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E N G I N E E R I N G T R I B O L O G Y
Gwidon W. StachowiakDepartment of Mechanical and Materials Engineering,University of Western Australia, Australia
Andrew W. BatchelorDepartment of Mechanical and Materials Engineering,University of Western Australia, Australia
R W O R T H
Boston Oxford Auckland Johannesburg Melbourne New Delhi
C O N T E N T S
1
2
INTRODUCTION1.1
1.2
1.3
1.4
Background
Meaning of tribology
Lubrication
Wear
Cost of friction and wear
Summary
References
PHYSICAL PROPERTIES OF LUBRICANTS
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Introduction
Oil viscosity
Dynamic viscosity
Kinematic viscosity
Viscosity temperature relationship
Viscosity-temperature equations
Viscosity-temperature chart
Viscosity index
Viscosity pressure relationship
Viscosity-shear rate relationship
Pseudoplastic behaviour
Thixotropic behaviour
Viscosity measurements
Capillary viscometers
Rotational viscometers
Rotating cylinder viscometer
Cone on plate viscometer
Other viscometers
Viscosity of mixtures
Oil viscosity classification
11
11
11
12
13
13
14
14
15
16
22
22
24
24
24
26
27
28
29
30
31
Vin ENGINEERING TRIBOLOGY
SAE viscosity classification 31
ISO viscosity classification 33
2.10 Lubricant density and specific gravity 33
2.11 Thermal properties of lubricants 34
Specific heat 34
Thermal conductivity 35
Thermal diffusivity 35
2.12 Temperature characteristics of lubricants 35
Pour point and cloud point 36
Flash point and fire point 37
Volatility and evaporation 37
Oxidation stability 38
Thermal stability ' 39
Surface tension 40
Neutralization number 42
Carbon residue - 43
2.13 Optical properties of lubricants 43
Refractive index 43
2.14 Additive compatibility and solubility 44
Additive compatibility 44
Additive solubility 44
2.15 Lubricant impurities and contaminants 44
Water content 44
Sulphur content 45
Ash content 45
Chlorine content 45
2.16 Solubility of gases in oils 45
2.17 Summary 48
References 48
3 LUBRICANTS AND THEIR COMPOSITION 51
3.1 Introduction 51
3.2 Mineral oils 52
Sources of mineral oils 52
Manufacture of mineral oils 54
Types of mineral oils 56
Chemical forms 56
Sulphur content 57
Viscosity 57
CONTENTS IX
3.3 Synthetic oils 57
Manufacturing of synthetic oils 58
Hydrocarbon synthetic lubricants 60
Polyalphaolefins 60
Polyphenyl ethers 60
Esters 60
Cycloaliphatics 61
Polyglycols 61
Silicon analogues of hydrocarbons 62
Silicones 62
Silahydrocarbons 62
Organohalogens 62
Perfluoropolyethers 63
Chlorofluorocarbons 63
Chlorotrifluoroethylenes 63
Perfluoropolyalkylethers 63
3.4 Emulsions and aqueous lubricants 65
Manufacturing of emulsions 65
Characteristics 65
Applications 66
3.5 Greases 66
Manufacturing of greases 66
Composition 67
Base oils 67
Thickener 67
Additives 68
Fillers 69
Lubrication mechanism of greases 69
Grease characteristics 72
Consistency of greases 72
Mechanical stability 73
Drop point 74
Oxidation stability 75
Thermal stability 75
Evaporation loss 76
Grease viscosity characteristics 76
Classification of greases 78
Grease compatibility 80
Degradation of greases 80
ENGINEERING TRIBOLOGY
3.6 Lubricant additives 81
Wear and friction improvers 82
Adsorption or boundary additives 82
Anti-wear additives 83
Extreme pressure additives 85
Anti-oxidants 86
Oil oxidation 86
Oxidation inhibitors 88
Corrosion control additives 91
Contamination control additives 92
Viscosity improvers 93
Pour point depressants 95
Foam inhibitors 95
Interference between additives 95
3.7 Summary 96
References 97
HYDRODYNAMIC LUBRICATION 101
4.1 Introduction 101
4.2 Reynolds equation 101
Simplifying assumptions 103
Equilibrium of an element 103
Continuity of flow in a column 107
Simplifications to the Reynolds equation 109
Unidirectional velocity approximation 109
