PERFORMANCE MEASUREMENTS OF RAIL CURVE

LUBRICANTS

by

Lance Jon Wilson

Bachelor of Engineering (Mechanical)

Masters of Engineering Science

Queensland University of Technology, Australia

Thesis submitted for the degree of

Doctor of Philosophy

School of Engineering Systems Queensland University of Technology

2006

KEYWORDS

Rail Curve, Lubricant Performance, Elastohydrodynamic lubrication,

Rheology, Absorbed energy, Lubricating Grease, Rail/Wheel interface.

ABSTRACT

Wear of railroad rolling stock and rails costs millions of dollars annually in all

rail systems throughout the world. The rail industry has attempted to address

flange wear using rail curve lubricants and presently use a variety of lubricants

and lubricant applicators. The choice of lubricant and applicator is currently

based on considerations that do not address the wear problem directly.

This research quantified rail curve lubricant performance through laboratory

simulation. The effects of lubricants in the wheel/rail contact were

investigated. Rail curve lubricant performance was measured with a laboratory

rail/wheel simulator for the purpose of optimising the choice of lubricant.

New methods for measurement of rail curve lubricant performance have

been presented. These performance measurements are total absorbed energy,

the energy absorbed in the lubricant film instead of being utilised for wear

processes; total distance slid, the sliding distance or accumulated strain

achieved prior to development of a set tractive force limit; half life of

lubricant, the time taken for a lubricant to lose half of its sliding performance;

and apparent viscosity, a measure of the lubricity presented with respect to

accumulated strain.

The rail/wheel simulator used in this research consists of two dissimilar

wheels (disks) rotating in contact with one another simulating a conformal

gauge corner contact. The first wheel, a simulated rail, is driven by an electric

motor which then drives the second wheel, a simulated railroad wheel,

through the contact. Hydraulic braking on the railroad wheel is used to

simulate the rolling/sliding conditions.

The variables of the simulated contact that are controlled with this equipment

are normal force, input wheel speed, slip ratio between samples, sample

geometries and material properties, and lubricant types.

Rail curve lubricants were laboratory tested to define their properties using

the ASTM and other appropriate standards. The performance differences

measured using ASTM standards based tests were susceptible to repeatability

problems and did not represent the contact as accurately as the rail/wheel

simulator. This laboratory simulator was used to gather data in lubricated and

unlubricated conditions for the purpose of providing lubricant performance

measurements. These measurements were presented and the tested lubricants

were ranked conclusively using three industrially relevant performance

criteria.

Total sliding distance and total absorbed energy measurements of the rail

curve lubricants displayed clear differences in lubricant performance for both

of these criteria. Total sliding distance is equivalent to the number of axles in

the field situation, while total absorbed energy is the energy unavailable for

wear processes of rails and wheels. Lubricants designed using these

measurements will increase lubricant performance with respect to these

performance criteria which in turn will reduce wear to both rails and wheels.

Measurement of the apparent viscosity of rail curve lubricants, using the

rail/wheel simulator, displayed changes in rheological characteristics with

respect to accumulated strain. Apparent viscosity is a measure of the shear

stress transmitted from the wheels to the rails. Designing a rail curve lubricant

after analysing measurements taken from the rail/wheel simulator will assist in

identifying lubricant properties to reduce the wear producing shear stresses

generated in a rail wheel contact.

Decay of lubricant performance was measured for three different rail curve

lubricants under simulated conditions. The research found appreciable and

quantifiable differences between lubricants. Industrial application of the

findings will improve positioning of lubrication systems, improve choice of

lubricants and predict effective lubrication distance from the lubricant

application point.

Using the new methods of lubricant performance measurement developed in

this thesis, the objective of this research, to quantify rail curve lubricant

performance through laboratory simulation, has been achieved.

TABLE OF CONTENTS

Table of Contents................................................................................................................. i List of figures ....................................................................................................................... v List of tables ......................................................................................................................... x Statement of orginal authorship .....................................................................................xii Acknowledgments............................................................................................................xiii Nomenclature ...................................................................................................................xiv Chapter 1...............................................................................................................................1

Introduction .................................................................................................................. 1 1.1 Background.................................................................................................................... 1 1.2 Objective of Research.................................................................................................. 4 1.3 Summary and Thesis Outline ..................................................................................... 6 Chapter 2...............................................................................................................................7

Literature Review ......................................................................................................... 7 2.1 Rail/Wheel Wear Testing............................................................................................ 7 2.2 Rail/Wheel Wear Processes........................................................................................ 9

2.2.1 Rail/Wheel Wear: Surface initiated rolling contact fatigue.......................10 2.2.2 Rail/Wheel Wear Particles..............................................................................11

2.3 Rail Lubricant Characteristics...................................................................................12 2.4 Lubrication Regimes ..................................................................................................15 2.5 Rail Curve Lubricant Types Under Investigation.................................................16 2.6 Rail Curve Lubricating Grease Specifications .......................................................18 2.7 Rail Lubrication Research .........................................................................................19

2.7.1 Surface initiated rolling contact fatigue with lubrication...........................26 2.8 Lubricant Application Research...............................................................................28

2.8.1 Lubricant transport prediction/modelling ..................................................31 2.8.2 Summary ............................................................................................................36

2.9 Rail/Wheel Simulator - Description of equipment..............................................37 2.10 Lubricant Properties Testing..................................................................................39

2.10.1 ASTM D 1092 Standard Test Method for Measuring Apparent Viscosity of Lubricating Greases.............................................................................40 2.10.2 ASTM D 2596 Standard Test Method for Measurement of Extreme-Pressure Properties of Lubricating Grease ..........................................41 2.10.3 ASTM D 2266 Standard Test Method for Wear Preventive Characteristics of Lubricating Grease ....................................................................42 2.10.4 Rheometer Test ..............................................................................................43

2.11 Summary ....................................................................................................................45 Chapter 3.............................................................................................................................47

Theoretical calculations: Contact Mechanics of In-service and Rail Simulator conditions and lubricant film thickness...............................................47

3.1 Introduction.................................................................................................................47 3.2 Contact Mechanics Background ..............................................................................47

3.2.1 Wheel/rail contact models – A survey.........................................................49

ii

3.3 Geometry and Material Property Equations..........................................................52 3.4 Contact Mechanics Method......................................................................................54

3.4.1 Rectangular Contact Equations .....................................................................55 3.4.2 Elliptical Contact Equations...........................................................................56 3.4.3 Micro-slip/Creep Prediction ..........................................................................59

3.5 Conformal Rail/Wheel Contact...............................................................................62 3.6 Stress Distributions for In-service Conditions......................................................69 3.7 Stress Distributions for Simulator Conditions ......................................................75

3.7.1 Two Dimensional Line Contact Stress Distributions................................82 3.8 Elastohydrodynamic Film Thickness Calculation ................................................86

3.8.1 Shear rate of lubricant film .............................................................................88 3.8.2 Lubricant apparent viscosity calculation ......................................................92

3.9 Summary.......................................................................................................................95 Chapter 4.............................................................................................................................97

Commissioning and testing protocol of the rail/wheel interaction simulator ......................................................................................................................97

4.1 Introduction.................................................................................................................97 4.2 Equipment Modifications .........................................................................................98

4.2.1 Heat Dissipation ...............................................................................................98 4.2.2 Tread Loading Mechanism...........................................................................100 4.2.3 Data Acquisition .............................................................................................104 4.2.4 Tractive Force Application System.............................................................104 4.2.5 Slip/Creep Measurement ..............................................................................106

4.3 Testing equipment – construction/commissioning ...........................................106 4.3.1 Pre-Commissioning Testing Observations................................................106 4.3.2 Commissioning Testing Observations .......................................................107

4.4 Lubricated Testing Protocol ...................................................................................114 4.4.1 Preparation of the rail/wheel samples........................................................114 4.4.2 Material Properties .........................................................................................114 4.4.3 Test Sample Surface Roughness Results....................................................117 4.4.4 Testing Procedure ..........................................................................................117

4.5 Method of Measurements .......................................................................................118 4.5.1 Rotational Speed Measurement ...................................................................119 4.5.2 Output Torque Transducer ..........................................................................120 4.5.3 Input Torque ...................................................................................................120 4.5.4 Temperatures...................................................................................................122 4.5.5 Slip Calculation ...............................................................................................123 4.5.6 Torque Measurement for Tractive Force (Shearing Force) ...................124 4.5.7 Rail Flange Contact Conditions...................................................................127 4.5.8 Normal Load ...................................................................................................129

4.6 Measurement Errors ................................................................................................131 4.6.1 Thermal Expansion of Test Samples..........................................................131 4.6.2 Energy dissipation methods .........................................................................133 4.6.3 Slip From Lubrication Measurements (Zero slip predictions)...............135

4.7 Lubricant Performance Measures Error Analysis ..............................................137 4.8 Summary.....................................................................................................................149

iii

Chapter 5...........................................................................................................................152 Performance Measurement of Rail Curve Lubricants.......................................152

5.1 Introduction...............................................................................................................152 5.2 Testing Variables.......................................................................................................152 5.3 Unlubricated System Steady State Values ............................................................153

5.3.1 Lubricant Film Decay Half-Life Prediction ..............................................155 5.4 Input Data Variability ..............................................................................................156

5.4.1 Tread Load Temperature Dependence......................................................159 5.5 Rail/Wheel Simulator Results ................................................................................160

5.5.1 Group 1 Lubricant Performance Results (Tread Load = 9.5 kN, Braking Torque = 15 N.m, Rolling Speed = 20 km/hr)..................................161 5.5.2 Group 2 Lubricant Performance Results (Tread Load = 9.5 kN, Braking Torque = 15 N.m, Rolling Speed = 10 km/hr)..................................171 5.5.3 Group 3 Lubricant Performance Results (Tread Load = 9.5 kN, Braking Torque = 30 N.m, Rolling Speed = 20 km/hr)..................................180 5.5.4 Group 4 Lubricant Performance (Tread Load = 12.5 kN, Braking Torque = 15 N.m, Rolling Speed = 20 km/hr) .................................................189 5.5.5 Comparison and Discussion of All Groups..............................................197 5.5.6 Lubricant Performance Summary ...............................................................202 5.5.7 Apparent Viscosity Profiles ..........................................................................205

5.6 Experimental Observations ....................................................................................209 5.6.1 Temperature Profiles .....................................................................................209 5.6.2 Observed Lubricant Properties ...................................................................210 5.6.3 Lubricant Film Failure...................................................................................212 5.6.4 Braking Torque Setting .................................................................................212

5.7 Standards Based Lubricant Testing Results.........................................................213 5.7.1 Rheometry Method........................................................................................214 5.7.2 Rheometer Test Discussion and Results....................................................215 5.7.3 Experimental Rheometry Observations ....................................................216 5.7.4 ASTM D1092 Grease Pumpability .............................................................217 5.7.5 ASTM D2596 and ASTM D2266 Four Ball Tests ..................................217

5.8 Summary.....................................................................................................................221 Chapter 6...........................................................................................................................224

Discussion, future work and Conclusions...........................................................224 6.1 Introduction...............................................................................................................224 6.2 Discussion..................................................................................................................224 6.3 Future Work ..............................................................................................................227 6.4 Conclusions................................................................................................................229 References.........................................................................................................................233 Bibliography .....................................................................................................................238 APPENDIX A ................................................................................................................262 A. Seizure Wear ......................................................................................................262 B. Melt Wear ...........................................................................................................263 C. Oxidational wear ...............................................................................................265 D. Mild-oxidational wear.......................................................................................265 E. Severe-oxidational wear ...................................................................................268

iv

F. Plasticity dominated wear ................................................................................270 APPENDIX B.................................................................................................................271 A. Validation of Software for Rectangular Contact.........................................271 B. Validation of software for Elliptical Contact...............................................273 Appendix C – Technical Drawings..............................................................................277

v

LIST OF FIGURES

Number Page FIGURE 1 – TWIN DISK TEST APPARATUS FROM THE WORK OF DETERS AND PROKSCH

(2005)............................................................................................................................ 8 FIGURE 2 – (A) BALL ON DISK WEAR TEST APPARATUS, SPECIFIED LOADING REGIME AND (B)

TYPICAL WEAR SCAR OF THE WORK OF LEE AND POLYCARPOU (2005). ...................... 9 FIGURE 3 - STEEL PIN-ON-DISK WEAR MAP COMBINING RESULTS FROM MULTIPLE AUTHORS

BY LIM AND ASHBY (1986)......................................................................................... 10 FIGURE 4 - WEAR MAP SHOWING DEFINED WEAR MODES FOR BRITISH STANDARD RAIL

STEELS IN AN AMSLER WEAR TEST DEVICE (LEWIS AND OLOFSSON 2004).............. 12 FIGURE 5 – SEPARATION DISTANCES BETWEEN CONTACTING SURFACES FOR (A)

HYDRODYNAMIC LUBRICATION (HL)AND ELASTOHYDRODYNAMIC LUBRICATION, (B) MIXED-MODE LUBRICATION, AND (C) BOUNDARY LUBRICATION. .............................. 16

FIGURE 6 - WAYSIDE LUBRICATION DEVICE (PHOTO COURTESY OF QUEENSLAND RAIL). .. 28 FIGURE 7 – VOGEL ON-BOARD LUBRICATION DEVICE MOUNTED TO DISPLAY COMPONENTS

OF SYSTEM................................................................................................................... 29 FIGURE 8 - HI-RAIL LUBRICATION VEHICLE (PHOTO COURTESY OF QUEENSLAND RAIL). ... 29 FIGURE 9 - LUBRICANT APPLICATION BY HI-RAIL VEHICLE (PHOTO COURTESY OF

QUEENSLAND RAIL).................................................................................................... 30 FIGURE 10 - WAYSIDE LUBRICATOR LOCATION PLAN (FRANK 1981). ................................. 32 FIGURE 11 - RANGE OF LUBRICATION (FRANK 1981)........................................................... 33 FIGURE 12 - RAIL TRIBOMETER (PHOTO COURTESY OF QUEENSLAND RAIL)....................... 34 FIGURE 13 – RAIL/WHEEL SIMULATOR POST MODIFICATIONS BY THE AUTHOR. .................. 38 FIGURE 14 LOADING DIAGRAM FOR WEAR INVESTIGATION OF MARICH AND MUTTON(1989)

..................................................................................................................................... 39 FIGURE 15 – SCHEMATIC DRAWING OF ASTM D 1092 TEST DEVICE(ASTM 1999)............ 40 FIGURE 16 – SCHEMATIC DIAGRAM OF FOUR BALL TEST DEVICE SUITABLE FOR ASTM D

2266 AND ASTM D 2596 (ASTM 1991; ASTM 1997). ............................................ 42 FIGURE 17 – (LEFT) LUBRICANT FILM PRIOR TO ROLLING (~1MM THICKNESS). (RIGHT)

LUBRICANT FILM FOLLOWING ROLLING (~1µM)......................................................... 44 FIGURE 18- REFERENCE GEOMETRY USED FOR CONTACT MECHANICS CALCULATIONS

(ESDU 1984). ............................................................................................................. 52 FIGURE 19 - CONTACT DIMENSIONS, ELLIPSE RATIO, AND APPROACH COEFFICIENTS(ESDU

1995). .......................................................................................................................... 58 FIGURE 20 – CREEP PREDICTION FOR SIMULATOR WHEN CONTACT PATCH IS ASSUMED TO

HAVE NO REGIONS OF SLIP........................................................................................... 61 FIGURE 21 - CREEP PREDICTION FOR SIMULATOR WHEN CONTACT PATCH HAS REGIONS OF

SLIP.............................................................................................................................. 61 FIGURE 22 – WHEEL/RAIL CONTACT PROFILE(SATO 2005) (NOMENCLATURE FOR RADII IN

THIS FIGURE IS NOT USED)........................................................................................... 63 FIGURE 23 – WHEEL PROFILE FOR A CONED WHEEL (SATO 2005). ...................................... 64 FIGURE 24 – ROLLING RADIUS USED FOR CALCULATION OF LINE CONTACT WIDTH USING

WHEEL PROFILE FROM SATO (2005)............................................................................ 65 FIGURE 25 – CONTACT WIDTH PROFILE FOR CONSTANT NORMAL FORCE USING A VARIABLE

ROLLING RADIUS PROFILE. NOTE SCALE OF AXES DIFFERENT. ................................... 65 FIGURE 26 – MAXIMUM PRESSURE FOR CONSTANT TREAD LOAD ACROSS CONTACT AND

VARIABLE CONTACT RADIUS....................................................................................... 66 FIGURE 27- CONTACT WIDTH FOR CONSTANT TREAD LOAD AND CONSTANT MAXIMUM

PRESSURE ACROSS CONTACT FOR VARIABLE CONTACT RADIUS. ................................ 67

vi

FIGURE 28 – CONTACT PATCH DIMENSIONS FOR LINE AND ELLIPTICAL CONTACT FROM SAME NORMAL LOAD, 150,000 N.......................................................................................... 68

FIGURE 29 – STRESS DISTRIBUTION FOR TREAD CONTACT USING GEOMETRY OF SATO (2005) WITH A NORMAL LOAD OF 150 KN AND NO FRICTION FORCE. .................................... 71

FIGURE 30 - STRESS DISTRIBUTION FOR TREAD CONTACT USING GEOMETRY OF SATO (2005) WITH A NORMAL LOAD OF 150 KN AND FRICTION FORCE OF 0.185 TIMES THE NORMAL FORCE. ......................................................................................................................... 72

FIGURE 31 - STRESS DISTRIBUTION FOR TREAD CONTACT USING GEOMETRY OF SATO (2005) WITH A NORMAL LOAD OF 150 KN AND FRICTION FORCE OF 0.37 TIMES THE NORMAL FORCE. ......................................................................................................................... 72

FIGURE 32 – STRESS DISTRIBUTION FOR GAUGE CORNER CONTACT USING GEOMETRY OF SATO (2005) WITH A NORMAL LOAD OF 150 KN AND NO FRICTION FORCE. ............... 73

FIGURE 33 – STRESS DISTRIBUTION FOR GAUGE CORNER CONTACT USING GEOMETRY OF SATO (2005) WITH A NORMAL LOAD OF 150 KN AND FRICTION FORCE OF 0.185 TIMES THE NORMAL FORCE. ................................................................................................... 74

FIGURE 34 – STRESS DISTRIBUTION FOR GAUGE CORNER CONTACT USING GEOMETRY OF SATO (1994) WITH A NORMAL LOAD OF 150 KN AND FRICTION FORCE OF 0.37 TIMES THE NORMAL FORCE. ................................................................................................... 75

FIGURE 35 - STRESS DISTRIBUTION FOR A HEAVY HAUL CARRIAGE WITH A 27.5 TONNE AXLE LOAD TRAVELLING AT 42KM/HR INTO A 300M RADIUS CORNER USING THE RAIL PROFILE FROM SATO(2005) WITH A SUPER-ELEVATION OF 100MM AND RAIL GAUGE WIDTH OF 1067MM...................................................................................................... 77

FIGURE 36 – STRESS DISTRIBUTION FOR A SIMULATOR WITHOUT BRAKING TORQUE APPLIED...................................................................................................................................... 78

FIGURE 37 - STRESS DISTRIBUTION FOR A SIMULATOR WITH BRAKING TORQUE 15 N.M APPLIED. ...................................................................................................................... 79

FIGURE 38 - STRESS DISTRIBUTION FOR A SIMULATOR WITH BRAKING TORQUE 65 N.M APPLIED. ...................................................................................................................... 80

FIGURE 39 - STRESS DISTRIBUTION FOR A SIMULATOR TREAD LOAD OF 12.5 KN WITHOUT BRAKING TORQUE APPLIED. ........................................................................................ 80

FIGURE 40 - STRESS DISTRIBUTION FOR A SIMULATOR TREAD LOAD OF 12.5 KN WITH BRAKING TORQUE 15 N.M APPLIED............................................................................. 81

FIGURE 41 - STRESS DISTRIBUTION FOR A SIMULATOR TREAD LOAD OF 12.5 KN WITH BRAKING TORQUE 65 N.M APPLIED............................................................................. 82

FIGURE 42 – CONTACT STRESS MAGNITUDES FOR STRESS COMPONENTS USING CONDITIONS OF TREAD LOADING AT 9.5KN, 41.3MM CONTACT LENGTH........................................ 84

FIGURE 43 - CONTACT STRESS MAGNITUDES FOR STRESS COMPONENTS USING CONDITIONS OF TREAD LOADING AT 9.5KN, 20 MM CONTACT LENGTH. ......................................... 85

FIGURE 44 –CONTACT STRESS MAGNITUDES FOR STRESS COMPONENTS USING CONDITIONS OF TREAD LOADING AT 9.5KN, DYNAMOMETER TORQUE 15N.M, AND 41.3 MM CONTACT LENGTH. ...................................................................................................... 86

FIGURE 45 – ONE DIMENSIONAL SHEAR................................................................................ 89 FIGURE 46 – SHEAR RATE PREDICTION FOR AN EHL FILM UNDER THE RANGE OF

CONDITIONS FOR THE SIMULATOR. ............................................................................. 90 FIGURE 47 – SHEAR RATE PREDICTION FOR AN EHL FILM UNDER THE RANGE OF

CONDITIONS FOR IN-SERVICE CONDITIONS.................................................................. 91 FIGURE 48- SCHEMATIC DIAGRAM OF THE RAIL/WHEEL SIMULATOR................................... 97 FIGURE 49 – TREAD LOADING MECHANISM SHOWING ORIGINAL SCREW FORCE APPLICATOR.

................................................................................................................................... 100 FIGURE 50 – SIMPLIFIED WHEEL SAMPLE HOLDER ASSEMBLY. THE LARGE FLAT SECTION AT

THE LEFT IS THE SLIDER WHICH MOVES IN THE CHANNEL. AT THE LEFT END OF THE DEVICE THE CONTACT SURFACES CAN BE OBSERVED. .............................................. 102

FIGURE 51 – HYDRAULIC DYNAMOMETER SYSTEM............................................................ 105

vii

FIGURE 52 – RAIL SAMPLE WITH OXIDATIVE AND FATIGUE WEAR (A). WHEEL SAMPLE WITH OXIDISED MATERIAL REMOVED TO HIGHLIGHT PLASTIC DEFORMATION (B). ........... 107

FIGURE 53 – RAIL SAMPLE MOUNTED IN MACHINING JIG FOLLOWING INITIAL LATHE CUT, WITH PITTING AT THE OUTER EDGE OF THE RAIL SAMPLE(A). WHEEL SAMPLE WITH HARDENED MATERIAL, THE SMOOTHER RING, AT THE OUTER EDGE OF THE SAMPLE (B).............................................................................................................................. 108

FIGURE 54(A,B,C,D) – WEAR DEVELOPMENT OF RUNNING SURFACES ON WHEEL AND RAIL SAMPLES (LEFT TO RIGHT, TOP TO BOTTOM)............................................................. 109

FIGURE 55 – WEAR DEVELOPMENT OF RUNNING SURFACE FOLLOWING REPEATED LUBRICATED TESTS (A-C) WEAR PARTICLES AND EXCESS LUBRICANT (D). ............. 111

FIGURE 56 – GREASE APPLICATION PATTERN (A) AND SUBSEQUENT LUBRICANT FILM FAILURE OF RUNNING SURFACES (B). ........................................................................ 112

FIGURE 57 – (A)WEAR PARTICLES COLLECTED FROM LUBRICANT, TWO DISTINCT PARTICLE SIZES ARE ATTACHED TO THE MAGNETIC SAMPLE COLLECTOR (8MM DIAMETER). (B) DEMAGNETISED WEAR PARTICLES AT HIGHER MAGNIFICATION. ............................. 113

FIGURE 58 – (A) LUBRICANT FILM FAILURE ON RIGHT OF SAMPLE (B) LUBRICANT FILM FAILURE ON LEFT OF SAMPLE. MATERIAL REMOVED FROM THE SURFACE OF THE RAIL SAMPLE DESTROYS LUBRICANT FILM OVER A NOMINAL CONTACT WIDTH DEPENDING ON THE SIZE OF THE WEAR PARTICLES. ..................................................................... 114

FIGURE 59 – VARIABLE FREQUENCY DRIVE DISPLAY TORQUE VERSUS ANALOGUE OUTPUT CIRCUIT TO DATA ACQUISITION SYSTEM. NOTE: ALL VALUES FOR CALIBRATION NOT PLOTTED. ................................................................................................................... 121

FIGURE 60 – DIAGRAM OF TWIN-DISK ARRANGEMENT WITH NOMENCLATURE. ................ 124 FIGURE 61 – TORQUE COMPONENT DIAGRAM FOR OUTPUT SHAFT. ................................... 126 FIGURE 62 - MAXIMUM FLANGE SLIDING VELOCITY FOR A TYPICAL COMMUTER TRAIN

WHEEL DIAMETER (600MM). ..................................................................................... 128 FIGURE 63 - MAXIMUM FLANGE SLIDING VELOCITY FOR A TYPICAL HEAVY HAUL TRAIN

WHEEL DIAMETER (860MM). ..................................................................................... 129 FIGURE 64 – REFERENCE LOAD CELL CALIBRATION CURVE OR OUTPUT STRAIN VERSUS

INPUT LOAD AS APPLIED BY CALIBRATED MATERIALS TESTING DEVICE. ................. 130 FIGURE 65 – NORMAL VERSUS REFERENCE LOAD CELLS CALIBRATION CURVE. ............... 130 FIGURE 66 - POWER VERSUS TIME GRAPHS FOR WARM-UP PRIOR TO TESTING. DATA

PRESENTED HAS NOT BEEN PRE-PROCESSED. ............................................................ 134 FIGURE 67 – SLIP VERSUS TIME FOR THE TWO DEFINED WARM-UP PERIODS OF ZERO AND SET

BRAKING FORCES. ..................................................................................................... 136 FIGURE 68 – TEST SAMPLE TEMPERATURES AND SLIP VERSUS TIME FOR GROUP 1

LUBRICANT A TEST 1................................................................................................ 141 FIGURE 69 – EXPONENTIAL DECAY CURVE FITTED TO POWER LOSS DATA FOR GROUP 1

CONDITIONS............................................................................................................... 154 FIGURE 70 – EXPONENTIAL DECAY CURVE FITTED TO SLIP DATA FOR GROUP 1 CONDITIONS.

................................................................................................................................... 155 FIGURE 71 – BOX AND WHISKER PLOT OF NORMAL FORCE FOR EACH OF THE TESTS IN GROUP

1. ............................................................................................................................... 157 FIGURE 72 – BOX AND WHISKER PLOT OF INPUT ROLLING VELOCITY FOR EACH OF THE TESTS

IN GROUP 1................................................................................................................ 158 FIGURE 73 – BOX AND WHISKER PLOT OF BRAKING TORQUE UNDER FULLY DEVELOPED

CONDITIONS FOR EACH OF THE TESTS IN GROUP 1.................................................... 158 FIGURE 74 - NORMAL FORCE AND BULK SAMPLE TEMPERATURE VERSUS TIME FOR GROUP 1

TEST 1 LUBRICANT A................................................................................................ 159 FIGURE 75 - CUMULATIVE ABSORBED ENERGY OF LUBRICANT FILM VERSUS TIME FOR

GROUP 1. ................................................................................................................... 161 FIGURE 76 – POWER ABSORPTION RATES FOR EACH LUBRICANT IN GROUP 1 TESTS. NOTE

DIFFERENT TIME SCALES FOR EACH LUBRICANT....................................................... 162 FIGURE 77 - CUMULATIVE ABSORBED ENERGY VERSUS TIME FOR LUBRICANT C. ............ 163

viii

FIGURE 78 – TOTAL ENERGY ABSORBED PRIOR TO SET TRACTIVE FORCE LIMIT FOR GROUP 1.................................................................................................................................... 164

FIGURE 79 – OUTPUT TORQUE PROFILES FOR GROUP 1. ..................................................... 165 FIGURE 80 – SLIDING DISTANCE OF LUBRICANT PRIOR TO SET TRACTIVE FORCE LIMIT FOR

GROUP 1. ................................................................................................................... 166 FIGURE 81 – SLIDING VELOCITY PROFILE FOR GROUP 1..................................................... 167 FIGURE 82 – (TOP) HALF LIFE PREDICTION FOR GROUP 1 USING ( ) bxf x ae c−= + .

(BOTTOM) VALUE OF PREDICTED MINIMUM SLIP ‘C’. ............................................... 168 FIGURE 83 – REGRESSION PLOTS FOR LUBRICANT A TEST 2 GROUP 1 IN THE REGION < 5%

SLIP. ........................................................................................................................... 169 FIGURE 84 - HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

( ) bxf x ae−= . ....................................................................................................... 170 FIGURE 85 – APPARENT VISCOSITY FOR GROUP 1. ............................................................. 171 FIGURE 86 - SLIP PROFILES FOR GROUP 2 AFTER SET CUT OFF LIMIT OF SLIP ACHIEVED.

LUBRICANT B TESTS 2 AND 3 HAD LIMITS OF 8% AND 7% RESPECTIVELY. ............. 172 FIGURE 87 - CUMULATIVE ABSORBED ENERGY VERSUS TIME FOR GROUP 2. ENERGY IS

CALCULATED FROM THE DIFFERENCE BETWEEN INPUT AND OUTPUT ENERGY. NOTE THE DIFFERENT SCALES ON VERTICAL AND HORIZONTAL AXES. .............................. 173

FIGURE 88 – TOTAL ENERGY ABSORBED PRIOR TO SET TRACTIVE FORCE LIMIT FOR GROUP 2.................................................................................................................................... 174

FIGURE 89 – POWER ABSORPTION RATES FOR EACH LUBRICANT IN GROUP 2 TESTS. NOTE THE DIFFERENT SCALES ON THE HORIZONTAL AXIS. ................................................. 175

FIGURE 90 – SLIDING DISTANCE OF LUBRICANT PRIOR TO SET TRACTIVE FORCE LIMIT FOR GROUP 2. ................................................................................................................... 176

FIGURE 91 – SLIDING VELOCITY PROFILES FOR GROUP 2. NOTE THE DIFFERENT SCALES ON THE HORIZONTAL AXIS. ............................................................................................. 177

FIGURE 92 – (TOP) HALF LIFE PREDICTION FOR GROUP 2 USING ( ) bxf x ae c−= + . (BOTTOM) VALUE OF PREDICTED MINIMUM SLIP ‘C’ OR OFFSET COEFFICIENT......... 178

FIGURE 93 - HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 2 TESTING USING

( ) bxf x ae−= . ....................................................................................................... 179 FIGURE 94 - APPARENT VISCOSITY FOR GROUP 2............................................................... 180 FIGURE 95 - CUMULATIVE ABSORBED ENERGY VERSUS TIME FOR GROUP 3. ENERGY IS

CALCULATED FROM THE DIFFERENCE BETWEEN INPUT AND OUTPUT ENERGY. NOTE THE DIFFERENT SCALES ON VERTICAL AND HORIZONTAL AXES. .............................. 181

FIGURE 96 – TOTAL ENERGY ABSORBED PRIOR TO SET SLIP LIMIT FOR GROUP 3. ............. 182 FIGURE 97 – POWER ABSORPTION RATES FOR EACH LUBRICANT IN GROUP 3 TESTS. NOTE

THE DIFFERENT SCALES ON THE HORIZONTAL AXIS. ................................................. 183 FIGURE 98 – SLIDING DISTANCE OF LUBRICANT PRIOR TO SET TRACTIVE FORCE LIMIT FOR

GROUP 3. ................................................................................................................... 184 FIGURE 99 – SLIDING VELOCITY PROFILE FOR GROUP 3. NOTE THE DIFFERENT SCALES ON

THE HORIZONTAL AXIS. ............................................................................................. 185 FIGURE 100 – OUTPUT TORQUE SIGNAL FOR LUBRICANT A IN GROUP 3. .......................... 186 FIGURE 101 – (TOP) HALF LIFE PREDICTION FOR GROUP 3 USING ( ) bxf x ae c−= + .

(BOTTOM) VALUE OF PREDICTED MINIMUM SLIP ‘C’. ............................................... 187 FIGURE 102 - HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 3 TESTING USING

( ) bxf x ae−= . ....................................................................................................... 188 FIGURE 103 – APPARENT VISCOSITY FOR GROUP 3. ........................................................... 189

ix

FIGURE 104 - CUMULATIVE ABSORBED ENERGY VERSUS TIME FOR GROUP 4. ENERGY IS CALCULATED FROM THE DIFFERENCE BETWEEN INPUT AND OUTPUT ENERGY NOTE THE DIFFERENT SCALES ON VERTICAL AND HORIZONTAL AXES. .............................. 190

FIGURE 105 – TOTAL ENERGY ABSORBED PRIOR TO SET TRACTIVE FORCE LIMIT FOR GROUP 4. ............................................................................................................................... 191

FIGURE 106 – POWER ABSORPTION RATES FOR EACH LUBRICANT IN GROUP 4 TESTS. NOTE THE DIFFERENT SCALES ON THE HORIZONTAL AXIS. ................................................. 192

FIGURE 107 – SLIDING DISTANCE OF LUBRICANT PRIOR TO SET TRACTIVE FORCE LIMIT FOR GROUP 4. ................................................................................................................... 193

FIGURE 108 – SLIDING VELOCITY PROFILE FOR GROUP 4. NOTE THE DIFFERENT SCALES ON VERTICAL AND HORIZONTAL AXES. .......................................................................... 194

FIGURE 109 – (TOP) HALF LIFE PREDICTION FOR GROUP 4 USING ( ) bxf x ae c−= + . (BOTTOM) VALUE OF PREDICTED MINIMUM SLIP ‘C’. ............................................... 195

FIGURE 110 - HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 4 TESTING USING

( ) bxf x ae−= ........................................................................................................ 196 FIGURE 111 – APPARENT VISCOSITY FOR GROUP 4. ........................................................... 197 FIGURE 112 – TOTAL ABSORBED ENERGY FOR GROUPS OF TESTS. NOTE THE DIFFERENT

SCALES ON THE VERTICAL AXIS................................................................................ 198 FIGURE 113 – TOTAL SLIDING DISTANCE PRIOR TO SET TRACTIVE FORCE LIMIT. NOTE THE

DIFFERENT SCALES ON THE VERTICAL AXIS. ............................................................ 199 FIGURE 114 – HALF LIFE VALUES SUMMARY NOTE THE DIFFERENT SCALES ON THE

VERTICAL AXIS. ........................................................................................................ 201 FIGURE 115 – APPARENT VISCOSITY VERSUS TIME FOR GROUP 1. NOTE THE DIFFERENT

SCALES ON THE HORIZONTAL AXIS. .......................................................................... 205 FIGURE 116 - APPARENT VISCOSITY VERSUS TIME FOR GROUP 2. NOTE THE DIFFERENT

SCALES ON THE HORIZONTAL AXIS. .......................................................................... 207 FIGURE 117 - APPARENT VISCOSITY VERSUS TIME FOR GROUP 3. NOTE THE DIFFERENT

SCALES ON THE HORIZONTAL AXIS. .......................................................................... 208 FIGURE 118 - APPARENT VISCOSITY VERSUS TIME FOR GROUP 4. NOTE THE DIFFERENT

SCALES ON THE HORIZONTAL AXIS. .......................................................................... 209 FIGURE 119 – ARES RHEOMETER USED FOR RHEOLOGY TESTING. ................................... 213 FIGURE 120 – CONE AND PLATE ARRANGEMENT FOR RHEOMETER TESTING. .................... 214 FIGURE 121 – APPARENT VISCOSITY VERSUS SHEAR RATE USING A FLAT PLATE

RHEOMETER............................................................................................................... 215 FIGURE 122 – ASTM D1092 GREASE PUMPABILITY RESULTS. ......................................... 217 FIGURE 123 - ASTM D2596 FOUR BALL WEAR TEST RESULTS. ........................................ 218 FIGURE 124 – ASTM D2596 WELD LOAD RESULTS........................................................... 219 FIGURE 125 – ASTM D2266 SCAR DIAMETER RESULTS. ................................................... 220 FIGURE 126 – TWO CROSSED CYLINDERS CALCULATION EXAMPLE(ESDU 1995). ........... 273

x

LIST OF TABLES

TABLE 1 LUBRICATION EFFECTIVE DISTANCE (MARICH ET AL. 2001A). 36 TABLE 2 – INPUT PARAMETERS FOR CONTACT STRESS PREDICTIONS USING THE PROFILES OF

SATO (2005) 70 TABLE 3 – TEST PARAMETERS USED FOR CONTACT MECHANICS CALCULATIONS 77 TABLE 4 - MANUFACTURER SPECIFIED VISCOSITY VALUES FOR TESTED LUBRICANTS. 87 TABLE 5 – PREDICTED MINIMUM LUBRICANT FILM THICKNESSES FOR TESTED LUBRICANTS.

88 TABLE 6 – THEORETICAL RESULTS FOR INPUTS TO EHL CALCULATIONS. 95 TABLE 7 - MATERIAL PROPERTIES OF TEST SAMPLES (MARICH AND MUTTON 1989). 115 TABLE 8 – MECHANICAL PROPERTIES OF SIMILAR HIGH CARBON STEEL ALLOYS

(AUTOMATION CREATIONS 2005B; AUTOMATION CREATIONS 2005A). 115 TABLE 9- MEASURED HARDNESS RESULTS FOR RAIL AND WHEEL SAMPLES WITH MINIMAL

LOADING CYCLES. 116 TABLE 10 – RAIL SAMPLE HARDNESS RANGE IN HB (BRINELL 3000 KGF STD). 116 TABLE 11 - WHEEL SAMPLE HARDNESS RANGE IN HB (BRINELL 3000 KGF STD). 116 TABLE 12 – ROUGHNESS MEASUREMENTS TAKEN FROM WHEEL AND RAIL SAMPLES AFTER

MACHINING AND AT THE COMPLETION OF ALL LUBRICATED TESTING. 117 TABLE 13 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF SURFACE VELOCITIES

FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 139

TABLE 14 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF SURFACE VELOCITIES FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 139

TABLE 15 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF SLIP RATIO FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 140

TABLE 16 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF SURFACE VELOCITIES FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 142

TABLE 17 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF INPUT AND OUTPUT POWER FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 142

TABLE 18 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF DISTANCE ROLLED FOR GROUP 1 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 143

TABLE 19 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF DISTANCE SLID AND POWER ABSORBED FOR GROUP 1 LUBRICANT A TEST 1 RESULTS. 145

TABLE 20 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF DISTANCE SLID AND POWER ABSORBED FOR GROUP 1 LUBRICANT A TEST 1 RESULTS. 147

TABLE 21 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF SURFACE VELOCITIES FOR GROUP 1 TEST PARAMETERS. 148

TABLE 22 - VALUES FOR EXPERIMENTAL ERROR CALCULATION OF APPARENT VISCOSITY, SHEAR STRESS AND SHEAR RATEFOR GROUP 1 TEST PARAMETERS. 149

TABLE 23 – TESTING VARIABLE VALUES. 152 TABLE 24 – EXTRAPOLATED MINIMUM VALUES FROM EXPERIMENTAL DATA. 155 TABLE 25 – HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

( ) bxf x ae−= . 169 TABLE 26 – HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

( ) bxf x ae−= . 179

xi

TABLE 27 – HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

( ) bxf x ae−= . 188 TABLE 28 – HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

( ) bxf x ae−= . 196 TABLE 29 – LUBRICANT PERFORMANCE SUMMARY. 202 TABLE 30 – RELATIVE LUBRICANT PERFORMANCE SUMMARY. 203 TABLE 31 – QUALITATIVE PERFORMANCE OF LUBRICANTS. 204 TABLE 32 – EXAMPLE VALUES FOR NEEDLE ROLLER IN BEARING RACE (2003). 271 TABLE 33 – COMPARISON OF RESULTS BETWEEN CALCULATION METHODS. 271 TABLE 34 – EXAMPLE VALUES FOR TWIN-DISK FATIGUE TESTING DEVICE WITH IDENTICAL

STEEL SAMPLES (ESDU 1995). 272 TABLE 35 – COMPARISON OF RESULTS BETWEEN CALCULATION METHODS OF CONTACT

STRESSES FOR TWIN DISK FATIGUE TESTING MACHINE (VALUES IN PARENTHESES CALCULATED WITHOUT FRICTION/TRACTION FORCE). 272

TABLE 36 – EXAMPLE VALUES FOR CROSSED CYLINDERS OF DIFFERING MATERIALS (2003). 273

TABLE 37 – COMPARISON OF RESULTS BETWEEN CALCULATION METHODS. 274 TABLE 38 – COMPARISON OF RESULTS BETWEEN CALCULATION METHODS OF ESDU AND

AUTHOR’S FOR PRINCIPAL AXIS ANGLE OF 90 DEGREES. 274 TABLE 39 – ELLIPTICAL CONTACT EXAMPLE FOR TWO TOROIDS IN CONTACT (2003). 275 TABLE 40 - COMPARISON OF RESULTS BETWEEN CALCULATION METHODS OF BORESI AND

SCHMIDT (1985) AND AUTHOR’S. 275

xii

STATEMENT OF ORGINAL AUTHORSHIP

The work contained in this thesis has not been previously submitted for a

degree or diploma at any other higher education institution. To the best of my

knowledge and belief, the thesis contains no material previously published or

written by another person except where due reference is made.

Signature: _______________________________

Lance Jon Wilson

Date:____________________________________

xiii

ACKNOWLEDGMENTS

The author wishes to thank all the technical staff of the School of Mechanical

Manufacturing and Medical Engineering. Special thanks to Wayne Moore,

Mark Hayne, Terry Beach, David McIntosh, David Allen, Alf Small, Glen

Turner and Jonathan James. I would also like thank Queensland Rail who has

supported this project both financially and with expert opinion.

Thanks go to CIEAM and the AMM group at QUT for financial support.

Special thanks to the supervisors of this project, Doug Hargreaves, Richard

Clegg and John Powell.

Thank you to my friends and family who have supported me throughout this

project.

To Patrick, the most determined man on the planet, thanks for giving me the

“Harden up and dry your eyes” at the most opportune moment and reigniting

my interest in research.

To Cameron thanks for helping me out with the quantitative analysis, and for

the editing services.

