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Heavy vehicle suspension testing and analysis – dynamic load sharing
Report
Author: Lloyd Davis Department of Main Roads
Co-Author: Dr. Jonathan Bunker Queensland University of Technology
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1st Edition1st Edition1st Edition1st Edition
MarchMarchMarchMarch 200 200 200 2009999
© State of Queensland © State of Queensland © State of Queensland © State of Queensland (Department of Main Roads) & Queensland University of Technology (Department of Main Roads) & Queensland University of Technology (Department of Main Roads) & Queensland University of Technology (Department of Main Roads) & Queensland University of Technology 2002002002009999
Reproduction of this publication by any means except for purposes permitted under the Copyright Act is prohibited without the prior written permission of the Copyright owners.
Disclaimer This publication has been created for the purposes of road transport research, development, design, operations and maintenance by or on behalf of the State of Queensland (Department of Main Roads) and the Queensland University of Technology. The State of Queensland (Department of Main Roads) and the Queensland University of Technology give no warranties regarding the completeness, accuracy or adequacy of anything contained in or omitted from this publication and accept no responsibility or liability on any basis whatsoever for anything contained in or omitted from this publication or for any consequences arising from the use or misuse of this publication or any parts of it.
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Prepared by Lloyd Davis & Dr. Jon Bunker
Version no. Mk VII
Revision date June 2011
Status final (errata corrected)
DMS ref. no. 890/00037
File/Doc no. 890/00037
File string: C:\backup of hard drive\master copies\suspension load sharing report Mk VII.doc
Corresponding author contact:
Dr Lloyd Davis PhD GDipl(Control) BEng(Elec) Cert(QMgt) CEng RPEQ Fellow, Institution of Engineering & Technology Principal Engineer (Electrical) ITS & E Assets & Operations Division Transport & Main Roads PO Box 70 Spring Hill, Qld, 4004 P 61 (0) 7 3135 5596 M 61 (0) 417 620 582 E [email protected]
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Table of Contents
1 Introduction ....................................................................................................................................... 13
1.1 Background ........................................................................................................................................ 13
1.2 Objectives ........................................................................................................................................... 19
1.3 Scope ................................................................................................................................................... 20
1.4 Rationale............................................................................................................................................. 21
1.5 Organisation of this report............................................................................................................... 24
2 "Quarter-truck" model ...................................................................................................................... 26
2.1 Model of a single air spring of the semi-trailer ............................................................................. 26
2.2 Model of three air springs on one side of a semi-trailer .............................................................. 27
2.3 General................................................................................................................................................ 27
2.4 Input signal ........................................................................................................................................ 28
2.5 Varying the amount of dynamic load sharing .............................................................................. 30
2.6 Varying the amount of dynamic load sharing + attenuation of high frequency air ................ 30
2.7 Varying the amount of dynamic load sharing + altering the dampers .................................... 31
2.8 Transverse air lines - a final note .................................................................................................... 32
2.9 Summary of this section ................................................................................................................... 33
3 Results................................................................................................................................................. 34
3.1 General................................................................................................................................................ 34
3.2 Air spring data - LSF sensitivity analysis ...................................................................................... 36
3.3 FFTs air spring signals from the model.......................................................................................... 37
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3.4 Air spring data - LSF sensitivity analysis with low-pass filters.................................................. 42
3.5 Air spring data - LSF sensitivity analysis with modified shock absorbers ............................... 44
3.6 Air spring forces, LSF sensitivity analysis - modified shock absorbers + LP filters ................ 51
3.7 Summary of this section ................................................................................................................... 52
4 Analysis .............................................................................................................................................. 53
4.1 General................................................................................................................................................ 53
4.2 Perfect dynamic load sharing? ........................................................................................................ 53
4.3 Increasing LSF equals better load sharing? ................................................................................... 55
5 Discussion .......................................................................................................................................... 57
5.1 General................................................................................................................................................ 57
5.2 LSF - how much is beneficial? ......................................................................................................... 58
5.3 Air line sizing and LSF ..................................................................................................................... 59
6 Conclusion.......................................................................................................................................... 63
6.1 General................................................................................................................................................ 63
6.2 Dynamic load sharing - how much load should be transferred? ............................................... 63
Appendix 1. Definitions, Abbreviations & Glossary.................................................................................... 65
References ........................................................................................................................................................... 68
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Table of Figures
Figure 1. Schematic layout of the “Haire suspension system” and standard air suspension system ... 17
Figure 2. Large longitudinal air line (yellow) used in "Haire suspension system". ................................. 17
Figure 3. Showing larger longitudinal air lines connecting - Kenworth Airglide 200 suspension ........ 18
Figure 4. Detail of two Kenworth K104 chassis. ........................................................................................... 18
Figure 5. Detail inside LHS Kenworth K104 chassis in Figure 3. ............................................................... 19
Figure 6. Equalisation of air pressure in the air springs - semi-trailer rolling over a 65mm step.......... 23
Figure 7. Simulink Matlab model of one axle of the semi-trailer.............................................................. 26
Figure 8. Simulink Matlab model of the three axles in the tri-axle group of the semi-trailer. .............. 27
Figure 9. Simplified diagram of multi-axle HV air suspension. ................................................................. 28
Figure 10. Simulink Matlab model - three axles of the semi-trailer with low-pass filters (circled)...... 31
Figure 11. Simulink Matlab model - three axles of the semi-trailer, modified shock dampers. ........... 32
Figure 12. Front axle output from the Simulink Matlab model, LSF = 1.0. ............................................. 35
Figure 13. Middle axle output from the Simulink Matlab model, LSF = 1.0. .......................................... 35
Figure 14. Rear axle output from the Simulink Matlab model, LSF = 1.0................................................ 35
Figure 15. Air spring forces from the model vs. load sharing fraction - 60 km/h. .................................. 36
Figure 16. Air spring forces from the model vs. load sharing fraction - 80 km/h. .................................. 36
Figure 17. Air spring forces from the model vs. load sharing fraction - 90 km/h. .................................. 37
Figure 18. FFT of air spring forces, 60 km/h and LSF of 1 x 10-7................................................................ 38
Figure 19. FFT of air spring forces, 60 km/h and LSF of 1 x 10-6................................................................ 38
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Figure 20. FFT of air spring forces, 60 km/h and LSF of 1 x 10-5................................................................ 39
Figure 21. FFT of air spring forces, 60 km/h and LSF of 1 x 10-4................................................................ 39
Figure 22. FFT of air spring forces, 80 km/h and LSF of 1 x 10-7................................................................ 39
Figure 23. FFT of air spring forces, 80 km/h and LSF of 1 x 10-6................................................................ 40
Figure 24. FFT of air spring forces, 80 km/h and LSF of 1 x 10-5................................................................ 40
Figure 25. FFT of air spring forces, 80 km/h and LSF of 1 x 10-4................................................................ 40
Figure 26. FFT of air spring forces, 90 km/h and LSF of 1 x 10-7................................................................ 41
Figure 27. FFT of air spring forces, 90 km/h and LSF of 1 x 10-6................................................................ 41
Figure 28. FFT of air spring forces, 90 km/h and LSF of 1 x 10-5................................................................ 41
Figure 29. FFT of air spring forces, 90 km/h and LSF of 1 x 10-4................................................................ 42
Figure 30. Air spring forces vs. load sharing fraction - 60 km/h with LP filters. .................................... 43
Figure 31. Air spring forces vs. load sharing fraction - 80 km/h with LP filters. .................................... 43
Figure 32. Air Air spring forces vs. load sharing fraction - 90 km/h with LP filters............................... 44
Figure 33. Air spring forces - modified shock absorbers vs. load sharing fraction - 60 km/h. .............. 45
Figure 34. Air spring forces - modified shock absorbers vs. load sharing fraction - 80 km/h. .............. 46
Figure 35. Air spring forces - modified shock absorbers vs. load sharing fraction - 90 km/h. .............. 46
Figure 36. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-8 .................... 46
Figure 37. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-6 .................... 47
Figure 38. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-4 .................... 47
Figure 39. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-2 .................... 47
Figure 40. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1.0 ........................... 48
Figure 41. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10-8 .................... 48
Figure 42. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10-6 .................... 48
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Figure 43. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10-4 .................... 49
Figure 44. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10-2 .................... 49
Figure 45. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1.0 ........................... 49
Figure 46. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-8 .................... 50
Figure 47. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-6 .................... 50
Figure 48. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-4 .................... 50
Figure 49. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-2 .................... 51
Figure 50. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1.0 ........................... 51
Figure 51. FFT of air spring signals - modified suspension, semi-trailer loaded, 80 km/h, test 97....... 59
Figure 52. FFT of air spring signals - modified suspension, semi-trailer loaded, 90 km/h, test 99....... 59
Figure 53. FFT of air spring signals - std suspension, semi-trailer loaded, 80 km/h, test 136 ............... 60
Figure 54. FFT of air spring signals - std suspension, semi-trailer loaded, 90 km/h, test 138 ............... 60
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Executive Summary
When air-sprung HVs were granted concessions to carry greater mass at the end of
the 1990s, Australian road authorities knew that air-sprung HVs with industry-
standard (or conventionally sized) air lines between air springs did not load share in
the dynamica sense. It was known at the time that concomitant increases in dynamic
wheel loads from air-sprung HV suspensions as a result of ineffective dynamic load
sharing had the potential to cause greater road damage than might otherwise be the
case should air-sprung HVs have incorporated more dynamic load equalisation into
their design (OECD, 1992, 1998).
Noting that perfect load equalisation would give a LSC of 1.0 (Potter, Cebon, Cole,
& Collop, 1996) LSC values (Sweatman, 1983) for steel suspensions were
documented in the range 0.791 to 0.957. Air suspensions were placed somewhere in
the middle of this range with LSCs of 0.904 to 0.925. This was a decade before, and
referenced in, the first OECD report (OECD, 1992). In fine, the effects of poor
dynamic load equalisation were published and known at the time of granting air-
sprung HVs concessions to carry greater mass at the end of the 1990s. With the
clarity of hindsight, the disbenefits due to higher road network asset damage may
not have been recognised as having the potential to discount the societal and
economic benefits of higher HV payloads.
