Preface ......................................................... v
Notations ..................................................... xix
1 Introduction to Tribology .................................... 1
1.1 Introduction ............................................ 1
1.2 Regimes of Lubrication .................................. 4
1.3 Layout of the Book ...................................... 6
References ................................................... 7
2 The Nature of Rough Surfaces ................................. 9
2.1 Introduction ............................................ 9
2.2 Surface Roughness ...................................... 10
2.3 Measurement of Surface Texture ......................... 10
2.4 Types of Engineering Surface ........................... 12
2.5 Mathematical Representation of Surface Features ........ 15
2.5.1 Analogue solutions .............................. 15
2.5.2 Discrete interval solutions of profile height ... 17
2.5.3 Statistical representation of surface texture ... 17
2.6 Closure ................................................ 21
References .................................................. 21
3 Elastic Solids in Normal Contact ............................ 23
3.1 Introduction ........................................... 23
3.2 Deformation Characteristics ............................ 23
3.3 Surface Deformation in a Spherical Contact ............. 29
3.4 Various Contact Geometries ............................. 32
3.4.1 Line or circular footprint contacts ............. 32
3.4.2 Elliptical footprint contacts ................... 33
3.5 Onset of Yield ......................................... 35
3.5.1 Cylindrical surfaces ............................ 35
3.5.2 Spherical surfaces .............................. 37
3.6 Nominally Flat Rough Surfaces in Contact ............... 38
3.6.1 Idealized rough surfaces ........................ 38
3.6.2 Contact between real rough surfaces ............. 40
3.6.3 Plasticity index ................................ 44
3.6.4 Fully plastic surface contacts .................. 45
3.7 Contact Between Curved Rough Surfaces .................. 47
3.8 Hertzian Impact ........................................ 47
3.9 Contact Mechanics of Coated Surfaces ................... 49
3.10 Closure ................................................ 53
3.11 Appendix ............................................... 53
References .................................................. 54
4 Dry Friction and Wear ....................................... 57
4.1 Introduction ........................................... 57
4.2 The Basic Mechanisms of Dry Friction ................... 60
4.2.1 Adhesion and deformation ........................ 60
4.2.2 Adhesive friction ............................... 61
4.2.3 Deformation friction ............................ 66
4.3 Rolling Friction ....................................... 68
4.3.1 Elastic rolling friction ........................ 68
4.3.2 Tractive rolling of an elastic cylinder ......... 70
4.3.3 Creep ratio ..................................... 72
4.3.4 Other examples of rolling motion ................ 72
4.4 Thermal Effects of a Frictional Temperature Rise in
Concentrated Contacts .................................. 73
4.5 Wear of Surfaces ....................................... 74
4.5.1 Adhesive wear ................................... 75
4.5.2 Abrasive wear ................................... 77
4.5.3 Macroscopic fatigue wear ........................ 79
4.5.4 Microscopic sliding fatigue wear ................ 79
4.5.5 Corrosive wear .................................. 80
4.5.6 Fretting corrosion .............................. 81
4.6 Closure ................................................ 81
References .................................................. 81
5 Lubricant Properties ........................................ 83
5.1 Introduction ........................................... 83
5.2 Dynamic Viscosity ...................................... 83
5.3 Effect of Temperature on Viscosity ..................... 85
5.4 The American Society for Testing Materials (ASTM)
Chart .................................................. 86
5.5 Viscosity Index of Lubricants (VI) ..................... 86
5.6 Polymer Thickened Oils ................................. 87
5.7 Blends of Oils ......................................... 88
5.8 Grades of Oil .......................................... 89
5.9 Effect of Pressure on Viscosity ........................ 90
5.10 Lubricant Density ...................................... 91
5.11 Effect of Shear Rate on Viscosity ...................... 92
5.12 Greases ................................................ 94
5.13 Closure ................................................ 97
References .................................................. 97
6 The Reynolds and Energy Equations ........................... 99
6.1 Introduction ........................................... 99
6.2 Hydrodynamic Wedge ..................................... 99
6.3 The Reynolds Equation by Dimensional Analysis ......... 101
6.4 Derivation of the Reynolds Equation in Three
Dimensions ............................................ 104
6.4.1 Equilibrium of forces on a lubricant
element ........................................ 105
6.4.2 Velocity distribution .......................... 106
6.4.3 Mass continuity ................................ 107
6.5 Simplifications of the Reynolds Equation .............. 109
6.5.1 Long bearing ................................... 109
6.5.2 Long bearing approximation for rigid
cylinders ...................................... 110
6.5.3 Line contact pressure distribution ............. 111
6.5.4 Line contact load .............................. 114
