The steady state forces and moments on a railway wheelset including ange contact conditions.

396 Pages·2017·15.37 MB·English

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The steady state forces and
moments on a railway
wheelset including flange
contact conditions.
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by the/an author.
Additional Information:
• A Doctoral Thesis. Submitted in partial fulfilment of the requirements
for the award of Doctor of Philosophy of Loughborough University.
Metadata Record: https://dspace.lboro.ac.uk/2134/16979
Publisher: (cid:13)c Barrie Vaughan Brickle
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Please cite the published version.
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THE STEADY STATE FORCES AND MOMENTS ON A RAILWAY
WHEELSET . mCLUDmG FLANGE CONTACT CONDITIONS
by
Barde Vaughan Briclde
A Dootoral Thesis
Submitted in partial fulfilment of the requirements for
the award of Ph.D. of the Loughborough University of
Technology.
August 1973
Supervisor: Professor F. D. Hale8
Department of Transport Technology
~ by Barrie Vaughan Briclde, 1973.
SUMMARY
Railwa;y' vehicles aref'itted with ccned wheels to provide
a measure of stability, but it can be shcwn that since the forces,between
, wheel and track are non-conservative, dynamic instability occurs at
a certain critical speed. Under these oonditions the wheelsets sway from
side-to-side of the, track with the flanges of the wheels contacting the rails. '
This can lead to derailment when the wheel climbs up the' rail and
eventually jumps off'.
The forces which exist between wheel and rail are due to the
phenomenon known as "creepage", and various theories exist which predict
these forces in the plane of the contact area. An investigation has been
carried out into these theories with the railway wheelset problem in view,
particularly the flange contact case.
It is possible, by assuming small displacements which avoid
flange contact, to carry out a linearised of the lateral dynamics
stu~
of a wheelset, but the presence of the wheel flanges introduces a non
linearity into the problem.
A mathematical model of a wheelset and track has been defined
based on real wheels with a "worn" tyre profile and real track. Computer
programs have been written which calculate the contact points when the wheel
set is'displaced laterally and yawed by various amounts, including flange
,contact conditions. Up to three contact points can exist between the wheelset,
and track. Forces in the contact areas have been calculated using the
various theories assuming the wheelset to be rolling along the track ata
constant velocity in a displaced position. These forces have been
manipulated to give the total forces and, moments on thO', wheelset and are
presented for various vertical load dist'ributions and for ~arious 'angular
and lateral displacements of the wheelset from its central position.
Although theories exist which predict the forces for flange
type contact, i. e. very elongated contact ellipse with a large amount of spin
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present, it became apparent during the course of the investigation that very
little experimental evidence was available for such conditions. As a result
a roller rig was built to provide this data, and measurements were made of·
the lateral force due to various amounts of lateral creep and spin on
elongated contact ellipses. Results from these tests have been compared
with the available theories and show reasonable agreement.
CONTENTS
. Page
1. Introduction •••••••••••••••••••••••••••••••••••••••••••••••• 1
2. Review of Rollirig Contact Theories, and Experiments
2.1 Basic Theory ••••••••• ~. •••••••••••" • •••.••••••••• '• .••• ~. B
2.2 Theoretical Review • ~ ••••••••••••" • ••••••••••••••••••• e". 11
2.3 Review .••••••••••••••••••••••••••••••••••• 23
~xperimental
3. Theories used in Present Analysis
The Limiting Case of Infinitesimal Creepageand Spin• •• 47
The Limiting Case of Large Creepage and Spin •••••••••• 54
ArBitar,y Creepage and Spin •••••••••••••••••••••••••••• 57
Numerical Theory ••••••..•.•••••.• '• •.•.•.••...• 57
Simplified Theor,y ••••••••••••••••••••••••••••• 64
4. Mathematical Model of Wheelset and Track
I
Introduction ••••••••••••••••• .' •••••••••••••••••.•••••• 69
Rail Geometry ••..•.••••...••••..•••••••.•.•.••••• ~ ••.• 70
........................................
Wheel Geometry 74
........................................