Steady film thickness approximation 109
Isoviscous approximation 110
Infinitely long bearing approximation 110
Narrow bearing approximation 111
Bearing parameters predicted from Reynolds equation 113
Pressure distribution 113
Load capacity 113
Friction force 114
Coefficient of friction 115
Lubricant flow 115
Summary 115
4.3 Pad bearings 116
Infinite linear pad bearing 116
Bearing geometry 116
CONTENTS XI
Pressure distribution 117
Load capacity 119
Friction force 120
Coefficient of friction 123
Lubricant flow rate 124
Infinite Rayleigh step bearing 125
Other wedge geometries of infinite pad bearings 128
Tapered land wedge 128
Parabolic wedge 129
Parallel surface bearings 130
Spiral groove bearing 131
Finite pad bearings 132
Pivoted pad bearing 133
Inlet boundary conditions in pad bearing analysis 135
4.4 Converging-diverging wedges 137
Bearing geometry 138
Pressure distribution 138
Full-Sommerfeld boundary condition ' 140
Half-Sommerfeld boundary condition 141
Reynolds boundary condition 143
Load capacity 144
4.5 Journal bearings 146
Evaluation of the main parameters 146
Bearing geometry 146
Pressure distribution 148
Load capacity 149
Friction force 154
Coefficient of friction 155
Lubricant flow rate 156
Practical and operational aspects of journal bearings 158
Lubricant supply 159
Cavitation 163
Journal bearings with movable pads 164
Journal bearings incorporating a Rayleigh step 164
Oil whirl or lubricant caused vibration 165
Rotating load 167
Tilted shafts 169
Partial bearings 170
Elastic deformation of the bearing 171
xn ENGINEERING TRIBOLOGY
Infinitely long approximation in journal bearings 172
4.6 Thermal effects in bearings 172
Heat transfer mechanisms in bearings 173
Conduction 174
Convection 174
Conducted/convected heat ratio 175
Isoviscous thermal analysis of bearings 176
Iterative method 176
Constant flow method 178
Non-isoviscous thermal analysis of bearings with locally varying viscosity 178
Multiple regression in bearing analysis 179
Bearing inlet temperature and thermal interaction between pads of a
Michell bearing 181
4.7 Limits of hydrodynamic lubrication 182
4.8 Hydrodynamic lubrication with non-Newtonian fluids 184
Turbulence and hydrodynamic lubrication 184
Hydrodynamic lubrication with non-Newtonian lubricants 185
Inertial effects in hydrodynamics 186
Compressible fluids 187
Compressible hydrodynamic lubrication in gas bearings 189
4.9 Reynolds equation for squeeze films 191
Pressure distribution 192
Load capacity 193
Squeeze time 194
Cavitation and squeeze films 195
Microscopic squeeze film effects between rough sliding surfaces 196
4.10 Porous bearings 196
4.11 Summary 197
References 198
5 COMPUTATIONAL HYDRODYNAMICS 201
5.1 Introduction 201
5.2 Non-dimensionalization of the Reynolds equation 201
5.3 The Vogelpohl parameter 202
5.4 Finite difference equivalent of the Reynolds equation 204
Definition of solution domain and boundary conditions 206
Calculation of pressure field 207
Calculation of dimensionless friction force and friction coefficient 207
Numerical solution technique for Vogelpohl equation 210
CONTENTS xm
5.5 Numerical analysis of hydrodynamic lubrication in idealized journaland partial arc bearings 210
Example of data from numerical analysis, the effect of shaft misalignment 211
5.6 Numerical analysis of hydrodynamic lubrication in a real bearing 216
5.6.1 Thermohydrodynamic lubrication 216
Governing equations and boundary conditions in
thermohydrodynamic lubrication 217
Governing equations in thermohydrodynamic lubrication for a
one-dimensional bearing 218
Thermohydrodynamic equations for the finite pad bearing 221
Boundary conditions 222
Finite difference equations for thermohydrodynamic lubrication 223
Treatment of boundary conditions in thermohydrodynamic lubrication 226