To Fiona my life partner, special thanks for all the support.

xiv

NOMENCLATURE

a = Major ellipse semi axis or contact half width

cA = Contact area

cA∂ = Error in contact area

ya = Acceleration in the ‘y’ direction

,A B = Geometry parameters

b = Minor ellipse semi axis or contact half width

ob = Gauge width

D = Distance rolled

D∂ = Error in distance rolled

iD = Distance rolled of input shaft

iD∂ = Error in distance rolled of input shaft

oD = Distance rolled of output shaft

oD∂ = Error in distance rolled of output shaft

sD = Distance slid

sD∂ = Error in distance slid

xv

TD = Total distance slid

TD∂ = Error in total distance slid

e = Proportion of total value

E = Young’s modulus

'E = Effective modulus

E = Absorbed energy

E∂ = Error in absorbed energy

sE = Sliding energy

sE∂ = Error in sliding energy

TE = Total Absorbed energy

TE∂ = Error in absorbed energy

( )E m = Complete elliptical integral of the second kind

( )f x = Function of x

F = Friction force

BTF = Force from shearing lubricant

FF = Flange force

g = acceleration due to gravity

xvi

ah = Super-elevation of rail

minh% = Minimum film thickness

K = Contact width equation constant

ik = Material constant, i denotes body number

( )K m = Complete elliptical integral of the first kind

L = Length of rectangular contact

lΔ = Change in length

0l = Original length

Tm = Mass of train carriage

n = Number of measurements

( ) ( ) ( ), , , , , ,p p y p x y p x y z = Pressure or pressure at location

P = Normal force

fP = Power absorbed by friction in simulator

maxP = Maximum power

iP = Power of input shaft

iP∂ = Error in power of input shaft

0p = Maximum pressure

xvii

oP = Power of output shaft

oP∂ = Error in power of output shaft

sP = Power absorbed by lubricant

sP∂ = Error in power absorbed by lubricant

xQ = Tractive force in direction of rolling

r = Rolling radius

r∂ = Error in rolling radius

R = Effective contact radius

cR = Curve radius

DR = Curvature difference

iiR = Radius of curvature, first i denotes body number and second i axis

number

ir = Rolling radius of input shaft

ir∂ = Error in rolling radius of input shaft

or = Rolling radius of output shaft

or∂ = Error in rolling radius of output shaft

xR = Effective radius in ‘x’ direction

xviii

yR = Effective radius in ‘y’ direction

t = Sample time

T = Torque

T∂ = Error in torque

BFT = Bearing friction torque

CT = Transmitted torque through contact patch

tt = Thickness

TT = Torque transducer torque

TΔ = Change in temperature

iT = Torque of input shaft

iT∂ = Error in torque of input shaft

oT = Torque of output shaft

oT∂ = Error in torque of output shaft

maxT = Maximum torque

u% = Mean surface velocity

v = Surface velocity

v∂ = Error in surface velocity

xix

iv = Surface velocity of input shaft

iv∂ = Error in surface velocity of input shaft

ov = Surface velocity of output shaft

ov∂ = Error in surface velocity of output shaft

,s su v = Sliding velocity

sv∂ = Error in sliding velocity

Tv = Train velocity

VΔ = Change in volume

HV = Volume when heated

0V = Original volume

W = Dimensionless load parameter

w = Rotational Speed

w∂ = Error in rotational speed

iw = Rotational Speed of input shaft

iw∂ = Error in rotational speed of input shaft

ow = Rotational Speed of output shaft

ow∂ = Error in rotational speed of output shaft

xx

zw = Load per unit width

x = Distance slid

y = Lubricant film thickness

lα = Linear thermal expansion coefficient

μ = Coefficient of friction

ξ = Experimental slip ratio

PVξ = Pressure viscosity coefficient

ξ∂ = Error in experimental slip ratio

xξ = Slip ratio in the direction of rolling

Vα = Volume thermal expansion coefficient

φ = Diameter

δ = Normal approach of bodies

yσ = Yield stress

yτ = Shear yield stress

USσ = Ultimate tensile strength

USτ = Ultimate shear yield strength

xxi

σ = Poisson’s ratio

xσ , yσ , zσ = Stresses in principal directions

η = Apparent viscosity

η∂ = Error in apparent viscosity

τ = Shear stress

τ∂ = Error in shear stress

xyτ , yzτ , zxτ = Shear stresses in principal directions

eτ = Effective shear stress, square root of second invariant of deviator tensor

γ = Shear strain

γ& = Shear strain rate

γ∂ & = Error in shear strain rate

β = Ellipse semi-axes ratio

0η = Absolute viscosity

Subscripts i = Subscript denoting input shaft

o = Subscript denoting output shaft

, ,x y z = Subscript denoting direction

1, 2 = Subscripts denoting body number

C h a p t e r 1

INTRODUCTION

1.1 Background

Wear of railroad rolling stock and rails costs millions of dollars each year in all

rail systems throughout the world. Excessive levels of noise are generated at

the rail/wheel interface in conjunction with wear, which is unacceptable in an

environmentally responsible rail network. It is commonly accepted that wear

and noise can be reduced through the use of lubrication at the rail/wheel

interface (Scott et al. 1998).

Wear of rail rolling stock is generally divided into two main areas, flange wear

and tread wear. These areas of wear are related to the contact points at the

rail/wheel interface. This thesis focuses on rail curve lubrication, with specific

emphasis on lubrication in the gauge corner (the location where the external

corner of the rail and the internal corner of the wheel contact). The reasons

for targeting the flange area is that flange wear has a significantly higher

maintenance cost and that increased flange contact increases energy

consumption (Reiff 1986; O'Rourke et al. 1989).

In industry, attempts have been made to address flange wear using lubricants.

There are presently a large number of lubricants and lubricant applicators

used on existing rail networks. The choice of lubricant and applicator is

currently based on considerations that do not address the problem of wear

directly. This is reflected by a lack of fundamental knowledge in the

performance of rail curve lubricants.

In the work of Clayton et al. (1988; 1989) lubricants were investigated in both

track and laboratory conditions. The field testing was designed to measure the

four features that Clayton et al. proposed are important for flange lubrication:

mobility (lubricant transport from the application point); durability (number

2

of axles to dry conditions); lubricity (reduction of friction); and contamination

(migration of the lubricant to the rail tread). Aspects of lubricity and durability

were investigated in the laboratory using a twin disk Amsler device. The

results of the field testing yielded a low correlation between field and

laboratory. In addition to this low correlation it was found the lubrication

conditions in the two tests were different. Furthermore Clayton et al. (1989)

questioned the statistical variation in performance between the lubricants. In

summary Clayton et al. (1989) states “At the present time, no laboratory test

would appear to be able to be used with confidence to evaluate the in-service

performance of wheel/rail lubricants.” The rail/wheel simulator developed in

the current thesis was designed and tested to achieve confidence in laboratory

testing of rail curve lubricants.

Witte and Kumar (~1986) and Kumar et al. (1991) designed a new test and

apparatus for design of rail lubricants in response to an industry need for a

standard test. Their focus, in terms of lubricant properties, was on lubricant

mobility, durability and lubricity. Their work ignored the effects of lubricant

migration that was investigated in the work of Clayton et al. (1988; 1989).

Witte and Kumar's (~1986) new device focused on simulating the stress and

creep properties, which is in contrast to work of Clayton et al. (1988; 1989)

that utilised a standard laboratory wear test device.

The results of Witte and Kumar's (~1986) concluded that the new test

correlated with a larger wheel/rail simulator, but quantitative correlation with

field data was not performed as in the work of Clayton et al. (1989).

Qualitative comparison between the laboratory and field data yielded some

correlation but the results were inconclusive. In summary the results of this

work provided a methodology for the analysis of lubricants with respect to

the parameters relevant to the wheel/rail system.

3

This thesis will address the lack of fundamental knowledge in the

determination of lubricant performance in gauge corner contact, focussing on

the equipment and the methodology employed in testing performance.

The rail industry requires a method for predicting the in-service performance

of a flange lubricant from a laboratory environment. Clear identification of

the in-service conditions of the rail over a range of conditions is required to

achieve such a method. A replica can then be made within a laboratory

environment where conditions can be varied and the effect of the lubricant

on the rail/wheel contact directly quantified.

It is the author's opinion from discussion with rail industry professionals and

from the broad rail industry literature that an effective lubricant for the flange

contact must possess the following characteristics:

• It must be highly adhesive to pearlitic steel;

• It must be able to maintain a protective film despite high velocity

rolling contact;

• When the lubricant is struck by the opposite contact surface the

lubricant must spread across this surface and not be expelled from the

contact into an undesirable location (ground, top of rail, rail vehicle

body);

• The lubricant must have the ability to be spread from the initial

application point down the rail and around the wheel;

• The lubricant must have a predictable decay in coefficient of friction

or lubricant effectiveness as a catastrophic lubricant film failure

translates to maximum wear. If wear is considered an energy based

process (Huq and Celis 2002) then as the coefficient of friction

increases there is a corresponding increase in the wear energy.

4

• For the purposes of inspection of lubricator functionality by

maintenance personnel the lubricant could exhibit an observable

colour.

• The lubricant must have a high resistance to sliding and sliding wear

processes.

Anecdotally the most significant issue in rail curve lubrication is the

application of the lubricant. European railways disable their wayside

lubricators during the winter months and use snow as the flange lubricant

(Waara 2001). The reasons behind this are twofold, primarily the lubricant

applicators do not function in the cold and cannot be maintained whilst

buried beneath the snow, and the other reason is that the snow itself appears

to provide adequate lubrication. Wear measurements carried out during

winter and summer in Sweden confirmed that snow is an effective lubricant

(Nilsson 2002). This form of lubrication is unsuitable in a warm environment.

In a warm environment without frozen winters, such as the Australian

Queensland Rail network, an effective lubricant must be applied.

With the desired properties of rail/wheel lubrication identified, a suitable

method for quantifying the effect on the rail/wheel system to variations in

lubrication properties is required.

1.2 Objective of Research

The objective of this research is to quantify rail curve lubricant performance

through laboratory simulation. The steps to achieve the objective of this

thesis were:

Measure the properties of the lubricants currently in use.

The lubricants have been laboratory tested to define the properties using the

ASTM and other appropriate standards.

5

Calculate and predict the contact mechanics at the wheel and rail gauge face.

A literature survey identified the methodologies employed to measure and

predict the rail/wheel contact conditions. Upon review, a suitable method was

selected and used to analyse the laboratory simulation devices.

Identify the wear mechanisms at the wheel and rail gauge face.

The wear mechanisms were identified using the parameters of the contact and

comparison with the body of literature. Wear particles were gathered and

inspected to assist in verifying the wear mechanism identified. Microscopic

inspection of the surfaces was carried out.

Quantify the effect of lubrication on the wear mechanisms arising from sliding and transmitted forces.

The laboratory simulator was used to gather data in lubricated and

unlubricated conditions for the purpose of providing lubricant performance

measurements.

Identify the tribological parameters required to minimise wear without introducing competing wear mechanisms.

Analysis of the results from the lubricant testing and laboratory simulators

determined trends between them. These trends indicated the lubricant

properties' effects on the system.

In addition to these steps, new methods for rail curve lubricant performance

measurement will be presented. These measurements include total absorbed

energy, the energy absorbed in the lubricant film instead of being utilised for

wear processes; total distance slid, the sliding distance or accumulated strain

achieved prior to development of a set tractive force limit; half life of

lubricant, the time taken for a lubricant to lose half of its sliding performance;

and apparent viscosity, a measure of the lubricity presented with respect to

accumulated strain.

6

Lubrication can be optimised for industry to effect a reduction in flange wear

so that maintenance resources are minimised and the rail/wheel life

maximized. The method used to achieve this will quantify rail curve lubricant

performance through laboratory simulation

1.3 Summary and Thesis Outline

Chapter 2 will explore the issues surrounding rail/wheel lubrication to

provide an overview of the area. Chapter 3 will then present the contact

mechanics relevant to this thesis with examples of in-service and simulated

conditions. This chapter highlights the similarities and differences of

simulator and 'real world' conditions to gain an insight into the experimental

methodology of Chapter 4. The rail/wheel simulator used in this work was

formerly a device used for rail/wheel materials investigations. Chapter 4

details the modifications to the simulator to analyse lubricant performance, as

well as the method, measurements and their associated errors. Chapter 5

presents all the experimental results from standards-based lubricant testing

and results from the simulated rail conditions with discussion on industrial

relevance and experimental findings. Finally, Chapter 6 summarises the

findings of the research, presents the conclusions and discusses directions of

future work.

7

C h a p t e r 2

LITERATURE REVIEW

2.1 Rail/Wheel Wear Testing

Rail/wheel wear testing is of interest to this research as these devices are

designed to replicate the wear conditions of a rail/wheel contact. Testing of

rail and wheel materials has been and is carried out to optimise the costs

associated with the wear of these materials by researchers and commercial

interests (Marich and Mutton 1989; Lee and Polycarpou 2005). Tests are

usually carried out with scaled models as, in most cases, the feasibility of

constructing a full size system is impractical and the costs prohibitive. In the

smaller testing apparatus two main types of apparatus are popular, twin disk

testing (see Figure 1), and pin on disk testing. A variant of the pin on disk

testing, ball on flat is shown in Figure 2.

The scientific and engineering communities have investigated the validity of

laboratory simulation when compared to specific real world engineering

problems. Marich and Mutton (1989) and Witte and Kumar (~1986), have

attempted to model the rail/wheel interface with limited success. Tribological

simulations are particularly complex to simulate because small changes in

conditions can produce extreme changes in results.

Perfect simulation of wear system is achieved when all of the tribological

conditions are exactly the same as the engineering system being investigated.

This is difficult to achieve, as parameters such as chemical environment,

weather conditions and variations in machine output or load cannot be

simulated in a laboratory environment. A full scale test facility of a rail/wheel

simulator located in Pueblo USA (Hannafious 1995) is a good example of a

thorough simulation, however this facility still suffers from the inability to

control weather conditions.

8

Figure 1 – Twin disk test apparatus from the work of Deters and Proksch (2005).

The author postulates that simulation of the rail/wheel interface, with

particular emphasis on tribology, should therefore:

Identify the required tribological parameters such as geometry (scaled models), contact area, load, sliding speed, material temperature, lubrication (application rate, application area) and chemical environment.

Identify parameters which affect wear modes. In the case of a lubricated flange contact, lubricant application rate significantly affects the wear rate.

Consider the physical size or scale of the simulation. The magnitude of the variation as a result of scale is unknown and must be verified experimentally.

Consider time as a scale factor. In a rail system wear takes several years.

Compare experimental results with the 'real' situation.

9

Swedish researchers Jendel and Nilsson (Jendel 1999; Nilsson 2002) have

begun to address these simulation problems by measuring sections of their

rail network in order to empirically predict the wear rates and investigate

lubricant performance.

Figure 2 – (a) Ball on disk wear test apparatus, specified loading regime and (b) typical wear scar of the work of Lee and Polycarpou (2005).

2.2 Rail/Wheel Wear Processes

Rails and wheels are exposed to a wide range of conditions and wear modes

or processes which lubrication is used to minimise. In order to simulate the

rail/wheel interface a simulator is required to be capable of these processes. A

suitable method of representing the conditions under which each of these

wear processes can occur was presented by Lim and Ashby (1986). They

plotted the results of wear testing and wear models in a non-dimensional

format as shown in Figure 3.

Lim and Ashby (1986) summarise wear modes into four main classifications,

seizure, melt wear, oxidation-dominated wear and plasticity dominated wear.

It is possible for all of the wear process types to occur is a rail/wheel system.

A detailed description of the wear processes, including mathematical models,

is included in Sections A through F in the Appendix A.

10

Figure 3 - Steel pin-on-disk wear map combining results from multiple authors by Lim and Ashby (1986).

2.2.1 Rail/Wheel Wear: Surface initiated rolling contact fatigue

Rail industry infrastructure experiences rolling contact fatigue as a material

failure in rails and wheels due to repeated loading. Two main types of fatigue

cracks occur, surface initiated cracks and subsurface cracks. Surface cracks are

initiated when the surface material reaches its plasticity (strain) limit: further

loading past this point results in cracking. Ratchetting is the process of

accumulated plastic strain from repeated loading. The repeated loading must

be a combination of normal and tractive forces, as the compressive stress

alone is not responsible for the plastic strain. Surface forces, such as traction

11

and creep forces, plastically deform the bulk material. The combination of

stresses and strains gives rise to hardening of materials and residual stresses, at

which point, if the further loading exceeds the material capabilities, will lead

to fatigue failure.

Rolling contact fatigue cracks propagate differently in the mating rail and

wheel faces. Wheels have cracks which penetrate into the material and branch

once the cracks reach a nominal depth. This branching then commonly

proceeds in a circumferential direction until further cracks are reached, then a

piece of the material may detach from the surface. The same process occurs

in rails but the crack can proceed in a direction perpendicular to the contact

and cause a rail break. A driving factor for crack propagation is the friction

associated with the crack faces, which is important when considering the

environment where rolling contact fatigue cracks develop.

2.2.2 Rail/Wheel Wear Particles

Wear particles from rails and wheels are grouped according to wear modes.

The tread contact primarily experiences rolling and micro-slip, whereas closer

to the flange sliding becomes more dominant because of the conical wheel

profile. The rolling and micro-slip region at the tread contact experiences

chemical (oxidative) and fretting wear processes which progress to plastic

deformation wear processes as the proportion of sliding increases (Bolton and

Clayton 1984; Olofsson and Telliskivi 2003). The wear debris from

rolling/sliding processes in the work of Bolton and Clayton (1984) is divided

into three classes. Type I wear is characterised by thin small oxidised wear

particles. Type II wear is characterised by a range of wear particle sizes with

the ability to form agglomerated particles. Type III wear is characterised by

high wear rates, large particle size and extremely rough surface texture.

Later work by Lewis and Dwyer-Joyce (2004) also define three modes of wear

using a wear mapping technique (see Figure 4). The definition of each mode

is based on wear particles, surface appearance, and wear rate. Each work

12

defines the wear modes with a different terminology but the metallurgical

analysis is consistent between them.

Deters and Proksch (2005) also reported similar findings with respect to wear

particles and hypothesised similar wear processes.

Figure 4 - Wear map showing defined wear modes for British Standard rail steels in an Amsler Wear Test Device (Lewis and Olofsson 2004).

2.3 Rail Lubricant Characteristics

Railway systems use a wide variety of lubricants to combat the effects of wear

in the flange contact. These lubricants are usually of three main types, oil,

grease and water. Railway systems often use a combination of lubricants.

Some European rail systems use grease wayside lubricators for six months of

the year and rely on snow (water) for the remaining months (Waara 2001). In

Australia grease wayside lubricators are most widely used, with on-board

lubricators beginning to be used as well. It is still not clear as to what

parameters make a ‘good’ lubricant.

The parameters of amount and location are generally agreed upon to ensure

best practice for lubrication. If the lubricant is not applied correctly it can be

13

spread to the tread of the wheel causing a dangerous loss of traction. Likewise

if the lubricant is applied in the correct location but is in excess, lubricant can

migrate to the tread contact area, again dangerous. Therefore right amount,

right location, is the focus for industry.

Lubricant manufacturers specify the benefits of rail curve lubrication in their

advertising material. They include:

reduction of friction and wear;

reduction or fuel/energy consumption

reduction of noise

reduction of maintenance of rolling stock and rail infrastructure

The lubricant properties they describe as beneficial are:

low toxicity

water resistant

wide temperature operating range

high adhesion to rail and wheel surfaces

good pumpability and compatibility with lubricant applicators

Recent studies by Hannafious (1995) showed benefits of rail lubrication to be

reduced fuel consumption, reduced wheel wear and reduced rail wear. The

lubricant applicators in these studies were of three general types, wayside,

onboard and high rail. The lubricators each had a preferred lubricant type:

wayside and high rail applicators used grease and onboard lubricators used

liquids sprayed onto the contacting surfaces. In addition to the benefits of

lubrication there are a number of negative issues:

Loss of traction from spread to TOR (top of rail)

Environmental damage from used lubricants

Locomotive fires from excess build up of lubricant

14

Increased creep forces resulting in rail roll-over and derailment.

Lubrication is generally applied for two reasons, both based on economics.

Firstly lubrication reduces rolling friction and energy lost to friction, a

reduction in the running costs of a rail network. Secondly reduced wear

provides a reduction in maintenance of rail infrastructure and rolling stock.

Research has focused on the first reason due to the relative ease of measuring

performance (Kumar et al. 1991). Unfortunately the research of Kumar et

al.(1991) has yet to provide any conclusive results as to which lubricant is the

best.

In Australia and USA grease is widely used as oil is considered unsuitable

(International Heavy Haul Association 2001). This paradigm arises from a

number of reasons. The fact that grease will stay adhered to a surface is an

important one as lubricant waste is an environmental and safety issue. Grease

also tends to be more resistant to environmental effects such as temperature

and rain. It is also far easier to add solid lubricants to grease; suspension of

graphite or molybdenum disulfide is difficult to achieve in oil.

Assuming that grease will be the optimum lubricant, parameters that improve

performance need to be targeted. Temperature stability is important, as well

as apparent viscosity. It is of little value if a grease has excellent temperature

stability and a viscosity which prevents it from being pumped. In situation

where flange temperatures may exceed 250°C in the rail/wheel system,

suitable soaps to suspend in grease are limited. Metal soaps are currently used

in lubricating greases to achieve temperature stability. Calcium soap greases

are considered to be suitable for lower temperature conditions, as above 87°C

stability is lost. Calcium greases also have excellent hydrophobic properties

(Polishuk 1998). Lithium soap greases, such as those in use in the Queensland

Rail network, have far higher temperature stability but lack the same

hydrophobic properties as calcium soap greases.

15

The next ingredient, solid lubricant, is responsible for the high load carrying

capacity of grease. Two main types are used, graphite and molybdenum

disulfide. Queensland Rail specify that graphite must be used and in a

minimum concentration. Each solid lubricant displays similar tribological

performance, the differences being impurity concentrations and hydrophobic

behaviour. There are other types of solid lubricants, but not in wide use in rail

curve lubrication.

2.4 Lubrication Regimes

Rail contacts experience a wide range of lubrication regimes in the field and

following is a concise summary of these regimes. Fluid film lubrication is

commonly divided into regimes according to lubricating film thickness

(Hamrock 1994). By listing the regimes, in order, from the largest separation

between bodies to the smallest, gives hydrodynamic lubrication,

elastohydrodynamic lubrication, mixed lubrication and boundary lubrication.

The type of lubrication condition is determined by the load carrying capacity

of the lubricant film. In hydrodynamic lubrication the full load can be

supported by the hydrodynamic forces within the lubricant film.

Elastohydrodynamic lubrication (EHL) is characterised by pressures which

cause local elastic deformation of the surfaces separated by the lubricant film.

EHL is the last regime in which the lubricant film still separates the bodies.

Under mixed-mode lubrication, the lubricant film cannot maintain the

hydrodynamic forces needed to separate the bodies and so partial asperity

contact occurs between the opposing surfaces. Boundary lubrication is the

final regime where surface asperities are supporting the load fully. The rail

curve lubricants under investigation are typically in the EHL lubricating

regime and this will be assumed throughout the thesis.

16

Figure 5 – Separation distances between contacting surfaces for (a) hydrodynamic lubrication (HL)and elastohydrodynamic lubrication, (b) mixed-mode lubrication, and (c) boundary lubrication.

2.5 Rail Curve Lubricant Types Under Investigation

Currently there are two main types of lubricant used on the Queensland Rail

network, Aluminium and Lithium based lubricating greases. These greases will

be measured for performance using standards based tests and the rail/wheel

simulator for the thesis objective, to quantify rail curve lubricant performance.

17

Polishuk (1998) states that aluminium complex greases commonly have the

following properties.

High dropping point

High temperature stability

Excellent water resistance

Low water emulsibility

Good reversibility

Ease of pumpability

Excellent work stability

Reduced oil bleed potential

Good oxidation resistance

Polishuk (1998) also presents that historically aluminium soaps are considered

a polymer. The polymeric property is that upon heating the soap becomes

liquefied and subsequent cooling reforms the structure.

Polishuk (1998) presents the advantageous characteristics of lithium greases

as:

High temperature stability

Water insoluble

Hydrophobic

Good low temperature pumpability

Long shelf life

There are other types of lubricant available, calcium based and

environmentally adapted, but they are not in wide use in the Queensland Rail

network.

18

2.6 Rail Curve Lubricating Grease Specifications

Lubricants are designed to meet the specifications of a tribological system. In

the case of rail/wheel lubrication this system lacks definition. Rolling element

bearings, for example, have well defined specifications. Therefore in a system

where specifications are broad, lubricant manufacturers are not able to target

specific features of rail/wheel contact.

Rail companies specify properties of the lubricant which may or may not be

directly relevant to the wear processes encountered at the interface. These

properties are: specific soap type; solid lubricants; suitability for specific grease

applicators.

The soap type, as previously discussed, is chosen for two main reasons,

temperature stability and water resistance. In an indirect way these properties

reduce wear. Temperature stability allows for pumping of the grease and

keeps the grease in the correct area. Water resistance allows the grease to stay

in the flange contact zone despite adverse weather conditions. In Queensland

different greases are used in regions of adverse weather because of the

empirical data and 'gut feel' of the track maintainers.

The solid lubricant components of the lubricating grease are specified as they

are known to have good wear characteristics, but the question remains

whether they are effective in the rail/wheel system. The amount (percentage)

of solid lubricant does not have a significant effect on the wear rate (Waara

2001). Conversely too little solid lubricant does not reduce wear to the

minimum attainable.

In order to reduce the costs associated with track maintenance, lubricants

must be compatible with existing lubrication systems. The detrimental effect

of this philosophy is that new lubricants which cannot be used with existing

infrastructure tend not be used. Rail wear can take many years to achieve a

reduction in rail head area that can be measured with accuracy. This

19

corresponds to lengthy trial periods in which experimental control is very

difficult, if not impossible to achieve.

It is interesting to note that lubricant manufacturers lack a consistent

approach to flange and gauge face lubrication. The outcomes from this

research will enable manufacturers to develop optimised lubricants.

2.7 Rail Lubrication Research

The current research issues in flange/gauge face lubrication are:

Lubricant transport prediction/modelling

Lubricator efficiency is measured by determining the distance of lubrication from the application point. In the body of literature, modelling of the lubricant transport process is deficient/absent (Frank 1981).

Wayside lubricator positioning

There has been work in this area to determine algorithms for placement. The research of Thelen and Lovette (1996) proposes that through direct measurement of lubricator effectiveness more efficient placement can be achieved.

Lubricators/Lubricator application methods

Lubricators have progressed through a series of iterations from mechanical through hydraulic to electronic devices. The lubricant applicator methodology has changed to remedy the negative aspects of wayside lubricators specifically to ensure increased device reliability.

Lubricant technology and performance measurement

Lubricants are a commercial product and the research in their development is therefore not available for review. Performance measurements of rail curve lubricants require further research (Clayton et al. 1988; Kumar et al. 1991; Mulvihill et al. 1994; Waara 2001)

Rail/wheel contact is an extremely complicated interface to simulate.

Geometric and physical considerations change rapidly in actual contacts, thus

there are a vast number of variables to consider. Drawing comparisons

20

between field and laboratory is difficult and direct comparisons have not been

made from scaled simulation results (Kumar et al. 1991; Waara 2001; Witte

and Kumar ~1986). Full scale test facilities are yet to publish significant

conclusions on optimal lubricant and lubrication strategies. Field trials using

in-service equipment are nearly impossible to manage due to the shear

number of variables that require recording, from the weather to axle loading.

Another difficulty in all of the testing types is the length of time involved in

gathering data for wear rates.

American researchers have attempted to overcome the simulation difficulties

with a full scale test facility. The track, named FAST (Facility for Accelerated

Service Testing) is yet to produce definitive research results in rail/wheel

tribology. Another full scale test facility exists in Sweden and is used by

Chalmers University, but there have been no publications relating to lubricant

performance at the time of writing. The value of testing using full scale

facilities will come with the sheer volume of results, to be analysed once the

rail/wheel interface is better understood.

Laboratory simulation is considered a useful tool in other tribological systems

and development of such a tool is important. The review of laboratory

lubricant testing devices is limited due to the paucity of recent publications.

There are four groups (Clayton et al. 1988; Kumar et al. 1991; Mulvihill et al.

1994; Waara 2001) that have published in the area of rail lubrication, the most

current work being that of Waara (2001). The recent work of Waara in

Sweden has focussed on the correlation between laboratory and field

lubrication. The field testing of rail curve lubricants, which Waara started in

1997, has investigated the influence of mineral oil based greases, such as the

ones tested in this thesis, environmentally adapted greases and the influence

of solid lubricant additives to these greases. Waara’s laboratory testing used a

Plint and Partner High Frequency Apparatus with a “cylinder on flat”

arrangement. The cylinder is applied to the flat with a force, then slid in an

oscillating motion. This apparatus is in direct contrast to the three other

21

groups of researchers, all of whom used a different variant of a twin disk

apparatus.

The research of Waara (2001) using the cylinder on flat device has similarities

and differences between field and laboratory:

The cylinder sliding forwards and backwards matches the gauge face contact as trains travel in both directions. The exception in the field is heavy haul lines that have trains travelling loaded in one direction and unloaded in the other, creating a primarily unidirectional loading situation.

The cylinder sliding backwards and forwards is different to the field in that it does not incorporate the rolling component of the field contact.

The section of the cylinder that is sliding (the contact patch) remains in a constant state of stress allowing no time for stress relaxation to occur. The field situation is a cyclic loading one, a single point on the wheel is compressed once per revolution. Without cyclic loading the fatigue component of the wear processes is minimised.

The shape and stress distribution of the contact is similar to the field but the area of contact is much smaller. As the contact area decreases for simulators, the effect of surface roughness increases. In this situation the wear processes may change from the field wear processes.

The spread of lubricant is achieved by sliding the cylinder across the flat whereas the field process is primarily a rolling motion. The spread of lubricant by sliding is desirable when it is considered that the process is more damaging to the lubricant and forces more lubricant from the contact. However, spreading the lubricant by sliding does not reflect the rolling and sliding that occurs in the field.

The final important difference between field and laboratory is the shearing rate across the flat block. The shearing rate is variable from stopped to full velocity at the centre across the flat block. The lubricant film thickness will be affected by the different shear rate and entrainment velocity. In contrast, the field situation has a train velocity, and consequently the shear rate of lubricant, which is constant through the curve.

22

The limitations in shear rate and sliding in the laboratory apparatus of Waara

(2001) led to choosing a twin disk device for the work in this thesis. The twin

disk devices appear more suitable with respect to the criteria for simulation

discussed in this chapter.

The twin disk devices have their limitations with simulating field conditions as

well. Similar to the cylinder on flat device, the contact area is small.

Compared to field conditions the stress conditions can be replicated quite

accurately using a twin disk device. The most important similarity for twin

disk devices to field conditions is the rolling/sliding contact. Slide to roll ratio

or slip percentage in these devices is fixed for a particular test and geometry.

The test device enables any slide to roll ratio to be set for examination. Some

devices have no method for adjustment during a test, whereas others do

(Tyfour et al. 1995; Beynon et al. 1996; Fletcher and Beynon 2000). This style

of laboratory apparatus is commonly used for rail steel wear investigations

under unlubricated conditions.

An important difference to the field conditions is the uni-directional loading

of the samples and lubricant. As previously mentioned, trains are a

bidirectional load system. In twin disk devices the disks can be rotated

backwards by installing the metal test samples backwards. In the research of

Kumar et al. (1991) and Clayton et al. (1988) the testing did not include

bidirectional examinations. In works published on unlubricated wear testing

of rail steels there is also no mention of this practice being employed (Clayton

1995; Huq and Celis 2002; Olofsson and Telliskivi 2003).

Twin disk devices typically have the limitation of a variable shearing force,

which is measured and presented as a friction force. When a train travels

through the corner there is a constant lateral force from the balance between

centrifugal and gravitational forces. This lateral force is proportional to the

shearing force on the gauge corner and is designed to be within a range to

prevent trail derailments. Therefore, to test for a rail curve it is suitable to

23

control this shearing force. The rail/wheel simulator used in this thesis is

capable of controlling the shearing force applied to the test sample.

The spread of lubricant in twin disk devices is achieved by rolling and sliding.

The direction the lubricant can escape in the device is the direction

perpendicular to rolling. The spread of lubricant in the device is similar to

field conditions due to the rectangular contact of a twin disk test device,

which has the maximum pressure in a line in the axis of rolling. Thus the

lubricant is forced forwards and to the outer edge of the contact. To more

closely match the lubricant spread, the metal test samples can be machined to

a barrel shape to generate the contact patch shape of the field conditions.

Kumar et al. (1991) changed the test sample geometry in this way, however in

the field, the elliptical contact moves up and down the gauge face, not in a

single line as in the twin disk situation.

Mulvihill et al. (1994) investigated rail/wheel lubrication with a twin disk

machine. Their work identified the following requirements for a scale

rail/wheel simulator:

Mimic the stress and creep experienced at the contact.

Generate two dimensional creep for the flow of lubricant from the contact.

Measure lubricant performance continuously throughout testing.

Accurately control lubricant application.

Results from their experiments indicated that the relationship between

lubricating grease ingredients and performance was not clearly defined.

Varying amounts of extreme pressure additives and solid lubricants had an

unpredictable effect on the test outcome. The definitive conclusion from the

experiments is that lubricants reduce power consumption and increase wear

life of the components.

24

Clayton et al. (1989) identified a need for a “simple inexpensive laboratory test

method” for the performance characterisation of rail curve lubricants.

Following his earlier research (Clayton et al. 1989), Clayton (1996) reviewed

the tribological issues in rail wheel contact. In this review, Clayton (1996)

identified a need for a laboratory test device that can measure lubricant

performance under a starved lubricant film. The work presented later in this

thesis represents a method of predicting the decay or half life of the starved

lubricant film to address this deficit in rail curve lubricant research.

The twin disk device of Clayton et al. (1989) was commissioned to replicate

the wear processes of an unlubricated five degree curve (approximately 350m

radius (Frank 1981)) and measured wear reduction and retention of

lubrication. Their test aimed to screen potential lubricant candidates for full

field trials. Nine lubricants were investigated using the commissioned

conditions.

Clayton et al. (1989) identified large variability in newly machined rollers and

excluded the data from analysis without providing explanation as to the cause

of the increased wear. Experimentally the author has found that with newly

machined samples there is a process of strain hardening which lowers the

wear rate. Probably the source of increased wear in the work of Clayton et al

(1989) was the lower material strength during the development of strain

hardening in the newly machined samples. . Clayton et al. (1989) also found

experimentally, that increased or decreased applied lubricant did not increase

test variability. This finding would suggest that there is a limit to the lubricant

that can be maintained in the system and any excess does not improve

performance.

Clayton et al. (1989) measured the lubricant performance as the number of

revolutions to lubricant film failure and the wear rate. The number of

revolutions is representative of the number of axles or strain history and was

defined as retentivity. The retentivity measurement, the revolutions prior to

25

the measured friction force to reaching 50% of the normal force, in the work

of Clayton et al. (1989) had large variability ( ± 45%). The variability between

tests was larger than the range of presented results for comparison between

lubricants. The paper did not make clear if the variability was from the

accuracy and resolution of measurements of the device or the test method

itself. Under fully lubricated conditions the wear rate was reduced by 1400

times as compared to the unlubricated case.

In addition Clayton et al. (1989) found that as the rate of friction force

increased, there was a corresponding reduction in retentivity performance,

which was also found in the experimental testing in this thesis. The final

phase of the tests of Clayton et al. (1989), the phase in which the lubricant film

is failing, was observed to be more consistent with the results from field

testing, with respect to the observed lubricant film and friction force

development. Performance measurement of a similar phase in the rail/wheel

simulator testing from this thesis will present the decay in lubricant film.

Clayton et al. (1989) proposed that research was required to determine the

lubricant film thickness and the decay of this thickness. This research

shortfall has been advanced by this thesis with the presentation of a

performance criterion to address the issue of film decay, namely half life.

Kumar et al. (1991) stresses that three test parameters are vital to the success

of laboratory simulation: contact stress; creep or slip; and lubricant quantity.

Emphasising lubricant quantity as an important test parameter indicates that

the volume of lubricant was not sufficient to the point of excess in any of

their testing. This implication is contrary to the work of Clayton et al. (1989).

Therefore to remove this parameter as a source of test variability, sufficient

lubricant volume is imperative.

Kumar et al. (1991) used input power from the driving motor as the measure

of lubricant performance and stated that power measurements were difficult

because the change in power was small in magnitude. The author believes that

26

the measurement resolution of the equipment was inadequate for the

objectives of Kumar’s research.

From the four groups of researchers that have published work on rail/wheel

lubrication in the last twenty years, the current research builds upon the

foundations of their research, refines the method for testing lubricant

properties, and poses more accurate methods that exploit the gaps identified

in the body of rail/wheel lubrication research.

2.7.1 Surface initiated rolling contact fatigue with lubrication

In addition to the wear research presented in the previous section, research

into rolling contact fatigue under lubricated conditions has been carried out.

This research is of importance due to the influence of lubrication of surface

fatigue crack propagation. Surface cracks on rails and wheels are exposed to

environmental conditions which can reduce crack face friction and

consequently increase crack propagation. Lubrication of the crack faces can

be provided by water in the environment or added as part of the maintenance

effort in gauge face lubrication. The negative effects of lubrication on fatigue

crack propagation has been divided into three hypotheses by Bower (1988):

1) Crack face friction is reduced with the introduction of lubrication, which increases the forces responsible for crack propagation.

2) Hydraulic forces from the compression of the crack containing trapped lubricant increasing the Mode I stress intensity.

3) Hydraulic forces from the compression of the crack containing trapped lubricant preventing the re-bonding of the crack surfaces.

Ekberg and Kabo (2005b) summarised the experimental findings of

lubricated rolling contact fatigue testing, and reported that: lubrication is

essential for surface cracks to propagate, and rate of crack propagation is

27

driven by the lubricant viscosity. Ekberg and Kabo (2005b) highlight the

important aspects of rolling contact fatigue in a rail environment:

The rolling contact provides a moving and rotating stress field.

Cracks begin as a Mode I failure and as the length increases change to a mixed Modes II and III.

Despite the primary mode of fatigue failure being Mode I, typically the failures do not conform to the Paris Law of fatigue life which predicts that primarily compressive loading will not result in a fatigue failure.

Rail and wheel contact experience very diverse loading regimes which make failure prediction difficult.

Surface fatigue cracks are typically not encountered in tunnels (Ishida and Abe

1996; Kondo et al. 1996), which give credence to the hypothesis that water

promotes crack propagation. Seasonal variations in recorded rail degradation

were found by Kalousek et al. (1996) which pointed to water being the main

contributing factor.

Franklin et al. (2005) investigated lubricated rolling contact fatigue using water

as the lubricant (at a rate of 2 drops per second). Previous research (Clayton

and Su 1996) has identified that water lubricated contacts fail faster than those

lubricated with grease or oil (including biodegradable materials). Water is the

most commonly encountered lubricant in a rail system and yet leads to the

largest reduction in fatigue life of rail materials. Tractive forces from driven

or braked surfaces promote the growth of surface fatigue cracks, which was

found experimentally by Ishida and Abe (1996). Despite the increased surface

fatigue crack propagation rates from lubrication, Ekberg and Kabo (2005a)

also detailed the positive influences of lubrication. The positive influences are

reduction of friction (locomotive power), reduction in wear rates and

reduction in noise. The reduction of friction is of importance to surface

fatigue crack initiation as the tractive force is a contributing factor.

28

2.8 Lubricant Application Research

It is important to consider the lubricant application system for the purpose of

improving simulation conditions. Railroads have three main methods for

applying lubricant to the gauge corner (Kumar et al. 1991):

Wayside lubricators, see Figure 6.

On-board lubricators, see Figure 7.

High rail lubricators, see Figure 8 and Figure 9.

Figure 6 - Wayside lubrication device (photo courtesy of Queensland Rail).

29

Figure 7 – Vogel on-board lubrication device mounted to display components of system.

Figure 8 - Hi-rail lubrication vehicle (photo courtesy of Queensland Rail).

30

Figure 9 - Lubricant application by hi-rail vehicle (photo courtesy of Queensland Rail).

The lubricant types investigated in this research are applicable to wayside

lubricators. Research into wayside (trackside) lubrication has primarily focused

on evaluating the effectiveness of lubrication on the cost incurring aspects of

rail infrastructure and rolling stock. Marich et al. (2001a) and Thelen and

Lovette (1996) investigated the rail system and the effect of lubrication on this

system. Their research focuses on the reduction of wear and energy

consumption (tractive effort) associated with the flange/gauge face contact.

Commercial research into wayside lubricators has been slow due to the low

demand of new systems. New systems are implemented following a major

breakthrough, or existing system maintenance costs exceed the cost of

replacement systems. These new systems are often developed commercially

and the results unpublished.

Research by Marich et al. (2000; 2001b) measured efficiency of lubrication

strategies in the Hunter Valley in Australia by obtaining the friction

coefficients at the head of the rail. The projects modified the system

31

parameters of lubricator location with respect to direction, loading and

whether on hi-rail and low-rail or both. Details of precise location are not

provided by Marich et al. (2000; 2001b) . There is also no indication that an

analytical algorithm was used in the determination of lubricator location.

The work of Marich et al. (2000; 2001b) identified an issue of contact pressure

between gauge face and flange where it decreased the efficiency of the

lubricator system. High flange forces forced the lubricant from the contact

zone either wasting the lubricant into the ballast material or onto the running

surface of the rail. Large compressive forces, such as those described in the

work of Marich et al. (2000; 2001b), were found to have a similar effect on the

response of lubricants in the rail/wheel simulator. The problem of lubricator

location with respect to a set level of flange force or shearing force could be

investigated to provide a design which enhances lubricant transport.

2.8.1 Lubricant transport prediction/modelling

The body of knowledge in rail/wheel lubrication provides general principles

of lubrication, not specific lubrication regimes. General principles prevent

accurate simulation of industry practice, an important simulation parameter.

These lubrication regimes are generally developed from field experience and

measurement. The extensive number of variables in a lubrication system and

their interactions are not well defined in the literature. Despite this dearth,

‘rules of thumb’ exist which provide guidance for suitable lubricant

application strategies.

Frank (1981) suggested that the lubrication device be placed at the point on

the curve where wear from flange contact is observed, as Figure 10 illustrates.

This location is easily measured and can therefore be located by track

personnel. The implication is that only after wear occurs can the location for

lubrication can be determined. Predicting the location for lubricators prior to

wear is the desired outcome. Measuring retentivity performance of a lubricant,

as measured with the rail/wheel simulator in this thesis, may allow for

32

placement based of effective lubricating distance rather than the point of

wear.

Figure 10 - Wayside lubricator location plan (Frank 1981).

Optimal lubricant spread may not occur using Frank's placement method

(1981) as the contact pressures may be sufficient to force the lubricant from

the desired location. Conversely if the contact pressure is inadequate excessive

amounts of lubricant can be transported by the wheel to locations other than

the rail gauge face (fling off).

The actuation system has a direct bearing on lubricant waste in the case of

excess applied lubricant. If the flange is not in contact with each passing axle

the system will continue to pump lubricant to the application point to form

large pools of lubricant. These large pools will be forced from the contact to

be thrown from the wheel or spread to the tread contact with only a small

proportion being used at the desired application point.

33

Figure 11 - Range of lubrication (Frank 1981).

Frank also proposed that the length of the lubricator delivery system be equal

to that of the wheel's circumference. This length ensures that the entire

flange receives lubricant. In the event that wheel contact is not maintained

over the length of the lubricator, excess lubricant (puddles) can again occur.

34

The proposed application methodology of Frank (1981) was employed in the

lubricated testing of the rail/wheel simulator.

Figure 11 is taken from the work of Frank (1981) and details the work that

they carried out to determine the effective range of lubricators. The

downstream lubricated distance can be seen to be related to the curve radius.

This curve radius dictates the speed at which a train can negotiate a corner

and also has a direct effect on the contact conditions at the flange. The

relationship in this table is empirical and considers the variable of curve radius

only. Maintaining a set flange force and corresponding lubricant shear force

could be used to generate further tables such as those presented by Frank

(1981). The experimental testing in this thesis measured lubricant

performance by setting a maximum shearing force and setting a simulated

flange force. These set points could be correlated against field data, using the

method Frank (1981) in the future.

Figure 12 - Rail tribometer (photo courtesy of Queensland Rail).

35

In the work of Marich et al. (2001a), lubricator position was determined

through the use of a tribometer, see Figure 12. Measurements of gauge face

friction were recorded following the application of lubricant to the rail.

Marich et al. (2001a), with respect to wayside lubricator location, concluded

that:

The ideal position for the wayside lubricator is at the same location as that presented by Frank (1981), at the onset of wear on the gauge face. Marich also proposed that this location is only applicable to curves of radius 400m-600m.

Lubricators placed in curves of radius 600m-1000m provide excellent lubrication where flanging occurs. The flanging forces in these curves are generally less than tighter curves ensuring more efficient use of the applied lubricant.

Lubricators should not be placed on curves of 300m or less. The reasons for this is flanging forces are high and force the lubricant from the contact zone. Carry distance for the lubricant is this case is short.

These conclusions do not address the issues that are associated with these

tight radius curves, that wear is usually more significant. In the case of tight

radius curves industry practice is to place the lubricators prior to the curve in

a position where flange contact forces are at a suitable level.

Marich et al. (2001a) has also developed guidelines to determine effective

lubrication distances (range) based on track structure and loading conditions.

These results are in Table 1 but minimal details of track conditions makes

application of these findings difficult.

The work of Thelen and Lovette (1996) identified a lack of mathematical

modelling of the lubrication transport mechanism. Thelen and Lovette, as

with other authors, defines the system as one in which the parameters are too

numerous parameters to model. Their work also tested the hypothesis that

lubrication effectiveness decreases exponentially with distance. Other authors

have suggested a similar model and Thelen and Lovette concluded with field

36

testing results that this was the case. Thelen et al. (1996) and Marich et al.

