al. (1974) modelled the dipped rail joint as a dipped continuous beam supported
by sets of springs and dashpots at the location of sleepers. Contact between the wheel and
the railhead was assumed to be HCT. They predicted the dynamic contact force factors
(defined as the ratio of dynamic to static load) between the rail and the wheel at the joints.
As shown in Figure 2-24, there existed two contact impact force factors: the first being
the amplitude (3~4) and high frequency peak (500Hz), and the second being lower
amplitude (2~3) and lower frequency peak (30~100Hz). The first peak damps out in a few
milliseconds and affects only the local contact area. The second peak damps slowly and
affects most track and wagon components.
Figure 2-24: History of contact force over the rail joint (Jenkins et al. 1974)
Sun and Dhanasekar (2002) developed a whole wagon and rail track multi-body dynamic
model to investigate the dynamic rail-vehicle interactions (Figure 2-25(a)). The rail track
was modelled as a four layer sub-structure and the non-linear Hertz spring was employed
for the contact mechanism. The IRJ in this study was considered as an impulse velocity
relevant to the dip angles of the joint and as shown in Figure 2-25(b). The effect of
the properties of the rail track and the wagon components on the impact forces and other
dynamic responses of the rail track and wagon system were studied, and numerical results
were compared with several published model or experiments, predicting good agreement.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10 12 14 16 18 20
Imp
act
fact
or
Time (ms)
P1
P2
33
Chapter 2: Literature Review 33
(a) Dynamic model of rail and wagon system (b) Rail joint in the dynamic model
Figure 2-25: Multi-body dynamic model (Sun and Dhanasekar, 2002)
Wu and Thompson (2003) developed a dynamic rail wheel contact model for rail joint
impact analysis. Rail and wheel contact interaction was modelled using the Hertz non-
linear spring that allowed for a loss of contact. In this model, the wheel centre trajectory
was employed to model the dipped joint. The rail support was modelled as discrete double
layer system with spring, mass and damping parameters to model the pad, sleeper and
ballast characteristics. Gap size, vertical misalignment and dip of rail joint were studied.
The impact force was shown to have 400%~800% of static load at certain conditions for
various velocities and depths of joint dip. Result demonstrated that the ―step‖ at the rail
joint generated high impact force, which can accelerate the structural damage of IRJ
Suzuki et al. (2005) propose a track dynamic model to investigate the influence of vertical
track irregularity around a rail joint on dynamic contact force and rail seat forces. Similar
to Sun and Dhanasekar (2002), by treating the rail joint as the excitation velocity generated
over a rail joint by a passing wheel. As shown in Figure 2-26, they illustrated that the
differential settlement of sleepers around the rail joint has a great influence on the dynamic
impact load. Similar result is also found by Davis and Akhtar (2005) and Askarinejad et al.
(2012). In reality, the variation on the stiffness of the sleepers and geometrical
irregularities around IRJ could generate higher impact force and the duration of the impact
could last longer during the wheel passing the joint.
Geometric dip at IRJ
Wheel
Wagon
Track
model
34
34 Chapter 2: Literature Review
Figure 2-26: Contact impact force at different settlement around IRJ
2.5.3 DYNAMIC WHEEL/RAIL CONTACT SIMULATIONS USING FINITE
ELEMENT METHOD
Whilst the RMD deals with contact-impact force, finite element method (FEM) provides
more refined stress analysis of the components of the IRJs.
Koro et al. in 2004 established a dynamic finite element model to investigate the edge
effects of the rail joint. A modified constitutive relation of Herzian contact spring
(Kataoka, 1997) was adopted to model the wheel/rail contact. Timoshenko beam elements
were used to model the joint structures including the joint bars. Tie springs were employed
to connect the joint bars to the rail supported on a discrete elastic foundation. Gap size and
train speed effects on impact force were carefully investigated. The results showed that for
velocities lower than 150Km/h, impact force was sensitive to the gap size. Later, Wen et
al. (2005) performed a dynamic elasto-plastic finite element analysis of the standard rail
joints containing a gap and joint bars (Figure 2-27(a)). They employed a coupled implicit-
explicit technique that imported the initial steady state implicit solution prior to impact into
the explicit solution to determine the impact dynamic forces. They reported that the impact
load varied linearly with the static axle load but was largely insensitive to the speed of
travel of the wheel. This finding on wheel speed is similar to that of Koro et al. (2004).
More importantly, high stress concentration was observed during the wheel passing over
the joint (Figure 2-27(b)), especially for the von Mises stress that is well beyond the rail
steel yield strength.
t (s)
10.750.50 0.25
20
40
60
80
100
120
Joint without differential settlement
Joint with differential settlement
35
Chapter 2: Literature Review 35
(a) (b)
(a) Finite FE model (b) Hisotry of the maximum stresses
Figure 2-27: 3D dynamic FE analysis (Wen et al. (2005))
Pang and Dhanaskear (2006) developed a 3D dynamic wheel/rail rolling contact model to
study the contact impact at the wheel/rail interface adjacent to insulated rail joints (Figure
2-28). Contact impact force history as well as stresses at IRJ was investigated. Results
showed that the contact impact force increased by 19%, whilst the von Mises stress
increased by 58%, showing nonlinearity.
(a) Dynamic FE model (b) Contact force history
Figure 2-28: Dynmic FE analysis of whee contact-impact at IRJ
Cai et al. (2007) conducted a dynamic elastic-plastic stress analysis when a wheel passed
over a rail joint with height difference between the two sides of a gap. Contact elements
were used to simulate the interactions between the wheel and the rails; the rails and the
joint bars; the joint bars and the bolts; and the bolts and the rails. The effects of train speed,
axle load and height difference on the contact forces, stresses and strains at railhead are
Str
ess
(MP
a)
t (ms)
Wheel
IRJ
Wheel
IRJ
36
36 Chapter 2: Literature Review
reported. Numerical results have shown that the height difference significantly affects the
contact force, stress and strains. The results also indicate that the train speed has a larger
effect on the contact force, stress and strains than the axle load, which contradicts the
conclusions of Wen et al. (2005). In this research, effect of speed on the wheel-rail
dynamic impact load at IRJ is examined and reported in Chapter 8; generally, it is shown
that the stresses and contact-impact forces increase with the increase in speed.
2.6 SOME MODIFIED NOVEL DESIGNS OF IRJ
With a view to minimise the problems that adversely shorten the service life of IRJ in field,
many designs of IRJs appear in the market with a claims of enhancing the structural
integrity and durability. In this section, some modified designs in the market are reviewed
with regard to their merits and demerits.
Plaut et al. (2007) proposed the use of a tapered design to improve the performance. In the
tapered joints (Figure 2-29), the modifications include increased thickness of the rail web
and extensive taper cut, through part of the width of the rail (corresponding to the web
thickness), while both sides of the rails are cut at right angles to their centre-line. There is
no significant different to the cross-section of the joint bar, which represent two designs
that are commercially available.
Based on the results obtained from Plaut et al. (2007), in comparison with a conventional
insulated butt joint, the tapered joint can be seen exhibiting lower bending moment in the
rails and joint-bars, and lower shear stress within the adhesive compared to traditional
joints. However, preliminary field measurements conducted by the TTCI showed that
although smaller impact load and higher resistance to longitudinal loads were achieved in
the tapered joints, occurrence of significant metal flow along the running surface was not
eliminated. In addition, the asymmetrical section within the tapered length leads to some
additional torsional displacements. Further, the use of the thick-web rail, add to the cost
and possibly poor usage of rail material.
37
Chapter 2: Literature Review 37
(a) Section view (b) Plan view
Figure 2-29: Cross section and plan view of tapered insulated rail joint (Plaut et al. 2007)
Another design emerged recently is reported by Igwemezie and Nguyen (2009) from the
Applied Rail Research Technologies. This joint introduces a new design of joint saddle. As
shown in Figure 2-30, a pair of metal saddles embrace around the underside of a standard
joint. The saddles are connected using two bolts underneath the rail base. Based on the
finite element analysis, the contact and bending stresses at the top of the joint bars and the
bottom of the joint bars are shown to have reduced by 30% and 14% respectively, by
applying the saddle design to the standard joint. It is concluded that the use of a saddle
underneath the joint can reduce the probability of the joint bar cracking and also provide
additional protection by holding the joint with broken bar so as to prevent catastrophic
failures.
Figure 2-30: New design of IRJ with a joint saddle
In summary, it can be stated that many attempts are made to improve the performance of
IRJs by using better insulators, different shape of joint-bars and additional supporting
components. Although these improvements have made some positive effects to the IRJ
performance as illustrated above, its service life still remains significantly less and a source
A tapered cut joint gap<30 ̊
Thickened rail web
Saddle
design
38
38 Chapter 2: Literature Review
of concern. In this research, better designs are developed through fundamental
understanding of the behaviour of the IRJs. The outputs of the analyses from this thesis
have shown that fundamentally sound designs have emerged without any wasteful of
materials and/ or high cost modern materials.
2.7 SUMMARY
IRJs exhibit geometric discontinuity, high level of stress concentration and wheel impact in
the vicinity of the gaps and are susceptible to accelerated mechanical failure. This is
particularly so in heavy haul corridors where the axle load and annual gross haulage are on
the rise.
Due to the edge effect of the rail ends, classical wheel-rail contact mechanics is no longer
valid to model the wheel-rail contact interaction in the vicinity of the joint gap.
Fundamental studies on the contact problems associated with edge effect are particularly
reviewed for obtaining the preliminary understanding essential for this research. This
review draws conclusion that in the vicinity of the joint gap, due to the loss of the
structural stiffness, the sharp corner of the rail end experiences contact pressure /stress
singularities, leading to accelerated metal flow and delamination of end post material.
These local failure modes further adversely influence the structural integrity of IRJ.
Various methods are reviewed for enhanced understanding of the performance of IRJs
subjected to wheel loading. Static wheel-rail contact FE models provided easy and efficient
comparative study between the IRJs and normal CWR in terms of the structural deflection
and stress distribution in the vicinity of the joint gap.
For the dynamic analysis of the IRJ, there are two major methods employed by the rail
engineering researchers: RMD and FE methods. In the RMD models, the wheel/rail
vertical contact interaction was normally modelled as ‗single point contact‘ and described
using HCT. Furthermore, the geometrical feature of the IRJs were usually idealised as a
surface defects. The structural components of IRJ are not modelled; hence the details of
stress analysis for them cannot be obtained using RMD method. 3D wheel-rail dynamic
contact FE model has the ability of achieving the contact/ stress analysis as well as the
analysis of the interaction amongst the complex structural components of IRJ. Moreover,
39
Chapter 2: Literature Review 39
with the development of improved computing facilities, the wheel-rail interactions are
solved by numerical methods with ease.
This chapter has also provided a general review of IRJ designs and failure mechanisms.
Some new designs emerged in the market are also reported; none of the designs have
attempted to minimise the problems of contact pressure/ railhead stress singularities. In
Chapter 3, conceptual designs are presented, with particular focus on minimising the
problems due to the stress concentration and the failure modes of various components.
Chapter 3: Conceptual Designs of IRJ for Improved Performance 41
Chapter 3: Conceptual Designs of IRJ for
Improved Performance
3.1 INTRODUCTION
A review of the functions, performance and failure modes of the IRJs is contained in
Chapter 2. It has been shown that new designs of IRJs are emerging in the market with
claims of superior performance to others. Unfortunately, all designs emerged to date are
fundamentally replicating butt joint with the two vertically cut (to the axes) rails that are
separated by a gap and the rail webs (in sometimes the rail foot also) connected with joint
bar/saddles of various geometry and material. These designs allow the wheels contacting
the railhead on the top of the unsupported free edge similar to the conventional designs;
hence, local contact pressure and railhead stress singularities and subsequent damages (e.g.
ratchetting) are not fundamentally eliminated in these new designs. Driven by the pursuit
of a more reliable and simpler design and with a view to fundamentally eliminating the
problems and failure modes identified in the Conventional IRJ (CIRJ), conceptual designs
for improved performance of IRJ have been developed and reported in this chapter.
3.2 CONCEPTUAL DESIGN PRINCIPLES
The conceptual design principles considered are:
1) To retain the basic functions of the IRJ; and
2) To minimise as many failure modes as possible.
The basic functions of the IRJ are to act as an electrical insulator of track circuit whilst
ensuring safer passage of wheels. Therefore, providing a gap between two sections of the
rail (similar to the CIRJ) is unavoidable. However, wheel contact at the top of the
unsupported free edge of the railhead can be avoided through suitable shaping of the
railhead profile close to the gap; this is one of the innovations that has been pursued in this
thesis. Furthermore, the joint bars, bolt holes and the bolts themselves introduced for the
purpose of providing structural stiffness across the gap add to complexity of the
42
42 Chapter 3: Conceptual Designs of IRJ for Improved Performance
performance in the CIRJ, resulting in several failure modes. This complexity is considered
as an opportunity for further examination of alternate means of achieving the essential
structural stiffness across the gap in this thesis. The above stated principles are
schematically summarised in Figure 3-1.
Figure 3-1: Overall schematic conceptual design principles
As shown in Figure 3-1, in the CIRJ, the vertical rail ends at the gap acts as a source of
contact pressure and railhead stress singularities leading to excessive metal flow and end
post delamination. To avoid these problems, one of the conceptual designs is aimed at
altering the characteristics of the wheel-rail contact mechanism at the rail ends with a view
to minimising/eliminating local stress singularities.
The discontinuity of the stiffness at the gap and the complexity of various structural
components lead to the bolt loosening, joint bar cracking and ultimate functional failure;
therefore, one of the conceptual designs of the IRJ is aimed at simplifying the current
design, whilst retaining the basic functions of the IRJs; namely their ability to retain
electrical insulation at all times with structural deformation commensurate to the other
continuous rail sections.
These two conceptual designs are addressed in the subsequent sections.
Design Principles
Eliminate
LOCAL failure modes1) Railhead metal flow;
2) Delaminated end post
Eliminate
Global failure modes1) Bolt loosening;
2) Joint bar cracking;
Design Principles:1) Eliminate where possible
or minimise stress
concentration
2) Modify Wheel rail contact
mechanism at rail end
Design Principles:1) Simplify complexity of
current design
2) Retain basic functions of
IRJ
43
Chapter 3: Conceptual Designs of IRJ for Improved Performance 43
3.3 A CONCEPTUAL DESIGN OF STRESS MINIMISED RAILHEAD (SMRH)
In real-life structural design, it is usually possible to minimise the stress concentration or
redistribute the stress field through appropriate profiling of the geometry without
intervention to the basic structural functions. Stress minimisation through shape
optimisation is carried out routinely in many structural problems as can be seen in a
number of published articles, such as the composite laminate structures (Cho and
Rowlands 2007), fillet designs (Xie and Steven 1997, Pedersen 2008, Corriveau et al.
2010, Le et al. 2011,), cams structure (Lampinen 2003), holes in plates (Wu 2005), notches
or bracket (McDonald and Heller 2004, Rajan et al. 2008) amongst others. These articles
present that the minimisation of stress is associated with the adoption of fillet curve design
or addition, redistribution or removal of materials; the location of stress concentration may
or may not alter depending on the application considered.
Currently, the localised stress concentration and subsequent early damage problem in the
gap-jointed structures are being solved by the engineering industry through the use of high
yield material that is expensive. For example, Stainless steel welding by replacing the
current rail steel by high yield strength steel (Rathod et al 2012). No alternative strategies
for solving the problem appeared to have been examined to date. The lack of research on
the solution of the stress minimisation through shape optimisation for the localised railhead
end is considered as an opportunity and examined in this PhD research. The conceptual
stress minimisation of the localised Sharp Cornered Railhead (SCRH) is implemented and
illustrated through Figure 3-2.
As depicted in Figure 3-2(a), due to material discontinuity in the vicinity of the joint gap,
the unsupported free edges and sharp corners are introduced in the CIRJ, Subsequently; as
the wheel load is positioned over the vertical free edge, contact region extends to the sharp
corner, resulting in a high level of stress concentration crowded in the proximity of these
sharp corners. Such severe stress concentration is capable of inflicting local rail head
damage and can subsequently inhibit the basic functions of IRJs.
44
44 Chapter 3: Conceptual Designs of IRJ for Improved Performance
(a) Sharp Cornered Railhead in Conventional IRI
(b) Design principles for Stress Minimised Railhead
Figure 3-2: Conceptual design of local railhead shape for stress minimisation
An arc shape introduced for the Stress Minimised Railhead (SMRH) as shown in Figure
3-2(b) can withstand the same loading condition with much reduced level of stress field
due to the following reasons:
1) The intersection point (shown ―B‖ in Figure 3-2(b)) between the fillet arc and the
unsupported free edge exists below the horizontal normal contact surface. In this
UnsupportedFree edge
Top railhead surface
SharpCorner
Stress concentration
Contact pressure
Wheel loadWheel load
Wheel
UnsupportedFree edge
Arc shape
Stress concentration
Contact pressure
Design variables:l: Longitudinal arc lengthd: Vertical arc depth
d
l
Top railhead surface
Wheel loadWheel load
Wheel
A
B
45
Chapter 3: Conceptual Designs of IRJ for Improved Performance 45
context, this localised geometrical alteration will change the location of the initial
contact point between the wheel and the railhead surface; the corresponding final
contact region could, therefore, be relocated and moved away from the free edge.
2) As a result, the lack of the lateral support at the free edge could be compensated
through the relocation of the contact. More importantly, it is expected that the
maximum stress magnitude could be reduced; and the location of the stress
concentration could migrate back to the subsurface of railhead, similar to the HCT
prediction for the semi infinite bodies as shown in point A in Figure 3-2(b).
Based on the above expectations, the design problem for eliminating local failure
mechanism can be outlined in Figure 3-3.
Figure 3-3: Definition of design problem for eliminating the local failure modes
3.4 A CONCEPTUAL DESIGN OF EMBEDDED IRJ
Most available designs of the IRJs replicate butt jointed rail, cut vertically either
perpendicular or inclined to their longitudinal axis. These designs incorporate joint bars
and bolts, with each component introducing their own failure mechanisms, adding to the
complex behaviour of IRJ assemblies.
Some designs focus on structural innovations involving shape modifications of the joint
bars to increase the stiffness of the assembly and provide more support to the railhead end,
thereby minimising the deflection and resultant impact forces due to wheel passage (AK
Arc shape of railhead surface at free edge
INPUTGeometrical design
parameters
Alteration of wheel-rail contact
Alteration of stress field
OUTPUTMinimised stress
magnitude
46
46 Chapter 3: Conceptual Designs of IRJ for Improved Performance
Railroad, 2006). Other structural innovations include supporting the joint directly on a
sleeper or closely spaced sleepers defining a slab support subsystem (Igwemezie and
Nguyen, 2009).
Some designs focus on material innovations such as replacing the rail steel with high yield
steel with welding technologies (Rathod et. al., 2012) and the use of high strength fibre
composite joint bars.
In this PhD thesis, a conceptual design of IRJ is developed from the idea of embedded rail
structure (ERS) that is widely used in slab track networks (Markine, 1998 and Markine et
al., 2000). Figure 3-4 shows the major components of the concept design of the Embedded
IRJ (EIRJ).
Figure 3-4: Assembly of conceptual design of EIRJ
Figure 3-5: Insulating material between the embedded steel rail and the concrete sleeper
Rail
Embedding concrete sleeper
Insulating rubber material
Prestressed concrete sleeper
Unchanged railhead curvatures
compatible to the wheel tread
47
Chapter 3: Conceptual Designs of IRJ for Improved Performance 47
The concept design consists of three major components, including two lengths of rails, a
modified geometry of the prestressed concrete sleeper incorporating insulation material.
The basic functions of the CIRJ can be alternatively fulfilled by this EIRJ design as below:
To ensure safe passage of wheels across the gap of the IRJ, the rail ends are embedded
into the prestressed concrete sleeper, with the expectation that the sleeper can be
designed to provide the stiffness that was otherwise provided by the joint bars in the
CIRJ. Figure 3-4 shows that the rail foot and part of the rail web of the two rail ends
are firmly embedded into the concrete sleeper.
Since electrical conductivity between the rail steel and the concrete sleeper is possible,
a layer of insulation material must be detailed between the embedded rail surface and
the inner concrete sleeper surface. This ensures that the new design of preventing the
direct contact between the rail and the sleeper, resulting in the failure of signalling.
Embedding steel rail into concrete sleeper can be problematic, because the vibration
characteristics that could cause damage to concrete due to its brittle nature. Isolating
the vibrating steel rail (due to wheel excitations) from concrete using rubber pads
should also be considered. Insulating rubber as shown in Figure 3-5. By isolating
vibrations, the risks of early cracking of the sleeper can be minimised and can be
carried out as a separate study. Details of the design of embedding concrete sleeper is
considered out of scope in this research
The EIRJ design proposed above can be susceptible to larger deformation that can be
safety hazard due to the elimination of the joint bars and the associated bolt connection. In
other words, the deformation of the railhead at the unsupported free edges should be
designed in such a way that they do not exceed the deflection occurring in the CIRJ
containing bolted joint bars. Therefore, the following design constraints must be
considered in the conceptual design of EIRJ:
1) The first design requirement is the vertical displacement at the rail ends under the
wheel load as shown in Figure 3-6(a). The vertical displacement should not exceed
the vertical deflection of the CIRJ under the same load condition in order to avoid
larger impact force during the wheel passage and the damage of EIRJ.
is the maximum vertical deflection of the CIRJ at the railhead end.
48
48 Chapter 3: Conceptual Designs of IRJ for Improved Performance
(a) Side view
(b) Plane view
Figure 3-6: Design requirements for the EIRJ
2) The second design requirement is the longitudinal displacement of the rail ends under
the wheel load in the vicinity of the joint gap. As shown in Figure 3-6(a), due to the
bending of the rail ends as well as the local railhead end deformation, the corners at
both of the rail ends moves towards each other, resulting in the reduction of the joint
gap. Large longitudinal displacement will crush the insulation material (end post)
inserted in the joint gap. Eventually two rail ends can potentially touch, causing the
signalling failure.
is the maximum longitudinal deflection of the CIRJ at the railhead end.
3) The third design requirement is the lateral displacement of the rail ends, as the
wheel load is located in the middle of the joint gap. The lateral displacement occurs
Wheel load P
ulongitudinal
Rail enduvertical
ulateral
Flateral1/20
Wheel load F
Flateral
Joint gap
z
xo
y
xo
49
Chapter 3: Conceptual Designs of IRJ for Improved Performance 49
due to the inclined rail position and wheel conicity shape. In Australia heavy haul
industry, the wheel profile without any wear or flat is perfectly conical with the
conicity of 1/20. The vertical axis of rail cross section also has an inclination of 1/20 as
shown in Figure 3-6(b). The magnitude of the lateral displacement should not exceed a
predefined limit so that the joint possesses enough lateral strength to avoid the gauge
widening and ultimately train derailment.
is the allowable vertical deflection of the CIRJ at the railhead end.
3.5 SUMMARY
Two conceptual designs of the IRJs have been developed with a view to providing
fundamentally sound performance under the wheel-rail contact. The designs are:
(1) Stress minimised rail head (SMRH): In this design the longitudinal railhead profile
is shaped in such a way that it would eliminate the occurrence of the wheel contact
at the unsupported railhead end as the sharp cornered railhead (SCRH) of the CIRJs
do. This design subsequently eliminates the contact pressure and the railhead stress
singularities that are common in the CIRJs; the location of the stress concentration
is also expected to shift back into the railhead in contrast to the CIRJ where the
stress concentration lingers at the sharp corner.
(2) Embedded insulated rail joint (EIRJ): This design simplifies the CIRJ through
optimal shaping of the rail section (head and web) and embedding them into a
wider and/ or deeper concrete sleeper to achieve the required structural stiffness for
the safe passage of the loaded wheels across the gap of the IRJ. Joint bars and bolts
(and hence bolt holes) are eliminated in this design; the loss of stiffness due to
these components is to be provided by the sleeper and the embedded, re-shaped
rails.
Chapter 4: Development of Stress Minimised Railhead (SMRH) 51
Chapter 4: Development of Stress Minimised
Railhead (SMRH)
4.1 INTRODUCTION
The conceptual designs of the IRJs described in Chapter 3 consist of both a simple Stress
Minimised Railhead (SMRH) and a more elaborate design of Embedded IRJ (EIRJ) that
have the joint bars and pre-tensioned bolts replaced with the embedded rails into the
concrete sleeper. This chapter presents the development of the SMRH in the proximity of
the gap, aiming at minimising the high level of stress concentration through coupling a
parametric finite element with suitable search algorithms; grid search, genetic algorithm
and hybrid genetic algorithm have been used and their merits compared.
Problem description and the mathematical representation of the railhead end shape
optimisation are provided in Section 4.2. Optimisation models in the numerical simulation
framework are presented in Section 4.3. The application of the optimisation models to the
stress minimisation of railhead end is presented and discussed in Section 4.4. Hybrid GA
with the view to improving the convergence rate of the optimal solution is presented in
Section 4.5. Section 4.6 summaries this chapter with several conclusions.
4.2 PROBLEM DEFINITION FOR STRESS MINIMISATION
As depicted in Chapter 3, loaded wheel crossing the gap induces a high level of stress
concentration crowded in the proximity of the sharp corners. Such severe stress
concentration is capable of inflicting local rail steel damage and can inhibit the basic
functions of IRJs. Therefore, it is necessary to minimise or relocate the stress concentration
away from the vulnerable unsupported free edges.
Stimulated by the application of fillet arc instead of sharp corner to the vertical free edge
(Figure 3-2(b) in Chapter 3), stress minimisation at the localised railhead ends of an
insulated rail joint was conceived to be implemented by modifying the sharp corners into a
smooth arc surface as shown in Figure 4-1. Arc surface at the railhead end can be achieved
52
52 Chapter 4: Development of Stress Minimised Railhead (SMRH)
by two local surface design parameters, namely the length ( ) and the depth ( ). It should
be noted that the railhead curvature in the lateral plane is not altered (kept the same as the
original railhead profile). Geometrically this arc shape can be constructed by sweeping the
lateral railhead curvature along the arc line defined by using these two design parameters.
Figure 4-1 also shows typical 3D view of the curved railhead geometry.
(a) Isometric view (b) Side view
Figure 4-1: Design parameters defining arc shape at rail end corner
4.2.1 OPTIMISATION FORMULATION
Subjected to wheel contact loading at the rail end, the objective function is to reduce the
maximum von Mises (equivalent) stress that is a commonly used parameter for describing
the material deformation and deterioration. The optimisation problem can therefore be
generalised as a single objective optimisation problem. The mathematical description can
be expressed as follows:
Design parameters:
Minimise:
Design constraints:
in which:
is the maximum von Mises stress under the contact loading;
is the vector consisting of two design variables, namely l and d; and
53
Chapter 4: Development of Stress Minimised Railhead (SMRH) 53
and are lower and upper limit vectors for design parameters
and respectively. It defines the search space of whole possible solution.
4.2.2 SCOPE OF THE OPTIMISATION FORMULATION
The single objective shape optimisation works reported in the literature (Wu 2005,
McDonald and Heller 2004, Rajan et al. 2008 and Pedersen 2008) deal with far field
loading,: the complexity in the current problem is that the wheel loading is near field (i.e.,
applied on the modified shape itself) involving contact nonlinearity. Therefore, although
single objective, the objective function itself is affected by the contact nonlinearity, making
the problem complex. In other words, for this single-objective optimisation problem,
analytical optimisation algorithms, e.g. gradient-based methods, cannot be directly
employed as the shape objective function in the design space is affected by the contact
nonlinearity and might contain multiple local minima. Such a complex problem often
requires the assistance of numerical simulation (e.g., finite element analysis) for solving
the objective value. Furthermore, numerical optimisation methods that are computationally
expensive have to be adopted, therefore, compromise on the material and dynamic
nonlinearity were made. It is shown in Chapter 2 that the main source of the low life CIRJ
is due to the occurrence of contact of loaded wheels at the unsupported rail ends; and Pang
(2007) has also shown that the maximum wheel impact was only 15% increased.
Therefore, wheel dynamic was not included in the optimisation modelling.
As stated in Chapter 3, the objective is to determine the best arc shape at the railhead end
for minimising the stress magnitude and possibly moving the stress concentration away
from the critical sharp cornered edge. This research applies two optimisation methods,
namely a Grid Search Method (GSM) (Rao (1996), Rardin (1998) and Ataei and Osanloo
(2004)) and Genetic Algorithm (GA). The reasons for selecting these two methods are:
GSM initially applies evenly spaced grid over the entire design space, which
clearly provides the information on the objective function containing possibly
multiple local minima and discontinuities.