Two reports commissioned by the NTC (Estill & Associates Pty Ltd, 2000;
Roaduser Systems Pty Ltd, 2002) have recommended, inter alia, evaluations of
countermeasures, via testing, which have corrected HV handling problems in air-
suspended HVs. The Roaduser report, p68, recommended tests to assess the effect
of installing larger “pipes” or air lines so that, p31, “longitudinal air flow between
axles is increased; this should improve the load-sharing capability of the suspension;
in both cases where this was implemented, it was reported to fix the problem”
(Roaduser Systems Pty Ltd, 2002). Further, as far back as 2000, the NTC had the
recommendation put to it on p32 of the report by Estill & Associates to “investigate
a Wheel-loads loads were not spread as evenly and as quickly as they could have been during travel of air-sprung
trucks over undulations.
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and evaluate ‘after market improvements’ to air suspensions” from installation of
“larger diameter pipes to supply and exhaust air flow to the bag quickly and hence
improve the response time of the air bag. The modification also reduces the roll and
has improved stability.” (Estill & Associates Pty Ltd, 2000). Since then, the 2005
test programme funded by the Queensland Department of Main Roads (Davis,
2006b) and the 2007 test programme (Davis, 2007; Davis & Kel, 2007) comprise the
only known published testing of HVs with larger longitudinal air lines since those
recommendations were made.
Previous work (Davis, 2006b; Davis & Sack, 2004) has shown that RFS do not load
share dynamically when in multi-axle groups. That testing, in Feb 2003 (Davis &
Sack, 2004), was on a semi-trailer fitted with standard longitudinal air lines (6.5mm
inside diameter, 9.5mm outside diameter). The results showed that the transfer of
air between air springs on the test vehicle was in the order of 3 s. Simple logic
yields that if the axle spacings on a HV are 1m apart at their closest (worst case),
then at 100 km/h (27.7 ms-1
) the reaction time for air to start to transfer between air
springs as described above needs to be in the order of 1/28 s (0.036 s) for any
reasonable dynamic load sharing to occur. This value may be relaxed to about 1/21 s
(0.047 s) for axle spacings of 1.3m at 100 km/h. Hence, air transfer with time
constants in the order of 3 s will not load share dynamically, causing more distress
to the road network than the case where air-sprung HVs have a better ability to load-
share than the current fleet. Quad-axle semi trailers are being introduced to
Australia. If previously the inability of air suspensions to equalise (say) 22.5 t loads
across tri-axle groups resulted in unequal loadings on one axle over another for that
group, the emerging scenario will be 27 t similarly imbalanced within a group of 4
axles. Arising from this, road authorities in Australia, officially or otherwise, are
becoming increasingly concerned that HVs with air springs are not as sympathetic to
the network asset as they might otherwise be. Recent work on tri-axle and quad-axle
semi-trailers (Blanksby, George, Peters, Ritzinger, & Bruzsa, 2008) has
substantiated that load sharing in air-sprung HVs with conventionally sized air lines
does not occur in the dynamic sense, confirming current concerns.
Davis and Bunker (Davis & Bunker, 2008b) described the testing and frequency
spectrum analysis of the suspension forces, including the air springs in three HVs.
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In the results of that study, body-bounce forces predominated in the air spring
spectra, regardless of speed. That study also showed that, as speed increased, so did
the magnitudes of axle-hop and concomitant wheel forces.
Maximum transfer of air from one air spring to its associated rear air spring could be
seen to be an ideal situation for load equalisation. However, the practicality of the
phenomenon of axle-hop requires that some imperfection needs to be introduced into
the transfer mechanism to reduce the possibility of standing waves in the air spring
connector exciting sympathetic oscillations in neighbouring air springs. This
phenomenon has been modelled and the outputs are presented in this report.
Axle inertia combined with suspension damping act to de-couple the pavement
frequencies from the chassis. Alternately, another explanation in systems
engineering terms is the suspension acts as a low-pass filter, isolating high-
frequency road irregularities from the chassis. A result of the suspension design
meeting one of its criteria in that the range of frequencies measured for the unsprung
masses below the axle is not the same as the resonant body bounce frequencies.
This effectively isolates the chassis as much as is possible (and therefore the payload
and/or the passengers) from the harshness and vibration due to pavement
irregularities.
The rationale for work in this field serves both road authorities and the heavy
vehicle industry. The benefits of increasing the load sharing ability between
consecutive axles have been shown previously in the joint QUT/Main Roads project
Heavy vehicle suspensions – testing and analysis. Better load sharing than found on
most current HV suspensions would reduce wheel-forces, reduce body vibrations,
lower chassis and suspension forces and provide a more comfortable ride for
passengers and drivers. The benefits of these measures would be reduced road
damage, reduced payload damage (especially for fragile goods) less fatigued drivers
and passengers and greater life from heavy vehicle chassis, suspension and
coachwork components.
Other work in the joint QUT/Main Roads project Heavy vehicle suspensions –
testing and analysis has postulated that an imperfect transfer of air between air
springs by the use of (say) some constriction device, such as a smaller pipe, to join
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the connection mechanism to the air springs would be advantageous in that it would
damp out pneumatic excitation of resonant frequencies in such air spring systems
(Davis & Bunker, 2008b).
The results and analysis in this report bear out this contention. Increasing load
sharing fraction (LSF) values, implying as lessening of the constrictions between air
springs are useful for reducing dynamic peak loads up to a point. After a particular
value of load sharing fraction, to be determined by other research beyond the scope
of this project, further increases in load sharing fractions between air springs allow
axle hop and the associated ride harshness to be transmitted into the chassis of the
vehicle.
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1 Introduction
1.1 Background
When air-sprung HVs were granted concessions to carry greater mass at the end of
the 1990s, Australian road authorities knew that air-sprung HVs with industry-
standard (or conventionally sized) air lines between air springs did not load share in
the dynamicb sense. It was known at the time that concomitant increases in dynamic
wheel loads from air-sprung HV suspensions as a result of ineffective dynamic load
sharing had the potential to cause greater road damage than might otherwise be the
case should air-sprung HVs have incorporated more dynamic load equalisation into
their design (OECD, 1992, 1998). That poor load sharing as defined by the load
sharing coefficient (LSC) could contribute to increased road network damage was
addressed (OECD, 1992) and estimated as shown in Table 1.
Type of damage ∆ increase in pavement damage (%) due to imperfect load sharing
(LSC= 0.8)
Rutting 43 - 100
Fatigue 23 - 200
Table 1. Pavement damage increase for a load sharing coefficient of 0.8
Noting that perfect load equalisation would give a LSC of 1.0 (Potter et al., 1996),
LSC values (Sweatman, 1983) for steel suspensions were documented in the range
0.791 to 0.957. Air suspensions were placed somewhere in the middle of this range
b Wheel-loads loads were not spread as evenly and as quickly as they could have been during travel of air-sprung
trucks over undulations.
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with LSCs of 0.904 to 0.925. This was a decade before, and referenced in, the first
OECD report (OECD, 1992). In fine, the effects of poor dynamic load equalisation
were published and known at the time of granting air-sprung HVs concessions to
carry greater mass at the end of the 1990s. With the clarity of hindsight, the
disbenefits due to higher road network asset damage may not have been recognised
as having the potential to discount the societal and economic benefits of higher HV
payloads. Nonetheless, there is now a growing recognition of (and therefore
renewed research effort into) the phenomenon of imperfect dynamic load sharing
within air-sprung HV suspension groups. This is not before time.
Two reports commissioned by the NTC (Estill & Associates Pty Ltd, 2000;
Roaduser Systems Pty Ltd, 2002) have recommended, inter alia, evaluations of
countermeasures, via testing, which have corrected HV handling problems in air-
suspended HVs. The Roaduser report, p68, recommended tests to assess the effect
of installing larger “pipes” or air lines so that, p31: “longitudinal air flow between
axles is increased; this should improve the load-sharing capability of the suspension;
in both cases where this was implemented, it was reported to fix the problem”
(Roaduser Systems Pty Ltd, 2002). Further, as far back as 2000, the NTC had the
recommendation put to it on p32 of the report by Estill & Associates to “investigate
and evaluate ‘after market improvements’ to air suspensions” from installation of
“larger diameter pipes to supply and exhaust air flow to the bag quickly and hence
improve the response time of the air bag. The modification also reduces the roll and
has improved stability.” (Estill & Associates Pty Ltd, 2000). Since then, the 2005
test programme funded by the Queensland Department of Main Roads (Davis,
2006b) and the 2007 test programme (Davis, 2007; Davis & Kel, 2007) comprise the
only known published testing of HVs with larger longitudinal air lines since those
recommendations were made.
Dynamic load sharing can be defined as the equalisation of the axle group load
across all wheels/axles under typical travel conditions of a HV (that is, in the
dynamic sense at typical travel speeds and operating conditions of that vehicle).
Attempting to quantify this concept has resulted in a number of methods proposed
and documented (Sweatman, 1983), amongst which were the load sharing
coefficient (LSC) and the dynamic load coefficient (DLC). Potter (1996) clarified
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various methods for quantitative derivation of measures to describe the ability of an
axle group to distribute the total axle group load during travel. Despite this work,
that of Mitchell & Gyenes (1989) and Gyenes (1994), more recently Potter et al.
(1997) and Fletcher (2002), there is no agreed testing procedure to define or measure
dynamic load sharing at the local nor national level in Australia. The Australian
specification for RFS, VSB 11 (Australia Department of Transport and Regional
Services, 2004c), does not address dynamic load sharing.
Even if dynamic load sharing is too complex to define, the issue of static load
sharing has proven to be, paradoxically, equally elusive; even given that it is a
somewhat simpler concept than its dynamic counterpart. The Australian
specification for RFS, VSB 11 (Australia Department of Transport and Regional
Services, 2004c), nominates that RFS suspensions must have static load sharing, to a
defined value, “between axles in the axle group”. Surprisingly, it does not define a
formal methodology (Prem, Mai, & Brusza, 2006) to determine a static load sharing
value; that detail has been left to a method suggested in a monograph (official status
unknown) issued by Mr KC Wong of DoTaRS.