6.5.5 Narrow bearings ................................ 114
6.5.6 Squeeze film bearings .......................... 116
6.6 Rolling Contacts ...................................... 116
6.7 The Energy Equation ................................... 117
6.7.1 Significance of terms in the energy -
equation ....................................... 118
6.7.2 Convected heat only ............................ 119
6.7.3 Conducted heat only ............................ 119
6.7.4 Heat flow ratio ................................ 120
6.8 Closure ............................................... 120
References ................................................. 121
7 Thrust Bearings ............................................ 123
7.1 Introduction .......................................... 123
7.2 Analysis of Thrust Bearings ........................... 124
7.2.1 Geometry ....................................... 124
7.2.2 Pressure distribution .......................... 125
7.2.3 Load capacity .................................. 127
7.2.4 Pivot point location ........................... 128
7.2.5 Friction force ................................. 130
7.2.6 Mass flow ...................................... 131
7.2.7 Temperature effect ............................. 132
7.2.8 Effective temperature .......................... 134
7.3 Finite Length Plane Thrust Bearings ................... 135
7.3.1 Introduction ................................... 135
7.3.2 Thermal design of finite length bearings ....... 135
7.3.3 Power balance for the effective viscosity ...... 136
7.3.4 Effective temperature design coefficients ...... 137
7.4 Examples of Thermal Design ............................ 138
7.5 Other Thrust Bearing Geometries ....................... 142
7.5.1 The taper land bearing ......................... 142
7.5.2 The Rayleigh step bearing ...................... 143
7.5.3 The pocket step bearing ........................ 144
7.6 Closure ............................................... 145
7.7 Appendix .............................................. 145
References ................................................. 146
8 Journal Bearings ........................................... 147
8.1 Introduction .......................................... 147
8.2 Film Geometry ......................................... 147
8.3 The Pressure Equation for a Narrow Bearing ............ 148
8.4 Load .................................................. 150
8.5 Attitude Angle ........................................ 152
8.6 Lubricant Flow ........................................ 153
8.6.1 Side flow from hydrodynamic action ............. 153
8.6.2 Pressurized flow from a single supply hole ..... 154
8.6.3 Total pump delivery flow ....................... 155
8.6.4 Double 180° journal bearings ................... 155
8.6.5 Circumferential groove bearings ................ 155
8.7 Friction in Journal Bearings .......................... 156
8.7.1 Effect of the Reynolds boundary condition
on friction .................................... 159
8.7.2 Coefficient of friction ........................ 159
8.8 Thermal Design of Journal Bearings .................... 160
8.8.1 Introduction ................................... 160
8.8.2 Finding the effective viscosity ................ 160
8.8.3 Design example ................................. 163
8.9 Mass Unbalance in Rotors .............................. 165
8.9.1 Natural frequency of journal bearings .......... 166
8.9.2 Half speed cylindrical whirl of journal
bearings ....................................... 168
8.9.3 Natural frequency of the complete rotor/
bearing system ................................. 170
8.10 Journal Bearings with Periodic and Rotating Loads ..... 170
8.11 Closure ............................................... 170
8.12 Appendix .............................................. 170
References ................................................. 171
9 Externally Pressurized (EP) Bearings ....................... 173
9.1 Introduction .......................................... 173
9.2 Some Applications of EP Bearings ...................... 174
9.3 Principles of Hydrostatic Bearings .................... 174
9.3.1 Optimization ................................... 177
9.3.2 Stiffness ...................................... 178
9.3.3 Compensators ................................... 180
9.4 Principles of Aerostatic Bearings ..................... 182
9.4.1 Introduction ................................... 182
9.4.2 Flow through the gas film ...................... 183
9.4.3 Gas flow through the feed hole ................. 184
9.4.4 Matching the gas flows ......................... 186
9.4.5 Aerostatic gas bearing load capacity ........... 187
9.4.6 Aerostatic bearing film stiffness .............. 187
9.4.7 Aerostatic journal bearings .................... 190
9.4.8 Aerostatic journal bearing instability ......... 191
9.5 Closure ............................................... 192
References ................................................. 1Э2
10 Elastohydrodynamic Lubrication (EHL) ....................... 193
10.1 Introduction .......................................... 193
10.2 Principles of EHL ..................................... 193
10.3 The Reynolds Equation under Piezo-viscous Conditions .. 196
10.4 Discussion on EHL Line Contact Film Shape ............. 200
10.5 Circular Footprint EHL Contacts ....................... 200
10.6 Numerical Predictions ................................. 201
10.6.1 Elastic deflection ............................ 201
10.6.2 Film shape .................................... 202
10.6.3 Equations of state of the lubricant ........... 203
10.6.4 The Reynolds equation ......................... 203
10.6.5 Load .......................................... 203