(2001a) propose that location of lubricators is best determined through

measurement of performance.

Range Sleeper Type Grade Traffic 8km-10km Wooden Moderate Normal 6km-7km Concrete Moderate Passenger and unloaded freight

trains 5km-6km Concrete Moderate Passenger and loaded freight

trains 3km-4.5km Concrete Severe Normal

Table 1 Lubrication effective distance (Marich et al. 2001a).

2.8.2 Summary

Existing methods of wayside lubrication used by the rail industry perform

adequately. In the case of systems where empirical methods use locally

gathered data the lubrication can be effective, if not the optimal for that

system. The research issue in this case is the poor applicability to other

systems. In order to address this problem new research in wayside lubrication

needs to address mathematical prediction of lubrication performance.

Specifically there are three areas in which there is a deficiency.

Lubrication transport prediction/modelling is currently at the stage of

collating field data and compiling tables of lubricator performance for curves

of a particular dimension. This data could be expanded to include type and

speed of rail traffic, providing wider applicability of the tables. Further

research into the physical system of lubricant transport on rail and wheels

needs to be carried out to move away from the empirical methods currently

employed.

Mathematical prediction of lubricant transport will assist in developing

models for wayside lubricator positioning, the next area of deficiency.

Currently the empirical positioning system of locating a lubricator is effective

but with knowledge of the transport mechanism could be optimised.

37

Further to the research into lubricants and their transport mechanisms,

lubricators require investigation to ensure that the methods that they employ

optimise the lubrication system. The current systems perform adequately but

too little is known about the system to optimise the design of the lubricant

application. The work into improving the reliability of the lubricators has

advanced the efficiency but this efficiency is not quantified. The additional

work required is optimization of the rail curve lubricant.

2.9 Rail/Wheel Simulator - Description of equipment

Having identified the issues in the field situation in the previous sections a

brief description of the rail/wheel simulator used in this thesis will be

presented. The rail/wheel simulator developed and used for this research

originated from the BHP Melbourne Research Laboratories in Australia. This

machine was purpose built by the laboratories to investigate wear of

rail/wheel couples (Marich and Mutton 1989). BHP Billiton is a major

supplier of materials to the rail industry and conducts their own heavy haul

rail operations.

In its original form the rail/wheel simulator was used to test wear rates of

rail/wheel couples. These couples consisted of different grades of rails and

wheels, from those currently in use to laboratory prepared samples. The

prepared samples had a range of hardness, chemical compositions and heat

treatments. Results from the wear machine were used to compare materials

varying in both strength and hardness. Wear rates were also measured for

continuously lubricated conditions, which is where the importance of this

equipment lies for the current thesis.

The wear test machine has two load parameters:

Tread Load to simulate the axle load of the system. In the centre rear of the photograph in Figure 13, the tread load pneumatic ram can be seen.

38

Flange Load for the simulation of curvature (flange contact). In the front right of the photograph in Figure 13, the flange load pneumatic ram can be seen.

Figure 13 – Rail/wheel simulator post modifications by the author.

These loads are depicted in Figure 14 from Marich and Mutton (1989). This

arrangement is suitable for imitating a range of loading conditions, such as

those experienced in the field.

Slip percentage is important in determining the velocity profile across a given

contact area. The slip percentage of the samples used in the work of Marich

and Mutton (1989) was approximately 20%, compared to a maximum value

of approximately 5% from a real rail/wheel system.

The simulated system of Marich and Mutton (1989) and modified rail/wheel

simulator used in this thesis is flexible to allow the use of a variety of wheel

and rail profiles. These profiles can be taken from new design drawings or

profiles of worn rolling stock and then be machined into the blank samples.

39

In addition to the physical geometry there is the contact geometry which can

be adjusted. In Figure 14, Angle of attack, or axis perpendicular to the page,

can be selected to give lateral slip and approach angle for the flange contact.

Figure 14 Loading Diagram for wear investigation of Marich and Mutton(1989)

2.10 Lubricant Properties Testing

Simulating a tribological system tends to have limited applicability for

commercial lubricant testing. Typically standards based tests are used to

characterise the lubricants. Lubricating grease is difficult to characterise and as

such there is a limited number of testing standards applicable. The tests

selected for this research are detailed, followed by an overview of the

rheology tests performed.

40

2.10.1 ASTM D 1092 Standard Test Method for Measuring Apparent

Viscosity of Lubricating Greases

Lubricating greases respond in a different way to most lubricants and as such

require modified viscosity testing. This test is used to produce a chart of the

apparent viscosity at a variety of shear rates.

Figure 15 – Schematic drawing of ASTM D 1092 test device(ASTM 1999).

The standard summarises the test method as:

The sample is forced through a capillary by means of a floating piston

actuated by the hydraulic system. From the predetermined flow rate and

the force developed in the system, the apparent viscosity is calculated by

means of Poiseuille’s equation. A series of eight capillaries and two pump

speeds are used to determine the apparent viscosity at sixteen shear rates.

The results are expressed as a log-log plot of apparent viscosity versus

shear rate.(ASTM 1999)

41

This test was used for two primary reasons. Pumping of grease is an

important component of rail lubricating systems. If the grease never reaches

its intended application point then its effectiveness is zero. In addition the

way in which lubricant is spread from the application point is a shearing

process and this test measures shearing performance over a range of shear

rates.

The limitation of ASTM D1092 with respect to this research is the original

purpose of the test is to predict pumping characteristics for grease in

pipelines, for example on a dragline boom. This is one characteristic in

optimising a rail curve lubricant, but not directly related to the performance in

the contact. To make this test suitable for rail application would require

varying the temperature and creating a map of apparent viscosity to ensure

good lubricant application practices.

2.10.2 ASTM D 2596 Standard Test Method for Measurement of

Extreme-Pressure Properties of Lubricating Grease

The standard summarises the test method as:

The tester is operated with one steel ball under load rotating against three

steel balls held stationary in the form of a cradle. The rotating speed is

1770 rpm. Lubricating greases are brought to 27 °C (80 °F) and then

subjected to a series of tests of 10-s duration at increasing loads until

welding occurs. (ASTM 1997)

Typically this test is used to rank lubricants qualitatively rather than quantify

performance. This test method is limited in its general application from the

low precision of the test results and the high inter-sample variability. In the

case of testing rail curve lubricants, only sliding occurs, whereas rolling is a

significant component in a rail/wheel contact. Despite the limitations this is a

42

suitable test method from the perspective that the contact pressure

characteristics are comparable to a gauge corner contact.

Figure 16 – Schematic diagram of four ball test device suitable for ASTM D 2266 and ASTM D 2596 (ASTM 1991; ASTM 1997).

2.10.3 ASTM D 2266 Standard Test Method for Wear Preventive

Characteristics of Lubricating Grease

The standard summarises the test method as:

A steel ball is rotated under load against three stationary steel balls

having grease-lubricated surfaces. The diameters of the wear scars on the

stationary balls are measured after completion of the test. (ASTM 1991)

This method was chosen for the same reasons as ASTM D 2596.

43

2.10.4 Rheometer Test

The context of rheometric testing is the prediction of the shear characteristics

of the test lubricants. In the case of lubricating greases the strain history of

the lubricant directly affects the structural properties (Nolan ~2000). Another

method of considering the structural changes with respect to shear history, is

the effect that energy absorbed or transmitted through a lubricating grease

affects the structural properties.

The ability to predict the energy capacity of a grease preceding full failure

using a relatively quick method, such as rheometry, is another tool for

lubricant designers.

There are two main components to a grease and as such two main effects.

The oil component behaves as liquid and the soap component as a solid. In

the short lifespan of rail curve grease it is assumed that the change in oil

properties is insignificant. Therefore the shearing of the solid soap is the main

factor in performance degradation.

In the case of the rail simulator three regions of distinctly different shearing

conditions may be considered. The initial region is when the lubricant film is

developing, see Figure 17. Prior to rolling, an excess of lubricant is applied to

the rail sample, the larger of the two, then the wheel sample is pressed against

the rail sample with the test load. The rail sample is then rotated which rotates

the wheel sample. The lubricant film in this process begins at approximately

1mm and rapidly decreases to approximately 1µm. This reduction is three

orders of magnitude and introduces significant accumulated strain.

Experimentally, observed in the work of the thesis, the majority of the applied

lubricant is expelled from between the cylinders. To predict the strain history

of the lubricant remaining in the contact, the initial and final volumes of

lubricant are considered. Initially with a 1mm thick surface we have 30g of

lubricant, following rotation this becomes 30mg and 1µm thickness.

44

Figure 17 – (Left) Lubricant film prior to rolling (~1mm thickness). (Right) Lubricant film following rolling (~1µm).

To apply this information in a practical sense the final mass, 30mg, is the

minimum lubricant application for each revolution if we assume total

lubricant degradation with each revolution. Now it was observed that the

lubricant does not degrade in a single revolution but with accumulated strain.

Experimentally this is observed by an increase in tractive coefficient.

Therefore a decision must be made regarding limits of tractive coefficient

which in this thesis was set by limiting the dynamometer to the required test

parameter.

There are competing factors in reaching a set value; consumable lubricant

costs, lubricant infrastructure and maintenance, wheel and rail wear

(replacement and maintenance), locomotive tractive power, and energy. If a

correlation between in-service performance or parameters can be reached

with rheological testing the advantages would be extremely valuable.

45

2.11 Summary

For the purpose of identifying issues in rail curve lubrication to ensure

optimal simulation and performance measurements of rail curve lubricants,

this chapter has explored the following areas:

The process and limitations of simulated tribological testing focusing on issues specific to rail/wheel simulators were discussed.

Mathematical models for wear processes used to identify the parameters that are required to be targeted with lubrication strategies were presented.

Solid mechanics models have been discussed to introduce contact mechanics of in-service and rail simulators.

Issues regarding lubricating the rail/wheel interface have been discussed with specific reference to the lack of specifications required for this interface.

Existing standard lubricant tests considered suitable for rail/wheel interfaces have been discussed and their limitations highlighted..

The following major points have been identified:

There has been some success with simulated lubrication testing (Clayton et al. 1988; Marich and Mutton 1989; Kumar et al. 1991; Mulvihill et al. 1994; Waara 2001)

A definitive choice of lubricant has not been found.

Measurement of lubricant performance has been focussed on wear (Clayton et al. 1988; Marich and Mutton 1989; Kumar et al. 1991; Mulvihill et al. 1994; Waara 2001).

Lubricant manufacturers do not have a consistent approach to rail curve lubrication.

Limited laboratory simulation has been performed on rail curve lubricants.

Primarily two types of laboratory simulators were used to investigate rail curve lubricants, reciprocating cylinder on flat

46

and twin disk. The majority of research has been carried out with twin disk devices.

The choice of simulator type used in this research is based on the advantages of the twin disk devices when compared to the cylinder on flat devices.

Shear force control is typically lacking in twin disk devices which have fixed slide to roll ratios. Shear force control was implemented in the twin disk device used in this thesis to overcome this limitation in investigating rail curve lubricant performance.

Clayton (1988) identified a need to measure lubricant performance throughout simulated testing, specifically targeting the end of the lubricant film's life. This has been achieved in this thesis and a model for the lubricant film decay presented. The decay is given as the lubricant performance measurement, half life.

The overall conclusion from this cross-section of literature is that a shortfall

in the knowledge surrounding lubrication of the gauge corner interface

existed. The proposed methodology to reduce this gap in knowledge was to

develop a scaled simulator to investigate the lubricants under simulated field

conditions. There was an examination of the contact mechanics of the in-

service and simulated wheel contact conditions. The simulator was then used

to test three rail curve lubricants currently employed by Queensland Rail for

comparison with the discussed standards based tests and the findings

discussed. Finally recommendations for further work and the conclusions

from the current work were presented.

47

C h a p t e r 3

THEORETICAL CALCULATIONS: CONTACT MECHANICS OF IN-SERVICE AND RAIL SIMULATOR CONDITIONS AND

LUBRICANT FILM THICKNESS

3.1 Introduction

Waara (2001), Kumar et al. (1991), and Clayton et al. (1989) all highlight the

need for accurate representation of the stress conditions in a rail/wheel

simulator. From this conclusion it is necessary to have the ability to calculate

the stress distributions for both the field and laboratory simulator using

contact mechanics.

The aim of this chapter is to provide the theoretical background to the

contact between wheel and rail and to demonstrate the use of software

developed to predict the contact dimensions and stresses. This chapter is

divided into presentation of the equations for elliptical and rectangular

contacts, comparison of software with published results, and examples of

typical stress distributions for in-service and simulator conditions.

3.2 Contact Mechanics Background

Tribology in essence is a combination of physics, chemistry and engineering.

The ratios of each part differ depending upon the problem and their

interaction with each other. Tribological processes must be studied using the

scientific disciplines simultaneously. A primary consideration in these

processes is mechanics of solids, specifically contact mechanics and fracture

mechanics. The contact mechanics is a description of the stress and strain

state of the bodies in contact.

In this project there are two general regimes of contact encountered. The

first, rolling contact, relates to the stresses and forces experienced by the tread

of the wheel. Second is the rolling/sliding regime experienced by the flange

and by the tread, only under adverse conditions. It is important to consider

48

both regimes as there may be stress field interactions between the two but the

area of interest in this thesis is the flange contact.

Studies of contact mechanics began with Hertz (1882), and remains the basis

for much of the current work in contact mechanics. Hertz's work focused on

Newton’s optical interference rings and the possible influence of elasticity.

Extensions of this theory include bearing design, real contact areas and rolling

and sliding contacts.

Hertz's theory however is based on a number of assumptions, which limits its

application to sliding contacts. These assumptions are:

the contact bodies are perfect materials, homogeneous, elastic and isotropic.

the strains are small.

smooth and non-conforming surfaces.

time changes do not affect geometry.

friction is negligible.

Both rails and wheels may not be assumed to be perfect materials, as they may

have work hardened contact surfaces which may also have been heat treated.

High stresses are experienced in this contact, which may negate the small

strain assumption. Both rail and wheel can suffer from geometric and

mechanical inhomogeneity. Finally friction is an important part of the contact

as the interface experiences both lateral and longitudinal creep.

The model used for the contact analysis in this thesis is the methods

proposed by the Engineering Sciences Data Unit (ESDU). Their work is an

extension to the work of Hertz and incorporates methods for minimising the

effects of the Hertz model assumptions. Their work also includes a method

for calculation of the stress tensor at any point in a body under contact. The

difficulty with using the methods of the ESDU is that the equations used for

solving the stress components are not suitable for use with a computer. The

49

method involves the use of graphs to estimate the equation parameters.

Historically, these parameters were used due to the necessity to calculate

values which are mathematically intensive.

In order to improve the accuracy of the contact mechanics analysis, software

to analyse rectangular and elliptical contacts was developed by the author,

using the methods of the ESDU as a basis. The software improves the

accuracy of results by calculating the equation parameters directly. These

parameters are for elliptical integrals and multiple simultaneous equations.

This software has been validated against other published contact mechanics

results (Hamrock 1994; Boresi and Schmidt 2003) and proven to be a valid

method with a greater accuracy and resolution than the ESDU method.

3.2.1 Wheel/rail contact models – A survey

The results of the development of wheel/rail models are used in a number of

areas with railway engineering, in particular the dynamics of the vehicles. This

information is used in the design of rail vehicles and rail infrastructure. This

project is looking for the stress and force behaviour of the wheel flange

contact (rail gauge face). In addition to force and stress, long term

performance of the rail materials can also be predicted from these models

(Bruni et al. 2000).

The most accurate but computationally intensive models have been

developed by Kalker (1990). The models then range in complexity and

computational intensity depending on the application. The models examined

in relation to this thesis had to focus on two main areas when dealing with a

wheel rail contact: the geometric system and the elasto-frictional system.

The geometric system must be able to encompass the rapid changes

experienced at the wheel/rail interface. These changes arise from the conicity

of the wheels and the changes of curvature of the head of the rail. There is

also the case in curving rail vehicles where three points of contact per axle

50

exist simultaneously, two normal and one tangential. The three point contact

is the geometrical situation where flange wear is encountered.

The elasto-frictional system must be able to predict the forces at the

rail/wheel interface whilst predicting the contact patch areas. From this a

prediction can be made of the stresses and creep experienced at the interface.

It is important that the geometrical contact model is able to take into account

multiple contacts that can occur in tight curves, where both the tread and

flange may be in contact with the rail. 'Lookup' tables can be used to lessen

the computational effort, but they are inferior to models that calculate the

geometry at each time step (Bruni et al. 2000). Increasing the model

complexity by predicting the geometry with respect to time is advantageous in

modelling the existing track, thereby allowing for better models through

verification. To further complicate the system, two dimensional descriptions

are only applicable for tangent track and long radius curves. Current interest

on wear in the literature is generally focused on short radius curves (Jendel

1999; Nilsson 2002). While outside the scope of this thesis, in future work,

three dimensional models could be considered to increase the accuracy of

geometric description.

Using the geometric description/model of Kalker (1990), the forces at the

rail/wheel interface, normal and tangential, can be calculated. The model uses

an elastic half space approximation for the contact patches, which, for most

cases, is sufficiently accurate. Elastic half space models are flawed when

applied to worn wheels and rails that have conformal profiles, as the

assumption of small contact patch compared to the rest of the body is invalid.

In these cases more intensive analysis must be carried out to formulate the

stresses.

Splitting the normal and tangential force calculations simplifies the system.

There is interaction between the forces but this is considered negligible.

Currently, the most rigorous method is by Kalker (1990), who describes a

51

non-linear method with a discretisation of the contact patch. This contact

patch calculated from the geometric model is used to determine the

deformation of the surfaces by an iterative method. This method is

advantageous in that the solution is the most rigorous, as previously

mentioned, but comes at a high computational cost.

The problem of modelling the forces at the rail/wheel interface is addressed

in other solutions by simplifying the situation. Kik and Piotrowski (1996)

proposed using an elliptical contact patch and an estimated deformation

distance/depth of the materials. This depth is chosen by the modeller and is

generally verified or calculated with the Kalker method. Another solution

from Bruni et al. (2000) and Pascal (1993) uses multi-elliptical Hertzian

contacts, which suffers from the inaccuracies previously mentioned.

Tangential problem solutions also use Kalker (1990) as the basis upon which

they are judged. Hertzian contact solutions use the creep values from the

normal solution to provide the tangential solutions. Other methods (Shen et

al. 1983) have an iterative solution of high computational intensity. Heuristic

models are also widely used and can give valid solutions (Kik and Piotrowski

1996).

In general, rail/wheel modelling is concerned with the dynamics of the

vehicle. This focus has been extended to include rail/wheel contacts but this

tends to be specifically focused on the tread contacts rather than the flange.

This is an area where the models can be extended to give a further

understanding of the interface. It is outside this thesis to develop a new model

for rail/wheel force interactions, but it does use a combination of Hertz

(1882), Johnson (1985) and the methods of the ESDU literature on contact

mechanics (ESDU 1984; ESDU 1994; ESDU 1995) to analyse the complex

rail/wheel interface system.

52

3.3 Geometry and Material Property Equations

The notation convention where applicable is the same as that used in the

ESDU methods (ESDU 1984; ESDU 1994; ESDU 1995). The geometry

labelling and orthogonal axes system is shown in Figure 18

Figure 18- Reference geometry used for contact mechanics calculations (ESDU 1984).

The material properties for each body were calculated with Equations (3.1)

and (3.2)

( )21

ikEσ

π−

= (3.1)

( )1 2

2'Ek k

π=+

(3.2)

ik = material constant, i denotes body number

53

σ = Poisson’s ratio

E = Young’s modulus

'E = Effective modulus

The geometric properties for each body were calculated with Equations (3.3)

and (3.4)

11 21 12 22

1 1 1 1 1R R R R R

⎛ ⎞ ⎛ ⎞= + + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(3.3)

12 22

11 21

1 1 12

1 1 12

AR R

BR R

⎛ ⎞= +⎜ ⎟

⎝ ⎠⎛ ⎞

= +⎜ ⎟⎝ ⎠

(3.4)

R = Effective contact radius

iiR = Radius of curvature, first i denotes body number and second i

axis number

,A B = Geometry parameters

In the case where the principal axes of the contacting bodies are not aligned

the following equations for geometry, must be used.

54

12 2 2

11 12 21 22

11 12 21 22

11 12 21 22

2 2

11 12 21 22

11 12 21 22

11 12

1 1 1 11 1 1 1 14 1 1 1 12 cos 2

1 1 1 11 1 1 1 14 1 12

R R R RA

R R R R

R R R R

R R R RB

R R R R

R R

ω

⎡ ⎤⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥⎢ ⎥− + −⎜ ⎟ ⎜ ⎟⎢ ⎥⎢ ⎥⎝ ⎠ ⎝ ⎠⎢ ⎥= + + + − ⎢ ⎥⎢ ⎥⎛ ⎞⎛ ⎞⎢ ⎥+ − −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦⎢ ⎥⎣ ⎦

⎛ ⎞ ⎛ ⎞− + −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠= + + + +⎛ ⎞

+ −⎜ ⎟⎝ ⎠

12

21 22

1 1 cos 2R R

ω

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎛ ⎞⎢ ⎥−⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎢ ⎥⎣ ⎦

(3.5)

121

21 1 1

y

x

x y

D

RA

RB

R R R

B ARA B

=

=

= +

−=+

(3.6)

DR = Curvature difference

xR = Effective radius in ‘x’ direction

yR = Effective radius in ‘y’ direction

3.4 Contact Mechanics Method

The theoretical predictions for stresses arising from and in the contact area

are calculated using a combination of mathematical methods. The collection

of methods is based on work carried out by the Tribology section of the

Engineering Sciences Data Unit (1994). Additions and modifications to this

method were required as a result of the inability to directly apply the

equations to computerized calculation. Mathematical methods for calculating

the necessary elliptical integrals have been incorporated into this research to

improve the accuracy of results. Previously, computational methods for

55

elliptical integrals were time consuming and tables were used in the ESDU

method.

3.4.1 Rectangular Contact Equations

The rectangular contact is approximated by a contact ellipse with an infinite

dimension in the major axis.

The contact width is calculated by

( )1

211 21

1 211 21

4 R RPb k kL R R

⎡ ⎤⎡ ⎤⎛ ⎞= +⎢ ⎥⎢ ⎥⎜ ⎟ +⎝ ⎠ ⎣ ⎦⎣ ⎦ (3.7)

b = Minor ellipse semi axis or contact half width

P = Normal force

L = Length of rectangular contact

The distance of surface deformation at the centre of the contact is given by

Equation (3.8).

11 211 1

4 41 12 ln 2 ln2 2

R RP Pk kL b L b

δ ⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞= − + −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦ (3.8)

δ = Normal approach of bodies

The pressure distribution across the rectangular contact is given by

( )1

2 2

0 21 yp y pb

⎡ ⎤= −⎢ ⎥

⎣ ⎦ (3.9)

( ) ( ) ( ), , , , , ,p p y p x y p x y z = Pressure or pressure at location

0p = Maximum pressure

The maximum direct stress 0( )p is given by

56

02Pp

L bπ⎛ ⎞= ⎜ ⎟⎝ ⎠

(3.10)

3.4.2 Elliptical Contact Equations

The contact dimensions are calculated using the methods of Hamrock (1995)

and the ESDU (1995).

ba

β = (3.11)

( )1

2 36'

E m PRb

Eβ

π⎛ ⎞

= ⎜ ⎟⎝ ⎠

(3.12)

( )1

36'

E m PRa

Eπβ⎛ ⎞

= ⎜ ⎟⎝ ⎠

(3.13)

( ) ( )

12 3

92 '

PK mE m R E

δπβ

⎡ ⎤⎛ ⎞= ⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦

(3.14)

a = Major ellipse semi axis or contact half width

β = Ellipse semi-axes ratio

( )E m = Complete elliptical integral of the second kind

( )K m = Complete elliptical integral of the first kind

The method proposed by ESDU (1994) is

( )

13

aC W AaA B B

−⎛ ⎞= ⎜ ⎟+ ⎝ ⎠

(3.15)

57

( )

13

bC W AbA B B

⎛ ⎞= ⎜ ⎟+ ⎝ ⎠ (3.16)

W = Dimensionless load parameter

Where the coefficients are given by

( )1 13 3

2

2a

E m ACBπβ

⎡ ⎤ ⎛ ⎞= ⎢ ⎥ ⎜ ⎟⎝ ⎠⎣ ⎦

(3.17)

( )1 13 32

b

E m ACB

βπ

−⎡ ⎤ ⎛ ⎞= ⎢ ⎥ ⎜ ⎟

⎝ ⎠⎣ ⎦ (3.18)

The values of each coefficient are given in a series of graphs, see Figure 19.

The graphs do not allow for an accurate prediction of the coefficients and a

method for calculating the parameters for solution was developed by the

author. The method of solving these is a transcendental solution and the

author uses the methodology of Hamrock (1994). The new method was

verified against the ESDU, Hamrock (1994) and published elliptical integral

tables (Byrd and Friedman 1971).

Common to both equations is Equation (3.19).

( )( )1

321 2

34

W P k k A Bπ⎡ ⎤= + +⎢ ⎥⎣ ⎦ (3.19)

The distance of surface deformation at the centre of the contact is given by

Equation (3.20).

( )

12 3C W AA B B

δδ ⎛ ⎞= ⎜ ⎟+ ⎝ ⎠ (3.20)

58

Figure 19 - Contact dimensions, ellipse ratio, and approach coefficients(ESDU 1995).

59

Where the coefficient is given by Equation (3.21).

( ) ( )

1 132 34 AC K mE m Bδ

βπ

−⎡ ⎤ ⎛ ⎞= ⎢ ⎥ ⎜ ⎟⎝ ⎠⎣ ⎦

(3.21)

The pressure distribution across an elliptical contact is given by Equation

(3.22).

( )1

2 2 2

0 2 2, 1 x yp x y pa b

⎡ ⎤= − −⎢ ⎥

⎣ ⎦ (3.22)

Where the maximum stress is given by Equation (3.23).

03

2Ppabπ

= (3.23)

3.4.3 Micro-slip/Creep Prediction

In the lubricated testing a key measurement is the slip, but this slip is

composed of the micro-slip component calculated in this section and the slip

component due to lubrication. It is therefore imperative to predict the micro-

slip component to isolate the effect of lubrication on the rail/wheel contact.

Rolling contact of elastic bodies produces deformation on the surface of both

contacting bodies and subsequently creep or slip between these bodies. Free

rolling is defined as rolling in which there is no tractive force. In the case of

the simulator and field conditions there is always a tractive force applied, and

in all practical (real) rolling applications this force will exist. Tractive rolling

therefore has a strain component associated with the tractive force. This

tractive force can be a nominated value or defined as a proportion of the

normal force. Calculations of friction or traction coefficient will be based on

Amonton’s Law of Friction.

60

In the work of Johnson (1882) two methods, equations (3.24) and (3.25) are

given for predicting the creep of a line contact interface.

when 2

xx x

bQ Q PRP

ξ μ= << (3.24)

1

2

1 1 xx

QbR Pμξ

μ

⎧ ⎫⎛ ⎞⎪ ⎪= − − −⎨ ⎬⎜ ⎟⎝ ⎠⎪ ⎪⎩ ⎭

(3.25)

xξ = Slip ratio in the direction of rolling

xQ = Tractive force in direction of rolling

The first method, Equation (3.24), gives the limit of creep as the proportion

of slip across the contact surface approaches zero. The second method

Equation (3.25) is used for contacts where the ratio of tractive force to

friction force limit is such that the contact has a stick-slip interface.

Measurement of slip in laboratory simulated conditions requires a prediction

of the minimum slip. This minimum slip is used to check the values of the

input measurements and as an offset amount for the prediction of the decay

in slip of a lubricated contact.

Figure 20 shows the minimum values of creep using the first method, over

the range of shearing force the laboratory simulator is capable of producing.

In the case of maximum tractive force the value of creep is 0.06%.

Figure 21 displays the values of creep that will be used for all calculations that

involve slip. This graph is generated using the second method, Equation

(3.25), and it is assumed that the ratio of shearing force to maximum capable

tractive force is significant.

61

0 200 400 600 800 1000 1200 14000

1

2

3

4

5

6x 10

-4

Shear Force Qx (N)

ξ x

Normal Force 9500 NNormal Force 12500 N

Figure 20 – Creep prediction for simulator when contact patch is assumed to have no regions of slip.

0 200 400 600 800 1000 1200 14000

1

2

3

4

5

6

7

8x 10

-4

ξ x

Shear Force Qx (N)

Normal Force 9500 NNormal Force 12500 N

Figure 21 - Creep prediction for simulator when contact patch has regions of slip.

62

3.5 Conformal Rail/Wheel Contact

Rail/wheel contact in the gauge corner can be classified as a conformal

contact. While the contact mechanics of Hertz (1882) is not directly

applicable to conformal profiles, the rail/wheel profile is conformal in one

plane only, which can be seen in Figure 22. It is reasonable then to suggest

that rail/wheel contact can be approximated as a line contact with variable

contacting radii. The purpose of this comparison is to highlight the similarities

of the simulator, which has a line contact, and the field.

The following assumptions are made in order to apply Hertz contact

mechanics to rail/wheel contact.

The load per unit length is constant over the entire contact.

The approach or deformation is constant.

The material properties are constant over the entire surface.

Load will not vary depending on the angle between the normal

contact vector and the load vector.

Deformation or approach is not influenced by the ratio of contact

radii which is changing.

Locations of higher wear will not have a different strain accumulation

to those of lower wear and corresponding changes in material

properties.

Using the assumptions and modifying the rectangular contact width equation

gives Equation (3.26).

1

211 21

11 21

R Rb KR R

⎡ ⎤⎛ ⎞= ⎢ ⎥⎜ ⎟+⎝ ⎠⎣ ⎦

(3.26)

63

K = Contact width equation constant

This formula allows exploration of the theory that the conformal contact may

be approximated as a line contact with variable rolling radius.

Figure 22 – Wheel/rail contact profile(Sato 2005) (Nomenclature for radii in this figure is not used).

The contact radius can be calculated by considering that a conformal rail

wheel contact is approximated as a cylinder on a plate and the plate has an

infinite radius in the direction of rolling. The contact radius may be taken as

the wheel radius giving Equation (3.27).

11 22

22

11

1 1 1

1 1 0

R R R

RR R

= +

= =∞

∴ =

(3.27)

The original equation for line contact cannot be used now as the infinity term

overwhelms the equation. Rearranging the work of Hamrock (1994) gives an

Equation (3.28) for contact width.

64

12

12

8'

8'

Pb RL E R

PKL E

Kb RR

b K R

π

π

⎛ ⎞= ⎜ ⎟× × ×⎝ ⎠

=× ×

⎛ ⎞= ⎜ ⎟⎝ ⎠

= ×

(3.28)

Equation (3.28) states that the change in contact width is proportional to the

square root of the change in rolling radius. The rolling radius, shown in Figure

24, is a discontinuous function of two parts; a linear equation for the tread

and a circular equation for the gauge corner taken from the profile in Figure

23. The radius function was constructed by plotting the rolling radius versus

the surface position. The start point of the radius function will be the central

axis of the matching rail head profile and the end point will be where the

external 12mm radius joins the internal 14 mm radius. Both locations can be

seen in Figure 23. This forms a total contact length of approximately 30mm.

Figure 24 displays the position of contact along the tread, defined as surface

position versus the rolling radius with the zero point as the centre of the

tread.

Figure 23 – Wheel profile for a coned wheel (Sato 2005).

65

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350.43

0.432

0.434

0.436

0.438

0.44

0.442

Surface Position (m)

Rol

ling

Rad

ius

(m)

Figure 24 – Rolling radius used for calculation of line contact width using wheel profile from Sato (2005).

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0353.47

3.475

3.48

3.485

3.49

3.495

3.5

3.505

3.51

3.515x 10

-3

Surface Position (m)

Con

tact

Wid

th "

b" (m

)

Constant Normal Force

Figure 25 – Contact width profile for constant normal force using a variable rolling radius profile. Note scale of axes different.

66

Using the modified equation for contact width and substituting values of

radius from Figure 24, with an axle load of 30 000 N gives a constant K value

of 2.8045E-5m and a contact profile given in Figure 25. The change in

contact width is small, 40 μ m, indicating that the hypothesis is plausible.

Investigating the change in contact pressure as a result of the radius profile

function in Figure 26 it can be seen that the pressure drops as the rolling

radius increases with a constant load. The assumption of constant load across

the surface, used in this plot, will become invalid as more of the curved gauge

corner is in contact. The contact forces will not be normal to the surface at

these locations and will invalidate the assumptions.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0359.06

9.08

9.1

9.12

9.14

9.16

9.18x 108

Surface Position (m)

Max

imum

Con

tact

Pre

ssur

e (P

a)

Figure 26 – Maximum pressure for constant tread load across contact and variable contact radius.

67

Changing the assumption of constant tread load (force) across the surface to a

constant maximum pressure across the surface and repeating the analysis, it is

necessary to develop a maximum pressure equation that is independent of

contact width, presented in Equation (3.29).

1

2

0 2Pkp

LRπ⎡ ⎤= ⎢ ⎥⎣ ⎦

(3.29)

Rearranging Equation (3.29) to determine the load distribution across the

surface due to the constant contact pressure gives Equation (3.30).

2

0p RLPkπ= (3.30)

Using this distribution of normal load and substituting into the contact width

Equation (3.28) gives the dashed line in Figure 27.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0353.46

3.47

3.48

3.49

3.5

3.51

3.52

3.53

3.54

3.55x 10-3

Surface Position (m)

Con

tact

Wid

th "

b" (m

)

Constant Normal ForceConstant Maximum Pressure

Figure 27- Contact width for constant tread load and constant maximum pressure across contact for variable contact radius.

68

The contact pressure used in Figure 27 for the constant maximum pressure

line is the mean pressure of the constant load situation. It can be seen that

there is a small difference in contact profile between the two situations. Figure

27 highlights these small differences by magnification of the contact width

axis (‘y’ axis), without which the change in contact width would appear to be

negligible (approximately 1%). Calculating the change in area between a

normal line contact of rolling radius, set to the mean value of the variable

radius profile (0.4314m) and the two special cases presented in Figure 27 gives

a difference of 0.12%.

-20 -15 -10 -5 0 5 10 15 20-15

-10

-5

0

5

10

15

x (mm)

y (m

m)

Figure 28 – Contact patch dimensions for line and elliptical contact from same normal load, 150,000 N.

Comparing the results of an elliptical contact at the rail head to three other

conditions, line contact, line contact with variable radius and constant load,

and line contact with variable radius and constant maximum pressure shows

that all conformal profiles have a maximum contact pressure of

approximately 0.9 GPa compared to an elliptical contact pressure of 1.5 GPa.

69

To achieve the same maximum pressure in the line contact as in the elliptical

contact requires an increase of wheel force from 150 kN to 440 kN. The

width of the line contact allows the stresses to be dissipated over a

significantly larger contact area which can be observed in Figure 28. In

summary conformal rail profiles offer a significant reduction in contact

pressure.

An important observation from this analysis is conformal wheel/rail contacts

can be approximated by a line contact of constant radius. Approximations in

terms of contact geometry and loading condition taken for the simulator to

mimic a gauge corner contact are proved valid.

3.6 Stress Distributions for In-service Conditions

The stress distributions for field conditions for rail/wheel contact are

presented for two reasons. Firstly to compare and contrast the gauge corner

and tread contacts and secondly to compare these distributions with the

rail/wheel simulator.

The plots of stress in this section will be for geometry taken from the work of

Sato (2005). Three different tractive forces will be used to generate the stress

distributions, zero tractive force, 50% of the limiting tractive force and the

full limiting tractive force. The tractive forces will be based on the maximum

coefficient of friction taken from the work of Lee and Polycarpou (2005).

Their work experimentally determined the friction coefficient to be 0.37 for a

maximum Hertzian pressure of 1.3 GPa and pearlitic rail steel.

Using the input parameters of Table 2, the stress tensor and the effective

maximum shear stress, eτ , shown in Equation (3.31), will be presented.

Maximum effective shear stress is presented in addition to the stress tensor

components, as fatigue failure has been shown to occur at the point of

maximum equivalent shear stress (ESDU 1984; Fletcher and Beynon 2000).

70

( ) ( ) ( )2 2 2

2 2 2

6x y y z z x

e xy yz zx

σ σ σ σ σ στ τ τ τ

− + − + −= + + + (3.31)

In the first case of zero tractive force, the stress distribution for a point

directly beneath the contact is shown in Figure 29. The maximum effective

shear stress, 390 MPa, is located beneath the surface at a depth of 3.9 mm.

The depth of maximum shear stress is the location where shelling fatigue

failures can occur and in this case a 3.9 mm thick section would be lost when

the material had reached its fatigue limit. It should be noted that there are no

shear stress components except the effective shear stress in figure 25 as a

result of the fact that there are no tractive forces. The effective shear stress

arises from the combination of all stress components.

PARAMETER VALUE UNITS Normal Force, P 150 kN

Coefficient of traction 0, 0.185, 0.37 Young’s modulus 207 GPa

Poisson’s ratio 0.3 Body 1 – Tread Contact

Maximum radius ∞ m Minimum radius 0.6 m

Body 2 - Tread Contact Maximum radius ∞ m Minimum radius 0.43 m

Body 1 – Gauge Corner Contact Maximum radius ∞ m Minimum radius 0.014 m

Body 2 - Gauge Corner Contact Maximum radius 0.43 m Minimum radius 0.012 m

Table 2 – Input parameters for contact stress predictions using the profiles of Sato (2005)

Applying a tractive force of 0.185 times the normal force increases the

maximum effective shear stress to 395 MPa and reduces the depth to 3.7 mm,

see Figure 30. Note that the tractive force introduces shear stresses that were

not evident in the case of zero applied tractive force. The maximum effect of

71

these stresses is at the surface of the materials in contact. The relatively minor

change in effective shear stress, 5 MPa, is due to minor increase of stress

penetration into the bodies, practically this translates to continued

accumulated damage from rolling contact beneath the surface and increased

stresses at the surface.

-1200 -1000 -800 -600 -400 -200 0 200 4000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τE

Figure 29 – Stress distribution for tread contact using geometry of Sato (2005) with a normal load of 150 kN and no friction force.

As the maximum effective shear stress moves close to the surface the greater

the likelihood of increased wear from the limited capacity of rail and wheel

steel to withstand the level of shear stress in Figure 30.

For full tractive force, Figure 31, the maximum effective shear stress, 423

MPa, occurs at the surface. In the event of sliding under these conditions the

effective shear stress would have the greatest damaging effects as there is no

material in which to contain the steel, to disperse the stress, under the applied

shear stress.

72

-1200 -1000 -800 -600 -400 -200 0 200 4000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 30 - Stress distribution for tread contact using geometry of Sato (2005) with a normal load of 150 kN and friction force of 0.185 times the normal force.

-1200 -1000 -800 -600 -400 -200 0 200 400 6000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 31 - Stress distribution for tread contact using geometry of Sato (2005) with a normal load of 150 kN and friction force of 0.37 times the normal force.

73

The worst or largest loading case is one in which a normal load of 150kN is

transmitted through the gauge corner will now be discussed. The contact in

this example is analogous to a toroid in an infinitely long round groove (or a

ball bearing in a race), where the force is transmitted through the axis of the

toroid as compared to the previous tread contact which is the same as two

crossed cylinders. The maximum contact pressure in this situation is much

larger than the more common tread contact situation, 2.3 GPa as compared

to 1.1 GPa.

Figure 32 shows the stress distribution for the gauge corner case of zero

tractive force, achievable only in a pure rolling case. The location of

maximum effective shear stress, 811 MPa, where fatigue failure is prevalent, is

below the surface at 2.2 mm and exceeds the shear yield stress, 330 MPa

(Table 8), for this material.

-2500 -2000 -1500 -1000 -500 0 500 10000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τE

Figure 32 – Stress distribution for gauge corner contact using geometry of Sato (2005) with a normal load of 150 kN and no friction force.

74

Figure 33 shows the contact case with a friction coefficient equivalent to half

the maximum value determined by Lee and Polycarpou (2005). Shear stress

components are becoming significant and the maximum effective shear stress,

830 MPa, is 0.2mm closer to the surface at 2mm depth

-2500 -2000 -1500 -1000 -500 0 500 10000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 33 – Stress distribution for gauge corner contact using geometry of Sato (2005) with a normal load of 150 kN and friction force of 0.185 times the normal force.

Figure 34 shows the contact case using the friction coefficient of 0.37

determined by Lee and Polycarpou (2005). Two shear stress components are

reaching the yield shear stress of 330 MPa, see Table 8, and the maximum

effective shear stress, 935 MPa, is at the surface.

In all cases of gauge corner contact as compared to tread contact the

increased state of stress would result in more wear. These stress distributions

provide a plausible explanation for the increased wear rates experienced by

the gauge corner in the field.

75

-2500 -2000 -1500 -1000 -500 0 500 10000

5

10

15

20

25

30

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 34 – Stress distribution for gauge corner contact using geometry of Sato (1994) with a normal load of 150 kN and friction force of 0.37 times the normal force.

3.7 Stress Distributions for Simulator Conditions

The purpose of the contact mechanics analysis for this project is to calculate

and visualise the stress distributions for contacting bodies. Presented in this

section is a typical stress distribution for a gauge corner, rather than the

maximum stress conditions presented in the previous section, in comparison

with the stress distributions for the rail/wheel simulator.

The stress distribution used for comparison, see Figure 35, is for a heavy haul

carriage with a 27.5 tonne axle load travelling at 42km/hr into a 300m radius

corner using the rail profile from Sato (2005) with a super-elevation of

100mm and rail gauge width of 1067mm.

The force used for the stress analysis was calculated using Equation (3.32)

from Waara (2001).

76

F T yF m a= (3.32)

FF = Flange force

ya = Acceleration in the ‘y’ direction

Tm = Mass of train carriage

The acceleration in the 'y' plane, perpendicular to the gravity acceleration

vector, is the balance between the centrifugal acceleration and the acceleration

from the super-elevation of the rail given by Equation(3.33)

2

2aT

yC o

ghvaR b

= − (3.33)

Tv = Train velocity

cR = Curve radius

g = acceleration due to gravity

ah = Super-elevation of rail

ob = Gauge width

Exploration of the stress distributions for all the different conditions tested in

the rail wheel simulator will now be presented. The simulator stress

distributions are for a line contact, representative of a conformal gauge corner

contact as in Section 3.5 using set values for the four groups of tests.

Groups 1 to 3 were tested at 9.5 kN and Group 4 tested at 12.5 kN normal

force levels. The plots will show the stress distributions for the static load and

the stress distributions for the set tractive torques in Table 3. The following

plots display the similarities in shape of stress distributions between in-service

and rail simulator conditions.

77

-600 -500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τE

Figure 35 - Stress distribution for a heavy haul carriage with a 27.5 tonne axle load travelling at 42km/hr into a 300m radius corner using the rail profile from Sato(2005) with a super-elevation of 100mm and rail gauge width of 1067mm

The 9.5 kN normal force case is plotted following Table 3 using the input

parameters from this table.

INPUT PARAMETER VALUE (UNITS) Rail Diameter 296.22 mm Wheel Diameter 97.21 mm Tread Load 9.5 kN Braking Torques 0, 15, 65 N.m Contact Length 41.3 mm

Table 3 – Test parameters used for contact mechanics calculations

78

-500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τE

Figure 36 – Stress distribution for a simulator without braking torque applied.

In the first case of no applied tractive force, see Figure 36 for the stress

distribution. The maximum effective shear stress, 153.5 MPa, is located

beneath the surface at a depth of 0.224 mm. Applying a braking torque of 15

Nm, which equates to 0.03 times the normal force, increases the effective

shear stress to 153.6 MPa and reduces the depth to 0.216 mm, see Figure 37.

The full tractive force, in Figure 38 moves the maximum effective shear

stress, 154.3 MPa, to 0.208 mm beneath the surface. It can be observed from

these results that the simulator is designed to measure low tractive forces such

as those experienced in a lubricated gauge corner contact.

