Principles of Tribology

Prof. Wen Shizhu, Tsinghua University, China Wen Shizhu is a Professor at Tsinghua University and a CAS Academician. His research fields cover lubrication theory, nano-tribology and the mechanism and control of friction and wear. In 1956, he participated in drafting 12th "National Scientific Development Plan," and finished the first development planning of friction, wear and lubrication engineering. In the late 80s, he was involved in drafting the "Tribology Field Plan and Development Strategy Report" for the National Science and Technology Committee, the Education Committee, and the National Natural Science Foundation Committee. Prof. Huang Ping, South China University of Technology, China Huang Ping is a Professor at South China University of Technology. He obtained his PhD degree from Department of Engineering Mechanics, Tsinghua University, and has worked in the State Key Laboratory of Tribology at Tsinghua University for eight years. He is the head of Institute of mechanical design and equipment, and the State Experimental Training Center of Basic Mechanics of South China University of Technology.

About the Authors xv Preface xvii Introduction xix PART I LUBRICATION THEORY 1 1 Properties of Lubricants 3 1.1 Lubrication States 3 1.2 Density of Lubricant 6 1.3 Viscosity of Lubricant 7 1.3.1 Dynamic Viscosity and Kinematic Viscosity 7 1.3.2 Relationship between Viscosity and Temperature 9 1.3.3 Relationship between Viscosity and Pressure 11 1.3.4 Relationships between Viscosity, Temperature and Pressure 12 1.4 Non-Newtonian Behaviors 12 1.4.1 Ree-Eyring Constitutive Equation 13 1.4.2 Visco-Plastic Constitutive Equation 13 1.4.3 Circular Constitutive Equation 14 1.4.4 Temperature-Dependent Constitutive Equation 14 1.4.5 Visco-Elastic Constitutive Equation 14 1.4.6 Nonlinear Visco-Elastic Constitutive Equation 15 1.4.7 A Simple Visco-Elastic Constitutive Equation 16 1.5 Wettability of Lubricants 17 1.5.1 Wetting and Contact Angle 17 1.5.2 Surface Tension 18 1.6 Measurement and Conversion of Viscosity 19 1.6.1 Rotary Viscometer 19 1.6.2 Off-Body Viscometer 20 1.6.3 Capillary Viscometer 20 References 22 2 Basic Theories of Hydrodynamic Lubrication 23 2.1 Reynolds Equation 24 2.1.1 Basic Assumptions 24 2.1.2 Derivation of Reynolds Equation 24 2.2 Hydrodynamic Lubrication 27 2.2.1 Mechanism of Hydrodynamic Lubrication 27 2.2.2 Boundary Conditions and Initial Conditions of Reynolds Equation 28 2.2.3 Calculation of Hydrodynamic Lubrication 29 2.3 Elastic Contact Problems 30 2.3.1 Line Contact 30 2.3.2 Point Contact 33 2.4 Entrance Analysis of EHL 36 2.4.1 Elastic Deformation of Line Contacts 36 2.4.2 Reynolds Equation Considering the Effect of Pressure-Viscocity 37 2.4.3 Discussion 37 2.4.4 Grubin Film Thickness Formula 39 2.5 Grease Lubrication 40 References 42 3 Numerical Methods of Lubrication Calculation 43 3.1 Numerical Methods of Lubrication 44 3.1.1 Finite Difference Method 44 3.1.2 Finite Element Method and Boundary Element Method 50 3.1.3 Numerical Techniques 53 3.2 Numerical Solution of the Energy Equation 57 3.2.1 