Previous work (Davis, 2006b; Davis & Sack, 2004) has shown that RFS do not load
share dynamically when in multi-axle groups. That testing, in Feb 2003 (Davis &
Sack, 2004), was on a semi-trailer fitted with standard longitudinal air lines (6.5mm
inside diameter, 9.5mm outside diameter). The results showed that the transfer of
air between air springs on the test vehicle was in the order of 3 s. Simple logic
yields that if the axle spacings on a HV are 1m apart at their closest (worst case),
then at 100 km/h (27.7 ms-1
) the reaction time for air to start to transfer between air
springs as described above needs to be in the order of 1/28 s (0.036 s) for any
reasonable dynamic load sharing to occur. This value may be relaxed to about 1/21 s
(0.047 s) for axle spacings of 1.3m at 100 km/h. Hence, air transfer with time
constants in the order of 3 s will not load share dynamically, causing more distress
to the road network than the case where air-sprung HVs have a better ability to load-
share than the current fleet. Recent work on tri-axle and quad-axle semi-trailers
(Blanksby et al., 2008) has substantiated that load sharing in air-sprung HVs with
conventionally sized air lines does not occur in the dynamic sense, confirming the
current concerns.
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Quad-axle semi trailers are being introduced to Australia. If previously the inability
of air suspensions to equalise (say) 22.5 t loads across tri-axle groups resulted in
unequal loadings on one axle over another for that group, the emerging scenario will
be 27 t similarly imbalanced within a group of 4 axles. Arising from this, road
authorities in Australia, officially or otherwise, are becoming increasingly concerned
that HVs with air springs are not as sympathetic to the network asset as they might
otherwise be.
A test programme to gather data on HV suspension dynamics was executed in 2007
(Davis & Bunker, 2008b). One HV used for the testing was a tri-axle semi-trailer
towed by a prime mover. Instrumentation consisting of strain gauges,
accelerometers and air pressure transducers (APTs) was installed on the tri-axle
group of the semi-trailer.
Before (standard longitudinal air lines) and after (the “Haire suspension system”)
testing was performed with the vehicles loaded to as close as practicable to full legal
axle masses and driving them on typical, uneven roads at speeds from 40 km/h to 90
km/h. Quasi-static testing was performed on the instrumented axles to determine
empirical values for damping ratio and body-bounce (Davis & Kel, 2007; Davis,
Kel, & Sack, 2007).
The “Haire suspension system” is a proprietary suspension system that connects
heavy vehicle air springs using larger-than-standard diameter air lines longitudinally
as shown in Figure 1. Note that, referring to Figure 1 (some detail has been removed
for clarity): larger air lines (in black) run longitudinally and connect the air springs
fore-and-aft. The transverse air line is left as standard for fitment of this system.
Figure 1 shows the larger longitudinal air lines for the semi-trailer but the
arrangement shown was typical for each air bag on axle/s of interest for this series of
tests.
The manufacturer of the “Haire suspension system” has claimed that, by installation
of this proprietary system, air-sprung heavy vehicle (HV) suspensions may be made
“friendlier” than air-sprung HV suspensions possessing Australian industry-standard
sized longitudinal air lines.
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HV suspension testing – dynamic load sharing analysis
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Figure 1. Schematic layout of the “Haire suspension system” (left) and standard air suspension
system (right).
Figure 2. Large longitudinal air line (yellow) used in "Haire suspension system".
The “Haire suspension system” is not the only proprietary suspension system that
connects heavy vehicle air springs using larger-than-standard diameter air lines
longitudinally, however. Figure 3 to Figure 5 show details of the Airglide 200
suspension system as fitted to a Kenworth K104 chassis. Note the larger
longitudinal air lines connected to the air spring top plate (Figure 3) and the larger
longitudinal air lines between air springs (green arrow, Figure 5).
Regarding Figure 5, note also the standard-sized transverse air line (blue arrow).
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From the approaches by both Kenworth and the developers of the "Haire suspension
system", clearly there is a place for larger longitudinal air lines between air springs
on HVs. The alterations to wheel forces, air spring forces and dynamic load sharing
have been documented previously (Davis, 2006b, 2007, 2008; Davis & Bunker,
2008b; Davis & Kel, 2007; Davis & Queensland Department of Main Roads, 2006a,
2006b). More results from the 2007 test programme are scheduled in future
publications.
Figure 3. Showing larger longitudinal air lines connecting into the air spring of a Kenworth
Airglide 200 suspension on a K104 chassis.
Figure 4. Detail of two Kenworth K104 chassis.
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Figure 5. Detail inside LHS Kenworth K104 chassis in Figure 3.
1.2 Objectives
The QUT/Main Roads project Heavy vehicle suspensions – testing and analysis
continues to consider the mechanism of load sharing between axles on air-sprung
HVs. In addition to other activities outlined for the project (Davis & Bunker, 2007)
this report presents:
� the development of a computer model of three consecutive air springs on one
side of a semi-trailer suspension;
� incorporation into that model of a load sharing fraction (LSF) with the ability
to allocate a variable proportion of air distribution between air springs;
� the results of a sensitivity analysis varying the LSF through a wide range of
values;
� the resultant peak forces and force standard deviations in the air springs from
that sensitivity analysis; and
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� fast Fourier transform (FFT) frequency-spectrum analysis of the air spring
signals for varying LSF values.
This is, in part, to inform the project Heavy vehicle suspensions – testing and
analysis as well as to contribute to research into HV suspensions by documenting
reference data for future analysis by other researchers.
1.3 Scope
It is noted that, whilst VSB 11 (Australia Department of Transport and Regional
Services, 2004a) defines a limited scope for HV load sharing, it does not address
transverse load sharing, only load sharing between axles (i.e. front-to-back load
sharing). Accordingly, the unmodified transverse air lines of the “Haire suspension
system”, Kenworth's Airglide 200 and the lack of definition of load sharing between
wheels on the same axle require this report to confine its scope to the effects of
improving “front-to-back” air flow between axles.
The scope of this report is:
� time-domain analysis of air spring peak forces;
� time-domain analysis of standard deviations of air spring forces; and
� frequency-domain analysis of the air spring forces
from a model of a semi-trailer suspension system. That model, its development and
validation has been documented previously (Davis & Bunker, 2008a). The model
used for the analysis in this report used accelerometer data gathered from on-road
testing with the HV at full load as an input. The model output was for three
consecutive air springs as installed in a typical instillation on a semi-trailer with
1.4m axle spacing. As mentioned above, VSB 11 does not deal with transverse load
sharing. Increasing this feature in air sprung HV suspensions would result in more
body-roll; this report and its model suspension will be confined to "front-to-back" or
longitudinal load sharing ability.
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1.4 Rationale
In the 1980s and 1990s a great effort in Europe went into in the research and testing
of HV suspensions and their effects on bridges and pavements from the dynamic
loading of air-sprung heavy vehicles (OECD, 1992, 1998). Within these
programmes, Gillespie et al. (1993) noted that static loads were equalised in most
HV multi-axle suspension configurations but that load sharing in the dynamic sense
varied markedly between different suspension designs. Referring to the final report
of the DIVINE project, p77 (OECD, 1998), authors’ italics for emphasis:
“…large dynamic responses and multiple fatigue cycles were observed. These
responses were up to 4.5 times the dynamic load allowance specified in bridge
design. Where axle hop was not induced, the dynamic response was much smaller.
A probable explanation for this is the fact that the very limited dynamic load sharing
in air suspensions allows the axles in a group to vibrate in phase at axle-hop
frequencies. “Crosstalk” between conventional steel leaf suspensions limits this
possibility…”
The final DIVINE report from the OECD (1998), was used in Australia to support
the argument that air-sprung heavy vehicles (HVs) should carry greater mass under
the micro-economic reform popular at the time. That report acknowledged:
� these types of suspensions did not load share in the dynamic sense; and
� the nature of the design of air suspensions was such that they created greater
dynamic loads than loads induced in conventional steel suspensions under
similar circumstances.
Nonetheless, that report was used in Australia to justify the introduction of air-
sprung HVs at HML loads. The implications of this decision with respect to
allowing heavier HVs with greater axle loads (and, later, more axles) onto the road
network with untested and undefined load sharing ability have been dealt with
previously (Davis & Bunker, 2007). The result was HVs carrying more mass in
return for, amongst other requirements, having “road friendly” suspensions (RFS).
The first “road friendly” suspensions were air-sprung and most still are, although
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some steel RFS have been certified in the recent past (Australia Department of
Transport and Regional Services, 2004b).
Reassessment of the research into the dynamic forces imparted to road assets by air-
sprung HVs has revealed that the original research showed very clearly that transfer
of air within a HV axle group was not a feature of air suspensions (Simmons, 2005),
particularly “front-to-back” sharing, that is; between consecutive axles. Subsequent
review of that work has now confirmed that small longitudinal air lines do not allow
quick movement of air between air springs on sequential HV axles (Davis, 2006b;
Davis & Sack, 2004). This reassessment has shown that the original research in the
1980s and 1990s indicated very clearly that transfer of air within a HV axle group
was not a feature of air suspensions (Simmons, 2005). Mr. Simmons tested air
suspended HVs with various longitudinal air pipe sizes between 8mm and 12mm
outside diameter and co-authored reports in this field (Gyenes & Simmons, 1994;
Simmons & Wood, 1990). He noted (2005) “these pipe sizes will not provide
dynamic equalisation as there will not be sufficient transfer between displacers [air
springs]...”
Karamihas and Gillespie put it more bluntly, p37 (Karamihas & Gillespie, 2004):
“Air spring suspensions do not possess a dynamic load sharing mechanism.”
The inability of conventional air suspensions to load share dynamically in “front-to-
back” equalisation mode (i.e.; between consecutive axles) and with a time constant
necessary for road travel was confirmed by Davis and Sack (2004). That work
measured, inter alia, the air pressure in the high-pressure supply to the air springs of
a quad-axle semi-trailer as it was driven over a 65mm step-down profile at 5km/h.
The “base case” for that programme of work was on vehicles with standard
longitudinal air lines of 6.5mm inside diameter and 9.5mm outside diameter.
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Figure 6. Equalisation of air pressure in the air springs of a quad-axle semi-trailer rolling over
a 65mm step-down profile.
The equalisation of air pressure during that process is shown in Figure 6 (Davis &
Sack, 2004), showing that equalisation during and after the 2nd
axle passed over the
step took approximately 3 s. Given that HV axles at highway travel speeds traverse
the same point on the road surface separated by about 1/20 s, 3 s is too slow for any
sort of effective and pragmatic dynamic load equalisation to occur. Given a 3 s
time-constant for air transfer (Davis & Sack, 2004), HVs with conventionally-sized
air lines are not having their air-spring pressures equalised within time-scales with
similar orders of magnitude as the time-scales of wheel-force impacts between
consecutive axles at highway speeds. This does not allow effective dynamic load
equalisation between successive axles within an air-sprung multi-axle group during
typical operation. This phenomenon creates the potential for unnecessarily high
pavement and suspension loads, with respect to the other axles in the group, when
any given wheel encounters a bump. Confirmation of this effect has continued in
recent work (Blanksby et al., 2008).