Computer program for the analysis of an infinitely long pad bearing inthe case of thermohydrodynamic lubrication 227Example of the analysis of an infinitely long pad bearing in the case ofthermohydrodynamic lubrication 228
5.6.2 Elastic deformations in a pad bearing 231
Computer program for the analysis of an elastically deforming one-dimensional pivoted Michell pad bearing 233
Effect of elastic deformation of the pad on load capacity and film thickness 233
5.6.3 Cavitation and film reformation in grooved journal bearings 236
Computer program for the analysis of grooved 360° journal bearings 240
Example of the analysis of a grooved 360° journal bearing 240
5.6.4 Vibrational stability in journal bearings 246
Determination of stiffness and damping coefficients 246
Computer program for the analysis of vibrational stability in a partial arc
journal bearing 251
Example of the analysis of vibrational stability in a partial arc journal bearing 251
5.7 Summary 254
References 254
HYDROSTATIC LUBRICATION 257
6.1 Introduction 257
6.2 Hydrostatic bearing analysis 258
Flat circular hydrostatic pad bearing 258
Pressure distribution 258
Lubricant flow 259
Load capacity 259
Friction torque 260
x i v ENGINEERING TRIBOLOGY
Friction power loss 262
Non-flat circular hydrostatic pad bearings 262
Pressure distribution 263
Lubricant flow 264
Load capacity 265
Friction torque 265
Friction power loss 265
6.3 Generalized approach to hydrostatic bearing analysis 266
Flat circular pad bearings 266
Flat square pad bearings 266
6.4 Optimization of hydrostatic bearing design 267
Minimization of power 267
Low speed recessed bearings 269
High speed recessed bearings 269
Control of lubricant film thickness and bearing stiffness 270
Stiffness with constant flow method 271
Stiffness with capillary restrictors 271
Stiffness with an orifice 273
Stiffness with pressure sensors 274
6.5 Aerostatic bearings 275
Pressure distribution 276
Gas flow 276
Load capacity 277
Friction torque 277
Power loss 278
6.6 Hybrid bearings 278
6.7 Stability of hydrostatic and aerostatic bearings 278
6.8 Summary 279
References 279
7 ELASTOHYDRODYNAMIC LUBRICATION 281
7.1 Introduction 281
7.2 Contact stresses 282
Simplifying assumptions to Hertz's theory 282
Stress status in static contact 283
Stress status in lubricated rolling and sliding contacts 283
7.3 Contact between two elastic spherical or spheroidal bodies 284
Geometry of contacting elastic bodies 285
Two elastic bodies with convex surfaces in contact 286
CONTENTS X V
Two elastic bodies with one convex and one flat surface in contact 287
Two elastic bodies with one convex and one concave surface incontact 288
Contact area, pressure, maximum deflection and position of themaximum shear stress 289
Contact between two spheres 289
Contact between a sphere and a plane surface 292
Contact between two parallel cylinders 294
Contact between two crossed cylinders with equal diameters 297
Elliptical contact between two elastic bodies, general case 299
Total deflection 304
7.4 Elastohydrodynamic lubricating films 305
Effects contributing to the generation of elastohydrodynamic films 306
Hydrodynamic film formation 306
Modification of film geometry by elastic deformation 306
Transformation of lubricant viscosity and rheology under pressure 307
Approximate solution of Reynolds equation with simultaneous elastic
deformation and viscosity rise 307
Pressure distribution in elastohydrodynamic films 311
Elastohydrodynamic film thickness formulae 312
Effects of the non-dimensional parameters on EHL contact pressures and
film profiles 313
Effect of the speed parameter 313
Effect of the materials parameter 314
Effect of load parameter 314
Effect of elliptidty parameter 315