Conduction and Convection of Heat 57 3.2.2 Energy Equation 59 3.2.3 Numerical Solution of Energy Equation 61 3.3 The Numerical Solution of Elastohydrodynamic Lubrication 62 3.3.1 EHL Numerical Solution of Line Contacts 62 3.3.2 EHL Numerical Solution of Point Contacts 67 3.4 Multi-Grid Method for Solving EHL Problems 70 3.4.1 Basic Principles of Multi-Grid Method 70 3.4.2 Nonlinear Full Approximation Scheme of Multi-Grid Method 72 3.4.3 V and W Iterations 74 3.4.4 Multi-Grid Solution of EHL Problems 74 3.4.5 Multi-Grid Integration Method 76 References 79 4 Lubrication Design of Typical Mechanical Elements 81 4.1 Slider and Thrust Bearing 81 4.1.1 Basic Equations 81 4.1.2 Solutions of Slider Lubrication 82 4.2 Journal Bearing 85 4.2.1 Axis Position and Clearance Shape 85 4.2.2 Infinitely Narrow Bearing 86 4.2.3 Infinitely Wide Bearing 88 4.3 Hydrostatic Bearing 92 4.3.1 Hydrostatic Thrust Plate 93 4.3.2 Hydrostatic Journal Bearings 94 4.3.3 Bearing Stiffness and Throttle 94 4.4 Squeeze Bearing 96 4.4.1 Rectangular Plate Squeeze 97 4.4.2 Disc Squeeze 98 4.4.3 Journal Bearing Squeeze 99 4.5 Dynamic Bearing 100 4.5.1 Reynolds Equation of Dynamic Journal Bearings 101 4.5.2 Simple Dynamic Bearing Calculation 103 4.5.3 General Dynamic Bearings 104 4.6 Gas Lubrication Bearings 107 4.6.1 Basic Equations of Gas Lubrication 107 4.6.2 Types of Gas Lubrication Bearings 108 4.7 Rolling Contact Bearing 111 4.7.1 Equivalent Radius R 111 4.7.2 Average Velocity U 112 4.7.3 Carrying Load Per Width W/b 112 4.8 Gear Lubrication 113 4.8.1 Involute Gear Transmission 113 4.8.2 Arc Gear Transmission EHL 117 4.9 Cam Lubrication 119 References 121 5 Special Fluid Medium Lubrication 123 5.1 Magnetic Hydrodynamic Lubrication 123 5.1.1 Composition and Classification of Magnetic Fluids 123 5.1.2 Properties of Magnetic Fluids 124 5.1.3 Basic Equations of Magnetic Hydrodynamic Lubrication 126 5.1.4 Influence Factors on the Magnetic EHL 129 5.2 Micro-polar Hydrodynamic Lubrication 129 5.2.1 Basic Equations of Micro-polar Fluid Lubrication 130 5.2.2 Influence Factors on Micro-polar Fluid Lubrication 133 5.3 Liquid Crystal Lubrication 135 5.3.1 Types of Liquid Crystal 136 5.3.2 Deformation Analysis of Liquid Crystal Lubrication 138 5.3.3 Friction Mechanism of Liquid Crystal as a Lubricant Additive 142 5.4 Electric Double Layer Effect in Water Lubrication 143 5.4.1 Electric Double Layer Hydrodynamic Lubrication Theory 144 5.4.2 Influence of Electric Double Layer on Lubrication Properties 148 References 151 6 Lubrication Transformation and Nanoscale Thin Film Lubrication 153 6.1 Transformations of Lubrication States 153 6.1.1 Thickness-Roughness Ratio 153 6.1.2 Transformation from Hydrodynamic Lubrication to EHL 154 6.1.3 Transformation from EHL to Thin Film Lubrication 155 6.2 Thin Film Lubrication 159 6.2.1 Phenomena of Thin Film Lubrication 159 6.2.2 Time Effect of Thin Film Lubrication 161 6.2.3 Shear Strain Rate Effect on Thin Film Lubrication 163 6.3 Analysis of Thin Film Lubrication 165 6.3.1 Difficulties in Numerical Analysis of Thin Film Lubrication 165 6.3.2 Tichy's Thin Film