The robustness of the GA in identifying the global optimum as well as its
popularity in solving various engineering optimisation problems are strong reason
for adoption in the optimisation model reported in this research.
54
54 Chapter 4: Development of Stress Minimised Railhead (SMRH)
Both the GSM and GA require finite element modelling to evaluate the objective function
repetitively. This requires that the geometry of the bodies within the optimisation design
space should be parameterised. In Section 4.3, a scheme of parametric FE modelling is
presented. In Section 4.4, this simulation-based optimisation model is applied into the
stress minimisation at railhead subjected to wheel contact load. Results show two methods
provide similar optimal solutions that dramatically reduce the magnitude of the stress
concentration and move its location to less critical zones, leading to significant
improvement to the load carrying capabilities of the IRJ.
4.3 MODELLING OF SIMULATION-BASED OPTIMISATION
In this section, a parametric FE modelling method for analysing the stress in the proximity
of the railhead end is presented. The implementation of the selected optimisation
algorithms and the integration of the parametric FE modelling into the optimisation
algorithms are described.
4.3.1 FE MODELLING USING PYTHON
It is fairly complex to simulate the behaviour of the IRJ subjected to contact load due to the
wheel passage. The performance of the IRJ can be affected by many factors such as the
geometrical and material configurations, the characteristics of the rolling stock and the
supporting types. However, as the major interest is on the free end of the top of the
railhead under the wheel thread contact, a simplified FE modelling strategy is proposed to
ensure the efficiency and the accuracy of the optimisation model. More importantly, the
nature of the optimisation model requires a fully parameterised modelling procedure, so
that the geometry, materials, loading, contact definition can all be accounted for with
relative ease using the current values in each iteration (GSM)/ generation (GA); analysis
can, therefore, be performed in an automated manner. Post-processing can also be executed
automatically and repetitively without any human intervention. These specifications lead to
the usage of an objective-oriented programming language Python as the code for the
parametric FE modelling in Abaqus.
55
Chapter 4: Development of Stress Minimised Railhead (SMRH) 55
Conventionally, when the Abaqus/CAE graphical user interface (GUI) is used to create a
FE model, commands are generated internally by following each human operation. GUI
generates structures of the commands in an object-oriented programming language called
Python, and these commands are sent to the kernel of the Abaqus. Finally the kernel
interprets the commands and realise the user‘s operation as required. The kernel is
regarded as the brain behind Abaqus/CAE; and the GUI is the interface between the user
and the kernel. Since shape optimisation depends on optimising evolutions involving the
repetitive FE modelling and objective analysis, it is important that modelling method can
be automated and communicates directly with the kernel. For this purpose, a Python script
is utilised to complete the following tasks:
Create the dimensions of the geometry provided by the design parameters at each
step/process of evolution;
Define material property, boundary conditions, meshing to establish input data for
FE analysis;
Submit the input data to invoke the FE solver; and
Access to the simulated results file (.odb file) and output the prescribed objective
value.
Figure 4-2 outlines the basic procedure of FE modelling and analysis using the Python
script. In the remainder of this section, the strategy for modelling wheel rail contact
problems at railhead end is presented. A simple example of FE modelling, FE analysis and
post-processing using Python is presented in Appendix A as an illustration.
Figure 4-2: Python script interacting with Abaqus
Pythonscript
Python interpreter
Geometry modelling
Material definition
Contact modelling
Boundary conditions
Meshing
Abaqus/StandardAbaqus/Explicit
Output database
Modelling modules
Solver Abaqus .odb file
Updated design parameters for repetitive FE analysis
56
56 Chapter 4: Development of Stress Minimised Railhead (SMRH)
a) Wheel rail geometry and idealisation
To evaluate the stresses in the vicinity of railhead end, a three dimensional (3D) model,
containing part of wheel and a length of rail, is presented in Figure 4-3. The rail inclination
and the wheel conicity are not accounted for simplicity, and the wheel is positioned at the
symmetric plane of the rail (xoz). Half of the axle load is applied at the centre of the
wheel. The position of the wheel vertical axis can be illustrated by the x coordinate, whilst
the corner of the railhead end is set as the origin of the xoz coordinates system.
Figure 4-3: Sketch of wheel rail contact model at free end
In the geometric modelling, the most important matter is to parameterise the arc surface at
the top of the railhead (Figure 4-1) so that it can be repetitively created based on the design
parameters and . To achieve it, Python programming is used to construct the arc shape
as shown in Figure 4-4; the modelling steps are summarised as follows:
Step 1: Create the cross section of the original railhead;
Step 2: Create the cross section of the railhead end, by making sure that the height
difference between the railhead top curvature is and the distance from these two cross
sections are set as (Figure 4-4 (a)). Railhead profile remained same throughout the design
parameter .
Step 3: In the symmetric plane of the railhead, a unique fillet arc of connecting point A and
point B (see Figure 4-4(b)) and its centre along the centre line of the original railhead cross
section can be determined by the given design parameters and .
3
12
4
5
6
F F Wheel centre
Wheel part
y
Rail Unsupported
free edge
z z
x o
Wheel centre
57
Chapter 4: Development of Stress Minimised Railhead (SMRH) 57
Step 4: The railhead arc surface is generated by sweeping the railhead curvature along the
created arc fillet as shown in Figure 4-4(b).
Step 5: Create other non-contacting surface and form the railhead part (Figure 4-4 (c)).
(a) Create cross sections of railhead
(b) Construct the arc shape at top railhead contact surface
(c) Create the non-contacting surface and construct the railhead part
Figure 4-4: Arc surface modelling using Python programming
d
l
Original railhead section
Centre
line Centre
line
Railhead end section A
B
Arc fillet
Original railhead section
Railhead end section
Arc surface
Normal railhead surface
Arc surface
l
58
58 Chapter 4: Development of Stress Minimised Railhead (SMRH)
b) Material idealisation
In the current optimisation model, the material is considered elastic. The reason for
excluding the material plasticity is mainly to reduce the computational cost of the
optimisation model. It should be noted that although the material is kept elastic, the
problem is nonlinear due to contact, which is unavoidable. To ensure simplicity and
repeatability, it was decided not to introduce material plasticity for the optimisation
procedure. However, the optimal shape obtained from the optimisation will be examined
through experimental study (for assessing the optimal railhead using real world material)
as well as simulation of rolling wheel across the gap in which the railhead material is
modelled nonlinear and plastic. The wheel and the rail have the same elastic material
property in terms of Young‘s modulus and Poisson‘s ratio . The material parameters
(Pang and Dhanasekar (2007)) are outlined in Table 4-1.
Table 4-1: Elastic property of wheel rail steel and end post
Material Property Wheel and rail steel
Young’s Modulus =210GPa
Poisson’s ratio =0.3
c) Boundary conditions and loading
In real track, the IRJ support system consists of rail pad, tie plate, sleeper and supporting
substructure. Modelling of this whole supporting system is complicated and expensive.
Since this research focus of this chapter is the localised zone of the railhead, the modelling
of these components is disregarded. In the FE modelling, the rail bottom surface was
assumed to be firmly fixed for simplicity. In other words, the translational Degree of
Freedom (DOF) 1, 2 and 3 at the rail bottom surface as depicted in Figure 4-3 were
arrested. It should be also noted that for the simplicity of modelling, the rail is divided into
two major parts, namely the railhead part with arc surface using Python and the rest of rail
geometry. Tie constraints are particularly used to connect these two parts together
59
Chapter 4: Development of Stress Minimised Railhead (SMRH) 59
The wheel loading and its boundary conditions are realised by creating a reference point
containing all six degrees of freedoms (DOF) at the centre for ease of simulation of the
rolling wheels whilst contacting the railhead. Since the wheel is modelled using solid
elements that do not have rotational DOF 4, 5 and 6, the reference point created as the
master control point that couple with the nodes at the top surface of the wheel part as
illustrated in Figure 4-5 enable the simulation of rolling of the wheel. In this manner, the
wheel load and the boundary definition are assigned to the reference point. In the FE model,
the wheel DOF 3 was set free, allowing for only vertical movement, and the other DOFs
were arrested. The wheel load F was also applied to the reference point.
Figure 4-5: Wheel coupling strategy
d) Definition of wheel rail contact
The master/slave contact surface method was employed throughout the FE analysis. The
wheel tread surface was defined as master contact surface, while the top surface of the
railhead was defined as slave contact surface. The contact surface pair was allowed for
finite sliding with the maximum friction of coefficient 0.3. Hard contact algorithm was
chosen for the contact pressure-over closure relationship in Abaqus/Standard. Penalty
method was used to enforce the contact constraints, which searched for slave node
penetrations into the current configuration in all iterations. Contact forces as a function of
the penetration distance (0.01% of the minimum element size) were applied to the slave
Wheel centre
F
3
12
4
5
6
Reference
point
Wheel part
Coupling
Coupled
surface
60
60 Chapter 4: Development of Stress Minimised Railhead (SMRH)
nodes to prevent excessive penetration, while equal and opposite forces acted on the master
surface at the penetration point. As the master surface was defined using the element faces,
the master surface contact forces were distributed to their nodes.
e) Meshing
Meshing is an important part of FE modelling, which has a strong influence on the
reliability and accuracy of results as well as the model efficiency. Refined mesh usually
provides more accurate results. However, the refined mesh also increases the
computational cost significantly especially for the repetitive optimisation iterations. Hence,
some meshing strategies are employed to set up a reliable FE model with reasonable cost.
A typical meshed geometry of wheel – railhead is shown in Figure 4-6.
Figure 4-6: Finite element model
For the regions far away from the contact/stress concentration zone, coarse mesh and 8-
node reduced integration element (C3D8R) was used to reduce the model size. While for
the regions that undergo contact interaction or high level of stress, refined mesh and 8-
node fully integrated element (C3D8) were adopted. To find efficient and accurate element
size in this region, a mesh sensitivity analysis was conducted.
Railhead with
arc surface
61
Chapter 4: Development of Stress Minimised Railhead (SMRH) 61
Figure 4-7 shows the variations of maximum von Mises stress as the wheel contacting at
the original railhead end and computational time with respective to the mesh size. It can be
seen that the element size 0.5 is mostly suitable, because the FE model was providing
result, while keeping desired efficiency. There were 47303 solid elements for the rail,
53736 elements for the wheel part and 303117 DOFs in the whole system of the most
optimal mesh.
Figure 4-7: Result of mesh sensitivity study
4.3.2 IMPLEMENTATION OF OPTIMISATION ALGORITHMS
a) Grid Search Algorithm
If the search space is known to be within a finite area defined by the upper and the lower
bounds of each of the independent design parameters, then the grid search method (GSM)
can be applied. In the current optimisation problem, the search method starts with an initial
grid over the space of the interest and evaluates the objective values at each node of the
grid. The density of the grid depends on the complexity of the problem as well as the
search range of each design parameter. Figure 4-8 shows an example of initial search grid
0
20
40
60
80
100
120
140
1790
1800
1810
1820
1830
1840
1850
1860
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Co
mp
uta
tion
al t
ime
(min
s)
Max
imu
m v
on
Mis
es
stre
ss (
MP
a)
Mesh size (mm)
Maximum von Mises stress
Computational time
Optimal mesh
size 0.5mm
62
62 Chapter 4: Development of Stress Minimised Railhead (SMRH)
(7×7) of two design variables ( , ) with upper bound of =( , ) and lower bound of
=( , ).
Initially, the objective value at each node marked as ―●‖ is evaluated, and the node with
the minimum objective value is located. This node then becomes the centroid of a smaller
search space. Normally this smaller space is defined by the adjacent nodes from the initial
grid as zoomed grid. As a result, new grid (5×5) and additional nodes marked as ―▲‖ are
evaluated. In such a manner, successive narrowing of the search space is continued until
optimisation iterations meet the predefined converging criterion such as the maximum
number of iterations or the tolerance for the minimum value is attained.
Figure 4-8: Scheme of grid search method
b) Genetic algorithm (GA)
Genetic algorithms have a theoretical background developed by Holland (1992). The
efficiency of GAs is problem dependent and has been proved positively in various
structural design problems (Deb (2002) and Renner and Ekart (2003)). GAs are search
algorithms based on the mechanics of natural selection and Darwinian evolutionary theory.
In the form of computer simulations, GA is typically implemented through a population of
candidates (individuals) to an optimisation problem and gradually evolves towards optimal
x1
x2
U2
L2
U1L1
Min
Min
Initial Grid Zoomed Grid
63
Chapter 4: Development of Stress Minimised Railhead (SMRH) 63
solutions. The evolution starts from a population of randomly generated individuals. In
each generation, the fitness value of each individual is evaluated in regard to the objective
function and the constraints. Based on the performance of these individuals, multiple
individuals are stochastically selected and subjected to crossover and mutation operations
associated to probabilities and respectively. Such evolution procedures are repeated
in the successive generations until the optimal solution converges.
Chromosome Representing Individual
In GAs, an individual is defined using a particular coding arrangement (chromosome) for
the design variables. A finite length of binary coded strings consisting of 0s and 1s is
widely used to describe the design variables for each solution. For the arc shape design
defined by the two variables and as described in Section 4.2, coding for each design
variable is concatenated into a complete string as shown in Figure 4-9. Each 8 digits can be
decoded as one of the design variables. The length of the chromosome can be adjusted
depending on the desired precision and the domain of design variables. The mapping form
a binary string back to a real number for the design variable is obtained by:
where denotes the jth
digit of the ith
design variable .
0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1
Figure 4-9: Binary coding of design parameters in GA
Selection
The selection procedure in GAs allows individuals to be retained in the basic pool for the
next generation prior to the crossover and mutation processes. Different selection methods
exist such as the proportional selection, tournament selection, ranking selection, etc. In this
research, tournament selection is used. The tournament selection randomly selects some
8 digits 8 digits
l d
64
64 Chapter 4: Development of Stress Minimised Railhead (SMRH)
individuals to compete with each other. The one with highest fitness value survives. This
process continues until the size of the required population is reached. Furthermore, this
research also applied an elitist strategy for preserving the optimal solution (individuals
with high fitness values). In the elitist strategy, some individuals of the current population
with the highest-ranking fitness values are directly retained for the subsequent generation.
This technique guarantees that the best performed design variables will never be eliminated
by the GA and will evolve progressively. In this research, a parameter of 0.1 is taken,
which means that the top 10% of the individuals with the best performance will survive
into the next generation.
Crossover and Mutation
Crossover and mutation are the next two processes following the selection. Figure 4-10
shows the process of crossover and mutation respectively.
0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1
1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1
0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1
1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1
(a) Process of crossover operation
0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1
0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1
(b) Process of mutation operation
Figure 4-10: Genetic operators
Different types of crossover are used, including single-point, double-point, uniform and
weighted crossover. In this research, a single point crossover was adopted for its simplicity.
In the single crossover operation, two parent chromosomes are initially selected from the
Swapped
Cross point
Parent 1:
Parent 2:
Child 1:
Child 2:
One bit mutation
Prior to mutation
After mutation
65
Chapter 4: Development of Stress Minimised Railhead (SMRH) 65
population and a random number between 0 and 1 is generated and compared with the
crossover probability . If the number is less than , a cross-point in the length of the
parent chromosomes is randomly determined and portions of the parent chromosomes are
swapped. The crossover probability between 0.6 and 0.9 is generally recommended.
Different values have been adopted in the analysis (included in Section 4.4.4). After the
crossover operation, the uniform mutation operates and brings the diversity into the
population. The uniform mutation progresses over each bit through the length of
chromosome and change a bit from 0 to 1 or vice versa with a probability . The
mutation probability is normally very small ( <1%), since a high mutation probability
might destroy the efficiency and turn the GA into a simple random walk.
4.3.3 OPTIMISATION FRAMEWORK
To integrate the parametric FE into the selected optimisation algorithms for an automatic
optimisation loop, there must be two major frameworks: the first is the numerical
simulation to obtain the objective value with regard to different individuals in each
generation; and the second is to evaluate fitness value, prepare for next iteration through
GSM or GA respectively and interface with the numerical analysis for a progressive
optimisation evolution.
To achieve this goal, Python scripting is integrated into the optimisation algorithms coded
in Matlab. In each FE analysis, Python script is called by either the GSM or the GA under
the Matlab environment for the calculation of the objective function with regard to each
design parameters of the iteration. In the GSM optimisation model, the objective values at
each node of the grid, namely the maximum von Mises stress is evaluated and compared
with the previous iteration; and the best candidate with the minimum value is selected. A
refined search grid is then generated around the minima and objective evaluation is
repeated for this newly updated search grid. The search grid progressively converges in the
optimisation loop and terminates when the process fully converged. The integration with
GA is implemented by using GA operators. By receiving the objective values of each
design individual in the current generation, the fitness evaluation and genetic operations
are implemented in the GAs for creating the next generation. Such optimisation loop is
formed and continued until the optimal design is converged. Figure 4-11 presents the
optimisation procedures of using the GA coupled with the FEA.
66
66 Chapter 4: Development of Stress Minimised Railhead (SMRH)
Figure 4-11: Schematic diagram for the proposed optimisation model
4.4 APPLICATION TO THE DEVELOPMENT OF SMRH
The design objective in this example is to work out the optimal arc shape at the railhead
end to minimise the stress concentration due to the wheel contact. FE analysis to this
particular wheel rail contact problem was carefully developed as described in Section 4.3.1.
The main idea is to retain the railhead profile as per the Standard AS 60kg/m rail (AS1085.
12, 2002) all along the design parameter ― ‖ but by just lowering the railhead ―top‖ from
the original position to the design parameters ― ‖ at the free end. In this manner, the wheel
Pre-processing:Geometry Definition;Material Description;
Contact definition;Boundary condition;Finite element mesh.
FEM analysis
FE Solver
Post-processing:Obtain objective value
GAs parameters:Generation;Population;
Selection method;Crossover/mutation.
StartGA Evolution
Initialise Population
Current Generation
Fitness evaluationElitism strategy
SelectionCrossover/mutation
Termination criterion
NO
YES
Optimal Design
Integrated FEA
Using Python Script
Optimisation Model Based on GA
67
Chapter 4: Development of Stress Minimised Railhead (SMRH) 67
tread-railhead contact is not inadvertently altered. The applied constraints were 0mm<
<100mm, 0mm< <5mm.
In the GSM method, two initial search grids, namely a fine search grid 20×20 and a coarse
search grid 10×5 were employed to ensure the local minima are identified. In each grid,
based on the objective values, a new 5×5 local search grid in next iterative search was
generated. The termination criterion for GSM was that the difference of the percentage in
the optimal objective value between last iteration and the current iteration was less than
0.5%. In GA method, several key genetic parameters are shown in Table 4-2. Convergence
of subsequent design evolutions in GA is not checked (as in GSM), because: 1) GA might
be trapped into the local minima in several consecutive generations; 2) Most engineering
optimisation in the literature have adopted specified generation number (maximum
evolution number) as termination criterion.
Table 4-2: GA parameter values used in optimisation
GA parameters Parameter values
Chromosome 16-bit binary coding
Population size 20
Generation 20
Selection Tournament
Crossover One bit-point
Crossover rate 0.7
Mutation rate 0.005
Optimisation termination criteria Maximum evolution number
4.4.1 COMPARISON OF OPTIMAL RESULT FROM GSM AND GA
A typical loaded wagon wheel =130kN in a heavy haul transport network is considered.
Results from GSM and GA are compared and discussed. The wheel rail contact and stress
variations under the optimal shape are nondimensionlised by the maximum contact
pressure , major semi-axis in longitudinal direction and minor semi-axis in lateral
68
68 Chapter 4: Development of Stress Minimised Railhead (SMRH)
direction calculated from the Hertzian Contact Theory (HCT) as presented in Chapter 2 for
convenience of comparison. The HCT results are valid when the wheel is far away from
the unsupported rail end.
First, the optimal result from GSM based on the initial search grid 20×20 and coarse search
grid 10×5 are presented respectively in Figure 4-12.
(a) Iso-von Mises stress plot for 20×20 grid
(b) Iso-von Mises stress plot for 10×5 grid
Figure 4-12: Profile of optimal result using GSM
Curve Depth (d)
Cu
rve
Len
gth
(l)
0.73P0
0.83P00.73P0
0.73P0
0.83P0
0.97P0
1.08P0
1.23P0
1.42P0
1.42P0
0.97P0
Minima 1
Minima 2
Local search Grid
Curve Depth (d)
Cu
rve
Len
gth
(l)
Minima 1
(d=1.5 l=40)
Curve Depth (d)
Cu
rve
Len
gth
(l)
0.76P0
0.91P0
1.24P0
0.91P01.24P0Minima 1
Minima 2
Local search Grid
Curve Depth (d)
Cu
rve
Len
gth
(l)
Minima 1
(d=3.0 l=70)
0.72p0
0.74p0
0.72p0
0.69p0
69
Chapter 4: Development of Stress Minimised Railhead (SMRH) 69
Figure 4-12 shows that the iso-stress plot based on the objective value from the initial grid
nodes. It can be seen that the fine initial grid 20×20 (see Figure 4-12(a)) has a better
recognition of the stress response to the shape of the rail end; three local minimum zones
were found and the two nodes with the best two objective values were located at two of the
local minimum zones. However, the coarse search grid 10×5 (see Figure 4-12(b)) can only
predict a single and relatively larger optimal zone, in which two near-optimal nodes are
selected. Subsequently, the optimal result based on the information provided by the initial
grid could be entirely different. Result shows that the optimal parameters based on the fine
grid yield at =40.00mm and =1.50mm with the optimal stress magnitude of 0.69 . The
coarse gird on the other hand has resulted in the final solution of =70mm and =3.12mm
with the optimal stress, value at approximate 0.72 . Such a difference in terms of the final
optimal design parameters indicates that the coarse grid has provided a poor estimate of the
objective function, where the global minimum was missed and the optimisation tended to
be diverted to a local minimum (responding to minima 2 in fine grid in this case).
Although this optimisation problem contains a single objective function, result from the
GSM demonstrates the existence of multiple local minima due to the nature of the problem
compounded by the wheel-rail contact nonlinearity. Refined initial grid might be able to
identify more local minima; however, it can be computationally expensive. Further, to
ensure whether or not finally converged result is globally optimal, an independent method
would be necessary. GA provides such an opportunity.
In the GA optimisation procedure, the optimisation evolution was limited to a maximum of
20 generations and was found sufficient to provide stable and convergent solutions. As
shown in Figure 4-13. At the load of , the initial stress concentration is 1.16 . Gradually
the optimal stress has decreased to 0.69 in 15 generations with less than 0.006%
difference among the last 7 generations. The optimal design parameter are =40.05mm and
=1.47mm. It is found that the optimal result from GA is similar to the one obtained by
using fine search grid in GSM.
The GA method and the fine grid search in GSM are CPU time intensive with the
numerical analysis consisting of large percentage of the optimisation iterations. In a
supercomputer of 4CPUs and 3GB memory, it took 172 hours for the GSM and 167 hours
70
70 Chapter 4: Development of Stress Minimised Railhead (SMRH)
for the GA. The coarse grid GSM took only 29.8 hours, but unfortunately could not
provide global optimal result. As the objective is to obtain reliable optimum design
parameters, and since the cost of CPU time is progressively reducing with the advent of
computers, GA coupled with FEA was considered acceptable for the complex wheel-rail
contact problem; more efficient genetic algorithms to minimise CPU time is a subject of
further research and some work towards this is reported in Section 4.5.
Figure 4-13: Evolution of optimal maximum von Mises stress at load
4.4.2 EFFECT OF WHEEL LOADS TO OPTIMAL SHAPE
It can be seen from the discussion contained in Section 4.4.1 that GA provides reliable
results avoiding being trapped into the local minima. It should be noted that result
predicted was for a fully loaded wagon wheel. As the wheel load affects the contact and
since contact nonlinearity is an important factor that affects the parameter of the objective
function (maximum von Mises stress), it is essential that a lower wheel load case is
examined. From a practical perspective, unloaded wagons do travel and hence an
optimisation study with wheel loads corresponding to unloaded wagon would be sensible.
Therefore, the GA optimisation was re-run under a wheel load reduced to 0.2 =26kN.
0.6
0.7
0.8
0.9
1
1.1
1.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimal stress
Generation
Op
tim
al s
tres
s σ
ema
x /p
0
1.16p0
Initial generation
5th generation
0.94p0
10th generation
0.75p0
15th generation
0.692p0
20th generation
0.688p0
71
Chapter 4: Development of Stress Minimised Railhead (SMRH) 71
The evolution of the optimal maximum von Mises stresses under the unloaded wheel
0.2 at rail end is compared in Figure 4-14. The result is similar to the fully loaded wheel
result in Figure 4-13. The optimal stress is 1.12 in the initial generation. As the
generation increases, the stress concentration reaches a stable solution less than 0.3%
deviation in the last five generations. The final optimal solution yields at 0.68 . The final
optimal shapes of the two load cases (loaded and unloaded) are presented in Figure 4-14
and Figure 4-15 (optimal arc shape defined by the optimal design parameters at the
symmetrical plane of the railhead).
Figure 4-14: Evolution of optimal von Mises stress at unloaded 0.2
Table 4-3: Comparison of optimal design parameters at wheel load and 0.2
Wheel Load l (mm) d (mm) Optimal
von Mises
Loaded wheel 40.05 1.47 0.69
Unloaded wheel 0.2 38.05 1.44 0.68
500
600
700
800
900
1000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimal stress
Generation
Initial generation
5th generation
0.99p0
10th generation
0.74p0
15th generation
0.684p0
20th generation
0.682p0
1.12p0
Op
tim
al st
ress
σem
ax/p
0
72
72 Chapter 4: Development of Stress Minimised Railhead (SMRH)
Figure 4-15: Optimal shape at the symmetrical plane of the rail edge
It should be noted that the optimal stress and the optimal design variables at these two
loads values and 0.2 are very similar to each other (as one would expect for stress
minimisation problems – however, these two analyses prove the stability and dependability
of the optimisation model developed in this study).
The optimal stress is 0.688 at and 0.682 at 0.2 , with only 0.9% difference. The
difference of the design parameters and is 5% and 2%, respectively. A 2mm shorter ― ‖
for the unloaded wheel positioned at the railhead end will not adversely affect the travel of
the unloaded wheel on a railhead optimised for the loaded wheel. This is because when the
unloaded wheels are at 40.05mm away from the unsupported free edge, the contact does
not extend to the free edge and the affect of the wheel will not be felt much at the free edge.
Thus, having optimal shape for an extra 2mm will not harmful to the IRJ, should
unloaded/empty wagon or light trains (e.g., passenger/track recording train) travel.
Therefore, designing the IRJ from optimal shapes obtained from the fully loaded wheel is
considered appropriate. The effect of this optimal shape to the contact pressure and stress
distribution at the unsupported rail end is discussed in the following section.
0
0.5
1
1.5
2
2.5
3
-10 0 10 20 30 40 50
Optimal shape at load F
Optimal shape at load 0.2FRail edge
Optimal arc
shape
l
d
z co
ord
ina
tes
(mm
)
x coordinates (mm)
73
Chapter 4: Development of Stress Minimised Railhead (SMRH) 73
4.4.3 EFFECT OF SMRH TO CONTACT PRESSURE
Figure 4-16 shows the SMRH exhibits the maximum contact pressure as 1.25 , which is
25% smaller than the stress in SCRH (1.49 ) of the CIRJ.
(a) SMRH
(b) SCRH
Figure 4-16: Distribution of contact pressure at railhead surface
Moreover, the contact region at the optimal shape exhibits approximately an elliptical
shape and located away from the rail edge (see Figure 4-16(a)) (although the wheel axis is
located at the rail edge). This is in contrast to the SCRH that has the maximum contact
pressure bounded by the free unsupported rail edge (see Figure 4-16(b)). The result
1.5
1.0
0.5
0.0
-0.5
2b
b
0
-b
-2b 0a
2a3a
4a
p/p0=1.25
y x
p/p
0 Rail end
x=0
1.5
p/p
0
0.0
0b
0
y x
p/p0=1.49
1.0
0.5
-0.5
2b
-b-2b
a2a
3a4a
Rail end
x=0
74
74 Chapter 4: Development of Stress Minimised Railhead (SMRH)
indicates that under the same wheel load, the optimal shape has effectively changed the
load transfer characteristics into the railhead.