79

-500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 37 - Stress distribution for a simulator with braking torque 15 N.m applied.

There is little difference between the stress distributions of the braked and un-

braked situations in the case of the simulator. This is due to a relatively small

maximum tractive force.

Consider now the maximum braking force condition which gives a ratio or

shearing force to normal force of 0.14 in Figure 38. The components of shear

stress can be observed to have increased in magnitude from the near zero

values in Figure 37 but are still insignificant when compared to the stresses

arising from the normal force. In all the situations plotted in this section the

position of maximum effective shear stress is below the surface. This

condition of shear stress will fatigue the underlying material and give a

shelling failure on the surface.

80

-500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 38 - Stress distribution for a simulator with braking torque 65 N.m applied.

-600 -500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τE

Figure 39 - Stress distribution for a simulator tread load of 12.5 kN without braking torque applied.

81

The tests carried out at the higher tread load of 12.5 kN have the same shape

stress distribution patterns as the lower tread load. However the shear stresses

contribute less to the stress tensor as the magnitude of the tractive forces are

equal but the proportion as compared to the increased normal force is

reduced. The ratios of shearing force to normal force for each of the braking

torque conditions given in Table 3 are 0.025 and 0.11.

In the first case of no applied tractive force, see Figure 39, the maximum

effective shear stress, 176.1 MPa, is located beneath the surface at a depth of

0.256 mm. Applying a braking torque of 15 Nm, which equates to 0.025 times

the normal force, increases the effective shear stress to 176.2 MPa and

reduces the depth to 0.248 mm, see Figure 40. The full tractive force, in

Figure 41, moves the maximum effective shear stress, 176.6 MPa, to 0.24 mm

beneath the surface.

-600 -500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 40 - Stress distribution for a simulator tread load of 12.5 kN with braking torque 15 N.m applied.

82

It is possible to observe in Figure 35 and Figure 39 that the stresses are similar

in magnitude at the surface. Into the body, of the heavy haul conditions, the

stress field extends further into the body as compared to the simulator.

However, the surface is the location of importance to this research as this is

the location of the lubricant film and observing the good correlation, indicates

it is appropriate to use this rail/wheel simulator.

-600 -500 -400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Stress (MPa)

Dep

th (m

m)

σX

σY

σZ

τXY

τYZ

τZX

τE

Figure 41 - Stress distribution for a simulator tread load of 12.5 kN with braking torque 65 N.m applied.

3.7.1 Two Dimensional Line Contact Stress Distributions

In the previous section the line plots of stress give an indication to the stress

state of the contacting bodies directly beneath the contact. In this section a

two dimensional slice is taken through the bodies to visualise the stresses

within the body. The effective shear stress plot is of particular interest as it

presents the region of maximum shear stress, providing an explanation for the

fatigued steel wear flakes that were encountered in the experimental testing.

83

The theoretical plots of contact stress that are presented within this section

are calculated using the assumption that the real contact width and measured

contact width are the same. This assumption becomes more valid as the real

contact area approaches the apparent contact area. The contact surfaces

develop, with loading history, to reduce the contact stress below the yield

stress for both rail and wheel samples, increasing the real contact area to

approach that of the apparent contact area. Figure 42 shows the theoretical

stress distribution for tread loading conditions for the simulator using a two

dimensional line contact. It can be seen that the most significant stress is the

compressive stress in the direction of the tread load (fz), and is in the yield

strength range of 380-580 MPa. Maximum effective shear stress for this

contact is subsurface at ~0.2mm, but is below the predicted shear yield

strength of 200-300 MPa (see Table 8).

Figure 43 shows the contact stress conditions for the same loading conditions

as Figure 42 with a reduction in contact length of fifty percent (20mm). The

compressive stresses, fz, for this case is in the range of plastic yielding. The

area of real contact for a newly machined sample may be lower than this case,

therefore the surface may plastically deform to reduce the surface pressure.

The previous contact stress predictions in this section do not include the

influence of surface traction forces. Figure 44 shows the contact stress

conditions for the same loading conditions as Figure 42 with an additional

braking torque of 15N.m applied. The addition of a surface traction force

varies the shear stresses. The maximum effective shear stress and the

position of maximum effective shear stress are not altered significantly by the

addition of the surface traction force. This can be observed by comparing the

effective shear stress plots between Figure 42 and Figure 44.

84

-252 -224-196 -168-140 -112-84.6

-28.9 -

fx Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-250-200

-150-100

-50

-410-365 -319-274 -229-184 -139-93.8-48.6 -48.6

fy Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-400

-300

-200

-100

-429-382-334

-286-238

-191-191

-143 -143

-95.4-95.4-47.7 -47

fz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-400

-300-200

-100

-60

-40

-20

0

4060

-80

80-40-100

100

-20

qyz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-100

0

100

173

47.3

77.792.8

108 123

138

108

154

qe Effective Shear Stress Component

y (mm)

z (m

m)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0.2

0.4

0.6

50

100

150

Contact Pressure =477.0319MPa, Half width =0.30698mm,Coefficient of Friction=0, Poisson Ratio=0.3

Figure 42 – Contact stress magnitudes for stress components using conditions of tread loading at 9.5kN, 41.3mm contact length.

85

-359-319-279 -240-200 -161-121

81.3 81.3

-41.7 -4

fx Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

0.8

-300

-200

-100

-579 -516-452-388 -325-261 -198-134-70.4 -70.4

fy Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

0.8

-600

-400

-200

-617-548-480 -411-343

-274-274

-206 -206-137 -137

-68.5 -6

fz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

0.8

-600

-400

-200-500

50100-100

-50150 -150

qyz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

0.8

-100

0

100

25.2 46.968.6 90.3112

134155

177

199221

qe Effective Shear Stress Component

y (mm)

z (m

m)

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

50

100

150

200

Contact Pressure =685.4999MPa, Half width =0.44113mm,Coefficient of Friction=0, Poisson Ratio=0.3

Figure 43 - Contact stress magnitudes for stress components using conditions of tread loading at 9.5kN, 20 mm contact length.

86

-252-223-195-167

-139-111

-82.9

-54.8 -54.8-26.7 -26.7

fx Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-200

-100

0

-410-364-318-271-225-179-133

-87.3-41.2

-41.2 -41

fy Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-400

-300

-200

-100

0

-429-382

-334-286

-238

-191 -191-143 -143-95.4 -95.4-47.7 -47.7

fz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-400

-200

0

-60-40-20

0204060

-8080 -100 -40100-20

-120

qyz Stress Component

y (mm)

z (m

m)

-0.5 0 0.5

0.2

0.4

0.6

-100

0

100

15.4 30.8

46.261

76.9

92.3108

123

138 154

qe Effective Shear Stress Component

y (mm)

z (m

m)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0.2

0.4

0.6

50

100

150

Contact Pressure =477.0319MPa, Half width =0.30698mm,Coefficient of Friction=0.032485,Poisson Ratio=0.3

Figure 44 –Contact stress magnitudes for stress components using conditions of tread loading at 9.5kN, dynamometer torque 15N.m, and 41.3 mm contact length.

3.8 Elastohydrodynamic Film Thickness Calculation

The next theoretical calculation for the rail wheel simulator is the lubricant

film thickness. The lubricant film thickness will be used to predict the

apparent viscosity and shear rate of the lubricant films during testing.

Taking the assumption that the contact has a fully developed lubricant film,

by using the known parameters of oil in grease, a lubricant film thickness can

be predicted. A contact condition of pure rolling between two cylinders as

presented in ESDU85027 will now be discussed.

87

The contact conditions that will be used are those of the simulated testing in

Table 3. It will be assumed that the lubricant film thickness is only a function

of the oil, not the solid lubricants or soap.

Lubricant manufacturers do not supply detailed information regarding the

contents of lubricating grease and as a result some assumptions need to be

made regarding the contents. It was not possible to extract the oil from the

soap matrix without contaminating the oil, so direct measurement of the

properties of the lubricant constituents was not possible. Therefore, the

missing values were taken as a high viscosity index light machine oil and were

obtained from ESDU85027 for use within the simulation. The lubricants and

their properties are presented in Table 13.

Lubricant Type Kinematic Viscosity of Base Oil @ 40˚C cSt

Density kg/m3

Lubricant A 150 900 Lubricant B 100 900 Lubricant C 179 947

Table 4 - Manufacturer specified viscosity values for tested lubricants.

The method proposed by Hamrock (1997) is presented in Equation (3.34):

0.128 0.694 0.5680min 1.714( ) ( ) ( ')

' 'z

PVuwh E

E R E Rη ξ−=%% (3.34)

minh% = Minimum film thickness

zw = Load per unit width

u% = Mean surface velocity

PVξ = Pressure viscosity coefficient

0η = Absolute viscosity

88

Inspecting Equation (3.34) the minimum film thickness can be calculated if it

is assumed that the following variables are constant:

entrainment velocity

normal force

temperature

viscosity

pressure viscosity index

The minimum film thickness values that were calculated using software from

ESDU 85027 are presented in Table 5 and will be used later for analysis of

lubricant performance.

Test Conditions and Minimum Film Thickness Lubricant Type Normal Force: 9.5

kN Velocity: 6 m/s

Normal Force: 9.5 kN Velocity: 3 m/s

Normal Force: 12.5 kN Velocity: 6 m/s

Lubricant A 3.55 x 10-6 m 2.24 x 10-6 m 3.55 x 10-6 m Lubricant B 2.71 x 10-6 m 1.71 x 10-6 m 2.71 x 10-6 m Lubricant C 4.14 x 10-6 m 2.6 x 10-6 m 4.13 x 10-6 m

Table 5 – Predicted minimum lubricant film thicknesses for tested lubricants.

3.8.1 Shear rate of lubricant film

Using the predicted lubricant film thickness the shear rate of the lubricant

films can be determined. The lubrication model assumed for in-service and

rail simulator contacts is elastohydrodynamic lubrication (EHL). The rolling

velocity entrains the lubricant into the contact forming an EHL film,

assuming that conditions are of sufficient lubrication. The sliding velocity

component, of the rolling/sliding conditions, shears the lubricant, which

degrades the performance of the lubricating grease. Therefore there are two

effects coming into play, development of an EHL film, and degradation of

the EHL film by shear.

89

The lubricant film of a greased surface may be thicker than that predicted by

the EHL theory due to the soap content of the lubricating grease. Assuming

that the film thickness is modelled by an EHL conjunction, it is possible to

calculate the predicted shear rates.

Body 1

Body 2

Sliding Velocity

x

Figure 45 – One dimensional shear.

In Figure 45 Body 1 is moving with a constant velocity with respect to Body

2. This relative velocity gives rise to a shearing effect in the region between

the bodies that is filled with lubricating grease. The equations of shear for

these boundary conditions are presented in Equation (3.35).

Note: Small angle theory tan

xy

xy

γ

γ γ

=

= = (3.35)

γ = Shear strain

x = distance slid

y = Lubricant film thickness

90

s

s

xt y tx ut

uy

γ

γ•

∂ ∂=∂ ∂∂ =∂

=

(3.36)

γ& = Shear strain rate

,s su v = Sliding velocity

Figure 46 – Shear rate prediction for an EHL film under the range of conditions for the simulator.

Using Equation (3.36) the strain rate can now be predicted for the simulator

across the typical range of parameters, see Figure 46. In the case of the

simulator, the rolling velocity is fixed for a given test but the sliding velocity is

91

constantly changing. It is a similar situation the for the lubricant film thickness

in that the film thickness is greatest at time zero and decays over time.

The in-service conditions are now considered using EHL theory. The

theoretical shear rate and sliding velocity are reduced by an order of

magnitude for the in-service conditions of the rail/wheel interface compared

to the theoretical simulator conditions. This variation in the shear rate is a

consequence of the difference in sliding speeds experienced by each of the

contacts. Typically for in-service conditions slip will not exceed 5% compared

to simulator conditions of up to 100% slip as a result of controlling the

maximum shearing force.

Figure 47 – Shear rate prediction for an EHL film under the range of conditions for in-service conditions.

Comparing these shear rates in Figure 47 to the results from the pumpability

testing in Section 5.7.4 shows that there is a difference in shear rate of three

orders of magnitude. This difference will not allow for prediction of the

92

apparent viscosity from the pumpability tests unless some assumptions

concerning the rheology of the greases are made. The comparisons between

the simulator viscosity results and the ASTM tests and rheometer results will

be discussed later in Section 5.7

3.8.2 Lubricant apparent viscosity calculation

If the lubricant film thickness and flange gap can be identified, the shear rate

and therefore the viscosity of the lubricant can be determined. The real film

thickness is difficult to measure for both the rail system and the simulator.

The value of the film thickness must therefore be estimated using EHL

theory presented in Section 3.8. In the simulated system, the shear stress can

be predicted from the measured braking torque of the system by assuming the

contact patch dimensions and by assuming that the contact patch dimensions

will remain constant with respect to time. The contact patch dimensions will

remain constant if the normal force remains constant, and is independent in

variations in the lateral force (braking torque). The nominal load of the

simulator possesses slight fluctuations about a mean value. These slight

fluctuations allow the assumption of constant normal force and contact patch

dimensions to be made. The mean nominal load value is used in the

calculations of shear stress within the lubricant film.

To predict the apparent viscosity of the lubricants from the simulator, the

shear stress and shear strain must be calculated.

BT

c

FA

τ = (3.37)

BTF = Force from shearing lubricant

cA = Contact area

τ = Shear stress

93

The shear stress predicted by Equation (3.37) is commonly used for solid

bodies, that is, the lubricant film between the bodies in Figure 45 is

considered to be a solid. If the lubricant film is considered to be a liquid then

the relationship for viscosity, Equation (3.38), is used.

τ η γ•

= (3.38)

η = Apparent viscosity

Considering these relationships and the measurements from the simulator, a

prediction of the apparent viscosity of the lubricating grease can be made.

If the applied shear stress from the braking torque of the simulator is below

that which the lubricant can support, then the lubricant film will remain as a

solid and transmit the input torque. This effect was observed experimentally.

This effect is seen as the slip approaches zero despite an observable lubricant

film. During the progression of the simulation test, the lubricity of the

lubricant decreases with accumulated strain. Alternatively, presenting this with

respect to apparent viscosity, the viscosity increases with accumulated damage

from shear strain.

Preceding the point of limiting shear stress, the lubricant film behaves as a

fluid allowing slip to occur. Therefore at some point the yield shear stress of

the lubricant becomes larger than the applied shear stress and traction is

obtained. Predicting the point of traction with the use of rheological testing

would be fast and relatively inexpensive, if there was a correlation, and if it

was relevant as a performance criterion.

The simulator may assist in predicting the development of this yield stress

with respect to accumulated strain. The problem with this method is the

unknown film thickness and its development with time. Assuming that

lubricant film thickness is that of an EHL contact for the base oil of the

94

lubricant, plots of the stress versus strain rate curves for each lubricating

grease can be constructed.

The apparent viscosity is now investigated using Equation (3.39) by equating

Equation (3.37) and Equation (3.38).

BT

C S

F yA v

τ η γ

η

•= ×

= × (3.39)

In this equation there are four variables, two mathematically predicted and

two measured. The calculated shear stress is generated from the transmitted

torque by the lubricant, or the shearing of the lubricant applies a torque to the

output shaft. This shearing force can be calculated from the measured output

torque divided by the output radial vector. The contact area is predicted from

the contact mechanics calculations and is assumed to be constant for each

test. Sliding velocity is measured as the difference in rolling speeds between

input and output shafts. Film thickness is predicted from an EHL calculation

of the base oil of the lubricating grease. This parameter is assumed to be

constant during each test. From these values it can be seen that viscosity is a

function of time, or as previously mentioned, accumulated strain.

There are issues with predicting the value of film thickness. Film thickness

will change with time as the temperature of the lubricant increases, the effect

of which is to lower viscosity. In addition the soap matrix decaying with

accumulated strain will also decrease the film thickness. The contact velocity

for the EHL calculation is assumed to be constant, as the input velocity is

fixed for the duration of each test. However the velocity can vary during

testing. Lubricant manufacturers supply kinematic viscosity results in their

lubricant specification details which then requires an estimation of the oil

density to predict the dynamic viscosity required for an EHL film thickness

95

calculation. A nominal value was chosen from tables of physical constants or

the manufacturer specification if available.

Additional example conditions are given for the lubricant films to determine

the appropriate average stress range in Table 6.

Parameter Value Theoretical maximum braking torque 65 N.m Experimental maximum braking torque 62 N.m Experimental contact radius 50 mm Theoretical maximum tractive force 1300 N Theoretical contact area at 12.5 kN 28.8 mm2 Theoretical tractive shear stress at 12.5 kN normal load

45 MPa

Table 6 – Theoretical results for inputs to EHL calculations.

All the required parameters have been presented to calculate film thickness,

shear rate, and apparent viscosity for the simulator, including their limitations.

3.9 Summary

The following major points have been identified:

Software was developed and validated based on the methods of the ESDU to calculate the stresses in bodies in contact.

Under simulated conditions with the maximum tractive force the value of creep is 0.06%.

Conformal rail profiles can be approximated by a line contact, similar to that used in the simulated rail curve lubricant testing.

The maximum contact pressure in gauge corner contact is much larger than the more common tread contact situation, 2.3 GPa as compared to 1.1 GPa.

The tested simulator conditions match the stress distribution for a heavy haul carriage with a 27.5 tonne axle load travelling at 42km/hr into a 300m radius corner using the rail profile from Sato (2005) with a super-elevation of 100mm and rail gauge width of 1067mm.

96

Lubricant film thickness is calculated using elastohydrodynamic film theory for the calculation of shear strain. Shear strain is then used in conjunction with shear stress to predict the apparent viscosity of the rail curve lubricants.

This chapter presented the theoretical background of contact mechanics

specifically between wheel and rail to develop an understanding of the stress

conditions. Stress distributions for typical in-service and simulator conditions

were presented to demonstrate the similarities between the two conditions.

These highlighted the effects of geometry and changes in shear force on the

stress distributions and the reasons for increased wear in the gauge corner.

The model for apparent viscosity calculation using the rail/wheel simulator

was then detailed. These theoretical calculations form the basis of the next

chapter on the experimental method applied to the simulator and inputs for

the data analysis in Chapter 5.

97

C h a p t e r 4

COMMISSIONING AND TESTING PROTOCOL OF THE RAIL/WHEEL INTERACTION SIMULATOR

4.1 Introduction

This chapter details the rail/wheel simulator, see Figure 48, with specific

reference to the current work.

Hydraulic Dynamometer

Wheel Sample

M

Rail Sample

Torque Transducer

AC Motor

Normal ForceLoad Cell

Shaft Encoders

Heat Exchanger

Pneumatic Ram(Normal Force)

Support Bearings

Figure 48- Schematic diagram of the rail/wheel simulator.

The first section on equipment modifications broadly outlines the deficiencies

for lubrication research in the simulator and the steps taken to address them.

The experimental method and procedure follows. Details of the measurement

system and errors associated with each of the components and calculated

values of this system complete this chapter.

98

4.2 Equipment Modifications

The rail/wheel simulator was originally configured for rail/wheel wear

investigation. Unfortunately the maintenance and design information for the

simulator was unavailable which led to a full disassembly of the rail/wheel

simulator. This disassembly served two purposes, to overhaul all of the

components of the simulator that were worn as a result of previous use and

to understand the design of the system. Communication with the previous

researchers also highlighted some design deficiencies of the equipment that

were then rectified for the purposes of this research project. Significant

modifications were then proposed when considering heat dissipation, the

tread load mechanism and the data acquisition system to carry out the

objective of quantifying rail curve lubricant performance through laboratory

simulation.

4.2.1 Heat Dissipation

The primary concern with the operation of the rail/wheel simulator in the

previous research was the dissipation of heat generated during testing. A full

description of the issues concerning the heat dissipation was not provided

with the simulator. The simulator also arrived without the hydraulic

dynamometer and with the remnants of the heat exchanger for the hydraulic

oil disassembled. The previous heat exchanging system consisted of a coiled

copper tube of 12mm internal diameter wound in a continuous loop in the

main oil storage tanks. During a preliminary investigation into the heat load it

was determined that the input power from the variable frequency drive is

converted to heat, with minor losses to noise and vibration. Given this

information it was believed that the heat exchanger was required to have a 22

kW minimum capacity. A new heat exchanger was therefore required as the

existing heat exchanger possessed a capacity (approximately 2 kW capacity)

smaller than 22 kW.

The original heat transfer system, a copper pipe coil placed in the hydraulic oil

reservoirs with water input, was used as the basis for the new design. The

99

simplicity of the original design led to consideration of retrofitting the existing

pipe with extra length to increase the surface area. However, the length of

pipe required for the surface area to remove the heat load (approximately 100

m) would not physically fit into the existing oil storage reservoir. The increase

in pipe friction was also an issue for the increase in pipe length.

Existing decommissioned heat exchangers were disassembled and their heat

transfer characteristics determined using convection heat transfer equations

(name plate data for the heat exchangers was not available). The heat

exchangers that were investigated included a water-oil single pass shell and

tube heat exchanger and a water-oil plate heat exchanger. Two problems

were encountered when investigating the single pass shell and tube heat

exchanger. The first was that six of the units were necessary to achieve the

required energy dissipation. The second was that the back pressure of the oil

through each shell and tube heat exchanger would apply an undesirable

braking load to the system.

The analysis of the water-oil plate heat exchanger was carried out using the

methods of Holman (1997). This type was selected due its high surface area to

volume ratio, compact design and low fluid resistance. These advantages are

essential when considering the overall heat transfer coefficient of oil-water

compared to water-water is at least an order of magnitude smaller.

The plate heat exchanger used was originally selected for a 1 MW milk-water

application. In an oil-water application this capacity is reduced to 100 kW,

which is greater than the required 22 kW. With the plate exchanger installed

and at full heat load, the outlet water of the heat exchanger is imperceptibly

hotter than at the inlet when operating at full capacity. The hydraulic

dynamometer is sensitive to variations in the oil temperature. It is therefore

important to maintain a moderate and constant oil temperature. In this case

the oil temperature is limited to between 40˚C to 45˚C to reduce the friction

forces in bearings lubricated with the hydraulic oil.

100

4.2.2 Tread Loading Mechanism

The original tread and flange loading mechanisms utilised a mechanical screw

to apply the load, see Figure 49. A rubber cylinder was located between the

end of the screw and the load application point (within the encasing indicated

in red). The measured tread load in this configuration varied widely as a result

of vibrations. In addition, the applied load would change with temperature

and creep due to the viscoelastic properties of the rubber.

Figure 49 – Tread loading mechanism showing original screw force applicator.

The screw load applicator relied on displacement to provide a force. For a

constant force the screw load applicator required a fixed displacement.

Therefore, as wearing of the samples occurred the force transmitted between

the samples would reduce. The screw load applicator therefore did not

maintain a constant load throughout the duration of the wear tests in the

work of Marich and Mutton (1989). These considerations led to a redesign of

the tread loading mechanism.

101

A pneumatic system for tread loading was designed to replace the existing

mechanical system. The advantages of the pneumatic system is that it reduces

the amplitude of loading oscillations (dynamic loading) and reduce load

variations by eliminating factors such as the rubber cylinder and the influence

of wear that were present within the original system. A high capacity

pneumatic source supplying a single pressure control valve which supplies a

pneumatic actuator was used.

Pneumatic pressure control devices typically do not sense downstream

pressure variations. In practice this means that if the load experienced by the

pneumatic ram increases, there is a corresponding increase in the pressure of

the cylinder and piping to the outlet side of the pressure control valve. This

increase in pressure cannot be dissipated through the pressure control valve

but must be bled off through another mechanism, in this case a controlled

system bleed. The bleed is tuned to provide the minimum amplitude of load

oscillation.

The effects of this modification have been twofold. The variation of load with

time has been measured with the new configuration and found to be

negligible whereas previously this was a serious concern. Previously constant

changes to the mechanical system were required to hold the load within ten

percent of target load limits. Outcomes of increasing load stability and system

control have been achieved with this modification.

The wheel sample head has three bearing surfaces upon which friction acts.

This friction modifies the load experienced at the contact between rail and

wheel samples. Two of the surfaces are equipped with Teflon bearing pads

which are then lubricated with oil to provide as low a friction component as

possible. The third surface originally was a steel-steel contact and is now a

lubricated brass-steel contact. The contact surfaces are depicted in Figure 50.

102

Figure 50 – Simplified wheel sample holder assembly. The large flat section at the left is the slider which moves in the channel. At the left end of the device the contact surfaces can be observed.

In its original configuration the wheel sample head could rotate about its

vertical axis in the running channel and apply pressure at the corners of the

guide block. The pressure in the corners would increase from an increase in

wheel head temperature from thermal expansion as the test progressed. The

effect of this was to reduce the sensed/measured load while applying an

increasing tread load to the rail and wheel samples. In the previous research

this may have gone undetected as the problem was only detected by using a

measured extraction force which was not possible in the configuration used

by Marich and Mutton (1989). Mechanical advantage in the mechanical screw

loading system may have masked the appearance of this phenomenon.

Identification of the steel on steel bearing surface also highlighted the need

for improved load alignment. It was initially believed that the contact width of

the samples would minimise loading alignment issues. Investigation into this

matter showed that alignment issues existed as plastic deformation and

103

associated wear accumulated on one end of the test samples during a

commissioning test discussed further in Section 4.3. Rectification of the

alignment was carried out through guide rail adjustments.

The primary concern for alignment was that the loading force was not central

to the test samples, but offset to one side by approximately 10 mm. This

offset may have provided a torque about the vertical axis, and may have

applied a variable force across the test sample contact surfaces. This variable

force can only occur if the wheel sample holder is not sufficiently restrained.

The guide rails on the simulator frame now restrain the wheel sample holder

in the vertical and lateral directions. Experimentally there was no evidence of

a variable tread force across the contact surface.

The force to move the wheel sample holder can be a component of the

measured applied force from the pneumatic ram under static conditions, a

source of error in this measurement. The friction force remains after moving

the wheel sample holder into position. During testing the vibrations through

the contact patch into the wheel sample holder caused a reduction in the

friction force, such that it approached zero and the measured normal force is

the applied normal force. The friction force arose from the two normal

forces, the force of gravity from the mass of the sample holder and the force

from the applied braking torque. A variation of the force will cause a

corresponding variation in the friction force to move the wheel sample

holder. In addition as the wheel sample holder expands within the alignment

rail channel, from an increase in temperature, the friction force may increase.

A maximum friction force of less than 500N was required. It was therefore

necessary to know the tolerance of the alignment rails as this is the only

adjustment available to reduce the friction force in moving the wheel sample

holder.

Experimental measurement of the tolerances of the alignment rails was

carried out by measuring the force required to move the sample head in both

104

directions and the tolerance gap set to an acceptable friction force of 300N.

Verification, under a range of operating temperatures, that the friction force

was less than 500N under test conditions was carried out and found to be less

than the threshold value of 500N (approximately 350N).

4.2.3 Data Acquisition

In the process of checking the tread loading system, deficiencies in the data

feedback system became apparent. High frequency and resolution data were

acquired from the original load cell electronics to find the source of the issues.

Harmonic noise was found. The load cells were sensitive to electronic noise

from the 50 Hz single phase supply power and magnetic or electronic noise

from the variable frequency drive.

The entire loading measurement system was checked with respect to the

mechanical and electronic components. The load cells were a custom design

of a membrane type installed between the loading mechanism and the wheel

sample holder. These were physically inspected for damage to the strain

gauges and calibrated. There were no mechanical issues. The strain gauge

amplifiers were checked and found to be faulty. Upon replacement the noise

issues were still apparent. Two changes were made, addition of a 50 Hz filter

to the electronics and installation of an earthing circuit. Verification by repeat

data collection showed elimination of the power supply noise at 50 Hz and

reduction to barely detectable levels of the variable frequency drive noise.

Mechanical vibration of the entire simulator was now the dominant

component of signal noise.

4.2.4 Tractive Force Application System

In the work of Marich and Mutton (1989) it is not clear as to the purpose or

settings of their hydraulic braking system. It is not mentioned in the published

work but is apparent in the photographs of the simulator. The braking system

had been removed prior to its relocation so reverse engineering was

impossible.

105

Safety Relief Valve

Main Tank

Pressure Relief Valve Ball Valve

MWheel SampleDriving Input

Torque Transducer

Hydraulic Pump

Pressure Transducer Heat Exchanger

Figure 51 – Hydraulic dynamometer system.

A design study was carried out and a hydraulic dynamometer system installed.

The dynamometer system controlled braking torque only, contrary to other

twin-disk systems which measure friction force (Marich and Mutton 1989;

Markov 1995; Tyfour et al. 1995; Olofsson and Telliskivi 2003). The

controlled braking torque creates high slip conditions at the beginning of

lubricated tests. It is unlikely that in-service conditions would ever achieve this

level of slip except under extreme circumstances.

The hydraulic system design was vital due to the change in sample shape from

the work of Marich and Mutton (1989). Previously the wheel samples had a

flange upon which a load was applied. The slip in the work of Marich and

106

Mutton (1989) was purely related to geometry, and was variable across the

flange surface from root of the flange to the tip. The testing in this thesis used

a twin-disk design, with slip controlled by the dynamometer. Contact patch

dimensions and loads are easily measured and calculated with this sample

geometry. Future work will investigate changing the wheel profile to

investigate elliptical contacts.

4.2.5 Slip/Creep Measurement

The rotational speed measurement system for slip calculation has been totally

redesigned to increase the resolution of speed and slip measurements of the

rail and wheel samples. Previously the speed of shaft rotation was measured

with a proximity probe and notched wheel outputting to a digital display. This

method lacks the resolution and accuracy required to measure slip.

Inductance proximity probes are sensitive to changes in speed and distance to

inductive material (notch on wheel). To address the issues with the original

inductance probes shaft encoders were installed. The encoders have a

resolution of 5400 encoder counts per revolution to gather high resolution

data for the shaft position and speed. This modification increased the

accuracy of slip/creep measurement by two orders of magnitude and is

unique to twin disk rail curve lubricant devices.

4.3 Testing equipment – construction/commissioning

The commissioning testing results are presented to provide the background

for the testing methodology in the following sections.

4.3.1 Pre-Commissioning Testing Observations

The commissioning testing used recycled test samples, which had been used

in the work of Marich and Mutton (1989). Following use of the recycled test

samples, with a variety of testing protocols used to determine the capabilities

of the simulator, the samples displayed wear characteristics comparable to

that encountered in service (Marich and Mutton 1989). Two distinct wear

processes were observed, oxidative and fatigue wear. Oxidative wear can be

107

observed in Figure 52(a) as the darker section of the contact surface. The

fatigue wear was observed by the surface changing to an appearance matching

ratchetting fatigue wear and vibration and noise emanating from the contact.

This ratchetting is shown in Figure 52(b).

(a)

(b)

Figure 52 – Rail sample with oxidative and fatigue wear (a). Wheel sample with oxidised material removed to highlight plastic deformation (b).

4.3.2 Commissioning Testing Observations

Commissioning testing was carried out to develop the lubricated test methods

employed in this thesis. The wheel and rail samples used in commissioning

tests were recycled from the testing of Marich and Mutton (1989) and the rail

geometry changed to a flat twin-disk configuration. The samples were

prepared by machining the surfaces of both samples to flat, removing any

work hardened material. The samples were placed in the simulator and

prepared by applying loads which exceeded the yield stress of the wheel and

rail steels.

During the ‘run-in’ period a narrow ring of worn material was observed on

both wheel and rail samples, see Figure 53. An investigation was carried out

to determine the cause of this wear patch, which was only a small fraction of

the total width of the contact. Initially the contact zone was investigated with

methylene blue to ascertain whether the samples were indeed contacting

108

across the full width. The methylene blue test indicated that full contact was

achieved despite the obviously worn ring.

The samples were measured in-situ for trueness using dial indicators

(resolution ±0.01mm) and were found to be in the range below the resolution

of the measuring equipment. The loading mechanism on the wheel sample

holder was then investigated for alignment problems and no skew, to cause

the wear at the outer edge of the sample, could be found.

The samples were then removed to quantify the change in surface profile

from the ‘run-in’ period and for machining to re-prepare the surfaces. Surface

preparation was achieved by machining in a lathe using machining jigs which

have an axial run-out of less than 0.01mm. Measurements of surface profile

taken in the lathe did not have the resolution necessary to quantify the worn

section.

(a)

(b)

Figure 53 – Rail sample mounted in machining jig following initial lathe cut, with pitting at the outer edge of the rail sample(a). Wheel sample with hardened material, the smoother ring, at the outer edge of the sample (b).

During machining of the rail sample, material was observed to be plucked

from the surface, where the corresponding pits can be seen in Figure 53(a).

These pits could not be observed prior to the machining process, only a ring

of different surface texture. It was also noticed that the material hardness was

109

fairly constant across the surface. Conversely for the wheel sample the

material hardness was significantly higher at the worn region. Sparks from the

lathe cutting tool were observed during machining of the wheel sample which

is indicative of high hardness material.

Further investigation into the literature (Tyfour et al. 1995; Lewis and Dwyer-

Joyce 2004) gave indication that the phenomena observed was characteristic

of this type of contact. Sample preparation or pre-conditioning was resumed

with a freshly prepared pair of samples for investigation of lubricated contact.

(a)

(b)

(c)

(d)

Figure 54(a,b,c,d) – Wear development of running surfaces on wheel and rail samples (left to right, top to bottom).

There were three main phases observed during the lubricated testing:

lubricant spread and sample acceleration; gross sliding; and traction

development. In the first phase the lubricant is forced to the outer edges of

the samples where it is flung from the surface and the surfaces are observed

110

to have a consistent coverage of lubricant, Figure 54(a). The end of this phase,

when the samples are reaching the set velocity, marks the beginning of the

second phase: the wheel sample (output shaft) slowing down and gross sliding

of both surfaces occurs. This gross sliding continues until the lubricant film

breaks down and metal to metal contact occurs, Figure 54(b). This metal

contact can be seen in Figure 54(c) at the outer right edge of the samples.

The wear rings develop at a randomly different location with each test run,

but always on the newly machined material. The newly machined material was

measured and found to be softer than the worn rings. This surface

development is similar to the shake-down process experienced by new rails.

Figure 55 shows the development of the surface from two wide bands in (a)

to approximately fifty percent coverage in (b) and (c). The wear material that

was not transferred to the other surface collected at the outlet of the rolling

contact as shown in Figure 55(d).

Wear particles collected after testing consisted of two main particle sizes,

large flat flakes (> 1 mm) and small flakes (< 1 mm). The large flakes appear

to be from the initial breakdown of the lubricant film. Material removed

from the samples during this phase was seen to leave the contact zone which

can be observed clearly in Figure 56(b) by the ring of 'shiny' steel. The small

particles cannot be seen to form as testing progresses and can only be

observed in the collected excess lubricant.

The lubricant application method depicted in Figure 56(a), not the method

used in the later lubricated testing, does not spread a consistent thickness

layer over both samples, but does apply a reasonably uniform amount of

lubricant to the central region of the rail sample. The lubricant is spread by

the action of the samples rolling together where the excess lubricant is

forced from the contact patch forward and to the outer edges of the wheel

sample.

111

(a) (b)

(c)

(d)

Figure 55 – Wear development of running surface following repeated lubricated tests (a-c) Wear particles and excess lubricant (d).

Little excess lubricant collected at the edges of the rail sample using this

application method. There are two reasons for this, firstly the rail sample has a

much larger radius than the wheel sample, and therefore a larger centrifugal

force is generated, causing the lubricant to leave the rail sample, which has

been observed. Secondly the wheel sample is of a much smaller diameter and

therefore the volume of lubricant which can be supported through the

contact region is significantly less than the rail sample, forcing the excess

lubricant to the outer edges. The point at which the surplus lubricant collects

can be seen in Figure 55(d).

112

(a)

(b)

Figure 56 – Grease application pattern (a) and subsequent lubricant film failure of running surfaces (b).

The measurements of the rolling diameter of the rail and wheel samples

stabilised following an initial period of change. The period of change is typical

of pearlitic steels as the material strain hardens through repeated plastic strain

(Fletcher and Beynon 2000). Initially the freshly machined surfaces of the rail

and wheel samples would experience plastic deformation to increase the ‘real’

contact area. Then the strain will accumulate to a point where either the

material hardness or surface yield strength are above that of the contact

pressure. If the material cannot achieve the amount of strain hardening to

increase the material strength above the applied stress then the material will

reach the ductility limit and fail.

A wear characteristic similar to ratchetting was observed on the rail sample as

the contact surface has a pocked appearance. Ratchetting in rails appears as

small flakes of material being removed from the samples by the tractive force

after sufficient plastic deformation has taken place.

113

(a)

(b)

Figure 57 – (a)Wear particles collected from lubricant, two distinct particle sizes are attached to the magnetic sample collector (8mm diameter). (b) Demagnetised wear particles at higher magnification.

Changing the braking torque (applied shear force) generated new contact

surfaces by removing material from the rail and wheel samples that was at its

ductility limit, see Figure 57. In the work of Tyfour et al. (1995) steady state

wear conditions developed after a number of loading cycles. This behaviour

was also exhibited by the simulated system. Upon increase of surface traction

the cumulative strain distribution changed and greater material removal rates

were observed. The lubricant film would be completely destroyed in a ring

pattern as the large metal flakes left the surface, see Figure 58. Steady state

conditions were reached when the rings of new (shiny) material stop

appearing during the lubricated testing. In the commissioning tests preceding

the lubricated testing, surface traction was kept constant and steady state

conditions were reached.

114

(a)

(b)

Figure 58 – (a) Lubricant film failure on right of sample (b) Lubricant film failure on left of sample. Material removed from the surface of the rail sample destroys lubricant film over a nominal contact width depending on the size of the wear particles.

4.4 Lubricated Testing Protocol

The primary objective of the testing protocol was to determine the

performance properties of rail curve lubricants using the rail/wheel simulator

in line with the overall objective of the thesis.

4.4.1 Preparation of the rail/wheel samples

Following selection of a suitable material couple, the rail/wheel samples were

machined to the required profile. Following this the samples were installed in

the machine and the machine parameters set. The rail/wheel samples were

machined at the beginning of the lubricated testing and no further machining

was carried out on these samples. Test samples were never removed from the

test equipment to ensure alignments issues were constant throughout testing.

4.4.2 Material Properties

The chemical constituents and material properties for the rail and wheel

samples are detailed in Table 7 and Table 8.

115

Chemical Composition Brinell Hardness (HRC)

Material Type

C Mn Si Cr Mo Wheel samples 0.72 0.80 0.32 0.31 0.045 320-385

(34.2- 41.7) Rail samples 0.72 0.80 0.32 0.31 0.045 257-272

(25.3- 27.7) Table 7 - Material properties of test samples (Marich and Mutton 1989).

Material Brinell Hardness (HRC)

Shear Yield Strength (MPa)

Ultimate Shear Strength (MPa)

Tensile Yield Strength (MPa)

Ultimate Tensile Strength (MPa)

AISI 1080(Automation Creations 2005a)

293 (30.7) 330 536 585 965

AISI 1070(Automation Creations 2005a; Automation Creations 2005b)

212 (16.9) 217 390 385 703

Table 8 – Mechanical properties of similar high carbon steel alloys (Automation Creations 2005b; Automation Creations 2005a).

The shear properties presented in Table 8 were calculated using the work of

Guduru et el (1989), Equation (4.1) and Equation (4.2):

1.77y yσ τ= (4.1)

yσ = Yield stress

yτ = Shear yield stress

1.8US USσ τ= (4.2)

116

USσ = Ultimate tensile strength

USτ = Ultimate shear yield strength

The shear strength was predicted as this value was not available.

MIN MAX MEAN STD. DEV. Rail Surface (HB) 246 280 259 12 Wheel Surface (HB) 311 362 325 19 Rail Bulk Material (HB) 241 249 245 4 Wheel Bulk Material (HB) 287 307 295 11

Table 9- Measured hardness results for rail and wheel samples with minimal loading cycles.

NEWLY MACHINED TEST 1 TEST 2 TEST 3 TEST 4

Range 241-249 238-275 257-285 249-289 248-288 Mean 245 255 267 263 254 Std Dev. 4 17 11 16 31

Table 10 – Rail Sample Hardness Range in HB (Brinell 3000 kgf Std).

NEWLY MACHINED

TEST 1 TEST 2 TEST 3 TEST 4

Range 287-307 324-371 310-384 324-347 320-360 Mean 295 345 336 335 343

Std Dev. 11 20 31 9 17 Table 11 - Wheel Sample Hardness Range in HB (Brinell 3000 kgf Std).

Comparing the hardness values between those measured, in Table 9, and the

work of Marich and Mutton (1989), Table 7, shows similar values. Comparing

the experimental values to the quoted values in Table 8 it can be seen that the

rail alloys are harder than the 1070 steel but similar to the 1080 steel.

Hardness testing was carried out on the rail and wheel samples following each

of the lubricated tests to measure the hardness development from repeated

117

cycling. Table 10 and Table 11 show that after initial loading subsequent

loading does not increase the measurable surface hardness.

4.4.3 Test Sample Surface Roughness Results

Roughness testing was carried out after machining of the wheel and rail

samples and at the completion of all lubricated testing, the results contained

in Table 12. The measured surface roughness achieved post-machining was

less than the specified machining tolerance of 1.6 µm and less than the

predicted EHL film thickness.

Average roughness value range for newly machined surface. (Ra)

Average roughness value range at completion of all testing. (Ra)

1.08-1.22 µm 4.7-5.8 µm Table 12 – Roughness measurements taken from wheel and rail samples after machining and at the completion of all lubricated testing.

Roughness at the completion of all testing was more than the minimum film

thickness calculated for the assumed EHL conditions. The film thickness

calculations were conservative and based on lubricating oil component of the

lubricating grease. Experimentally it was found that during the lubricated tests

the surfaces did not experience metal on metal contact except at the lubricant

film failure point, not from initial contact as the film thickness calculations

would suggest. The lubricant film failures which were observed as rings of

removed lubricant film would probably have resulted from localised

roughness exceeding the lubricant film thickness.

4.4.4 Testing Procedure

Clean both samples in situ, initially with white spirit or similar, then finally with hexane to ensure any residue is removed.

Measure diameter of rail sample three times using pi tape (resolution ± 0.01mm).

Measure diameter of wheel sample three times using external micrometer (range 75-100mm, resolution ± 0.01mm).

118

Measure ambient temperature with infrared thermometer on surface of constant emissivity (Temperature range: -50 to + 500 degrees C, Accuracy: +/-2% of reading or +/-2 deg C) .

Position wheel sample holder to place rail and wheel samples in contact at specified tread load.

Start variable frequency drive and accelerate to test speed at a rate of 0.1 Hz per second.

After approximately five minutes a tractive force is applied by way of the hydraulic dynamometer. This force is set by adjusting the pressure in the hydraulic system and is measured at the wheel holder by the torque transducer.

The system is then shut down and lubricant is applied to the running surface of the rail sample.

Start variable frequency drive and accelerate to test speed (e.g. 20 Hz) at a rate of 0.1 Hz per second. Sixty seconds after start-up the dynamometer is activated at the set pressure.

Ensure wheel sample is rotating to prevent damage.

Measure data until set point is reached, the set point for each test was a time following development of full traction conditions.

Monitor slip conditions with HP5315A Universal Counter in frequency ratio mode.

Measure temperature of test samples with infra-red thermometer.

4.5 Method of Measurements

The method of measurements is presented here in order to aid understanding

of the test equipment and presented results in Chapter 5. A short summary of

each of the measurements is presented in this section followed by more

details of each particular measurement and its calibration.

The tread loads are measured indirectly, as it is not possible to measure at the

contact point during a test, but in the same axis as the direction of loading.

The pneumatic loading rams apply force to a diaphragm load cell placed

between the sample holder and the ram, see Figure 48. The load cells are then

119

calibrated in situ by placing a reference load cell at the loading point for a

direct measurement of the contact force.