The rationale for work in this field serves both road authorities and the heavy
vehicle industry. The benefits of increasing the load sharing ability between
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consecutive axles have been shown previously in the joint QUT/Main Roads project
Heavy vehicle suspensions – testing and analysis. Better load sharing than found on
most current HV suspensions would reduce wheel-forces, reduce body vibrations,
lower chassis and suspension forces and provide a more comfortable ride for
passengers and drivers. The benefits of these measures would be reduced road
damage, reduced payload damage (especially for fragile goods) less fatigued drivers
and passengers and greater life from heavy vehicle chassis, suspension and
coachwork components.
Commercial applications of larger air lines in HV suspensions have been deployed
on Australian roads. Innovative suspension systems from Kenworth and the “Haire
suspension system” utilise larger-than-standard longitudinal air lines (Figure 1 to
Figure 5). Any alteration to dynamic load sharing arising from changing the size of
air-spring HV suspension air lines need to be investigated adequately.
1.5 Organisation of this report
The body of this report for the project Heavy vehicle suspensions – testing and
analysis is organised as follows:
Section 1, “Introduction” outlines a general summary of the issues surrounding the
dynamic load equalisation for air-sprung HV suspensions and sets out the scope and
rationale for this report;
Section 2, “"Quarter-truck" model” documents the development of the model used to
provide the data analysed later in the report;
Section 3, “Results” provides the background to the derivation of the forces
measured in this test programme;
Section 4, “Analysis” introduces the appendices showing the results of the FFT plots
for the dynamic forces at the air springs and wheels. Accelerometer data is also
introduced as a reference for this project and future research;
Section 5, “Discussion” outlines where the research has found differences in the two
test cases and proposes further avenues of endeavour, both for the project Heavy
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vehicle suspensions – testing and analysis and further post-graduate research that
may prove useful; and
Section 6, “Conclusion” sums up the report with conclusions drawn from the
previous three sections.
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2 "Quarter-truck" model
2.1 Model of a single air spring of the semi-trailer
The development and validation of the model shown in Figure 7 has been
documented and validated in earlier work for the QUT/Main Roads project Heavy
vehicle suspensions – testing and analysis (Davis & Bunker, 2008a). The inputs to
the model were the accelerometer signals (Signal 2 in Figure 7) from the hub of a
wheel on a 3-axle semi-trailer. The output of the model was the air spring signal as
measured at the "Scope" block in Figure 7. The accelerometer signals were derived
empirically and validated against the empirical signals measured from the air springs
(Davis & Bunker, 2008a, 2008b).
spring k
427 .18
rebound damping
coefficient
28 .86
count /g
-K- bump damping
coefficient
18 .45
air spring
pressure
scaling
factor
-K-
add 2
add 1
add
Signal Builder
Signal 2
Scope
Integrating
y double dot
1
s
Integrating
y dot
1
s
Integrating
x double dot
1
s
Integrating
x dot
1
s
1/ms
1/2.9
- ve limiter
+ve limiter
y double dot
ms*x double dot
y
xx double dot x dot
y dot
Figure 7. Simulink Matlab
model of one axle of the semi-trailer.
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2.2 Model of three air springs on one side of a semi-trailer
2.3 General
Regarding the model in Figure 7, connecting three of these axle models in series
allowed the implementation of a model of the air springs on one side of a 3-axle
semi-trailer. This arrangement is shown in Figure 8.
spring k2
427 .18
spring k1
427 .18
spring k
427 .18
rebound damping
coefficient 2
28 .86
rebound damping
coefficient 1
28 .86
rebound damping
coefficient
28 .86 load sharing fraction
0.01
counts/ms^(-2)rear axle
-K-
counts/ms^(-2)middle axle
-K-
counts/ms^(-2)front axle
-K-
bump damping
coefficient 2
18 .45
bump damping
coefficient 1
18 .45
bump damping
coefficient
18 .45
air spring
pressure
scaling
factor 2
-K-
air spring
pressure
scaling
factor 1
-K-
air spring
pressure
scaling
factor
-K-
add 8
add 7
add 6
add 5
add 4
add 3
add 2
add 1
add
Transport
Delay 1
Transport
Delay
Signal Builder
Signal 2
Scope 2
Scope 1
Scope
Integrating
y double dot 2
1
s
Integrating
y double dot 1
1
s
Integrating
y double dot
1
s
Integrating
y dot 2
1
s
Integrating
y dot 1
1
s
Integrating
y dot
1
s
Integrating
x double dot 2
1
s
Integrating
x double dot 1
1
s
Integrating
x double dot
1
s
Integrating
x dot 2
1
s
Integrating
x dot 1
1
s
Integrating
x dot
1
s
Add 6
1/ms2
1/2.9
1/ms1
1/2.9
1/ms
1/2.9
-ve limiter 1
- ve limiter 2
- ve limiter
+ve limiter 2
+ve limiter 1
+ve limiter
y
xx double dot x dot
y dot
y double dot
y
xx double dot x dot
y double dot
ms*x double dot
y
xx double dot x dot
y dot
y dot
ms*x double dot
ms*x double dot
y double dot
Figure 8. Simulink Matlab
model of the three axles in the tri-axle group of the semi-trailer.
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For the purposes of this report, the input to the three-spring model was empirical
accelerometer data from the hub of the front wheel on a 3-axle semi-trailer (Davis &
Bunker, 2008b). This data was entered per test speed via the "Signal builder" block,
upper LHS Figure 8. The outputs from the model were the analogues of the air
spring signals as measured at the "Scope" blocks in Figure 8.
2.4 Input signal
Consider the simplified diagram of one side of a HV with air suspension in Figure 9.
Assume that all wheels are of equal mass, all axles are of equal mass, etc.
Figure 9. Simplified diagram of multi-axle HV air suspension.
Considering Figure 9 the time delay between successive wheels travelling over a
bump encountered by one side of the HV may be denoted:
t = d / v Equation 1
where:
v = speed (ms-1
);
d = distance between the axles (m); and
t = time in s.
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The diagram in Figure 9 shows the axle spacing at 1.4m. This was the axle spacing
for the semi-trailer used for the testing (Davis & Bunker, 2008b) from which the
data for the simulation on this report was taken.
The time between two successive wheels encountering the same pavement
imperfection is dependent on travel speed (Equation 1). The time between
sequential axles passing the same spot on the pavement for 1.4 m axle spacing is
shown in Table 2, therefore.
speed (km/h)
elapsed time between axles
(ms)
60 0.084
80 0.063
90 0.056
Table 2. Relationship between different speeds and the elapsed time between wheels at 1.4 m
spacing.
For the purposes of the exercise in this report, empirical accelerometer signals were
used as the input to the model. These accelerometer signals were gathered by
driving a test vehicle at speeds ranging from 60 to 90 km/h over typical suburban
and highway road segments in Brisbane (Davis & Bunker, 2008b).
Since each wheel passed over the same point, it is reasonable to use the same
accelerometer signal applied to each air spring and separate these signals by the time
delay representing the time between each wheel (Equation 1). Accordingly, the
accelerometer signal from the front wheel was used as an input to each subsequent
wheel; the delay being the travel time between wheels as the particular wheel
reaches the same irregularity on the road surface encountered by its immediate front
neighbour. The time delay between axles was provided by the "transport delay"
blocks on the LHS of Figure 8. This was dependant on travel speed and was as
shown in Table 2.
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2.5 Varying the amount of dynamic load sharing
The amount of dynamic load sharing between the air springs was introduced as a
fraction in a gain block connecting the air springs together. This was denoted the
load sharing factor (LSF). It was not related to any other load sharing variable or
load sharing metric, such as LSC; it merely represented the proportion of air allowed
to travel to from one air spring to the other air springs. Alternately, it may be
thought of as representing the transmission of air through the manifold connecting
the air springs down one side of the semi-trailer. Figure 8 shows this as 0.01. The
modelling varied the values of the LSF from 1 x 10-8
to 1.0.
2.6 Varying the amount of dynamic load sharing plus adding some attenuation of higher frequency air pulses in the air lines
After varying the amount of dynamic load sharing as a fraction, further iterations
were performed in the process of determining outcomes for different parametric
variables of the model. This arose from the results that showed that, above certain
values of LSF, axle-hop could be transmitted more readily between air springs. This
will be shown later but is mentioned here as part of the rationale for the introduction
of a low-pass filter in the transfer of air between air springs. This addition was to
determine if, by attenuating axle-hop influences within the air lines, a greater
proportion of low-frequency air redistribution would be more effective for dynamic
load sharing. The iteration after the process described in section 2.5 used a low-pass
filter with a 3 Hz knee-point between each of the Simulink Matlab
models’ air
springs and the main transfer manifold as shown in the circles in Figure 10.
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spring k2
427 .18
spring k1
427 .18
spring k
427 .18
rebound damping
coefficient 2
28 .86
rebound damping
coefficient 1
28 .86
rebound damping
coefficient
28 .86 load sharing fraction
.000012
counts /ms^(-2)rear axle
-K-
counts/ms^(-2)middle axle
-K-
counts /ms^(-2)front axle
-K-
bump damping
coefficient 2
18 .45
bump damping
coefficient 1
18 .45
bump damping
coefficient
18 .45
air spring
pressure
scaling
factor 2
-K-
air spring
pressure
scaling
factor 1
-K-
air spring
pressure
scaling
factor
-K-
add 8
add 7
add 6
add 5
add 4
add 3
add 2
add 1
add
Transport
Delay 1
Transport
Delay
Signal Builder
Signal 2
Scope 2
Scope 1
Scope
Integrating
y double dot 2
1
s
Integrating
y double dot 1
1
s
Integrating
y double dot
1
s
Integrating
y dot 2
1
s
Integrating
y dot 1
1
s
Integrating
y dot
1
s
Integrating
x double dot 2
1
s
Integrating
x double dot 1
1
s
Integrating
x double dot
1
s
Integrating
x dot 2
1
s
Integrating
x dot 1
1
s
Integrating
x dot
1
s
Analog
Filter Design 4
butter
Analog
Filter Design 3
butter
Analog
Filter Design
butterAdd 6
1/ms2
1/2.9
1/ms1
1/2.9
1/ms
1/2.9
-ve limiter 1
- ve limiter 2
- ve limiter
+ve limiter 2
+ve limiter 1
+ve limiter
y
xx double dot x dot
y dot
y double dot
y
xx double dot x dot
y double dot
ms*x double dot
y
xx double dot x dot
y dot
y dot
ms*x double dot
ms*x double dot
y double dot
Figure 10. Simulink Matlab
model of the three axles in the tri-axle group of the semi-trailer
with low-pass filters (circled).
