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CONTENTS 1 INTRODUCTION 1 1.1 Background 1 1.2 Meaning of tribology 2 Lubrication 3 Wear 5 1.3 Cost of friction and wear 5 1.4 Summary 7 Revision questions 8 References 9 2 PHYSICAL PROPERTIES OF LUBRICANTS 11 2.1 Introduction 11 2.2 Oil viscosity 11 Dynamic viscosity 12 Kinematic viscosity 13 2.3 Viscosity temperature relationship 13 Viscosity-temperature equations 14 Viscosity-temperature chart 14 2.4 Viscosity index 15 2.5 Viscosity pressure relationship 17 2.6 Viscosity-shear rate relationship 22 Pseudoplastic behaviour 22 Thixotropic behaviour 24 2.7 Viscosity measurements 24 Capillary viscometers 24 Rotational viscometers 26 · Rotating cylinder viscometer 27 · Cone on plate viscometer 29 Other viscometers 29 2.8 Viscosity of mixtures 31 2.9 Oil viscosity classification 31 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 2.13 Other lubricant characteristics 40 Surface tension 40 Neutralization number 43 Carbon residue 43 2.14 Optical properties of lubricants 43 Refractive index 43 2.15 Additive compatibility and solubility 44 Additive compatibility 44 Additive solubility 44 2.16 Lubricant impurities and contaminants 44 Water content 44 Sulphur content 45 Ash content 45 Chlorine content 45 2.17 Solubility of gases in oils 45 2.18 Summary 48 Revision questions 48 References 49 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 3.4 Emulsions and aqueous lubricants Manufacturing of greases Composition · Base oils · Thickener · Additives · Fillers Lubrication mechanism of greases Grease characteristics · Consistency of greases · Mechanical stability · Drop point · Oxidation stability · Thermal stability · Evaporation loss · Chemical forms · Sulphur content · Viscosity 3.3 Synthetic oils Manufacturing of synthetic oils Hydrocarbon synthetic lubricants · Polyalphaolefins · Polyphenyl ethers · Esters · Cycloaliphatics · Polyglycols Silicon analogues of hydrocarbons · Silicones · Silahydrocarbons Organohalogens · Perfluoropolyethers · Chlorofluorocarbons · Chlorotrifluoroethylenes · Perfluoropolyalkylethers Cyclophosphazenes Manufacturing of emulsions Characteristics Applications 3.5 Greases 56 57 57 57 58 60 60 60 60 61 61 62 62 62 62 63 63 63 64 64 64 64 66 66 67 67 67 67 68 68 69 69 73 73 74 75 75 76 77 · Grease viscosity characteristics 77 Classification of greases 79 Grease compatibility 81 Degradation of greases 81 3.6 Lubricant additives 82 Wear and friction improvers 82 · Adsorption or boundary additives 83 · Anti-wear additives 83 · Extreme pressure additives 86 Nanoparticle additives 87 Anti-oxidants 87 · Oil oxidation 87 · Oxidation inhibitors 90 Corrosion control additives 93 Contamination control additives 93 Viscosity improvers 95 Pour point depressants 96 Foam inhibitors 96 Interference between additives 96 3.7 Summary 98 Revision questions 98 References 98 4 HYDRODYNAMIC LUBRICATION 103 4.1 Introduction 103 4.2 Reynolds equation 103 Simplifying assumptions 105 Equilibrium of an element 105 Continuity of flow in a column 109 Simplifications to the Reynolds equation 111 · Unidirectional velocity approximation 111 · Steady film thickness approximation 111 · Isoviscous approximation 112 · Infinitely long bearing approximation 112 · Narrow bearing approximation 113 Bearing parameters predicted from Reynolds equation 115 · Pressure distribution 115 · Load capacity 115 · Friction force 116 · Coefficient of friction 117 117 117 · Lubricant flow Summary 4.3 Pad bearings 118 118 118 119 121 122 125 126 127 Infinite linear pad bearing · Bearing geometry · Pressure distribution · Load capacity · Friction force · Coefficient of friction · Lubricant flow rate Infinite Rayleigh step bearing · Parabolic wedge 131 132 133 134 135 · Parallel surface bearings · Spiral groove bearing Finite pad bearings Pivoted pad bearing Other wedge geometries of infinite pad bearings · Tapered land wedge 130 Inlet boundary conditions in pad bearing analysis 137 