Rotational speeds of both samples are measured with high precision shaft

encoders. The rotational speeds are also used to determine the slip ratio

between the samples, the sliding velocity of the flange contact, and the linear

velocity of samples.

In the work of Marich and Mutton (1989) the rotational speeds were

measured using notched wheels with a very low resolution for measuring

shaft position and speed. The modified method used in this thesis allows for a

more accurate prediction of the contact mechanics of the interface. The

limiting factor with the new method of slip calculation, as determined by error

analysis present in Section 4.7, is the resolution of the sample diameter

measurements.

The measurements of the sample diameters have been taken with a contact

measurement device. Higher resolution devices were considered but the

samples will experience thermal expansion effects of magnitude larger than

the resolution of the measuring equipment. The thermal effects have been

predicted from sample bulk temperatures and are presented in Section 4.6.1.

A further limitation in the slip prediction is the wear of samples in the tread

contact area. Sample geometry was measured to provide a suitable prediction

of the rate of diameter change. This change in diameter corresponds to a

change in slip and output ratio of the system and a variance in the sliding

speed of the contact. Experimentally it was found that a change in diameter

following testing could not be measured. Additionally testing was always

ceased prior to full lubricant film failure.

4.5.1 Rotational Speed Measurement

Rotation was measured using 5400 pulse per revolution incremental shaft

encoders. The encoders were physically connected to the input and output

120

shafts by timing belts which eliminates error from belt slip. This mounting

arrangement only allows an absolute error of one pulse in the total of pulses

over the sample period. Another method of interpreting this is the system has

a rotational resolution of 0.00116 radians/pulse (0.067 degrees/pulse).

The resolution of speed and slip measurements is dictated by the sampling

period. Therefore to increase resolution and accuracy, a suitable sampling rate

must be selected from the rotational speed of the slower shaft. The specified

minimum sampling rate was 1 Hz which correlates with a 16bit resolution

(0.0015 %) on the slower input shaft, and three times this resolution on the

faster output shaft.

4.5.2 Output Torque Transducer

A HBM T30FN industrial torque transducer was used to measure the output

torque. It is mounted between the end of the shafts holding the wheel sample

and the hydraulic dynamometer. It is specified to have a maximum torque of

2000 N.m and rotational speed limit of 10,000 RPM. The accuracy and

resolution of the transducer and associated electronics prior to data

acquisition was not specified by the manufacturer but the error bounds were

taken as ± 0.1 N.m.

Calibration of the transducer was carried out by a torque arm rigidly mounted

to the output shafts and restraining the dynamometer side of the torque

transducer. The results of the calibration and resulting regression were used to

verify that the transducer had not been damaged and the calibration correct as

the units are sold pre-calibrated.

4.5.3 Input Torque

Input torque was measured as an output from the variable frequency drive. It

is internally calculated by the variable frequency drive using the magnetic flux

density. The details of this calculation were unavailable from the

manufacturer.

121

The method used to calibrate this output was to apply known loads to the AC

motor, record the displayed value from the variable frequency drive and

acquire the analogue output data. This method relies on the AC motor having

the same characteristics as its name plate specifies. The preliminary data

gathered can be seen in Figure 59. Additional data was gathered across the

load range to verify the preliminary calibration but is not presented in Figure

59.

Further testing was carried out and was found to match the regression line

calculated from the preliminary data. The regression line coefficients are used

to adjust the output signal to torque input. The error associated with this data

was given by the manufacturers as ±5.0%.

Display % Torque vs DAQ Measured Torque

y = 67.414xR2 = 0.911

0

1000

2000

3000

4000

5000

6000

7000

0 20 40 60 80 100

% Torque

Inpu

t Tor

que

(mV)

Series1

Linear (Series1)

Figure 59 – Variable frequency drive display torque versus analogue output circuit to data acquisition system. NOTE: All values for calibration not plotted.

The variable frequency drive output was then converted to Nm using the

name plate specification of the electric motor of 22 kW at 975 RPM.

122

Input PowerInput Torque

Input Rotational Velocity= (4.3)

Substituting the values into equation (4.3) to determine the torque at 100%,

gives Equation (4.4) and the result.

22000 215Nm102.1018

ININ

IN

PTω

= = = (4.4)

The regression equation from Figure 59 is then applied at 100% input torque

to find the mV output value, then the calculated maximum input torque is

used to find the conversion between mV output and input torque giving

equation (4.5) for the analogue output signal of the variable frequency drive

(input torque).

1 mV 0.031962 Nm= (4.5)

4.5.4 Temperatures

All recorded temperatures were taken with an infra-red thermometer of fixed

emissivity (0.95). The resolution of this device is given as 0.1ºC, range of -50

ºC to 500 ºC, and accuracy of ±2%. The thermometer is calibrated at the

factory and was checked against reference thermometers and found to be

within the specified accuracy and resolution quoted.

The ambient temperature was taken from a surface of constant emissivity

close to the simulator. Bulk sample temperatures were taken through a

viewing port in the safety enclosure at a point in the centre of the track and

just prior to entry of the contact. In all cases a laser sighting system was used

to measure the same location. During testing it was observed that temperature

measurements taken while samples were stationary were reduced by

approximately 5 degrees as compared to those taken when the samples were

rotating.

123

4.5.5 Slip Calculation

The measurement of longitudinal slip is an approximation which takes into

account a number of factors, which are discussed further in Section 0 and

summarised here. The rolling diameters of the wheel and rail were taken using

contact measuring devices which have a level of precision below that required

for a high precision calculation of slip/creep (> 0.01% slip). The method used

in this thesis also cannot account for the worn rings and surface texture which

is necessary for measuring the ‘real’ diameters. Another source of error,

thermal expansion, is a factor which is difficult to account for as the thermal

profile and heat transfer system is highly variable. Thicknesses of the

remaining lubricants influenced the value of rolling diameters and therefore

the slip ratio as well.

The sampling of the rolling speeds through the encoders was taken at a 1Hz

rate. The reasoning for this is to maximise the precision of the rotational

speed ratio, close to 16bit precision (0.0015 %). The measurement point was

not taken at the same location on the rail rolling diameter, because there were

a number of rotations between each sample point; so the sampling point was

at a random location on both the rail and wheel samples.

This ‘slow’ sample rate averaged the rotational speeds during the period. The

other channels of data that were acquired stored only a single non-averaged

data value. Finding harmonic signal noise from stick slip phenomena in the

rotational speed data below a frequency of 2 Hz was impossible.

The slip ratio is calculated by Equation (4.6).

1 o ox

i i

w rw r

ξ⎛ ⎞

= −⎜ ⎟⎝ ⎠

(4.6)

iw = Rotational Speed of input shaft

ow = Rotational Speed of output shaft

124

ir = Rolling radius of input shaft

or = Rolling radius of output shaft

wIn

put

wO

utpu

t

R Input

ROutput

Figure 60 – Diagram of twin-disk arrangement with nomenclature.

At the conclusion of all testing in this research a lubricant film was present

and as such the subsequent wear rate was assumed to be negligible. The

values of radius for this research were therefore assumed to be constant

during each test.

4.5.6 Torque Measurement for Tractive Force (Shearing Force)

Tractive force in the simulator system is generated by applying a braking

torque to the output shaft. Power is transmitted from the input shaft through

the contact, then measured and controlled by the output shaft. The contact

can be a lubricant film or direct surface contact.

The output power of the shaft is limited by the transmissive characteristics of

this contact. In the case of a lubricant with zero viscosity and a film thickness

greater than the combined surface roughness, the output power would

125

approach zero. Similarly, if the surfaces of each sample could be polished

such that the coefficient of friction approached zero the output power would

also approach zero. Real systems have neither of these characteristics.

Tractive power is of interest because this power is a rolling resistance or

power loss. The level of tractive power absorbed by the lubricant before film

failure is a measure of performance of the test lubricant. The more power

absorbed by the lubricant, the less power absorbed in wear processes and

other associated losses. Quantifying power and absorbed energy may allow

for prediction of lubricant life in varying conditions.

The magnitude of the maximum tractive force and torque can be predicted

from the power characteristics of the AC motor using Equation (4.7).

x

Wheel

maximummaximum

TQr

PTω

=

= (4.7)

T = Torque

maxT = Maximum torque

maxP = Maximum power

Substituting values:22,000 65N.m

3 975 260

65N.m 1300N0.050m

maximum

x

T

Q

π= =

×⎛ ⎞×⎜ ⎟⎝ ⎠

= =

(4.8)

This maximum force and torque is a constant value for the system as these

values are directly related to the current limits in the motor and variable

126

frequency drive. These values, though, do not take into consideration any

losses.

Figure 61 – Torque component diagram for output shaft.

Losses occur in the output shaft. The total torque measured by the torque

transducer, shown in Figure 61, is the sum of the bearing friction torque and

the tractive contact torque. If we take the hypothesis that bearing friction is

negligible compared to the tractive torque then the tractive torque is equal to

the measured torque. Mathematically, torque is formulated using the Equation

(4.9).

T C BFT T T= − (4.9)

BFT = Bearing friction torque

CT = Transmitted torque through contact patch

TT = Torque transducer torque

127

The hypothesis is null if bearing friction torque is greater than 5% of

measured torque. The worst conditions of maximum tread load and

minimum braking torque are calculated using Equation (4.10).

T

o

F PTe Pr

μ

μ

=

× = × (4.10)

F = Friction force

e = Proportion of total value

Substituting values into the equation gives a coefficient of friction of 0.001.

This value is typical for the needle rollers used in the wheel head assembly

(Bailey and Association of Iron and Steel Engineers. 1996). Therefore at the

selected level of 5% of the measured torque the hypothesis is valid and

bearing friction can be ignored. Extrapolating from this hypothesis, it is then

reasonable to assume that the torque or shearing force experienced by the

contact patch is that of the measured torque.

4.5.7 Rail Flange Contact Conditions

The in-service flange contact is a highly variable contact as its location on the

wheel is variable. Its size can vary according to rail profile and/or wheel

profile from a point contact to a full conformal contact.

When the case of a two point contact for a wheel is considered, there is one

point on the tread surface and another point on the flange surface. The

contact ellipse on the tread is a rolling/sliding contact, with a dominant rolling

mode. The contact ellipse on the flange is a rolling/sliding contact with a

larger sliding component caused by the difference in the rolling radius to the

tread contact.

128

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

Rolling Velocity (km/hr)

Slid

ing

Vel

ocity

(m/s

)Rolling Velocity Vs Maximum Flange Sliding Velocity

Wheel Diameter = 600mmFlange Height = 25mm

Figure 62 - Maximum flange sliding velocity for a typical commuter train wheel diameter (600mm).

Figure 62 and Figure 63 show the relationship of maximum theoretical flange

velocity versus rolling velocity for a commuter train wheel and heavy haul

wheel respectively. These charts are presented to allow comparison between

field and simulated conditions. The figures are calculated with Equation (4.11)

using geometry of typical rolling stock used in the Queensland Rail network.

Wheel rotational velocity (rad/s)

Rolling Tread

Sliding Tread Flange

Sliding

v r

v r r

v r

ωω ωω

ω

=

= −

=

=

(4.11)

129

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Rolling Velocity (km/hr)

Slid

ing

Vel

ocity

(m/s

)

Rolling Velocity Vs Maximum Flange Sliding VelocityWheel Diameter = 860mm

Flange Height = 25mm

Figure 63 - Maximum flange sliding velocity for a typical heavy haul train wheel diameter (860mm).

4.5.8 Normal Load

The normal load was measured with a diaphragm load cell. The diaphragm is

located between the pneumatic ram and the sample holder and is only capable

of measuring compression force. Two factors affect the accuracy and

resolution of the measurements from the load cell. Firstly some proportion of

force is lost or gained due to friction between sample holder and simulator

frame as previously discussed in Section 4.2.2, and secondly the non-linearity

of the load cell introduces an error as the calibration assumes a linear

response.

Measurement of the linearity of the load cell was carried out using a reference

load cell attached to a load cell amplifier of known characteristics (Yokogawa

oscilloscope). The reference load cell was verified against a calibrated

130

Hounsfield materials testing device prior to testing and its calibration results

are shown in Figure 64.

Reference Load Cell Calibration Curve

y = 0.0951xR2 = 0.9996

0

200

400

600

800

1000

1200

0 2000 4000 6000 8000 10000 12000

Load (N)

mV

Figure 64 – Reference load cell calibration curve or output strain versus input load as applied by calibrated materials testing device.

y = 1.0644x + 67.696R2 = 0.9954

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Reference Cell (mV)

Nor

mal

Loa

d D

iaph

ragm

(mV)

Figure 65 – Normal versus Reference load cells calibration curve.

The result of the calibration testing, for the load cell, is shown in Figure 65. It

can be seen in both calibration figures that the regression correlation statistics

131

are high. Also of note is the offset voltage (67.7 mV) in the diaphragm load

cell, whereas the reference load cell does not have such an effect, 0 mV was

equal to 0 N.

4.6 Measurement Errors

The relative errors in each of the measurements have been discussed in the

previous section. This section will discuss the method used for error

propagation and the assumptions used in calculating results.

4.6.1 Thermal Expansion of Test Samples

The rail and wheel samples increase and decrease in size with respect to

temperature arising from frictional energy absorbed by the system. Predicting

the effect of thermal expansion on rolling diameter is important in order to

make an accurate prediction of slip/creep.

If a rail sample is considered as a thin hollow cylinder which is then unrolled

to a single length, it is possible to use the linear thermal expansion Equation

(4.12).

0

11 m/m C

l

l

l Tl

α

α μ

Δ = Δ

= ° (4.12)

lΔ = Change in length

0l = Original length

lα = Linear thermal expansion coefficient

Substituting experimental values gives Equation (4.13):

132

0.44mm @ 400.44 0.14mm

300mm 0.14mm0.05%

l T C

φπ

φφ φ

Δ = Δ = °

Δ = =

= ±= ±

(4.13)

TΔ = Change in temperature

φ = Diameter

Checking the linear thermal expansion assumption using the volume thermal

expansion with Equation (4.14) may provide a more rigorous value for the

change in sample diameter.

0

333 m/m C

V

V l

V

V TV

α

α αα μ

Δ = Δ

= ×= °

(4.14)

VΔ = Change in volume

0V = Original volume

Vα = Volume thermal expansion coefficient

The rail sample remains approximated as a cylinder and the volume is

calculated using Equation (4.15).

( )2 20 o i tr r tV π π= − (4.15)

tt = Thickness

Assuming that all the thermal expansion is in the radial direction, the worst

case, and the internal radius is constant, Equation (4.16), for heated volume

can be used.

133

( )( )2 2H o o iV r r r tπ π= + Δ − (4.16)

HV = Volume when heated

Rearranging and solving for the increase in radius for experimental conditions

gives Equation (4.17):

( )2 2

0.04mm2

300 0.08mm0.03%

o o o

o

o

V t r r r

rr

π

φ φφφ φ

Δ = Δ + Δ

Δ == ± Δ= ±= ±

(4.17)

The volume expansion method gives a slightly lower value of error, therefore

the linear expansion solution will be used in this thesis to predict the error.

4.6.2 Energy dissipation methods

Lubricant performance is measured in Chapter 5 as the power absorbed by

the lubricant film. The power measurement, dissipated power, is the

measured difference between the input and output power and subtracting any

extra power losses with the remaining power assigned to the effects of the

lubricant film. Power is dissipated in the simulator system by a number of

processes. The power dissipation of interest is that related to wear processes,

which is energy dissipated through sliding (frictional energy).

The sources of energy loss in the system are:

Frictional sliding at the contact interface

Friction in rolling bearings of sample holders

Noise from system

Electrical losses in variable frequency drive

Electrical losses in AC motor

134

Mechanical losses in AC motor

Thermal losses

Wear of rail/wheel test samples

In order to estimate the frictional sliding, some assumptions must be made

about the manner in which the remaining losses affect the system. All losses

associated with the input system will be assumed to be constant for a given

speed during the lubricated testing. The mechanical losses are considered to

be the most significant for this part of the system as they are directly related

to the rotational velocity, which for the input is fixed for any given test.

0 200 400 6002000

2500

3000

3500

4000Input Power vs Time

Time (s)

Pow

er (W

)

0 200 400 600-500

0

500

1000

1500

2000

2500Output Power vs Time

Time (s)

Pow

er (W

)

0 200 400 6000.05

0.1

0.15

0.2

0.25Slip % vs Time

Time (s)

Slip

(%)

0 200 400 600

1500

2000

2500

Power Dissipated vs Time

Time (s)

Pow

er (W

)

Figure 66 - Power versus Time graphs for warm-up prior to testing. Data presented has not been pre-processed.

The output shaft rotational velocity is variable throughout the test. Any

power loss that is dependent on velocity will also be variable. The friction

coefficient for the fully lubricated needle roller bearings is predicted to be at

least an order of magnitude smaller than the fully lubricated testing surface.

135

Therefore the bearing frictional power loss is assumed to be a negligible and

in constant proportion to the sliding frictional energy.

In Figure 66(left upper) the input power can be seen to reduce with respect to

time in sections of the curve with (Time > 180 s) and without braking torque

(Time < 180 s). The same can be observed for the output power, Figure

66(right upper) but is more difficult to observe from the signal noise. Slip

percentage in Figure 66(left lower) displays the same decay effect as the power

measurements. It can also be observed that with the application of tractive

force there is a corresponding increase of measured slip (Time > 180 s), in

accordance the theoretical calculations of Section 0.

Figure 66(right lower) is the most important chart and display the power

absorbed by the system in processes not attributable to a lubricant film, as in

the presented test none was applied. The power absorbed by the system is not

influenced by the application of an increased braking torque (shearing force)

but decays with time to a minimum value. This minimum value was

subtracted from the measured power losses in the lubricated testing to leave

the remaining power as that absorbed by the lubricant film.

The decay effect, observed in Figure 66, is used to predict the final values of

slip and power in the presentation of test results and will be discussed further

in Section 0.

4.6.3 Slip From Lubrication Measurements (Zero slip predictions)

The measured slip in the lubricated testing is composed of two components,

the micro-slip from the contact conditions, and the slip from the applied

lubricant. Isolating the slip due to lubrication requires removal of the micro-

slip component, which the method presented in this section has achieved.

Preceding each group of lubricated tests, there was a period of warm-up to

establish consistent operating conditions. This warm-up is divided into two

distinct periods, the first with no applied braking torque and the second with

136

the set braking torque. The braking torque for the lubricated tests was set

during the warm-up period and fixed for all the following tests in a particular

group to ensure consistency.

0 50 100 150 200 250 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Slip

(%)

Slip Vs TimeNormal Force: 5 kN

Braking Force: 0.28 kN

No Applied TorqueBraking Torque Applied

Figure 67 – Slip versus time for the two defined warm-up periods of zero and set braking forces.

In Figure 67 each of the warm-up periods is plotted separately rather than

consecutively, as occurs in the experiment. It can be observed from the graph

that there is decay in slip to some nominal level with each of the applied

torques.

In the work of Johnson (1985) the micro-slip or creep, as seen experimentally

in Figure 67, is presented as an effect of material elasticity in tractive rolling

contact. This type of unlubricated slip/creep is the result of surface strains

caused by the normal and tangential forces on the contact and is predicted by

Johnson (1985) in equation (4.18).

137

12{1 (1 ) }x

xQa

R Pμξ

μ−= − − (4.18)

Johnson also defines the limits of micro-slip to be Equation (4.19):

1 and 1x xR Qa P

ξμ μ

< < (4.19)

In the case of the simulator, the variable frequency drive and braking system

are incapable of achieving the required tractive force to exceed the upper

micro-slip limit in Equation (4.19). Using Johnson's method the observable

slip percentage is predicted for the warm-up loading conditions in Figure 67

and calculated to be 0.017%. The calculated value is at the resolution limit of

measurable slip.

The importance of this value is not in its absolute value but in applying a

suitable equation to predict the stabilised value of slip in the lubricated testing.

The value of predicted minimum slip is subtracted from the measured values

in the presentation of results for the lubricated testing in Chapter 5.

4.7 Lubricant Performance Measures Error Analysis

The magnitudes of errors in each measurement are presented here for the

purpose of checking recorded experimental variability against measurement

errors. These values will be used to interpret the validity of the experimental

method and the presented data in Chapter 5. Equation (4.20) will be used to

calculate the errors from all results calculated from measured values

138

( )1

2 2 2

, ,....

....

Result Predicted error

, ,... Input parameters, ,... Errors in input parameters

R f A B

R RR A AA A

RR

A BA B

=

⎡ ⎤⎛ ∂ ⎞ ⎛ ∂ ⎞⎛ ⎞ ⎛ ⎞Δ = ∂ + ∂ +⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦=

Δ ==

∂ ∂ =

(4.20)

Calculation of the estimated total error for each of the lubricant performance

criteria is important to ensure that the error does not overwhelm the

measurement.

The rotational speed and the estimated error are calculated using Equation

(4.21). The maximum error in the count measurement is 1 count and the

sample frequency error (5.0E-8 Hz) is assumed to be negligible.

25400

2 0.00116 radians/sec

5400

counts

wsample frequency

w

π

π

⎛ ⎞⎜ ⎟⎝ ⎠=

∂ = =

(4.21)

w = Rotational Speed

w∂ = Error in rotational speed

The surface velocity and the estimated error are calculated using Equation

(4.22).

2 2

v wr

v vv w rw r

=

⎛ ∂ ⎞ ⎛ ∂ ⎞⎛ ⎞ ⎛ ⎞∂ = ∂ + ∂⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

(4.22)

v = Surface velocity

139

v∂ = Error in surface velocity

r = Rolling radius

r∂ = Error in rolling radius

Using the values in Table 13 and Equation (4.22) the error in surface velocity

was calculated for the rail and wheel test pieces and presented in Table 14.

Variable Value Variable Error Value iw 39.813 rad/s

iw∂ 0.001 rad/s

ow 120.851 rad/sow∂ 0.001 rad/s

ir 148.10 mm ir∂ 0.005 mm

or 48.605 mm or∂ 0.005 mm

Table 13 - Values for experimental error calculation of surface velocities for Group 1 test parameters. Subscripts refer to input and output shafts.

Measurement error in surface velocity is small compared to the variation in

velocity experienced by a wheel in the field.

Variable Value Variable Error Value iv 5.8963 m/s

iv∂ 0.0003 m/s

ov 5.8739 m/sov∂ 0.0006 m/s

Sv 5.8963 m/sSv∂ 0.0007 m/s

Table 14 - Values for experimental error calculation of surface velocities for Group 1 test parameters. Subscripts refer to input and output shafts.

Sliding velocity is the difference between the input and output velocities and

is given by Equation (4.23) and the error presented in Table 14.

( ) ( )2 2

s i o

s i o

v v v

v v v

= −

∂ = ∂ + ∂ (4.23)

140

,s su v = Sliding velocity

sv∂ = Error in sliding velocity

The slip ratio and the estimated error are calculated using Equation (4.24).

12 2 2 2 2

2 2

1

; ; ;

o o

i i

o i o io i o i

o o o o o o

o i i i i i o i i i i i

w rw r

w w r rw w r r

r w r w w rw w r w w r r w r r w r

ξ

ξ ξ ξ ξξ

ξ ξ ξ ξ

⎛ ⎞= −⎜ ⎟⎝ ⎠

⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞∂ ∂ ∂ ∂⎢ ⎥Δ = ∂ + ∂ + ∂ + ∂⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦∂ ∂ ∂ ∂= − = = − =∂ ∂ ∂ ∂

(4.24)

Variable Value Variable Error Value iw 39.813 rad/s

iw∂ 0.001 rad/s

ow 120.851 rad/sow∂ 0.001 rad/s

ir 148.10 mm ir∂ 0.005 mm

or 48.605 mm or∂ 0.005 mm

Table 15 - Values for experimental error calculation of slip ratio for Group 1 test parameters. Subscripts refer to input and output shafts.

Using Equation (4.24) and the values of variables in Table 13 the

experimental error in slip ratio is predicted to be 1.11E-4 or presented as slip

percentage 0.011%. This value is small compared to the experimentally

recorded slip ratio, and gives confidence to the prediction of slip and to the

measurement of sliding speeds and distances.

Using the error prediction of 0.05% in diameter, from the thermal expansion

calculations, in addition to the measurement error presented in Table 15 the

drift or error in slip ratio with respect to temperature can be calculated. The

predicted experimental error becomes larger at 0.065%. In the high slip part

of each test the frictional energy from sliding is converted to heat, which

expands the test pieces (see Figure 68 for time less than 600 seconds). Energy

141

lost to convection, from the test pieces in the testing region of high slip, is less

than the energy from friction absorbed by the test pieces. Subsequently the

temperatures of the test pieces rise. In the region of lower slip the

temperature of the wheel sample begins to approach that of the rail sample

from the convection coefficient increasing as a result of the increasing rolling

speed. As the surface velocities approach one another the convection

coefficients approach one another and the temperatures of both samples

approaches the temperatures of the unlubricated test.

0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

70

80

90

100

Time (s)

Tem

pera

ture

(o C)

0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

70

80

90

100

Slip

(%)

Slip %

Wheel TemperatureRail Temperature

Figure 68 – Test sample temperatures and Slip versus time for Group 1 Lubricant A Test 1.

If the temperatures of the test pieces in the lubricated testing match that of

the unlubricated testing then the predicted slip will have the error from the

thermal expansion of the samples removed. Therefore at the high slip region

where the error in slip measurement is greatest the absolute error is small in

proportion to the measured value. Also at the low slip region where the

142

measured value of slip is small the error from thermal expansion is also small

approaching that of a constant temperature test.

The next step in the measurements is determination of the errors in the input

and output power results using Equation (4.25) and Table 16.

2 2

Power Torque w

Power PowerPower Torque wTorque w

= ×

⎛ ⎞⎛ ⎞∂ ⎛ ∂ ⎞⎛ ⎞∂ = ∂ + ∂⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠

(4.25)

Variable Value Variable Error Value

iT 88.8 N.miT∂ 0.1 N.m

oT 14.8 N.moT∂ 0.1 N.m

Table 16 - Values for experimental error calculation of surface velocities for Group 1 test parameters. Subscripts refer to input and output shafts.

The errors for power in Table 17 show that the smaller diameter and lower

torque of the output shaft increase the magnitude of the error as compared to

the input power. It is however less that 1% of the measured value of output

power and correspondingly the power values for both input and output can

be assumed valid.

Variable Value Variable Error Value iP 3535 W

iP∂ 4 W (0.1%)

oP 1788 W oP∂ 12 W (0.7%)

Table 17 - Values for experimental error calculation of input and output power for Group 1 test parameters. Subscripts refer to input and output shafts.

The distance travelled by each sample is calculated using Equation (4.26) but

for the purposes of error calculation the sample time term is assumed to have

143

no error as in the rolling velocity calculations. Removing the sample time term

(constant for all tests as 1 second) gives Equation (4.22) with distance

travelled equal to the magnitude of the velocity term, with the same level of

error presented in Table 18.

D wrt= (4.26)

D = Distance rolled

D∂ = Error in distance rolled

Variable Value Variable Error Value

iD 5.8963 miD∂ 0.0003 m

oD 5.8739 moD∂ 0.0006 m

Table 18 - Values for experimental error calculation of distance rolled for Group 1 test parameters. Subscripts refer to input and output shafts.

Using all of the calculated parameters for the input and output shafts the

effects of the lubricant film can be isolated. Prior to testing the simulator was

used under unlubricated conditions to gather baseline data. The baseline data

was then removed from the lubricated testing to give only the results assigned

to the lubricant. Any errors in the prediction of the baseline values to be

subtracted from the lubricated testing results were constant for all lubricants

in a particular group.

An issue for lubricant performance measurement error analysis is that the

baseline data between groups is not consistent from the different test

parameters and can limit test group comparisons. Investigation of this

parameter yielded no conclusive results as to the errors in baseline data

between groups, but the baseline data applied to each of the nine tests in a

group were checked for inconsistencies and none were found. Therefore

comparisons between test groups are assumed to be valid.

144

The lubricant film performance criteria of distance slid is calculated using

Equation (4.27) and the values from Table 18

( ) ( )2 2

s i o

s i o

D D D

D D D

= −

∂ = ∂ + ∂ (4.27)

iD = Distance rolled of input shaft

iD∂ = Error in distance rolled of input shaft

oD = Distance rolled of output shaft

oD∂ = Error in distance rolled of output shaft

sD = Distance slid

sD∂ = Error in distance slid

Power absorbed by the lubricant film is calculated similarly to the distance

slid. The difference in power between the input and output shafts minus the

power absorbed by friction in the simulator is defined as power absorbed.

The power absorbed by friction is a constant, calculated from the

unlubricated data, and will not be included in the error analysis.

( ) ( )2 2

s i o f

s i o

P P P P

P P P

= − −

∂ = ∂ + ∂ (4.28)

iP = Power of input shaft

iP∂ = Error in power of input shaft

oP = Power of output shaft

oP∂ = Error in power of output shaft

145

sP = Power absorbed by lubricant

sP∂ = Error in power absorbed by lubricant

fP = Power absorbed by friction in simulator

The values of error in the results of distance slid and power absorbed due the

lubricant film are small and presented in Table 19.

Variable Value Variable Error Value SD 5.8963 m

SD∂ 0.0007 m

SP 600 W SP∂ 13 W (2.1%)

Table 19 - Values for experimental error calculation of distance slid and power absorbed for Group 1 Lubricant A Test 1 results.

Energy at each time step is calculated using Equation (4.29) with the

measurement error taken as the same error as for power. This is valid as the

error in the time variable is negligible.

E Power t= × (4.29)

E = Absorbed energy

E∂ = Error in absorbed energy

The cumulative measurement errors will be calculated using Equation (4.30)

146

( )

( )

1

2

measured value sum of measured value

error in measured value

n

f x x

ff n xx

f x nxf xx

=

⎛ ∂ ⎞⎛ ⎞∂ = ∂⎜ ⎟⎜ ⎟∂⎝ ⎠⎝ ⎠

∂ = ∂=

=∂ =

∑

(4.30)

The two cumulative lubricant performance criteria of total absorbed energy

and total slid distance are calculated using Equation (4.31) and Equation

(4.32) .

1

2

n

T s

TT s

s

T s

E E

EE n EE

E E n

=

⎛ ⎞⎛ ⎞∂∂ = ∂⎜ ⎟⎜ ⎟⎜ ⎟∂⎝ ⎠⎝ ⎠

∂ = ∂

∑

(4.31)

sE = Sliding energy

sE∂ = Error in sliding energy

TE = Total Absorbed energy

TE∂ = Error in absorbed energy

n = Number of measurements

1

2

n

T s

TT s

s

T s

D D

DD n DD

D D n

=

⎛ ⎞⎛ ⎞∂∂ = ∂⎜ ⎟⎜ ⎟⎜ ⎟∂⎝ ⎠⎝ ⎠

∂ = ∂

∑

(4.32)

147

sD = Distance slid

sD∂ = Error in distance slid

TD = Total distance slid

TD∂ = Error in total distance slid

It is important to note that the errors for the cumulative lubricant

performance criteria are affected by the number of summed values. The larger

the number of values the smaller the relative error, but the larger the absolute

error. Therefore the errors presented in Table 20 are the maximum for all

Group 1 tests.

Variable Value Variable Error Value TD 2850 m

TD∂ 0.02 m

TE 37740 JTE∂ 330 J (0.9%)

Table 20 - Values for experimental error calculation of distance slid and power absorbed for Group 1 Lubricant A Test 1 results.

Apparent viscosity, as discussed in Section 0, is the relationship between shear

stress and shear rate, see Equation (4.33).

τηγ

=&

(4.33)

Shear stress is defined in Equation (4.34) using the measured shear force and

the predicted contact area and the error defined in Equation (4.35). Shear

strain is the ratio between sliding speed and lubricant film thickness given

with its equation for error in Equation (4.36) Predicted contact area and

lubricant film thickness, CA and y , are calculated values and will be assumed

to have no error. The errors presented in this section are for measured values

only.

148

oBT

C o C

TFA r A

τ = = (4.34)

2 2

2 2

2

1

o oo o

oo o

o C o C

T rT r

TT rr A r A

τ ττ

τ

⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞∂ ∂∂ = ∂ + ∂⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞∂ = ∂ + ∂⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

(4.35)

S

S

vy

v

γ

γ

=

∂ = ∂

&

&

(4.36)

Variable Value Variable Error Value oT 14.8 N.m

oT∂ 0.1 N.m

or 48.605 mm or∂ 0.005 mm

CA 2.54 E-5 m^2CA∂ 0 m^2

Sv 5.8963 m/s Sv∂ 0.0007 m/s

Table 21 - Values for experimental error calculation of surface velocities for Group 1 test parameters.

The magnitudes of measurement error in shear stress, shear strain and

apparent viscosity are small, see Table 22. It is important to note that these

values are only the measurement errors and do not take into consideration the

errors involved in predicting the contact area and lubricant film thickness. Of

these two parameters lubricant film thickness is of most concern as its

magnitude has the greatest influence on the calculation of shear stress and

subsequently apparent viscosity.

Assigning an error to the film thickness of 1 μ m (approximately 30% of the

film thickness), increases the predicted error in apparent viscosity from 0.005

Pa.s to 2 Pa.s. The absolute measurement of apparent viscosity then has an

error of 30% associated with it. This high level of error is not representative

149

however as can be observed in Table 22. The measured values are high

resolution with low associated errors. It is beyond the scope of this thesis to

investigate lubricating grease film thickness, but it is important to be aware of

the issues involved in predicting apparent viscosity

Variable Value Variable Error Value τ 12.009 MPa τ∂ 0.008 MPa γ& 1.66 E6 1/s γ∂ & 0.0007 1/s η 7.23 Pa.s η∂ 0.005 Pa.s

Table 22 - Values for experimental error calculation of apparent viscosity, shear stress and shear ratefor Group 1 test parameters.

The values of error in this section are not absolute for all tests. The errors

presented are calculated for a specific test in Group 1 but are typical for all

the Groups.

4.8 Summary

Details of the modifications to the experimental device have been presented,

highlighting the need for modifications and improvements to achieve the

objective to quantify rail curve lubricant performance through laboratory

simulation. Temperature of the rail/wheel simulator can be regulated with the

installation of the plate heat exchanger to improve simulation conditions.

Loading of the test samples has been modified with pneumatic rams to

improve simulation by applying a more constant force. Data acquisition has

been modified and improved across all measurements especially in the area of

slip measurement. High resolution slip measurements were attainable using

the newly installed shaft encoders for measuring lubricant film decay. Tractive

force control was achieved through the installation of a hydraulic

dynamometer.

Investigations of the performance capabilities of the rail/wheel simulator

prior to the lubricant analysis were presented detailing the wear characteristics

of newly machined samples. The wear encountered was found to match that

150

of in-service conditions. Additional issues with the wheel sample holder were

found and rectified which improved the simulation capability of the

rail/wheel simulator.

The commissioning results were then used to develop a suitable testing

protocol for investigation of rail curve lubricant performance. Presented in

the testing protocol section were the material properties of the rail and wheel

test samples for inspection of the chemical compositions and presentation of

the strength characteristics for interpreting the contact mechanics results of

Chapter 3.

Methods for the measurement of the variables of interest were then

presented. Rotational speed was measured with shaft encoders for the

purpose of measuring rolling velocity, sliding velocity and slip ratio. Output

torque was measured with a torque transducer in the hydraulic dynamometer

system for calculating output power, shear force, shear stress and power

absorbed by a lubricant film. The variable frequency drive on the input shaft

was used to measure input torque, for calculating input power and power

absorbed by a lubricant film. Temperatures of the rail and wheel samples

were measured during testing using a hand held infra red thermometer.

Normal load, important for calculating the stress distribution of the contact

between rail and wheel samples, was measured using a calibrated force

transducer.

Experimental methods and procedures have been outlined prior to the

presentation of the limitations in these measurements. Thermal expansion of

the rail and wheel samples was explored with reference to the changes in

measured slip conditions. The findings were that during the periods of

maximum thermal expansion the relative magnitude of the error in diameter

measurement is small and at test completion where the magnitude of slip is

small, the error was also small. Next the limitation in the measurement of

output torque due to frictional losses was calculated and found to be

151

negligible. The effects of lubrication were then isolated from the measured

values of absorbed power and slip by measuring and calculating the

unlubricated system responses across all tested parameters.

The final part of Chapter 4 presents the measurement errors to highlight the

improvements made to the rail/wheel simulator when comparing to standard

twin disk simulators. The levels of measurement error calculated for all

lubricant performance criteria give confidence to the lubricant performance

results. The next chapter will present the results from the discussed method

including standards based lubricant testing results.

152

C h a p t e r 5

PERFORMANCE MEASUREMENT OF RAIL CURVE LUBRICANTS

5.1 Introduction

The current chapter presents the results of lubricant testing with the focus on

the thesis objective; to quantify rail curve lubricant performance through

laboratory simulation

The first part of the chapter will outline the lubricant performance

measurement method using the Group 1 data set. The remainder of the

chapter discusses the results of the lubricant testing and the relevance to the

optimisation of rail/wheel lubrication.

5.2 Testing Variables

The experimental results were taken from four tests (sets of parameters),

referred to as groups. The first group, Group 1, was taken as a reference then

each of the input variables of normal force, braking torque and rolling speed

changed individually. Each group investigates the effect of a single input

variable change and is detailed in Table 23. In addition to the three input

parameters the stress from the normal force and the shearing force are

presented.

Group Number

Normal Force (N)

Compressive Stress (MPa)

Braking Torque (N.m)

Shearing Stress (MPa)

Rolling Speed (m/s)

1 9500 480 15 12 6 2 9500 480 15 12 3 3 9500 480 30 24 6 4 12500 550 15 12 6

Table 23 – Testing variable values.

In each group three different rail curve lubricants were tested. Lubricants A

and B were lithium complex greases with mineral oil and solid lubricants.

153

Lubricant C was an aluminium complex grease with mineral oil and solid

lubricants.

5.3 Unlubricated System Steady State Values

In order to isolate the effect of lubrication on the system, steady state values

for the recorded data need to be predicted or measured. The parameters of

interest are the power absorbed by the system as discussed in Section 4.6.2

and the minimum attainable slip. Subtracting the values of system power and

minimum slip, predicted from unlubricated conditions, from the

measurements under lubricated conditions gives only the measurement

attributable to the lubricant film. Prior to the prediction of the equilibrium

values all data was filtered through a five point moving average filter. The

filter was applied to identify linear trends in the collected data. The level of

filtering was selected to minimise data corruption from the filter and to

maximise the appearance of performance trends.

Power losses not directly attributable to the lubricant film are estimated. The

process for this estimation was to plot the power loss curve for unlubricated

test conditions, with the same testing variables as the lubricated tests. Decay

in the measurements of power and slip were assumed to have an exponential

function. Regression was carried out on the data using Equation (5.1) to find

the steady state power loss:

( )( ) Power loss

Time Steady state power lossAmplitude of the exponential

Exponential coefficient

bxf x ae c

f xxcab

−= +

=====

(5.1)

The steady state power loss was then subtracted from the total power loss

measured in lubricated testing to give the losses associated with the lubricant

film in the contact. Figure 69 shows the exponential regression fitted to the

154

non-lubricated Group 1 conditions. Minimum power loss values for all

groups are presented in Table 24. The residuals of the regression analysis were

tested with a Lilliefors normality test at a 5% significance level and found to

be normally distributed.

0 50 100 150 200 250 300-100

-50

0

50

100

Time (Seconds)

Pow

er (W

atts

)

Residuals

0 50 100 150 200 250 3001850

1900

1950

2000

2050

2100

2150

Time (Seconds)

Pow

er (W

atts

)

Data and Fits

Absorbed PowerExponential Decay

Residuals of Exponential Decay

Figure 69 – Exponential decay curve fitted to power loss data for Group 1 conditions.

A similar process was applied to the slip data to determine the minimum

attainable slip. The value for minimum attainable slip was theoretically

calculated using the method of Johnson (1985) but experimentally the

minimum attainable slip was found to differ from this value. The results of

this test for Group 1 conditions are shown in Figure 70. The values used in

lubricant performance analysis in each group are detailed in Table 24. The

residuals of the regression analysis of slip in Figure 70 were tested with a

Lilliefors normality test at a 5% significance level and found to be normally

distributed. In addition, a harmonic can be observed in the residuals with a

long period and amplitude of 2.5% of the signal. The source of the harmonic

is as yet unidentified.

155

0 50 100 150 200 250 300-2

-1

0

1

2

3x 10-3

Time (Seconds)

Slip

(%)

Residuals

0 50 100 150 200 250 3000.15

0.155

0.16

0.165

0.17

Time (Seconds)

Slip

(%)

Data and Fits

SlipExponential Decay

Exponential Decay

Figure 70 – Exponential decay curve fitted to slip data for Group 1 conditions.

The large difference in minimum slip values for Group 2 and 4 when

compared to Group 1 and 3, as observed from the error analysis in Section

4.7, is from the measurement of sample diameters.

Group Number Minimum power loss (Watts) Minimum slip (%) 1 1466 0.15 2 836 0.02 3 1734 0.15 4 1667 0.03

Table 24 – Extrapolated minimum values from experimental data.

5.3.1 Lubricant Film Decay Half-Life Prediction

The performance decay of lubricants is of interest for two purposes, first to

predict reapplication rates and second to predict the lubricated distance from

a lubricant application point. In this thesis the decay will be measured from

the slip measurement, following the system reaching the set shear stress value.

156

The x axis data (time) was normalised using the mean and standard deviation

to improve the accuracy of regression analysis results using Equation (5.2).

( )ˆ

ˆ normalised values values mean of standard deviation of

x xx

xxx x

x

σ

σ

−=

====

%

%

(5.2)

Regression was carried out on the slip data using Equation (5.3).

( )( ) Variable of interest

Time Amplitude of the exponential Exponential coefficient Minimum value of variable of interest

bxf x ae c

f xxabc

−= +

=====

(5.3)

The time for slip performance to degrade by 50% or half life was then

calculated with Equation (5.4) (Giancoli 1988).

( )ln 2

half lifebσλ

λ

=

= (5.4)

5.4 Input Data Variability

The three input parameters were analysed for discrepancies between tests

within a group to ensure consistent input parameters. The normal load, input

rolling velocity and fully developed braking torque for Group 1 are presented

in Figure 71, Figure 72 and Figure 73 respectively.

The box and whisker plots have lines for lower quartile, median and upper

quartile values. The whisker lines are 1.5 times the inter-quartile range with

any values outside the whiskers marked with a cross as an outlier.

157

9200 9300 9400 9500 9600 9700 9800 9900 10000

Lubricant A Test 1

Lubricant A Test 2

Lubricant A Test 3

Lubricant B Test 1

Lubricant B Test 2

Lubricant B Test 3

Lubricant C Test 1

Lubricant C Test 2

Lubricant C Test 3

Normal Force (N)

Figure 71 – Box and whisker plot of normal force for each of the tests in Group 1.

The normal force in Figure 71 has a high variability which is the results of two

noise components, dynamic loading and thermal expansion effects, which is

discussed later in section 5.4.1. Dynamic loading is accounted for in the

calculations of lubricant performance by using the measured value rather than

the nominal value.

In Figure 72 for rolling velocity, the tests for Lubricant C highlighted the

difficulty in speed control from the variable frequency drive by the large

number of outliers in Test 2 and 3. The longer test times of Lubricant A and

B allowed the speed controller to more closely track the changing loading

conditions experienced. In practical terms the variability in velocity is less than

0.1km/hr (0.02m/s) and was considered to be negligible.

Variability in the output torque in Figure 73 is the result of the lubricant film

continuing to decay as the lubricated test progressed.

158

5.85 5.86 5.87 5.88 5.89 5.9

Lubricant A Test 1

Lubricant A Test 2

Lubricant A Test 3

Lubricant B Test 1

Lubricant B Test 2

Lubricant B Test 3

Lubricant C Test 1

Lubricant C Test 2

Lubricant C Test 3

Rolling Speed (m/s)

Figure 72 – Box and whisker plot of input rolling velocity for each of the tests in Group 1.