Lubrication Models 166 6.4 Nano-Gas Film Lubrication 168 6.4.1 Rarefied Gas Effect 168 6.4.2 Bounardy Slip 169 6.4.3 Reynolds Equation Considering the Rarefied Gas Effect 172 6.4.4 Calculation of Magnetic Head/Disk of Ultra Thin Gas Lubrication 173 References 176 7 Boundary Lubrication and Additives 177 7.1 Types of Boundary Lubrication 177 7.1.1 Stribeck Curve 177 7.1.2 Adsorption Films and their Lubrication Mechanisms 178 7.1.3 Chemical Reaction Film and its Lubrication Mechanism 183 7.1.4 Other Boundary Films and their Lubrication Mechanisms 185 7.2 Theory of Boundary Lubrication 186 7.2.1 Boundary Lubrication Model 186 7.2.2 Factors Influencing Performances of Boundary Film 187 7.2.3 Strength of Boundary Film 190 7.3 Lubricant Additives 191 7.3.1 Oily Additives 191 7.3.2 Tackifier 192 7.3.3 Extreme Pressure Additives (EP Additives) 193 7.3.4 Anti-Wear Additives (AWAdditives) 193 7.3.5 Other Additives 194 References 195 8 Lubrication Failure and Mixed Lubrication 197 8.1 Roughness and Viscoelastic Material Effects on Lubrication 197 8.1.1 Modifications of micro-EHL 197 8.1.2 Viscoelastic Model 198 8.1.3 Lubricated Wear 199 8.2 Influence of Limit Shear Stress on Lubrication Failure 202 8.2.1 Visco-Plastic Constitutive Equation 203 8.2.2 Slip of Fluid-Solid Interface 203 8.2.3 Influence of Slip on Lubrication Properties 204 8.3 Influences of Temperature on Lubrication Failure 207 8.3.1 Mechanism of Lubrication Failure Caused by Temperature 208 8.3.2 Thermal Fluid Constitutive Equation 208 8.3.3 Analysis of Lubrication Failure 209 8.4 Mixed Lubrication 210 References 215 PART II FRICTION AND WEAR 217 9 Surface Topography and Contact 219 9.1 Parameters of Surface Topography 219 9.1.1 Arithmetic Mean Deviation Ra 219 9.1.2 Root-Mean-Square Deviation (RMS) s or Rq 219 9.1.3 Maximum Height Rmax 220 9.1.4 Load-carrying Area Curve 220 9.1.5 Arithmetic Mean Interception Length of Centerline Sma 220 219 9.2 Statistical Parameters of Surface Topography 222 9.2.1 Height Distribution Function 222 9.2.2 Deviation of Distribution 224 9.2.3 Autocorrelation Function of Surface Profile 225 9.3 Structures and Properties of Surface 226 9.4 Rough Surface Contact 227 9.4.1 Single Peak Contact 228 9.4.2 Ideal Roughness Contact 229 9.4.3 Random Roughness Contact 230 9.4.4 Plasticity Index 232 References 232 10 Solid Friction and Control 233 10.1 Basic Characteristics of Friction 233 10.1.1 Influence of Stationary Contact Time 234 10.1.2 Jerking Motion 234 10.1.3 Pre-Displacement 235 10.2 Macro-friction Theory 236 10.2.1 Mechanical Engagement Theory 236 10.2.2 Molecular Action Theory 237 10.2.3 Adhesive Friction Theory 238 10.2.4 Plowing Effect 241 10.2.5 Deformation Energy Friction Theory 243 10.2.6 Binomial Friction Theory 245 10.3 Micro-friction Theory 246 10.3.1 Cobblestone Model 246 10.3.2 Oscillator Models 248 10.3.3 Phonon Friction Model 251 10.4 Sliding Friction 251 10.4.1 Influence of Load 252 10.4.2 Influence of Sliding Velocity 252 10.4.3 Influence of Temperature 253 10.4.4 Influence of Surface Film 253 10.5 Rolling Friction 254 10.5.1 Rolling Friction Mechanism 