PERFORMANCE MEASUREMENTS OF RAIL CURVE ... - QUT ePrints

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

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 ii

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 iii

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

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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

v

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

vi

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

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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 f ( x ) = ae

− bx

+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

f ( x ) = ae − bx ........................................................................................................ 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 f ( x ) = ae

− bx

+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

f ( x ) = ae − bx ........................................................................................................ 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 f ( x ) = ae

− bx

+c.

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

f ( x ) = ae − bx ........................................................................................................ 188

FIGURE 103 – APPARENT VISCOSITY FOR GROUP 3. ........................................................... 189

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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 f ( x ) = ae

− bx

+c.

(BOTTOM) VALUE OF PREDICTED MINIMUM SLIP ‘C’. ............................................... 195 FIGURE 110 - HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 4 TESTING USING

f ( x ) = ae − bx ........................................................................................................ 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

ix

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 117 MACHINING AND AT THE COMPLETION OF ALL LUBRICATED TESTING. 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 1 140 TEST PARAMETERS. SUBSCRIPTS REFER TO INPUT AND OUTPUT SHAFTS. 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

f ( x ) = ae − bx .

169

TABLE 26 – HALF LIFE VALUES FOR EACH LUBRICANT IN GROUP 1 TESTING USING

f ( x ) = ae − bx .

179

x


f ( x ) = ae − bx .

188


f ( x ) = ae − bx .

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

xi

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:____________________________________

xii

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.

xiii

NOMENCLATURE

a = Major ellipse semi axis or contact half width

Ac = Contact area ∂Ac = Error in contact area

a y = Acceleration in the ‘y’ direction A, B = Geometry parameters b = Minor ellipse semi axis or contact half width

bo = Gauge width

D = Distance rolled ∂D = Error in distance rolled

Di = Distance rolled of input shaft ∂Di = Error in distance rolled of input shaft

Do = Distance rolled of output shaft ∂Do = Error in distance rolled of output shaft

Ds = Distance slid ∂Ds = Error in distance slid

xiv

DT = Total distance slid ∂DT = 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

Es = Sliding energy ∂Es = Error in sliding energy

ET = Total Absorbed energy ∂ET = Error in absorbed energy E ( m ) = Complete elliptical integral of the second kind f ( x ) = Function of x

F = Friction force FBT = Force from shearing lubricant FF = Flange force

g = acceleration due to gravity

xv

ha = Super-elevation of rail h%min = Minimum film thickness

K = Contact width equation constant ki = Material constant, i denotes body number K ( m ) = Complete elliptical integral of the first kind

L = Length of rectangular contact Δl = Change in length

l0 = Original length mT = 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 Pf = Power absorbed by friction in simulator Pmax = Maximum power Pi = Power of input shaft ∂Pi = Error in power of input shaft

p0 = Maximum pressure xvi

Po = Power of output shaft ∂Po = Error in power of output shaft

Ps = Power absorbed by lubricant ∂Ps = Error in power absorbed by lubricant

Qx = Tractive force in direction of rolling

r = Rolling radius ∂r = Error in rolling radius

R = Effective contact radius Rc = Curve radius RD = Curvature difference Rii = Radius of curvature, first i denotes body number and second i axis number

ri = Rolling radius of input shaft ∂ri = Error in rolling radius of input shaft

ro = Rolling radius of output shaft ∂ro = Error in rolling radius of output shaft

Rx = Effective radius in ‘x’ direction

xvii

Ry = Effective radius in ‘y’ direction t = Sample time

T = Torque ∂T = Error in torque

TBF = Bearing friction torque TC = Transmitted torque through contact patch tt = Thickness TT = Torque transducer torque

ΔT = Change in temperature Ti = Torque of input shaft ∂Ti = Error in torque of input shaft