2.7 Varying the amount of dynamic load sharing and altering the damping coefficients of the shock absorbers
After varying the amount of dynamic load sharing as a fraction, further iterations
were performed in the process of determining outcomes for different parametric
variables of the model. This iteration used the damper bump and rebound
parameters from a passenger coach (Davis & Bunker, 2008a) instead of a semi-
trailer. The alterations to the damping coefficients of the suspension dampers
(circled) are shown Figure 11.
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HV suspension testing – dynamic load sharing analysis
32
spring k2
427 .18
spring k1
427 .18
spring k
427 .18
rebound damping
coefficient 2
34
rebound damping
coefficient 1
34
rebound damping
coefficient
34
counts/ms^(-2)rear axle
-K-
counts /ms^(-2)middle axle
-K-
counts /ms^(-2)front axle
-K-
bump damping
coefficient 2
6
bump damping
coefficient 1
6
bump damping
coefficient
6
amount of load sharing
1
air spring
pressure
scaling
factor 2
-K-
air spring
pressure
scaling
factor 1
-K-
air spring
pressure
scaling
factor
-K-
add 8
add 7
add 6
add 5
add 4
add 3
add 2
add 1
add
Transport
Delay 1
Transport
Delay
Signal Builder
Signal 2
Scope 3
Scope 2
Scope 1
Integrating
y double dot 2
1
s
Integrating
y double dot 1
1
s
Integrating
y double dot
1
s
Integrating
y dot 2
1
s
Integrating
y dot 1
1
s
Integrating
y dot
1
s
Integrating
x double dot 2
1
s
Integrating
x double dot 1
1
s
Integrating
x double dot
1
s
Integrating
x dot 2
1
s
Integrating
x dot 1
1
s
Integrating
x dot
1
s
Add 6
1/ms2
1/2.9
1/ms1
1/2.9
1/ms
1/2.9
-ve limiter 1
- ve limiter 2
- ve limiter
+ve limiter 2
+ve limiter 1
+ve limiter
y
xx double dot x dot
y dot
y double dot
y
xx double dot x dot
y double dot
ms*x double dot
y
xx double dot x dot
y dot
y dot
ms*x double dot
ms*x double dot
y double dot
Figure 11. Simulink Matlab
model of the three axles in the tri-axle group of the semi-trailer
with modified shock absorber characteristics (circled).
2.8 Transverse air lines - a final note
Since transverse air lines are not altered in any of the proprietary systems, the
modelling did not need to consider this variable. It is for noting, also, that altering
the transfer of air from one side of a HV affects the handling, particularly the roll
stability, adversely. This consideration has led all developers of systems using
larger-than-standard air lines in HV suspensions to concentrate only on altering
longitudinal air line sizing, leaving the transverse air line sizes unaltered from
standard.
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HV suspension testing – dynamic load sharing analysis
33
2.9 Summary of this section
In this section, a model developed previously as an analogue of axle-to-chassis data
using accelerometer signals has been referenced as a building block to develop a
model of three air springs down one side of a semi-trailer tri-axle group. This model
will be used in the next section to determine the sensitivity of air spring forces to the
amount of air transmitted between air springs as previously proposed for the project
Heavy vehicle suspensions – testing and analysis.
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HV suspension testing – dynamic load sharing analysis
34
3 Results
3.1 General
All axles were analysed for variations in peak forces and standard deviation of
forces in their air spring signals for varying levels of load sharing fraction (LSF). Of
note was the middle axle’s sensitivity to axle hop frequency influences from the
other two axles; its air spring signal was affected by the feedback from the other two
axles. Figure 12 to Figure 14 shows the outputs from the Simulink Matlab
model
air spring for a load sharing fraction (LSF) of 1.0 or 100%, which is the limiting
case for dynamic load sharing using passive systems. It is for noting that the results
for the middle axle when this LSF was used, Figure 13, indicated a high proportion
of axle-hop frequencies in a combination of influences from the front and rear axles.
After running the simulation for all three axles, the highest overall air spring forces,
the greatest sensitivity to variations in LSF and greatest reduction in peak loads for
any axle when the LSF was varied was for the case of the rear axle. The results
from this axle were therefore chosen for presentation in the following section. This
choice and the finding that the rear axle was the worst for peak forces tallied with
previous work that had shown the rear axle had the greatest peak loads (Gyenes &
Simmons, 1994; Hahn, 1987; Woodroofe & Le Blanc, 1988).
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HV suspension testing – dynamic load sharing analysis
35
0 1 2 3 4 5 6 7 8 9 10
-150
-100
-50
0
50
100
150
model front air spring response to empirical data input
time (s)
Magnitude o
f sim
ula
ted s
uspensio
n r
esponse (
arb
itra
ry lin
ear
scale
)
Figure 12. Front axle output from the Simulink Matlab
model, LSF = 1.0.
0 1 2 3 4 5 6 7 8 9 10
-150
-100
-50
0
50
100
150
model mid air spring response to empirical data input
time (s)
Magnitude o
f sim
ula
ted s
uspensio
n r
esponse (
arb
itra
ry lin
ear
scale
)
Figure 13. Middle axle output from the Simulink Matlab
model, LSF = 1.0.
0 1 2 3 4 5 6 7 8 9 10
-150
-100
-50
0
50
100
150
model rear air spring response to empirical data input
time (s)
Magnitude o
f sim
ula
ted s
uspensio
n r
esponse (
arb
itra
ry lin
ear
scale
)
Figure 14. Rear axle output from the Simulink Matlab
model, LSF = 1.0.
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HV suspension testing – dynamic load sharing analysis
36
3.2 Air spring data - LSF sensitivity analysis
The load sharing fraction (LSF) was varied over the range 1 x 10-8
to 1.0 for typical
examples of air spring outputs from the rear axle of the semi-trailer. Figure 15 to
Figure 17 show the results of a sensitivity analysis varying the LSF for travel speeds
from 60 to 90 km/h, respectively, using the model in Figure 8 and the transmission
delay values shown in Table 2.
Peak and std. dev. of air spring forces vs. load sharing fraction - 60 km/h
0
20
40
60
80
100
120
140
160
1.0
E-0
8
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve
mean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
Std
dev o
f air
sp
rin
g f
orc
e a
bo
ut
mean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 15. Air spring forces from the model vs. load sharing fraction - 60 km/h.
Peak and std. dev. of air spring forces vs. load sharing fraction - 80 km/h
0
20
40
60
80
100
120
140
160
1.0
E-0
8
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve m
ean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
40
45
Std
dev o
f air
sp
rin
g f
orc
e a
bo
ut
mean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 16. Air spring forces from the model vs. load sharing fraction - 80 km/h.
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HV suspension testing – dynamic load sharing analysis
37
Peak and std. dev. of air spring forces vs. load sharing fraction - 90 km/h
0
20
40
60
80
100
120
140
1601
.0E
-08
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve m
ean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
40
Std
dev o
f air
sp
rin
g f
orc
e a
bo
ut
mean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 17. Air spring forces from the model vs. load sharing fraction - 90 km/h.
The data shown in Figure 15 to Figure 17 indicate that the intuitive response to
allowing an air suspension a greater ability to move air between its air springs is
justified. In this, the peak air spring forces and the air spring force standard
deviations reduce considerably with an order-of-magnitude reduction of 50% for
LSFs greater than 1 x 10-4
. The straightforward assumption from the results in
Figure 15 to Figure 17 is that a higher LSF is more beneficial, since this trends
toward axle-to-body forces that have lower maxima and standard deviations than for
lower LSF values. This phenomenon will be explored later.
As a check, the frequency domain was explored with results as shown in the
following section.
3.3 FFTs air spring signals from the model
Fast-Fourier transforms (FFTs) of the model's air spring signals were taken for the
"knee-points" in LSF values that led to the dramatic reductions in peak and standard
deviations of the air spring forces.
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HV suspension testing – dynamic load sharing analysis
38
It was not necessary to perform FFTs on all of the outputs for all LSF values. This
since a flattening in benefits was evident for LSFs of less than 1 x 10-7
and greater
than 1 x 10-4
. This particularly for LSFs greater than 1 x 10-4
since there was no
concomitant reductions in peaks or standard deviations of air spring forces where
LSFs in the range 1 x 10-3
to 1.0 were used; this was a clear trend as seen from the
graphs in Figure 15 to Figure 17.
Figure 18 to Figure 29 show the results of the FFTs of the rear axle air spring force
for the speeds 60 km/h to 90 km/h with varying levels of LSF.
0 5 10 15 20 25 30 35 400
5
10
15
20
25
30FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 18. FFT of air spring forces, 60 km/h and LSF of 1 x 10-7
0 5 10 15 20 25 30 35 400
5
10
15
20
25
30FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 19. FFT of air spring forces, 60 km/h and LSF of 1 x 10
-6
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HV suspension testing – dynamic load sharing analysis
39
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 20. FFT of air spring forces, 60 km/h and LSF of 1 x 10
-5
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 21. FFT of air spring forces, 60 km/h and LSF of 1 x 10
-4
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 22. FFT of air spring forces, 80 km/h and LSF of 1 x 10
-7
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HV suspension testing – dynamic load sharing analysis
40
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 23. FFT of air spring forces, 80 km/h and LSF of 1 x 10
-6
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 24. FFT of air spring forces, 80 km/h and LSF of 1 x 10
-5
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 25. FFT of air spring forces, 80 km/h and LSF of 1 x 10
-4
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HV suspension testing – dynamic load sharing analysis
41
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 26. FFT of air spring forces, 90 km/h and LSF of 1 x 10
-7
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 27. FFT of air spring forces, 90 km/h and LSF of 1 x 10
-6
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 28. FFT of air spring forces, 90 km/h and LSF of 1 x 10
-5
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HV suspension testing – dynamic load sharing analysis
42
0 5 10 15 20 25 30 35 400
2
4
6
8
10
12
14
16
18
20FFT of air spring force
Frequency (Hz)
Magnitude o
f air s
pring f
orc
e (
arb
itra
ry lin
ear
scale
)
Figure 29. FFT of air spring forces, 90 km/h and LSF of 1 x 10
-4
The plots in Figure 15 to Figure 17 did indicate that the magnitude of the air-spring
forces reduced for increasing LSF values. However, the graphs in Figure 18 to
Figure 29 show that, for increasing LSF values, there was a shift in the transmission
of suspension frequencies away from the body-bounce predominant for LSFs in the
1 x 10-8
to 1 x 10-5
range and toward axle-hop frequencies for LSFs in the 1 x 10-3
to
1.0 range. This phenomenon will be explored later.