The contact pressure distribution and the vertical deflection of the rail contact surface
along the symmetric plane (z=0) in the end vicinity is shown in Figure 4-17.
Figure 4-17: Contact pressure and deflection of the contact surface along the rail
symmetric plane (z=0)
It can be seen that the SMRH has larger contact length than the SCRH. For the same load
magnitude, the larger contact length could lead to less average (also peak) contact pressure,
which has been confirmed as shown in Figure 4-16. More importantly, the spatial
alteration in the position of the contact length at the SMRH has also favoured reduction in
the deflection of the rail end. The maximum deflection point at SMRH is almost 50%
reduced, compared to the SCRH with the maximum deflection point located at the sharp
corner. This larger deflection is closely associated with larger plastic deformation and early
material deterioration. The loss of stiffness closer to the free edge is in agreement with
some of the literature reported in Chapter 2 (Hanson and Keer (1989) and Chen (2003)).
Contact pressure at SCRH
Contact pressure at SMRH
Deflection at SCRH
Deflection at SMRH
2.0
1.5
1.0
0.5
0
0.05
0.10
0.15
p/p
0D
efle
ctio
n u
z(m
m)
x coordinate (mm)
Contact pressure
distribution
Deflectedprofile
5 10 15 20 25 30 35 40
75
Chapter 4: Development of Stress Minimised Railhead (SMRH) 75
4.4.4 EFFECT OF SMRH TO STRESS DISTRIBUTION
Figure 4-18 shows the equivalent stress field close to the end at load .
(a) SMRH
(b) SCRH
Figure 4-18: Distribution of von Mises stress in the SMRH and SCRH
The maximum von Mises stress was 1852MPa in the SCRH, whilst that of the SMRH was
923MPa. Apart from the significant reduction of stress concentration, the position of the
maximum equivalent stress is translated away from the sharp corner of the railhead end.
923.32
838.02
762.81
687.54
612.23
536.96
461.66
386.32
311.02235.77
160.45
85.13
0.00
Stress (MPa)
von Mises
x y
z
Rail Symmetric
Surface
Railhead
Surface
Rail Edge
x y
z
1852.86
1698.85
1544.83
1390.82
1236.81
1082.80
928.78
774.77
620.76466.74
312.73
158.72
0.00
Stress (MPa)
von Mises
Railhead
Surface
Rail Edge Rail Symmetric
Surface
76
76 Chapter 4: Development of Stress Minimised Railhead (SMRH)
The spatial alteration of the stress concentration is consistent with the contact distribution
as discussed in Figure 4-16 and Figure 4-17; it can, therefore, be concluded that when the
wheel approaches the rail end, the SMRH will effectively modify the contact load transfer
characteristics into the railhead with significantly reduced the stress concentration
(magnitude and location) that will improve its life.
In some instances, the wheel axis might extend out to the geometric end, resulting in more
severe stress concentration. Therefore, the stress concentration at three different wheel
contact positions, namely x/a=0, -0.5 and -1.5 were also examined. Results at loaded wheel
and unload wheel 0.2 are presented in Table 4-4.
Table 4-4: Comparison of SCRH and SMRH at different wheel positions
Wheel
Positions
(x/a)
Load Load 0.2
SCRH SMRH SCRH SMRH
0 1.38 0.69 1.37 0.66
-0.5 2.32 0.72 2.29 0.73
-1.5 3.73 0.79 3.65 0.78
With the wheel axis extended beyond the railhead edge, the maximum von Mises stress in
the SMRH at load is around 0.72 at x=-0.5a and 0.79 at x=-1.5a, increased by only
3.8% and 15.3%, compared to the one at l/a=0. However, the peak Mises stress in the
SCRH is around 2.32 at x=-0.5a and 3.73P0 at x=-1.5a, increased by 61.6% and 169.6%
comparing to the one at l/a=0. Similar observation can also be found for the wheel load
0.2 . The peak Mises stress increased by 166%, from 1.37 to 3.65 in the SCRH;
whilst in the SMRH, it just increased from 0.66 to 0.78 . It is obvious that the stress
increase is significantly less pronounced in the SMRH compared to SCRH. Also
invariantly the stress concentration and the peak stress are located underneath of the rail
head surface and shifted away from the edge.
77
Chapter 4: Development of Stress Minimised Railhead (SMRH) 77
4.4.5 SENSITIVITY OF GA PARAMETERS
GA solutions may be affected by the genetic parameters chosen (population size, crossover
rate and mutation rate ). In this section, the effect of these genetic parameters on the
efficiency of the GA and the optimal result emerged are reported.
The sensitivity study is conducted by considering a higher mutation rate, higher crossover
rate and larger population size than the ones used in the previous section. It has been
known that a larger mutation rate might reduce the efficiency, but in the current
optimisation problem, since there are only 16 bits for each individual and the elitism
selection strategy has the capability of retaining the top individuals with best performance
from one generation to another, a relatively larger mutation rate was used; it was possible
to keep a more efficient exploration of the design space, e.g. 0.05 instead of 0.005.
Similarly, relatively higher crossover rate and larger population size might also provide
more robust converging efficiency. Therefore, the study on the higher mutation rate
=0.05 instead of 0.005 was conducted as well as the higher crossover probability
( =0.9 instead of 0.7) and larger population size (40 individuals instead of 20).
As shown in Figure 4-19, Figure 4-20 and Figure 4-21, the final optimal shape from the
three GA parameters are quite similar to the one described in Section 4.4.1 (around 0.69 ).
It indicates that the final optimal design is not very sensitive to the GA operators (mutation,
crossover and population size) for our optimisation problem. However, the efficiency of
GA in optimal evolution can be different by using different mutation rate. It can be seen
from Figure 4-19 that with higher mutation rate, the final optimal solution tends to
converges at around 12th generation, compared to the 15
th generation in the original result.
Moreover, the optimal stress level decreased from first generation up to the 12th generation.
It shows that the larger mutation rate does provide more capability of the search better
solution within the search space and less possibility of being locally trapped. Compared to
the effect of mutation rate, the crossover rate and population size is not very obvious. They
both have the final optimal solution yielded around 14th generation. In Figure 4-21,
because the population size is doubled, the time taken for analysing each generation was
correspondingly doubled, resulting in the overall reduction of the efficiency.
78
78 Chapter 4: Development of Stress Minimised Railhead (SMRH)
Figure 4-19: GA evolution using larger mutation rate 0.05 instead of 0.005
Figure 4-20: GA evolution using larger crossover rate 0.9 instead of 0.7
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimal stress Pm=0.05
Generation
1.20p0
Initial generation
5th generation
1.04p0
10th generation
0.74p0
15th generation
0.690p0
20th generation
0.688p0Op
tim
al st
ress
σem
ax/p
0
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimal stress Pc=0.9
Generation
1.24p0
Initial generation
5th generation
1.05p0
10th generation
0.784p0
15th generation
0.690p0
20th generation
0.689p0Op
tim
al st
ress
σem
ax/p
0
79
Chapter 4: Development of Stress Minimised Railhead (SMRH) 79
Figure 4-21: GA evolution using larger population size 40 instead of 20
4.5 HYBRID GA FOR DEVELOPMENT OF SMRH
In Section 4.4, it has been shown that the GA generally has provided effective and reliable
search capability and ensures the global optimality for the development of the SMRH.
Furthermore, the sensitivity study has demonstrated that the optimal solution was not
affected by the genetic parameters (population size, mutation rate and crossover rate). The
process, however, is time consuming; therefore, it is prudent to find methods to solve the
problem more efficiently. With a view to improving the search efficiency, a hybrid genetic
algorithm is applied to the stress minimisation problem. This section, therefore, deals with
a hybrid GA method in search of efficiency.
4.5.1 HYBRID GENETIC ALGORITHMS
To enhance the convergence performance and the searching efficiency, it has been
proposed to incorporate the classical optimisation methods into GAs (Bethke, 1981;
Goldberg, 1983; Angelo, 1986; Back et al., 1997; Dozier et al. 1998). As indicated in
Section 4.4, GAs are good at identifying global optimum, whilst the conventional
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimal stress Population size=40
Generation
1.18p0
Initial generation
5th generation
1.043p0
10th generation
0.765p0
15th generation
0.690p0
20th generation
0.689p0Opti
mal st
ress
σem
ax/p
0
0.72p0
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80 Chapter 4: Development of Stress Minimised Railhead (SMRH)
optimisation methods are relatively more efficient at local refined optimum searching but
lack a global perspective. However, the hybrid GAs integrates the global exploration
capability of GAs and the local exploitation capability of conventional optimisation
methods, hence, compromising their individual weak points and outperforming either one
individually (Gen & Chen, 1997). Various types of hybrid GAs have been reported in
literature. Generally, they can be classified into three major categories:
1) Incorporate the problem-specified information into the existing genetic operators
(Yamade and Nakano 1992 and Cheng et al. 1996);
2) Create new heuristic-inspired operators to replace or insert into the existing genetic
operators (Magyar et al. 2000);
3) Incorporate the conventional optimisation methods (local optimisation algorithms) into
GAs (Liu et al. 2000, Xu et al. 2001and Costa et al., 2010).
Integrating the conventional local optimisation methods into GAs has been widely used in
various engineering optimisation problems. The preference to the hybridisation of GAs
with various conventional optimisation methods is due to its relatively easy
implementation. Moreover, such a hybridisation can integrate the advantages of these two
different methods, combining the global search capability of GA and efficient local search
capability of the conventional optimisation methods. The mostly used hybrid GAs is the
conventional optimisation algorithm, as a local search optimiser, being embedded into the
GA. During each genetic generation, GA applies selection, crossover and mutation
operator for global search and generates a population of new offspring. Before these new
offspring are set as the next generation, local optimiser selects some of the current
individuals as the initial search point and search for new optimal solutions, which inherits
the good or better quality in terms of the fitness value. In this manner, hybrid GAs aims at
searching for best global optimum more efficiently and more effectively.
It is possible to have a few generations of GA combined with gradient-based methods.
Unfortunately, this cannot guarantee a faster solution. This is because locally the objective
function is largely affected by two factors that define the shape of the objective function.
1) Nonlinearity due to the contact, which itself is very sensitive to shape (which are the
main design parameters in this chapter); and
2) Adoption of the numerical analysis in this thesis cannot be guaranteed to gain the local
derivative information due to the numerical nature.
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Chapter 4: Development of Stress Minimised Railhead (SMRH) 81
These difficulties will certainly make the objective function as multiple minima and
possibly highly non-continuous/noisy. Therefore, trialling gradient-based method for local
search is not simply considered as practical in this thesis.
To overcome the lack of efficiency of using classical gradient-based methods in hybrid
GAs for minimising computational cost, a hybrid GA incorporated with a local optimiser
based on the direct search methods has been generally recommended (Xu et al., 2001 and
Costa et al., 2010). Compared with gradient-based methods, the local optimiser based on
direct search methods possesses the following two major advantages:
1) It only requires function evaluations and objective values. For the optimisation
problem requiring numerical analysis that is computational expensive, this methods
can decrease the computation cost in the entire optimisation process.
2) The technical implementation of integrating this local optimiser into the basic loop of
GAs is simple and straightforward. As the direct search methods can be easily
programmed as an independent subroutine module, this ideal of hybridisation is also
easy to incorporate into the existing GAs
Based on the above discussion, the hybrid GA with the local optimiser based on the direct
search methods are applied for the development of the SMRH through shape optimisation.
In particular, a heuristic pattern move, one of the direct search methods, is used, which is
expected to keep the common advantages of the general hybrid algorithms, and
simultaneously avoid the shortcoming of expensive computational cost usually required in
the hybridisation process. The hybridisation of GA with heuristic pattern move has been
previously reported and applied into several typical mathematical optimisation problems
and limited engineering problems (Xu et al., 2001). Whilst it is first time that such methods
is used in the stress minimisation involving in wheel-rail contact problem. The details of
optimisation procedure and the optimal results are discussed in the ensuing sections.
4.5.2 HYBRIDISATION OF GA WITH HEURISTIC PATTERN MOVE
a) Local optimiser using heuristic pattern move
The heuristic pattern move has been successfully employed in the Hooke-Jeeves method
(Kalyanmoy, 1998) to find an even better solution around the local optimum. In the current
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82 Chapter 4: Development of Stress Minimised Railhead (SMRH)
optimisation problem, the heuristic pattern move was implemented by first selecting the
best individual from the previous generation and the current generation respectively, and
then these two individuals are used to generate two new individuals by conducting the
interpolation and extrapolation along the direction connecting the best individual in the
previous generation. There is no additional function evaluation required in this process.
The two newly generated individuals are used to replace two worst individuals in the
present population. These two new individuals together with other offspring obtained using
the conventional GA operators form the next generation. In this way, the hybridisation of
two kinds of optimisation methods (GA and local optimiser) is realised. The objective of
local optimiser in this hybrid algorithm is focused on finding out better individual
neighbouring to the best one in the previous and present population. The local heuristic
pattern move finds the two new individuals based on the following formulations:
in which:
and
are two newly generated two individuals;
and
are the individual with the best fitness value (objective value) in the
previous and current generation respectively;
and are the control parameters of a local optimiser. Both of them are recommended to
be within the range from 0.3 to 0.7. (Xu et al., 2001).
The local optimiser only takes a rather less computation cost for obtaining two new
individuals and
, no evaluation of objective function is required in this process.
The computation cost for the hybrid GA to reproduce each of new generations has hardly
increased when compared with the conventional GAs.
b) Procedure of hybrid GA with heuristic pattern move
Based on the above discussion, the procedure for the proposed hybrid GA can be
illustrated through the following steps:
Step 1: Let j=0, initialise the population of a number of n individuals in GA, =
( );
Step 2: Evaluate the objective value/fitness values of ;
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Chapter 4: Development of Stress Minimised Railhead (SMRH) 83
Step 3: Check the termination condition. If ―yes‖, the evolution process terminates.
Otherwise, j=j+1 and continue to the next step;
Step 4: Conduct the genetic operations: selection, crossover and mutation to generate the
initial offspring = ( );
Step 5: Evaluate the objective values of the current offspring , and sort out two
individuals with the worst fitness values and two individuals with the best fitness values;
Step 6: Implement the heuristic pattern move to generate two new individuals and
based on the selected top two individuals;
Step 7: Replace the two worst individuals with and
to form the final offspring
= (
), and then start the next round of evolution;
Step 8: Go back to Step 3.
Figure 4-22: Flow chart of hybrid GA based on heuristic pattern move
StartGA Evolution
Initialise population
Evaluate fitness value
Heuristic pattern moveSelection
CrossoverMutation
Elitism
Termination criterion
EndOptimum
NO
Current population
YES
Obtain two local individuals
Evaluate fitness value
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84 Chapter 4: Development of Stress Minimised Railhead (SMRH)
The flow chart of the hybrid GA procedure is depicted in Figure 4-22. In the next section,
by incorporating the hybrid GA with the FE model using python as described in Section
4.3, the stress minimisation at the railhead end subjected to wheel contact loading is
conducted, and the relative result is presented and compared with that from the simple GA
in Section 4.4. Conclusion was made in terms of improvement on the optimal result and
genetic searching efficiency.
4.5.3 PERFORMANCE IN STRESS MINIMISATION OF RAILHEAD END
In this section, the proposed hybrid GA is applied for the development of the SMRH. The
design optimisation problem has been stated in Section 4.2 and hence not repeated. FE
modelling and analysis was developed as described in Section 4.3. The applied constraints
were also kept the same: 0 mm < < 100mm, 0mm < < 5mm.
Because the effect of the simple GA operators (population size, crossover and mutation) on
the optimal solution as well as the convergence performance is not obvious as discussed in
Section 4.4.5, this section use the same parameter values for the GA operators. As for the
two control parameters and in the local optimiser, both of them were set as 0.5
initially. The effect of the control parameters to the evolutionary process is also reported in
this section. The parameters used in the hybrid GA is outlined in Table 4-5.
Table 4-5: Hybrid GA parameter values used in optimisation
GA parameters Parameter values
Chromosome 16-bit binary coding
Population size 20
Generation 20
Selection Tournament
Crossover One bit-point
Crossover rate 0.7
Mutation rate 0.005
Optimisation termination criteria Maximum evolution number
Local parameter 0.5
Local parameter 0.5
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Chapter 4: Development of Stress Minimised Railhead (SMRH) 85
a) Optimal result from hybrid GA
In the optimisation procedure, two wheel loads are selected for the ease of comparison
with simple GA in Section 4.4, namely =130KN (loaded wagon wheel) and 0.2 =26KN
(unloaded wagon wheel). From the first generation until the evolution terminates, the
optimisation algorithm leads to the minimisation of the maximum von Mises stress
by modifying the two design parameters and . The final optimal maximum von Mises
stress and the optimal shape for the SMRH using the hybrid GA are presented in Table 4-6
and Table 4-7 respectively.
As presented in Table 4-6, compared to the simple GA, the final optimal von Mises stress
are slightly reduced by less than 2% for both of the loaded wagon wheel and the
unloaded wagon wheel. Similarly, the optimal design parameters (Table 4-7) also indicate
that the hybrid GA yields a similar global solution as the simple GA does. The final
optimal design parameters at load is =40.03mm and =1.48mm that are less than 0.5%
difference compared to that of the simple GA; whilst in load 0.2 , the optimal design
parameters are =38.31mm and =1.44mm with less than 1% difference, compared to the
simple GA. Based on the optimal stress value, although there is no improvement in terms
of the optimal design parameters, it reconfirms the effectiveness of the proposed
optimisation model, ensuring the capability of searching global optimum.
Table 4-6: Optimal stress from hybrid GA
Wheel Load
Optimal von Mises stress
(MPa) % difference
Simple GA Hybrid GA
Loaded wheel 923.8 921.3 0.27%
Unloaded wheel
0.2 560.6 558.4 0.39%
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86 Chapter 4: Development of Stress Minimised Railhead (SMRH)
Table 4-7: Optimal design parameters from hybrid GA
Wheel Load
Optimal design parameters
Simple GA Hybrid GA
(mm) (mm) (mm) (mm)
Loaded wheel 40.05 1.47 40.03 1.48
Unloaded wheel 0.2 38.05 1.44 38.31 1.44
% Difference 5.0% 2.0% 4.3% 2.7%
b) Convergence performance of hybrid GA
In the optimisation procedure using the hybrid GA, the optimisation evolution is also
limited to a maximum of 20 generation. The progressive evolution of the optimal stress
with respective to each generation is examined and compared with the simple GA in this
section.
Figure 4-23 shows the evolution process of the optimal von Mises stress under the
wheel load . In the hybrid GA, the initial optimal stress value is around 1439MPa, and it
quickly drops to 1171MPa at the 3rd
generation. After that, it continues decreasing at
relatively slower rate and finally yields to around 921.32MPa in 8th generation, with the
difference less than 0.05% in the rest of the genetic evolution. Whilst in the simple GA, the
optimal stress has decreased to 924.82MPa in 15 generations with less than 0.006%
difference among the last 7 generations and finally reaches 923.78MPa. It shows that the
hybrid GA has much faster convergence rate and can obtain the global optimum in just 8
generations instead of the 15 required by the simple GA.
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Chapter 4: Development of Stress Minimised Railhead (SMRH) 87
Figure 4-23: Evolution of optimal solution at wheel load F
It should be also noted that throughout the whole evolution process, hybrid GA has
remained more robust to search for better solution from one generation to the next. This
can be observed from the gradient of the evolution from the above figures. In simple GA,
before the global optimal result is found, the evolution has had the tendency of getting
trapped at several consecutive generations. For example, from the 9th to the 10
th generation,
the optimal stress magnitude is in plateau; such phenomenon is not observed in the
proposed hybrid GA.
This interesting observation suggests that the local optimiser in the current hybrid GA
affects the evolution process in a self-adaptive manner especially in the later stage of the
genetic evolution. In other words, the conventional genetic operations based on the
stochastic model have a larger possibility to generate the individuals better than the local
optimiser does. As a result, the conventional genetic operators have great dominance in the
early stage of the genetic evolution. This can be seen that in the first four generations, both
of the simple GA and the hybrid GA can efficiently search for better solution, leading to
apparent reduction on the maximum stress level. However, in the subsequent generations,
the local optimiser has played a more dominant role. This self-adaptive feature of local
optimiser was very beneficial to the better solution searching. Difference in the
convergence rate can be observed between the hybrid GA and the simple GA. The larger
800
900
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1100
1200
1300
1400
1500
1600
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optim
al v
on M
ises
str
ess
(MP
a)
Generation
Hybrid GA
Simple GA
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88 Chapter 4: Development of Stress Minimised Railhead (SMRH)
effect of local optimiser could greatly accelerate the convergence of the evolution process.
This can be attributed to the fact that most of searching is to focus on finding a better
solution neighbour to the present best individual, until the global optimum is reached.
To further illustrate computational save by using hybrid GA for the stress minimisation at
railhead end, the time consumed by the simple GA and the hybrid GA within 20
generations is presented Table 4-8. It should be noted that both of these GA methods are
studied in a supercomputer of 4CPUs and 3GB memory. It has taken 15 generations for the
simple GA to obtain stable optimal solution, while the hybrid GA only needs 8
generations. For obtaining the similar optimal result, the number of FE analyses in simple
GA is 300; whilst that of the hybrid GA is 167, a reduction of 44.3%, which is significant.
When human monitoring of the genetic evolution occurs, the hybrid GA can provide better
efficiency, with the potential time saving for the practical optimal design.
Table 4-8: Comparison of converging runs from simple GA and hybrid GA
No. of runs
Difference (%) Stabilised generation
Simple GA Hybrid GA Simple GA Hybrid GA
Loaded wheel F 300 167 44.3% 15 8
c) Effect of the control Parameters and
It is very interesting to investigate the effect of the local optimiser and on the
evolutionary process in the shape optimisation. For this purpose, different combination of
these two local parameters was studied for the wheel load . Results are shown in Figure
4-24 and Figure 4-25 respectively. The following features can be observed:
For the same genetic operators, the hybrid GA for all combinations of and always
has exhibited faster convergence compared to the simple GA.
Different combinations of and lead to different convergence performance. It can
be seen that too small or too high values for and (e.g. =0.1 or 0.9 =0.5 and
=0.5, =0.1 or 0.9) generally have slower search speed compared to other
combinations. The optimal result is generally obtained in around 12th
generation with
89
Chapter 4: Development of Stress Minimised Railhead (SMRH) 89
small values of and ; whilst the other combinations provide the same result much
faster in the 8th or 9
th generation. Because the objective evaluation is using the FE
analysis. Such different can result in reduction of FEA runs and converging time.
Figure 4-24: Effect of local parameter on the genetic evolution ( =0.5)
Figure 4-25: Effect of local parameter on the genetic evolution ( =0.5)
800
900
1000
1100
1200
1300
1400
1500
1600
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.1
0.3
0.5
0.7
0.9
α=0.5
β:
Generation
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al vo
n M
ises
stre
ss (
MP
a)
800
900
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1300
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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0.7
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β=0.5
α:
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Opti
mal von M
ises
stre
ss (
MP
a)
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90 Chapter 4: Development of Stress Minimised Railhead (SMRH)
4.6 SUMMARY
In this chapter, a simulation based optimisation model is developed and successfully
applied for the development of the SMRH subjected to wheel loads. Three optimisation
methods, namely grid search method, genetic algorithm and hybrid genetic algorithm are
applied for this optimisation search combined with parametric finite element evaluation of
the objective functions. Relative merits of these three methods in respective of the optimal
results obtained and their rate of convergence to the optimal solutions are discussed and
their suitability for rail end stress minimisation problem is confirmed. The following
conclusions are drawn:
Simple GA method provides comparable results to the GSM and is marginally
cheaper computationally to GSM for the problems considered in this research.
The coupled simple GA – parametric FE method converges to the optimal solution
within less than 15 generations. The coupled hybrid GA – parametric FE method
converges within 8 generations.
The SMRH eliminates the contact pressure and the railhead stress singularities that
are problematic for the SCRH in the CIRJ designs. The rail edge effect resulted
from the gap at the unsupported rail end is proved to be less pronounced with the
SMRH optimal shape, providing the contact pressure and stress concentration
shifted away from the railhead edge, which can potentially make the IRJ similar to
the CWR.
The SMRH is insensitive to wheel positions. The effectiveness of the stress
reduction as the wheel extends beyond rail end (x/a=-0.5 and -1.5) is consistent
with the wheel location over the rail edge (x/a=0).
Because the evolutionary process in the simple GA is time consuming, the hybridisation of
GA with heuristic patter move local search method is applied to solve the problem more
efficiently. The hybrid GA is proved to be more efficient than the simple GA. In many
engineering optimisation problems that is associated with the computationally expensive
analysis and objective evolution, such higher rate of convergence performance could, to
great extent, benefit the industry.
It appears encouraging to apply the SMRH optimal shape closer to the unsupported rail
ends of IRJ. The results can be adapted to other rail joints and similar engineering
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Chapter 4: Development of Stress Minimised Railhead (SMRH) 91
structures. The sharp discontinuity lead loss of local structural stiffness is, generally, the
source of significant problem in various engineering designs. By reducing the magnitude
of the stresses and relocating the maximum stresses within the railhead using the SMRH
shape, the life of engineering joints where gaps are unavoidable can be potentially
improved.
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 93
Chapter 5: Experimental Validation of the
Stress Minimised Railhead (SMRH)
5.1 INTRODUCTION
To validate and examine the performance of the Stress Minimised Railhead (SMRH)
developed in Chapter 4, laboratory tests on rail specimens were conducted. For this
purpose, a full scale wheel rail contact load rig at the Centre for Railway Engineering
(CRE), Rockhampton, (developed as part of the Cooperative Research Centre (CRC)
research project of which this PhD program belongs to), was utilised. The experimental
data were used to understand the effect of the SMRH to the wheel contact. This chapter
describes the preparation of the rail specimens, the test procedure and the methods of strain
measurement. Comparative analysis of the experimental data and the finite element results
is presented in Chapter 6.
5.2 PREPARATION OF TEST SPECIMENS FOR STRAIN MEASUREMENT
5.2.1 MANUFACTURING OF TEST SPECIMENS
Four rail specimens of 400mm long were prepared using AS60kg/m rail (full details shown
in Figure 2-2 in Chapter 2). The railhead of the specimens was made from either the SCRH
or the SMRH; two specimens for each railhead shape were included.
To provide optimal arc surface in the SMRH specimens, a benchmark stencil was profiled
with the optimal arc defined by the two design parameters and as shown in Figure 5-1.
For practical convenience, the design parameters were set as =40mm and =1.5mm. The
railhead close to the rail end was carefully ground off into the optimal arc shape. Figure
5-1 shows the stencil and the rail end with the optimal shape.
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94 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
Figure 5-1: Manufacture of optimal arc shape in SMRH
In Chapter 4, the rail bottom was considered fully fixed in the parametric FE modelling, as
the attention was the localised railhead stress. It was, therefore, required to create the same
fixed boundary condition of the test specimens.
This was achieved by embedding the rail foot into a concrete footing. The concrete footing
supported rail specimens resembled the EIRJ discussed in Chapter 3. However, there was
no attention of testing EIRJ experimentally. The concrete footing is only provided to
simulate fixed boundary conditions used in Chapter 4 for SMRH optimisation.
The concrete footing was manufactured as follows:
1) A reinforced cage consisting of steel bars (12mm diameter) was manufactured and
welded with the rail bottom surface and the base plate (see Figure 5-2);
2) The rail specimen together with base plates and reinforced cage were placed into a
wooden formwork. The formwork was firmly clamped down with the base plate to
minimise the misalignment during vibration of the concreting (see Figure 5-3(a)).
3) Concrete was poured into the formwork, vibrated, covered using a polythene and left
for air curing (see Figure 5-3(b)). The fabricated rail specimens are shown in Figure
5-3(c).