Contact Points 79
4.4.t Wheelset in Central Position •.•••.•••.. ~ ....•• 81
4.J...2 Wheelset Moved Laterally Only •••••••••••• '• •••• 82
4.4·3 Wheelset Yawed Onl\v ............................ . 88
4.4.4 Wheelset Moved Laterally and Yawed •••••••••••• 100
Ellipses •••.•...•...••••••.•••....•.........•• 105
.Contac~
Creepages and Spin ..................................... . 116
Forces ••.••••.•...•.•••.•........•••.••.•.•••...•.••.. 121
5. Comparison of Theories
'1
.........................................•
Introduction 124
Results ............................................... . 125
Page
Discussion •••••••••••••••••••••••••••••••••••••••••••••• 129
Wheelset Displaced No Yaw •••••••••••• ,129
Lateral~,
= = =
!ZA TZe -82.29kN , Tz" 0
Wheels et Displaced No Yaw •••••••••••• 131
Lateral~,
T = -82.29kN , Tz = 0 , Tz = -82.29kN
zA , 8 ,c
Wheelset Displaced and Yawed •••••••••• 132
Lateral~
Tz = - 82.29kN , Tz = 0 • 'Tz ~ - 82.29kN
A 8 e ,
Conclusions ••••••••••••••••••••••••••••••••••••••• -•••••• 134
6. Comparison of Wheels et Forces Using New and Worn Rails
..........................................•.
6.1 Introduction 137
6.2 Results ••••••••••••••.•••••••••••••.••••••••••••••••• ~ •• 137
Discussion and Conclusions •••••••••••••••••••••••••••••• 138
7. Derailment Ratio
Introduction 159
••••••••••• 4 ••••••••••••••••••••••••••••••••
Existing Formulae for Derailment Ratio ••••••••••••.••••• 160
Nadal's Formula •••••••••••••••••••••••.•••••.••• 160
Wagner's Formula ••••••••••••••••••••••••••••••••
Johansen's Fo~ula ••••••••••••••••••••••••••• ~ ••
•.................................•.............•
Results
Discussion and Conclusions
••••••••••••••••••••••••••••••
8. Experimental Investigation
8.1 Introduction •••••••••••••••••••••••••••••••••••••••••••• 170
,
8.2 Rig Description ••..••••••••••••••••••••••••••••••••••••• 171
Creepages and Forces .••• ~-•••••••••••••••..•.•.•••••••••• 185
.............•....•..•.........................
8.4 Procedure 190
............................... ................ .
8.5 Results 197
~
,..-------------------------------
----
Page
8.6 Discussion •..............•........... ~ ........•..•.•••• 207
8.6.1 . Validity, Accuracy and Repeatability o~ Results 207
8.6.2 Correlation with Theor,y, ••••••••••••••••••••••• 219
.......................
Conclusions and Recommendations 229
General Discussion and ConcluSions •••••••••••••••••••••••••• 235
16. References •.......•.....•..•.•...••.•••.•.•.••••.•.•.•••..•• 246
Acknowledgements •••••••••••••••••••••••••••••••••••••••••••• 254
12. Appendices
Derivation of the Relative Slip Equations for
Steady Rolling ••••• 255
2. Simplified Theory •••••••••••••••••••••••••••••••••••••• 257
Adaption of Governing Parameters for use in
Simplified Theory ••••••••
4. Comparison of Results Obtained Using Subroutine ROL
with Kalker's Simplified Theory Program ••• 268
Program Descriptions •.•.•••.•••••••••.••••••.•• '• •••••••
6. Coordinate Geometry ••••••••••••.•••••••••••••••••••••••
7. Longitudinal Creep, Lateral Creep and Spin on
Roller Rig ••••••• 363
8. Angle of Yaw, 'i', of Upper Wheel Relative to
Lower Wheel
••••••••
9. Contact Ellipse Semi Axes, a,b ••••••••••••••••••••••••• 370
Sheet •................................
10. Experimenta.l Data 374
11. Roll Effects on Experimental Rig •••••••••••••• "• •••••••• 376