Lubrication regimes in EHL - film thickness formulae 316
Isoviscous-rigid 317
Piezoviscous-rigid 318
Isoviscous-elastic 318
Piezoviscous-elastic 318
Identification of the lubrication regime 319
Elastohydrodynamic film thickness measurements 319
7.5 Micro-elastohydrodynamic lubrication and mixed or partial EHL 322
Partial or mixed EHL 323
Micro-elastohydrodynamic lubrication 325
7.6 Surface temperature at the conjunction between contacting solids and
its effect on EHL 327
Calculation of surface conjunction temperature 328
Flash temperature in circular contacts 331
xv i ENGINEERING TRIBOLOGY
Flash temperature in square contacts 331Flash temperature in line contacts 334
True flash temperature rise 335Frictional temperature rise of lubricated contacts 339Mechanism of heat transfer within the EHL film 341Effect of surface films on conjunction temperatures 342Measurements of surface temperature in the EHL contacts 342
7.7 Traction and EHL 343A simplified analysis of traction in the EHL contact 346Non-Newtonian lubricant rheology and EHL 348EHL between meshing gear wheels 350
7.8 Summary 352References 352
8 BOUNDARY AND EXTREME PRESSURE LUBRICATION 3578.1 Introduction 3578.2 Low temperature - low load lubrication mechanisms 3598.3 Low temperature - high load lubrication mechanisms 360
Model of adsorption on sliding surfaces 361Physisorption 362Chemisorption 364Influence of the molecular structure of the lubricant onadsorption lubrication 365Influence of oxygen and water 369Dynamic nature of adsorption under sliding conditions 371Mixed lubrication and scuffing 372Metallurgical effects 379Interaction between surfactant and carrier fluid 380
8.4 High temperature - medium load lubrication mechanisms 381Chain matching 381Thick films of soapy or amorphous material 384
Soap layers 384Amorphous layers 385
8.5 High temperature - high load lubrication mechanisms 388Model of lubrication by sacrificial films 389Additive reactivity and its effect on lubrication 390Nascent metallic surfaces and accelerated film formation 393Influence of oxygen and water on the lubrication mechanism bysacrificial films 395
CONTENTS XVII
Mechanism of lubrication by milder E.P. Additives 398
Function of active elements other than sulphur 398
Lubrication with two active elements 399
Temperature distress 401
Speed limitations of sacrificial film mechanism 403
Tribo-emission from worn surfaces 403
8.6 Boundary and E.P. lubrication of non-metallic surfaces 404
8.7 Summary 404
References 405
SOLID LUBRICATION AND SURFACE TREATMENTS 411
9.1 Introduction 411
9.2 Lubrication by solids 411
9.2.1 Lubrication by lamellar solids 412
Friction and wear characteristics of lamellar solids 415
Graphite and molybdenum disulphide 415
Carbon-based materials other than graphite 419
Minor solid lubricants o 420
9.2.2 Reduction of friction by soft metallic films 421
Reduction of friction by metal oxides at high temperatures 422
9.2.3 Deposition methods of solid lubricants 422
Traditional methods of solid lubricant deposition 423
Modern methods of solid lubricant deposition 423
Solid lubricants as additives to oils and polymers 424
9.3 Wear resistant coatings and surface treatments 426
9.3.1 Techniques of producing wear resistant coatings 427
Coating techniques dependent on vacuum or gas at very low pressure 427
Physical vapour deposition 427
Chemical vapour deposition . - 430
Physical-chemical vapour deposition 430
Ion implantation 431
Coating processes requiring localized sources of intense heat 432
Surface welding 432
Thermal spraying -433
Laser surface hardening and alloying 436
Coating processes based on deposition in the solid state 436
Miscellaneous coating processes 438
Application of coatings and surface treatments in wear and friction control 438