Stencil with
optimal profile
l
Rail End
d
95
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 95
Figure 5-2: Reinforced cage welded with rail bottom and base plate
(a) Clamping formwork with base plate (b) Pouring & compacting of concrete
(c) Fabricated rail specimens
Figure 5-3: Setup for concreting and the final product
Rail sample
400mm
Reinforced
cage
Base plate
Formwork Clamps
Vibrator
SCRH
SMRH
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96 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
5.2.2 STRATEGY FOR MEASURING RAIL END STRAIN
The accuracy of the rail end strain measurement is important to understand the difference
in the strain distribution at the rail end in the SMRH and the SCRH. Strain gauge is most
widely used for this purpose; unfortunately, measuring the localised stress
concentration/strain magnitude in the top of the railhead poses a challenge in locating the
strain gauges at the most desirable point due to finite range of these gauges. Furthermore,
depending on the glue, these gauges often experience early delamination because of the
wheel contact close to the localised railhead zone. In addition, the strain gauges can
normally measure strain in a single direction limited to the point where it is attached. Since
the localised railhead zone suffers from multiaxial strain field, in this experimental study,
an emerging state-of-the-art Digital Image Correlation (DIC) technique (known as the
Particle Image Velocimetry, or, PIC) was used. DIC has the following advantages:
Being a non-contacting method, there is less intrusion into or on the surface of the
specimen;
Digital image can be used over a area unlike the strain gauges that is limited to its
point of attachment;
Can measure relatively much larger strain magnitude and eliminate the problems of
delamination suffered by the strain gauge.
In this research, a specified DIC module known as the Particle Image Velocity (PIV),
originally developed in the field of experimental fluid mechanics (Adrian, 1991), was used
for the localised strain measurement. PIV was originally implemented using double-flash
photography of a seeded flow. The resulting photographs contain image pairs of each seed
particle. For PIV analysis, the photograph is divided into a grid of test patches. The
displacement vector of each patch during the interval between the images is found by
locating the peak of the autocorrelation function of each patch. The peak in the
autocorrelation function indicates that both images of each seeding particle captured during
the flashes are overlying each other. The correlation offset is equal to the displacement
vector. Later, White (2002) developed a MATLAB module of the PIV for geotechnical
application. The development and performance of the software are described in detail by
White (2002) and Take (2002). Concise details are presented in White et al. (2001a,
2001b). In the experimental study, the Matlab module was provided as in-kind for the
Cooperative Research Project, of which this PhD thesis is part for the railhead strain
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Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 97
determination. The application of PIV to the railhead strain measurement is new and is
attempted in a companion PhD thesis (Bandula-Heva, 2012).
a) Principle of image analysis for strain tensor
The principle of PIV for measuring displacement vector is illustrated in Figure 5-4. PIV
operates by tracking the texture and colour (i.e. the spatial variation of brightness) through
a series of images. The initial image is divided into a mesh of square test patches. Each test
patch consists of an L×L matrix of image pixels. Consider a single test patch, whose
central point is located at coordinates (u1, v1) in Image 1 of Figure 5-4. To find the
displacement vector of this patch in a subsequent Image 2, a search patch is extracted from
the Image 2. The boundary of the search patch extends beyond the test patch to ensure that
the central point of the displaced test patch is still included into the search patch. The
correlation between the test patch from Image 1 (time= t1) and the search patch from Image
2 (time= t2) is evaluated. The location at which the correlation is the best is set as the
displaced coordinates (u2, v2) of the central point of the test patch in time t2. The location
of the correlation peak is established to sub-pixel precision by fitting a bicubic
interpolation around the highest integer peak (White, 2002).
Figure 5-4: Principles of PIV analysis
v
u
Initial position of
test patch (u1, v1) Search patch in
Image 2
Image 1 (t=t1) Image 2 (t=t2)
Test patch from
Image 1 (L×L pixels)
Search patch in
Image 2
Best correlation
Final position of
test patch (u2, v2)
Degree
of match
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98 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
This operation is repeated for the entire mesh of patches within the image, and then
repeated for each image within the series, to produce complete coordinates of each test
patch in the series of images. The coordinates were used then in the determination of the
strain tensors, namely lateral strain , vertical strain and in plane shear strain .
To calculate the lateral strain at a point of interest, two horizontally located test
patches next to the point were selected. The coordinates (position) of the two test patches
in the initial image (Image 1) and the subsequent image (Image 2) are shown in Figure
5-5(a) and Figure 5-5(b) respectively. The lateral strain of the point between the
patches is determined by:
(a) Image 1 (b) Image 2
Figure 5-5: Calculation of lateral strain using two patches
To calculation the vertical strain , the two vertically located test patches next to the
measuring point were selected as shown in Figure 5-6. The vertical coordinates of the two
patches in Image 1 and Image 2 were used to determine the vertical strain
Patch 1(u1,v1)
Patch 2(u2,v2)
Image 1
Measuring
point
v
u
Patch 1(u’1,v’1)
Patch 2(u’2,v’2)
Image 2
Measuring
point
v
u
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Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 99
(a) Image 1 (b) Image 2
Figure 5-6: Calculation of vertical strain using two patches in (a) Image 1 (b) Image 2
As the in plane shear strain is concerned, four test patches neighbouring the measuring
point were required as shown in Figure 5-7(a). The four displaced patches in Image 2 and
their coordinates are shown in Figure 5-7(b). The shear strain is the summation of the
angle α and angle β as presented in Eq. (5-3):
(a) Image 1 (b) Image 2
Figure 5-7: Calculation of shear strain using two patches in (a) Image 1 (b) Image 2
Patch 1(u1,v1)
Patch 2(u2,v2)
Image 1
Measuring
point
v
u
Patch 1(u’1,v’1)
Patch 2(u’2,v’2)
Image 2
Measuring
point
v
u
Patch 1(u1,v1)
Patch 2(u2,v2)
Image 1
Measuring
point
v
u
Patch 3(u3,v3)
Patch 4(u3,v3)
Measuring
point
Patch 2(u’2,v’2)
Patch 1(u’1,v’1)
Patch 3(u’3,v’3)
Patch 4(u’4,v’4)
β
α
Image 2
v
u
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100 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
In the PIV method, displacement is measured in pixels from images, which is used later in
the strain calculation; therefore, the accuracy of the strain measurements is closely
associated with the resolution and clarity of the digital images (pixel density). The higher
the resolution of the digital images, the better the accuracy of the strains. Therefore,
selection of camera with high resolution is important.
In this research, Canon EOD 7D digital SLR was selected for this task. Since the
stress/strain concentration at the railhead area is the focus, this localised railhead zone
should be zoomed into the digital image. This was achieved using K2/SC long-distance
microscope attached to the Canon EOD 7D camera. The assembly of the camera body and
the microscope is shown in Figure 5-8.
Figure 5-8: Camera body and long-distance microscope
b) Strain-gauged rail end
Because PIV is new for the railhead strain measurement, to gain confidence with PIV,
strain gauges were used. An SCRH specimen and an SMRH specimen were provided with
strain gauges.
Positioning of the strain gauge is critical to the accuracy of the strain data. To acquire
strain responses close to the railhead, which is of interest in this study, four linear single
strain gauges (Gauge-1 to Gauge-4) were attached as shown in Figure 5-9. The central line
of the top gauge (Gauge-1) is 3mm away from the railhead top surface, the distance
between the strain gauge centres were 5mm. To withstand the vibration during the wheel
K2/SC long-distance
microscope
Canon EOD 7D
101
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 101
loading process, Vishay Micro-measurement CEA gauges with a fully encapsulated grid
and exposed copper coated integral solder tabs were selected.
(a) Sketch of strain gauge position (b) Enlarged image of strain gauge
Figure 5-9: Location of four strain gauges at railhead end
In addition, another four strain gauges (Gauge 5 to Gauge 8) were applied from the rail
web to the rail foot as a means of obtaining strain distribution along the whole height of the
rail at the free end. Figure 5-10 shows the location of the total eight strain gauges at rail
end. The response of the vertical strain was obtained from these eight gauges.
(a) Sketch of strain gauge position (b) Strain gauges installed at rail end
Figure 5-10: Location of strain gauges along the depth of rail end
Gauge -1
Gauge -2
Gauge -3
Gauge -4
3mm from the top edge
to centre of Gauge-1
5mm between
gauge centers
Symmetric line
of rail end
z
yx
Gauge
1, 2, 3, 4
Gauge -5
Gauge -6
Gauge -7
Gauge -8
130mm
110mm
60mm
20mm
z
yx
102
102 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
5.3 LOADING PROGRAM IN EXPERIMENTAL STUDY
In this section, details of the loading procedure for the laboratory test are presented. The
loading procedure contains two major programs, namely static wheel loading at different
locations and repetitive rolling of wheel crossing the unsupported rail end. Both of the
loading programs were applied to each of the SCRH and the SMRH. Strain data from
strain gauges and PIV photographs were collected. The performance of the two shapes is
determined and presented in Chapter 6.
a) Static loading program
Loaded wheel was positioned at four locations (x=5mm, 3mm, 0mm and -3mm) along the
length of the railhead as shown in Figure 5-11. Each of the four positions was subjected to
six load magnitudes (F=30KN, 50KN, 100KN, 130KN, 150KN and 200KN). The static
loading program was implemented through the following steps:
1) Position the vertical axis of the wheel at the first loading position (x=5mm).
2) Apply the first load magnitude (F=30KN) and retain it for 10s, allowing for strain
recording and PIV photographing.
3) Increase the wheel load to the next predefined load magnitude.
4) Repeat Step 2 and 3 until the load magnitude reaches 200kN.
5) Move the wheel vertical axis to the next loading position and repeat step 1, 2, 3 and 4.
Figure 5-11: Static wheel loading positions
x
z
o
5mm 3mm 0mm -3mm
Load positions
Railhead top surface
Railhead
Unsupported
rail end
103
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 103
b) Repetitive rolling of wheel
In this loading program, the strain variations at the rail end subjected to repetitive rolling of
loaded wheel were recorded. Six load magnitudes (F=30KN, 50KN, 100KN, 130KN,
150KN, 200KN) were considered; and the loaded wheel was rolled repetitively 100 times.
The following steps were used to implement this loading program:
1) Position the vertical axis of the wheel at the start point A as shown in Figure 5-12. The
coordinate of the vertical wheel axis is x=20mm.
2) Increase the wheel load to the first load magnitude (F=30KN).
3) Roll the wheel horizontally (x axis) to the end point B.
4) Reduced the wheel load to F=10KN, then roll the wheel back to the start point A.
5) Repeat step 1, 2, 3 and 4 for another 99 cycles.
6) Apply the other load magnitudes respectively by following steps 1, 2, 3, 4 and 5.
Figure 5-12: Repetitive rolling of loaded and unloaded wheel
5.4 EXPERIMENTAL TEST SETUP
The overall test setup consists of three systems: 1) Loading rig system; 2) Data recording
system; and 3) Synchronised control system.
x
z
o
Loaded (F=30kN, 50kN,…, 200kN)
Unloaded (F=10kN)
Start point A
x=20mm
End point B
x=-3mm
Railhead
Unsupported
rail end
Railhead top surface
104
104 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
a) Loading rig system
In this experimental test, a full scale wheel rail contact load rig developed at the Centre for
Railway Engineering (CRE), Rockhampton, as part of the cooperative research centre
(CRC) project R3.100, of which this PhD thesis is part of, was utilised. The pre-determined
load programs were applied through the rig, which is equipped with two 500kN servo-
hydraulic actuators that are vertically and horizontally positioned respectively as shown in
Figure 5-13(a). The two actuators are connected to a cylindrical wheel (460mm in radius
milled from a real new wheel). In this manner, the pre-determined load magnitudes as well
as the horizontal wheel movement could be supplied by the vertical actuator and the
horizontal actuator respectively. A closer view of wheel connection to actuators is shown
in Figure 5-13(b). The two actuators are mounted to the supporting frame with pin joints at
one end, and the other end connected via load cells to yokes. The modified cylindrical
wheel with a hard rolling contact surface is mounted on a shaft with bearings and
connected to the yokes.
(a) General view of load rig
Vertical
actuator
Wheel
Rail
specime
n
Base
frame
Side
frame
Horizontal
actuator
105
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 105
(b) Closer view of loading wheel
Figure 5-13: Design of load rig
To place the test specimens onto the load rig, the concrete base of the rail specimen was
firmly bolted onto the base frame of the loading rig as shown in Figure 5-14. The
installation was carefully conducted with the assistant from CRE lab technicians, so that
the symmetric plane of the rail was in line with the symmetric axis of the vertical actuator.
This was to ensure that the load transferred from the vertical actuator remained
symmetrically onto the railhead top surface.
Figure 5-14: Installation of rail specimen onto the load rig
Load
cell
Vertical
actuator
Vertical
yoke
Wheel
Load
cell
Horizontal
actuator
Horizontal
yoke
Concrete
footing
Bolt
Clamp
Base
plate
106
106 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
The operation of the vertical and the horizontal actuators in the static loading program and
the repetitive rolling of wheel program were controlled by a computer control system. In
the static loading program, for example, a typical trajectory of for the load of the vertical
actuator and the position (x coordinate) of the horizontal actuator is shown in Figure 5-15.
The action of the actuators is illustrated as follows:
1) Prior to the loading application, the wheel was initially positioned at 20mm away
from the rail end (x=20mm). The wheel was then moved to the first load position
x=5mm (point A), while remaining load at 10kN.
2) The load was increased from 10kN to 130kN (point B) and kept stationary. The
load was maintained for 10s up to point C for getting accurate strain gauge data and
PIV photographs.
3) The load magnitude was reduced back to 10KN (point D).
4) The wheel was moved to the next three load positions (x=3mm, 0mm and -3mm)
and repeated the above three steps.
5) Finally the wheel was moved back to the initial position (x=20mm) to complete a
static load magnitude. Similar action was repeated to complete the whole static
loading program.
Figure 5-15: Trajectories of vertical and horizontal actuators at static load 130kN
In the repetitive rolling of wheel program, a typical trajectory of the vertical and horizontal
actuators for one passage of the moving load of 130kN is shown in Figure 5-16. The action
of the actuators is illustrated as follows:
-5
0
5
10
15
20
25
0
30
60
90
120
150
0 10 20 30 40 50 60 70 80
Wh
eel Ho
rizon
tal p
ositio
n(m
m)
Wh
eel
Ver
tica
l lo
ad
(K
N)
Time (s)
Load Horizontal position
A
B C
D
107
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 107
1) Prior to each moving loading cycle, the wheel was initially positioned at 20mm
away from the rail end (x=20mm), and the load magnitude was 10kN (point A).
2) The load magnitude increased to 130kN (point B), while the horizontal actuator
remained stationary (x=20mm).
3) The load magnitude was maintained at 130kN between point B and point C, whilst
the horizontal actuator started acting and the wheel position was translated from
x=20mm to x=-3mm.
4) The horizontal actuator stayed at x=-3mm, and the load magnitude decreased to
10kN (point D).
5) The horizontal actuator returned back to x=20mm (point E).
Figure 5-16: Typical one time moving load procedure
b) Data recording system
Two types of data were recorded using two separate PC based data acquisition systems and
subsequently synchronised. The data gathered were: 1) PIV photographs; and 2) Load cell
and strain gauge signatures. The PIV photographs were taken during the two pre-
determined loading programs as explained below:
Prior to applying loading, one photo was taken for the fresh railhead end; this
particular photo was set as the initial image during the PIV analysis. The
A
B C
D
E
108
108 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
subsequent images during the wheel load application along with this initial image
would contribute to the analysis of railhead end strains.
In the static loading program, as the wheel was moved to each load position, a pre-
determined load magnitude was applied and retained for 10s. During the time, five
photos were taken. This was conducted for 24 times (6 load magnitudes×4 load
positions), and 120 photos (5 photos×24 times) were collected for PIV analysis.
In the repetitive rolling wheel load program, each load magnitude repeated for 100
times. PIV photos taken in the selected load cycles are summarised in Table 5-1. In
each selected photographing cycle, a set of photos was taken at several predefined
wheel positions. The selected positions are presented in Table 5-2. It took 17.5s to
complete one photographing cycle, while each non-photographing cycle took 7s.
Table 5-1: Selected PIV photographing cycles
Load cycles of
each load magnitude
Selected
PIV photo cycles
100 1, 10, 20, 30, 40, 50, 60, 70, 80, 90,100
Table 5-2: Selected wheel positions at moving load cycle
Positions for photographing as wheel moving forward (x coordinates mm)
20 15 10 5 3 0 -3
Positions for photographing as wheel moving forward (x coordinates mm)
-3 20
To acquire good quality of photos for PIV analysis, it was required to carefully install the
camera. Any minor movement of the camera during the loading procedure could affect the
accuracy of the PIV strain measurement. As shown in Figure 5-17, to minimise the
movement of the camera during the operation of the loading rig, the camera together with
the K2/SC long-distance microscope was firmly mounted onto an adjustable bracket,
which was then fixed to a steel frame connected directly to the strong floor of the lab. The
adjustable bracket was used to adjust the position of the camera to ensure that the
interested zone at the railhead end was appropriately captured.
109
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 109
Figure 5-17: Camera installation for PIV photographing
The clarity of the image required proper camera focusing, illumination and rail end surface
treatment. To acquire clear image, the camera was controlled through software installed in
a computer. By adjusting the focusing screw of the K2/SC lens, the image was previewed
from the monitor to ensure its clarity. Two 1000 watt narrow beam lights were used to
illuminate the rail end surface to obtain sufficient brightness. Because the PIV analysis
operates by tracking the texture and the color of the image, for the accuracy and efficiency
of the PIV analysis, the localised railhead end zone was sprayed using red and yellow paint
for the purpose of increasing the color texture as shown in Figure 5-18.
In the current lab test, the resolution of PIV image was set as 5184×3456 (18 Mega Pixels).
Computer control of the opening of the shutter of the camera helped preventing any need
for human touch and subsequent jerks. A scaled ruler (Figure 5-18) was attached at the
bottom the image frame, the distance from the ruler to the railhead top was set as 30mm.
The scaled ruler was used later as the reference for generating the test patches in PIV
analysis.
Illumination
Steel frame
Fixed into
ground
Camera
Adjustable
bracket
110
110 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
Figure 5-18: Typical image at railhead end surface
One SCRH specimen and one SMRH specimen were strain gauged. The strain gauge
recording for these two specimens was implemented by four 14-channel National
Instruments DAQ cards as shown in Figure 5-19(a). In this lab test, all of eight strain
gauges at the rail end surface were connected to the DAQ card for data collection as shown
in Figure 5-19(b). Prior to applying the load programs and starting the PIV photographing,
the strain gauges have been triggered and recording the strain data.
(a) DAQ (b) Strain gauged specimen with cables
Figure 5-19: Strain gauge recording
Scaled ruler
Red and yellow
colour spot using
painting spray
30mm from
top railhead
30mm
Test
specimen
Eight strain
gauges plugs
111
Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH) 111
c) Synchronised control of lab test
The overall scheme of operating the lab test is shown in Figure 5-20. The actuator
controller, camera controller and DAQ system were operated using Labview software
installed in a lab computer. The synchronisation of the actuator controller and camera
controller using Ethernet connection allowed taking images as per the pre-defined loading
programs. During the test, the action of loading rig, the camera and the DAQ system could
be monitored through the lab computer.
Figure 5-20: Flowchart of the overall control during the lab test
A test script was developed and uploaded to the lab computer. This test script synchronised
the action of the camera and the loading rig in the same time frame. An example of the
control program is presented in Table 5-3. The first column represents the horizontal
position of the wheel; and the second column represents the load magnitude. When the
load was increased to the pre-defined magnitude, the wheel was moved along the railhead
top surface. At the pre-defined positions for photographing, a ―T‖ was inserted in front of
the position value to trigger the camera. The complete control program was developed
according to the loading programs as described in Section 5.3.
Vertical actuator
Horizontalactuator
Wheel
Rail specimenz
y x
Actuator controller
Camera controller
DAQsystem
Load magnitude
Horizontal position
Strain gauge recording
Camera
Trigger
Images
Control program
Lab computer
112
112 Chapter 5: Experimental Validation of the Stress Minimised Railhead (SMRH)
Table 5-3: Example of control program
Horizontal
displacement (mm)
Load
magnitude (kN)
T20 130
19.5 130
… …
T15 130
14.5 130
… …
T10 130
… …
5.5 SUMMARY
In this chapter, a detailed laboratory study of rail specimens is reported, which has
provided a platform of examining the performance of the Stress Minimised Railhead
(SMRH) obtained through the optimisation methods presented in Chapter 4. This test was
carried out using a full scale wheel-rail contact load rig. To acquire the localised strain
response subjected to wheel loadings, an innovative non-contact strain measuring
technique, PIV, was used. This chapter has described the preparation of the rail specimens,
the loading programs, the principle of the strain measurement at the rail end surface and
the test control respectively. The collected data from the tests are used to examine the
effect of different railhead shapes and the result is reported in Chapter 6.
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 113
Chapter 6: Performance of the Stress
Minimised Railhead (SMRH)
6.1 INTRODUCTION
This chapter reports the data analysis to investigate the effect of the load-carrying
characteristics of the stress minimised railhead (SMRH) and the sharp cornered railhead
(SCRH). Analysis of the vertical strain collected from the eight strain gauges along the
rail end depth is introduced in Section 6.2. In Section 6.3, feasibility of PIV for the strain
measurement in critical zone (localised railhead end) is validated through the comparison
with the strain gauge data. The comparative study of the numerical result and the PIV data
is presented in Section 6.4. The strain components: vertical strain , lateral strain and
the in plane shear strain due to the static wheel load were selected for the comparison.
The comparison has generally been regarded as satisfactory. Conclusions obtained from
the analysis are presented in Section 6.5.
6.2 STRAIN GAUGE DATA
In this section, the analysis of the typical strain gauge data is reported based on the two
load programs: 1) static wheel load; 2) repetitive rolling wheel load. The vertical strain
along the rail end depth is reported. In the following figures, tensile strain is considered
positive ―+‖, whilst the compressive strain is considered negative ―-‖.
6.2.1 DATA FROM STATIC WHEEL LOAD
a) Gauge-1
The response of the vertical strain in the top strain gauge (Gauge-1) is presented in
Figure 6-1. Each data line represents a load magnitude, and four markers in each line stand
for the four pre-determined loading positions (x=5mm, 3mm, 0mm, and -3mm) in the static
wheel load program.
114
114 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(a) SCRH (b) SMRH
Figure 6-1: Gauge-1 data
The characteristics of the top Gauge-1 can be summaries as follows:
1) The vertical strain in the SCRH was compressive; however, the SMRH was under
tension at the Gauage-1 location. With the wheel position changed from x=5mm to x=-
3mm, the tensile strain increased consistently for all wheel load magnitudes.
2) Both of the SCRH and the SMRH exhibit increase in vertical strain magnitude with the
increase in load magnitude.
3) For all wheel loads and loading positions, the SMRH exhibit much lower vertical strain
than the SCRH. The maximum difference is found at the load =200kN and load
position =-3mm, with the compressive strain of 13263s in the SCRH and the tensile
strain of 527s in the SMRH, with almost 96% reduction in absolute magnitude. The
strain magnitude in the SMRH is far below the yield limit of the railhead steel.
b) Gauge-2
The response of the vertical strain in Gauge-2 is presented in Figure 6-2. In the SCRH,
the vertical strain remained compressive at all wheel loads and positions. As the wheel
position changed from x=5mm to x=-3mm, the magnitude increased at a relatively lower
rate, compared to Gauge-1 (Figure 6-1(a)). In the SMRH, however, the vertical tensile
strain decreased at Gauge-2 location, as the wheel position moved from x=5mm to x=-
3mm. Moreover, as the wheel moved to -3mm at load 150kN or 200kN, the state of the
vertical strain at Gauge-2 shifted from tension to compression. Similar to Gauge-1, the
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm) )
Original shape
Load 30KN
Load 50KN
Load 100KN
Load 130KN
Load 150KN
Load 200KN0
100
200
300
400
500
600
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm) )
Optimal shapeLoad 30KN
Load 50KN
Load 100KN
Load 130KN
Load 150KN
Load 200KN
115
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 115
absolute magnitude of the vertical strain in the SMRH was much lower than that in the
SCRH and remained elastic (approximately 450 microstrain << 4300 microstrain (yield)).
(a) SCRH (b) SMRH
Figure 6-2: Gauge-2 data
c) Gauge-3 & 4
The response of the vertical strain from Gauge-3 and Gauge-4 is presented in Figure
6-3 and Figure 6-4 respectively. Generally, the trend of vertical strain variation was the
same for the SCRH and the SMRH. With the wheel position moved from +5mm to -3mm,
the vertical strain remained compressive state and was increasing. In addition, the
SMRH also exhibited lower compressive strain magnitude compared to the SCRH for all
load magnitudes. However, its reduction is much gentler than Gauge-1 and Gauge-2.
(a) SCRH (b) SMRH
Figure 6-3: Gauge-3 data
-12000
-10000
-8000
-6000
-4000
-2000
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN
Load 50KN
Load 100KN
Load 130KN
Load 150KN
Load 200KN-200
-100
0
100
200
300
400
500
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN
Load 50KN
Load 100KN
Load 130KN
Load 150KN
Load 200KN
-5000
-4000
-3000
-2000
-1000
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN
Load 50KN
Load 100KN
Load 130KN
Load 150KN
Load 200KN
116
116 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(a) SCRH (b) SMRH
Figure 6-4: Gauge-4 data
d) Gauge-5 to 8
The response of the vertical strain from Gauge 5 to Gauge-8 is presented in Appendix B.
There is no significant difference between the original and the stress minimised railhead
end in terms of the strain magnitude and its state (tension/compression). The strain level
remained elastic for all wheel load magnitudes. As the wheel moved from +5mm to -3mm,
the strain had slightly increased.
Figure 6-5: Distribution of vertical strain along depth of rail end
-3000
-2500
-2000
-1500
-1000
-500
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN-1400
-1200
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
0
20
40
60
80
100
120
140
160
-10000-8000-6000-4000-200002000
Dep
th a
lon
g
rail e
nd
sy
mm
etri
c ax
is
Vertical strain εzz (microstrain)
SCRH SMRH
Symmetric axis of rail end
(z axis)y
z
―Critical ― zone
117
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 117
Figure 6-5 presents the variation of vertical strain along the whole rail end depth, as the
wheel axis is positioned at the rail end (x=0mm) with the wheel load 130kN. It
demonstrates that the vertical strain magnitude between the SCRH and the SMRH is
similar from Gauge-5 to 8. However, the top four gauges (Gauge-1 to Gauge-4) at the
railhead end exhibited significantly larger strain. This justifies the attention provided in the
FE modeling in Chapter 4 to the railhead top. This localised railhead end is defined as
―critical‖ zone in this thesis.
6.2.2 TYPICAL DATA FROM REPETITIVE ROLLING WHEEL LOAD
PROGRAM
In this section, the typical strain gauges data for the repetitive rolling wheel load is
reported. The scanning frequency of DAQ system for strain gauge recording was kept as
100 data points per second (100Hz) and the average test duration for each rail specimen
was around 3.5 hours, which corresponds to approximately 12.6×105 data points. The
vertical strain at the ―critical‖ zone (Gauge-1 to Guage-4) in both the SCRH and the
SMRH are presented in Figure 6-6. Generally, the strain gauge data can be divided into six
groups, standing for six load magnitudes. These groups can be identified easily from this
figure. With the increase in load magnitude, the recorded peak value of increased, and
this formed ―step‖ as the data points being recorded.
(a) SCRH
0 2 4 6 8 10 12 14 16
×105Data points
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
0
-15000
-12500
-10000
-7500
-5000
-2500
30KN
50KN
100KN
130KN
150KN200KN
118
118 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(b) SMRH
Figure 6-6: Strain gauge signature from Gauge-1 to Gauge-4
For the repetitive rolling wheel load, Figure 6-6 shows that the vertical strain at the
―critical‖ zone exhibited significant difference between the SCRH and the SMRH. The
recorded peak value of in the SMRH with the optimal arc shape is much lower than the
corresponding in the SCRH and most importantly remained well below the yield limit
of the head hardened railhead steel.
The vertical strain measured from Gauge-5 to Guage-8 is presented in Appendix C.
There was also no significant difference between the original shape and the stress
minimised shape for the value of . The strain level consistently remained elasticity for
all the load magnitudes. This observation is consistent in the static load program as
discussed in Section 6.2.1.
Based on the observation of the test data from the two load programs (the static wheel load
and repetitive rolling wheel load), it can be clearly observed that the ―critical‖ zone in the
SCRH is the major problematic zone, where strain is often beyond the material yield limit.
With the adoption of the optimal arc surface along the longitudinal profile without any
change to the profile of the railhead cross section, the ―critical‖ zone‘s current problems
are largely alleviated. Therefore, the railhead end in the SMRH will no longer suffer the
high yield strain concentration, leading to local damage.
0 2 4 6 8 10 12 14 16
×105Data points
-1500
-1000
-500
0
500
1000
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
30KN50KN
100KN
130KN
150KN
200KN
119
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 119
To better understand the characteristics of the strain at the local railhead end under the
repetitive rolling of the loaded wheel, a closer examination of the test data was carried out.
