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

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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

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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

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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

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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