4.4 Converging-diverging wedges 139 Bearing geometry 140 Pressure distribution 140 · Full-Sommerfeld boundary condition 142 · Half-Sommerfeld boundary condition 143 · Reynolds boundary condition 145 146 Load capacity 4.5 Journal bearings 148 148 148 150 151 156 157 159 Evaluation of the main parameters · Bearing geometry · Pressure distribution · Load capacity · Friction force · Coefficient of friction · Lubricant flow rate Practical and operational aspects of journal bearings 161 · Lubricant supply 161 · Cavitation 165 · Journal bearings with movable pads 166 · Journal bearings incorporating a Rayleigh step 167 · Oil whirl or lubricant caused vibration 167 · Rotating load 170 · Tilted shafts 172 · Partial bearings 173 · Elastic deformation of the bearing 174 · Infinitely long approximation in journal bearings 174 4.6 Thermal effects in bearings 175 Heat transfer mechanisms in bearings 175 · Conduction 176 · Convection 176 · Conducted/convected heat ratio 177 Isoviscous thermal analysis of bearings 178 · Iterative method 178 · Constant flow method 179 Non-isoviscous thermal analysis of bearings with locally varying viscosity 180 Multiple regression in bearing analysis 182 Bearing inlet temperature and thermal interaction between pads of a Michell bearing 183 4.7 Limits of hydrodynamic lubrication 185 4.8 Hydrodynamic lubrication with non-Newtonian fluids 186 Turbulence and hydrodynamic lubrication 186 Hydrodynamic lubrication with non-Newtonian lubricants 187 Inertia effects in hydrodynamics 188 Compressible fluids 189 Compressible hydrodynamic lubrication in gas bearings 191 4.9 Reynolds equation for squeeze films 193 Pressure distribution 194 Load capacity 195 Squeeze time 196 Cavitation and squeeze films 197 Microscopic squeeze film effects between rough sliding surfaces 197 4.10 Porous bearings 198 4.11 Summary 200 Revision questions 200 References 202 5 COMPUTATIONAL HYDRODYNAMICS 205 5.1 Introduction 205 5.2 Non-dimensionalization of the Reynolds equation 205 5.3 The Vogelpohl parameter 206 5.4 Finite difference equivalent of the Reynolds equation 208 Definition of solution domain and boundary conditions 210 Calculation of pressure field 211 Calculation of dimensionless friction force and friction coefficient 211 Numerical solution technique for Vogelpohl equation 214 5.5 Numerical analysis of hydrodynamic lubrication in idealized journal and partial arc bearings 214 Example of data from numerical analysis, the effect of shaft misalignment 215 5.6 Numerical analysis of hydrodynamic lubrication in a real bearing 220 5.6.1 Thermohydrodynamic lubrication 220 Governing equations and boundary conditions in thermohydrodynamic lubrication 221 · Governing equations in thermohydrodynamic lubrication for a one-dimensional bearing 222 · Thermohydrodynamic equations for the finite pad bearing 225 · Boundary conditions 226 Finite difference equations for thermohydrodynamic lubrication 227 Treatment of boundary conditions in thermohydrodynamic lubrication 230 Computer program for the analysis of an infinitely long pad bearing in the case of thermohydrodynamic lubrication 231 Example of the analysis of an infinitely long pad bearing in the case of thermohydrodynamic lubrication 232 5.6.2 Elastic deformations in a pad bearing 235 Computer program for the analysis of an elastically deforming one- dimensional pivoted Michell pad bearing 237 Effect of elastic deformation of the pad on load capacity and film thickness 237 5.6.3 Cavitation and film reformation in grooved journal bearings 240 Computer program for the analysis of grooved 360° journal bearings 244 Example of the analysis of a grooved 360° journal bearing 244 5.6.4 Vibrational stability in journal bearings 250 Determination of stiffness and damping coefficients 250 Computer program for the analysis of vibrational stability in a partial arc journal bearing 255 Example of the analysis of vibrational stability in a partial arc journal bearing 255 5.7 Summary 