To = Torque of output shaft ∂To = Error in torque of output shaft

Tmax = Maximum torque u% = Mean surface velocity v = Surface velocity

∂v = Error in surface velocity

xviii

vi = Surface velocity of input shaft ∂vi = Error in surface velocity of input shaft

vo = Surface velocity of output shaft ∂vo = Error in surface velocity of output shaft

us , vs = Sliding velocity ∂vs = Error in sliding velocity

vT = Train velocity ΔV = Change in volume

VH = Volume when heated V0 = Original volume W = Dimensionless load parameter w = Rotational Speed ∂w = Error in rotational speed

wi = Rotational Speed of input shaft ∂wi = Error in rotational speed of input shaft

wo = Rotational Speed of output shaft ∂wo = Error in rotational speed of output shaft xix

wz = Load per unit width x = Distance slid

y = Lubricant film thickness

α l = Linear thermal expansion coefficient

μ = Coefficient of friction ξ = Experimental slip ratio ξ PV = Pressure viscosity coefficient ∂ξ = Error in experimental slip ratio

ξ x = Slip ratio in the direction of rolling αV = Volume thermal expansion coefficient φ = Diameter δ = Normal approach of bodies

σ y = Yield stress τ y = Shear yield stress σ US = Ultimate tensile strength τ US = Ultimate shear yield strength

xx

σ = Poisson’s ratio

σ x , σ y , σ z = Stresses in principal directions

η = Apparent viscosity ∂η = Error in apparent viscosity

τ = Shear stress ∂τ = Error in shear stress

τ xy ,τ yz ,τ zx = Shear stresses in principal directions τ e = 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 η0 = 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 xxi

Chapter 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

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.

2

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. 3

•

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.

4

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.

5

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.

6

Chapter 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.

7

This figure is not available online. Please consult the hardcopy thesis available from the QUT Library

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. 8

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. 9


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 10

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 11

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 12

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 13

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.

14

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.

15

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.

16

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.

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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

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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 19

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 20

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.

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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 22

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.

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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 24

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 25

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

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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.

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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.

This image is not available online. Please consult the hardcopy thesis available from the QUT Library

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

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


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

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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 30

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 31

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.

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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.

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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).

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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

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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.

This table is not available online. Please consult the hardcopy thesis available from the QUT Library

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.

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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.

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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. 38

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. 39

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) 40

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

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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. 42

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.

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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.

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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

45

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 inservice 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.

46

Chapter 3

THEORETICAL CALCULATIONS: CONTACT MECHANICS OF INSERVICE 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 47

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 48

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

49

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 50

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.

51

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)

(1 − σ ) = 2

ki

E'=

πE

2π ( k1 + k2 )

ki = material constant, i denotes body number 52

(3.1)

(3.2)

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) 1 ⎛ 1 1 ⎞ ⎛ 1 1 ⎞ =⎜ + + ⎟+⎜ ⎟ R ⎝ R11 R21 ⎠ ⎝ R12 R22 ⎠

1⎛ 1 1 ⎞ + A= ⎜ ⎟ 2 ⎝ R12 R22 ⎠ 1⎛ 1 1 ⎞ + B= ⎜ ⎟ 2 ⎝ R11 R21 ⎠

(3.3)

(3.4)

R = Effective contact radius Rii = 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.

53

1 ⎡ 2 2 ⎡⎛ 1 ⎤ 2⎤ ⎞ ⎛ ⎞ 1 1 1 ⎢ ⎢⎜ ⎥ ⎥ − − ⎟ +⎜ ⎟ ⎢ R R R R 1 1 1 1 1 ⎢⎝ 11 ⎥ ⎥ ⎝ 21 12 ⎠ 22 ⎠ A= ⎢ + + + −⎢ ⎥ ⎥ 4 ⎢ R11 R12 R21 R22 ⎢ +2 ⎛ 1 − 1 ⎞⎛ 1 − 1 ⎞ cos 2ω ⎥ ⎥ ⎢ ⎟ ⎢ ⎜⎝ R11 R12 ⎟⎜ ⎥ ⎥ ⎠⎝ R21 R22 ⎠ ⎣ ⎦ ⎥⎦ ⎢⎣ 1 ⎡ 2 2 ⎡⎛ 1 ⎤ 2⎤ ⎞ ⎛ ⎞ 1 1 1 ⎢ ⎢⎜ ⎥ ⎥ − − ⎟ +⎜ ⎟ ⎢ R R R R 1 1 1 1 1 ⎢⎝ 11 ⎥ ⎥ ⎝ 21 12 ⎠ 22 ⎠ B= ⎢ + + + +⎢ ⎥ ⎥ 4 ⎢ R11 R12 R21 R22 ⎢ +2 ⎛ 1 − 1 ⎞ ⎛ 1 − 1 ⎞ cos 2ω ⎥ ⎥ ⎢ ⎢ ⎜⎝ R11 R12 ⎟⎠ ⎜⎝ R21 R22 ⎟⎠ ⎥ ⎥ ⎣ ⎦ ⎥⎦ ⎢⎣