Characteristics of wear resistant coatings 439
XVIII ENGINEERING TRIBOLOGY
9.4 Summary 442
References 442
10 FUNDAMENTALS OF CONTACT BETWEEN SOLIDS 447
10.1 Introduction 447
10.2 Surfaces of solids 447
Surfaces at a nano scale 448
Surface topography 449
Characterization of surface topography 452
Characterization of surface topography by statistical parameters 452
Multi-scale characterization of surface topography 455
Characterization of surface topography by Fourier transform 455
Characterization of surface topography by wavelets 456
Characterization of surface topography by fractals 457
Optimum surface roughness 460
10.3 Contact between solids 461
Model of contact between solids based on statistical parameters of roughsurfaces 462Model of contact between solids based on the fractal geometry of roughsurfaces 465
Effect of sliding on contact between solid surfaces 467
10.4 Friction and wear 468
Onset of sliding and mechanism of stick-slip 469
Structural differences between static and sliding contacts 471
Friction and other contact phenomena in rolling 473
Concentration of frictional heat at the asperity contacts 476
Wear between surfaces of solids 477
10.5 Summary 478
References 478
11 ABRASIVE, EROSIVE AND CAVITATION WEAR 483
11.1 Introduction 483
11.2 Abrasive wear 483
Mechanisms of abrasive wear 484
Modes of abrasive wear 486
Analytical models of abrasive wear 487
Abrasivity of particles 494
Abrasive wear resistance of materials 499
Abrasive wear resistance of steels 502
Abrasive wear resistance of polymers and rubbers 504
CONTENTS XLX
Abrasive wear resistance of ceramics 505
Effect of temperature on abrasive wear 506
Effect of moisture on abrasive wear 507
Control of abrasive wear 507
11.3 Erosive wear 509
Mechanisms of erosive wear 509
Effect of impingement angle and impact speed on erosive wear rate 511
Effect of particle shape, hardness, size and flux rates on erosive wear rate 512
Erosive wear by liquid 513
Effect of temperature on erosive wear 515
Effect of erosion media on erosive wear 516
Erosive wear resistance of materials 518
Erosive wear resistance of steels 520
Erosive wear resistance of polymers 521
Erosive wear of ceramics and cermets 523
11.4 Cavitation wear 524
Mechanism of cavitation wear 524
Cavitation wear resistance of materials 525
11.5 Summary 526
References 527
12 ADHESION AND ADHESIVE WEAR 533
12.1 Introduction 533
12.2 Mechanism of adhesion 533
Metal-metal adhesion 533
Metal-polymer adhesion 536
Metal-ceramic adhesion 537
Polymer-polymer and ceramic-ceramic adhesion 537
Effects of adhesion between wearing surfaces 538
Friction due to adhesion 538
Junction growth between contacting asperities as a cause of
extreme friction 539
Seizure and scuffing 542
Asperity deformation and formation of wear particles 542
Transfer films 544
12.3 Control of the adhesive wear 548
Contaminant layers formed due to surface oxidation and bulk impurities 549
Lubricants 549
Favourable combinations of sliding materials 550
XX ENGINEERING TRIBOLOGY
12.4 Summary 550
References 550
13 CORROSIVE AND OXIDATIVE WEAR 553
13.1 Introduction 553
13.2 Corrosive wear 553
Transition between corrosive and adhesive wear 557
Synergism between corrosive and abrasive wear 559
Tribochemical polishing 560
13.3 Oxidative wear 560
Kinetics of oxide film growth on metals at high and low temperatures 561
Oxidative wear at high sliding speeds 562
Oxidative wear at low sliding speeds 563
Oxidative wear at high temperature and stress 564
Oxidative wear at low temperature applications 565
Transition between oxidative and adhesive wear 566
Oxidative wear under lubricated conditions 566
Means of controlling corrosive and oxidative wear 567
13.4 Summary 567
References 568
14 FATIGUE WEAR 571
14.1 Introduction 571