12 12.5 13 13.5 14 14.5 15 15.5 16

Lubricant A Test 1

Lubricant A Test 2

Lubricant A Test 3

Lubricant B Test 1

Lubricant B Test 2

Lubricant B Test 3

Lubricant C Test 1

Lubricant C Test 2

Lubricant C Test 3

Output Torque (N.m)

Figure 73 – Box and whisker plot of braking torque under fully developed conditions for each of the tests in Group 1.

159

5.4.1 Tread Load Temperature Dependence

The tread load data was tested with a Lilliefors normality test and found not

to be normally distributed, even at a 20% significance level. The cause of this

non-normal load distribution is most likely the effect of frictional heat

absorption. The wheel and rail samples expand with temperature which

applies a larger load. The wheel sample holder appears to not move in

proportion with the thermal expansion. The friction forces in the normal

loading pneumatic ram and the contact surfaces of the wheel sample holder

may prevent the load from reducing back to the set value.

0 100 200 300 400 500 600 700 800 900 100020

40

60

80

Tem

pera

ture

(° C)

Time (secs)0 100 200 300 400 500 600 700 800 900 1000

9600

9800

Nor

mal

Loa

d (N

)

WheelRail

Normal Force

Figure 74 - Normal force and bulk sample temperature versus time for Group 1 Test 1 Lubricant A.

Figure 74 shows the temperature and normal load curves for a single test

sample in which the dependence of normal load on sample temperature is

observed by the matching curves. In the tests where full traction force was

reached quickly, it was impossible to gather enough temperature

measurements to verify this hypothesis. However, monitoring of the

160

temperatures showed the same trends, and inspecting the gathered tread

loading data post test, verified the findings of temperature versus tread load

interaction.

The slight (~2%) increase in normal force during testing was taken into

consideration during results analysis by using each normal force data point

separately, rather than a mean value.

5.5 Rail/Wheel Simulator Results

The results for each group are divided into two sections. The division is

created by separating all results above and below the in-service slip limit of

5% also approximately the point at which the nominated shear force is

reached. The readings above this limiting slip value are conditions unlikely to

be experienced in a rail/wheel situation but give a better understanding of the

lubricants’ capabilities, under extreme sliding and energy absorption

conditions. Results below the limiting slip value are applicable to rail/wheel

contacts where the tractive force is fixed. Slip will decrease to a minimum

value, a point at which there is no lubricating effect, and the time taken to

reach this point is of great importance. Predicting a half life for a lubricant

under set conditions aids in determining location of lubricator and/or

lubrication rates.

Note: In all plots the markers on the lines, circle, dot or cross, do not indicate

the number of results taken in a test. They are only plotted to identify the

different lines on each plot. All data points are spaced at 1 second intervals as

specified in the error analysis, Section 4.7. The time scales on all graphs must

be observed as there are differences between each of the lubricants depending

on the length of test time.

161

5.5.1 Group 1 Lubricant Performance Results (Tread Load = 9.5 kN,

Braking Torque = 15 N.m, Rolling Speed = 20 km/hr)

0 100 200 300 400 500 600 700 800 900 10000

0.5

1

1.5

2

2.5

3

3.5

4x 105

Time (s)

Cum

ulat

ive

Abs

orbe

d E

nerg

y (J

)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 75 - Cumulative absorbed energy of lubricant film versus time for Group 1.

Lubricant B had a higher rate of energy absorption than either Lubricant A or

C in the time preceding 300 seconds. In Figure 76 the power absorbed by the

lubricant film is more easily observed. Lubricant A can be observed to be

constant in the middle part of the test, between 100 and 500 seconds, whereas

Lubricant B steadily declines from its maximum. The time in which Lubricant

C is absorbing power is an order of magnitude smaller than the other

lubricants.

162

0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

Times (s)

Abs

orbe

d P

ower

(Wat

ts)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 100 200 300 400 500 600 700 800 9000

200

400

600

800

Times (s)

Abs

orbe

d P

ower

(Wat

ts)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 70 80 90 1000

200

400

600

800

Times (s)

Abs

orbe

d P

ower

(Wat

ts)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 76 – Power absorption rates for each lubricant in Group 1 tests. Note different time scales for each lubricant.

Lubricant C cannot be observed on Figure 75 as the amount of energy

dissipation is negligible. Plotting Lubricant C separately in Figure 77 shows

the minimal energy absorption as compared to Lubricants A and B. In

addition one of the tests for Lubricant C shows two times the total energy

absorption of the other two tests in this group. Assuming power absorbed by

lubricant is power that is not used in wear processes, ranks the lubricants in

terms of performance, as A with the best performance then B, then C as the

worst performer.

163

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 104

Time (s)

Cum

ulat

ive

Abs

obed

Ene

rgy

(J)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 77 - Cumulative absorbed energy versus time for Lubricant C.

Plotting the total absorbed energy for each of the tests shows a clear

difference in performance between each of the lubricants (see Figure 78).

Lubricant A absorbed more energy than the two other lubricants, before the

set tractive force was achieved, which is the desired effect of the lubricant.

164

Lubricant A Lubricant B Lubricant C0

0.5

1

1.5

2

2.5

3

3.5

4x 105

Tota

l Abs

orbe

d E

nerg

y (J

)

Figure 78 – Total energy absorbed prior to set tractive force limit for Group 1.

The sliding distance over which a lubricant is considered effective was also

under investigation. Effective lubricant performance was defined, for the

purpose of this thesis, as the point at which the transmitted torque from input

to output reaches the defined value, in this group set to 15 N.m. Noise on the

torque signal made identification of this point in the recorded data difficult,

see Figure 79, and as such the point at which slip reached 5 % was taken as

the cut-off value.

The results on distance give an estimation of lubricant performance for a fully

lubricated case under extreme sliding conditions. Normal load and input

rolling speed were relatively constant over the test. The only parameter that

changed during the test was the transmitted tractive force through the

lubricant film. The closest in-service conditions to match the test conditions

are of a lubricated curve with a functioning lubricator which is suddenly

turned off.

165

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

Time (s)

Out

put T

orqu

e (N

.m)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 100 200 300 400 500 600 700 800 9000

5

10

15

20

Time (s)

Out

put T

orqu

e (N

.m)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

Time (s)

Out

put T

orqu

e (N

.m)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 79 – Output torque profiles for Group 1.

The trend in the previous absorbed energy results can again be seen in Figure

80 for total sliding distance, with the lubricants performing in the same rank

order A,B,C. Lubricant A has at least twice the performance of Lubricant B

which has twice the performance of Lubricant C.

The total sliding distance is a measure of the strain history that the lubricant

can withstand prior to development of the set tractive force. The set tractive

force can also be thought of as a shear stress limit. Sliding distance is

calculated as the difference between the rolled distance of the rail sample and

wheel sample which has been mathematically presented in Section 4.7.

166

Lubricant A Lubricant B Lubricant C0

500

1000

1500

2000

2500

3000

Dis

tanc

e (m

)

Figure 80 – Sliding distance of lubricant prior to set tractive force limit for Group 1.

The sliding velocity profiles over the test are given in Figure 81. Lubricant B

has a sliding velocity profile that steadily reduces over the course of the test.

Damage from sliding/shearing accumulated in this lubricant appears to

constantly degrade the performance. In comparison, Lubricant A reaches a

steady value of sliding velocity and remains at this value for a period then fails

in a manner similar to Lubricant C, except for the extreme differences in

lubricant life between Lubricants A and C.

Upon reaching the critical accumulated damage history in Lubricant C, there

was a definite point at which the lubricant film was observed to fail and reach

the full tractive load. This point was heard during testing, as the output shaft

rapidly increased in rotational velocity and was observed in Figure 81 as a

reduction in sliding velocity. The length of time for this transition, see Figure

81, is approximately 10 seconds for Lubricant C. Lubricant A and B did not

display this effect.

167

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

Time (s)

Vel

ocity

(m/s

) Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 100 200 300 400 500 600 700 800 9000

2

4

6

8

Time (s)

Vel

ocity

(m/s

) Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

Time (s)

Vel

ocity

(m/s

)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 81 – Sliding velocity profile for Group 1.

The data in the in-service conditions section of the tests, the portion where

the set shear stress had been reached, was analysed to find the expected half

life of the remaining lubricant using the method in Section 5.3.1.

168

Lubricant A Lubricant B Lubricant C0

200

400

600H

alf L

ife (s

)

Lubricant A Lubricant B Lubricant C0

2

4

6

Min

imum

Slip

(%)

Figure 82 – (top) Half life prediction for

Group 1 using ( ) bxf x ae c−= + .

(bottom) Value of predicted minimum slip ‘c’.

Predicting the half life was highly dependent on the coefficient ‘c’ in the

exponential curve fit, which has the expected value of zero but the regression

analysis did not agree, see Figure 82 (bottom).

Inspecting the example in Figure 83, the fit of the equation with the

displacement coefficient ‘c’ has a better fit. This cannot exist in practice, as

the lubricant film will fully degrade and zero slip conditions will be reached.

While mathematically this equation is a better fit (R2=0.9545 versus

R2=0.9814), the equation without ‘c’ was used to reflect the expected

outcome. Presentation of half-life lubricant performance in the summary,

Section 5.5.5 will use the equation without the offset coefficient.

169

0 10 20 30 40 50 60 70 80 90 100

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

Time (s)

Slip

(%)

Slipy=a*e (̂-bx)y=a*e (̂-bx)+c

Figure 83 – Regression plots for Lubricant A Test 2 Group 1 in the region < 5% slip.

HALF LIFE (S) Lubricant Type Mean Standard Deviation

A 274.51 144.37 B 983.9 592.77 C 87.75 8.5956

Table 25 – Half life values for each lubricant

in Group 1 testing using ( ) bxf x ae−= .

Lubricant C had a small but predictable half life, seen by the small standard

deviation, which may be the result of testing into the region of slip below 1%.

The other lubricant tests ceased prior to the reduction in slip reached by

Lubricant C. Lubricant B clearly had the longest half life but predictability of

total film failure would be problematic with the large standard deviation.

Next, in terms of performance, Lubricant A had large variability and longer

life than Lubricant C.

170

Lubricant A Lubricant B Lubricant C0

200

400

600

800

1000

1200

1400

1600

1800

Hal

f Life

(s)

Figure 84 - Half life values for each lubricant

in Group 1 testing using ( ) bxf x ae−= .

Figure 85 shows the apparent viscosity profiles for Group 1, calculated using

the method presented in Section 4.7. All lubricants in Figure 85 have a high

degree of linearity for apparent viscosity, especially Lubricant C. Lubricants A

and B have some extraneous results deviating from the linear behaviour

which can be attributed to the tests not yet having reached the set shear force

level. The source of the deviation from linearity is that the apparent viscosity

is continuing to change with accumulated strain, indicating that the shear life

of the lubricant has not been reached. Lubricant C is the exception in Figure

85 where it had reached its shear life. The development of apparent viscosity

with accumulated shear will be discussed further in Section 5.5.5

171

104

105

106

107

100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 85 – Apparent viscosity for Group 1. 5.5.2 Group 2 Lubricant Performance Results (Tread Load = 9.5 kN,

Braking Torque = 15 N.m, Rolling Speed = 10 km/hr)

The data for Lubricant B required a change in the cut off point between high

slip and the set traction force regions from 5% slip to 8% and 7% slip for

Tests 2 and 3 respectively due to the slip data not reaching the set cut off

level, which can be observed in Figure 86. This reduces the total absorbed

energy and slid distance by a small amount.

172

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6

7

8

9

Time (s)

Slip

(%)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 86 - Slip profiles for Group 2 after set cut off limit of slip achieved. Lubricant B Tests 2 and 3 had limits of 8% and 7% respectively.

173

0 500 1000 1500 20000

1

2

3x 105

Time (s)

Abs

orbe

d E

nerg

y (J

)

0 100 200 300 400 500 6000

2

4

6x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

0 20 40 60 80 100 120 140 1600

1

2

3x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 87 - Cumulative absorbed energy versus time for Group 2. Energy is calculated from the difference between input and output energy. Note the different scales on vertical and horizontal axes.

The cumulative absorbed energy profiles, see Figure 87, for Lubricants B and

C are consistent across each test whereas Lubricant A had a test which was

not consistent with the other two. Experimental observations of the tests for

Lubricant A highlighted the development of a wear ring from a section of

wear debris leaving the contact. The rank order for lubricant performance was

the same as Group 1, Lubricant A then B then C.

174

Lubricant A Lubricant B Lubricant C0

0.5

1

1.5

2

2.5x 105

Tota

l Abs

orbe

d E

nerg

y (J

)

Figure 88 – Total energy absorbed prior to set tractive force limit for Group 2.

The total absorbed energy or energy capacity of the lubricants in Figure 88

does not show the same magnitude of difference of performance between

lubricants as the Group 1 tests, but the same performance trend is present.

Halving the input rolling speed has decreased the energy capacity of

Lubricants A and B, with Lubricant C remaining approximately the same. The

speed reduction has also increased the variability of performance of Lubricant

A.

175

0 500 1000 1500 2000

0

100

200

300

Time (s)

Abo

sorb

ed P

ower

(W)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 100 200 300 400 500 600

0

100

200

300

Time (s)

Abo

sorb

ed P

ower

(W)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 50 100 150

0

100

200

300

Time (s)

Abo

sorb

ed P

ower

(W)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 89 – Power absorption rates for each lubricant in Group 2 tests. Note the different scales on the horizontal axis.

The power absorption rates for Group 2 are shown in Figure 89. Lubricant C

has an increasing power profile until lubricant failure, which may indicate

increased lubricant performance with increased temperature. Conversely

Lubricant B has the opposite profile with a steady reduction in absorbed

power over the test. Lubricant A, excluding Test 1 (the profile of absorbed

power at 250W at the beginning of the test time), has a similar absorbed

power profile to Lubricant C, except for the large period of minimal power

absorption in the first half of the test. The maximum power absorption rate

for each lubricant is similar. This rate is limited by the input power which is

also limited.

176

Lubricant A Lubricant B Lubricant C0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Dis

tanc

e (m

)

Figure 90 – Sliding distance of lubricant prior to set tractive force limit for Group 2.

The total sliding distance for Group 2 is presented in Figure 90. Lubricant B

is capable of sliding for half the distance at half the input rolling speed when

compared to Group 1 results. This indicates that the time to failure for

Lubricant B may be related to the lubricant film being forced from the

contact at a similar rate despite the rolling speed, a rheology effect. Lubricant

A had the opposite result with an increase in total sliding distance when

compared to Group 1 results, except Test 1 which had a similar magnitude to

the results of Group 1. Performance of Lubricant C remained similar to

Group 1 testing. Ranking of the lubricants changed with Lubricant C slightly

outperforming Lubricant B to give the order A, C, then B. The difference in

sliding distance performance of Lubricant B and C may not be significant.

177

0 500 1000 1500 20000

1

2

3

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 100 200 300 400 500 6000

1

2

3

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 20 40 60 80 100 120 140 1600

1

2

3

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 91 – Sliding velocity profiles for Group 2. Note the different scales on the horizontal axis.

Sliding velocity profiles for Group 2 are presented in Figure 91, where

Lubricants A and C have definite points of lubricant failure as previously

observed in Group 1. The exception is Lubricant A Test 1. The deceleration

is smaller than the other two tests. Lubricant C also had a grossly different

test with an almost immediate failure. Lubricant B had a similar profile to the

Group 1 tests with a steady decay observed.

178

Lubricant A Lubricant B Lubricant C0

50

100

150H

alf L

ife (s

)

Lubricant A Lubricant B Lubricant C0

2

4

6

8

Min

imum

Slip

(%)

Figure 92 – (top) Half life prediction for

Group 2 using ( ) bxf x ae c−= + .

(bottom) Value of predicted minimum slip ‘c’ or offset coefficient.

The slip profiles shown in Figure 86 highlight the differences in test

completion conditions. These conditions have a direct influence on the offset

coefficient in Figure 92 (bottom) which theoretically should be zero. Higher

measured slip at test completion gave a higher predicted offset coefficient,

which indicates a deficiency in the chosen regression model. The predicted

half lives, without an offset coefficient, shown in Figure 93, are different to

those shown in Figure 92 because of the different test completion conditions

between lubricants.

The half lives in Figure 92 for all lubricants are similar. In Figure 93 the half

life for Lubricant B dramatically increases and is much larger than Lubricants

A and C. The exception is Lubricant A Test 1 in which the half life is

179

approximately ten times larger than the other two samples. Ignoring this

sample as an outlier, the performance ranking is Lubricant B, C then A.

Considering all readings the performance ranking is Lubricant B, A then C,

which is the same as Group 1 and is presented in Table 26.

HALF LIFE (S) Lubricant Type Mean Standard Deviation

A 502.98 665.56 B 916.42 393.7 C 205.99 50.282

Table 26 – Half life values for each lubricant

in Group 1 testing using ( ) bxf x ae−= .

Lubricant A Lubricant B Lubricant C0

200

400

600

800

1000

1200

1400

Hal

f Life

(s)

Figure 93 - Half life values for each lubricant

in Group 2 testing using ( ) bxf x ae−= .

180

104 105 106100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

104 105 106100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

104 105 106100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 94 - Apparent viscosity for Group 2.

All lubricants in Figure 94 have a high degree of linearity, especially Lubricant

C, similar to Group 1. Lubricants A and B have the same apparent viscosity

development when compared to Group 1 for the reasons presented in

Section 5.5.1.

5.5.3 Group 3 Lubricant Performance Results (Tread Load = 9.5 kN,

Braking Torque = 30 N.m, Rolling Speed = 20 km/hr)

Group 3 investigated the increase of tractive force limit, or increased applied

shear stress to the lubricants. Compared to Group 1, the performance

indicators should be higher as the limiting shear stress was higher, however

this was not the case. The change in limiting shear stress caused further ‘shake

181

down’ or plastic deformation and removal of material, large wear particles,

which influenced the duration of tests in Group 3.

0 50 100 150 200 250 3000

1

2

3

4x 105

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 20 40 60 80 1000

5

10

15x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 700

5

10x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 95 - Cumulative absorbed energy versus time for Group 3. Energy is calculated from the difference between input and output energy. Note the different scales on vertical and horizontal axes.

The inter-test variability seen in Figure 95 and Figure 96 is high for Lubricant

A, and consistent with previous groups for Lubricants B and C. The

magnitude of energy absorbed by Lubricant A is smaller than Group 1 but

slightly larger than Group 2, which may indicate a limit to the shear force

capability of this lubricant. Approximately twice the absorbed energy,

compared to Group 1, was recorded for Lubricant C. This finding is in line

with the hypothesis that doubling the limiting shearing force increases the

measured performance. Lubricant B absorbed approximately half the energy,

as in Group 1, in direct contradiction to the hypothesis of increased capacity

182

with increased shear force limit. The capabilities of Lubricant B are

significantly reduced with increased shear stress. The performance of

lubricants was the same order as Group 1, A, B then C, however the

difference in performance between Lubricants B and C is small.

Lubricant A Lubricant B Lubricant C0

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

Tota

l Abs

orbe

d E

nerg

y (J

)

Figure 96 – Total energy absorbed prior to set slip limit for Group 3.

183

0 50 100 150 200 250 3000

500

1000

1500

2000

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 20 40 60 80 1000

500

1000

1500

2000

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 700

500

1000

1500

2000

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 97 – Power absorption rates for each lubricant in Group 3 tests. Note the different scales on the horizontal axis.

Power absorption rates for Group 2 are shown in Figure 97. Total test times

for Lubricant C are similar around 60 seconds, where Lubricants A and B

have highly variable test times. The rate of decay of power, at the end of each

test, was consistent for each lubricant despite the differences in time at which

this occurred.

184

Lubricant A Lubricant B Lubricant C0

100

200

300

400

500

600

700

800

900D

ista

nce

(m)

Figure 98 – Sliding distance of lubricant prior to set tractive force limit for Group 3.

The same trend of small appreciable differences in performance between

Lubricants B and C can be seen in Figure 98 for total sliding distance. Their

performance is similar to that shown in Group 2 and is still markedly smaller

than Lubricant A. Ranking of the lubricants has changed to A, C then B, with

the mean value of Lubricant C, 2% higher than the mean value for Lubricant

B. The difference in performance may not be significant.

185

0 50 100 150 200 250 3000

2

4

6

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 20 40 60 80 1000

2

4

6

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 10 20 30 40 50 60 700

2

4

6

Time (s)

Slid

ing

Spe

ed (m

/s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 99 – Sliding velocity profile for Group 3. Note the different scales on the horizontal axis.

Lubricants B and C have similarly shaped velocity profiles, see Figure 99,

which confirm the previous result of similar sliding distance performance.

Lubricant A has a velocity profile which is not consistent across tests and has

a harmonic pattern in it. The source of this harmonic is unclear as the

dominant contributor to the value of sliding velocity is braking torque, shown

in Figure 100. The hydraulic system has a much larger dominant frequency,

>1Hz, where this noise has a frequency of 0.05 Hz and is probably not the

source.

186

50 100 150 200 25018

20

22

24

26

28

30

Time (s)

Out

put T

orqu

e (N

.m)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Figure 100 – Output torque signal for Lubricant A in Group 3.

187

Lubricant A Lubricant B Lubricant C0

50

100

150

200

Hal

f Life

(s)

Lubricant A Lubricant B Lubricant C0

0.5

1

1.5

Min

imum

Slip

(%)

Figure 101 – (top) Half life prediction for

Group 3 using ( ) bxf x ae c−= + .

(bottom) Value of predicted minimum slip ‘c’.

Lubricant B Test 2 has been excluded from the half life prediction plot in

Figure 101 as the raw data was noisy and appeared to be an outlier. The noise

influenced the half life prediction and an unreasonable value was calculated.

The offset coefficient predictions, Figure 101 (bottom), are smaller than

Group 1 and 2 results, and more consistent between tests. The magnitudes

are still greater than zero. In addition the half life performance ranking is the

reverse of the power performance rankings, Lubricant C, B, then A. Half lives

for Lubricants A and B are reduced when compared to Groups 1 and 2,

which may be expected, for these groups had a smaller limiting shear stress

than Group 3 and therefore less damaging conditions for the lubricant film.

Lubricant C however had a longer half life than its results from Group 1 and

188

the expected result of a shorter half life when compared to the Group 2

results. A summary of half life values is given in Table 27 and graphically

presented in Figure 102.

HALF LIFE (S) Lubricant Type Mean Standard Deviation

A 75.523 33.981 B 102.5 9.1104 C 157.24 75.278

Table 27 – Half life values for each lubricant

in Group 1 testing using ( ) bxf x ae−= .

Lubricant A Lubricant B Lubricant C0

50

100

150

200

250

Hal

f Life

(s)

Figure 102 - Half life values for each lubricant

in Group 3 testing using ( ) bxf x ae−= .

189

104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 103 – Apparent viscosity for Group 3.

All lubricants in Figure 103 have a high degree of linearity, especially

Lubricant C, similar to Groups 1 and 2. Lubricants A and B have some

extraneous results deviating from the linear behaviour that are larger than

previously observed in Groups 1 and 2. The increase in tractive force has

increased the variability in apparent viscosity for Lubricant A and B.

5.5.4 Group 4 Lubricant Performance (Tread Load = 12.5 kN, Braking

Torque = 15 N.m, Rolling Speed = 20 km/hr)

The final group, with an increased normal force, was expected to have

reduced performance when compared to Groups 1 and 2. Group 4

investigated whether increased compressive stress was more damaging to

lubricant films than the increased shear stress of Group 3.

190

0 50 100 150 200 250 300 350 4000

0.5

1

1.5

2x 105

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 10 20 30 40 50 60 700

1

2

3

4x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 50 100 150 200 2500

2

4

6x 104

Time (s)

Abs

orbe

d E

nerg

y (J

)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 104 - Cumulative absorbed energy versus time for Group 4. Energy is calculated from the difference between input and output energy Note the different scales on vertical and horizontal axes.

Lubricants A and B experienced a large reduction in performance and test

duration, seen in Figure 104, compared to Group 1, 2 and 3. Again Lubricant

C displayed a different trend by performing similarly to its results for Groups

1 and 2 but reduced performance when compared to Group 3. This lubricant

appears to be unaffected by the increased normal force for this performance

criterion.

191

Lubricant A Lubricant B Lubricant C0

2

4

6

8

10

12

14

16x 104

Tota

l Abs

orbe

d E

nerg

y (J

)

Figure 105 – Total energy absorbed prior to set tractive force limit for Group 4.

In Figure 105 for total absorbed energy Lubricant A remains the best

performer followed by Lubricant C then Lubricant B. The difference in

performance between lubricants has reduced, and the difference between

Lubricants B and C is not clear with this performance criterion.

192

0 50 100 150 200 250 300 350 4000

200

400

600

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 10 20 30 40 50 60 700

200

400

600

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 50 100 150 200 2500

200

400

600

Time (s)

Abs

orbe

d P

ower

(W)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 106 – Power absorption rates for each lubricant in Group 4 tests. Note the different scales on the horizontal axis.

Power absorption rates for Lubricants A and B are higher than Lubricant C

and have a distinct point at which the absorbed power reduces rapidly, seen in

Figure 106. Lubricant C has a continuous decay in power over the course of

the test.

193

Lubricant A Lubricant B Lubricant C0

200

400

600

800

1000

1200

Dis

tanc

e (m

)

Figure 107 – Sliding distance of lubricant prior to set tractive force limit for Group 4.

The absorbed power performance criterion does not highlight the poor

performance of Lubricant C when considering total slid distance in Figure

107. Experimentally Lubricant C did not have a period of gross sliding and

was considered to have failed from start-up. The performance rankings from

Figure 107 are clear, Lubricant A , B then C.

194

0 50 100 150 200 250 300 350 4000

2

4

6

Time (s)

Sld

ing

Spe

ed (m

/s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

0 10 20 30 40 50 60 700

2

4

6

Time (s)

Sld

ing

Spe

ed (m

/s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

0 50 100 150 200 2500

0.01

0.02

0.03

Time (s)

Sld

ing

Spe

ed (m

/s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 108 – Sliding velocity profile for Group 4. Note the different scales on vertical and horizontal axes.

It is important to note that the sliding speed recorded for Lubricant C, see

Figure 108, is approaching zero (0.02 m/s) whereas the other lubricants have

periods of sliding, before a definite reduction in velocity.

195

Lubricant A Lubricant B Lubricant C0

100

200

300

400

Hal

f Life

(s)

Lubricant A Lubricant B Lubricant C0

0.2

0.4

0.6

0.8

Min

imum

Slip

(%)

Figure 109 – (top) Half life prediction for

Group 4 using ( ) bxf x ae c−= + .

(bottom) Value of predicted minimum slip ‘c’.

Small offset coefficients of slip were calculated for Group 4, see Figure 109,

similar in magnitude to Group 3 but smaller than Groups 1 and 2. Lubricant

B performed best, then Lubricants C and A respectively. Differences between

A and C, using the exponential with offset regression formula, are difficult to

observe in Figure 109.

Considering an exponential decay to zero the performance rankings are

reordered, Lubricant C, B then A with details in Table 28 and Figure 110. The

difference between Lubricant B and C is small and there is a high variability in

the mean value of performance for C, but not for Lubricant B. Lubricant C

half life will be affected by the low slip measured during testing and may skew

the results.

196

HALF LIFE (S) Lubricant Type Mean Standard Deviation

A 148.76 16.151 B 353.22 50.317 C 393.14 226.16

Table 28 – Half life values for each lubricant

in Group 1 testing using ( ) bxf x ae−= .

Lubricant A Lubricant B Lubricant C0

100

200

300

400

500

600

Hal

f Life

(s)

Figure 110 - Half life values for each lubricant

in Group 4 testing using ( ) bxf x ae−= .

197

103 104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

103 104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

103 104 105 106 107100

102

104

Strain Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 111 – Apparent viscosity for Group 4.

Apparent viscosity results for Group 4 in Figure 111 show Lubricant C to

have a high degree of linearity, similar to Groups 1, 2 and 3 but is over a

much smaller range of strain rate corresponding to the small range in sliding

velocity. Lubricants A and B have some extraneous results deviating from the

linear behaviour previously observed in Groups 1 and 2, the increase in

normal force has increased the variability in apparent viscosity.

5.5.5 Comparison and Discussion of All Groups

The different phenomena observed between each set of conditions for a

lubricant, with respect to energy absorbed, can be more readily observed in

Figure 112. Lubricant A has reduced absorbed energy performance for all

changes in test parameters from Group 1. Reducing rolling speed reduced

198

the absorbed energy capacity by half, with the most plausible explanation

being the lubricant film cannot sustain the compressive force at the reduced

entrainment velocity. Lubricant B showed an even greater reduction in energy

capacity at the reduced rolling velocity whereas Lubricant C reduced

marginally.

Group 1 Group 2 Group 3 Group 40

1

2

3

4x 105 Lubricant A

Tota

l Abs

orbe

d E

nerg

y (J

)

Group 1 Group 2 Group 3 Group 40

1

2

3x 105 Lubricant B

Tota

l Abs

orbe

d E

nerg

y (J

)

Group 1 Group 2 Group 3 Group 40

5

10x 104 Lubricant C

Tota

l Abs

orbe

d E

nerg

y (J

)

Figure 112 – Total absorbed energy for groups of tests. Note the different scales on the vertical axis.

The increasing level of shearing force of Group 3 allowed Lubricant C to

absorb a greater amount of energy prior to development of full tractive force.

This absorption indicates a higher apparent viscosity than either Lubricants A

or B which will be discussed further in Section 5.5.7. The reduction in

absorbed energy capacity for Lubricant A from increased shear force in

199

Group 3 was not as drastic as the reduction of performance from reducing

rolling velocity in Group 2. A similar reduction in absorbed energy

performance was observed in the Lubricant B results when compared to

Group 1 and 3.

Group 1 Group 2 Group 3 Group 40

2000

4000

6000Lubricant A

Dis

tanc

e (m

)

Group 1 Group 2 Group 3 Group 40

200

400

600

800Lubricant B

Dis

tanc

e (m

)

Group 1 Group 2 Group 3 Group 40

100

200

300

400Lubricant C

Dis

tanc

e (m

)

Figure 113 – Total sliding distance prior to set tractive force limit. Note the different scales on the vertical axis.

Group 4 tests increased the normal load by 30% and reduced the absorbed

energy performance of Lubricants A and B more than the other parameter

changes, indicating a relationship between normal force and energy capacity.

In contrast Lubricant C did not appear to be affected by changes in test

parameters except the increase of limiting shear stress in Group 3. The

difference of soap between Lubricants A and B, lithium based, and Lubricant

200

C, aluminium based, is a likely source of differences in performance despite

similar additives and base oils.

Sliding distance performance for the lubricants does not have the same

characteristics as the energy absorbed results, see Figure 113. Lubricant A

sliding distance performance increases with a reduction in rolling velocity in

Group 2, in contrast to Lubricant B which loses about 75% of the sliding

distance performance when compared to results from Group 1. Lubricants A

and B also have reduced sliding distance performance with the increased

tractive force limits in Group 3. Lubricant C however has a high variability

and it is difficult to differentiate between Groups 1 through 3. Group 4 is the

exception. The increased tread load reduced the sliding distance performance

to negligible values for Lubricant C. Lubricants A and B also performed at a

reduced level of sliding distance performance with the application of greater

normal load but still had a definite period of sliding in which tractive force is

being absorbed by the lubricant rather than the contacting bodies in wear

processes.

201

Group 1 Group 2 Group 3 Group 40

500

1000

1500Lubricant A

Hal

f Life

(s)

Group 1 Group 2 Group 3 Group 40

1000

2000

3000Lubricant B

Hal

f Life

(s)

Group 1 Group 2 Group 3 Group 40

200

400

600Lubricant C

Hal

f Life

(s)

Figure 114 – Half life values summary Note the different scales on the vertical axis.

The performance values for half life in Figure 114 do not have the same

trends as the previous two summaries of absorbed energy and sliding

distance. The data has wide inter-group ranges, making observations difficult

to present with certainty.

Lubricants A and B have reduced half life performance with increased normal

load in Group 4 and increased shearing force in Group 3. Half life appears to

be unaffected by rolling speed for Lubricants A and B. Lubricant C is

observed to have increased performance with changes to the input parameters

of reduced rolling speed, increased shearing force and increased normal load

compared to those of Group 1. The increases of shear force and normal load

202

appear to improve the performance of Lubricant C, contrary to expected

outcomes.

5.5.6 Lubricant Performance Summary

Lubricant Type Group No. Performance Criteria A B C

Total energy absorbed (J) 324440 215320 28564 Total sliding distance (m) 2379 749 216 1 Half life of lubricant (s) 275 984 88 Total energy absorbed (J) 143200 36786 18094 Total sliding distance (m) 3597 224 246 2 Half life of lubricant (s) 503 916 206 Total energy absorbed (J) 202800 83200 75560 Total sliding distance (m) 574 184 187 3 Half life of lubricant (s) 76 782 157 Total energy absorbed (J) 78857 22298 28929 Total sliding distance (m) 614 123 3 4 Half life of lubricant (s) 149 353 393 Average Total energy absorbed (J) 106283 89401 37786 Average Total sliding distance (m) 1791 319 162 ALL Average Half life of lubricant (s) 250 758 211

Table 29 – Lubricant performance summary.

The overall performance of each lubricant was calculated by comparing the

mean values of each performance criteria, the absolute values presented in

Table 29, and assigning the best performing lubricant 100% and assigning

fractions to the other lubricants.

The purpose in presenting in this format is to compare lubricant performance

quantitatively while removing the absolute magnitudes of the values, which

have yet to be correlated with field data. The results of this analysis are in

Table 30. In addition to the group data is an overall performance ranking, the

‘ALL’ rows, which is calculated by taking the mean of the results of a

particular performance criterion from the 4 groups.

203

Lubricant Type Group No. Performance Criteria A B C

Total energy absorbed 100% 66% 9% Total sliding distance 100% 31% 9% 1 Half life of lubricant 28% 100% 9% Total energy absorbed 100% 26% 13% Total sliding distance 100% 6% 7% 2 Half life of lubricant 55% 100% 22% Total energy absorbed 100% 41% 37% Total sliding distance 100% 32% 33% 3 Half life of lubricant 10% 100% 20% Total energy absorbed 100% 28% 37% Total sliding distance 100% 20% 0% 4 Half life of lubricant 38% 90% 100% Total energy absorbed 100% 84% 36% Total sliding distance 100% 18% 9% ALL Half life of lubricant 33% 100% 28%

Table 30 – Relative lubricant performance summary.

Alternatively, taking a qualitative analysis approach to the results from the

groups and assigning each lubricant a numeric rank according to

performance, lower being better, give the ranks given in Table 31. The inter-

group performance values in Table 31 were calculated by taking the mean of

the ranks for a particular lubricant.

If each performance criterion has equal weight or importance, then the

lubricants have the performance order A, B then C. The tabled results do not

take into account the quantitatively large or small differences between

lubricants, which for some tests are extreme. Taking each performance

criterion separately the ranking of lubricant performance was not conclusive.

Lubricant A is the best performer under all test conditions for total energy

absorbed and total sliding distance. Total absorbed energy is a representation

of the stress history whereas sliding distance is a representation of strain

history, both are clearly important and Lubricant A is the best performer.

204

Lubricant Type Group No. Performance Criteria A B C

Total energy absorbed 1 2 3 Total sliding distance 1 2 3 1 Half life of lubricant 2 1 3

Inter-group performance 1.33 1.67 3.00 Total energy absorbed 1 2 3 Total sliding distance 1 3 2 2 Half life of lubricant 2 1 3

Inter-group performance 1.33 2.00 2.67 Total energy absorbed 1 2 3 Total sliding distance 1 3 2 3 Half life of lubricant 3 2 1

Inter-group performance 1.67 2.33 2.00 Total energy absorbed 1 3 2 Total sliding distance 1 2 3 4 Half life of lubricant 3 2 1

Inter-group performance 1.67 2.33 2.00 Total energy absorbed 1.00 2.25 2.75 Total sliding distance 1.00 2.50 2.50 ALL Half life of lubricant 2.50 1.50 2.00

Total Performance Rank 1.50 2.08 2.42 Table 31 – Qualitative performance of lubricants.

Strain life, calculated from total sliding distance, is similar between Lubricants

B and C, indicating that the strain history limits between lubricants is also

similar. Lubricant A has best strain history limit or sliding distance under all

conditions. Stress absorption capacity, from total absorbed energy, has the

same performance rankings as strain life with the exception of a slight

performance advantage to Lubricant B. Lubricant C only outperforms

Lubricant B in total absorbed energy when the normal force is increased.

Half life of the lubricants is a performance criterion that does not display clear

differences under all conditions. Lubricant B is the overall best performer in

this category, but it can be observed that an increase in normal load or

shearing force reduces the half life and Lubricant C becomes the best

205

performer. Lubricant A also loses half life performance with increased normal

load or shearing force similar to Lubricant B.

5.5.7 Apparent Viscosity Profiles

0 200 400 600 800 1000 1200100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 200 400 600 800 1000 1200100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 100 200 300 400 500 600100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 115 – Apparent viscosity versus time for Group 1. Note the different scales on the horizontal axis.

Accumulated strain causes structural changes in the lubricants, represented by

increasing values of apparent viscosity (Kuhn 1995; Kuhn and Balan 1997;

Yonggang and Jie 1998). Two parts of the apparent viscosity profile are

important in terms of lubricant performance. Firstly the length of time or

amount of accumulated strain for which a lubricant remains at a reduced

viscosity and secondly the plateau viscosity. The first part of reduced viscosity

minimises the transmission of force and stress between the two contacting

206

bodies, thereby reducing the wear and fatigue processes. The second part of

the apparent viscosity profile is the proportion of the input shear force

imparted to the output contact. Lowering the value of shear force reduces the

wear producing shear stress experienced by the contacting bodies. Therefore

the optimum characteristics of apparent viscosity are extended accumulated

strain life, presented in the apparent viscosity profiles as test time, and

minimal plateau viscosity at test completion.

Plotting apparent viscosity versus time for the lubricated testing in Group 1 to

4 displays the characteristic of increasing viscosity with strain history, which is

represented in this case as time elapsed. In Figure 115 to Figure 118

Lubricants A, B and C appear to have a limiting shear stress value, seen by the

profiles becoming ‘horizontal’ with the progression of time.

Lubricant C consistently has the highest finishing apparent viscosity across all

groups of tests followed by Lubricant A then Lubricant B. Inter-test

variability for Lubricant A is high when compared to Lubricants B and C

which appear to have predictable apparent viscosity profiles. The exceptions

to the predictable apparent viscosity profiles are periods in which the

apparent viscosity reduces, seen for Lubricant B in Group 1 and Lubricant C

in Group 2. The exceptions may be explained by extraneous lubricant

entering the contact area. The extraneous lubricant occurs from two

phenomena, lubricant flung from the outer edge of the samples where it has

been pushed, and lubricant falling from the safety guard where it may collect

from the centrifugally flung excess lubricant from the samples at the

beginning of the test.

207

0 500 1000 1500 2000 2500100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 100 200 300 400 500 600 700 800100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 100 200 300 400 500 600100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 116 - Apparent viscosity versus time for Group 2. Note the different scales on the horizontal axis.

208

0 100 200 300 400 500100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 100 200 300 400 500 600100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 50 100 150 200 250 300 350100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 117 - Apparent viscosity versus time for Group 3. Note the different scales on the horizontal axis.

209

0 100 200 300 400 500 600 700100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 100 200 300 400 500 600100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

0 50 100 150 200 250100

102

104

Time (s)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant A Test 1Lubricant A Test 2Lubricant A Test 3

Lubricant B Test 1Lubricant B Test 2Lubricant B Test 3

Lubricant C Test 1Lubricant C Test 2Lubricant C Test 3

Figure 118 - Apparent viscosity versus time for Group 4. Note the different scales on the horizontal axis.

5.6 Experimental Observations

5.6.1 Temperature Profiles

In the low speed testing, the lubricant films maintained integrity for far longer

than at high speed testing. The bulk temperature of the samples was lower

than the high speed testing under the same loading conditions. Frictional

energy is halved in the low speed case if we consider sliding velocity alone.

During the tests, the sliding velocity is not constant which does not allow for

comparison between high and low speed frictional energy heating.

It can be observed that the sample temperatures continue to rise during the

low speed testing whereas the temperature drops at the end of the test for the

210

high speed case. A plausible explanation for this phenomenon is the air

velocity across the samples in the high speed case gives a much larger

convection heat transfer coefficient. The testing may also be short enough

that the bulk of the heat energy is not transmitted into the simulator body

which is a significant thermal mass.

Thermal energy is added to the system through the hydraulic dynamometer

where the braking energy is converted into thermal energy. In addition to its

use in the dynamometer, oil is used to lubricate and cool the bearings of both

sample holders. The hydraulic oil for lubricating bearings in the sample

holders experiences a large increase in temperature through the testing

process and is returned to the main reservoir, whereas oil for the

dynamometer experiences a small increase in temperature and is returned to

the reservoir via the heat exchanger. Volume flow for the dynamometer is

two orders of magnitude larger than the lubricating system, which maintains

the reservoir temperature, ~30˚, but this does little to reduce the simulator

body temperature during a long test.

5.6.2 Observed Lubricant Properties

Separation of oil from the grease phase was observed in all lubricant samples.

Lubricant C had the largest volume of oil with similar handling conditions for

each of the lubricants. Lubricant samples were taken from minimum 20kg

containers and stored in 1 kg packages until used. All testing, except rheology

testing, was carried out using the single sample container. A backup set of

containers was stored for the duration of the project and the backup

container of Lubricant C displayed the same characteristics as the used

sample.

Separate tests were carried out to investigate the variable consistency of

Lubricant C. The absolute values of these tests were not recorded as the test

protocol differed from the main testing. Time for lubricant film development

and slip percentage with respect to time were recorded and compared.

211

Despite the oil bleed there was no easily discernable performance difference,

using the simulator, between an application of ‘oily’ grease or the consistent

grease.

The results would indicate that the oil, the main lubrication component, is still

reaching the target area whether oil bleed is present or not. In the case of a

gauge corner oil bleed would precipitate the oil from the contact zone down

the gauge face onto the rail web and not provide any lubricating effect.

The order in which each lubricant was applied during a battery of tests was

random, which meant that the temperature of the rail and wheel samples were

variable at the time of lubricant application. Lubricant B was observed to

spread much more readily onto a hot metal sample. Lubricants A and C did

not display this effect.

Application of larger braking torque in Group 3 introduced an effect where

the lubricant film would regain effectiveness as the temperature decreased.

Temperature of the test samples increased as frictional energy was absorbed

into the bodies. The system has a heat energy balance between input and

output. At the start of testing, with high sliding speed, input energy is greater

than output energy and the samples increase in temperature. As sliding speed

decreases and output shaft rotational velocity increases the output energy

from convection heat transfer becomes larger than the frictional input energy

and subsequently the samples decrease in temperature. This reduction in

temperature coincided with the regeneration of lubricant effectiveness.

It is postulated that due to the higher temperatures experienced during the

Group 3 tests, temperature reactive components of the lubricant become

active, which previously could not be observed. All lubricants displayed this

behaviour during testing. Additionally this phenomenon was explored by

allowing the samples to cool post test then testing without cleaning. The

lubricant performed as before with a reduction in performance. Practically

this translates to a situation where a train passes, there is a delay, and then

212

another train passes. It was not determined what temperature must be

achieved to get the most benefit from the temperature reactive lubricant

components.

Increasing the tread load from 9.5 kN to 12.5 kN resulted in no gross sliding

for Lubricant C. The lubricant appeared unable to adhere to the surfaces, with

this larger normal force. The lubricant film is visible and detectable by a larger

slip value than the unlubricated case, but is allowing for a full transmission of

the input power. Practically, this represents probable protection of the

surfaces from wear but high tractive power losses and full transmission of

forces related to fatigue. This high tractive power may be advantageous where

lubricant migration to the tread and traction loss is an issue, as this lubricant

acts as a friction modifier rather than a lubricant.