1 2A 1 Rx = 2B 1 1 1 = + R Rx Ry

(3.5)

Ry =

RD =

(3.6)

B− A A+ B

RD = Curvature difference Rx = Effective radius in ‘x’ direction Ry = 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 54

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 ⎡ ⎛P⎞ ⎡ R R ⎤⎤ b = ⎢ 4 ⎜ ⎟ ( k1 + k2 ) ⎢ 11 21 ⎥ ⎥ ⎣ R11 + R21 ⎦ ⎦ ⎣ ⎝L⎠

1

2

(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). ⎛ P ⎞ ⎡ ⎛ 4 R11 ⎞ 1 ⎤ ⎛ P ⎞ ⎡ ⎛ 4 R21 ⎞ 1 ⎤ ⎟ ⎢ln ⎜ ⎟ − ⎥ + 2k1 ⎜ ⎟ ⎢ln ⎜ ⎟− ⎥ ⎝ L ⎠ ⎣ ⎝ b ⎠ 2⎦ ⎝ L ⎠ ⎣ ⎝ b ⎠ 2⎦

δ = 2k1 ⎜

(3.8)

δ = Normal approach of bodies The pressure distribution across the rectangular contact is given by ⎡ y2 ⎤ p ( y ) = p0 ⎢1 − 2 ⎥ ⎣ b ⎦

1

2

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

p0 = Maximum pressure The maximum direct stress ( p0 ) is given by 55

(3.9)

⎛P⎞ 2 p0 = ⎜ ⎟ ⎝ L ⎠ πb

(3.10)

3.4.2 Elliptical Contact Equations The contact dimensions are calculated using the methods of Hamrock (1995) and the ESDU (1995).

β=

b a

(3.11)

⎛ 6 β 2 E ( m ) PR ⎞ b=⎜ ⎟ πE' ⎝ ⎠

⎛ 6 E ( m ) PR ⎞ a=⎜ ⎟ ⎝ πβ E ' ⎠

1

1

3

(3.12)

3

(3.13)

2 ⎡ ⎛ P ⎞ ⎤ 9 δ = K ( m) ⎢ ⎜ ⎟ ⎥ ⎢⎣ 2 E ( m ) R ⎝ πβ E ' ⎠ ⎥⎦

1

3

(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

CaW ⎛ A ⎞ a= ( A + B ) ⎜⎝ B ⎟⎠

56

−1

3

(3.15)

C W ⎛ A⎞ b= b ( A + B ) ⎜⎝ B ⎟⎠

1

3

(3.16)

W = Dimensionless load parameter

Where the coefficients are given by 1

⎡ 2E ( m) ⎤ 3 ⎛ A ⎞ Ca = ⎢ ⎜ ⎟ 2 ⎥ ⎣ πβ ⎦ ⎝ B ⎠ 1

1

⎡ 2E ( m) β ⎤ 3 ⎛ A ⎞ Cb = ⎢ ⎥ ⎜ ⎟ π ⎣ ⎦ ⎝B⎠

3

−1

(3.17)

3

(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). 2⎤ ⎡3 W = ⎢ Pπ ( k1 + k2 )( A + B ) ⎥ ⎣4 ⎦

1

3

(3.19)

The distance of surface deformation at the centre of the contact is given by Equation (3.20).

C W2 ⎛ A⎞ δ= δ ( A + B ) ⎜⎝ B ⎟⎠

57

1

3

(3.20)


Figure 19 - Contact dimensions, ellipse ratio, and approach coefficients(ESDU 1995).