By enlarging a segment of the data points in Guage-1 of the SCRH, vertical strain
signature between the 21st and 40
th representing the rolling wheel loaded with 130kN is
shown in Figure 6-7. Because it took time for the PIV photographing cycles, these
photographing cycles contained more data points; hence they can easily be identified. It
can also be seen that one photographing cycle occurred after every nine non-photographing
cycles. Similar characteristics of data points for the SMRH were also observed.
Figure 6-7: Enlarged view of vertical strain history of Guage-1 at 130kN
By further enlarging into one of the load cycles, the characteristics of the strain signature
under the rolling wheel load can be examined. Figure 6-8(a) and (b) show the typical strain
signature of a photographing cycle (30th cycle at 130KN) in the original shape and the
stress minimised shape respectively. The strain signature can be divided into four segments
according to the moving load program:
In the first segment (Seg.1), the wheel is positioned at 20mm away from the rail end,
the load magnitude increased from 10kN to 130kN.
In the second segment (Seg.2), the loaded wheel commenced rolling from the start
point (x=20mm) to the end point (x=-3mm), the strain magnitude increased to a peak
0 3 6 9 12 15 18 21 24
×103Data points
-8000
-9000
-10000
-11000
-12000
Photographing 30th cycle
Non-photographing21-29 cycles
(Unloaded)
-7000
-6000
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
(Unloaded)
(Unloaded)
Photographing40th cycle
Non-photographing31-40 cycles
120
120 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
value of approximate 11,500s for the original shape and 450s for the stress
minimised shape.
In the third segment (Seg.3), as the load magnitude dropped back to 10kN, the strain
decreased to approximate 7300s for the original shape and 120s for the stress
minimised shape.
In the forth segment (Seg.4), as the wheel moved back to the start point (x=20mm), the
strain magnitude further reduced to approximate 6,600s in the original shape and 85s
in the stress minimised shape, and it completed one time rolling wheel load.
(a) SCRH
(b) SMRH
Figure 6-8: Typical strain signature in one time rolling wheel load at gauge-1
2117.51410.57.03.50
Time (s)
-12000
-11000
-10000
-9000
-8000
-7000
-6000
Vert
ical st
rain
zz
(mic
rost
rain
)
400
500
300
200
100
0
Vert
ical st
rain
εzz
(mic
rost
rain
)
2117.51410.57.03.50
Time (s)
Seg.1 Seg.2 Seg.3 Seg.4
Seg.1 Seg.2 Seg.3 Seg.4
121
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 121
6.3 FEASIBILITY OF PIV
Based on the observation from strain data, it can be seen that the ―critical‖ zone (localised
railhead end) is the problematic zone for the original sharp-cornered shape, where the
vertical strain exceeded the material yield limit. The SMRH significantly improved the
characteristics through reduction in the magnitude of the vertical strain at the ―critical‖
zone. To further understand the behaviour of arc shape in the SMRH under the wheel load,
it is necessary to acquire multiple axial strain information. Such information may be
possible through the use of strain gauge rosettes but still will be limited as strain gauge
rosette data is limited to the point of attachment. PIV on the other hand can provide
information covering the full range of the critical zone of the railhead end.
As mentioned in the Chapter 5, the application of PIV analysis for strain measuring at the
―critical‖ zone of the railhead end is relatively new, therefore, it is important and necessary
to examine strains determined carefully prior to applying to adopting for the performance
study of the various designs. For this purpose, PIV analysis was initially conducted to
compare with the strain gauges (Gauge-1 to Gauge-4). The comparison was studied for
both of static wheel load and repetitive rolling wheel load programs. The comparison has
generally been regarded quite satisfactory, thereby providing confidence in the strains
determined from PIV method especially at the ―critical‖ zone of the rail end.
6.3.1 STATIC LOAD EXPERIMENTS
Two vertical load magnitudes (30kN and 150kN) were selected for examining the
appropriateness of the strains measured using the PIV in the static load experiment. These
two loads approximately represent the unloaded wagon wheels and loaded wagon wheels
in the heavy haul railway lines in Australia respectively. The vertical strain of at the
locations of the four strain gauges (Gauge-1 to Gauge-4) was investigated using PIV. The
result presented in the body of the thesis contains only Gauge-1; other gauge data are
presented in Appendix D.
To obtain accurate strain value from the PIV procedure, it is critical that good quality of
test patches around the interested location is generated. For example, to measure the
vertical strain at the point where Gauge-1 (3mm below the top edge of the railhead) is
122
122 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
located, a group of test patches was generated as shown in Figure 6-9. It can be seen that
the measuring point Gauge-1 is located at the shared boundary of test patches 1 and 2.
These two test patches were used to calculate the vertical strain using the procedure
described in Chapter 5. It should be noted that to ensure the maximum accuracy, a number
of trials have been conducted for obtaining the most suitable and effective patch size L×L
set as 80×80 pixels.
Figure 6-9: Test patches generated surrounding the point of Gauge-1
In Figure 6-10 and Figure 6-11, the vertical strain obtained from the PIV and Gauge-1
for the SCRH and the SMRH is presented respectively. The horizontal axis represents the
static loading positions and the vertical axis represents the vertical strain .
Figure 6-10: Comparison of vertical strain at point of Gauge-1 in the SCRH
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Gauge-1 at load 30KN
Gauge-1 at load 150KN
PIV at load 30KN
PIV at load 150KN
Measuring
point
3mm
Measuring
point
Test
patch 1
Test
patch 2
123
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 123
Figure 6-11: Comparison of vertical strain at point of Gauge-1 in the SMRH
Figure 6-10 shows that the PIV measured agrees very well with the strain gauge
measured at central (Gauge-1) location for 30kN and 150kN. Both methods predicted
that the maximum compressive strain occurred when the wheel was located at 3mm
beyond the railhead end (x=-3), where the difference was the maximum, for instance, the
result of the strain gauge at static load 150kN was 11,716s (microstrain), while the PIV
determined strain was 11974s (microstrain), with the difference being 2.2% ((11,974-
11,716)/11,716). Overall, the difference at all the four loading positions of these two load
magnitudes was below 2.2%, which can be regarded as good quality PIV analysis.
Figure 6-11 shows that generally measured from the PIV and the strain gauge are in
good agreement. The SMRH exhibited tensile ; and its strain magnitude was much
lower than the one in the SCRH and well below elastic limit. However, the error in
percentage between the PIV and strain gauges was generally larger than the one in the
original shape for all the four load positions. For instance, the maximum difference was
60s (microstrain), about 12.7% ((470s -410s)/470s) for the 150kN load positioned at
x=-3mm. The high error is attributed to the low level of strains in the SMRH. The accuracy
of PIV in such low magnitude range was not as high as large strain zones in the SCRH;
however, PIV prediction can be considered reliable.
0
100
200
300
400
500
600
5 3 0 -3
Ver
tica
l str
ain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Gauge-1 at load 30KN
Gauge-1 at load 150KN
PIV at load 30KN
PIV at load 150KN
124
124 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
6.3.2 REPETITIVE ROLLING WHEEL LOAD
A repetitive rolling wheel during a photo cycle was selected (30th cycle at 130KN). A set
of nine photos was recorded at each of the photographing load cycles; each photo recorded
the image of the ―critical‖ zone at one of the pre-determined wheel positions as described
in Table 2 of Chapter 5. These photos were analysed to validate the feasibility of PIV. The
vertical strain was worked out to compare with the strain gauge data.
a) SCRH
Figure 6-12 shows the vertical strain determined from the PIV and strain gauge
(Gauge-1) in the SCRH. The red curve represents the strain gauge signature, and each blue
marks represents the vertical strain at one of the wheel load positions measured from the
PIV. It can be seen that the vertical strain from PIV exhibited a satisfactory match with the
strain gauge curve. Prior to applying the wheel load (x=20mm and F=10kN), the strain was
6,775microstrain and 6,710microstrain for the strain gauge and the PIV respectively. As
the wheel is loaded and rolled to the end point (x=-3mm and F=130kN), the peak strain
reached approximately 11,500microstrain for the strain gauge and 11400microstrain for the
PIV. The error is 1.6% ((11,500-11,400)/11,500). After the load magnitude decreased back
to 10kN, the vertical strain from the strain gauge and PIV were 6810microstrain and
6900microstrain respectively. Therefore, the PIV is proved to be a reliable method of
measuring vertical strains at critical zone of the railhead end.
Figure 6-12: Comparison of vertical strain in the SCRH
-6000
-7000
-8000
-9000
-10000
-11000
-12000
20mm
15mm 10mm
5mm
3mm
0mm
-3mm
-3mm unload
20mm unload
Strain gauge
PIV
0 5 10 15 20 25 30Time (s)
Ver
tica
l str
ain
εzz
125
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 125
b) SMRH
Figure 6-13 shows the vertical strain determined from the strain gauge and the PIV in
the SMRH. Both results showed that the vertical strain at the critical point considered was
in the tensile state. The vertical strains measured by both methods are in very good
agreement with each other. The PIV has predicted higher value of up to 460microstrain,
with an error of 4.5%. Although this error is relatively higher than the one in the SCRH, it
should be reminded that the strains in the SMRH are quite small leading to higher
percentages.
Figure 6-13: Comparison of vertical strain in the SMRH
Based on the results presented, it can be concluded that PIV can successfully measure the
vertical strains in the ―critical‖ zone of the railhead end, even if strains are just 100‘s of
microstrains. The following section, therefore, presents the performance examination of
the SMRH using the PIV.
6.4 PERFORMANCE EXAMINATION OF THE SMRH
In this section, PIV was applied to examine variations of the strain components at railhead
end subjected the two different load programs. In section 6.4.1, the PIV results from the
static wheel load are presented; results from the numerical model described in Chapter 4
are also presented. Three strain components, namely the vertical strain , the in plane
shear strain and the lateral strain are considered in the comparative examination. In
500
400
300
200
100
0
0 5 10 15 20 25 30
20mm 15mm10mm
5mm3mm
0mm
-3mm
-3mm unload
20mm unload
126
126 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
section 6.4.2, similar information is presented with reference to the repetitive rolling of the
loaded wheels.
6.4.1 DISTRIBUTION OF STRAIN COMPONENTS
The selected wheel load for this comparison is 130kN, and the wheel axis is positioned at
the rail end (x=0mm). In order to demonstrate the plausibility of the results, the strain
contour from the FE model together with the strain distribution along the critical path at
the ―critical‖ zone is jointly presented. It should be noted that due to the symmetry of the
wheel-rail loading characteristics, only half of the railhead end surface is shown for better
visibility of FE result.
a) Vertical strain
The vertical strain at the SCRH and the SMRH is presented as shown in Figure 6-14
and Figure 6-15 respectively. The vertical strain contour at the localised 20mm×20mm
railhead zones of the SCRH and SMRH obtained from the FE result is shown in Figure
6-14(a) and Figure 6-15(a) respectively.
(a) FE contour vertical strain
0
5
10
15
2005101520
Y direction(mm)
Symm
etric axis of Rail end (m
m)
Railhead top surface
127
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 127
(b) Comparison of vertical strain between PIV and FE
Figure 6-14: Vertical strain variation at 130kN in the SCRH
(a) FE contour of vertical strain
0
2
4
6
8
10
12
14
16
18
20
-0.02-0.015-0.01-0.0050
Dep
th a
lon
g sy
mm
etri
c ax
is (
mm
)
Vertical strain εzz (microstrain)
FE
PIV
0 -5000 -10000 -15000 -20000
0
5
10
15
2005101520
Y direction(mm)
Symm
etric axis of Rail end (mm
)
Railhead top surface
128
128 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(b) Comparison of vertical strain between PIV and FE
Figure 6-15: Vertical strain variation at 130kN in the SMRH
It can be seen that the pattern of strain distribution and the magnitude of the strains are
entirely different between these two shapes – SCRH and SMRH. In the SCRH, the peak
vertical strain is located at the sharp corner of the railhead top surface (18,806microstrain
compression); it then decreased rapidly to 9350microstrain at 2mm depth to the tip and
continues to decrease relatively mildly to 1531microstrain at 20mm depth. Whilst in the
SMRH, the edge of the railhead is almost not strained. More importantly, the signs of ―+‖
and ―-‖ indicate that this ―critical‖ zone is subjected to tension / compression strain states.
The transitional position is located at around the 9mm depth to the railhead corner.
In order to validate the FE result, PIV analysis was conducted along the symmetrical axis
of the rail end as shown in Figure 6-14(b) and Figure 6-15(b). Seven points along the axis
were selected. PIV result at these seven points forms a close agreement with the FE for
both the SCRH and the SMRH. In particular, PIV can analyse some locations, where the
normal strain gauge method cannot use. For example, at the point of 1mm depth to railhead
top corner, the PIV analysis was applied. It has strongly revealed that the top 2mm depth in
the SCRH is subjected to high vertical strain intensity as the wheel axis is above the rail
end. While in the SMRH the magnitude yields to zero, similar to the FE prediction.
0
2
4
6
8
10
12
14
16
18
20
-0.001 -0.0005 0 0.0005 0.001
Dep
th a
long s
ym
met
ric
ax
is (m
m)
Vertical strain εzz (microstrain)
FE
PIV
-1000 -500 500 1000
Depth 9mm
129
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 129
Although it is possible to choose additional points along the symmetric axis for PIV
analysis and the result could have tended to more fitting with the FE curve, the major
characteristics of the strain and its maximum zone was traceable, For the purpose of
validating the numerical model, such number of points was considered sufficient.
b) Shear strain
Figure 6-16 and Figure 6-17 present the shear strain between the PIV and FE result in
the SCRH and the SMRH respectively.
For the SCRH, FE result (Figure 6-16(a)) shows that the maximum shear strain is
6,312microstrain and located at about 4mm beneath the railhead top surface and 5.5mm
away from the symmetric axis of the rail end. To validate the numerical result, the strain
distribution along this vertical path (5.5mm deviated from the symmetric axis of the rail
end) was extracted and compared with the PIV analysis at the seven points along the path.
Comparison of the FE and PIV (Figure 6-16(b)) shows very good agreement. The
maximum shear strain (5,950microstrain) from PIV appears at the point of 3mm beneath
the top surface. A marginal shift of the location is evident but the error of them was less
than 6% (6,312-5,950)/6,312=5.74%). It can therefore claim that the concentration zone of
shear strain is well predicted both the PIV and the FE.
In the SMRH, Figure 6-17(a) shows the distribution of the shear strain at the ―critical‖
zone is different. In order to reveal the effect of the optimal arc shape, the comparison of
the shear strain between the PIV and the FE at the same vertical path was presented (Figure
6-17(b)). Result shows that they are in good agreement. Moreover, the shear strains are one
order magnitude less than those observed from the SCRH. Reduction in shear strain is
significant to the life of the engineering components as per well established fatigue failure
criteria in engineering.
130
130 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(a) FE contour of in plane shear strain
(b) Comparison of shear strain between PIV and FE
Figure 6-16: Shear strain variation at 130kN in the SCRH
0
5
10
15
2005101520
Y direction(mm)
Sym
metric
axis o
f Rail e
nd (m
m)
Railhead top surface
0
2
4
6
8
10
12
14
16
18
20
-0.008-0.006-0.004-0.0020
Ax
is a
lon
g m
ax
imu
m s
hea
r (m
m)
Shear strain εyz (microstrain)
FE
PIV
0 -2000 -4000 -6000 -8000
5.5 mm
4 mm
131
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 131
(a) FE contour of in plane shear strain
(b) Comparison of shear strain between PIV and FE
Figure 6-17: Shear strain variation at 130kN in the SMRH
0
5
10
15
2005101520
y direction(mm)
Sy
mm
etric
ax
is of ra
il en
d (m
m)
Railhead top surface
0
2
4
6
8
10
12
14
16
18
20
-0.0009 -0.0006 -0.0003 0 0.0003
Ax
is a
lon
g m
ax
imu
m s
hea
r (m
m)
Shear strain εyz (microstrain)
FE
PIV
-900 -600 -300 0 300
5.5 mm deviation
132
132 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
c) Lateral strain
The lateral strain in the SCRH and the SMRH are presented in Figure 6-18 and Figure
6-19 respectively.
(a) FE contour of lateral strain
(b) Comparison of lateral strain between PIV and FE
Figure 6-18: Lateral strain variation at 130kN in the SCRH
0
5
10
15
2005101520
Railhead top surface
Sym
metric
axis o
f rail e
nd (m
m)
y direction(mm)
0
2
4
6
8
10
12
14
16
18
20
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
Dep
th a
long s
ym
met
ric
ax
is (m
m)
Lateral strain εyy (microstrain)
FE
PIV
0 500 1500 2000 30001000 2500
133
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 133
(a) FE contour of lateral strain
(b) Comparison of lateral strain between PIV and FE
Figure 6-19: Lateral strain variation at 130kN in the SMRH
Compared to the other two strain components ( and ), the lateral strain distribution
has shown negligible effect of the optimal shape adoption (i.e., SCRH and SMRH). The
maximum lateral strain is located 5mm beneath the railhead top for the SCRH and 8mm
for the SMRH; on the other hand, the strain remained tensile for both shapes. This is an
expected result, because the profile of the railhead cross sectional shape is kept the same in
0
5
10
15
2005101520
Railhead top surface
Sym
metric
axis o
f rail e
nd (m
m)
y direction(mm)
0
2
4
6
8
10
12
14
16
18
20
0 0.0003 0.0006 0.0009 0.0012
Dep
th a
long s
ym
met
ric
ax
is (m
m)
Lateral strain εyy (microstrain)
FE
PIV
0 300 600 900 1200
134
134 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
the optimisation procedure, with only the longitudinal profile modified with the two design
parameters and . Therefore, the contact effect between the wheel tread and railhead in
the lateral direction remained approximately the same between the SCRH and the SMRH.
The magnitude of the lateral strain exhibited reduction, less pronounced than and .
The peak value decreases from 2,472 microstrain of the SCRH to 983microstrain of the
SMRH, reduced by 64% ((2472-983)/2472). It is interesting to note that in the SMRH, the
lateral strain become the largest compared to the other two strain components ( and )
in the ―critical‖ zone.
6.4.2 CONTACT-STRESS RESPONSE OF THE SMRH
An interesting observation is the relation between the strain reduction in the SMRH and the
wheel-rail contact interaction. As the wheel axis is positioned at the rail end (x=0), the
wheel and the railhead top surface must satisfy static contact equilibrium. However, the
spatial alteration of the wheel-rail contact can be observed as shown in Figure 4-17 of
Chapter 4. The equilibrium state of the master nodes and slave nodes between the wheel
and the rail contact surface indicates that the contact is shifted away from the sharp corner
of the rail end, resulting in the tip free of contact pressure. Subsequently, this alteration of
the contact is believed to be the direct cause for the redistribution of the strains in the
vicinity of the rail end.
To examine the effect of the contact interaction on the strain variation, the distribution of
the vertical strain component in the symmetrical plane (xoz) of rail end is particularly
presented as shown in Figure 6-20. The change in magnitude and pattern of the vertical
strain is mostly pronounced, therefore, it can explicitly elaborate the problem.
In the SCRH, the vertical strain distribution inside the body is shown in Figure 6-20(a), it
can be seen that the peak strain is located at the corner of the rail end (18,810microstrain
compression), which is consistent with the prediction as for the strain contour at the rail
end plane (yoz). Due to the wheel/rail contact bounded at the unsupported rail end, the
sharp corner of the rail end acts as the source of high level of stress/strain concentration,
resulting in severe material deterioration. The strain contour explicitly demonstrates that
135
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 135
the strain gradient is very steep at the corner and gradually reduces along the radius
direction (as shown in arrows) to the rail end corner.
However, in the SMRH, the alteration of the wheel-rail contact interaction has significantly
changed the strain distribution. Figure 6-20(b) shows that the strain concentration is shifted
away from the corner of the rail end, to the underneath of the wheel-rail contact region.
The peak magnitude is 8055microstrain in compression, almost reduced by 57% ((18810-
8055)/18810). This is equivalent to the Herztain prediction, which generally considers the
problem of wheel contact with Continuously Welded Rail (CWR) without vertical
geometrical edge effect. It indicates the optimal arc shape has the ability of retaining the
structural stiffness by changing the contact configuration and subsequent stress/strain
distribution.
Furthermore, the trajectory of the strain flow from the peak zone to the rail end is also
interesting. The arrow in dot line shows that the zone of compressive strain concentration
is diminishing towards to the rail end. However, it could not expand further to the rail end
corner. In contrast, the zone in red colour shows that the rail end corner is in the tensile
state, which is consistent with the result in Figure 6-15. The physical explanation can be
drawn that due to the contact region away from the corner, the material underneath the
contact is subjected to compressive strain, while material close to both side of the contact
including to the corner tends to tipped up so as to compensate the partial volume reduction.
From the above discussion, the numerical result of the optimal design has been
successfully validated through the comparison with the experimental data. Also the
interpretation of the optimal shape on the resultant alteration of the strain magnitude and
distribution is well explained together with the experimental data and numerical result. The
following section is to further justify the behaviour of the optimal shape under the
repetitive rolling wheel load.
136
136 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
(a) Distribution of in the SCRH
(b) Distribution of in the SMRH
Figure 6-20: Vertical strain in symmetric plane of the rail
0 5 10 15 20x direction(mm)
0
5
10
15
20
z dire
ctio
n(m
m)
0
5
10
15
20
25
300 10 20 30 40
x direction(mm)
zd
irectio
n(m
m)
Wheel axis
Wheel axis
137
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 137
6.4.3 BEHAVIOUR OF THE SMRH UNDER REPETITIVE ROLLING WHEEL
As illustrated above, the peak vertical strain at the ―critical‖ zone was an important to
depict the effect of the optimal arc shape on the strain alteration. This section highlights the
difference in the history of the peak vertical strain subjected to repetitive moving load.
The vertical strain from PIV analysis was compared with the stain gauges (Gauge-1 to
Gauge-4) in the ―critical‖ zone.
Firstly, the peak vertical strain from the strain gauges at selected load cycles was
identified. In each load magnitude, the peaks were sorted out at every 10 cycles. Therefore,
there were 60 data points for each strain gauge (10 cycles for each load magnitude × 6 load
magnitudes) through the entire repetitive rolling wheel load program.
Secondly, PIV analysis was conducted to acquire the peak vertical strain at selected
photographing cycles. In each load magnitude, three photographing cycles were selected
namely the 1st cycle, the 50th cycle and the 100th cycle. Overall, there were 18 data points
at each position of the strain gauges (3 cycles for each load magnitude × 6 load
magnitudes) from PIV analysis, resulting in a total of 72 peak strain values for the optimal
arc shape (18 data points×4 strain gauges).
Figure 6-21 and Figure 6-22 show the comparison of the peak vertical strain in the
SCRH and the SMRH respectively. It can be seen that the result of PIV analysis was
similar to the strain gauge in both of the two shapes. PIV analysis also reconfirmed the
information as discussed in Section 6.2.1. This information includes:
For both of the two shapes (SCRH & SRH), the peak vertical strain magnitude
increases, as the wheel load magnitude increases;
In the SCRH, strain concentration (much higher than yield strain of head hardened
rail steel) occurs at the point closer to the railhead top corner. In the SMRH, the
magnitude of the strain at the railhead end was far lower than the material yield
limit for all the load magnitudes considered in this thesis. The optimal arc shape
has successfully shifted the stress/strain concentration into the railhead and away
from the ―critical‖ zone. At the point of Gauge-1, the strain was changed into
tension and kept increasing as the load increased.
138
138 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
Figure 6-21: Vertical strain history under the repetitive moving load in the SCRH
Figure 6-22: Vertical strain history under the repetitive moving load in SMRH
-15000
-12500
-10000
-7500
-5000
-2500
0
0 50 100 150 200 250 300 350 400 450 500 550 600
Ver
tica
l pla
stic
str
ain
Cycles
Gauge-1
Gauge-2
Gauge-3
Gauge-4
PIV(Gauge-1)
PIV(Gauge-2)
PIV(Gauge-3)
PIV(Gauge-4)
-1500
-1000
-500
0
500
1000
0 50 100 150 200 250 300 350 400 450 500 550 600
Ver
tica
l pla
stic
str
ain
Cycles
Gauge-1
Gauge-2
Gauge-3
Gauge-4
PIV(Gauge-1)
PIV(Gauge-2)
PIV(Gauge-3)
PIV(Gauge-4)
139
Chapter 6: Performance of the Stress Minimised Railhead (SMRH) 139
After the repetitive rolling wheel load, the contact patches on the top railhead surface in the
SCRH and the SMRH are shown in Figure 6-23(a) and Figure 6-23(b) respectively.
For the SCRH, as the wheel approached the rail end, the contact also reached to the end,
resulting in the obvious increase of the contact length in lateral direction (y axis). This was
similar to the result in Figure 4-16(b) of Chapter 4.
However, in the SMRH, the contact patches kept their elliptical shape throughout the
moving wheel load. More importantly, the contact never has extended to the rail end. This
reconfirmed the observation in Figure 4-16(a) of Chapter 4 that the optimal arc shape has
effectively modified the contact characteristics of the rail end, by shifting the contact
patches away from the end. Such alteration in the contact behaviour contributed the
reduction of the strain as well as its status. This mechanically inspired design will stand the
test of time; field adoption potential is discussed in chapter 8.
(a) SCRH; (b) SMRH
Figure 6-23: Contact patch after repetitive rolling of loaded wheel
6.5 SUMMARY
In this chapter, the effects of the optimal arc shape of the SMRH on the contact behaviour
and the strain variations were examined through the comparative study of the experimental
data and the numerical result. Some conclusions are made:
21mm
15mm
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140 Chapter 6: Performance of the Stress Minimised Railhead (SMRH)
1. The strain gauge data from both of the SCRH and the SMRH provided a platform
to validate the feasibility of PIV analysis at the ―critical‖ zone.
2. The vertical strain predicted by the PIV and the strain gauge data have been
found in good agreement.
3. The performance study of the SMRH has illustrated that the strain variations at the
―critical‖ zone of the rail end exhibited significant reduced level of the vertical, in
plane shear strain and lateral strain. The strain magnitude has remained well below
the head hardened rail steel yield limit. Furthermore, the ―critical‖ strain no longer
remains at the corner of the rail end. The SMRH, therefore, expects to exhibit
longer service life.
4. The performance examination of the SMRH under the repetitive wheel load has
shown that the optimal arc shape significantly reduce the stress/strain.
5. The contact patches after the repetitive wheel load clearly stated that the SMRH
was better for protecting the railhead end from the accelerated material
deterioration typical of the SCRH shaped CIRJ.
Chapter 7: Development of Embedded Insulated Rail Joint (EIRJ) 141
Chapter 7: Development of Embedded IRJ
(EIRJ)
7.1 INTRODUCTION
A basic conceptual design of Embedded IRJ (EIRJ) that eliminates several structural
components including the joint bars and the pre-tensioned bolts in the Conventional IRJ
(CIRJ) is reported in Chapter 3. In this chapter the design is further developed through a
procedure of multi-objective optimisation using a coupled second generation non
dimensional sorting algorithm (NSGA- II) and a parametric FE modelling similar to the
one previously described in Chapter 4.
In Section 7.2, the formulation of the formulation of the multi-objective optimisation
problem is described. The design objective is to minimise the increase in volume of the rail
and the increase in volume of the modified rail sleeper. The design constraint is to ensure
the maximum vertical, lateral and horizontal deflections of the joint do not exceed the
corresponding deflections occur in the CIRJ for the same wheel loading. The design
variables that define the shape of the EIRJ are also outlined. In Section 7.3, a parametric
FE model specific for the EIRJ design for evaluating the critical deflections of the railhead
is described. The NSGA- II is also described in this section and its usage as the
optimisation algorithm and its integration with the developed FE model for the
optimisation problem are illustrated. The optimisation result is discussed in Section 7.4;
three optimal solutions of the EIRJ, representing extremes of the two objective functions
used in the optimisation, are particularly also discussed with respective to their practical
implementation in this section. Section 7.5 summarises this chapter.
7.2 FORMULATION OF THE OPTIMISATION MODEL FOR EIRJ
7.2.1 FUNCTIONS OF THE EIRJ
The major components of the concept design of EIRJ have been described in Chapter 3.