14.2 Fatigue wear during sliding 572
Surface crack initiated fatigue wear 573
Subsurface crack initiated fatigue wear 575
Effect of lubrication on fatigue wear during sliding 577
Plastic ratchetting 578
14.3 Fatigue wear during rolling 579
Causes of contact fatigue 580
Asperity contact during EHL and the role of debris in the lubricant
in contact fatigue 580
Material imperfections 581
Self-propagating nature of contact fatigue cracks 581
» Subsurface and surface modes of contact fatigue 581
Effect of lubricant on contact fatigue 585
Hydraulic pressure crack propagation 585
Chemical effects of lubricant additives, oxygen and water on contact fatigue 586
Materials effect on contact fatigue 587
CONTENTS XXI
Influence of operating conditions on rolling wear and contact fatigue 588
14.4 Means of controlling fatigue wear 589
14.5 Summary 589
References 590
15 FRETTING AND MINOR WEAR MECHANISMS 593
15.1 Introduction 593
15.2 Fretting wear 594
Microscopic movements within the contact under applied loads 594
Elastic model for fretting contacts 594
Elasto-plastic model for fretting contacts 596
Effect of amplitude and debris retention on fretting wear 597
Environmental effects on fretting wear 599
Effects of temperature and lubricants on fretting 602
Effect of materials properties and surface finish on fretting 604
Fretting fatigue 604
Practical examples of fretting 607
Means of controlling fretting 608
15.3 Melting wear 609
15.4 Wear due to electrical discharges 611
15.5 Diffusive wear 612
15.6 Impact wear 613
15.7 Summary 615
References 616
16 WEAR OF NON-METALLIC MATERIALS 619
16.1 Introduction 619
16.2 Tribology of polymers 619
Sliding wear of polymers, transfer layers on a harder counterface 621
Influence of counterface roughness, hardness and material type on
transfer films and associated wear and friction of polymers 622
Counterface hardness 623
Counterface roughness 623
Counterface surface energy 626
Influence of temperature on polymer wear and friction 626
Limit on frictional temperature rise imposed by surface melting 627
Effect of high frictional temperatures and sliding speeds on wear 630
Combined effect of high surface roughness and elevated contacttemperature on wear 631
Fatigue wear of polymers and long term wear kinetics 633
XXII ENGINEERING TRIBOLOGY
Visco-elasticity and the rubbery state 634
Friction and wear in the rubbery state 635
Schallamach waves 635
Visco-elasticity and friction of rubbers 636
Wear mechanisms particular to rubbery solids 637
Effect of lubricant, corrosive agents and microstructure on wear and
friction of polymers 638
Effects of lubricants 638
Effects of corrosive agents 639
Effect of oxidizing and biochemical reagents 640
Effects of polymer microstructure 641
16.3 Tribology of polymer composites 643
Polymer blends 643
Fibre reinforced polymers 643
Chopped fibre reinforced polymers 644
Unidirectional and woven fibre reinforcements 644
Modelling of wear of fibre reinforced polymers 646
Powder composites 647
16.4 Wear and friction of ceramics 648
Unlubricated wear and friction of ceramic-ceramic contacts 650
Dry friction and wear of ceramics at room temperature 650
Dry friction and wear of ceramics at elevated temperatures 652
Friction and wear of ceramics in the presence of water or humid
air 652
Quantitative wear model of ceramics 653
Dry wear and friction characteristics of individual ceramics 655
Lubricated wear and friction of ceramic-ceramic contacts 656
Liquid lubrication 656
Solid lubricants 658
Wear and friction of ceramics against metallic materials 659
Wear and friction of ceramics against polymers 662
Wear and friction of ceramic matrix composites 662
16.5 Summary 663
References 663
APPENDIX 669
Introduction 669
A.I User friendly interface 669
A.2 Program 'VISCOSITY' 671