258 Revision questions 258 References 259 6 HYDROSTATIC LUBRICATION 261 6.1 Introduction 261 6.2 Hydrostatic bearing analysis 262 Flat circular hydrostatic pad bearing 262 · Pressure distribution 262 · Lubricant flow 263 · Load capacity 263 · Friction torque 264 · Friction power loss 266 Non-flat circular hydrostatic pad bearings 266 · Pressure distribution 267 · Lubricant flow 268 · Load capacity 269 · Friction torque 269 · Friction power loss 269 6.3 Generalized approach to hydrostatic bearing analysis 270 Flat circular pad bearings 270 Flat square pad bearings 270 6.4 Optimization of hydrostatic bearing design 271 Minimization of power 271 · Low speed recessed bearings 273 · High speed recessed bearings 273 Control of lubricant film thickness and bearing stiffness 274 · Stiffness with constant flow method 275 · Stiffness with capillary restrictors 275 · Stiffness with an orifice 277 · Stiffness with pressure sensors 278 6.5 Aerostatic bearings 279 Pressure distribution 280 Gas flow 280 Load capacity 281 Friction torque 281 Power loss 282 6.6 Hybrid bearings 282 6.7 Stability of hydrostatic and aerostatic bearings 282 6.8 Summary 283 Revision questions 283 References 284 7 ELASTOHYDRODYNAMIC LUBRICATION 287 7.1 Introduction 287 7. 2Contact stresses 288 Simplifying assumptions to Hertz's theory 288 Stress status in static contact 289 Stress status in lubricated rolling and sliding contacts 289 7.3 Contact between two elastic spherical or spheroidal bodies 290 Geometry of contacting elastic bodies 291 · Two elastic bodies with convex surfaces in contact 292 · Two elastic bodies with one convex and one flat surface in contact 293 · Two elastic bodies with one convex and one concave surface in contact 294 Contact area, pressure, maximum deflection and position of the maximum shear stress 295 · Contact between two spheres 295 · Contact between a sphere and a plane surface 298 · Contact between two parallel cylinders 300 · Contact between two crossed cylinders with equal diameters 303 · Elliptical contact between two elastic bodies, general case 305 Total deflection 310 7.4 Elastohydrodynamic lubricating films 311 Effects contributing to the generation of elastohydrodynamic films 312 · Hydrodynamic film formation 312 · Modification of film geometry by elastic deformation 312 · Transformation of lubricant viscosity and rheology under pressure 313 Approximate solution of Reynolds equation with simultaneous elastic deformation and viscosity rise 313 Pressure distribution in elastohydrodynamic films 317 Elastohydrodynamic film thickness formulae 318 Effects of the non-dimensional parameters on EHL contact pressures and film profiles 319 · Effect of the speed parameter 319 · Effect of the materials parameter 320 · Effect of the load parameter 320 · Effect of the ellipticity parameter 321 Lubrication regimes in EHL - film thickness formulae 322 · Isoviscous-rigid 323 · Piezoviscous-rigid 324 · Isoviscous-elastic 324 · Piezoviscous-elastic 324 Identification of the lubrication regime 325 Elastohydrodynamic film thickness measurements 325 7.5 Micro-elastohydrodynamic lubrication and mixed or partial EHL 328 Partial or mixed EHL 329 Micro-elastohydrodynamic lubrication 331 7.6 Surface temperature at the conjunction between contacting solids and its effect on EHL 333 Calculation of surface conjunction temperature 334 · Flash temperature in circular contacts 337 · Flash temperature in square contacts 337 · Flash temperature in line contacts 340 True flash temperature rise 341 Frictional temperature rise of lubricated contacts 345 Mechanism of heat transfer within the EHL film 347 Effect of surface films on conjunction temperatures 348 Measurements of surface temperature in the EHL contacts 348 7.7 Traction and EHL 349 A simplified analysis of traction in the EHL contact 352 Non-Newtonian lubricant rheology and EHL 354 EHL between meshing gear wheels 356 7.8 Summary 358 Revision questions 358 References 360 8 