5.6.3 Lubricant Film Failure

Lubricant film failure was observed during testing when material was

removed from either contact surface. Newly machined rail/wheel samples

tested with lubricant and applied braking torque had a high rate of material

removal. Subsequent tests had progressively lower material removal rates as

surface hardness increased. Plastic deformation of both surfaces, accumulated

during testing, increased the wear resistance of the surfaces.

Upon application of a larger braking torque, high material removal rates were

observed again. Narrow bands (< 5 mm width) of contact surface were

observed without lubricant film following material removal. It is hypothesised

that the removed material reached its ductility limit with the increase in

shearing stress, causing material failure.

5.6.4 Braking Torque Setting

Braking torque was set by adjusting a hydraulic pressure relief valve to a

nominal value. This value was set using an inline oil pressure transducer

which was not accurately calibrated against the output torque transducer

signal. The nominal line pressure was adjusted during the warm-up and

213

monitored during testing to maintain a constant set point. The set point

would move with changes in lubricant temperature and flow rate. Minimising

output signal noise was achieved by maintaining oil temperature and setting

the valve position under maximum expected flow and not adjusting during

testing. The torque quoted in the testing results is an approximate value but

the experimental values of torque presented and used in the calculation of

results are the measured values.

5.7 Standards Based Lubricant Testing Results

Figure 119 – ARES Rheometer used for rheology testing.

The following sections will present and discuss the results obtained from the

standards based testing. The exception to this is the tests performed with the

214

rheometer (see Figure 119), which are not standards based, but use the test

device manufacturer's recommendations for testing (Yonggang and Jie 1998;

Nolan ~2000). This method is detailed in the following section.

5.7.1 Rheometry Method

Clean interface surfaces with solvents as per ASTM standard method. Refer to Figure 120 to observe surfaces and test piece arrangement.

Install top and bottom plates, zero gap and normal force.

Move top plate to furthest position and apply lubricant to bottom plate. Lubricant is applied using a spatula, the bulk of the product located in the centre of the plate.

Lower top plate to set gap. Ensure excess lubricant is observed around circumference of plates.

Perform selected test.

Move top plate to furthest position and clean lubricant from top and bottom plates as specified by ASTM standard method.

Figure 120 – Cone and plate arrangement for rheometer testing.

215

5.7.2 Rheometer Test Discussion and Results

The rheometer tests were quick to perform, which, if a correlation between

performance and rheological properties could be determined, would make

this a suitable test. However there is not a clear measured difference that

matches the trends seen in the simulator testing. This form of test does not

reach the shear rates experienced in a simulated or real rail wheel contact.

In the low shear rate region of Figure 121 Lubricant B has a higher viscosity

than Lubricant A and Lubricant C, conversely at the higher shear rate

Lubricant B and C swap positions. Lubricant B is therefore shear thinning at a

greater rate than Lubricants A and C. The decreased shear thinning of

Lubricant C at the higher shear rates may explain the observed behaviour of

short times to achieve tractive force in the simulator testing.

10-2 10-1 100 101 102 103100

101

102

103

104

Shear Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant ALubricant BLubricant C

Figure 121 – Apparent Viscosity versus Shear Rate using a flat plate rheometer.

216

5.7.3 Experimental Rheometry Observations

Lubricant was expelled from the surfaces using the cone and plate setup as

the strain accumulated. Moving the testing surfaces apart showed a reduction

in lubricant surface area. This ‘climbing’ effect was explained in the operating

manual of the rheometer and is often experienced by substances with elastic

properties.

The calibrated gap between cone and plate, 55µm, was difficult to reach. The

grease appeared to resist the applied normal movement similar to

compressing a viscoelastic solid. This compression applies a radial strain

history to the samples.

In the case of the parallel plates, lowering the top plate would introduce a

normal force on the plate as the lubricant was expelled. The magnitude of this

force was different for each grease tested. The magnitude of this force was

less than that experienced during the cone and plate rheometer testing. Plate

gap for the parallel plate testing was 1000µm.

Preliminary testing with the parallel plates used varying amounts of lubricant.

Tests with lubricant volume approximately equal to the nominal gap volume

had lubricant roll up at the outer edge which decreased the contact surface

area. The roll up would begin at a location where slightly more lubricant had

flowed out. Tests with a full ring of excess lubricant did not display this

property and maintained a full contact area for the test duration.

All of the greases tested displayed thixotropic effects. The aluminium

complex based grease structure appeared to reform its structure. This

reversible structure effect was observed following an applied strain. In

contrast the lithium complex greases displayed high strain history dependent

behaviour.

217

5.7.4 ASTM D1092 Grease Pumpability

The results of this capillary rheology test, Figure 122, do not highlight any

great difference between lubricants. The consistency NLGI rating for these

lubricants is the same, which this test confirmed. This test may be important

for the implementation of lubrication systems in designing the pumping and

plumbing of lubricants but no wear performance criteria are discernable.

100 101 102 103 10410

0

101

102

103

Shear Rate (s-1)

App

aren

t Vis

cosi

ty (P

a.s)

Lubricant ALubricant BLubricant C

Figure 122 – ASTM D1092 Grease Pumpability results.

5.7.5 ASTM D2596 and ASTM D2266 Four Ball Tests

The lubricants under investigation were tested using ASTM D2596 and

ASTM D2266, the four ball tests of wear and extreme pressure properties.

The purpose of this testing was to determine the performance characteristics

of the lubricants, measured by standard lubricant testing, which indicates the

extreme pressure and wear characteristics. Lubricant A achieved marginally

better results in both the extreme pressure and wear testing. Figure 123 shows

Lubricant A to have a consistently smaller scar diameter over the load range.

218

Lubricant B had a smaller scar diameter than Lubricant C, except at the 200

kgf point, but the weld point is lower.

0 50 100 150 200 250 300 350 4000

0.5

1

1.5

2

2.5

3

Load (kgf)

Sca

r Dia

met

er (m

m)

Lubricant ALubricant BLubricant C

Figure 123 - ASTM D2596 Four ball wear test results.

219

Lubricant A Lubricant B Lubricant C0

50

100

150

200

250

300

350

400

450

500

550

Wel

d Lo

ad (k

gf)

Figure 124 – ASTM D2596 Weld load results.

Weld point results in Figure 124 identify Lubricants A and C as the best

performers. Lubricant B is two load steps below the others, and is probably a

result of the smaller solid lubricant volume in this lubricant type.

220

Lubricant A Lubricant B Lubricant C0

0.2

0.4

0.6

0.8

1

1.2

1.4S

car D

iam

eter

(mm

)

Figure 125 – ASTM D2266 Scar diameter results.

Figure 125 displays a similar trend in performance, as the simulated testing,

with Lubricant A having the smallest scar diameter in the wear testing and

Lubricant C the largest. The differences in performance may not be

significant and are not conclusive.

The quicker development of set tractive force in the simulated tests for

Lubricant C is related to transfer of input force to output force. The output

surface then experiences this force and accumulates wear damage. In the case

of ASTM D2266 there is no limit to the tractive force. The higher viscosity of

Lubricant C transfers a greater force, damaging the surfaces at a greater rate

than either Lubricants A and B, seen by the larger wear scar results. Design of

a rheology test to explore the high end of shear rates could assist in predicting

the energy transfer available for wear processes.

221

5.8 Summary

Prior to the presentation of the lubricant performance tests in this chapter the

input variables and corresponding stress values were presented for each of the

four test groups. The test groups were structured to investigate the effect of

changing a single input parameter on the lubricant performance of the three

rail curve lubricants tested.

The method used to isolate the effect of lubrication from the total system

effects was presented, detailing the values of micro-slip and absorbed power

that are used in the analysis of lubricant performance. In addition the same

method for predicting the steady state values of unlubricated absorbed power

and micro-slip is used to predict the decay in lubricant performance,

measured as a half-life. The half-life was defined as the time for sliding

performance (slip) to reduce by 50%.

Results of the half-life performance of the rail curve lubricants may not

provide an accurate measurement of the wear performance but assuming that

the presence of lubricant reduces wear, the best performance would arise

from the longest half-life.

The input parameters were measured for all groups of tests and the results of

the first test were presented to display the variability in the input parameters

of normal load, rolling velocity and limiting braking torque. Rolling velocity

had a low variability of approximately 0.1 km/hr. Normal load had a higher

variability resulting from thermal effects but was reasonably consistent

between tests. Braking torque variability arose from the continuing decay in

lubricant performance but was reasonable consistent between tests. Variability

in all input parameters was larger than the predicted experimental error in the

measurements of the input parameters.

Each group of tests were presented to define and identify the differences in

performance between rail curve lubricants. Results for each lubricant were

then collated to measure changes in performance with changes to input

222

parameters. Lubricant A outperformed Lubricant B and C under all test

conditions for total absorbed energy and total sliding distance, both

performance criteria important for rail and wheel wear reduction. Lubricant B

outperformed Lubricant A and C for half-life, except for Group 3 in which

Lubricant C was the best performer. Considering all performance criteria,

with equal weights for each, ranks the lubricants with Lubricant A first then

Lubricant B then Lubricant C.

Apparent viscosity versus time profiles were presented in this chapter to

display the decay in apparent viscosity with accumulated strain damage.

Lubricant A and C had similarly shaped apparent viscosity profiles, with

Lubricant C having a reduced accumulated strain capacity when compared to

Lubricant A. Lubricant B was observed to have a slower rate of decay of

lubricity than Lubricant A and C and had lower apparent viscosity at test

completion.

In addition to the measured results some experimental observations were

made. Different temperature profiles were measured for each lubricant, which

was the result of differing amounts of frictional energy being absorbed into

the rail and wheel samples. Rolling speed also affected the heat transfer

characteristics of the system, reduced rolling velocity decreased the heat

transfer coefficient and increased sample temperatures were observed.

Lubricant film failure was observed when fatigued material, wear particles,

became loose from the rail or wheel samples. The film failure was observed

by a removed ring of lubricating film. The development of these rings

influenced the test results by reducing the performance indicators.

Shear force control issues were presented. The shear force or braking torque

applied by the hydraulic dynamometer was influenced by viscosity changes in

the hydraulic oil. Temperature control of the hydraulic oil was employed to

control viscosity and was identified as an important control issue.

223

Temperature control was achieved with the newly designed and installed heat

exchanger.

Lubricating grease has a limited number of applicable standards based tests.

Results of the applicable tests, ASTM D1092, ASTM D2266, and ASTM

D2596 were presented. Lubricant performance differences between the rail

curve lubricants could be observed, but concerns with the resolution of

measurements and repeatability and reproducibility of the tests reduced the

level of confidence in the results. Wear performance in the standards based

tests matched the wear related performance criteria of absorbed energy and

sliding distance in the rail/wheel simulator testing with Lubricant A

performing better than Lubricant B which performed better than Lubricant

C. Rheology testing using ASTM D1092 and an Aries rheometer displayed

similar results to the apparent viscosity results from the rail/wheel simulator.

Simulated and standards based lubrication tests have been completed and

their results presented and discussed. The simulated results had a practical

outcome of the selection of a lubricating grease which is most suitable when

using three separate performance criteria. Standards based tests agreed with

this assessment but the confidence in measurements was low from poor

repeatability of results. Across all tests the limitations and practical

observations have been discussed with further recommendations in the

following chapter.

224

C h a p t e r 6

DISCUSSION, FUTURE WORK AND CONCLUSIONS

6.1 Introduction

Chapter 2 explored the issues surrounding rail/wheel lubrication and

provided an overview of methodologies for rail/wheel lubrication for in

service and simulated conditions. Chapter 3 presented a contact mechanics

method to present stress distributions for examples of in-service and

simulated conditions. These results highlight the similarities and differences

between the simulated and 'real world' conditions to gain an insight behind

the experimental methodology in Chapter 4. Chapter 4 details the

modifications to the simulator, formerly a device used for rail/wheel materials

investigations, to analyse a simulated lubricated gauge corner contact. Chapter

4 also included the method, measurements and measurement errors

associated with the experimental procedure. Chapter 5 presented all of the

experimental results from standards-based lubricant testing and compared

them to the results obtained from the simulated rail conditions. Finally, this

current chapter summarises the findings of the research, presents the

conclusions and discusses the possible directions of future work.

6.2 Discussion

The objective of this thesis was to quantify rail curve lubricant performance.

Theoretical and experimental methodologies were developed for use with a

rail/wheel simulator. The rail/wheel simulator that was acquired for this

research was modified and improved to measure slip accurately on a larger

than typical twin disk device which has the capacity to use a number of

sample shapes for the purpose of investigating different contact patches. The

effect of lubrication was investigated with high resolution slip measurements,

not previously possible in the work of Marich and Mutton (1989).

225

The work in this thesis has highlighted the performance difference under

simulated conditions between lubricants designed for the rail industry and has

demonstrated the requirement for more specific parameters to be targeted by

lubricant manufacturers. This research has also highlighted the need for

lubricant suppliers and customers to identify performance requirements and

the methods of achieving them with lubricant ingredients with a more

transparent information sharing process.

Standard lubricant tests, such as those from ASTM provide inadequate

information for rolling stock and rail infrastructure managers to make

informed decisions as to which lubricant to use. The standards based testing

present results which may not be relevant to rail curve lubrication, whereas

the rail/wheel simulator gives results for performance criteria that are relevant

to rail curve lubrication. Performing a group of tests such as those presented

in this research can highlight advantages and deficiencies in a range of contact

conditions that standards based testing cannot achieve.

Possible improvements to current rail lubricant tests include the specification

of strain history at a particular strain rate from a standard twin disk test device

such as an Amsler machine. This value of strain history could be calculated

from a survey of the rail network using the common length of curves in

combination with rail profiles to give a representative slip value. The

specification of absorbed energy could be substituted for strain history or

made an additional criterion.

The twin disk tests would require specified input parameters of compressive

stress to match the loading regime of the rail network, rolling speed to match

typical cornering speed, and temperature to match the expected

environmental conditions. Using this type of laboratory simulator it would be

possible and useful to perform the tests at a range of strain rates or slip to

characterise the lubricant for most conditions experienced in the gauge

226

corner. The work presented in this thesis tested across a range of slip

conditions but the focus was on investigating limiting shear stress conditions.

Another suitable parameter to be included in lubricant specifications is

apparent viscosity. Limits of this value at nominated shear rates could reduce

the shear force transmission between contact surfaces. Fatigue related wear,

which is dependent upon shear stress, could be reduced using this method.

Tractive effort and fuel consumption may also be reduced through the

specification of apparent viscosity. Savings through lubrication have already

been identified (Clayton 1996) and increased savings may be possible using

the apparent viscosity testing method.

The predictions of half life are sensitive to the errors in the final value of slip.

These errors are dependent upon the temperature of test pieces, which is

dependent upon the number of samples taken after the set traction force is

reached. In the calculations of half life the offset coefficient is representative

of the thermal expansion error. Therefore to reduce the offset coefficient,

sufficient samples after the frictional power has reduced below the convective

power losses must be allowed for the test piece temperatures to stabilise as

near to unlubricated conditions as possible.

Observing that the decay in measured slip is the result of two processes, decay

of lubricant film and decay of sample temperature, the prediction of half life

could be improved by modelling each of these processes. Taking each of

these components as having an exponential decay gives Equation (6.1)

measured slip ratio, , , regression coefficients

bt dtae ce

a b c d

ξξ

− −= +=

= (6.1)

Using this model to perform a regression analysis of the slip gives a higher

correlation coefficient than the single exponential problem. A difficulty with

using this model is that there is no method of differentiating between the

227

effects of thermal expansion and lubricant film decay. The error analysis for

thermal expansion of the test pieces shows that the component of slip from

thermal expansion becomes small, rapidly leaving only the lubricant film

decay component.

Relating the half life predictions to the field is somewhat difficult. The

simulator test failure criteria is the reaching of a set tractive force, whereas the

field lubricant film failure criteria is that there is no lubricant remaining on the

rail. Considering the magnitude of wear in each case, for the simulator the

wear is negligible as the lubricant film still exists, for the field, wear is

considerable as the protective film has been totally removed. Simulator test

conditions therefore are not representative of the field situation in this aspect

but do represent the desired level of lubrication from an industry view point.

The slip calculation/measurement taken by the simulator is not affected by

film thickness which allows for the estimation of film thickness as the

magnitude of the value of film thickness will always reach zero despite

calibration or measurement errors. Film thickness is not required to be

specified but sliding distance is required. For a lubricant manufacturer, the

higher the film thickness there is a correspondingly smaller shear rate.

6.3 Future Work

Further work is required to set a final slip value that must be reached to

improve comparisons between lubricants. Modelling the half-life of a rail

curve lubricant could be improved by setting a final slip value to end the test,

which would result in eliminating the offset coefficient in the regression

equation. A dual exponential term equation was explored to account for the

two effects of lubricant film decay and thermal changes. The statistical

difference between the two regression models was small but observable.

However, the dual exponential model was unsuitable for predicting the time

to lubricant failure.

228

The rail/wheel simulator cannot control shearing force and shear strain rate

simultaneously. This research focussed on testing to a maximum shearing

force, in this case a set braking torque, for the duration of testing to monitor

the slip under varying loading conditions. A control system monitoring the

inputs to shearing force would be required, controlling the hydraulic

dynamometer and pneumatic ram, in order to achieve simultaneous control of

the shearing force and the shear strain rate.

A design for slip control was proposed and installed to the dynamometer

system to simultaneously control shear force and shear strain. In place of

controlling pressure alone, a dual control, flow and pressure system was

installed. The flow control has the effect of limiting the maximum slip

conditions experienced during the test. This modification was completed for

the purposes of future research and is yet to be fully validated.

Wider simulation could be achieved with different contact patch shapes. This

could be investigated further to model more closely the lubrication transport

mechanisms. Of particular interest is decreasing the contact width to increase

the maximum contact pressure, and change the contact shape using curved

surface samples. At this point the simulator is incapable of generating

pressures that are as high as the maximum in-service contact pressures

presented in Section 0. Modification of the simulator to allow assessment of

lubricant performance with in-service contact pressures approaching the

maximum attainable values would be a valuable improvement to the

rail/wheel simulator.

Wear of the samples was not measured as full lubricant film was maintained

throughout testing. Detecting wear by changes in profile geometry is

impossible for tests of limited duration therefore a mass loss method is

required. It was determined that a mass comparator was required to measure

at the specified resolution as conventional weighing devices are three orders

of magnitude of precision deficient. Due to the limitations in obtaining the

229

use of a commercial mass comparator, a novel inexpensive design was carried

out. The design, and results when carried out, will be published as work

ancillary to this project.

6.4 Conclusions

The objective of this research was to quantify rail curve lubricant performance

through laboratory simulation. The steps to achieve the objective of this

thesis were:

Quantified the performance of the typical rail curve lubricants using standard tests.

The lubricants have been laboratory tested to define the properties using the

ASTM and other appropriate standards. The lubricants were laboratory tested

to define the properties using the ASTM and other appropriate standards.

Information was gathered from both literature and field personnel as to the

performance properties of the lubricants. The results were inconclusive from

the standards based tests as to which lubricant was the best performer. The

performance differences measured were susceptible to repeatability problems

and did not represent the in-service conditions as accurately as the rail/wheel

simulator.

Quantified the contact mechanics of field and simulated conditions.

A literature survey was carried out to identify the methodologies employed to

measure and predict the rail/wheel contact. Upon review, a suitable method

for predicting the contact conditions was selected and used to analyse the

laboratory simulation device and representative in-service conditions. The

method was computerised and the software validated. The software will be

useful for all contact mechanics analysis especially for further rail curve

lubrication research.

Identified the wear mechanisms at the wheel and rail gauge face for the purpose of matching the simulator to field conditions.

230

The primary focus of this project was on optimisation of the lubrication in a

rail gauge corner contact and as such this objective was not explored in great

depth. The wear mechanisms were predicted using the parameters of the

contact and comparison with the body of literature. Wear particles were

gathered and inspected to assist in verifying the wear mechanism or

mechanisms identified and the simulator was confirmed as having the same

wear characteristics as the field. This work has demonstrated that the

simulator is capable of exploring wear mechanisms and generates wear typical

of rail/wheel contacts.

Quantified the effect of lubrication.

The laboratory simulator was used to gather data in lubricated and

unlubricated conditions for the purpose of providing lubricant performance

measurements. Analysis of the results from the lubricant testing and

laboratory simulators was carried out to determine trends between them.

These trends indicate performance differences between lubricants. The results

for the lubricants presented here also show that a single value for ranking a

lubricants performance is yet to be achieved, but using a number of criteria a

lubricant can be ranked quantitatively. Using the lubricant performance

measurements the tested lubricants were ranked conclusively with three

innovative industrially relevant performance criteria.

The outcome for the use of this thesis is to provide a method of quantitatively

ranking wheel/rail flange lubricants. However, to achieve performance

ranking with industrial relevance, correlation with field data must be carried

out. Despite the lack of correlation in this thesis the performance criteria

presented are relevant to field conditions. Accuracy of the contact stresses in

the rail/wheel simulator give credence to the results of lubricant performance

presented.

The unique contributions to rail curve lubricant research include the

development of a prediction model of lubricant half life under simulated

231

conditions. Lubricant half life represents the decay of lubricant performance

under a set shear stress level. Half life prediction is a relevant performance

criterion and research output for industry. Following correlation with field

results, the half life performance criterion will allow for improved lubricant

design and better placement of lubricators and the associated benefits of

improving the lubrication system.

Another significant contribution unique to the body of rail curve lubricant

research is the measurement of apparent viscosity of lubricating grease using a

twin-disk simulator. Measurement of the rheological development of a rail

curve lubricant using the rail/wheel simulator will assist in the design of

lubricants to achieve the performance requirements of the rail industry.

Rheological development is directly related to the tractive effort and

fuel/energy consumption of the locomotive, which is of great interest to the

rail industry.

The lubricating capacity of rail curve lubricants was defined and measured in

this thesis as total absorbed energy and total sliding distance. Total absorbed

energy is important to the rail industry for the purpose of reducing the

frictional energy and wear from flange contact. Increased energy capacity

translates to less energy available for wear processes. Total sliding distance is

important to the rail industry for the purpose of obtaining maximum

lubricating capacity from each lubrication system. Greater measured total

sliding distance translates to improved lubricant performance by increasing

the lubricating capacity of the rail curve lubricant. Applying total absorbed

energy and total sliding distance performance criteria to rail curve lubricant

specifications will improve the outcomes for the rail industry.

To summarise, new methods for rail curve lubricant performance

measurement have been presented. These performance measurements are

total absorbed energy, the energy absorbed in the lubricant film instead of

being utilised for wear processes; total distance slid, the sliding distance or

232

accumulated strain achieved prior to development of a set tractive force limit;

half life of lubricant, the time taken for a lubricant to lose half of its sliding

performance; and apparent viscosity, a measure of the lubricity presented with

respect to accumulated strain. Using the new method of lubricant

performance measurement the objective of this research to quantify rail curve

lubricant performance through laboratory simulation has been achieved.

233

REFERENCES

ASTM, I. (1991). ASTM D 2266-91 Standard Test Method for Wear Preventive Characteristics of Lubricating Grease.

ASTM, I. (1997). ASTM D 2596-97 Standard Test Method for Measurement of Extreme-Pressure Properties of Lubricating Grease (Four-Ball Method). ASTM International.

ASTM, I. (1999). ASTM D 1092-99 Standard Test Method for Measuring Apparent Viscosity of Lubricating Greases. ASTM International.

Automation Creations, I. (2005a). AISI 1070 Steel, hot rolled, 19-32 mm (0.75-1.25 in) round. http://www.matweb.com/search/SpecificMaterial.asp?bassnum=M1070B

Automation Creations, I. (2005b). AISI 1080 Steel, as rolled. http://www.matweb.com/search/SpecificMaterial.asp?bassnum=M1080G

Bailey, C.A., Association of Iron and Steel Engineers. (1996). The lubrication engineers manual. 2nd ed. Pittsburgh, Pa., Association of Iron and Steel Engineers.

Beynon, J.H., Kapoor, A., Tyfour, W.R. (1996). Deterioration of rolling contact fatigue life of pearlitic rail steel due to dry-wet rolling-sliding line contact. Wear 197(1-2): 255-65.

Bolton, P.J., Clayton, P. (1984). Rolling--sliding wear damage in rail and tyre steels. Wear 93(2): 145.

Boresi, A.P., Schmidt, R.J. (2003). Advanced mechanics of materials. 6th ed. ed. New York, John Wiley & Sons.

Bowden, F.P., Tabor, D. (2001). The friction and lubrication of solids. Oxford

New York, Clarendon Press Oxford University Press. Bower, A.F. (1988). The Influence Of Crack Face Friction And Trapped

Fluid On Surface Initiated Rolling-Contact Fatigue Cracks. Journal Of Tribology-Transactions Of The Asme 110(4): 704-11.

Bruni, S., Collina, A., Diana, G. (2000). Wheel-rail Contact Models For The Simulation of Rail Vehicle Dynamics - A Survey. AIMETA International Tribology Conference, L'Aquila, Italy.

Byrd, P.F., Friedman, M.D. (1971). Handbook of elliptic integrals for engineers and scientists. 2d ed., rev. ed. Berlin; New York, Springer-Verlag.

Clayton, P. (1995). Predicting the wear of rails on curves from laboratory data. Wear 181-183(1): 11.

234

Clayton, P. (1996). Tribological aspects of wheel-rail contact: A review of recent experimental research. Wear 191(1-2): 170-83.

Clayton, P., Danks, D., Steele, R. (1988). Laboratory Assessment of Lubricants for Wheel/Rail Applications. Lubrication Engineering 45(8): 501-6.

Clayton, P., Reiff, R., Steele, R. (1989). Wheel/Rail Lubricant Performance: In-Track and Laboratory Test Comparisons. The Fourth International Heavy Haul Conference, Brisbane, Queensland, Australia.

Clayton, P., Su, X. (1996). Surface initiated fatigue of pearlitic and bainitic steels under water lubricated rolling/sliding contact. Wear 200(1-2): 63-73.

Deters, L., Proksch, M. (2005). Friction and wear testing of rail and wheel material. Wear 258(7-8): 981-91.

Ekberg, A., Kabo, E. (2005a). Fatigue of railway wheels and rails under rolling contact and thermal loading--an overview. Wear

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1288-300. Ekberg, A., Kabo, E. (2005b). Fatigue of railway wheels and rails under

rolling contact and thermal loading-an overview. Wear 258(7-8): 1288-300.

ESDU (1984). Contact Phenomena II: Stress Fields and Failure Criteria in Concentrated Elastic Contact Under Combine Normal and Tangential Loading. Item No. 84017. ESDU International.

ESDU (1994). Contact Phenomena III: Calculation of Individual Stress Components in Concentrated Elastic Contacts Under Combine Normal and Tangential Loading. Item No. 85007. ESDU International, London.

ESDU (1995). Contact Phenomena. I: Stresses Deflections and Contact Dimensions for Normally-loaded Unlubricated Elastic Components. Item No. 78035. ESDU International.

Fletcher, D.I., Beynon, J.H. (2000). The effect of contact load reduction on the fatigue life of pearlitic rail steel in lubricated rolling-sliding contact. Fat Frac Eng Mat Struct 23(8): 639-50.

Frank, E.E. (1981). Locations of Lubricators. First Rail and Wheel Symposium, Memphis TN, USA.

Franklin, F.J., Weeda, G.J., Kapoor, A., Hiensch, E.J.M. (2005). Rolling contact fatigue and wear behaviour of the InfraStar 2-material rail. Wear 258(7-8): 1048-54.

Giancoli, D.C. (1988). Physics For Scientists and Engineers With Modern Physics. Prentice-Hall International.

Hamrock, B.J. (1994). Fundamentals of Fluid Film Lubrication. McGraw Hill Book Co.

Hannafious, J.H. (1995). Results of rail wear test at FAST, Volume 1: FAST/HAL test summaries. AAR Research Review.

235

Hertz, H. (1882). On The Contact of Elastic Solids. J. reine und angewandte Mathematik 92: 156-71.

Holman, J.P. (1997). Heat transfer. 8th ed. ed. New York, McGraw-Hill Companies.

Huq, M.Z., Celis, J.-P. (2002). Expressing wear rate in sliding contacts based on dissipated energy. Wear 252(5-6): 375-83.

International Heavy Haul Association (2001). Guidelines to Best Practices for Heavy Haul Railway Operations: Wheel and Rail Interface Issues. International Heavy Haul Association.

Ishida, M., Abe, N. (1996). Experimental study on rolling contact fatigue from the aspect of residual stress. Wear 191(1-2): 65.

Jendel, T. (1999). Prediction of Wheel and Rail Wear - A Pilot Study. TRITA - FKT Report 1999:03. Railway Technology, Department of Vehicle Engineering, Royal Institute of Technology, Stockholm. 50

Johnson, K.L. (1985). Contact mechanics. Cambridge [Cambridgeshire]; New York, Cambridge University Press.

Kalker, J.J. (1990). Three-dimensional elastic bodies in rolling contact. Dordrecht, Netherlands, Kluwer Academic.

Kalousek, J., Magel, E., Strasser, J., Caldwell, W.N., Kanevsky, G., Blevins, B. (1996). Tribological interrelationship of seasonal fluctuations of freight car wheel wear, contact fatigue shelling and composition brakeshoe consumption. Wear 191(1-2): 210.

Kik, W., Piotrowski, J. (1996). A fast approximate method to calculate normal load at contact between wheel and rail and creep forces during rolling. 2nd Mini-conference on Contact Mechanics and Wear of Rail-Wheel Systems.

Kondo, K., Yoroizaka, K., Sato, Y. (1996). Cause, increase, diagnosis, countermeasures and elimination of Shinkansen shelling. Wear 191(1-2): 199.

Kuhn, E. (1995). Description of the energy level of tribologically stressed greases. Wear 188(1-2): 138.

Kuhn, E., Balan, C. (1997). Experimental procedure for the evaluation of the friction energy of lubricating greases. Wear 209(1-2): 237-40.

Kumar, S., McDuff, P.J., Witte, A.C., McInerney, D.G. (1991). Development of a Laboratory Test for Rail Lubricants. NLGI 58th Annual Meeting, Phoenix, Arizona, USA.

Lee, K.M., Polycarpou, A.A. (2005). Wear of conventional pearlitic and improved bainitic rail steels. Wear 259(1-6): 391.

Lewis, R., Dwyer-Joyce, R.S. (2004). Wear mechanisms and transitions in railway wheel steels. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 218(6): 467-78.

Lewis, R., Olofsson, U. (2004). Mapping rail wear regimes and transitions. Wear 257(7-8): 721.

236

Lim, S.C., Ashby, M.F. (1986). Wear-Mechanism Maps. CUED/C-mat./TR.123. Cambridge University Engineering Department, Cambridge. 88

Marich, S., Kerr, M., Fogarty, R. (2001a). Optimising Trackside Lubrication for the Wheel/Rail System. RTA Conference.

Marich, S., Mackie, S., Fogarty, R. (2000). The Optimisation of Rail/Wheel Lubrication Practice in the Hunter Valley. RTSA Technical Conference CORE, Adelaide.

Marich, S., Mackie, S., Hill, I. (2001b). The Management of Wheel/Rail Interaction in the High Axle Load Coal Lines of the Hunter Valley. Heavy Haul Conference, Brisbane.

Marich, S., Mutton, P.J. (1989). An Investigation of Severe Wear Under Rolling/Sliding Contact Conditions Existing in Heavy Haul Railways. 7th International Wheelset Conference, Vienna.

Markov, D. (1995). Laboratory tests for wear of rail and wheel steels. Wear 181-183(Part 2): 678-86.

Mulvihill, M.A., Witte, A.C., Kumar, S. (1994). A New Approach to Wheel/Rail Lubrication. NLGI 61st Annual Meeting, Rancho Mirage, California, USA, NLGI (National Lubricating Grease Institute).

Nilsson, R. (2002). Rail Wear Development - Measurements and Evaluation. TRITA - FKT Report 2002:22. Railway Technology, Department of Vehicle Engineering, Royal Institute of Technology, Stockholm. 52

Nolan, S.J. (~2000). The Use of a Controlled Stress Rheometer to Evaluate the Rheological Properties of Grease. 0213. National Lubricating Grease Institute.

O'Rourke, M.D., Johnston, G., Ruvidini, A., Hagaman, B. (1989). Australian Road-Rail Lubrication Tests. The Fourth International Heavy Haul Railway Conference, Brisbane, Queensland, Australia.

Olofsson, U., Telliskivi, T. (2003). Wear, plastic deformation and friction of two rail steels--a full-scale test and a laboratory study. Wear 254(1-2): 80-93.

Pascal, J.P. (1993). About multi-hertzian contact hypothesis and equivalent conicity in the case of S1002 and UIC analytical wheel/rail profiles. Vehicle System Dynamics 22: 57-8.

Polishuk, A.T. (1998). A Brief History or Lubricating Greases. Llewellyn &McKane, Inc.

Quinn, T.F.J. (1991). Physical analysis for tribology. Cambridge; New York, Cambridge University Press.

Reiff, R. (1986). Rail/Wheel Lubrication Studies at FAST. Journal of the American Society of Lubrication Engineers 42(6): 340-9.

Sato, Y. (2005). Historical study on designing Japanese rail profiles. Wear 258(7-8): 1064-70.

237

Scott, W., Mercer, T., Donelan, J. (1998). Laboratory Evaluation of Rail/Wheel Lubricants/Friction Modifiers. Austrib '98 - Tribology at Work, Brisbane, Queensland Australia, The Institution of Engineers Australia.

Shen, Z.Y., Hedrick, J.K., Elkins, J.A. (1983). A comparison of alternative creep force models for rail vehicle dynamic analysis. 16th IA VSD Symp, Cambridge MA.

Thelen, G., Lovette, M. (1996). A parametric study of the lubrication transport mechanism at the rail-wheel interface. Wear 191(1-2): 113-20.

Tyfour, W.R., Beynon, J.H., Kapoor, A. (1995). The steady state wear behaviour of pearlitic rail steel under dry rolling-sliding contact conditions. Wear 180(1-2): 79-89.

Waara, P. (2001). Lubricant influence on flange wear in sharp railroad curves. Industrial Lubrication and Tribology 52(4): 161-8.

Witte, A.C., Kumar, S. (~1986). Design and Laboratory Testing of Rail Lubricants.

Yonggang, M., Jie, Z. (1998). A rheological model for lithium lubricating grease. Tribology International 31(10): 619-25.

238

BIBLIOGRAPHY

Adachi, K., Hutchings, I.M. (2003). Wear-mode mapping for the micro-scale

abrasion test. Wear 255(1-6): 23-9.

Afferrante, L., Ciavarella, M., Demelio, G. (2004). A re-examination of rolling

contact fatigue experiments by Clayton and Su with suggestions for

surface durability calculations. Wear 256(3-4): 329-34.

Ahlstroem, J., Karlsson, B. (2005). Fatigue behaviour of rail steel - a

comparison between strain and stress controlled loading. Wear 258(7-

8): 1187-93.

Ahlstrom, J., Karlsson, B. (2005). Fatigue behaviour of rail steel--a

comparison between strain and stress controlled loading. Wear 258(7-

8): 1187-93.

Akama, M., Mori, T. (2002). Boundary element analysis of surface initiated

rolling contact fatigue cracks in wheel/rail contact systems. Wear

253(1-2): 35-41.

Allen, P.D. (2000). The critical speed of a railway vehicle on a roller rig.

Proceedings of the Institution of Mechanical Engineers 215(2): 55.

Allwood, J., Ciftci, H. (2005). An incremental solution method for rough

contact problems. Wear 258(11-12): 1601-15.

Alwahdi, F., Franklin, F.J., Kapoor, A. (2005). The effect of partial slip on the

wear rate of rails. Wear 258(7-8): 1031-7.

ASTM, I. (1991). ASTM D 2266-91 Standard Test Method for Wear

Preventive Charateristics of Lubricating Grease.

239

ASTM, I. (1997). ASTM D 2596-97 Standard Test Method for Measurement

of Extreme-Pressure Properties of Lubricating Grease (Four-Ball

Method). ASTM International.

ASTM, I. (1999). ASTM D 1092-99 Standard Test Method for Measuring

Apparent Viscosity of Lubricating Greases. ASTM International.

Atzori, B., Meneghetti, G., Susmel, L. (2005). Material fatigue properties for

assessing mechanical components weakened by notches and defects.

Fatigue & Fracture of Engineering Materials and Structures 28(1-2): 83-97.

Automation Creations, I. (2005a). AISI 1070 Steel, hot rolled, 19-32 mm

(0.75-1.25 in) round.

http://www.matweb.com/search/SpecificMaterial.asp?bassnum=M1070B

Automation Creations, I. (2005b). AISI 1080 Steel, as rolled.

http://www.matweb.com/search/SpecificMaterial.asp?bassnum=M1080G

Bailey, C.A., Association of Iron and Steel Engineers. (1996). The lubrication

engineers manual. 2nd ed. Pittsburgh, Pa., Association of Iron and

Steel Engineers.

Bailey, W.J., Weir, I.S. (1998). Investigation of methods for direct rheological

model parameter estimation. Journal of Petroleum Science and Engineering

21(1-2): 1-13.

Ben Cheikh Larbi, A., Cherif, A., Tarres, M.A. (2005). Improvement of the

adhesive wear resistance of steel by nitriding quantified by the energy

dissipated in friction. Wear 258(5-6): 712-8.

Bernasconi, A., Davoli, P., Filippini, M., Foletti, S. (2005). An integrated

approach to rolling contact sub-surface fatigue assessment of railway

wheels. Wear

240

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 973-80.

Bernasconi, A., Filippini, M., Foletti, S., Vaudo, D. (2006). Multiaxial fatigue

of a railway wheel steel under non-proportional loading. International

Journal of Fatigue 28(5-6): 663-72.

Beynon, J.H., Kapoor, A., Tyfour, W.R. (1996). Deterioration of rolling

contact fatigue life of pearlitic rail steel due to dry-wet rolling-sliding

line contact. Wear 197(1-2): 255-65.

Blau, P.J. (1989). Friction and wear transitions of materials: break-in, run-in,

wear-in. Park Ridge, N.J., U.S.A, Noyes Publications.

Bogdanski, S. (2005). Liquid-solid interaction at opening in rolling contact

fatigue cracks. Wear

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1273-9.

Bogdanski, S., Brown, M.W. (2002). Modelling the three-dimensional

behaviour of shallow rolling contact fatigue cracks in rails. Wear

253(1-2): 17-25.

Bogdanski, S., Lewicki, P., Szymaniak, M. (2005). Experimental and

theoretical investigation of the phenomenon of filling the RCF crack

with liquid. Wear

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1280-7.

Bogdanski, S., Stupnicki, J., Brown, M.W., Cannon, D.F. (1999). A two

dimensional analysis of mixed-mode rolling contact fatigue crack

growth in rails. ESIS Publication 25(Multiaxial Fatigue and Fracture):

235-48.

241

Bolton, P.J., Clayton, P. (1984). Rolling--sliding wear damage in rail and tyre

steels. Wear 93(2): 145.

Boresi, A.P., Schmidt, R.J. (2003). Advanced mechanics of materials. 6th ed. ed.

New York, John Wiley & Sons.

Bowden, F.P., Tabor, D. (2001). The friction and lubrication of solids.

Oxford

New York, Clarendon Press

Oxford University Press.

Bower, A.F. (1988). The Influence Of Crack Face Friction And Trapped

Fluid On Surface Initiated Rolling-Contact Fatigue Cracks. Journal Of

Tribology-Transactions Of The Asme 110(4): 704-11.

Bruni, S., Collina, A., Diana, G. (2000). Wheel-rail Contact Models For The

Simulation of Rail Vehicle Dynamics - A Survey. AIMETA

International Tribology Conference, L'Aquila, Italy.

Bruzelius, K., Mba, D. (2004). An initial investigation on the potential

applicability of Acoustic Emission to rail track fault detection. NDT

and E International 37(7): 507-16.

Byrd, P.F., Friedman, M.D. (1971). Handbook of elliptic integrals for

engineers and scientists. 2d ed., rev. ed. Berlin; New York, Springer-

Verlag.

Chang, L.C. (2005). The rolling/sliding wear performance of high silicon

carbide-free bainitic steels. Wear 258(5-6): 730-43.

242

Chen, H., Ishida, M., Nakahara, T. (2005). Analysis of adhesion under wet

conditions for three-dimensional contact considering surface

roughness. Wear 258(7-8): 1209-16.

Chen, Y.-t., Liu, D.-y., Fang, H.-s., Bai, B.-z. (2000). Rolling contact fatigue of

rail steel. Gangtie Yanjiu Xuebao 12(5): 50-3.

Chevalier, L., Cloupet, S., Soize, C. (2005). Probabilistic model for random

uncertainties in steady state rolling contact. Wear 258(10): 1543-54.

Clayton, P. (1995). Predicting the wear of rails on curves from laboratory data.

Wear 181-183(1): 11.

Clayton, P. (1996). Tribological aspects of wheel-rail contact: A review of

recent experimental research. Wear 191(1-2): 170-83.

Clayton, P., Danks, D., Steele, R. (1988). Laboratory Assessment of

Lubricants for Wheel/Rail Applications. Lubrication Engineering 45(8):

501-6.

Clayton, P., Jin, N. (1996). Unlubricated sliding and rolling/sliding wear

behavior of continuously cooled, low/medium carbon bainitic steels.

Wear 200(1-2): 74-82.

Clayton, P., Reiff, R., Steele, R. (1989). Wheel/Rail Lubricant Performance:

In-Track and Laboratory Test Comparisons. The Fourth International

Heavy Haul Conference, Brisbane, Queensland, Australia.

Clayton, P., Su, X. (1996). Surface initiated fatigue of pearlitic and bainitic

steels under water lubricated rolling/sliding contact. Wear 200(1-2):

63-73.

Committee., A.I.H. (1992.). ASM handbook. Volume 18. Friction, lubrication

and wear technology. (Materials Park, Ohio), ASM International.

243

Decuzzi, P., Demelio, G. (2002). The effect of material properties on the

thermoelastic stability of sliding systems. Wear 252(3-4): 311-21.

Degaspari, J. (2001). Silencing the screech of wheel on rail. Engineering World.

11.

Denis, J., Briant, J., Hipeaux, J.-C., Institut Français du Pétrole Publications.

(2000). Lubricant properties analysis & testing. Paris, Editions

Technip.

Descartes, S., Desrayaud, C., Niccolini, E., Berthier, Y. (2005). Presence and

role of the third body in a wheel-rail contact. Wear 258(7-8): 1081-90.

Deters, L., Proksch, M. (2005). Friction and wear testing of rail and wheel

material. Wear 258(7-8): 981-91.

Donzella, G., Faccoli, M., Ghidini, A., Mazzu, A., Roberti, R. (2005). The

competitive role of wear and RCF in a rail steel. Engineering Fracture

Mechanics 72(2): 287.

Doquet, V., Pommier, S. (2004). Fatigue crack growth under non-

proportional mixed-mode loading in ferritic-pearlitic steel. Fatigue &

Fracture of Engineering Materials & Structures 27(11): 1051-60.

Duart, J.M., Pero-Sanz, J.A., Verdeja, J.I. (2005). Rails for high-speed trains.

Fatigue behavior. Revista de Metalurgia (Madrid, Spain) 41(1): 66-72.

Eden, H.C., Garnham, J.E., Davis, C.L. (2005). Influential microstructural

changes on rolling contact fatigue crack initiation in pearlitic rail

steels. Materials Science and Technology 21(6): 623-9.

Ekberg, A., Kabo, E. (2005). Fatigue of railway wheels and rails under rolling

contact and thermal loading--an overview. Wear Contact Mechanics and

Wear of Rail/Wheel Systems 258(7-8): 1288-300.

244

Enblom, R., Berg, M. (2005). Simulation of railway wheel profile development

due to wear--influence of disc braking and contact environment. Wear

258(7-8): 1055-63.

Epp, C.J. (1992). Wheel-Rail Lubrication and Alternative Technologies. NInth

International Rail Track Conference, Perth, Australia.

Epp, C.J., O'Rourke, M.D. (1989). Wheel/Rail Profiling and Lubrication.

Fourth International Heavy Haul Railway Conference, Brisbane, Australia.