The concept design consists of three major components, including two lengths of rails, a
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142 Chapter 7: Development of Embedded IRJ (EIRJ)
prestressed concrete sleeper incorporating modified geometry and insulation material. The
basic two functions of the CIRJ that can be alternatively fulfilled by the EIRJ as follows:
To secure safe passage of wheels across the gap, the railhead deflections (vertical,
lateral and longitudinal) at the joint gap should remain minimal. This requires
sufficient stiffness across the gap. In the CIRJ, the stiffness was achieved through joint
bars across the gap. As joint bars are eliminated in the EIRJ, the stiffness should be
realised by the rail itself and a reliable support (hence embedding part of the rail into
the concrete sleeper). Figure 3-4 of Chapter 3 shows that the rail foot and part of the
rail web at two rail ends are firmly embedded into the concrete sleeper. This
arrangement provides additional structural stiffness due to the elimination of joint bars
and bolt connection in the CIRJ.
Because both the rail steel and the concrete sleeper are electrically conductive, an
insulation material is essential and is inserted between the rail surface and the concrete
sleeper surface (Figure 3-5 of Chapter 3). This material can reduce the structural
effectiveness of the EIRJ due to its low stiffness (relative to concrete); however,
insulation is an essential part to prevent electrical conductivity. Therefore, the
optimisation procedure is developed such that it takes the reduced stiffness of the
insulating material into account in the calculation of the design constraints.
7.2.2 FORMULATION OF OPTIMISATION PROBLEM
a) Design constraints for the EIRJ
The new design proposed above provides the basic structural integrity and electrical
insulation for safe signalling. However, due to the elimination of the joint bars and the
associated bolt connection, the structural stability of the EIRJ is largely dependent on the
method of supporting the rails. As described in Chapter 3, the deflections limits are set to
ensure the maximum vertical, lateral and horizontal deflections of the railhead end at the
gap do not exceed the corresponding deflections in the CIRJ.
b) Design variables
To satisfy the design constraints described in Section 7.2.2.1, it is possible to change the
geometric shape and dimensions of the rail end and the concrete sleeper without
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Chapter 7: Development of Embedded IRJ (EIRJ) 143
intervening or adversely affecting the neighbouring rail infrastructure (e.g. fasteners,
sleepers) and the rolling-stock components especially the wheel tread conicity. Seven
design variables are introduced to define the overall geometry of the joint. For the sake of
clarity, only half of the EIRJ is shown in Figure 7-1.
Figure 7-1: Design parameters of half of EIRJ
The design variables are:
1. height of the railhead at the rail end ( );
2. height of the railweb at the rail end ( );
3. height of the railfoot at the rail end ( );
4. thickness of the railweb at the rail end ( );
5. length of the rail end shape transitioning from modified rail end to the original rail ( );
6. half width of the modified concrete sleeper engraving the rail ends ( ); and
7. height of the concrete sleeper along the rail end surface ( ).
The first five design variables ( , , , and ) define the modified shape of the rail
end; the final two variables and define the shape of the concrete sleeper. Some
limitations to the shape modification must be followed to keep the modified rail end simple
to be manufactured and compatible with the current rolling-stock designs. It includes:
1. Railhead top surface profile is kept unchanged so that it will remain compatible with
the current rail section and rolling stock wheels.
Wheel Load
407mm
237mm
170mm
200mm
Symmetric axis of EIRJ
x6
x5 x1
x2
x3
300mm
322mm
Ground
x4
x7
Insulation 5mm thickness
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144 Chapter 7: Development of Embedded IRJ (EIRJ)
2. The width of the rail foot is kept unchanged to ensure simple shape transition and ease
of assembly.
3. The thickness of insulation material is kept constant (5mm).
4. The total height from the bottom surface of the modified sleeper to the top railhead
running surface is kept constant (407mm). This ensures the current installation
instruments can also be used for the new design assembly.
(5mm=thickness of insulation material)
5. The total height of the modified rail end is no less than the 170mm (the original rail
height). Meanwhile, the height of the sleeper at the rail end should be larger than
200mm, so that it can be designed with enough strength for supporting the rail and the
wheel load:
6. The cross section of the concrete sleeper is kept constant. The height of the sleeper is
322mm, which is the summation of the original height of the rail sleeper (237mm) and
half height of the original rail (85mm). This ensures that the at least half height of the
rail end is embedded.
c) Design objective functions
To satisfy the design constraints, there can be numerous design solutions derived from
different combination of design parameters identified. For an optimal design of the EIRJ,
minimising the cost of manufacture is a major goal in order to make it practically viable.
Generally, the cost of manufacturing a new product largely depends on the process of
manufacture and the usage of the material. Simplified manufacturing procedure and
minimal (minimising the increase in volume of the rail and the sleeper) usage of the
material are clear goals of this optimisation design. The manufacturing, installation and
maintenance of the EIRJ designs will be discussed later in Chapter 8.
The mathematical formulation for the multi-objective design optimisation of the EIRJ is
outlined as follows:
Minimise:
Subject to design constraints:
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Chapter 7: Development of Embedded IRJ (EIRJ) 145
and constraints of design parameters:
in which:
is the increase in the volume of the modified rail;
is the increase in the volume of the modified sleeper;
is the limit of the longitudinal deflection in CIRJ;
is the limit of the lateral deflection in CIRJ;
is the limit of the vertical deflection in CIRJ;
is the vector of the design parameters.
7.3 MULTI-OBJECTIVE OPTIMISATION MODELLING
This section presents a scheme of incorporating parametric finite element modelling and
the multi-objective optimisation algorithm (NSGA-II). Section 7.3.1 illustrates the finite
element modelling procedure using Python language, which has been successfully applied
into the stress minimisation as described in Chapter 4. In Section 7.3.2, a review of the
different multi-objective optimisation methods is introduced, and the fundamentals of
NSGA-II are particularly illustrated. In Section 7.3.3, the integrated procedure of FE model
and the selected optimisation algorithm NSGA- II is presented.
7.3.1 FINITE ELEMENT MODELLING OF THE EIRJ
To evaluate the objective functions (increase in volume) and the structural responses
(vertical, lateral and longitudinal deflections), a parametric FE modelling was developed
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146 Chapter 7: Development of Embedded IRJ (EIRJ)
using the Python language, the elements of which is illustrated in Chapter 4 and Appendix
A. Python was also used for the global structural shape optimisation of the EIRJ.
Unlike the development of the SMRH, the EIRJ depends on the global behaviour of the
IRJ including appropriate representations of the boundary conditions (discretely located
sleepers and the stiffness of ballast and sub-ballast layers). This is in contrast to SMRH
(Chapter 4) where a rigid support was assumed. Further, the wheel-rail contact was
essential for the SMRH optimisation as the contact nonlinearity affected its outcome
(maximum von Mises stress at railhead end). In the development of the EIRJ, however, the
contact nonlinearity is of less important compared to the magnitude and the point of
application of the wheel load. Therefore, for the EIRJ optimisation, the contact
nonlinearity is disregarded in exchange of the complexities of the discrete support
condition modelling.
A discretely supported EIRJ is shown in Figure 7-2. For simplicity only half of the EIRJ is
shown. The model incorporates several idealisation/simplicities in geometry, material,
boundary conditions (including loading) and modelling methods as described in the
following subsections.
(a) Side view (b) End view
Figure 7-2: Schematic diagram for the simplified model of the EIRJ
a) Simplification of geometry modelling
The complexity of assembling the different components (rail, modified sleeper and
insulation material) demands simplification to reduce computational cost.
Ks Ks
Kb
F/2 F/2
Spring supporting 1/20 inclination
1600mm
Modified
Sleeper
147
Chapter 7: Development of Embedded IRJ (EIRJ) 147
Figure 7-3 shows the simplified EIRJ geometry. Firstly, due to the symmetric nature of the
EIRJ, loading and supporting condition, only half of the joint structure was modelled.
Secondly, as the structural response under the wheel load was evaluated at the railhead
ends, the finite element model was simplified to just one part model by ignoring the
interaction between the contact surfaces of the rail, the insulation material and the concrete
sleeper. In other words, the fully assembled joint was assumed as one instance partitioned
with different regions of material (concrete, rail steel and insulation). Lastly, because only
the straight rail track was considered in this study, no wheel flanging caused lateral load
was considered. As a result, single rail with only part of the modified sleeper that is
effectively used to embed the rail end was modelled.
Figure 7-3: One single part with different material regions
As shown in Figure 7-3, the initial design of the simplified EIRJ was provided with the
original rail cross section. The height, length and half width of the part of the sleeper were
322mm, 300mm and 200mm (lower bound of the design parameter ) respectively. The
initial volumes for the rail and the part of the sleeper were calculated based on the initial
design dimensions. Subsequently, the design objectives (volume increase of the rail and the
sleeper) were obtained by subtracting the initial design from the updated design.
Normal rail steel region
Insulation material region
Concrete material region
200mm
322mm
300mm
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148 Chapter 7: Development of Embedded IRJ (EIRJ)
b) Simplification of the loading
Because only half of the embedded insulated rail joint was modelled and the wheel load is
also assumed symmetrically located over the joint, it is pragmatic to apply half of the
wheel load over the single rail end. As explained, the contact loading is replaced by a
static concentrated load over the rail end.
Figure 7-4 shows the concentrated loading in the FE model. It should be noted that the
inclination (1/20) of the vertical axis of rail was still maintained. In the straight rail track,
such inclination is the major contributor to the lateral displacement of the rail end. The loss
of stiffness due to the elimination of joint bar connection exaggerated the lateral instability
of the joint.
Figure 7-4: Simplification of wheel contact load to concentrated load
c) Simplification of boundary condition
As the EIRJ is discretely supported on the normal prestressed concrete sleepers, which are
installed on the track consisting of ballast and subgrade layers, modelling such a
mechanical system is very expensive and unnecessary. To reduce the computational cost,
some simplifications were made in the modelling of the supporting system around the
joint.
Half of wheel load
1/20 inclination
149
Chapter 7: Development of Embedded IRJ (EIRJ) 149
The support system is modelled as shown in Figure 7-5. The normal prestressed concrete
sleepers supporting around the EIRJ, the interaction of the rail bottom surface and the
sleeper top surface were modelled through coupling at a single reference point that has six
DOFs. Because the straight rail track condition was considered in this study, five DOFs
except the vertical displacement DOF were arrested. The effective area of the coupling
zone was, therefore, determined by the width (200mm) of the prestressed concrete sleeper
and the width of the rail base (146mm). The sleepers are spaced at 700mm.
Figure 7-5: Idealisation of normal ballasted sleeper support
For the support under the modified sleeper with embedded rail, the interaction of the
sleeper bottom surface and the ballast was also modelled through coupling. The coupling
zone was determined by the area of the sleeper bottom surface (half width of the sleeper
× constant length of the sleeper 300mm). The reference point was located in the middle of
the coupling zone, and similarly only its vertical displacement DOF was set free. The
stiffness of the support varies with the geometry of the sleeper bottom surface.
Sleeper-rail interaction
200mm
146mm
300mm
Modified sleeper-ballast interaction
x6
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150 Chapter 7: Development of Embedded IRJ (EIRJ)
The property of the ballast supporting system is non-linear and complicated. To set up a
model with reasonable size, they are simplified as an elastic layer. In this study, a linear
single layer model was employed (Figure 7-2) to model the stiffness of the support
underneath the EIRJ. One end of each spring element is connected to the reference node
and the other end is fixed to the ground. As for the normal prestress concrete sleeper
support, the spring stiffness was set 30900N/mm (Sun, 2003). For the ballasted support
under the modified sleeper, the stiffness is dependent on the half width of the sleeper
. According to Ahlbeck et al (1975), the vertical stiffness of ballast and subballast is kept
approximately linear to the geometry parameters of the equivalent ballast pyramid.
Therefore, the stiffness for the initial modified sleeper design (200mm in half width, same
as that of the normal prestressed concrete sleeper) equals to . With the increase of , the
stiffness can be calculated from:
The full FE model is shown in Figure 7-6. The entire FE model consists of 169,655 nodes
and 147,322 eight-node linear hexahedral solid elements with reduced integration C3D8R.
Figure 7-6: Finite element model of EIRJ
Original rail shape
Initial concrete sleeper
151
Chapter 7: Development of Embedded IRJ (EIRJ) 151
7.3.2 MULTI-OBJECTIVE OPTIMISATION—NSGA-II
Multi-objective optimisation problem process results in multiple feasible solutions that
satisfy the design constraints. All feasible solutions satisfy the objective functions; yet
some can be superior to other from considerations of factors that are not explicitly
incorporated in the modelling and optimisation procedure. Therefore, it is prudent to
consider a select number of designs and examine their practicality prior to recommending a
particular design for field adoption. In a theoretical sense, the multi-objective optimisation
procedure determines a set of non-dominated solution points, known as Pareto-optimal. In
the non-dominated set, none of the solutions is absolutely better than any other; each of
them is an acceptable solution.
a) Classical methods
Many classical algorithms for nonlinear vector optimisation techniques define a substitute
problem by scalarising the multiple-objective optimisation to a single-objective one. Based
on the substituted single objective problem, a compromise solution is found subjected to
specified constraints. Such typical methods include methods of objective weighting,
method of distance functions, min-max formulation, etc. In these methods, multiple
objectives are combined to form one objective by using some knowledge of the problem
being solved. The optimisation of the single objective may guarantee a Pareto-optimal
solution but results in a single-point solution. These methods are sometimes expensive as
they require knowledge of the individual optimum prior to solving the optimisation. The
decision maker must have a thorough knowledge of the priority of each objective before
forming the single objective from a set of objectives. The solutions obtained largely
depend on the underlying weight vector or demand level. Thus, for different situations,
different weight vectors need to be used and the same problem needs to be solved a
number of times. However, in real-world situations decision makers often need different
alternatives in decision making. Therefore, finding the entire set of Pareto-optimal
solutions is often desired
In this study, the non-dominated sorting genetic algorithm (NSGA- II), as one of most used
stochastic search, was used for the current multi-objective optimisation of EIRJ. The
following section illustrates the basic principle of the method.
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152 Chapter 7: Development of Embedded IRJ (EIRJ)
b) Elitist non-dominated sorting genetic algorithm (NSGA-II)
Deb et al. (2002) proposed a fast elitist multi-objective GA that was able to find much
spread solutions over the Pareto-optimal front and required low computational cost.
According to the experimental results on different test problems in the literature, the
NSGA-II has exhibited better performance compared to other multi-objective evolutionary
algorithms. Generally, NSGA-II has the following features:
Be able to use elite-preserving operator to preserve the best solutions in the
subsequent generations;
Be able to use a non-dominated sorting technique in GAs;
Be able to use the crowded distance sorting technique so as to preserve the diversity
among non-dominated solutions in the lower level of non-dominated solutions.
This can provide a better spread of solutions.
The major contribution for enhancing the computing efficiency in NSGA-II is the usage of
two sorting operators as shown in Figure 7-7. These operators are briefly described as
follows:
Figure 7-7: Procedure of non-dominated sorting and crowding distance sorting
(Deb et al., 2002)
Non-dominated sorting
Pt
Qt
F1
F2
Ft
Rejected
Pt+1
Crowding distance sorting
Rejected
153
Chapter 7: Development of Embedded IRJ (EIRJ) 153
Non-dominated sorting
In the tth
generation, a combined population of the parent population and newly
generated population is first formed. Non-dominated sorting is then applied to divide
the combined population into separate levels of non-dominated fronts. In this process, two
entities are calculated for each individual: 1) domination count , the number of
individuals which dominate the individual , and 2) , a set of individuals that the
individual dominates. For the minimisation problem, if the individual dominates
another individual , it must satisfy the following:
for =1:
where is the number of the objective functions.
Based on the above comparisons, the first non-dominated front consists of all the
individuals with the domination count as zero. Thereafter, the domination count for the rest
of the population is reduced by one. Now based on the renewed domination count, any
individual with the domination count as zero will belong to the second non-dominated
front. This process continues until all the non-dominated fronts are identified in the
combined population.
Crowding distance sorting
Before the crowding distance sorting, the elitist method ensures that the top ranked non-
dominated individuals appear in the next population . The remaining vacancies of the
population are filled from the subsequent non-dominated front in the order of the
ranking. This procedure continues up to the front , beyond which no more vacancy is
available. In general, the number of the individuals from to will be larger than the
population size. Therefore, to choose exactly the defined population size and preserve the
diversity in population, the individuals of the last front are sorted using the crowding
distance sorting operator.
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154 Chapter 7: Development of Embedded IRJ (EIRJ)
In the crowding distance sorting, each individual is assigned with a crowding distance. The
crowding distance is the average distance between two neighbouring values at either side
of each objective value. Therefore in comparison between two individuals, the one located
in lesser crowded region (larger crowding distance) is chosen for the next population .
NSGA-II was successfully applied in various engineering optimisation problems. The
details of discussion for NSGA-II can be referred to Srinivas and Deb (1995) and Deb et
al. (2002). The basic steps for NSGA-II are outlined as follows:
Step 1: The initial population is randomly generated.
Step 2: Objective functions for all the individuals and the design constraint are evaluated.
Step 3: Non-dominated fronts are identified based on the non-dominated sorting.
Step 4: The Crossover and mutation operators are applied to generate an offspring
population .
Step 5: Objective functions for all the individuals in the offspring and the design constraint
are evaluated.
Step 6: Parent and offspring populations are combined. The non-dominated sorting and
crowding distance sorting are conducted to generate the new parent population .
Step 7: The Crossover and mutation operators are applied to generate the offspring
population .
Step 8: Return to Step 5 and continue to the next loop until the maximum generation is
reached.
7.3.3 COUPLING OF FEM AND NSGA-II
The integrated procedure coupled with FEM and NSGA-II for the design optimisation
EIRJ is shown in Figure 7-8. The procedure consists of two major parts:
1) Repetitive evaluation of objective functions and design constraints in FEM; and
2) Optimisation operators for searching the new non-dominated front solutions.
The genetic operators in NSGA-II during the optimisation evolution are defined as shown
in Table 7-1.
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Chapter 7: Development of Embedded IRJ (EIRJ) 155
Table 7-1: Genetic operators in NSGA-II
Population size 50
Number of generations 100
Selection Tournament selection
Crossover probability 0.7
Mutation probability 0.005
Figure 7-8: Integrated optimisation procedure coupled with FEM and NSGA-II
Start(t=0)
Initialise population P0
SelectionCrossovermutation
Offspring population Q0
Non-dominated sorting
Combination of population Pt and Qt
Non-dominated sorting
Crowding distance sorting
t=t+1
t>N?
New population Pt
Pareto front
Yes
No
SelectionCrossovermutation
New Offspring population Qt
Parametric geometry modelling
FEM preparation
1. Material property;2. Boundary condition;3. Meshing;4. Contact definition.
Submit job (.inp file)
Evaluate objective value
FEM analysis
Fitness value
FEM analysis
Fitness value
Python scripting
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156 Chapter 7: Development of Embedded IRJ (EIRJ)
7.4 OPTIMISATION RESULT AND DISCUSSION
This section presents the result for the multi-objective optimisation of EIRJ. Two design
objectives are considered: 1) the increase in the volume of the rail; and 2) the increase in
the volume of the sleeper part. In this study, the design constraints for the vertical, lateral
and longitudinal deflections were obtained from the analysis of the CIRJ model developed
similar to Pang (2007), in which half of the wheel load on either end of the railhead
was applied to the rail model shown in Figure 7-9. The dynamic analysis of wheel rolling
over the joint gap and the details of the CIRJ modelling are presented in Chapter 8. The
magnitude of the vertical ( ), lateral ( ) and longitudinal ( ) deflections calculated
were 3.13mm, 0.15mm and 0.25mm respectively.
Figure 7-9: Static wheel load at railhead ends in CIRJ
In the following sections, the evolutionary process of the optimal solutions over the entire
generations is firstly presented. Three different designs from the pareto-optimal solutions
are selected; and their design parameter, objective values and structural responses
(displacements) are presented respectively. Further discussion is also conducted with these
three typical designs. Their design characteristics and the feasibility in practice are
particularly discussed.
Ks Ks Ks Ks Ks Ks
F/2 F/2
F/2 F/2 Conventional IRJ
157
Chapter 7: Development of Embedded IRJ (EIRJ) 157
7.4.1 EVOLUTION OF PARETO-OPTIMAL SOLUTIONS
Figure 7-10 shows the progressive pareto-optimal searching history within the maximum
100 generation. To illustrate the evolution of optimal solutions, three stages during the
optimisation process are presented, namely the 50th
, 80th and 100
th generations.
It can be seen from Figure 7-10 that the feasible non-dominated designs was identified at
the last 20 generations (between the 80th and 100
th generation), because the pareto-front
points after 80 generations have only been slightly improved, compared to the last
generation (100th generation). However, the final optimal points were more scattered,
which formed a better pareto-optimal front boundary. This is probably due to the crowding
distance sorting technique during the process of generating the subsequent generation. This
technique has been approved that by preserving the diversity amongst the non-dominated
solutions and provides a better spread of solutions.
Figure 7-10: Evolution of pareto-optimal solutions
Within all the feasible non-dominated optimal points by the end of the optimisation, three
typical solutions are selected as shown Figure 7-10. Each of the points represents a set of
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
ΔV
sleep
er
ΔVrail
Generation 100
Generation 80
Generation 50
Solution 1
Solution 2 Solution 3
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158 Chapter 7: Development of Embedded IRJ (EIRJ)
optimal combination of the objectives values that define a unique set of optimal design
parameters (an optimal solution of EIRJ). At each design, improving one objective is
impossible without sacrificing the other objective.
Table 7-2 presents the objective values and the structural displacements of three selected
designs. For the initial design, the vertical, lateral and longitudinal deflections at the
railhead end are approximate 4.208mm, 0.330mm and 0.380mm respectively. Compared to
the design limits from the CIRJ subjected to the same loading and boundary condition,
they are increased by approximate 34.4%, 63.3% and 52% respectively.
Table 7-2: Objective values and structural displacements for the selected three solutions
Initial Design Solution 1 Solution 2 Solution 3
×106
(mm3)
N/A 0.008 1.439 0.668
×107
(mm3)
N/A 1.325 0.089 0.591
Vertical
deflection (mm)
4.208 3.125 3.019 3.118
Lateral
deflection
(mm)
0.245 0.112 0.148 0.141
Longitudinal
deflection
(mm)
0.380 0.244 0.216 0.238
Compared to the initial design, all of the three optimal solutions have larger volumes in
both of the rail and the sleeper part. The increased volume provides additional structural
stiffness to the EIRJ. As a result, the deflections for all of the three design solutions are
lower than the design limit (3.13mm for the vertical deflection, 0.15 for the lateral
deflection and 0.25 for the longitudinal deflection). Table 7-3 presents the corresponding
optimal design parameters for the three design solutions. The design characteristics of the
three solutions and their practical feasibility are further discussed in the following section.
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Chapter 7: Development of Embedded IRJ (EIRJ) 159
Table 7-3: Optimal design parameters for the selected three optimal solutions
Design variable (mm) Solution 1 Solution 2 Solution 3
46 65 57
104 90 99
21 43 31
22 62 38
53 359 287
343 203 267
236 209 223
7.4.2 DISCUSSION OF PRACTICAL FEASIBILITY FOR THE OPTIMAL
SOLUTIONS
Three typical optimal solutions selected from the pareto-optimal solutions are discussed in
details in this section.
a) Solution 1
Figure 7-11 shows the geometry of the Solution 1. For this design, it can be seen that the
increase in the volume of the rail is much lower than that of the sleeper. In other words, the
shape of the rail is similar to the normal rail, with only minor volume increase
( =0.008mm3). However, the height of the sleeper has increased from the original
200mm to 343mm. To satisfy the design constraints, the addition of the stiffness is
predominately provided from the modified sleeper.
(a) Cross section view
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160 Chapter 7: Development of Embedded IRJ (EIRJ)
(b) Iso view
Figure 7-11: Details of design Solution 1
Based on this design, it is possible for the designer or the manufacturer to achieve the new
design of EIRJ by only changing the shape of the sleeper, whilst the normal rail can be still
used with stress minimised shape described in Chapter 4. This design uses minimal rail
steel compared to the other design solutions (Solution 2 & 3). To check the structural
response of EIRJ using the normal rail and the optimal sleeper width (343mm), a finite
element analysis was conducted and the displacements for this design is 3.131mm (vertical
displacement), 0.113mm (lateral displacement) and 0.225mm (longitudinal displacement).
These are only marginally increased compared to the Solution 1.
b) Solution 2
Figure 7-12 shows the three dimensional geometry of the design solution 2. The design
was selected from one of the solution located at the right bottom corner of the pareto-
optimal points (Figure 7-10).
(a) Cross section view
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Chapter 7: Development of Embedded IRJ (EIRJ) 161
(b) Iso view
Figure 7-12: Details of design Solution 2
Contrast to the design Solution 1, this second design has larger increase in the volume of
the rail rather than the sleeper. By changing the shape of the rail in the vicinity of the joint,
the loss of the structural stiffness due to the elimination of the joint bars is compensated
through the addition of the rail steel. The shape at the rail end shows that the rail web is
built up with more rail steel, whose width is very close to that of the railhead. This increase
in web width is close to the thickness of the two joint bars; the advantage still is that there
is no bolt connection.
The advantage of using the design Solution 1 can be observed during the installation in
field. After the modified rail was manufactured and assembled into the sleeper, the track
engineers can still use the current installation instruments and procedure, because the
sleeper width is only marginally increased from 200mm to 203mm. Furthermore, the
normal ballast tamping can also be possibly applied for this design in railroad track
maintenance.
c) Solution 3
Figure 7-13 shows the three dimensional geometry of the design Solution 3. Compared to
the previous two designs, both of the rail and sleeper are the important factors for
satisfying the design constraints. It has an optimal trade-off between the design objectives,
namely the volume increase.
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162 Chapter 7: Development of Embedded IRJ (EIRJ)
(a) Cross section view
(b) Iso view
Figure 7-13: Details of design Solution 3
Although more elegant, both the sleeper and the rail manufacture should be modified
should Solution 3 is adopted.
7.5 SUMMARY
This chapter has presented a procedure for the multi-objective optimisation of the EIRJ
using the second generation non-dominated sorting algorithm (NSGA-II) and a parametric
finite element method. The following conclusions are made based on the result and
discussions presented in this chapter:
1. The EIRJ design retains the structural integrity and electrical insulation, by
eliminating the joint bars and the associated bolt connections. As a result, the joint
bar cracking and bolt loosening/ bolt hole cracking can all be prevented.
163
Chapter 7: Development of Embedded IRJ (EIRJ) 163
2. To satisfy the design constraints (structural displacements) and ensure the stability,
a modified shape of the rail end (both the railhead and web) and the sleeper are
proposed in order to provide the additional stiffness due to the loss of the joint bars
connection. The design objectives are to minimise the volume increase of these two
parts.
3. Through an innovative optimisation modelling coupled with NSGA-II and the
parametric FE model, the non-dominated solutions were obtained with in 100
generations of evolution. All solutions satisfy the design constraints and each
design solution is the trade-off the two design objectives.
4. Three typical optimal solutions from the non-dominated solutions were selected.
The design characteristics and their own advantages towards the practical
application were discussed. In general, the decision maker can select the
appropriate design based on his/her own design requirements through the entire set
of Pareto-optimal solutions.
Based on the conclusions, it is encouraging to further develop the EIRJ design through
field performance studies to fully understand the long term performance of the EIRJ. The
details of the embedding sleeper design, the insulation material manufacture and the
appropriate fabrication of the whole EIRJ structure are necessary and important to be
addressed in future; in this regard the developments in the current practices of slab track
designs are encouraging as it can provide potential synergy with the EIRJ design
development.
165
Chapter 8: Simulation of Field Application of the Optimal IRJs 165
Chapter 8: Simulation of Field Application of
the Optimal IRJ Designs
8.1 INTRODUCTION
Two optimal designs, namely the Stress Minimised Railhead (SMRH) and the Embedded
IRJ (EIRJ), are reported in Chapter 4 and 7 respectively. For minimising computational
effort, various idealisations have been made in their development; important amongst them
are the usage of the elastic railhead material, stationary positioning of loaded wheels (for
SMRH)/ treatment of wheel loads as concentrated point load (for EIRJ) and simplified
boundary conditions in the parametric FE analysis. Clearly, these assumptions contradict
the conditions to which the IRJs are subjected to in the field. The dynamic wheel-rail
contact impact and the rolling of the wheel across the gap of these designs are, therefore,
simulated in the FE environment and reported in this chapter. For this purpose, two field
adaptable designs, termed as improved designs and designated as IMD1 and IMD2 for
simplicity, are derived from the SMRH and the EIRJ and their performance to field
application illustrated through a contact – impact dynamic simulation of a loaded wheel
rolling across the gap. The results of the analysis are presented as the wheel-rail impact
factor, impact rate, peak contact pressure, peak von Mises stress and deflections as the
wheel passing over the joint gap. The sensitivity of several design parameters (wheel load
magnitudes, travelling speed and wheel radius) is discussed and compared the improved
designs with the CIRJ.