BOUNDARY AND EXTREME PRESSURE LUBRICATION 363 8.1 Introduction 363 8.2 Low temperature - low load lubrication mechanisms 365 8.3 Low temperature - high load lubrication mechanisms 366 Model of adsorption on sliding surfaces 367 · Physisorption 368 · Chemisorption 370 · Influence of the molecular structure of the lubricant on adsorption lubrication 371 · Influence of oxygen and water 375 · Dynamic nature of adsorption under sliding conditions 377 · Mixed lubrication and scuffing 378 · Metallurgical effects 385 · Interaction between surfactant and carrier fluid 386 8.4 High temperature - medium load lubrication mechanisms 387 Chain matching 387 Thick films of soapy or amorphous material 390 · Soap layers 390 · Amorphous layers 391 8.5 High temperature - high load lubrication mechanisms 395 Model of lubrication by sacrificial films 395 Additive reactivity and its effect on lubrication 396 Nascent metallic surfaces and accelerated film formation 399 Influence of oxygen and water on the lubrication mechanism by sacrificial films 401 Mechanism of lubrication by milder E.P. Additives 404 Function of active elements other than sulphur 404 Lubrication with two active elements 405 Temperature distress 407 Speed limitations of sacrificial film mechanism 409 Tribo-emission from worn surfaces 409 8.6 Boundary and E.P. lubrication of non-metallic surfaces 410 8.7 Summary 411 Revision questions 411 References 412 9 SOLID LUBRICATION AND SURFACE TREATMENTS 419 9.1 Introduction 419 9.2 Lubrication by solids 419 9.2.1 Lubrication by lamellar solids 420 Friction and wear characteristics of lamellar solids 423 · Graphite and molybdenum disulphide 423 · Carbon-based materials other than graphite 427 · Minor solid lubricants 428 9.2.2 Reduction of friction by soft metallic films 429 Reduction of friction by metal oxides at high temperatures 430 9.2.3 Deposition methods of solid lubricants 430 Traditional methods of solid lubricant deposition 431 Modern methods of solid lubricant deposition 432 Solid lubricants as additives to oils and polymers 433 9.3 Wear resistant coatings and surface treatments 434 9.3.1 Techniques of producing wear resistant coatings 435 Coating techniques dependent on vacuum or gas at very low pressure 435 · Physical vapour deposition 436 · Chemical vapour deposition 438 · Physical-chemical vapour deposition 439 · Ion implantation 440 Coating processes requiring localized sources of intense heat 440 · Surface welding 441 · Thermal spraying 441 · Laser surface hardening and alloying 443 Coating processes based on deposition in the solid state 445 Miscellaneous coating processes 445 9.3.2 Application of coatings and surface treatments in wear and friction control 447 Characteristics of wear resistant coatings 447 New trends in coating technology 450 · Diamond-like carbon coatings 450 · Carbide and nitride coatings 451 · Thick coatings 452 · Nano-engineered coatings 452 · Other coatings 453 9.4 Summary 453 Revision questions 453 References 454 10 FUNDAMENTALS OF CONTACT BETWEEN SOLIDS 461 10.1 Introduction 461 10.2 Surfaces of solids 461 Surfaces at a nano scale 462 Surface topography 463 Characterization of surface topography 466 · Characterization of surface topography by statistical parameters 466 Multi-scale characterization of surface topography 468 · Characterization of surface topography by Fourier transform 470 · Characterization of surface topography by wavelets 470 · Characterization of surface topography by fractals 470 · Characterization of surface topography by combination of wavelets and fractals 474 Optimum surface roughness 475 10.3 Contact between solids 475 Model of contact between solids based on statistical parameters of rough surfaces 477 Model of contact between solids based on the fractal geometry of rough surfaces 480 Effect of sliding on contact between solid surfaces 482 10.4 Friction and wear 483 Onset of sliding and mechanism of stick-slip 484 Structural differences between static