3.4 Air spring data - LSF sensitivity analysis with low-pass filters
A Simulink Matlab
model was used that included low-pass filters as shown in
Figure 10. This to explore the possibility that the shift to high-frequency
transmission of axle-hop from the range of LSFs above 1 x 10-5
might be
compensated for by blocking these frequencies, leading to a reduction in peak
loadings without the concomitant increase in harshness. Accordingly, the low-pass
filters' -3 dB frequency was set at 3.2 Hz to simulate the allowance of air at body-
bounce frequencies to move easily between the air springs but block air at axle-hop
frequencies. Similar to the previous section, the load sharing fraction (LSF) was
varied over the range 1 x 10-8
to 1.0 for typical examples of air spring outputs from
the rear axle of the semi-trailer using the Simulink Matlab
model shown in Figure
10. The loci in Figure 30 show indicative results of a sensitivity analysis for varying
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HV suspension testing – dynamic load sharing analysis
43
LSFs for travel speeds from 60 to 90 km/h, respectively and the transmission delay
values shown in Table 2.
Peak and std. dev. of air spring forces vs. load sharing fraction - 60 km/h -
with low pass filter
0
500
1000
1500
2000
-8.0
0
-7.0
0
-6.0
0
-5.0
0
-4.0
0
-3.0
0
Load sharing fraction (power of 10)
Peak a
ir s
pri
ng
fo
rce a
bo
ve m
ean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 30. Air spring forces vs. load sharing fraction - 60 km/h with LP filters.
Peak and std. dev. of air spring forces vs. load sharing fraction - 80 km/h - with low
pass filter
0
500
1000
1500
2000
2500
-8.0
0
-7.0
0
-6.0
0
-5.0
0
-4.0
0
Load sharing fraction (power of 10)
Pe
ak
air
sp
rin
g f
orc
e a
bo
ve
me
an
(arb
itra
ry l
ine
ar
sc
ale
)
max
std dev
Figure 31. Air spring forces vs. load sharing fraction - 80 km/h with LP filters.
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HV suspension testing – dynamic load sharing analysis
44
Peak and std. dev. of air spring forces vs. load sharing fraction - 90 km/h - with low pass filter
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
-8.0
0
-7.0
0
-6.0
0
-5.0
0
-4.0
0
Load sharing fraction (power of 10)
Pe
ak
air
sp
rin
g f
orc
e a
bo
ve
me
an
(a
rbit
rary
lin
ea
r s
ca
le)
max
std dev
Figure 32. Air Air spring forces vs. load sharing fraction - 90 km/h with LP filters.
The loci of the plots shown in Figure 30 to Figure 32 indicate that, above LSF values
of 1 x 10-5
at high speeds and 1 x 10-4
at low speeds, the air spring forces of the
model went into an unstable mode of oscillation. The results shown in Figure 30 to
Figure 32 indicate that, in changing one parameter of the suspension model to
compensate for perceived inadequacies of performance, we are confronted with
potentially greater negative consequences. This phenomenon will be explored in the
next section.
Empirical results of testing HVs with longitudinal air line diameters of the same
order-of-magnitude as the air springs themselves have been reported anecdotally.
This would be equivalent to our model having low-pass filters combined with a LSF
of less than 1 x 10-3
. Our model predicted that radical instability would occur.
Anecdotal evidence suggests that this prediction was borne out during early systems
development of larger longitudinal air lines between air springs (Davis, 2006a).
3.5 Air spring data - LSF sensitivity analysis with modified shock absorbers
A Simulink Matlab
model was created with modified suspension damping
coefficients. It is shown in Figure 11 and used suspension dampers with bump and
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HV suspension testing – dynamic load sharing analysis
45
rebound characteristics used in passenger coaches instead of those found in semi-
trailers (Davis & Bunker, 2008a). This to explore the possibility that the shift to
high-frequency transmission of axle-hop from the range of LSF above 1 x 10-5
might
be mitigated by altering the characteristics of the suspension dampers. The loci in
Figure 33 to Figure 35 show indicative results of a sensitivity analysis for varying
LSFs as before but with modified shock absorbers.
Peak and std. dev. of air spring forces (modified dampers) vs. load
sharing fraction - 60 km/h
0
50
100
150
200
250
1.0
E-0
8
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve
mean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
Std
dev o
f air
sp
rin
g f
orc
e
ab
ou
t m
ean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 33. Air spring forces - modified shock absorbers vs. load sharing fraction - 60 km/h.
Peak and std. dev. of air spring forces (modified dampers) vs. load
sharing fraction - 80 km/h
0
50
100
150
200
250
1.0
E-0
8
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve
mean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
40
45
Std
dev o
f air
sp
rin
g f
orc
e
ab
ou
t m
ean
(arb
itra
ry l
inear
scale
)
max
std dev
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HV suspension testing – dynamic load sharing analysis
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Figure 34. Air spring forces - modified shock absorbers vs. load sharing fraction - 80 km/h.
Peak and std. dev. of air spring forces (modified dampers) vs. load sharing
fraction - 90 km/h
0
50
100
150
200
250
1.0
E-0
8
1.0
E-0
7
1.0
E-0
6
1.0
E-0
5
1.0
E-0
4
1.0
E-0
3
1.0
E-0
2
1.0
E-0
1
1.0
E+
00
Load sharing fraction
Peak a
ir s
pri
ng
fo
rce a
bo
ve
mean
(arb
itra
ry l
inear
scale
)
0
5
10
15
20
25
30
35
40
45
Std
dev o
f air
sp
rin
g f
orc
e
ab
ou
t m
ean
(arb
itra
ry l
inear
scale
)
max
std dev
Figure 35. Air spring forces - modified shock absorbers vs. load sharing fraction - 90 km/h.
Figure 36 to Figure 50 show the results of the FFTs of the rear axle air spring force
for the speeds 60 km/h to 90 km/h with varying levels of LSF and modified damping
coefficients for the suspension dampers.
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitu
de o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 36. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10
-8
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HV suspension testing – dynamic load sharing analysis
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100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitu
de o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 37. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10
-6
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 38. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-4
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 39. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1 x 10-2
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100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 40. FFT of air spring forces - modified shock absorbers - 60 km/h, LSF of 1.0
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 41. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10-8
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 42. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10
-6
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100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 43. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10
-4
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 44. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1 x 10
-2
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 45. FFT of air spring forces - modified shock absorbers - 80 km/h, LSF of 1.0
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100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 46. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10
-8
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 47. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-6
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 48. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10
-4
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100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 49. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1 x 10-2
100
101
0
2
4
6
8
10
12
14
16
18
20FFT of signal
Frequency (Hz)
Magnitude o
f sig
nal (a
rbitra
ry lin
ear
scale
)
Figure 50. FFT of air spring forces - modified shock absorbers - 90 km/h, LSF of 1.0
3.6 Air spring forces - LSF sensitivity analysis with modified shock absorbers and low pass filters
A Simulink Matlab
model combining both the modified shock absorbers and low-
pass filtering was created. The results were extremely similar to those shown in
Figure 30 to Figure 32; the results were as unstable as those using just the low-pass
filter model as shown in Figure 10.
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3.7 Summary of this section
In this section, the plots in Figure 18 to Figure 29 show that, whilst the peak forces
had, indeed, been reduced by increasing the value of LSF, the frequency at which
the peak forces manifest themselves had shifted. The peaks had moved from the
body-bounce range of 1 - 4 Hz (Cebon, 1993; Davis & Bunker, 2008b; de Pont,
1994, 1997) and had migrated to the axle-hop end of the spectrum around 10 - 20 Hz
(Cebon, 1993; Davis & Bunker, 2008b; de Pont, 1994, 1997). As postulated
previously (Davis & Bunker, 2008b), the elapsed time between axles at 1.4 m
spacings yields a time constant which, when inverted, will provide a fundamental
frequency. When this frequency approached that of axle-hop, increased connectivity
between air springs, when above a certain threshold, will cause a positive feedback
loop to form. This will then increase high-frequency vibration in the suspension.
It is worth noting that the FFT plots for LSFs of 1 x 10-7
and 1 x 10-6
indicate body-
bounce around 1.8 Hz but also a strong signal around 3 Hz was also present. This 3
Hz phenomenon has been noted in previous research and was independent of
suspension type, load, speed or tyre type (Middleton & Rhodes, 1991).
An exercise of attenuating the transfer of axle-hop frequencies between the air
springs of the model was undertaken. In this summary of the section, it is germane
to make an interim comment that altering one parameter in a complex system may
indeed improve one metric but at the expense of another. This comment holds for
all LSFs above 1 x 10-3
for axle-hop propagation as well as the low-frequency filter
model.
Figure 36 to Figure 50 indicate that mitigation of frequency shift to the axle-hop
extreme was possible when different shock absorbers were fitted. This then allowed
LSFs up to 100% to be effective in reducing overall peak and standard deviations of
air spring forces.
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4 Analysis
4.1 General
Consider the simplified diagram of one side of a HV with air suspension in Figure 9
where the wheels, axle housings, etc. are assumed to be of equal mass to the mass of
their counterparts on any other axle. For a connection mechanism in the form of
industry-standard longitudinal air lines (order of magnitude: 10 mm diameter), then
the axles may be considered to be independent of each other, resulting in no load
sharing when one or the other wheel encounters a bump (Blanksby et al., 2008;
Davis & Sack, 2004). This means that, should the bump be large enough that tyre
elasticity and spring response were not able to accommodate it; one wheel could be
lifted off the ground momentarily with the weight of the group borne by one wheel
or axle. Now consider a connection mechanism in Figure 9 where air is transferred
effortlessly from one air spring to its sequential rear neighbour. Between those
scenarios (and with pavement varying from rough to perfectly flat and with loads
shared equally on all wheels via either perfect load sharing or no discontinuities) is a
continuum of possibilities for differing degrees of load sharing between the two
wheels in Figure 9.