58

Where the coefficient is given by Equation (3.21). 1

⎡ 4β 2 ⎤ 3 ⎛ A ⎞ Cδ = K ( m ) ⎢ ⎥ ⎜ ⎟ ⎣π E ( m) ⎦ ⎝ B ⎠

−1

3

(3.21)

The pressure distribution across an elliptical contact is given by Equation (3.22).

⎡ x2 y 2 ⎤ p ( x, y ) = p0 ⎢1 − 2 − 2 ⎥ ⎣ a b ⎦

1

2

(3.22)

Where the maximum stress is given by Equation (3.23).

p0 =

3P 2π ab

(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 microslip 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.

59

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.

ξx =

bQx when Qx 1Hz, where this noise has a frequency of 0.05 Hz and is probably not the source.

185

30 Lubricant A Test 1 Lubricant A Test 2 Lubricant A Test 3 28

Output Torque (N.m)

26

24

22

20

18 50

100

150 Time (s)

200

Figure 100 – Output torque signal for Lubricant A in Group 3.

186

250

200

Half Life (s)

150

100

50

0

Lubricant A

Lubricant B

Lubricant C

Lubricant A

Lubricant B

Lubricant C

Minimum Slip (%)

1.5

1

0.5

0

Figure 101 – (top) Half life prediction for Group

3

using

f ( x ) = ae − bx + 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 187

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

f ( x ) = ae − bx .

250

200

Half Life (s)

150

100

50

0

Lubricant A

Lubricant B

Lubricant C

Figure 102 - Half life values for each lubricant in Group 3 testing using

188

f ( x ) = ae − bx .

Apparent Viscosity (Pa.s)

4

10

Lubricant A Test 1 Lubricant A Test 2 Lubricant A Test 3

2

10

0

10 4 10

5

6

10

10

7

10


Strain Rate (s -1) 4

10

Lubricant B Test 1 Lubricant B Test 2 Lubricant B Test 3

2

10

0

10 4 10

5

6

10

10

7

10



10

Lubricant C Test 1 Lubricant C Test 2 Lubricant C Test 3

2

10

0

10 4 10

5

6

10

10

7

10

-1

Strain Rate (s )

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. 189

Absorbed Energy (J)

5

2

x 10

1.5 Lubricant A Test 1 Lubricant A Test 2 Lubricant A Test 3

1 0.5 0

0

50

100

150

200 Time (s)

250

300

350

400

Absorbed Energy (J)

4

4

x 10

3


2 1 0

0

10

20

30 40 Time (s)

50

60

70

Absorbed Energy (J)

4

6

x 10

4


2 0

0

50

100

150

200

250

Time (s)

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.

190

4

16

x 10

14

Total Absorbed Energy (J)

12 10 8 6 4 2 0

Lubricant A

Lubricant B

Lubricant C

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.

191

Absorbed Power (W) Absorbed Power (W) Absorbed Power (W)

600 400


200 0

0

50

100

150

200 Time (s)

250

300

350

400

600 400


200 0

0

10

20

30 40 Time (s)

50

60

70

600 400


200 0

0

50

100

150

200

250

Time (s)

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.

192

1200

1000

Distance (m)

800

600

400

200

0

Lubricant A

Lubricant B

Lubricant C

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.

193

Slding Speed (m/s)

6 4


2 0

0

50

100

150

200 Time (s)

250

300

350

400

Slding Speed (m/s)

6 4


2 0

0

10

20

30 40 Time (s)

50

60

70

Slding Speed (m/s)

0.03 0.02


0.01 0

0

50

100

150

200

250

Time (s)

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.

194

Half Life (s)

400 300 200 100 0

Lubricant A

Lubricant B

Lubricant C

Lubricant A

Lubricant B

Lubricant C

Minimum Slip (%)

0.8 0.6 0.4 0.2 0

Figure 109 – (top) Half life prediction for Group

4

using

f ( x ) = ae − bx + 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.

195

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

f ( x ) = ae − bx .

600

500

Half Life (s)

400

300

200

100

0

Lubricant A

Lubricant B

Lubricant C

Figure 110 - Half life values for each lubricant in Group 4 testing using

196

f ( x ) = ae − bx .