and sliding contacts 486 Friction and other contact phenomena in rolling 488 Concentration of frictional heat at the asperity contacts 491 Thermoelastic instability and transient hump formation 492 Tribo-electrification of sliding contacts 493 Wear between surfaces of solids 493 10.5 Summary 494 Revision questions 494 References 495 11 ABRASIVE, EROSIVE AND CAVITATION WEAR 501 11.1 Introduction 501 11.2 Abrasive wear 501 Mechanisms of abrasive wear 502 Modes of abrasive wear 504 Analytical models of abrasive wear 505 Abrasivity of particles 512 Abrasive wear resistance of materials 517 · Abrasive wear resistance of steels 520 · Abrasive wear resistance of polymers and rubbers 522 · Abrasive wear resistance of ceramics 523 Effect of temperature on abrasive wear 524 Effect of moisture on abrasive wear 525 Control of abrasive wear 526 11.3 Erosive wear 527 Mechanisms of erosive wear 527 Effect of impingement angle and impact speed on erosive wear rate 529 Effect of particle shape, hardness, size and flux rates on erosive wear rate 530 Erosive wear by liquid 532 Effect of temperature on erosive wear 533 Effect of erosion media on erosive wear 535 Erosive wear resistance of materials 536 · Erosive wear resistance of steels 539 · Erosive wear resistance of polymers 540 · Erosive wear of ceramics and cermets 541 11.4 Cavitation wear 542 Mechanism of cavitation wear 542 Cavitation wear resistance of materials 544 11.5 Summary 545 Revision questions 546 References 547 12 ADHESION AND ADHESIVE WEAR 553 12.1 Introduction 553 12.2 Mechanism of adhesion 553 Metal-metal adhesion 553 Metal-polymer adhesion 556 Metal-ceramic adhesion 557 Polymer-polymer and ceramic-ceramic adhesion 557 Effects of adhesion between wearing surfaces 558 · Friction due to adhesion 558 · Junction growth between contacting asperities as a cause of extreme friction 559 · Seizure and scuffing 562 · Asperity deformation and formation of wear particles 562 · Transfer films 564 12.3 Control of the adhesive wear 568 Contaminant layers formed due to surface oxidation and bulk impurities 569 Lubricants 569 Favourable combinations of sliding materials 570 12.4 Summary 570 Revision questions 570 References 571 13 CORROSIVE AND OXIDATIVE WEAR 573 13.1 Introduction 573 13.2 Corrosive wear 573 Transition between corrosive and adhesive wear 578 Synergism between corrosive and abrasive wear 580 Tribochemical polishing 581 13.3 Oxidative wear 582 Kinetics of oxide film growth on metals at high and low temperatures 582 · Oxidative wear at high sliding speeds 583 · Oxidative wear at low sliding speeds 585 · Oxidative wear at high temperature and stress 586 · Oxidative wear at low temperature applications 588 · Transition between oxidative and adhesive wear 588 · Oxidative wear under lubricated conditions 588 Means of controlling corrosive and oxidative wear 589 13.4 Summary 590 Revision questions 590 References 591 14 FATIGUE WEAR 595 14.1 Introduction 595 14.2 Fatigue wear during sliding 596 Surface crack initiated fatigue wear 597 Subsurface crack initiated fatigue wear 599 Effect of lubrication on fatigue wear during sliding 601 Plastic ratchetting 602 14.3 Fatigue wear during rolling 603 Causes of contact fatigue 604 · Asperity contact during EHL and the role of debris in the lubricant in contact fatigue 604 · Material imperfections 605 · Plastic deformation in wheel-rail contacts 605 Self-propagating nature of contact fatigue cracks 606 Subsurface and surface modes of contact fatigue 607 Effect of lubricant on contact fatigue 610 Hydraulic pressure crack propagation 610 Chemical effects of lubricant additives, oxygen and water on contact fatigue 611 Materials effect on contact fatigue 613 Influence of operating conditions on rolling wear and contact fatigue 614 14.4 Means of controlling fatigue wear 615 14.5 Summary 615 Revision questions 615 References 616 15 FRETTING AND MINOR WEAR MECHANISMS 621 15.1 Introduction 621 15.2 Fretting wear 622 