4.2 Perfect dynamic load sharing?
Perfect dynamic load sharing would result in equalisation across all air springs and
wheels of the load from the chassis and the unsprung mass as the HV travelled; even
when the wheels encountered bumps in the road surface. Nonetheless, forward
travel would mean that subsequent wheels would meet the same bump encountered
by the first wheel in a time inversely proportional to the speed of travel and
proportional to the distance between the axles. Considering Figure 9 again, a bump
encountered by the leading wheel would start axle-hop. This would then cause the
air spring to transmit a series of pneumatic pulses to the air spring of its rear
neighbour. If the suspension dampers were working properly, the shock absorbers
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would damp out this vibration but not before the second air spring received a series
of pressure pulses, via the connection mechanism, with the same frequency at which
its own axle is predisposed to hop. Shortly the subsequent wheel would encounter
the same bump experienced by its leading neighbour starting axle hop. The
frequency of the resonant system thus created would be at the axle-hop frequency.
Now consider the modes of vibration in the axles and the body (Davis & Bunker,
2008b) transmitted to the wheels as wheel forces. The axle-hop frequency would be
in the range 10 - 20 Hz and would tend to predominate (or at least increase in
contribution to wheel-forces) as the speed increased. The period between the wheels
would be inversely proportional to the speed of travel and proportional to the
distance between them.
The time delay between successive wheels travelling over a bump encountered by
one side of the HV for the example in Figure 9 has been shown previously in Table
2. The time between axles encountering the same bump can be denoted the time
constant of the resonant system. Where a time constant is present, its inverse is the
fundamental (or resonant) frequency of the system. By the simple expedient of
inverting the elapsed time between sequential axles encountering the same bump,
the system resonant frequency may be derived. Assuming an idealised transfer of
air from one air spring to its rear neighbour, then the model in Figure 9 can be
considered a resonant system with a frequency proportional to the inverse of the
times shown in Table 2; somewhere between 10 and 18 Hz, dependant on travel
speed. An additional column has been added to Table 2 and is shown, with some
data from Table 2 repeated for reference, in Table 3, to illustrate these frequencies.
These frequency bounds are coincident with the axle-hop frequencies in the range of
10-15 Hz as documented for the wheel-force FFTs and hub accelerometer FFTs
(Davis & Bunker, 2008a, 2008b).
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speed (km/h)
elapsed time (et) between axles
(ms)
Frequency (Hz)
= 1/ et
60 0.084 11.9
80 0.063 15.9
90 0.056 17.9
Table 3. Relationship between different speeds and the dominant frequency at 1.4 m axle
spacings.
4.3 Increasing LSF equals better load sharing?
From the plots in Figure 18 to Figure 29, it was clear that, whilst the peak forces had
been reduced by increasing the value of LSF, the frequency at which the peak forces
manifest themselves had shifted. This shift was a migration of resonant frequencies
from the range 1 - 4 Hz (corresponding to LSFs of 1 x 10-6
and less) to 10 - 18 Hz for
LSFs of 1 x 10-5
and greater. Figure 21, Figure 25 and Figure 29 show the limiting
states for increases in LSF and the concomitant shift to axle-hop resonance from the
spectra dominated by body-bounce in Figure 18, Figure 22 and Figure 26.
speed (km/h)
Frequency predicted
from Table 3 (Hz)
Dominant frequency
from FFT (Hz)
Error (Hz)
60 11.9 10 -1.9
80 15.9 15 -0.9
90 17.9 17 -0.9
Table 4. Greatest FFT magnitude, corresponding frequency for LSF above 1 x 10-5
and
predicted resonant frequency at 1.4 m axle spacings.
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Table 4 shows the comparison between the resonant frequency predicted from the
speed/axle-distance relationship and the peaks shown in the FFTs in Figure 18 to
Figure 29. The increase in LSF resulted in a relocation of the dominant resonance
from body-bounce to axle-hop frequencies in air spring spectra. This is clearly not
desirable from the point of view of isolating axle hop and harshness from the
passenger/cargo area. The early positive indication that forces were reduced with
greater values of LSF was then somewhat modified in its potential benefit by the
concept that the axle hop increased beyond a certain LSF value.
Increasing the transmissibility of only low-frequency signals between air springs was
ineffective. This since the model output went into unacceptably large excursions
when low-pass filters were used in an attempt to reduce transmission of air at axle-
hop frequencies between air springs. However, the alteration of suspension damping
characteristics to match more closely those of passenger coaches resulted in LSF
values being able to be increased to 100% without detriment. This implies that air
lines as large as the air springs themselves could be implemented with judicious
choice of shock absorber design.
This issue will be explored in the discussion section.
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5 Discussion
5.1 General
Vehicle suspensions, by design, are intended to equalise forces over the points of
contact on uneven road surfaces and isolate the passengers and/or the vehicle body
from the harshness and vibration of road surface irregularities. How well they do
this is determined by the vehicle designer’s specifications, the constraints imposed
by the vehicle dynamics, the masses of its various components and the vehicle
application. The outcome is a necessary compromise between cost, comfort,
robustness and use.
Dynamic loads at the springs of a vehicle will be different from the dynamic loads at
the wheels. This because dynamic wheel loads comprise a component due to
dynamic loadings from the springs and a component due to the unsprung mass of the
axle, wheels, brakes, hubs, tyres, etc. This unsprung mass has its own inertia and
will behave differently as it is more closely coupled to the dynamics induced by
irregularities from the road surface. That the unsprung mass dynamics are de-
coupled from the chassis to the greatest extent is also a design input directive for the
reduction of ride harshness, especially from road irregularities and axle-hop. Ride
harshness is defined as vibrations from the road or suspension in the 20 - 25 Hz
range (Firestone Industrial Products Company LLC, 2009; Tsymberov, 2009). One
design choice is how much isolation or de-coupling of axle vibration from the
chassis will occur by interposing a system of springs and dampers that, in
conjunction with the mass of the axle, have a resonant frequency lower than that of
the axles.
The frequency of an air spring system (including the axle) is proportional to the
square root of the inverse of the spring volume (Kinetic Systems Inc, 2009). The
use of air springs is part of the design choice and specifically for the isolation of the
passenger/cargo space from influences of harshness due to axle-hop and road
irregularities. This is evident in the results for the frequency spectra of the air
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springs as documented in previous work (Davis & Bunker, 2008a, 2008b). The air
spring suspensions can be seen to be effective in reducing the transmission
frequency of road imperfections into the chassis by an order of magnitude:
effectively de-coupling axle-hop from passenger perception. Referring to the input
parameters for suspension design, this indicates a successful design execution.
5.2 LSF - how much is beneficial?
The constant determining factors in formulae (Davis & Bunker, 2007) for quality
indicators of HV suspension dynamic measures are:
� peak forces, such as in peak dynamic force (PDF) and dynamic
impact factor (DIF) (Fletcher et al., 2002);
� standard deviation of forces (Eisenmann, 1975), such as in dynamic
load coefficient (DLC) (Sweatman, 1983); or
� frequency, such as used by the spatial modellers (Davis & Bunker,
2009).
Accordingly, for the model tested here, these were derived. Their relationship was
not mutually exclusive, however. Figure 18 to Figure 29 show clearly that
increasing the amount of air transferred between air springs beyond a certain point
does not improve harshness isolation. In fact, increasing LSF beyond a nominal
value of 1 x 10-4
reduces the quality of the ride in the passenger/cargo area by
allowing axle-hop to intrude. Therefore, while some increase in dynamic load
sharing between air springs is beneficial; there is a limit to the amount of LSF that
may be implemented before other factors start to reduce any gains in reduction of
peak forces.
For the air spring forces modelled:
� the body-bounce spectra predominated at lower LSFs;
� the frequency of greatest magnitude in the wheel-force FFT spectra shifted
toward the wheel-hop end of the spectrum with reducing LSFs;
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� at higher LSFs, axle-hop dominated as the contributor of greater magnitude
in the force spectra; and
� the axle-hop force component in the air spring spectra was proportional to
the LSF nominated for the model; this component migrated to dominate the
spectrum magnitude at LSFs greater than 1 x 10-5
.
5.3 Air line sizing and LSF
The spectra shown in Figure 19, Figure 23 and Figure 27 as outputs from the
simulation model are similar to those found for empirical data measured at the air
springs of test HVs (Davis & Bunker, 2008b). Indicative plots from that work are
reproduced below in Figure 51 to Figure 54.
100
101
0
5
10
15
20
25
30FFT of LHS APT signal
Frequency (Hz)
Magnitude o
f LH
S A
PT
sig
nal (a
rbitra
ry lin
ear
scale
)
100
101
0
5
10
15
20
25
30FFT of RHS APT signal
Frequency (Hz)
Magnitude o
f R
HS
AP
T s
ignal (a
rbitra
ry lin
ear
scale
)
Figure 51. FFT of air spring signals - modified suspension, semi-trailer loaded, 80 km/h, test 97
100
101
0
5
10
15
20
25
30FFT of LHS APT signal
Frequency (Hz)
Magnitude o
f LH
S A
PT
sig
nal (a
rbitra
ry lin
ear
scale
)
100
101
0
5
10
15
20
25
30FFT of RHS APT signal
Frequency (Hz)
Magnitude o
f R
HS
AP
T s
ignal (a
rbitra
ry lin
ear
scale
)
Figure 52. FFT of air spring signals - modified suspension, semi-trailer loaded, 90 km/h, test 99
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100
101
0
5
10
15
20
25
30FFT of LHS APT signal
Frequency (Hz)
Magnitude o
f LH
S A
PT
sig
nal (a
rbitra
ry lin
ear
scale
)
100
101
0
5
10
15
20
25
30FFT of RHS APT signal
Frequency (Hz)
Magnitude o
f R
HS
AP
T s
ignal (a
rbitra
ry lin
ear
scale
)
Figure 53. FFT of air spring signals - std suspension, semi-trailer loaded, 80 km/h, test 136
100
101
0
5
10
15
20
25
30FFT of LHS APT signal
Frequency (Hz)
Magnitude o
f LH
S A
PT
sig
nal (a
rbitra
ry lin
ear
scale
)
100
101
0
5
10
15
20
25
30FFT of RHS APT signal
Frequency (Hz)
Magnitude o
f R
HS
AP
T s
ignal (a
rbitra
ry lin
ear
scale
)
Figure 54. FFT of air spring signals - std suspension, semi-trailer loaded, 90 km/h, test 138
The plots in Figure 51 to Figure 54 indicate that, even at high speeds, body bounce is
the dominant frequency. What is also indicated is that the modified air line systems
such as the "Haire suspension system" already in the marketplace do not allow axle
hop to dominate the air spring frequency spectra, for good, design-based reasons.