Ertz, M. (2002). Creep Force Laws for Wheel/Rail Contact with

Temperature-Dependent Coefficient of Friction.

ESDU (1984). Contact Phenomena II: Stress Fields and Failure Criteria in

Concentrated Elastic Contact Under Combine Normal and

Tangential Loading. Item No. 84017. ESDU International.

ESDU (1994). Contact Phenomena III: Calculation of Individual Stess

Components in Concentrated Elastic Contacts Under Combine

Normal and Tangential Loadin. Item No. 85007. ESDU International,

London.

ESDU (1995). Contact Phenomena. I: Stresses Deflections and Contact

Dimensions for Normally-loaded Unlubricated Elastic Components.

Item No. 78035. ESDU International.

Esteban Fernandez, J., del Rocio Fernandez, M., Vijande Diaz, R., Tucho

Navarro, R. (2003). Abrasive wear analysis using factorial experiment

design. Wear 255(1-6): 38-43.

Fletcher, D.I., Beynon, J.H. (2000). The effect of contact load reduction on

the fatigue life of pearlitic rail steel in lubricated rolling-sliding contact.

Fat Frac Eng Mat Struct 23(8): 639-50.

245

Fletcher, D.I., Franklin, F.J., Kapoor, A. (2003). Image analysis to reveal crack

development using a computer simulation of wear and rolling contact

fatigue. Fatigue & Fracture of Engineering Materials and Structures 26(10):

957-67.

Frank, E.E. (1981). Locations of Lubricators. First Rail and Wheel Symposium,

Memphis TN, USA.

Franklin, F.J., Chung, T., Kapoor, A. (2003). Ratcheting and fatigue-led wear

in rail-wheel contact. Fat Frac Eng Mat Struct 26(10): 949-55.

Franklin, F.J., Weeda, G.-J., Kapoor, A., Hiensch, E.J.M. (2005a). Rolling

contact fatigue and wear behaviour of the infrastar two-material rail.

Wear Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1048-

54.

Franklin, F.J., Weeda, G.J., Kapoor, A., Hiensch, E.J.M. (2005b). Rolling

contact fatigue and wear behaviour of the InfraStar 2-material rail.

Wear 258(7-8): 1048-54.

Fridberg, A.M. (2005). Theory of friction and oscillation of two elastic bodies

in contact and its application to differential rotation of railw ay wheel

treads. Wear 258(7-8): 1091-9.

Galtier, A., Bettembourg, J.P., Perrin, J.L., Joeller, A., Coppola, T.,

Notargiacomo, S., Grijalvo, J. (2004). Contact fatigue of rails under

severe conditions. IRSID,Maizieres-les-Metz,Germany. 1-367

Gates, J.D., Gore, G.J. (1995). Wear of Metals: Philosophies and Practicalities.

Materials Forum 19: 53-89.

Giancoli, D.C. (1988). Physics For Scientists and Engineers With Modern

Physics. Prentice-Hall International.

246

Gladwell, G.M.L. (1980). Contact problems in the classical theory of elasticity.

Alphen aan den Rijn, The Netherlands, Sijthoff & Noordhoff.

Gomez, I., Vadillo, E.G. (2003). A linear model to explain short pitch

corrugation on rails. Wear 255(7-12): 1127-42.

Goryacheva, I.G. (1998). Contact mechanics in tribology. Dordrecht Boston

London, Kluwer Academic Publishers.

Goryacheva, I.G., Goryachev, A.P., Sadegi, F. (1995). Contact of elastic

bodies with thin visco-elastic coatings under conditions of rolling or

sliding friction. Journal of Applied Mathematics and Mechanics 59(4): 607-

14.

Grassie, S., Nilsson, P., Bjurstrom, K., Frick, A., Hansson, L.G. (2002).

Alleviation of rolling contact fatigue on Sweden's heavy haul railway.

Wear 253(1-2): 42-53.

Grassie, S.L. (1991). Mechanics and fatigue in wheel/rail contact: proceedings

of the Third International Conference on Contact Mechanics and

Wear of Rail/Wheel Systems, Cambridge, U.K. July 22-26, 1990.

Amsterdam New York, Elsevier.

Grassie, S.L. (2005). Rolling contact fatigue on the British railway system:

treatment. Wear

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1310-8.

Grassie, S.L., Elkins, J.A. (2005). Tractive effort, curving and surface damage

of rails: Part 1. Forces exerted on the rails. Wear 258(7-8): 1235-44.

Grohmann, H.-D., Schoech, W. (2002). Contact geometry and surface fatigue

- minimizing the risk of headcheck formation. Wear 253(1-2): 54-9.

247

Guduru, R.K., Darling, K.A., Kishore, R., Scattergood, R.O., Koch, C.C.,

Murty, K.L. (2005). Evaluation of mechanical properties using shear-

punch testing. Materials Science and Engineering A 395(1-2): 307-14.

Guicciardi, S., Melandri, C., Lucchini, F., de Portu, G. (2002). On data

dispersion in pin-on-disk wear tests. Wear 252(11-12): 1001-6.

Gunsel, S., Korcek, S., Smeeth, M., Spikes, H.A. (1999). Elastohydrodynamic

friction and film forming properties of lubricant base oils. Tribology

Transactions 42(3): 559-69.

Hamrock, B.J. (1994). Fundamentals of Fluid Film Lubrication. McGraw Hill

Book Co.

Hancock, H. (1958). Elliptic integrals. New York, Dover.

Hannafious, J.H. (1995). Results of rail wear test at FAST, Volume 1:

FAST/HAL test summaries. AAR Research Review.

Hansen, J., Calvert, J. (2003). Eddy current testing: a solution to detecting

rolling contact fatigue in rail. Proceedings - Corrosion & Prevention: Paper

54/1-Paper /9.

Hertz, H. (1882). On The Contact of Elastic Solids. J. reine und angewandte

Mathematik 92: 156-71.

Hiensch, M., Larsson, P.-O., Nilsson, O., Levy, D., Kapoor, A., Franklin, F.,

Nielsen, J., Ringsberg, J.W., Josefson, B.L. (2005). Two-material rail

development: field test results regarding rolling contact fatigue and

squeal noise behaviour. Wear 258(7-8): 964-72.

Hiraoka, N. (2005). A study on mild-to-severe wear transition due to

inconformity of wear-induced shape. Wear 258(10): 1531-5.

248

Holman, J.P. (1997). Heat transfer. 8th ed. ed. New York, McGraw-Hill

Companies.

Hong, H.-S. (2002). The role of atmospheres and lubricants in the oxidational

wear of metals. Tribology International 35(11): 725-9.

Hooke, C.J., Liao, P., Rao, M., Kukureka, S.N., Chen, Y.K. (1996). The

friction and wear of polymers in non-conformal contacts. Wear 200(1-

2): 83-94.

Hou, K., Kalousek, J., Magel, E. (1997). Rheological model of solid layer in

rolling contact. Wear 211(1): 134-40.

Huq, M.Z., Celis, J.-P. (2002). Expressing wear rate in sliding contacts based

on dissipated energy. Wear 252(5-6): 375-83.

Huq, M.Z., Celis, J.P. (1997). Reproducibility of friction and wear results in

ball-on-disc unidirectional sliding tests of TiN-alumina pairings. Wear

212(2): 151-9.

Huq, M.Z., Celis, J.P. (1999). Fretting wear of multilayered (Ti,Al)N/TiN

coatings in air of different relative humidity. Wear 225-229(1): 53-64.

International Heavy Haul Association (2001). Guidlines to Best Practices for

Heavy Haul Railway Operations: Wheel and Rail Interface Issues.

International Heavy Haul Association.

Ishida, M., Abe, N. (1996). Experimental study on rolling contact fatigue from

the aspect of residual stress. Wear 191(1-2): 65.

Iwnicki, S. (2003). Simulation of wheel-rail contact forces. Fatigue &amp;

Fracture of Engineering Materials and Structures 26(10): 887-900.

Iyer. [Personal Communication, Solidworks Instructions].

249

Jendel, T. (1999). Prediction of Wheel and Rail Wear - A Pilot Study. TRITA

- FKT Report 1999:03. Railway Technology, Department of Vehicle

Engineering, Royal Institute of Technology, Stockholm. 50

Jiang, J., Stott, F.H., Stack, M.M. (2004). A generic model for dry sliding wear

of metals at elevated temperatures. Wear 256(9-10): 973-85.

Jin, X., Wu, P., Wen, Z. (2002). Effects of structure elastic deformations of

wheelset and track on creep forces of wheel/rail in rolling contact.

Wear 253(1-2): 247-56.

Johnson, K.L. (1985). Contact mechanics. Cambridge [Cambridgeshire]; New

York, Cambridge University Press.

Judge, T. (2000a). Lubrication optimizes wheel-rail interface.

http://www.rtands.com/feb00/lubricational.html. Railway Track and

Structures.

Judge, T. (2000b). Rail lubrication gaining momentum. RT and S: Railway

Track and Structures 99(2): 23-4.

Kabo, E., Ekberg, A. (2005). Material defects in rolling contact fatigue of

railway wheels--the influence of defect size. Wear Contact Mechanics and

Wear of Rail/Wheel Systems 258(7-8): 1194-200.

Kalker, J.J. (1990). Three-dimensional elastic bodies in rolling contact.

Dordrecht, Netherlands, Kluwer Academic.

Kalousek, J. (2005). Wheel/rail damage and its relationship to track curvature.

Wear 258(7-8): 1330-5.

Kalousek, J., Magel, E., Strasser, J., Caldwell, W.N., Kanevsky, G., Blevins, B.

(1996). Tribological interrelationship of seasonal fluctuations of

250

freight car wheel wear, contact fatigue shelling and composition

brakeshoe consumption. Wear 191(1-2): 210.

Kato, H. (2003). Severe-mild wear transition by supply of oxide particles on

sliding surface. Wear 255(1-6): 426-9.

Kenderian, S., Boro Djordjevic, B., Green Jr., R.E. (2002). Laser based and air

coupled ultrasound as noncontact and remote techniques for testing

of railroad tracks. Materials Evaluation 60(1): 65-70.

Kik, W., Piotrowski, J. (1996). A fast approximate method to calculate normal

load at contact between wheel and rail and creep forces during rolling.

2nd Mini-conference on Contact Mechanics and Wear of Rail-Wheel Systems.

Kim, C.-S., Kim, J.-K., Kim, D.-S. (2002). Evaluation of fatigue strength and

life in rail steel under variable amplitude load. JSME International

Journal, Series A: Solid Mechanics and Material Engineering 45(4): 495-503.

Kim, J.-K., Kim, C.-S. (2002). Fatigue crack growth behavior of rail steel

under mode I and mixed mode loadings. Materials Science &

Engineering, A: Structural Materials: Properties, Microstructure and Processing

A338(1-2): 191-201.

Kondo, K., Yoroizaka, K., Sato, Y. (1996). Cause, increase, diagnosis,

countermeasures and elimination of Shinkansen shelling. Wear 191(1-

2): 199.

Kuhlmann-Wilsdorf, D. (1996). What role for contact spots and dislocations

in friction and wear? Wear 200(1-2): 8-29.

Kuhn, E. (1995). Description of the energy level of tribologically stressed

greases. Wear 188(1-2): 138.

251

Kuhn, E., Balan, C. (1997). Experimental procedure for the evaluation of the

friction energy of lubricating greases. Wear 209(1-2): 237-40.

Kumar, S., McDuff, P.J., Witte, A.C., McInerney, D.G. (1991). Development

of a Laboratory Test for Rail Lubricants. NLGI 58th Annual Meeting,

Phoenix, Arizona, USA.

Lee, K.M., Polycarpou, A.A. (2005). Wear of conventional pearlitic and

improved bainitic rail steels. Wear 259(1-6): 391.

Lewis, R., Dwyer-Joyce, R.S. (2004). Wear mechanisms and transitions in

railway wheel steels. Proceedings of the Institution of Mechanical Engineers,

Part J: Journal of Engineering Tribology 218(6): 467-78.

Lewis, R., Olofsson, U. (2004). Mapping rail wear regimes and transitions.

Wear 257(7-8): 721.

Lim, S.C. (1998). Recent developments in wear-mechanism maps. Tribology

International 31(1-3): 87-97.

Lim, S.C. (2002). The relevance of wear-mechanism maps to mild-oxidational

wear. Tribology International 35(11): 717-23.

Lim, S.C., Ashby, M.F. (1986). Wear-Mechanism Maps. CUED/C-

mat./TR.123. Cambridge University Engineering Department,

Cambridge. 88

Ling, F.F., Bryant, M.D., Doelling, K.L. (2002). On irreversible

thermodynamics for wear prediction. Wear 253(11-12): 1165-72.

Liu, Q.Y., Jin, X.S., Zhou, Z.R. (2005). An investigation of friction

characteristic of steels under rolling-sliding condition. Wear 259(1-6):

439.

252

Liu, Q.Y., Zhang, B., Zhou, Z.R. (2003). An experimental study of rail

corrugation. Wear 255(7-12): 1121-6.

Liu, Z.X., Gu, H.C. (2002). Fatigue failure of rail wheels and mechanical

behavior of wheel steels. Materials Performance 41(1): 58-61.

Lu, X., Cotter, J., Eadie, D.T. (2005). Laboratory study of the tribological

properties of friction modifier thin films for friction control at the

wheel/rail interface. 259(7-12): 1262.

Lundberg, J., Hoglund, E. (2000). A new method for determining the

mechanical stability of lubricating greases. Tribology International 33(3-

4): 217-23.

Magel, E. (1999). Optimizing wheel, rail profiles.

http://www.rtands.com/jul99/optimizing.html. Simmons-Boardman

Publishing Corp.

Magel, E., Kalousek, J., Caldwell, R. (2005). A numerical simulation of wheel

wear. Wear 258(7-8): 1245-54.

Magel, E., Roney, M., Kalousek, J., Sroba, P. (2003). The blending of theory

and practice in modern rail grinding. Fatigue & Fracture of Engineering

Materials and Structures 26(10): 921-9.

Malcolm, B., Raymond, M., Christoph, B., Richard, H., et al. (2005).

Predicting the Occurrence and Effects of Defects in Castings. JOM

57(5): 29.

Marich, S., Kerr, M., Fogarty, R. (2001a). Optimising Trackside Lubrication

for the Wheel/Rail System. RTA Conference.

253

Marich, S., Mackie, S., Fogarty, R. (2000). The Optimisation of Rail/Wheel

Lubrication Practice in the Hunter Valley. RTSA Technical Conference

CORE, Adelaide.

Marich, S., Mackie, S., Hill, I. (2001b). The Management of Wheel/Rail

Interaction in the High Axle Load Coal Lines of the Hunter Valley.

Heavy Haul Conference, Brisbane.

Marich, S., Mutton, P.J. (1989). An Investigation of Severe Wear Under

Rolling/Sliding Contact Conditions Existing in Heavy Haul Railways.

7th International Wheelset Conference, Vienna.

Markov, D. (1995). Laboratory tests for wear of rail and wheel steels. Wear

181-183(Part 2): 678-86.

Markov, D.P. (2001). Tribofatigue of wheel-rail steels. Trenie i Iznos 22(4): 400-

9.

Matsumoto, A., Sato, Y., Nakata, M., Tanimoto, M., Qi, K. (1996). Wheel-rail

contact mechanics at full scale on the test stand. Wear 191(1-2): 101-6.

Matsumoto, A., Sato, Y., Ohno, H., Tomeoka, M., Matsumoto, K., Ogino, T.,

Tanimoto, M., Oka, Y., Okano, M. (2005). Improvement of bogie

curving performance by using friction modifier to rail/wheel

interface: Verification by full-scale rolling stand test. Wear 258(7-8):

1201-8.

Matsumoto, A., Sato, Y., Ono, H., Wang, Y., Yamamoto, M., Tanimoto, M.,

Oka, Y. (2002). Creep force characteristics between rail and wheel on

scaled model. Wear 253(1-2): 199-203.

Matveevsky, R.M. (1965). Trans. ASTM 87: 754.

254

Meehan, P.A., Daniel, W.J.T., Campey, T. (2005). Prediction of the growth of

wear-type rail corrugation. Wear 258(7-8): 1001-13.

Melley, R., Wissner, P. (1997). The Real Costs of Lubrication. AGM-CIM

99th.

Milne-Thomson, L.M. (1950). Jacobian elliptic function tables: a guide to

practical computation with elliptic functions and integrals together

with tables of sn u, cn u, dn u, z(u). New York, Dover.

Mohrbacher, H., Celis, J.-P., Roos, J.R. (1995). Tribology International 28(5): 269.

Mulvihill, M.A., Witte, A.C., Kumar, S. (1994). A New Approach to

Wheel/Rail Lubrication. NLGI 61st Annual Meeting, Rancho Mirage,

California, USA, NLGI (National Lubricating Grease Institute).

Murry, C.R. (1985). Wheel Diameter Requirements for Canefield Railways.

1985 Conference of the Australian Society of Sugar Cane Technologists,

Bundaberg, Queensland, Australia, Watson Ferguson and Company.

Niccolini, E., Berthier, Y. (2005). Wheel-rail adhesion: laboratory study of

"natural" third body role on locomotives wheels and rails. Wear 258(7-

8): 1172-8.

Nilsson, R. (2002). Rail Wear Development - Measurements and Evaluation.

TRITA - FKT Report 2002:22. Railway Technology, Department of

Vehicle Engineering, Royal Institute of Technology, Stockholm. 52

Nolan, S.J. (~2000). The Use of a Controlled Stress Rheometer to Evaluate

the Rheological Properties of Grease. 0213. National Lubricating

Grease Institute.

255

O'Rourke, M.D., Johnston, G., Ruvidini, A., Hagaman, B. (1989). Australian

Road-Rail Lubrication Tests. The Fourth International Heavy Haul

Railway Conference, Brisbane, Queensland, Australia.

Oila, A., Bull, S.J. (2005). Assessment of the factors influencing micropitting

in rolling/sliding contacts. Wear 258(10): 1510-24.

Olofsson, U., Telliskivi, T. (2003). Wear, plastic deformation and friction of

two rail steels--a full-scale test and a laboratory study. Wear 254(1-2):

80-93.

Pascal, J.P. (1993). About multi-hertzian contact hypothesis and equivalent

conicity in the case of S1002 and UIC analytical wheel/rail profiles.

Vehicle System Dynamics 22: 57-8.

Plint, M.A. (1995). Proceeding of the XI NCIT.

Polach, O. (2005). Creep forces in simulations of traction vehicles running on

adhesion limit. Wear 258(7-8): 992-1000.

Polishuk, A.T. (1998). A Brief History or Lubricating Greases. Llewellyn

&McKane, Inc.

Quinn, T. (2002a). Special Issue on 'Wear in oxidative environments'. Tribology

International 35(11): 689.

Quinn, T.F.J. (1991). Physical analysis for tribology. Cambridge; New York,

Cambridge University Press.

Quinn, T.F.J. (2002b). The oxidational wear of low alloy steels. Tribology

International 35(11): 691-715.

Ravikiran, A., Lim, S.C. (1999). A better approach to wear-rate representation

in non-conformal contacts. Wear 225-229(2): 1309-14.

256

Reiff, R. (1986). Rail/Wheel Lubrication Studies at FAST. Journal of the

American Society of Lubrication Engineers 42(6): 340-9.

Riahi, A.R., Alpas, A.T. (2003). Wear map for grey cast iron. Wear 255(1-6):

401-9.

Ringsberg, J.W. (2005). Shear mode growth of short surface-breaking RCF

cracks. Wear

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 955-63.

RINGSBERG, J.W., BERGKVIST, A. (2003). On propagation of short

rolling contact fatigue cracks. Fatigue & Fracture of Engineering Materials

and Structures 26(10): 969-83.

Ringsberg, J.W., Franklin, F.J., Josefson, B.L., Kapoor, A., Nielsen, J.C.O.

(2005a). Fatigue evaluation of surface coated railway rails using

shakedown theory, finite element calculations, and lab and field trials.

International Journal of Fatigue 27(6): 680-94.

Ringsberg, J.W., Skyttebol, A., Josefson, B.L. (2005b). Investigation of the

rolling contact fatigue resistance of laser cladded twin-disc specimens:

FE simulation of laser cladding, grinding and a twin-disc test.

International Journal of Fatigue 27(6): 702-14.

Roussel, N., Le Roy, R., Coussot, P. (2004). Thixotropy modelling at local and

macroscopic scales. Journal of Non-Newtonian Fluid Mechanics 117(2-3):

85-95.

Sato, Y. (2005). Historical study on designing Japanese rail profiles. Wear

258(7-8): 1064-70.

Satoh, Y., Iwafuchi, K. (2005). Crystal orientation analysis of running surface

of rail damaged by rolling contact. Wear 258(7-8): 1126-34.

257

Sawley, K., Kristan, J. (2003). Development of bainitic rail steels with

potential resistance to rolling contact fatigue. Fatigue & Fracture of

Engineering Materials & Structures 26(10): 1019-29.

Sawley, K., Wu, H. (2005). The formation of hollow-worn wheels and their

effect on wheel/rail interaction. Wear 258(7-8): 1179-86.

Scherge, M., Shakhvorostov, D., Pohlmann, K. (2003). Fundamental wear

mechanism of metals. Wear 255(1-6): 395-400.

Scott, W., Mercer, T., Donelan, J. (1998). Laboratory Evaluation of

Rail/Wheel Lubricants/Friction Modifiers. Austrib '98 - Tribology at

Work, Brisbane, Queensland Australia, The Institution of Engineers

Australia.

Shen, Z.Y., Hedrick, J.K., Elkins, J.A. (1983). A comparison of alternative

creep force models for rail vehicle dynamic analysis. 16th IA VSD

Symp, Cambridge MA.

Shevtsov, I.Y., Markine, V.L., Esveld, C. (2005). Optimal design of wheel

profile for railway vehicles. Wear 258(7-8): 1022-30.

Shur, E.A., Bychkova, N.Y., Trushevsky, S.M. (2005). Physical metallurgy

aspects of rolling contact fatigue of rail steels. Wear 258(7-8): 1165-71.

Simanek, D. (1996). Error Analysis (Non-Calculus).

http://www.lhup.edu/~dsimanek/errors.htm. Lock Haven University.

Sladkowski, A., Sitarz, M. (2005). Analysis of wheel-rail interaction using FE

software. Wear 258(7-8): 1217-23.

Smith, R., Mulliah, D., Kenny, S.D., McGee, E., Richter, A., Gruner, M.

(2005). Stick slip and wear on metal surfaces. Wear 259(1-6): 459.

258

Stack, M.M., Chi, K. (2003). Mapping sliding wear of steels in aqueous

conditions. Wear 255(1-6): 456-65.

Tapp, C. (2005). Mechanical properties of rail steel after cyclic deformation.

Fortschritt-Berichte VDI, Reihe 5: Grund- und Werkstoffe/Kunststoffe 719: i-

vii,1-116.

Thelen, G., Lovette, M. (1996). A parametric study of the lubrication

transport mechanism at the rail-wheel interface. Wear 191(1-2): 113-

20.

Thomas E. Karis, R.-N.K.M.S.J. (2003). Harmonic analysis in grease rheology.

Journal of Applied Polymer Science 90(2): 334-43.

Timoshenko, S. (1951). Theory of elasticity. 2d ed. New York, McGraw-Hill.

Tomeoka, M., Kabe, N., Tanimoto, M., Miyauchi, E., Nakata, M. Friction

control between wheel and rail by means of on-board lubrication.

Wear In Press, Uncorrected Proof.

Tyagi, R., Nath, S.K., Ray, S. (2003). Modelling of dry sliding oxidation-

modified wear in two phase materials. Wear 255(1-6): 327-32.

Tyfour, W.R., Beynon, J.H., Kapoor, A. (1995). The steady state wear

behaviour of pearlitic rail steel under dry rolling-sliding contact

conditions. Wear 180(1-2): 79-89.

Ueda, M., Matsushita, K., Onodera, N., Yamamoto, T. (2005a). High carbon

steel rails with excellent resistance to surface scratching and internal

fatigue damaging. Application: JP

JP, (Nippon Steel Corp., Japan). 19 pp.

259

Ueda, M., Matsushita, K., Onodera, N., Yamamoto, T. (2005b). Pearlitic rails

with with resistance to surface scratching and internal fatigue

damaging and method for their manufacture. Application: JP

JP, (Nippon Steel Corp., Japan). 20 pp.

Ueda, S., Uchino, K. (2003). Pearlitic steel rails with high resistance to wear

and inner fatigue damage. Application: JP

JP, (Nippon Steel Corp., Japan). 11 pp.

Van, K.D., Maitournam, M.H. (2002). On some recent trends in modelling of

contact fatigue and wear in rail. Wear 253(1-2): 219-27.

Viafara, C.C., Castro, M.I., Velez, J.M., Toro, A. (2005). Unlubricated sliding

wear of pearlitic and bainitic steels. Wear 259(1-6): 405.

Waara, P. (2001). Lubricant influence on flange wear in sharp railroad curves.

Industrial Lubrication and Tribology 52(4): 161-8.

Waara, P., Hannu, J., Norrby, T., Byheden, A. (2001). Additive influence on

wear and friction performance of environmentally adapted lubricants.

Tribology International 34(8): 547-56.

Walther, F., Eifler, D. (2003). Evaluation of the fatigue behavior of wheel

steels on the base of strain, temperature and resistance measurements.

Zeitschrift fuer Metallkunde 94(5): 505-10.

Walther, F., Eifler, D. (2004). Fatigue behaviour of railway wheels at different

temperatures: Interrelation of the microstructure and the fatigue

behaviour of railway wheels at ambient and elevated temperatures.

Materialpruefung 46(4): 158-62.

260

Wang, F., Zhou, D., Shi, H.J., Mesmacque, G. (1999). Numerical analysis of

rail rolling contact fatigue. Fatigue '99, Proceedings of the International

Fatigue Congress, 7th, Beijing, China, June 8-12, 1999 4: 2591-6.

Wang, L., Pyzalla, A., Stadlbauer, W., Werner, E.A. (2003). Microstructure

features on rolling surfaces of railway rails subjected to heavy loading.

Materials Science and Engineering A 359(1-2): 31-43.

Wellman, R.G., Nicholls, J.R. (2004). High temperature erosion-oxidation

mechanisms, maps and models. Wear 256(9-10): 907-17.

Witte, A.C., Kumar, S. (~1986). Design and Laboratory Testing of Rail

Lubricants.

Wu, T.X., Thompson, D.J. (2005). An investigation into rail corrugation due

to micro-slip under multiple wheel/rail interactions. Wear 258(7-8):

1115-25.

Yang, S.H., Kong, H., Yoon, E.-S., Kim, D.E. (2003). A wear map of bearing

steel lubricated by silver films. Wear 255(7-12): 883-92.

Yonggang, M., Jie, Z. (1998). A rheological model for lithium lubricating

grease. Tribology International 31(10): 619-25.

Yousif, A.E. (1983). The tribological characteristics of lubricating greases in

heavily loaded contacts. 85(3): 273.

Yuan, C.Q., Peng, Z., Zhou, X.C., Yan, X.P. (2005). The surface roughness

evolutions of wear particles and wear components under lubricated

rolling wear condition. Wear 259(1-6): 512.

Zakharov, S.M., Goryacheva, I.G. (2005). Rolling contact fatigue defects in

freight car wheels. Wear

261

Contact Mechanics and Wear of Rail/Wheel Systems 258(7-8): 1142-7.

Zakharov, S.M., Zharov, I.A. (2005). Criteria of bogie performance and

wheel/rail wear prediction based on wayside measurements. Wear

258(7-8): 1135-41.

Zerbst, U., Madler, K., Hintze, H. (2005). Fracture mechanics in railway

applications--an overview. Engineering Fracture Mechanics 72(2): 163.

262

APPENDIX A

A. Seizure Wear

Lim and Ashby (1986) defines seizure wear as the catastrophic shear of

junctions formed at the interface. This wear is also referred to as adhesive

wear. Bowden and Tabor (Bowden and Tabor 2001) investigated the metallic

junctions which form at interfaces and later Tabor investigated the effects of

shear on these metallic junctions. Bowden and Tabor's (2001) work is the

basis for the seizure wear model.

The model is constructed by defining the asperity pressure

r

F HA

= (1.2)

Where

F = Normal force on sliding interface (N)

rA = Real area of contact (m2) (small compared to nominal contact area)

H = Hardness of sliding surface (N/m2)

This then is developed to include the shear stress ( / rs F Aμ= ) due to

friction.

2

2 2t

r

F s HA

α⎛ ⎞

+ =⎜ ⎟⎝ ⎠

(1.3)

tα is an experimentally determined coefficient with a typical value of 12.

Seizure occurs, according to this model, when the real area of contact ( rA )

263

equals the nominal area of contact ( nA ). Therefore substituting the shear

force and contact area, then rearranging into the dimensionless form gives

equation

( )1

2 21rt

F HA

=+α μ

(1.4)

( ) 12 2

1

1 ot

HFH

=+α μ

(1.5)

In the case of unlubricated sliding for steel the coefficient of friction can be

given by Equation (1.6). This relationship has been developed from the

literature by Lim and Ashby (1986).

100.88 0.13log ( )vμ = − % (1.6)

Lim and Ashby (1986) proposes that the ratio of hardness can be set to unity,

simplifying the model. This is explained by the two mechanisms, temperature

related hardness and velocity related strain rate. Hardness decreases with

increasing temperature but the increasing temperature arises from increasing

surface velocity. The increase in surface velocity increases the strain rate

changing the material response which increases the measured hardness.

B. Melt Wear

High sliding speeds and pressure can develop high surface temperatures

which can exceed the melting point of the materials. The melting material

then behaves as a lubricant in the hydrodynamic regime. The viscous energy

developed in the liquid material is then dissipated to the surfaces increasing

the temperature of the surrounding material and subsequently increasing the

volume of molten material. Melt wear can be identified by the molten material

leaving the contact area.

264

Lim and Ashby(1986) presented the following equations to predict melt wear.

Equation (1.7) describes frictional heat energy.

mm

n

Vq K T L

Aα = − ∇ + (1.7)

Where

α = heat distribution coefficient

q = power input per unit area

mK = thermal conductivity of metal

T∇ = temperature gradient

L = latent heat of fusion per unit volume

mV = volumetric rate of molten material production

Frictional heat energy, qα , is equal to the sum of the heat conducted away

and the latent heat absorbed by the molten material. Next we define the

frictional energy and the temperature gradient and include them in Equation

(1.7) to give Equation (1.8).

( )m m o m

n b n

K T T VFv LA l A

αμ −= + (1.8)

Further, the molten material is assumed to be totally lost and gives the normalised wear rate of the following equation.

m

n

VW

vA= (1.9)

Rearranging the previous equations give Equation 2.9 for melt wear in non-dimensional terms.

265

*

*

1( ) [ 1]( )

m o o

m o

T T H TW FvL v T TT

αμ−= −

−% (1.10)

This equation has constants which are approximated with developed

equations. Similar to the previous model these equations or constants need to

be modified to suit rail/wheel steels and lubricated sliding conditions.

Equations (1.7) to (1.10) need to be modified prior to their application to

rail/wheel steels and lubricated sliding conditions by varying the values of the

constants within the equations.

C. Oxidational wear

Wear particles from sliding systems can take the form of molten metal, metal

particles and metal oxide particles. Oxide particles form when the critical flash

temperature corresponding to the oxidation activation energy is reached in an

oxidative environment. Lim and Ashby (1986) found that flash temperature is

predominantly affected by sliding speed therefore indicating that oxidation

rate is a function of velocity. Load was not found to have a significant effect

on flash temperature (Lim and Ashby 1986).

The process of oxidation wear is divided into two categories according to the

severity of oxidation. Mild oxidation, which refers to sliding speeds below 1

m/s and surfaces that have thin patchy oxidised films and severe oxidation,

which occurs at higher sliding speeds and is signified by continuous and

thicker oxidised films.

It is important to remember that the names of the wear regimes do not refer

to their wear rates but rather to the extent of oxidation. Wear rates for severe

oxidation are commonly lower than those for mild oxidation.

D. Mild-oxidational wear

Quinn (1991) proposes that flash heating at the contacting asperities causes

oxidation at the surface of these asperities. Once the oxide film has reached a

266

critical thickness this becomes detached as a wear particle and the process of

oxide formation begins again.

The model which Quinn proposes (developed and iterated over ~30years) is

based on a parabolic kinetic equation. Iron and steel tested experimentally fits

this parabolic equation but it is not suitable for all material types (Lim and

Ashby 1986).

2pm k tΔ = (1.11)

mΔ = Mass of oxygen used per unit area

pk = Parabolic rate constant

exp[ ]op o

Qk A

RT= − (1.12)

oA = Arrhenius constant

oQ = Activation energy

R = Gas constant

T = Absolute temperature

The model assumes that at a critical thickness the oxidised material will

become a wear particle. This gives the next equation in which the oxide

proportions are used to calculate the oxides. In a sliding, steel on steel contact

different oxides can form. Lim proposes that the average composition is

3 4Fe O which gives the proportion of 1 mol of Fe to 2/3 of 2O . Oxides will

add mass to the surface with the following equation.

267

2

2 ( / )3 Fe Fe O Fem V M MρΔ = Δ (1.13)

FeVΔ = volume of iron

Feρ = density of iron

2OM = molecular weight of oxygen

FeM = molecular weight of iron

Substituting the thickness of oxides, Z is equal to FeVΔ , into equation (1.14).

2

2 2

32

p

Fe

O Fe

Z C k t

MCM ρ

=

⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠

(1.14)

Using equation (1.14) the time for a critical thickness to form is equated.

2

2 exp[ / ]c

co o f

tC A Q RT

Z=−

(1.15)

In this model, wear is taken to be the removal of this oxide volume. Wear is

the volume, the product of rA and cZ , lost in a specified time. Therefore

wear rate is the ratio of rA and cZ to the distance slid, cvt giving the equation

(1.16).

2

exp[ ]r o o

c f

A C A QW

vZ RT= − (1.16)

The equation proposed by Lim and Ashby (1986) differs from the equation

presented by Quinn (1991) in that the former removes a fraction which

268

relates to Quinn’s use of the Archard's Law and Hertzian contact in the

model. The value of this term approaches unity and is therefore ignored.

Finally the mathematical model is presented in the normalised variables in

equation (1.17).

2

expo o o

c f

c A r Q FWz a RT v

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠ ⎣ ⎦

β (1.17)

In this model there are two parameters, the Arrhenius activation constant and

the activation energy for oxidation, which need to be calibrated to the system.

Static measurements of these parameters do not provide a good correlation

with experimental wear data, because the mechanical loading changes the

system and therefore changes the constants. Lim proposes to keep the

activation energy constant, the same as that measured in static laboratory

testing. Thus the Arrhenius activation constant refers to how the oxides grew

and in this case the growth is promoted by mechanical deformation.

Martensite forms under these conditions which changes the material

properties at the interface. Measured wear data shows a reduction in wear rate

following the formation of martensite. The reduction is explained by the

increase in hardness of this phase. Prediction of this phase transition is not

modelled by these equations, but can be, by changing the hardness values

chosen. This model tries to encompass a transition portion of the wear map

and as such, has a large variability in parameters. There is still more work to

be done to develop a more robust model.

E. Severe-oxidational wear

Severe-oxidational wear is encountered in a system of high sliding speed

where extensive oxides are formed. The oxides form a protective layer where

they plastically deform, melt and solidify. Lim devised a new model for this

type of wear. The assumptions made are:

269

Contacts are hot enough to melt.

The molten oxides spread heat in a uniform manner.

The material which is not oxidised maintains the bulk temperature.

Molten oxides will be lost to some degree.

The heat input to the surface is dissipated in two ways, the first by conduction

and the second by melting material.

( )

( )ox

ox m b rox m

f n

K T T AL V q

l Aα −

= − (1.18)

oxL = latent heat of oxide

mV = Rate of molten material production

fl = Equivalent heat flow length

oxK = Thermal conductivity of oxide

oxmT = Oxide melting point

Using the relationship of input energy equals the frictional energy of the

interface and defining the normalised wear rate as /m mW f V v=% gives the

model equation (1.19).

1

2 12( ) ( ) [ ( ) 1]

( )

oxox m b o

m oxox ox m b

K T T aHFN FW f vL a v NK T T

αμ−= −

−% (1.19)

mf = Fraction of material lost

270

In this model the only adjustable parameter is the fraction of material lost

which Lim proposes is ~0.01. In the course of wear measurements within this

regime this parameter has been suitably adjusted.

F. Plasticity dominated wear

Plasticity dominated wear is encountered at low sliding speeds and as the

name suggests plastic deformation occurs at the surface. Shear forces can

deform, cut and or plough asperities from the surface. There is also

delamination in this wear mode where sub-surface cracks grow from the

cyclic loading until a wear particle is formed and removed.

Archard’s law is presented here as the overriding equation. This equation has

one adjustable parameter Ak which experimentally has been seen to change

over a number of orders of magnitude.

AW k F= (1.20)

*

2 o vA

A

fk

fγ

= (1.21)

The Archard wear constant, Ak is the relationship of the volume fraction of

inclusions in the materials vf , the rate of plastic strain, oγ , and the area

fraction of voids, *Af . These parameters are all variable and require calibration

against suitable wear data. This model is widely used but it lacks the depth to

accurately model a variety of systems without modification of the constant.

Despite this disadvantage until a more suitable model arises this one will be

used.

271

APPENDIX B

A. Validation of Software for Rectangular Contact

The rectangular contact method of the ESDU, used as the basis for the

computer method to calculate the values for a rectangular contact, is

compared against published results from Hamrock (2003) and Boresi and

Schmidt (Hamrock 1994). This process is carried out to show the variation in

methodologies and the applicability of the method selected for this

investigation.

PARAMETER VALUE UNITS Load, P 1000 N/m

Body 1 composition Silicon nitride steel Young’s modulus 314 GPa

Poisson’s ratio 0.26 Body 2 composition Stainless steel

Young’s modulus 193 GPa Poisson’s ratio 0.3

Body 1 – Radius 1 0.02 M Body 2 – Radius 1 0.1 M

Table 32 – Example values for needle roller in bearing race (2003).

PARAMETER HAMROCK RESULT

CURRENT METHOD

DIFFERENCE %

Major semi-axis (µm) 15.6 15.6 0 Normal approach (µm)

0.0405 0.0404 0.25

Maximum normal pressure (MPa)

40.68 40.71 0.07

Table 33 – Comparison of results between calculation methods.

The example of twin disk fatigue testing machine is now presented. The

results of the rectangular contact method presented by the ESDU are

compared to the results obtained from Boresi and Schmidt (2003). Two

272

testing machines are considered for this example, one without friction and

one with friction (μ=0.1).

PARAMETER VALUE UNITS Load, P 24100/0.02 N/m

Body composition Steel Young’s modulus 200 GPa

Poisson’s ratio 0.29 Body 1 – Radius 1 0.04 M Body 2 – Radius 1 0.04 M

Table 34 – Example values for twin-disk fatigue testing device with identical steel samples (ESDU 1995).

PARAMETER BORESI AND SCHMIDT RESULT

CURRENT METHOD

DIFFERENCE %

Major semi-axis (µm) 530.1 530.1 0 Normal approach (µm)

Not given 31.7 N.A.

Maximum normal pressure (MPa)

1447 1447 0

Maximum tensile stress with friction (MPa)

322 321.2 0.27

Maximum compressive stress with friction (MPa)

1635 (1445) 1616.5(1446.7) 1.13(0.11)

Maximum shear stress with friction (MPa)

449 (433) 442(434.5) 1.56(0.35)

Maximum octahedral shear stress with friction (MPa)

369 (361) 389(383) 5.14(5.74)

Table 35 – Comparison of results between calculation methods of contact stresses for twin disk fatigue testing machine (Values in parentheses calculated without friction/traction force).

273

Both methods present similar results and the errors between the methods do

not exceed 5.74%, showing that the two methods produce comparable

results.

B. Validation of software for Elliptical Contact

The ESDU method (ESDU 1995) gives examples to illustrate the calculation

procedure for elliptical contacts. These examples will be used to verify the

Contact Software against the graphical method presented by the ESDU. The

first example is of two crossed cylinders as shown in Figure 126.

Figure 126 – Two crossed cylinders calculation example(ESDU 1995).

The input parameters are given in Table 36.

PARAMETER VALUE UNITS Load, P 1250 N

Body 1 composition Mild steel Young’s modulus 207 GPa

Poisson’s ratio 0.3 Body 2 composition Brass

Young’s modulus 101 GPa Poisson’s ratio 0.35

Body 1 – Radius 1 ∞ M Body 1 – Radius 2 0.025 M Body 2 – Radius 1 ∞ M Body 2 – Radius 2 0.075 M

Angle between axes 40 Degree Table 36 – Example values for crossed cylinders of differing materials (2003).

274

The results from ESDU and from the author’s calculation method for the

example in Table 36 are presented in Table 37.

PARAMETER ESDU RESULT

CURRENT METHOD

DIFFERENCE %

Major semi-axis (mm) 1.896 1.90432 0.44 Minor semi-axis (mm) 0.404 0.4028415 0.29 Normal approach (mm)

0.01195 0.01214 1.59

Maximum normal pressure (MPa)

780 778 0.25

Table 37 – Comparison of results between calculation methods.

Further comparison between the ESDU and the author’s results are presented

in Table 38. The contact angle between the two cylinders presented in Figure

126 has been altered from 40 to 90 degrees for this analysis.

PARAMETER ESDU RESULT

CURRENT METHOD

DIFFERENCE %

Major semi-axis (mm) 1.142 1.14697 0.43 Minor semi-axis (mm) 0.551 0.55356 0.46 Normal approach (mm)

0.01494 0.01490 0.27

Maximum normal pressure (MPa)

940 940 0

Table 38 – Comparison of results between calculation methods of ESDU and author’s for principal axis angle of 90 degrees.

There is a limitation to the resolution of the interpretation of the graphs used

in the ESDU method. The error involved in reading values from the graphs

provided within the ESDU method could potentially become quite high as

there are often multiple graphs associated with any one calculation. It should

be noted that the solutions presented here from the ESDU graphical method

were included within the ESDU documentation and were not calculated by

the Author. In absolute terms the error between the ESDU graphical method

and the Contact Software is less than one percent.

275

Further validation of the Contact Software for an elliptical contact was carried

out via a comparison results presented by Boresi and Schmidt (2003). This

example is of two steel toroids in contact with an angle between the principal

axes.

PARAMETER VALUE UNITS Load, P 4500 N

Body composition Mild steel Young’s modulus 200 GPa

Poisson’s ratio 0.29 Body 1 – Radius 1 0.06 M Body 1 – Radius 2 0.13 M Body 2 – Radius 1 0.08 M Body 2 – Radius 2 0.2 M

Angle between axes 60 Degree Table 39 – Elliptical contact example for two toroids in contact (2003).

PARAMETER BORESI AND SCHMIDT RESULT

SOFTWARE METHOD

DIFFERENCE %

Major semi-axis (µm)

Not given 1309 NA

Minor semi-axis (µm)

965 1000 3.6

Normal approach (µm)

29 27 6.9

Maximum compressive stress (MPa)

1586 1642 3.5

Maximum shear stress (MPa)

529 525 0.8

Maximum octahedral shear stress (MPa)

485 482 0.6

Depth of maximum shear stresses (mm)

0.51 0.55 7.8

Table 40 - Comparison of results between calculation methods of Boresi and Schmidt (1985) and author’s.

276

The results in Table 40 show a larger difference in results between calculation

methods than in the previous examples presented in Table 37 and Table 8.

The larger than expected errors between these two methods is a consequence

of the fact that Boresi and Schmidt (2003) present their results in terms of

stresses of interest rather than as a stress tensor. Approximation coefficients

are used by Boresi and Schmidt (2003) to transform the single maximum

stress value into the stress parameters. Calculation of the stress parameters

from the principal stresses obtained from the contact software was then

required to compare results between the Contact Software and the results

presented by Boresi and Schmidt (2003).

277

APPENDIX C – TECHNICAL DRAWINGS

278

279