Microscopic movements within the contact under applied loads 622 · Elastic model for fretting contacts 622 · Elasto-plastic model for fretting contacts 624 Fretting regimes 625 Effect of amplitude and debris retention on fretting wear 626 Environmental effects on fretting wear 628 Effects of temperature and lubricants on fretting 632 Effect of materials properties and surface finish on fretting 633 Fretting fatigue 634 Practical examples of fretting 636 Means of controlling fretting 638 15.3 Melting wear 639 15.4 Wear due to electrical discharges and passage of electric current across a contact 641 15.5 Diffusive wear 643 15.6 Impact wear 643 15.7 Summary 645 Revision questions 646 References 646 16 WEAR OF NON-METALLIC MATERIALS 651 16.1 Introduction 651 16.2 Tribology of polymers 651 Sliding wear of polymers, transfer layers on a harder counterface 653 Influence of counterface roughness, hardness and material type on transfer films and associated wear and friction of polymers 654 · Counterface hardness 655 · Counterface roughness 655 · Counterface surface energy 658 PV limit 658 Influence of temperature on polymer wear and friction 659 · Limit on frictional temperature rise imposed by surface melting 660 · Effect of high frictional temperatures and sliding speeds on wear 663 · Combined effect of high surface roughness and elevated contact temperature on wear 664 Fatigue wear of polymers and long term wear kinetics 665 Visco-elasticity and the rubbery state 666 Friction and wear in the rubbery state 667 · Schallamach waves 668 · Visco-elasticity and friction of rubbers 669 · Wear mechanisms particular to rubbery solids 670 Effect of lubricant, corrosive agents and microstructure on wear and friction of polymers 670 · Effects of lubricants 670 · Effects of corrosive agents 671 · Effect of oxidizing and biochemical reagents 673 · Effects of polymer microstructure 674 16.3 Tribology of polymer composites 675 Polymer blends 676 Fibre reinforced polymers 676 · Chopped fibre reinforced polymers 676 · Unidirectional and woven fibre reinforcements 677 · Modelling of wear of fibre reinforced polymers 679 Powder composites 680 16.4 Wear and friction of ceramics 681 Unlubricated wear and friction of ceramic-ceramic contacts 683 · Dry friction and wear of ceramics at room temperature 684 · Dry friction and wear of ceramics at elevated temperatures 685 · Friction and wear of ceramics in the presence of water or humid air 685 · Wear modelling of ceramics 687 · Dry wear and friction characteristics of individual ceramics 689 Lubricated wear and friction of ceramic-ceramic contacts 689 · Liquid lubrication 690 · Solid lubricants 692 Wear and friction of ceramics against metallic materials 693 Wear and friction of ceramics against polymers 696 Wear and friction of ceramic matrix composites 697 16.5 Summary 697 Revision questions 698 References 699 17 FUTURE DIRECTIONS IN TRIBOLOGY 705 17.1 Introduction 705 17.2 Biotribology 705 Biotribology of living tissues and organisms 705 Biotribology of artificial materials in close contact with living tissues 708 17.3 Environmental implications of tribology 709 17.4 Nanotribology - basic concepts 711 Relevance to tribology 712 Nanolubrication and specialized materials for nanotribology 713 17.5 Summary 714 Revision questions 715 References 715 APPENDIX 719 Introduction 669 A.1 User friendly interface 669 A.2 Program 'VISCOSITY' 671 Program description 673 List of variables 674 A.3 Program 'SIMPLE' 674 Program description 676 List of variables 677 A.4 Program 'PARTIAL' 678 Program description 681 List of variables 684 A.5 Program 'THERMAL' 686 Program description 690 List of variables 693 A.6 Program 'DEFLECTION' 696 Program description 698 List of variables 701 A.7 Program 'GROOVE' 702 Program description 708 List of variables 714 A.8 Program 'STABILITY' 716 Program description 719 List of variables 721 INDEX 775
Library of Congress Subject Headings for this publication:
Tribology.