10.7 Computer Solution ..................................... 204
10.8 Experimental Methods .................................. 205
10.8.1 Optical interferometry ......................... 205
10.9 Results from Numerical Solutions ...................... 208
10.9.1 Regimes of concentrated contact lubrication .... 208
10.9.2 Numerical solution relationships for
concentrated contacts .......................... 209
10.10 EHL of Greases ....................................... 212
10.11 Friction Forces in EHL Contacts ...................... 216
10.11.1 A viscoelastic model of the oil behaviour ..... 216
10.11.2 Limiting shear stress ......................... 218
10.11.3 Regimes of traction ........................... 219
10.11.4 Determination of the friction coefficient ..... 220
10.12 Rough Surface EHL .................................... 224
10.13 Friction in Rough EHL Contacts ....................... 226
10.14 Closure .............................................. 233
References ................................................. 234
11 Fatigue" Life of Rolling Element Bearings .................. 237
11.1 Introduction .......................................... 237
11.2 Fatigue Stress Hypotheses ............................. 239
11.2.1 Asperity stress field .......................... 239
11.2.2 Subsurface stress field ........................ 239
11.3 Fatigue Life Dispersion ............................... 241
11.4 Effect of Load on Fatigue Life ........................ 245
11.5 Effect of EHL on Fatigue Life ......................... 247
11.6 A Unified Life Model .................................. 247
11.7 Closure ............................................... 249
References ................................................. 249
12 Transient Elastohydrodynamic Lubrication ................... 251
12.1 Introduction .......................................... 251
12.2 A Valve Train System .................................. 252
12.2.1 Contact load ................................... 254
12.2.2 Speed of entraining motion ..................... 256
12.2.3 A valve train example .......................... 261
12.3 EHL of Thin Shell Journal Bearings .................... 265
12.4 Transient EHL of Piston-to-Cylinder Liner ............. 272
12.4.1 Inertial dynamics .............................. 272
12.4.2 Contact forces and moments ..................... 276
12.5 Conjunction of Piston Compression Ring ................ 286
12.5.1 Simple analytical approach for a compression
ring conjunction ............................... 289
12.5.2 An example for a compression ring .............. 292
12.6 Closure ............................................... 298
References ................................................. 299
13 Nano-Tribology ............................................. 301
13.1 Introduction .......................................... 301
13.2 Important Forces in Nano-Tribology .................... 304
13.3 Van der Waals Forces .................................. 305
13.3.1 Concluding remarks on Van der Waals forces ..... 306
13.4 Electrostatic Forces .................................. 307
13.4.1 An example of electrostatic repulsion .......... 310
13.5 Meniscus/Surface Tension Force ........................ 313
13.5.1 Physics of surface tension ..................... 313
13.5.2 Determining surface tension .................... 315
13.5.3 Formation of menisci ........................... 320
13.5.4 Attractive meniscus force ...................... 323
13.5.5 An example of meniscus force ................... 328
13.6 Solvation Effect ...................................... 329
13.6.1 Introduction ................................... 329
13.6.2 The oscillatory solvation force ................ 331
13.6.3 An example of solvation effect ................. 333
13.7 Mechanisms of Friction in Nano-Conjunctions ........... 335
13.7.1 An example of friction in nano-tribology ....... 341
References ................................................. 344
14 Bio-Tribology .............................................. 347
14.1 Introduction .......................................... 347
14.2 Tribology in the Animal World ......................... 348
14.2.1 Allometry ...................................... 348
14.2.2 Forces and stresses ............................ 349
14.3 Attachment and Locomotion of Small Animals on
Smooth Surfaces ....................................... 349
14.4 Natural Human Synovial Joints ......................... 353
14.4.1 Measurement of friction ........................ 354
14.4.2 Lubrication of synovial joints ................. 355
14.4.3 Analysis of fluid-film lubrication in joints ... 355
14.4.4 Evidence of boundary lubrication in synovial
joints ......................................... 358
14.4.5 Overall view of human joint lubrication ........ 358
14.5 Total Joint Replacements .............................. 359
14.5.1 The hip ........................................ 360
14.5.2 Metal-on-metal total hip replacements .......... 361
14.5.3 Alternative material pairs ..................... 364
14.6 Further Examples of Bio-Tribology ..................... 365
14.6.1 Skin ........................................... 365
14.6.2 Hair ........................................... 366
14.6.3 Shaving ........................................ 366
14.6.4 Teeth .......................................... 367
14.7 eiosure ............................................... 367
References ................................................. 368
Appendix A Questions ......................................... 371
Appendix В Book of Solutions ................................. 391
Index ......................................................... 423
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