256 10.5.2 Resistances of Rolling Friction 256 10.6 Special Friction and Friction Control 257 10.6.1 Special Friction 257 10.6.2 Friction Control 258 References 261 11 Characteristics and Mechanisms of Wear 263 11.1 Classification of Wear 263 11.1.1 Wear Categories 264 11.1.2 Wear Process 264 11.1.3 Conversion of Wear 266 11.2 Abrasive Wear 266 11.2.1 Types of Abrasive Wear 267 11.2.2 Influence Factors on Abrasive Wear 267 11.2.3 Mechanism of Abrasive Wear 271 11.3 Adhesive Wear 272 11.3.1 Types of Adhesive Wear 272 11.3.2 Influence Factors on Adhesive Wear 273 11.3.3 Adhesive Wear Mechanism 275 11.3.4 Criteria of Scuffing 277 11.4 Fatigue Wear 280 11.4.1 Types of Fatigue Wear 280 11.4.2 Influence Factors on Fatigue Wear 281 11.4.3 Criteria of Fatigue Strength and Fatigue Life 285 11.5 Corrosive Wear 289 11.5.1 Oxidation Wear 289 11.5.2 Special Corrosive Wear 291 11.5.3 Fretting 291 11.5.4 Cavitation Erosion 292 References 295 12 Macro-wear Theory 297 12.1 Friction Material 298 12.1.1 Friction Material Properties 298 12.1.2 Wear-Resistant Mechanism 299 12.2 Wear Process Curve 300 12.2.1 Types of Wear Process Curves 300 12.2.2 Running-In 301 12.3 Surface Quality and Wear 304 12.3.1 Influence of Geometric Quality 304 12.3.2 Physical Quality 307 12.4 Theory of Adhesion Wear 308 12.5 Theory of Energy Wear 309 12.6 Delamination Wear Theory and Fatigue Wear Theory 311 12.6.1 Delamination Wear Theory 311 12.6.2 Fatigue Wear Theory 312 12.7 Wear Calculation 313 12.7.1 IBM Wear Calculation Method 313 12.7.2 Calculation Method of Combined Wear 314 References 319 13 Anti-Wear Design and Surface Coating 321 13.1 Selection of Lubricant and Additive 321 13.1.1 Lubricant Selection 322 13.1.2 Grease Selection 324 13.1.3 Solid Lubricants 325 13.1.4 Seal and Filter 326 13.2 Matching Principles of Friction Materials 326 13.2.1 Material Mating for Abrasive Wear 327 13.2.2 Material Mating for Adhesive Wear 328 13.2.3 Material Mating for Contact Fatigue Wear 329 13.2.4 Material Mating for Fretting Wear 330 13.2.5 Material Mating for Corrosion Wear 330 13.2.6 Surface Hardening 330 13.3 Surface Coating 331 13.3.1 Commonly Plating Methods 331 13.3.2 Design of Surface Coating 338 13.4 Coating Performance Testing 339 13.4.1 Appearance and Structure 339 13.4.2 Bond Strength Test 340 13.4.3 Hardness Test 344 13.4.4 Wear Test 345 13.4.5 Tests of Other Performances 345 References 346 14 Tribological Experiments 347 14.1 Tribological Experimental Method and Device 347 14.1.1 Experimental Methods 347 14.1.2 Commonly Used Friction and Wear Testing Machines 349 14.1.3 EHL and Thin Film Lubrication Test 349 14.2 Measurement of Wear Capacity 352 14.2.1 Weighing Method 352 14.2.2 Length Measurement Method 352 14.2.3 Profile Method 352 14.2.4 Indentation Method 353 14.2.5 Grooving Method 356 14.2.6 Precipitation Method and Chemical Analysis Method 357 14.2.7 Radioactive Method 357 14.3 Analysis of Friction Surface Morphology 358 14.3.1 Analysis of Surface Topography 358 14.3.2 Atomic Force Microscope (AFM) 358 14.3.3 Surface Structure Analysis 360 14.3.4 Surface Chemical Composition