4

10


2

10

0

10 3 10

4

10

5

6

10

10

7

10



10


2

10

0

10 3 10

4

10

5

6

10

10

7

10



10


2

10

0

10 3 10

4

10

5

6

10

10

7

10

-1

Strain Rate (s )

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 197

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.

5

4

Lubricant A

x 10

3 2 1 0

Group 1

Group 2

5

3

Group 3

Group 4

Group 3

Group 4

Group 3

Group 4

Lubricant B

x 10

2 1 0

Group 1

Group 2

4

10

Lubricant C

x 10

5

0

Group 1

Group 2

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 198

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.

Lubricant A

Distance (m)

6000 4000 2000 0

Group 1

Group 2

Group 3

Group 4

Group 3

Group 4

Group 3

Group 4

Lubricant B

Distance (m)

800 600 400 200 0

Group 1

Group 2 Lubricant C

Distance (m)

400 300 200 100 0

Group 1

Group 2

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 199

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.

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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

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appear to improve the performance of Lubricant C, contrary to expected outcomes. 5.5.6 Lubricant Performance Summary Lubricant Type Group No. 1

2

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4

ALL

Performance Criteria Total energy absorbed (J) Total sliding distance (m) Half life of lubricant (s) Total energy absorbed (J) Total sliding distance (m) Half life of lubricant (s) Total energy absorbed (J) Total sliding distance (m) Half life of lubricant (s) Total energy absorbed (J) Total sliding distance (m) Half life of lubricant (s) Average Total energy absorbed (J) Average Total sliding distance (m) Average Half life of lubricant (s)

A 324440 2379 275 143200 3597 503 202800 574 76 78857 614 149 106283 1791 250

B 215320 749 984 36786 224 916 83200 184 782 22298 123 353 89401 319 758

C 28564 216 88 18094 246 206 75560 187 157 28929 3 393 37786 162 211

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.

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Group No. Performance Criteria Total energy absorbed 1 Total sliding distance Half life of lubricant Total energy absorbed 2 Total sliding distance Half life of lubricant Total energy absorbed 3 Total sliding distance Half life of lubricant Total energy absorbed 4 Total sliding distance Half life of lubricant Total energy absorbed ALL Total sliding distance Half life of lubricant

Lubricant Type A B 100% 66% 100% 31% 28% 100% 100% 26% 100% 6% 55% 100% 100% 41% 100% 32% 10% 100% 100% 28% 100% 20% 38% 90% 100% 84% 100% 18% 33% 100%

C 9% 9% 9% 13% 7% 22% 37% 33% 20% 37% 0% 100% 36% 9% 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 intergroup 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.

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Group No. Performance Criteria Total energy absorbed 1 Total sliding distance Half life of lubricant Inter-group performance Total energy absorbed 2 Total sliding distance Half life of lubricant Inter-group performance Total energy absorbed 3 Total sliding distance Half life of lubricant Inter-group performance Total energy absorbed 4 Total sliding distance Half life of lubricant Inter-group performance Total energy absorbed ALL Total sliding distance Half life of lubricant Total Performance Rank

Lubricant Type A B C 1 2 3 1 2 3 2 1 3 1.33 1.67 3.00 1 2 3 1 3 2 2 1 3 1.33 2.00 2.67 1 2 3 1 3 2 3 2 1 1.67 2.33 2.00 1 3 2 1 2 3 3 2 1 1.67 2.33 2.00 1.00 2.25 2.75 1.00 2.50 2.50 2.50 1.50 2.00 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 204

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 Apparent Viscosity (Pa.s) Apparent Viscosity (Pa.s)

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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 205

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.

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Figure 116 - Apparent viscosity versus time for Group 2. Note the different scales on the horizontal axis.

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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 209

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. 210

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 211

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 212

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 213

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.

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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.

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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.

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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.

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Figure 122 – ASTM Pumpability results.

D1092

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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. 217

Lubricant B had a smaller scar diameter than Lubricant C, except at the 200 kgf point, but the weld point is lower.

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Figure 123 - ASTM D2596 Four ball wear test results.

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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.

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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.

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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 221

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.