8.2 IMPROVED DESIGNS OF IRJ
The improved designs are shown in Figure 8-1.
1. Improved design 1 (IMD1)
Chapter 4 presents the shape optimisation for the stress minmisation at the ―critical‖ zone
of the railhead and has presented the SMRH design; no attention has, however, been
provided to other components of the IRJ. The application of the SMRH in the field is,
166
166 Chapter 8: Simulation of Field Application of the Optimal IRJs
therefore, concieved similar to the CIRJ with only the railhead shape modified
longitudinally as shown in Figure 8-1(a).
(a) IMD1—CIRJ with SMRH
(b) IMD2—EIRJ with SMRH
Figure 8-1: Two improved designs of IRJ
Joint bar
6 bolts and 6 nuts
Rails
SMRH
Modified concrete sleeper
embedding rail ends Insulation
Normal Rails
SMRH
167
Chapter 8: Simulation of Field Application of the Optimal IRJs 167
The IMD1 has generally utilised the same assembling mechanism as the CIRJ, namely the
joint bar jointed rail end using bolt conection. However, the two SCRHs are replaced by
the SMRHs. This new design is only capable of reducing the stress/contact concentration at
the ―critical‖ zone of the rail end, it cannot solve the global failure modes (joint bar
cracking/ bolt hole cracking and bolt loosening) due to the existing complexity of the
design.
2. Improved design 2 (IMD2)
Chapter 7 reports an elaborately modifed design known as the EIRJ. In this design, the
conventional idea of using joint bars and bolt connecting is replaced by a modified wider
sleeper to embed the rail foot and part of rail web into concrete. One (Solution 1) of the
three selected Pareto optimal solutions reported in Chapter 7 is used in the rolling contact
simulation of the loaded wheel across the gap of the EIRJ in this Chapter. Moreover, the
EIRJ is also provided with the SMRH shape obtained from Chapter 4. The geometrical
shape of the IMD2 is shown in Figure 8-1(b).
For simplicity and optimising efficiency in the design optimisation procedures, the wheel
load applications in the numerical models were considerd as a static wheel-rail contact load
in the stress minimisation and a concentrated load in the multi-objective deisgn of EIRJ. In
reality, IRJ is sujected to the dynamic contact-impact under the wheel rolling passage.
Therefore, this chapter reports the dynamic behaviour of IRJ under the wheel rolling
contact-impact. The above two improved designs and the CIRJ were choesn for the
comparative study. Sensitivity study of design and operational parameters were also
conducted to show the robustness of the improved designs developed; these results would
also produce useful conclusions of practical relevance.
8.3 DYNAMIC FE MODELLING
To investigate the dynamic behaviour of the three chosen designs of the IRJs under rolling
contact of the loaded wheels across the gap, a dynamic wheel-rail contact FE model was
developed similar to the modelling techniques reported by Pang (2007). Generally, for
ensuring the accuracy as well as retaining the computational efficiency, the major attibutes
of the dynamic FE model are presented as follows:
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168 Chapter 8: Simulation of Field Application of the Optimal IRJs
8.3.1 IDEALISATION OF GEOMETRY
The two improved designs of the IRJs have been idealised as follows:
1) First, the complex interaction of contacting surfaces amongst various components in
the IMD1 and IMD2 designs was neglected by defining the whole body just as one part
model with several partitions to enable different material definitions. The idealised
geometry of the CIRJ and the IMD1 is shown in Figure 8-2(a); and the simplified
geometry of the IMD2 is shown in Figure 8-2(b).
2) Second, beam elements were connected to the solid elements representing the IRJs
with a view to simulating the continuiting along the longitudinal direction; this
approach also have minimised the computational cost. According to Sun (2003), the
effect of a single loaded wheel on a rail is felt for a distance of 6m on each side of the
wheel contact position along the rail longitudinal direction. Therefore, a full 12m
length of rail model was divided into three parts: the IRJ of length 2400mm in the
middle was modelled using solid elements. The rest of rail parts extended 4800m on
both sides of IRJ was modelled using beam elements. Coupling method was used to
ensure continuity. The solid IRJ model coupled with beam elements is shown in Figure
8-3.
(a) CIRJ & IMD1 (b) IMD2
Figure 8-2: Simplification of contact interaction amongst various components
Insulation
material
Concrete
Steel
169
Chapter 8: Simulation of Field Application of the Optimal IRJs 169
Figure 8-3: IRJ model consisting of solid rail and beam rail
8.3.2 IDEALISATION OF SUPPORT SYSTEM
The complexity of sleepers, ballast and subballast support syetem under IRJ was simplified
as a spring and dashpot system positioned beneath the concrete sleepers. The interaction of
the rail bottom surface was coupled with one end of each spring and dashpot system at a
single reference point that has six DOFs, of which five DOFs except the vertical
displacement DOF were arrested, while the other end was constrained with all of six DOFS
arrested. For the conventional joint bar connected IRJ (CIRJ and IMD1), the concrete
sleepers were discretly supporting around IRJ with even distance of 700mm as shown in
Figure 8-4 (a). The spring stiffness Ks and damping coefficient Cs were set as 30900N/mm
and 14.5Ns/mm respectively. In the IMD2, a modified sleeper with 686mm width was
applied directly under the joint gap as shown in Figure 8-4(b). The spring stiffness Kb and
damping coefficient Cb under the modifed embedding sleeper were selected as
106000N/mm and 50Ns/mm. The rest of sleeper around the EIRJ was also spaced at
700mm with same spring stiffness Ks and damping coefficient Cs.
2400mm 4800mm 4800mm
Solid IRJ model
Beam model Beam model
Solid rail
Rail-beam
170
170 Chapter 8: Simulation of Field Application of the Optimal IRJs
(a) CIRJ and IMD1
(b) Improved design 2 (IMD2)
Figure 8-4: Simplified supporting system different designs of IRJ
8.3.3 IMPLICIT TO EXPLICIT WHEEL-RAIL CONTACT
Due to the limited length of solid rail model along the wheel travelling in the longitudinal
direction, it is very important to attain a steady state of the railhead and the wheel contact
in order to ensure confidence in the solutions of the dynamic contact-impact at the IRJ. To
solve the problem, steady state contact solution was first obtained from an implicit analysis
and the numerical results (the deformed shape, prestresses and strains of the wheel and
IRJ) were transferred into the dynamic explicit analysis.
The implicit solution of wheel-rail static contact was analysed using the FE code
Abaqus/Standard. The wheel was initially positioned at 222mm away from the center of
the joint gap (Figure 8-5). Wheel load was applied to the its centre, and only the vertical
DOFs (DOF2) was activated. The static wheel-rail contact solution was obtained and then
transferred into the dynamic analysis code Abaqus/Explicit to determine the dynamic
behavior at the IRJ. This was accomplished by creating a database file that updates the
geometry and stress history of the explicit elements to match the final static solution. It
should be noted that a spring/dashpot system at wheel centroid was applied in the explicit
anaysis to simulate the wagon supension system. The spring stiffness Kw and the damping
coefficient Cw were set as 220N/mm and 0.138Ns/mm respectively. Same wheel load
700mm 700mm 700mm
Ks Cs
700mm 700mm
Ks Cs
Cb Kb
Embedding
sleeper
171
Chapter 8: Simulation of Field Application of the Optimal IRJs 171
was applied to one end of the spring/dashpot system, the whole solid wheel was assigned
an initial state of the horizontal velocity and the rotational velocity . Only the lateral
DOF (DOF1) was arrested to ensure the contact stability prior to impact. Mass of the wheel
as assigned at the center.
Figure 8-5: Wheel loading and boundary condition in implicit and explicit analysis
The wheel-rail dynamic contact FE model for the three designs are shown in Figure 8-6
(a) CIRJ (b) IMD1
Cw Kw F
F V
Joint gap
222mm
Joint gap
Implicit to Explicit
SMRH SCRH
172
172 Chapter 8: Simulation of Field Application of the Optimal IRJs
(c) IMD2
Figure 8-6: Finite element model of three chosen designs of IRJ
In general, fine mesh and fully integrated elements (C3D8) were used in the contact region
on the top of the railhead and the surface of the wheel. Coarse mesh and reduced integral
elements (C3D8R) were used in other non-contacting region. Approximately 99,132 nodes,
86,338 eight node solid elements (C3D8R) and 48 beam elements were used.
Definition of contact interaction between the surface of the wheel and the railhead surface
is very sensitive to iteration convergence, result accuracy and computational time. The
master/slave contact surface method was employed throughout the static and the dynamic
analyses. Wheel was defined as master contact surface, while the railhead surface was
defined as slave. The contact surface pair is allowed for finite sliding. Coefficient of
friction between them was set as 0.3. In the implicit analysis, the contacting surfaces were
considered hard with a defined limit on the contact pressure-overclosure relationship.
Penalty method was used in each of the iterations. In the explicit analysis, penalty contact
algorithm was adopted, which searched for slave node penetrations in each iteration for
determining the contact forces as a function of the depth of penetration and appling to the
slave nodes for equilibrium. When the master surface was formed by element faces, the
master surface contact forces were distributed to the nodes of the master faces being
penetrated.
SMRH
173
Chapter 8: Simulation of Field Application of the Optimal IRJs 173
8.4 DYNAMIC RESPONSES OF IRJ AT WHEEL CONTACT-IMPACT
This section reports numerical examples of wheel/rail contact impact at the gap of the three
chosen designs of IRJs. The results of the examples are presented as follows:
1. Contact impact force at the gap;
2. Maximum contact pressure as the wheel crossing the joint gap;
3. Maximum von Mises stress as the wheel crossing the joint gap; and
4. Deflections of the rail end as the wheel crossing the joint gap.
A wheel with a vertical load of =130kN was assumed to travel at a speed of 80km/h over
the IRJ. The wheel radius was set as 460mm. The simulations were run on the high
performance computing (HPC) facility at QUT. 4 CPUs and maximum memory allowance
of 4069Mb were allocated for each run. Typical computational time for the combined static
and dynamic analysis was around 3.5 hours.
8.4.1 CONTACT IMPACT FORCE AT IRJ
Dynamic contact force histories for the three chosen designs are presented in Figure 8-7. It
shows that before the wheel reached the joint gap, the contact force remained equal to
130kN (static wheel load) with minor fluctuations. As the wheel moved closer to the joint
gap, a drop in the contact force occurred to all the three designs due to the edge effect of
the rail ends and discontinuity of the material stiffness, resulting in momentary ―loss/
reduction‖ of contact. However, compared to the CIRJ (dropping to 113.9kN or 87% of
static wheel load), the two improved designs (IMD1 and IMD2) with the SMRH have
relatively larger drop, namely 98.6kN (76% of static wheel load) for the IMD1 and 96.5kN
(74% of static wheel load) for the IMD2. It is believed that the higher drop in these two
improved designs is because of the optimal arc shape that reduced the height of the contact
surface, resulting in the travelling wheel losing contact momentarily for a larger distance
compared to the CIRJ.
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174 Chapter 8: Simulation of Field Application of the Optimal IRJs
Figure 8-7: Contact force histories for the three chosen designs
As the wheel landed on the other railhead, impact occurred causing a sharper increase of
the contact force. In the CIRJ, It took approximately 1.1ms for the contact force to increase
from the lowest value of 113.9kN to the peak value of 149kN. The impact factor and
impact rate are defined from the peak and lowest contact forces shown in the insert of
Figure 8-7. For the CIRJ, the impact factor is 1.15 ((149kN-130kN)/130kN); and the
impact rate is 32kN/ms (149kN-113.9kN/1.1ms).
For the two improved designs (IMD1 and IMD2), the peak contact force increased to
153kN and 154kN, taking approximately 1.3ms and 1.4ms respectively. The impact factor
and impact rate are, therefore, 1.18 and 46kN/ms for the IMD1, and 1.19 and 41kN/ms for
the IMD2 respectively. These two values (impact factor and impact rate) indicate that the
optimal arc shape at the railhead ends act as a minor geometrical dip, resulting in higher
peak contact force (5kN = 154kN – 149kN, or an average increase of 5/130 = 3.8%) and
higher impact rate (46kN/ms vs 32kN/ms) of the load increase as the wheel crosses the
joint gap.
The increase of the peak contact force is generally acceptable in the practical application,
especially comparing to the much larger decrease in the magnitude of contact pressure and
40
60
80
100
120
140
160
2 2.002 2.004 2.006 2.008 2.01 2.012 2.014 2.016 2.018 2.02
Con
tact
forc
e (K
N)
Time (s)
CIRJ
IMD1
IMD2
Joint gap Peak contact force
Lowest contact force
175
Chapter 8: Simulation of Field Application of the Optimal IRJs 175
stress levels (discussed in the subsequent sections 8.4.2 and 8.4.3) in spite of the increased
impact.
8.4.2 CONTACT PRESSURE AT IRJ
Contact pressure distribution at the instant of the wheel crossing the joint gap is shown in
Figure 8-8. It shows the differential effect on the contact pressure between the designs with
and without the SMRH at the IRJs.
In the CIRJ with the SCRH, the contact at both of the rail ends extended to the unsupported
rail end. Due to the edge effect, high level of contact pressure occurred to both the shape
corners with the maximum magnitude of 2624MPa.
However, in the improved designs (IMD1 and IMD2) with embedded SMRH, the contact
characteristic of the contact changed entirely.
When the wheel was at the given location (of the mid thickness of the joint gap), the
dynamic analysis result showed that the contact region at both of the railhead top surface
had not extended to the edge. Moreover, the level of the maximum contact pressure
decreased to 1261MPa for the IMD1 and 1372MPa for the IMD2 (from 2624 MPa in CIRJ
– or 52% and 48% of the drop in IMD1 and IMD2 respectively).
This indicates that the adoption of the stress minimised shape has spatially altered the
contact location and avoided the contact pressure singularity at the sharp corners of the
CIRJ under the field condition of dynamic travel of loaded wheels.
176
176 Chapter 8: Simulation of Field Application of the Optimal IRJs
(a) CIRJ
(b) IMD1
(c) IMD2
Figure 8-8: Contact pressure distribution at wheel crossing the joint gap
Wheel
Travelling direction
Joint
gap
Joint
gap
Wheel
Travelling direction
Joint
gap
Wheel
Travelling direction
177
Chapter 8: Simulation of Field Application of the Optimal IRJs 177
8.4.3 VON MISES STRESS DISTRIBUTION AT IRJ
The magnitude of the maximum von Mises stress at the railhead end is presented in Figure
8-9.
(a) CIRJ
(b) IMD1
(c) IMD2
Figure 8-9: Von Mises distribution at wheel crossing the joint gap
Joint
gap Travelling direction
Wheel
Joint
gap Travelling direction
Wheel
Joint
gap Travelling direction
Wheel
178
178 Chapter 8: Simulation of Field Application of the Optimal IRJs
It is an important factor to evaluate and justify the effectiveness of the stress minimised
shape obtained from Chapter 4 under the dynamic wheel-impact at IRJ. Due to the change
of contact described in Section 8.4.2, the magnitude and location of the stress
concentration also exhibited differently between the CIRJ and the two improved designs.
As shown in Figure 8-9, in the CIRJ, the contact singularity resulted in high level of stress
concentration at the sharp corners. The maximum magnitude of von Mises stress was
1168MPa (higher than material yield stress). On the contrast, the other two designs with
the local optimum had the maximum von Mises decreased to 807MPa and 816MPa
respectively (lower than material yield stress of approximately 910MPa).
Furthermore, the location of the stress concentration migrated back to the subsurface of the
railhead, which was similar to the normal wheel-rail Hertzian contact problem involving
half space contact (e.g. CWR). Although the new designs use different assembling
mechanism globally, the optimal stress minimised shape was approved to be effective in
reducing the local stress concentration under the material yield limit. This can, to a great
extent, suppress the metal flow due to severe metal plasticity at the CIRJ and potentially
improve IRJ‘s service duration.
8.4.4 DEFLECTIONS OF RAILHEAD ENDS
To examine whether or not the new designs can satisfy the equivalent structural integrity as
the conventional IRJ, the deflections of the railhead ends as the wheel passing over the
joint gap are compared. The deflection history in the vertical, lateral and longitudinal
directions are presented in Figure 8-10(a), (b) and (c) respectively. When the wheel travels
across the joint gap, it can be seen from Figure 8-10(a) that both of the two improved
designs (IMD1 and IMD2) exhibited lower maximum vertical deflection (3.12mm in the
IMD1 and 3.18mm in IMD2) compared to the CIRJ (3.45mm). It should be noted that the
IMD1 uses the same assembling mechanism (joint-bar connection), but the momentary
maximum vertical deflection was still lower than the CIRJ. This difference inferred that the
SMRH contributed the reduction of the local material deformation. Under the dynamic
wheel contact-impact, the spatial alteration of the contact/stress concentration and the
dramatic reduction of the stress level resulted much lower vertical strain magnitude as
depicted in Chapter 6. The lower strain level contributed the overall reduction of the
vertical deflection at rail end.
179
Chapter 8: Simulation of Field Application of the Optimal IRJs 179
(a) Vertical deflection history
(b) Lateral deflection history
(c) Longitudinal deflection history
Figure 8-10: Deflections as wheel passing over joint gap
1.5
2
2.5
3
3.5
2 2.002 2.004 2.006 2.008 2.01 2.012 2.014 2.016 2.018 2.02
Ver
tica
l def
lect
ion
s (m
m)
Time (s)
CIRJ
IMD1
IMD2
0
0.03
0.06
0.09
0.12
0.15
0.18
2 2.002 2.004 2.006 2.008 2.01 2.012 2.014 2.016 2.018 2.02
Late
ral d
efle
ctio
n (m
m)
Time (s)
CIRJ
IMD1
IMD2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
2 2.002 2.004 2.006 2.008 2.01 2.012 2.014 2.016 2.018 2.02
Lo
ngit
ud
ianl d
efle
ctio
n (m
m)
Time (s)
CIRJ
IMD1
IMD2
180
180 Chapter 8: Simulation of Field Application of the Optimal IRJs
In contrast to the vertical deflection, the lateral and longitudinal deflections (Figure 8-10(b)
& (c)) were found to be similar amongst the three chosen designs.
The IMD2 was proved to be structurally stable and capable of carrying the moving wheel
load with no risk of excessive lateral deformation leading to wheel derailment (gauge
widening derailment); indeed it is realised that the sleeper will have to be designed
appropriately to offer the lateral and longitudinal moment capacities as well as to resist the
torsion induced by the eccentric wheel loading. As such design is implemented in slab
track, adopting the technology for the EIRJ is considered of routine engineering design,
although challenging. This is one of the recommendations reported in this thesis (Chapter
9).
Overall, the investigation of the deflections under the dynamic wheel contact-impact
revealed that both improved designs (IMD1 and IMD2) satisfy the structural requirement
and ensured that an engineering application was possible in field.
8.5 FIELD APPLICATIONS OF THE IMPROVED DESIGNS
These designs of the IRJs have been examined for the performance in the field with
particular attention to the safe passage of loaded wheels across the gap using FE
simulation. The structural response of the three chosen designs of the IRJ were examined
and it was found that the improved designs (IMD1 and IMD2) are equally competitive
from the point of view of safer passage of wheels in tangent tracks. Although the CIRJ can
also handle this aspect satisfactorily, the ―critical‖ zone of the railhead of the CIRJ suffers
from severe stress concentration induced damage. IMD1 and IMD2 designs have
successfully overcome this major problem through fundamental modification to the wheel-
railhead contact in the vicinity of the gap with the provisions of the longitudinal profile
which is an arc of length and depth . However, as the two improved designs are
installed in field, several practical challenges could exist as narrated below:
Manufacturing
The schematic diagram for manufacturing the improved designs is presented in Figure
8-11.
181
Chapter 8: Simulation of Field Application of the Optimal IRJs 181
Figure 8-11: Manufacturing procedure of improved designs of the IRJs
IMD1 is conceived to be the CIRJ with the modified longitudinal profile of the railhead
(SMRH). Therefore, this improved design can be manufactured exactly similar to the CIRJ
with an added grinding process of longitudinal profiling of the railheads (similar to the
manufacturing procedure detailed in experimental study, Chapter 5) prior to assembly.
IMD2 is conceived to be the EIRJ (Chapter 7) with the longitudinal profiling of the
railhead (SMRH). Railheads should, therefore, be ground to the optimal arc shape prior to
the manufacturing of the EIRJ. Once the grinding is completed, a specific length of rail
with the SMRH could be positioned in place in the form work surrounded by the insulating
rubber and then concreted to embed to rail. Once the concrete attained specified strength,
post tensioning applied and transport to site for installation.
Installation
IMD1 is to be installed at site exactly in the same manner as the CIRJ. The rail foot is
positioned on pad and clamped to the sleeper. The far ends of the IRJs (of specific length-
approximately 4m) are then field welded to the continuous rail as shown in Figure 8-12.
AS 60kg rail
Standard Australia
2002
Grinding
SMRH
IMD1
Assembling in factory Sleeper design and
Assemble in factory
IMD2
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182 Chapter 8: Simulation of Field Application of the Optimal IRJs
For the IMD2, the EIRJ can also be installed in traditional manner with only field welding
to the CWR performed.
Figure 8-12: Field installation of the improved designs
Maintenance
As the wheels roll over the railhead in the vicinity of the gap, top surface is worn out; the
SMRH could, therefore, be affected over a period of time. The wheel-rail interaction also
induces Rolling Contact Fatigue (RCF) (in railhead surface and wheel tread). The fatigued
material is actively removed through a rail grinding process involving heavy machinery. In
grinding continuous rails, the cross sectional profile of the railhead is maintained. For
instance, a fatigued railhead with cross section poorly shaped by the rolling wheel are
ground to the original cross sectional profile through the wheel grinding process. Figure
8-13 shows the concept of maintenance of the SMRH in the IMD1 and the IMD2. In this
figure, the optimal arc shape is shown as prescribed by the arc in Chapter 4. Points A and
B represent two ends of the optimal arc shape.
IRJ
IMD1 IMD2
Welding
on site
183
Chapter 8: Simulation of Field Application of the Optimal IRJs 183
Figure 8-13: Grinding process in the vicinity of the SMRH
Assume the railhead is ground to remove the RCF material. The grinding machine will
pass through the IRJ (IMD1 or IMD2) by removing railhead top surface till point C. This
will affect both design variables; will be shortened and will be reduced. It can be seen
that the normal rail grinding process can thus affect the optimal arc shape parameters
making the joint potentially less optimal over its life. It is therefore required to hand grind
the sections such that the profile is moved back to the original optimal arc shape (point A‘
to point B‘). One alternate way of overcoming the problem is to use the ―two-material
technology‖ developed by the EUROSTAR project (Ringsberg et al, 2005) where need for
grinding is minimised due to the Durac 222 laser coating method. The idea here is to fully
laser clad the SMRH. An appropriate cost-benefit analysis will be essential prior to
adopting this technology.
8.6 SENSITIVITY STUDY
There is a range of design and operational parameters that affect the performance of the
IRJs. Some of the parameters are identified in Chapter 2 for the CIRJs. The improved
designs (IMD1 and IMD2) can also be affected by these parameters. To fully understand
Ground railhead surface
Original railhead surface A
A‘ B
B‘
C
l
d
Rail web
Rail foot
Unsupported
rail end
Rail head
Direction of Grinding
184
184 Chapter 8: Simulation of Field Application of the Optimal IRJs
this aspect, sensitivity of three key parameters is reported in this section. The selected three
parameters in this sensitivity study are:
1) Wheel load magnitude: 130kN (loaded heavy haul trains)/30kN (Unloaded heavy
haul trains);
2) Travelling speed: 30km/h, 80km/h, 120km/h;
3) Wheel radius: 460mm/425mm.
Although there are many other design or operation parameters that influence the dynamic
behaviour of the IRJ, the above three parameters were only chosen, because they influence
the contact characteritics in the vicinity of the joint. The sensitivity of these parameters to
the contact impact factor, impact rate, maximum contact pressure, maximum von Mises
stress and deflections at IRJ are presented. Due to a number of analysis and results,
selected result comparison are presented in the reminder of this section. The complete data
can be found in Appendix E.
8.6.1 EFFECT OF LOAD MAGNITUDE
The effect of the load magnitude at travelling velocity of 80km/h on the maximum von
Mises stress and the vertical deflection at IRJ are presnted in Table 8-1and Table 8-2
respectively.
It can be seen from Table 8-1that as the wheel load manitude decrease from 130kN to
30kN (load reduced by 77%). In the convenional design, the difference in railhead stress is
around 45%. Whilst in the improved designs, they are higher up to 61% for both of the two
wheel diameters (460mm/425mm). It demonstrated the stress concentraion level at the
improved designs (IMD1 and IMD2) were consistently lower the CIRJ. Similar
observation can also be found for the maximum contact pressure in Appendix E.
185
Chapter 8: Simulation of Field Application of the Optimal IRJs 185
Table 8-1: Effect of load magnitude on maximum von Mises stress at speed of 80km/h
Wheel
radius
(mm)
CIRJ IMD1 IMD2
max
vonMises
(MPa)
%
Diff.
max
vonMises
(MPa)
%
Diff.
max
vonMises
(MPa)
%
Diff.
Loaded
(130kN) 460
1168
45%
807
61%
815
59% Unloaded
(30kN) 635 323 338
Loaded
(130kN) 425
1213
46%
813
58%
821
67% Unloaded
(30kN) 648 342 356
Table 8-2 shows that for the load reduction of 77%, all of the three designs have provided
approximate 72% difference in the vertical deflection. It indicates that the whole system
behaves linearly without the local edge effect. Similar observation can also be found for
the lateral and longitudinal deflections in Appendix E.
Table 8-2: Effect of load magnitude on vertical deflection at speed of 80km/h
Wheel
Radius
(mm)
CIRJ IMD1 IMD2
Vertical
deflection
(mm)
%
Diff.
Vertical
deflection
(mm)
%
Diff.
Vertical
deflection
(mm)
%
Diff.
Loaded
(130kN) 460
3.450
72%
3.120
72%
3.180
72% Unloaded
(30kN) 0.955 0.864 0.876
Loaded
(130kN) 425
3.490
72%
3.290
73%
3.240
73% Unloaded
(30kN) 0.959 0.881 0.879
8.6.2 EFFECT OF TRAVELLING SPEED
The Effect of travelling speed to the impact factor and the impact rate at wheel load of
130kN and wheel raduis of 460mm is presented in Figure 8-14(a) and (b) respectively.
It shows that the impact factor increases as the travelling speed increases from 30km/h to
120km/h. It can be easily predicted that as the wheel with higher speed ―hit‖ the railhead
end, higher impact force would occurred. Similarly, impact rate increases with the increase
186
186 Chapter 8: Simulation of Field Application of the Optimal IRJs
of the travelling speed. This is due to the reduction of the time used for the wheel passing
over IRJ from one end to the other. The increase of the impact factor and the impact rate at
higher speed is more likely to damage the railhead material in the ―critical‖ zone and
subsequently fail the structural integrity.
The result at wheel load of 30kN and wheel radius of 425mm also exhibited similar trend
as presented in Appendix E.
(a) Impact factor
(b) Impact rate
Figure 8-14: Contact impact facotr and impact rate with different travelling speed
0
0.05
0.1
0.15
0.2
0.25
0.3
20 30 40 50 60 70 80 90 100 110 120
Imp
act
fa
cto
r
Speed (km/h)
CIRJ
IMD1
IMD2
0
10
20
30
40
50
60
70
80
90
100
20 30 40 50 60 70 80 90 100 110 120
Imp
act
ra
te (
kN
/ms)
Speed (km/h)
CIRJ
IMD1
IMD2
187
Chapter 8: Simulation of Field Application of the Optimal IRJs 187
The maximum contact pressure at different travelling speed is shown in Figure 8-15. It
shows that with the increase of the traveling speed, the magnitude of the maximum contact
pressure in the improved designs (IMD1 and IMD2) have always remained much lower
than the CIRJ. More importantly, the effect of the travelling speed to the increase of the
contact pressure is more obvious in the CIRJ, while the improved designs have almost kept
similar with only mariginaly increase. This demonstates that although the impact load
increases with the increase of the tralveling speed, the adoption of the SMRH has
significantly suppressed the edge effect. Similar result can also be observed for the
maximum von Mises stress as presented in Appendix E.