The logical step from that result is that the LSF values for all known systems,
regardless of air line size, lie somewhere in the range from 1 x 10-8
to 1 x 10-6
(providing our model is correct).
If the LSFs of small, industry-standard air lines and the larger, proprietary
longitudinal air lines of the “Haire suspension system” and the Kenworth Airglide
200 range from 1 x 10-8
to 1 x 10-6
, the juncture to which that logic leads us is to
examining the domain area of fluid mechanics.
It is venturing outside the scope of the QUT/Main Roads project Heavy vehicle
suspensions – testing and analysis to explore the fluid mechanics of air flow between
air springs. However, a few points may be germane to future research in this area:
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� the comparison of wheel and suspension forces for standard vs. larger
longitudinal air lines between air springs have been documented (Davis, 2006b,
2007, 2008; Davis & Bunker, 2008b; Davis & Kel, 2007);
� the nature of improved air flow between air springs using larger longitudinal air
lines has been addressed and research still continues (Li & McLean, 2003a,
2003b; McLean, Lambert, & Haire, 2001); and
� the Li and McLean (2003b) study postulated an improvement of 22 times greater
air flow between air springs for 20 mm diameter air pipes vs. 4.15 mm diameter
pipes.
Given that the frequency spectra of the larger longitudinal air lines used in the "Haire
suspension system" did not move radically into axle-hop (Davis & Bunker, 2008b),
as shown by Figure 53 and Figure 54 vs. Figure 51 and Figure 52, the LSF for this
modification cannot be any greater than approximately 1 x10-6
. If then the smaller
air lines have velocities 22 times slower, this puts their LSFs in the order of
magnitude of sub-1 x10-7
. Further, given that body-bounce for the test case where
the "Haire suspension system" was fitted did not result in vehicle instability, it is
reasonable to infer that this system balances the benefits from easier transfer of air
between successive air springs facilitated by larger longitudinal air lines without the
potential for instability arising from low-frequency runaway.
The complexity involved in modifying HV suspension systems was indicated
because of the exercise in reducing the ability of our model to transmit axle-hop
frequencies. With this, seemingly beneficial, modification the suspension became
more unstable at high LSF values than for the cases where axle-hop was allowed to
resonate through the air spring connections. This phenomenon indicated strongly
that axle-hop, whilst undesirable in terms of perceived ride harshness, acted to
prevent runaway body-bounce in our model.
On the positive side, altering the shock absorber characteristics allowed the model to
maintain stability and have increased air line sizing. This series of results was
indicative that air lines between sequential air springs could have diameters in the
order of those of the air springs themselves, provided the shock absorber
characteristics were more aligned with those found on passenger coaches.
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The formulae to determine the increase in air flow between air springs for larger air
lines are not definitive. The various formulae as derivatives of the original Bernoulli
calculations rely on pressure and flow rates that vary greatly from one situation to the
next. Factors such as velocity profile, laminar or turbulent flow, etc. influence the
flow rates for this compressible gas. Various authorities give air flow formulae
varying proportional to the area of the orifice (≈ diameter2) through to proportional to
the square of the area of the orifice (≈ diameter4). There is also the issue of
determining whether larger longitudinal air lines are influential in the improvement
of air velocity or air mass flow mass flow. Accordingly, the determination of these
improvements will now be left to the domain experts on the fluid mechanics field,
this treatise having pushed slightly beyond the scope of the current project.
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6 Conclusion
6.1 General
Davis and Bunker (Davis & Bunker, 2008b) described the testing and frequency
spectrum analysis of the suspension forces, including the air springs in three heavy
vehicles (HVs). In the results of that study, body-bounce forces predominated in the
air spring spectra, regardless of speed. That study also showed that, as speed
increased, so did the magnitudes of axle-hop and concomitant wheel forces.
6.2 Dynamic load sharing - how much load should be transferred between air springs?
Maximum transfer of air from one air spring to its associated rear air spring could be
seen to be an ideal situation for load equalisation. However, the practicality of the
phenomenon of axle-hop requires that some imperfection needs to be introduced into
the transfer mechanism to reduce the possibility of standing waves in the air spring
connector exciting sympathetic oscillations in neighbouring air springs. This also
applies for the case of too much transmission of body-bounce frequencies.
It has been postulated previously in the QUT/Main Roads project Heavy vehicle
suspensions – testing and analysis that an imperfect transfer of air between air
springs by the use of (say) some constriction device, such as a smaller pipe, to join
the connection mechanism to the air springs would be advantageous in that it would
damp out pneumatic excitation of resonant frequencies in such air spring systems
(Davis & Bunker, 2008b).
Axle inertia combined with suspension damping act to de-couple the pavement
frequencies from the chassis. Alternately, another explanation in systems
engineering terms is the suspension acts as a low-pass filter, isolating high-
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frequency road irregularities from the chassis. A result of the suspension design
meeting one of its criteria in that the range of frequencies measured for the unsprung
masses below the axle is not the same as the resonant body bounce frequencies.
This effectively isolates the chassis as much as is possible (and therefore the payload
and/or the passengers) from the harshness and vibration due to pavement
irregularities. The results and analysis in this report bear out this contention for a
simple model of a HV suspension developed from previous work (Davis & Bunker,
2008a).
Increasing load sharing fraction (LSF) values, implied as a reduction of the
constrictions between air springs, were useful for reducing dynamic peak loads up to
a point. After a particular value, to be determined by other research beyond the
scope of this project, further increases in load sharing fractions between air springs
allowed axle hop and associated ride harshness to be transmitted into the chassis of
the vehicle. Attenuation of axle-hop frequencies in the transmission mechanism
between air springs also proved fractious. These results indicate that HV
suspensions are complex systems that require patient analysis to optimise the
necessary compromises between ride comfort and the required contact between the
wheels and the pavement. A promising area was indicated in that shock absorber
characteristics were central to allowing stable increases in air line sizing to facilitate
reduced peaks and smaller ranges of suspension forces. Any such reductions should
also be translated through to concomitant reductions in pavement forces.
The industry behind the supply of heavy vehicles should consider more research into
providing better load sharing than found currently in most HV suspensions. Societal
benefits accruing from reduced road damage, reduced payload damage (especially
for fragile goods) less fatigued drivers and passengers and greater life from heavy
vehicle chassis, suspension and coachwork components may be the result.
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Appendix 1. Definitions, Abbreviations & Glossary
Terms,
abbreviations
and acronyms
Meaning
APT Air pressure transducer. A device for emitting an electrical signal as a
proportional surrogate of input air pressure.
Axle hop Vertical displacement of the wheels (and axle), indicating dynamic
behaviour of the axle and resulting in more or less tyre force onto the
road. Usually manifests in the frequency range 10 – 15Hz.
Body bounce Movement of the sprung mass of a truck as measured between the axles
and the chassis. Results in HV body dynamic forces being transmitted
to the road via the axles & wheels.
Usually manifests in the frequency range 1 – 4Hz.
CoG Centre of gravity. The point at which a body’s mass may be said be
concentrated for purposes of determining forces on that body.
DIVINE Dynamic Interaction between heavy Vehicles and INfrastructurE.
DoTaRS Department of Transport and Regional Services. An Australian
Government department.
∆ Greek letter “delta” – denoting increment.
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Dynamic load
coefficient
(DLC)
Coefficient of variation of dynamic tyre force. It is obtained by
calculating the ratio of the root-mean-square (RMS) of the dynamic
wheel forces (std. dev. of Fmean) divided by the static wheel-force, i.e.
the coefficient of variation of the total wheel load:
DLC = σ / Fmean
Where:
σ = the standard deviation of wheel-force; and
Fmean = the mean wheel-force.
A perfect suspension would have a DLC of 0. The range in reality is
somewhere between 0 and 0.4 (Mitchell & Gyenes, 1989).
FFT Fast Fourier transform. A method whereby the Fourier transform is
found using discretisation and conversion into a frequency spectrum.
Fourier
transform
A method whereby the relative magnitudes of the frequency
components of a time-series signal are converted to, and displayed as, a
frequency series. If the integrable function is h(t), then the Fourier
transform is:
dtethtiω
ωφ−+∞
∞∫=-
)( )(
Where:
φ is the Fourier series;
ω is the frequency in radians/s; and
1−=i . (Jacob & Dolcemascolo, 1998).
HML Higher mass limits. Under the HML schemes in Australia, heavy
vehicles are allowed to carry more mass (payload) in return for their
suspension configuration being “road friendly”. See VSB 11.
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HV Heavy vehicle.
Hz Hertz. Unit of vibration denoting cycles per second.
LSC Load sharing coefficient – a measure of how well a suspension
group equalises the total axle group load, averaged during a
test. This is a value that shows how well the average forces of
a multi-axle group are distributed over each tyre and/or wheel
in that group.
(nom)stat
mean
F
)(F iLSC =
Where:
Fstat (nom) = Nominal static tyre force = n
F (total) group
Fgroup (total) = Total axle group force;
Fmean (i) = the mean force on tyre/wheel i ; and
n = number of tyres in the group (Potter et al., 1996).
LSF Load Sharing fraction. The amount of transmission of air between one
air spring and the others, within the manifold connecting them
longitudinally.
OECD Organisation for Economic Co-operation and Development
QUT Queensland University of Technology
RFS “Road-friendly” suspension. A HV suspension conforming to certain
limits of performance parameters defined by VSB 11. (Australia
Department of Transport and Regional Services, 2004a)
VSB 11 Vehicle Standards Bulletin 11. A document issued by DoTaRS that
defines the performance parameters of “road-friendly” HV suspensions.
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© State of Queensland (Department of Main Roads) & Queensland University© State of Queensland (Department of Main Roads) & Queensland University© State of Queensland (Department of Main Roads) & Queensland University© State of Queensland (Department of Main Roads) & Queensland University of of of of Technology 2009Technology 2009Technology 2009Technology 2009