Analysis 362 14.4 Wear State Detection 363 14.4.1 Ferrography Analysis 363 14.4.2 Spectral Analysis 365 14.4.3 Lubricant Composition Analysis 365 14.4.4 Mechanical Vibration and Noise Analysis 365 14.4.5 Lubrication State Analysis 365 14.5 Wear Failure Analysis 365 14.5.1 Site Investigation 365 14.5.2 Lubricant and its Supply System 366 14.5.3 Worn Part Analysis 366 14.5.4 Design and Operation 366 References 367 PART III APPLIED TRIBOLOGY 369 15 Micro-tribology 371 15.1 Micro-friction 371 15.1.1 Macro-friction and Micro-friction 371 15.1.2 Micro-friction and Surface Topography 372 15.1.3 Plowing Effect and Adhesion Effective 375 15.2 Micro-contact and Micro-adhesion 377 15.2.1 Solid Micro-contact 377 15.2.2 Solid Adhesion and Surface Force 378 15.3 Micro-Wear 380 15.3.1 Micro-Wear Experiment 380 15.3.2 Micro-Wear of Magnetic Head and Disk 382 15.4 Molecular Film and Boundary Lubrication 385 15.4.1 Static Shear Property of Molecular Layer 386 15.4.2 Dynamic Shear Property of Monolayer and Stick-Slip Phenomenon 387 15.4.3 Physical State and Phase Change 389 15.4.4 Temperature Effect and Friction Mechanism 390 15.4.5 Rheological Property of Molecular Film 390 15.4.6 Ordered Molecular Film 393 References 395 16 Metal Forming Tribology 397 16.1 Mechanics Basis of Metal Forming 397 16.1.1 Yield Criterion 397 16.1.2 Friction Coefficient and Shear Factor 398 16.1.3 Influence of Friction on Metal Forming 400 16.2 Forging Tribology 401 16.2.1 Upsetting Friction 401 16.2.2 Friction of Open Die Forging 403 16.2.3 Friction of Closed-Die Forging 403 16.2.4 Lubrication and Wear 404 16.3 Drawing Tribology 406 16.3.1 Friction and Temperature 406 16.3.2 Lubrication 407 16.3.3 Wear of Drawing Die 409 16.3.4 Anti-Friction of Ultrasound in Drawing 412 16.4 Rolling Tribology 415 16.4.1 Friction in Rolling 415 16.4.2 Lubrication in Rolling 417 16.4.3 Roller Wear 419 16.4.4 Emulsion Lubricity in Rolling 421 References 421 17 Bio-Tribology 423 17.1 Mechanics Basis for Soft Biological Tissue 423 17.1.1 Rheological Property of Soft Tissue 423 17.1.2 Stress-Strain Curve Analysis 423 17.1.3 Anisotropy Relationship 425 17.2 Characteristics of Joint Lubricating Fluid 426 17.2.1 Joint Lubricating Fluid 426 17.2.2 Lubrication Characteristics of Joint Fluid 427 17.3 Lubrication of Human and Animal Joints 430 17.3.1 Performance of Human Joint 430 17.3.2 Joint Lubricating Fluid 431 17.3.3 Lubrication Mechanism of Joint 432 17.4 Friction and Wear of Artificial Joint 434 17.4.1 Friction and Wear Test 434 17.4.2 Wear of Artificial Joint 435 17.5 Other Bio-Tribological Studies 438 References 438 18 Space Tribology 439 18.1 Features of Space Agency and Space Tribology 439 18.1.1 Working Conditions in Space 439 18.1.2 Features of Space Tribology Problems 441 18.2 Analysis of Performances of Space Tribology 442 18.2.1 Starved Lubrication 442 18.2.2 Parched Lubrication 443 18.2.3 Volatility Analysis 444 18.2.4 Creeping 446 18.3 Space Lubricating Properties 448 18.3.1 EHL Characteristics of Space Lubricant 448 18.3.2 Space Lubrication of Rolling Contact Bearing 449 References 450 Index 453