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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.

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Chapter 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).

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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

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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)

ξ = ae− bt + ce− dt ξ = measured slip ratio

(6.1)

a, b, c, d = regression coefficients 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 226

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.

227

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 228

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. 229

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 230

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 231

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.

232

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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

F =H Ar

(1.2)

Where

F = Normal force on sliding interface (N) Ar = 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 ( s = μ F / Ar ) due to friction. 2

⎛F ⎞ 2 2 ⎜ ⎟ + αt s = H A ⎝ r⎠

(1.3)

α t is an experimentally determined coefficient with a typical value of 12. Seizure occurs, according to this model, when the real area of contact ( Ar )

262

equals the nominal area of contact ( An ). Therefore substituting the shear force and contact area, then rearranging into the dimensionless form gives equation F H = 1 Ar (1 + α t μ 2 ) 2

(1.4)

1

(1.5)

= F

(1 + α μ ) 2

t

1

2

H Ho

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).

μ = 0.88 − 0.13log10 (v% )

(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.

263

Lim and Ashby(1986) presented the following equations to predict melt wear. Equation (1.7) describes frictional heat energy.

α q = − K m ∇T + L

Vm An

(1.7)

Where

α = heat distribution coefficient q = power input per unit area K m = thermal conductivity of metal ∇T = temperature gradient

L = latent heat of fusion per unit volume Vm = volumetric rate of molten material production Frictional heat energy, α q , 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).

αμ Fv An

=

K m (Tm − To ) V +L m lb An

(1.8)

Further, the molten material is assumed to be totally lost and gives the normalised wear rate of the following equation.  = Vm (1.9) W vAn Rearranging the previous equations give Equation 2.9 for melt wear in non-dimensional terms. 264

Tm − To H o 1 T*   % ) [αμ F v W =( − 1] (Tm − To ) L v T*

(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

265

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). Δm 2 = k p t

(1.11)

Δm = Mass of oxygen used per unit area

k p = Parabolic rate constant

k p = Ao exp[−

Qo ] RT

(1.12)

Ao = Arrhenius constant Qo = 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

Fe3 O4 which gives the proportion of 1 mol of Fe to 2/3 of O2 . Oxides will add mass to the surface with the following equation.

266

2 ΔVFe ρ Fe ( M O2 / M Fe ) 3

Δm =

(1.13)

ΔVFe = volume of iron

ρ Fe = density of iron M O2 = molecular weight of oxygen M Fe = molecular weight of iron Substituting the thickness of oxides, Z is equal to ΔVFe , into equation (1.14). Z 2 = C 2k pt

⎛ 3M Fe ⎞ C =⎜ ⎜ 2 M O ρ Fe ⎟⎟ 2 ⎝ ⎠

(1.14)

Using equation (1.14) the time for a critical thickness to form is equated.

tc =

Z

2 c

C 2 Ao exp[−Qo / RT f ]

(1.15)

In this model, wear is taken to be the removal of this oxide volume. Wear is the volume, the product of Ar and Z c , lost in a specified time. Therefore wear rate is the ratio of Ar and Z c to the distance slid, vtc giving the equation (1.16).

W =

Ar C 2 Ao Q exp[− o ] vZ c RT f

(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 267

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 ⎡ ⎤  = ⎛ c Ao β ro ⎞ exp ⎢ − Qo ⎥ F W ⎜ ⎟ ⎝ zc a ⎠ ⎣⎢ RT f ⎥⎦ v

(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:

268

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.

LoxVm = α q −

K ox (Tmox − Tb ) Ar ( ) lf An

(1.18)

Lox = latent heat of oxide Vm = Rate of molten material production l f = Equivalent heat flow length K ox = Thermal conductivity of oxide Tmox = Oxide melting point Using the relationship of input energy equals the frictional energy of the interface and defining the normalised wear rate as W% = f mVm / v gives the model equation (1.19). 1  1 K ox (Tmox − Tb ) (FN ) 2 aH o F  W = fm [αμ ( ) 2 v% − 1] (1.19) ox Lox a v K ox (Tm − Tb ) N

f m = Fraction of material lost

269

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 k A which experimentally has been seen to change over a number of orders of magnitude. =k F  W A

(1.20)

2γ o f v f A*

(1.21)

kA =

The Archard wear constant, k A is the relationship of the volume fraction of inclusions in the materials f v , the rate of plastic strain, γ o , and the area fraction of voids, f A* . 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.