Figure 8-15: Maximum contact pressure at different travelling speed
The vertical deflection at different travelling speed is shown in Figure 8-16. Consistently,
the increase of the impact load due to the increase of the travelling speed contribuet the
graduate increase in the vertical deflection. Similar trend also happened to the lateral and
the longitudinal deflection (Referred to Appendix E) subjected to different wheel load or
wheel radius. In general, the whole system of the IRJ in all of the designs behaved linearly
in terms of defecltion without the consideration of the local responses (contact/stress
concentration). The improved designs can performed well at different traveling speeds.
0
500
1000
1500
2000
2500
20 30 40 50 60 70 80 90 100 110 120
Maxim
um
con
tact
pre
ssu
re (
MP
a)
Speed (km/h)
CIRJ
IMD1
IMD2
188
188 Chapter 8: Simulation of Field Application of the Optimal IRJs
Figure 8-16: Vertical deflection at different travelling speed
8.6.3 EFFECT OF WHEEL RADIUS
The effect of the wheel radius in the all of the numerical results seems not to be sensitive
(Appendix E). Typical result of maximum von Mises stress at wheel speed of 80km/h is
shown in Table 8-3. It can be seen that the difference of the maximum von Mises stress is
only as high as 5.88% in the IMD1 subjected to the wheel load of 30kN. The insensitivity
of the wheel radius to the various dyanmic results provided the confidence of engineering
application of the improved designs into different railways networks.
Table 8-3: Effect of wheel radius on the maximum von Mises stress
Wheel
Radius
(mm)
Wheel
Load
(kN)
CIRJ IMD1 IMD2
max
vonMises
Stress
(MPa)
%
Diff.
max
vonMises
Stress
(MPa)
%
Diff.
max
vonMises
Stress
(MPa)
%
Diff.
460
130
1168
3.85%
807
0.74%
815
0.74%
425 1213 813 821
460 30
635 2.05%
323 5.88%
338 5.33%
425 648 342 356
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
20 30 40 50 60 70 80 90 100 110 120
Ver
tica
l d
efle
ctio
n (
mm
)
Speed (km/h)
CIRJ
IMD1
IMD2
189
Chapter 8: Simulation of Field Application of the Optimal IRJs 189
8.7 SUMMARY
This chapter has presented dynamic behaviour of the CIRJ and two optimal desings
(IMD1 and IMD2) subjected to wheel contact-impact. A few conclusion can be are drawn.
1. The contact impact force in the improved designs are slightly larger (up to 3.8%) than
the CIRJ due to the reduced height of the railhead contact surface in the vicinity of the
joint. Furthermore, in spite of the increase in impact force, the railhead stresses in the
improved designs remained significantly lower than the CIRJ.
2. The maximum contact pressure and the maximum von Mises stress when the wheel is
located in the middle of the joint gap have shown different characteristics between the
CIRJ and the two improved designs. The dynamic analysis further confirmed the
effectiveness and importance of adopting the SMRH from Chapter 4, by reducing the
contact/stress concentration level under the material yield limit and migrating them
away the vulnerable railhead end.
3. The study of the deflections shows that the improved designs satify the current
structural stiffness provided by the CIRJ. In particular, the IMD2 not only meets the
structrual integrity (deflections), but also elimiates the current complexity of using
different components (joint bars and bolt) and fundenmentally eliminating the various
global failures as discussed in Chapter 2.
To exmiane the reliability of the improved designs, sensitivity analysis of three major
parameters, namely the wheel load, travelling speed and the wheel radius were conducted.
Generally, all the plausible observation as mentioned above can still be observed under the
different combination of the three parameters. From a practical perspective, the improved
designs are approved reliable and technical optimal and applicable to the current railway
networks.
191
Chapter 9: Summary & Conclusion 191
Chapter 9: Summary & Conclusions
Insulated rail joint (IRJ) is a safety critical component that provides dual functions, namely
electrical isolation of track circuit for signalling control and adequate structural strength for
safe passage of wheels. Unfortunately, due to geometric discontinuity at rail ends of the
joint gap, the vertical rail ends are often subjected to high level of stress concentration,
leading to severe damages especially at the localised railhead end. Moreover, the
complexity of current designs of IRJs (joint bars and pre-tensioned bolts) results in various
failure modes such as joint bar cracking, bolts loosening and bolt-hole cracking leading to
the functional failure of the IRJs.
With a view to eliminating/ minimising these failure modes, two designs were developed
using novel shape optimisation methods in this thesis. In the first design (Stress Minimised
Railhead (SMRH)), the sharp corner shaped railhead in the conventional IRJ (CIRJ) is
replaced by an arc railhead profile along the longitudinal direction. This design
successfully eliminates the contact pressure and railhead stress singularities the CIRJs
suffer. The second design (Embedded IRJ (EIRJ)) was developed by eliminating the joint
bars and the pre-tensioned bolts in the CIRJ, hence, essentially eliminating the failure
modes these components exhibit. The performance of the improved designs has been
examined using experimental test and finite element methods.
In the development of the SMRH, the optimal shape of the longitudinal railhead profile
was determined using three non-gradient optimisation algorithms (Grid Search Method;
Genetic Algorithm Method and Hybrid Genetic Algorithm Method) coupled with the
parametric finite element method specifically for the evaluation of the objective function
allowing for the nonlinear wheel-rail contact. The optimisation problem was formulated to
minimise the stress concentration subjected to wheel contact load at the rail end. Optimal
shape was obtained through iterative searching evolutions.
The performance of the SMRH was validated and compared with the CIRJ through a full
scale wheel-rail interaction test rig. The test considered a fully supported mechanism at the
rail bottom through embedding half height of the rail web into a concrete footing with a
192
192 Chapter 9: Summary & Conclusion
view to simulating the fixed boundary conditions used in the parametric FE evaluations for
each shape optimisation search cycle. The railhead strains under the loaded wheel
(stationary and repetitive passage) were recorded using strain gauges and a non-contact
digital image correlation method, known as the particle image Velocimetry (PIV). Data
collected from the two recording methods were also compared to the numerical results
predicted by the FE simulation.
The developed EIRJ is an elegant and simplified design by achieving the structural
stiffness of the CIRJ through shaping of the rail end cross section and embedding half
height of the rail ends into a modified concrete sleeper. A multi-objective optimisation
model using Second Generation Non-Dimensional Sorting Genetic Algorithm (NSGA-II)
and parametric finite element method were employed for this purpose. The design
objectives were set to minimising the increase in the volume of the modified rail ends and
the embedding concrete sleeper. Multiple optimal solutions of EIRJ were obtained by
satisfying the three deflection components (vertical, lateral and longitudinal) of the
railhead at the joint gap and ensuring the required structural stiffness for the safe passage
of the loaded wheels. Three optimal solutions were selected, each with varying shapes and
sizes of the rail and sleeper, and their relative merits and demerits were discussed. A
design that made negligible changes to the rail shape and size with the most change
attributed to the sleeper was considered the best for the field adoption – this design is
denoted as EIRJ hereafter.
The relative merits of the improved designs of the IRJ were examined and compared to the
CIRJ using an implicit - explicit finite element simulation of a loaded wheel rolling across
the gap of the various designs of the IRJs. For this purpose two improved designs (IMD1
and IMD2) were identified. IMD1 is a combination of the CIRJ and the SMRH designs;
this design contains joint bars and bolts with the IMD1 IRJ suspended between the sleepers
similar to the CIRJ. IMD2 is a combination of the EIRJ and SMRH designs. These two
improved designs together with the CIRJ were simulated for several key operating and
design parameters that affect their performance under the wheel-rolling contact impact –
especially the wheel diameter and speed of travel. The two improved designs (IMD1 and
IMD2) were found superior to the CIRJ.
193
Chapter 9: Summary & Conclusion 193
9.1 CONCLUSIONS
From the work reported in this thesis, several general and specific conclusions have
emerged as stated in this section.
9.1.1 GENERAL CONCLUSIONS
1. The current designs of the CIRJ suffer from a number of failure modes. Through a
fundamental examination of the failure mechanisms, two new optimal designs have
been developed and is shown that they outperform the CIRJ.
2. The developed Stress Minimised Railhead (SMRH) is shown to eliminate the local
stress singularity commonly found at the SCRH of the CIRJ. Through the optimal
SMRH shape, the magnitude of the stress concentration at the critical zone of the
railhead edge is significantly minimised and its location is shifted away from the
―critical‖ zone of the railhead end into the subsurface of the railhead.
3. Through an experimental study, the SMRH has been shown to exhibit significantly
reduced levels of the vertical, in plane shear and lateral strains. The strain magnitudes
have remained well below the material yield limit typical of head hardened rail steel.
4. The contact patch observed in the experiment after the repetitive rolling of loaded
wheel has revealed that the contact in the SMRH has never extended to the vertical
unsupported railhead end, similar to the prediction from the FE analysis.
5. In the development of EIRJ, the Pareto optimal solutions of EIRJ have shown that
through the minimal increase in the volume of the rail end or the modified concrete
sleeper, structurally adequate designs with stiffness sufficient to sustain the safe
passage of the loaded wheels can be developed for field implementation. The EIRJ
design will provide the benefits of reducing the large number of failure modes the CIRJ
suffers from due to elimination of bolt holes, bolts and joint bars.
6. IMD1 (a combined design of SMRH and CIRJ) is shown to be a simple to manufacture
as it only require an additional process of shaping the longitudinal profile of the heads
of the two rails that form the CIRJ. This design retains the benefits of the SMRH
whilst keeping the process of installation and track maintenance with minimal changes.
7. IMD2 (a combined design of SMRH and EIRJ) requires a new design of the wide
sleeper where the two rails with their head shaped with the SMRH longitudinal profile
194
194 Chapter 9: Summary & Conclusion
embedded to half height into the concrete of the sleeper. This design offers the benefit
of elimination of the various failure modes suffered by the CIRJ.
9.1.2 SPECIFIC CONCLUSIONS
1. In the optimal design of SMRH, the optimisation model based on simple GA coupled
with parametric FEM has converged within 15 generations, whilst the hybrid GA has
provided similar optimal solutions in 8 generations.
2. The optimal values of the design parameters ( and ) defining the arc railhead profile
(for the standard AS60 kg/m rail) along the longitudinal direction are 40.05mm and
1.47mm respectively . This optimal shape is insensitive to the magnitude of the wheel
load and eliminates the contact pressure and railhead stress singularities suffered by the
CIRJ.
3. The SMRH design has shown that the maximum stress always remained less than yield
of the head hardened AS60 kg/m steel.
4. The adoption of hybrid GA can reduce the number of runs (300 in simple GA against
167 in hybrid GA) to search the exact optimal shape predicted by the simple GA.
5. The best performing local control parameters and of this hybrid GA is found to be
0.3 and 0.7 respectively.
6. In the experimental study, PIV technique is shown to capture the vertical, lateral and in
plane shear strains at ―critical‖ zone to a very good level of accuracy compared to the
FE analyses.
7. The multiple optimal solutions obtained from the multi-objective optimisation of the
EIRJ using NSGA-II were obtained within 100 generations of evolution.
8. Dynamic simulation of the two chosen improved designs (IMD1 and IMD2) has shown
that the contact impact force is slightly (3.8%) larger than the CIRJ. In spite of this
marginal 5% increase in impact, the strain remained well below yield.
9. Sensitivity study of wheel load magnitude (130kN/30kN) suggested that the improved
designs always have lower maximum von Mises stress compared to the CIRJ.
Moreover, the deflection linearly increased with the increase of wheel load, showing
elastic behaviour of the whole IRJ system, including the critical railhead zone.
10. The wheel diameters (920mm and 850mm) have shown that the numerical results
exibit negligiible difference, providing confidence for engineering application of the
improved designs into rail networks.
195
Chapter 9: Summary & Conclusion 195
9.2 RECOMMENDATION & FUTURE WORK
There are several recommendations listed as follows which could further improve the study
on the wheel/rail contact impact at the IRJs:
1. The IMD1 is relatively easier to implement in field. Additional grinding procedure is
necessary during the fabrication of the improved design. To exactly measure the
structural performance of the IMD1, a comprehensive field test is necessary. The
plausible results obtained from the FE analysis can be validated from such field test
data. The suitability of the optimal shape of the longitudinal railhead profile of the
SMRH design to the maintenance practice and reshaping of the SMRH in the field at
regular intervals require further examination.
2. To implement the IMD2, more attention needs to be paid on the design and
manufacture of the modified concrete sleeper. The insulation and the assembly between
the modified rail ends and the concrete sleeper are to be studied further. A standard
practice for assembling the EIRJ is required and practically applicable.
3. Testing the performance of EIRJ can be initially performed through laboratory. The
integrity and stiffness of the EIRJ can be investigated through the wheel-rail load rig
described in Chapter 5. Once the laboratory experiments approve its reliability, field
test can be implemented.
197
Reference 197
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Appendices 205
Appendices
APPENDIX A: EXAMPLE OF PARAMETRIC FE MODELING USING PYTHON
An example of parametric FE modelling of a loaded cantilever beam using Python
language is presented as shown in Figure A-1. The geometry of the cantilever beam is
parameterised, namely length , width and height . The upper surface of the cantilever
beam is subjected to the pressure loading . The Python script below incorporates the
geometric modelling, material definition, load and boundary conditions, meshing, FE
analysis and result processing. The extracted result is the deflection at the central point of
the cantilever end.
Figure A-1: A loaded cantilever beam
------------------------------------<<<<< PYTHON script >>>>>----------------------------------
#------------------------------- Assign Value to Design Parameters ------------------------------
=200
=25
=20
=10
#--------------------------- Initialise FE Environment for Modelling ----------------------------
from abaqus import *
import testUtils
testUtils.setBackwardCompatibility()
from abaqusConstants import *
# Create a FE model.
myModel = mdb.Model(name='Beam')
# Create a new viewport in which to display the model and the results of the analysis.
p (MPa)
c(mm)
b(mm)
a(mm)
E, v
Deflection?
206
206 Appendices
myViewport = session.Viewport(name='Cantilever Beam Example', origin=(20, 20),
width=150, height=120)
#---------------------------------------- Geometric Modelling ---------------------------------------
import part
# Create a sketch for the base feature.
mySketch = myModel.ConstrainedSketch(name='beamProfile', sheetSize=250.)
# Create the rectangle using design parameters and .
mySketch.rectangle(point1=(0,0), point2=( , ))
# Create a 3D, deformable cantilever beam using design parameter .
myBeam=myModel.Part(name='Beam', dimensionality=THREE_D,
type=DEFORMABLE_BODY)
myBeam.BaseSolidExtrude(sketch=mySketch, depth= )
#----------------------------------------- Material Definition ----------------------------------------
import material
# Create a material.
mySteel = myModel.Material(name='Steel')
# Create elastic property: Young’s Modulus =209000MPa and Poisson’s Ratio =0.3.
elasticProperties = (209000.0, 0.3)
mySteel.Elastic(table=(elasticProperties, ) )
import section
# Create the solid section.
mySection = myModel.HomogeneousSolidSection(name='beamSection', material='Steel',
thickness=1.0)
# Assign the defined section to the cantilever beam.
region = (myBeam.cells,)
myBeam.SectionAssignment(region=region, sectionName='beamSection')
#---------------------------------------------- Assembly ------------------------------------------------
import assembly
# Create a part instance.
myAssembly = myModel.rootAssembly
myInstance = myAssembly.Instance(name='beamInstance', part=myBeam,
dependent=OFF)
#--------------------------------------- Define Analysis Step -----------------------------------------
import step
# Create a static pressure loading step with time period of 1.0s and initial
incrementation of 0.1.
207
Appendices 207
myModel.StaticStep(name='beamLoad', previous='Initial', timePeriod=1.0, initialInc=0.1,
description='Load the top of the beam.')
#---------------------------- Define Load and Boundary Conditions -----------------------------
import load
# Find the end face using coordinates.
endFaceCenter = ( /2, , 0)
endFace = myInstance.faces.findAt((endFaceCenter,) )
# Create fixing boundary condition at one end of the beam.
endRegion = (endFace,)
myModel.EncastreBC(name='Fixed',createStepName='beamLoad', region=endRegion)
# Find the upper surface of the cantilever beam using coordinates.
topFaceCenter = ( /2, , /2)
topFace = myInstance.faces.findAt((topFaceCenter,) )
# Create a pressure load on the upper face of the cantilever beam.
topSurface = ((topFace, SIDE1), )
myModel.Pressure(name='Pressure', createStepName='beamLoad', region=topSurface,
magnitude= )
#----------------------------------------------- Meshing ------------------------------------------------
import mesh
# Assign an element type to the part instance.
region = (myInstance.cells,)
elemType = mesh.ElemType(elemCode=C3D8I, elemLibrary=STANDARD)
myAssembly.setElementType(regions=region, elemTypes=(elemType,))
# Seed the part instance.
myAssembly.seedPartInstance(regions=(myInstance,), size=5.0)
# Mesh the part instance.
myAssembly.generateMesh(regions=(myInstance,))
# Display the meshed beam.
myViewport.assemblyDisplay.setValues(mesh=ON)
myViewport.assemblyDisplay.meshOptions.setValues(meshTechnique=ON)
myViewport.setValues(displayedObject=myAssembly)
#---------------------------------- Create Set for Interest Point ------------------------------------
# Create the set 'EndPoint'
a = mdb.models['Beam'].rootAssembly
v1 = a.instances['beamInstance'].vertices
verts1 = v1.getSequenceFromMask(mask=('[#1 ]', ), )
a.Set(vertices=verts1, name='EndPoint')
208
208 Appendices
# Create the Deflection Output for the ‘End Point’
regionDef=mdb.models['Beam'].rootAssembly.sets['EndPoint']
mdb.models['Beam'].FieldOutputRequest(name='EndPoint', createStepName='beamLoad',
variables=('U', ), region=regionDef, sectionPoints=DEFAULT, rebar=EXCLUDE)
#------------------------------------ Create Job for Analysis ----------------------------------------
import job
# Create an analysis job for the model and submit it.
jobName = 'beam_tutorial'
myJob = mdb.Job(name=jobName, model='Beam', description='Cantilever beam tutorial')
# Wait for the job to complete.
myJob.submit()
myJob.waitForCompletion()
#----------------------------------------- Extracting Result--------------------------------------------
a = mdb.models['Beam'].rootAssembly
session.viewports['Viewport: 1'].setValues(displayedObject=a)
o3=session.openOdb(name='beam_tutorial.odb')
session.viewports['Viewport: 1'].setValues(displayedObject=o3)
odb=session.odbs['beam_tutorial.odb']
lastFrame = odb.steps['beamLoad'].frames[-1]
Displacement=lastFrame.fieldOutputs['U']
Point = odb.rootAssembly.instances['beamInstance'].nodeSets['EndPoint']
Deflection = Displacement.getSubset(region=Point)
Values=Deflection.values
# Vertical deflection at the ‘End Point’
VerticalDeflection=abs(float("%.4f" %Values.data[1]))
-------------------------------<<<<< PYTHON script end>>>>>----------------------------------
The vertical deflection of the cantilever beam subjected to the pressure load 10MPa as
defined in the Python script is 14.31mm. The FE contour for the vertical deflection of the
whole beam body is shown in Figure A-2.
Figure A-2: FE contour of the vertical deflection of the cantilever beam
Vertical deflection=14.31mm
Fixed end
209
Appendices 209
APPENDIX B: DATA OF STRAIN GAUGES 5, 6, 7 AND 8 AT STATIC WHEEL
LOAD PROGRAME
(a) SCRH
(b) SMRH
Figure B-1: Gauge-5 data.
-2000
-1500
-1000
-500
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
210
210 Appendices
(a) SCRH
(b) SMRH
Figure B-2: Gauge-6 data.
-2000
-1500
-1000
-500
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
211
Appendices 211
(a) SCRH
(b) SMRH
Figure B-3: Gauge-7 data.
-1500
-1000
-500
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
-1200
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
212
212 Appendices
(a) SCRH
(b) SMRH
Figure B-4: Gauge-8 data.
-90
-85
-80
-75
-70
-65
-60
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Original shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
-200
-150
-100
-50
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Optimal shape
Load 30KN Load 50KN
Load 100KN Load 130KN
Load 150KN Load 200KN
213
Appendices 213
APPENDIX C: DATA OF STRAIN GAUGES 5, 6, 7 AND 8 AT THE REPETITIVE
ROLLING OF LOADED WHEEL
Figure C-1: Data of strain gauges 5, 6, 7 and 8 under repetitive rolling of loaded wheel in
SCRH.
Figure C-2: Data of strain gauges 5, 6, 7 and 8 under repetitive rolling of loaded wheel in
SMRH.
0 2 4 6 8 10 12 14 16
105Data points
0
-2000
-1500
-1000
-500
Ver
tica
l str
ain ε
zz(m
icro
stra
in)
30kN
50kN
100kN
130kN
150kN
200kN
0 2 4 6 8 10 12 14 16
105Data points
0
-2000
-1500
-1000
-500 30kN50kN
100kN
130kN
150kN
200kN
Ver
tica
l str
ain ε
zz(m
icro
stra
in)
214
214 Appendices
APPENDIX D: COMPARISON OF VERTICAL STRAIN AT POINTS OF
GAUGES 2, 3, AND 4.
(a) SCRH (b) SMRH
Figure D-1: Comparison of vertical strain at point of Gauge-2.
(a) SCRH (b) SMRH
Figure D-2: Comparison of vertical strain at point of Gauge-3.
(a) SCRH (b) SMRH
Figure D-3: Comparison of vertical strain at point of Gauge-4.
-12000
-10000
-8000
-6000
-4000
-2000
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
-200
-100
0
100
200
300
400
500
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
-5000
-4000
-3000
-2000
-1000
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
-3000
-2500
-2000
-1500
-1000
-500
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
-1400
-1200
-1000
-800
-600
-400
-200
0
5 3 0 -3
Ver
tica
l st
rain
εzz
(mic
rost
rain
)
Wheel position (x coordinate (mm))
Strain gauge at load 30kN
Strain gauge at load 150kN
PIV at load 30kN
PIV at load 150kN
Appendices 215
APPENDIX E: SENSITIVITY OF DESIGN AND OPERATIONAL DESIGN PARAMETERS
Table E-1: Dynamic result at 130kN and 30km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
130kN
(FULLY LOADED WAGON) 30km/h
460mm
Impact Load Factor 0.076 0.094 0.102
Impact Rate (kN/ms) 6.20 9.312 8.453
Max Contact pressure (MPa) 2034 1318 1333
Max Von Mises stress (MPa) 1136 813.5 823.9
Max vertical Deflection (mm) 3.33 3.05 3.13
Max Longitudinal Deflection (mm) 0.27 0.29 0.25
Max lateral Deflection (mm) 0.14 0.15 0.16
425mm
Impact Load Factor 0.086 0.099 0.11
Impact Rate (kN/ms) 6.86 9.60 8.75
Max Contact pressure (MPa) 2046 1334 1351
Max Von Mises stress (MPa) 1177 819.5 826.9
Max vertical Deflection (mm) 3.37 3.13 3.16
Max Longitudinal Deflection (mm) 0.28 0.29 0.27
Max lateral Deflection (mm) 0.15 0.16 0.16
216
216 Appendices
Table E-2: Dynamic result at 130kN and 80km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
130kN
(FULLY LOADED WAGON) 80km/h
460mm
Impact Load Factor 0.15 0.18 0.19
Impact Rate (kN/ms) 31.99 45.72 41.27
Max Contact pressure (MPa) 2115 1298 1321
Max Von Mises stress (MPa) 1168 807 815
Max vertical Deflection (mm) 3.45 3.12 3.18
Max Longitudinal Deflection (mm) 0.29 0.30 0.29
Max lateral Deflection (mm) 0.17 0.17 0.17
425mm
Impact Load Factor 0.16 0.18 0.19
Impact Rate (kN/ms) 34.25 46.09 41.55
Max Contact pressure (MPa) 2078 1310 1339
Max Von Mises stress (MPa) 1213 813 821
Max vertical Deflection (mm) 3.49 3.29 3.24
Max Longitudinal Deflection (mm) 0.29 0.31 0.30
Max lateral Deflection (mm) 0.16 0.17 0.17
217
Appendices 217
Table E-3: Dynamic result at 130kN and 120km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
130kN
(FULLY LOADED WAGON) 120km/h
460mm
Impact Load Factor 0.23 0.26 0.27
Impact Rate (kN/ms) 69.55 88.15 78.99
Max Contact pressure (MPa) 2246 1291 1309
Max Von Mises stress (MPa) 1203 791.5 802.9
Max vertical Deflection (mm) 3.79 3.422 3.5324
Max Longitudinal Deflection (mm) 0.31 0.34 0.32
Max lateral Deflection (mm) 0.17 0.18 0.18
425mm
Impact Load Factor 0.23 0.28 0.28
Impact Rate (kN/ms) 74.88 96.66 83.28
Max Contact pressure (MPa) 2118 1297 1318
Max Von Mises stress (MPa) 1243 801 809
Max vertical Deflection (mm) 3.83 3.53 3.55
Max Longitudinal Deflection (mm) 0.32 0.35 0.33
Max lateral Deflection (mm) 0.17 0.18 0.18
218
218 Appendices
Table E-4: Dynamic result at 30kN and 30km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
30kN
(FULLY LOADED WAGON) 30km/h
460mm
Impact Load Factor 0.090 0.10 0.11
Impact Rate (kN/ms) 1.68 2.24 2.04
Max Contact pressure (MPa) 1123 410.2 413.9
Max Von Mises stress (MPa) 632 286.2 268
Max vertical Deflection (mm) 0.85 0.79 0.794
Max Longitudinal Deflection (mm) 0.069 0.073 0.066
Max lateral Deflection (mm) 0.036 0.039 0.043
425mm
Impact Load Factor 0.099 0.11 0.12
Impact Rate (kN/ms) 1.76 2.31 2.11
Max Contact pressure (MPa) 1128 415.3 417
Max Von Mises stress (MPa) 641 291 271.9
Max vertical Deflection (mm) 0.88 0.82 0.82
Max Longitudinal Deflection (mm) 0.073 0.076 0.070
Max lateral Deflection (mm) 0.039 0.042 0.043
219
Appendices 219
Table E-5: Dynamic result at 30kN and 80km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
30kN
(FULLY LOADED WAGON) 80km/h
460mm
Impact Load Factor 0.18 0.21 0.22
Impact Rate (kN/ms) 8.65 11.38 10.24
Max Contact pressure (MPa) 1133 416 415.1
Max Von Mises stress (MPa) 635 323 338
Max vertical Deflection (mm) 0.955 0.864 0.876
Max Longitudinal Deflection (mm) 0.08 0.081 0.079
Max lateral Deflection (mm) 0.0431 0.046 0.0468
425mm
Impact Load Factor 0.19 0.22 0.22
Impact Rate (kN/ms) 9.72 11.79 10.30
Max Contact pressure (MPa) 1136.2 419.2 418.3
Max Von Mises stress (MPa) 648 342 356
Max vertical Deflection (mm) 0.96 0.88 0.88
Max Longitudinal Deflection (mm) 0.082 0.081 0.079
Max lateral Deflection (mm) 0.045 0.046 0.047
220
220 Appendices
Table E-6: Dynamic result at 30kN and 120km/h
Wheel Load Speed Wheel
Diameter Parameter Examined CIRJ IMD1 IMD2
30kN
(FULLY LOADED WAGON) 120km/h
460mm
Impact Load Factor 0.27 0.33 0.30
Impact Rate (kN/ms) 18.19 23.00 19.44
Max Contact pressure (MPa) 1146.2 431.2 433.3
Max Von Mises stress (MPa) 644 301.2 297.2
Max vertical Deflection (mm) 1.05 0.948 0.979
Max Longitudinal Deflection (mm) 0.086 0.091 0.088
Max lateral Deflection (mm) 0.047 0.051 0.050
425mm
Impact Load Factor 0.32 0.34 0.37
Impact Rate (kN/ms) 21.05 25.03 22.20
Max Contact pressure (MPa) 1151.2 433.2 435.3
Max Von Mises stress (MPa) 658 301 301.2
Max vertical Deflection (mm) 1.06 0.96 0.98
Max Longitudinal Deflection (mm) 0.087 0.091 0.089
Max lateral Deflection (mm) 0.047 0.051 0.051
Appendices 221