270

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 Load, P Body 1 composition Young’s modulus Poisson’s ratio Body 2 composition Young’s modulus Poisson’s ratio Body 1 – Radius 1 Body 2 – Radius 1

VALUE 1000 Silicon nitride steel 314 0.26 Stainless steel 193 0.3 0.02 0.1

UNITS N/m GPa GPa M M

Table 32 – Example values for needle roller in bearing race (2003).

PARAMETER

HAMROCK RESULT Major semi-axis (µm) 15.6 Normal approach 0.0405 (µm) Maximum normal 40.68 pressure (MPa)

CURRENT METHOD 15.6 0.0404 40.71

DIFFERENCE % 0 0.25 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

271

testing machines are considered for this example, one without friction and one with friction (μ=0.1).

This table is not available online. Please consult the hardcopy thesis available from the QUT Library

Table 34 – Example values for twin-disk fatigue testing device with identical steel samples (ESDU 1995).

PARAMETER

BORESI AND CURRENT SCHMIDT METHOD RESULT Major semi-axis (µm) 530.1 530.1 Normal approach Not given 31.7 (µm) Maximum normal 1447 1447 pressure (MPa) Maximum tensile 322 321.2 stress with friction (MPa) Maximum 1635 (1445) 1616.5(1446.7) compressive stress with friction (MPa) Maximum shear 449 (433) 442(434.5) stress with friction (MPa) Maximum octahedral 369 (361) 389(383) shear stress with friction (MPa) 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

DIFFERENCE % 0 N.A. 0 0.27 1.13(0.11) 1.56(0.35) 5.14(5.74)

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 Load, P Body 1 composition Young’s modulus Poisson’s ratio Body 2 composition Young’s modulus Poisson’s ratio Body 1 – Radius 1 Body 1 – Radius 2 Body 2 – Radius 1 Body 2 – Radius 2 Angle between axes

VALUE 1250 Mild steel 207 0.3 Brass 101 0.35 ∞ 0.025 ∞ 0.075 40

Table 36 – Example values for crossed cylinders of differing materials (2003).

273

UNITS N GPa GPa M M M M Degree

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 Major semi-axis (mm) 1.896 Minor semi-axis (mm) 0.404 Normal approach 0.01195 (mm) Maximum normal 780 pressure (MPa)

CURRENT METHOD 1.90432 0.4028415 0.01214 778

DIFFERENCE % 0.44 0.29 1.59 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 Major semi-axis (mm) 1.142 Minor semi-axis (mm) 0.551 Normal approach 0.01494 (mm) Maximum normal 940 pressure (MPa)

CURRENT METHOD 1.14697 0.55356 0.01490 940

DIFFERENCE % 0.43 0.46 0.27 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. 274

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 Load, P Body composition Young’s modulus Poisson’s ratio Body 1 – Radius 1 Body 1 – Radius 2 Body 2 – Radius 1 Body 2 – Radius 2 Angle between axes

VALUE 4500 Mild steel 200 0.29 0.06 0.13 0.08 0.2 60

UNITS N GPa M M M M Degree

Table 39 – Elliptical contact example for two toroids in contact (2003).

PARAMETER

BORESI AND SCHMIDT RESULT semi-axis Not given

Major (µm) Minor semi-axis (µm) Normal approach (µm) Maximum compressive stress (MPa) Maximum shear stress (MPa) Maximum octahedral shear stress (MPa) Depth of maximum shear stresses (mm)

SOFTWARE METHOD

DIFFERENCE %

1309

NA

965

1000

3.6

29

27

6.9

1586

1642

3.5

529

525

0.8

485

482

0.6

0.51

0.55

7.8

Table 40 - Comparison of results between calculation methods of Boresi and Schmidt (1985) and author’s.

275

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).

276

APPENDIX C – TECHNICAL DRAWINGS

277

278

279

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