k kContents About the Authors xxi Second Edition Preface xxiii 1.3.3 Relationship between Viscosity and Pressure 10 1.3.3.1 Relationships between Viscosity, Temperature and Pressure 11 1
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k
Principles of Tribology
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Principles of Tribology
Shizhu Wen
Tsinghua UniversityBeijing, China
Ping Huang
South China University of TechnologyGuangzhou, China
Second Edition
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This edition first published 2018 by John Wiley & Sons Singapore Pte Ltd under exclusive licence granted by Tsinghua University Press (TUP) for all media and languages (excluding simplified and traditional Chinese) throughout the world (excluding Mainland China), and with non-exclusive license for electronic versions in Mainland China.
© 2018 Tsinghua University Press
Edition History
Tsinghua University Press (1e, 2012) All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law.
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Library of Congress Cataloging-in-Publication Data
Names: Wen, Shizhu, 1932- author | Huang, Ping, 1957- author.
Title: Principles of Tribology / Wen Shizhu, Huang Ping.
Description: 2nd edition | Hoboken, NJ : John Wiley & Sons Inc., 2018 | Includes bibliographical references and index.
Identifiers: LCCN 2017007236 (print) | LCCN 2017010423 (ebook) | ISBN
9781119214892 (cloth) | ISBN 9781119214922 (Adobe PDF) | ISBN
9781119214915 (ePub) Subjects: LCSH: Tribology.
Classification: LCC TJ1075 W43 2017 (print) | LCC TJ1075 (ebook) | DDC 621.8/9–dc23
LC record available at https://lccn.loc.gov/2017007236 Cover design by Wiley
Cover image: © peepo/Gettyimages Set in 10/12pt Warnock by SPi Global, Chennai, India
10 9 8 7 6 5 4 3 2 1
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Contents
About the Authors xxi
Second Edition Preface xxiii
1.3.3 Relationship between Viscosity and Pressure 10
1.3.3.1 Relationships between Viscosity, Temperature and Pressure 11
1.4 Non-Newtonian Behaviors 12
1.4.1 Ree–Eyring Constitutive Equation 12
1.4.2 Visco-Plastic Constitutive Equation 13
1.4.3 Circular Constitutive Equation 13
1.4.4 Temperature-Dependent Constitutive Equation 13
1.4.5 Visco-Elastic Constitutive Equation 14
1.4.6 Nonlinear Visco-Elastic Constitutive Equation 14
1.4.7 A Simple Visco-Elastic Constitutive Equation 15
Trang 52.2.1 Mechanism of Hydrodynamic Lubrication 26
2.2.2 Boundary Conditions and Initial Conditions of the Reynolds Equation 27
2.3.1.1 Geometry and Elasticity Simulations 29
2.3.1.2 Contact Area and Stress 30
2.3.2 Point Contact 31
2.3.2.1 Geometric Relationship 31
2.3.2.2 Contact Area and Stress 32
2.4 Entrance Analysis of EHL 34
2.4.1 Elastic Deformation of Line Contacts 35
2.4.2 Reynolds Equation Considering the Effect of Pressure-Viscosity 35
2.4.3 Discussion 36
2.4.4 Grubin Film Thickness Formula 37
2.5 Grease Lubrication 38
References 40
3 Numerical Methods of Lubrication Calculation 41
3.1 Numerical Methods of Lubrication 42
3.1.1 Finite Difference Method 42
3.1.1.1 Hydrostatic Lubrication 44
3.1.1.2 Hydrodynamic Lubrication 44
3.1.2 Finite Element Method and Boundary Element Method 48
3.1.2.1 Finite Element Method (FEM) 48
3.1.2.2 Boundary Element Method 49
3.1.3 Numerical Techniques 51
3.1.3.1 Parameter Transformation 51
3.1.3.2 Numerical Integration 51
3.1.3.3 Empirical Formula 53
3.1.3.4 Sudden Thickness Change 53
3.2 Numerical Solution of the Energy Equation 54
3.2.1 Conduction and Convection of Heat 55
3.2.1.1 Conduction Heat H d 55
3.2.1.2 Convection Heat H v 55
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3.2.2 Energy Equation 56
3.2.3 Numerical Solution of Energy Equation 59
3.3 Numerical Solution of Elastohydrodynamic Lubrication 60
3.3.1 EHL Numerical Solution of Line Contacts 60
3.3.1.1 Basic Equations 60
3.3.1.2 Solution of the Reynolds Equation 62
3.3.1.3 Calculation of Elastic Deformation 62
3.3.1.4 Dowson–Higginson Film Thickness Formula of Line Contact EHL 64
3.3.2 EHL Numerical Solution of Point Contacts 64
3.3.2.1 The Reynolds Equation 65
3.3.2.2 Elastic Deformation Equation 66
3.3.2.3 Hamrock–Dowson Film Thickness Formula of Point Contact EHL 66
3.4 Multi-Grid Method for Solving EHL Problems 68
3.4.1 Basic Principles of Multi-Grid Method 68
3.4.4.4 Numbers of Iteration Times 73
3.4.5 Multi-Grid Integration Method 73
3.4.5.1 Transfer Pressure Downwards 74
3.4.5.2 Transfer Integral Coefficients Downwards 74
3.4.5.3 Integration on the Coarser Mesh 74
3.4.5.4 Transfer Back Integration Results 75
3.4.5.5 Modification on the Finer Mesh 75
References 76
4 Lubrication Design of Typical Mechanical Elements 78
4.1 Slider and Thrust Bearings 78
4.2.1 Axis Position and Clearance Shape 81
4.2.2 Infinitely Narrow Bearings 82
4.2.2.1 Load-Carrying Capacity 83
4.2.2.2 Deviation Angle and Axis Track 83
4.2.2.3 Flow 84
4.2.2.4 Frictional Force and Friction Coefficient 84
4.2.3 Infinitely Wide Bearings 85
4.3 Hydrostatic Bearings 88
4.3.1 Hydrostatic Thrust Plate 89
4.3.2 Hydrostatic Journal Bearings 90
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4.3.3 Bearing Stiffness and Throttle 90
4.3.3.1 Constant Flow Pump 91
4.5.1 Reynolds Equation of Dynamic Journal Bearings 96
4.5.2 Simple Dynamic Bearing Calculation 98
4.5.2.1 A Sudden Load 98
4.5.2.2 Rotating Load 99
4.5.3 General Dynamic Bearings 100
4.5.3.1 Infinitely Narrow Bearings 100
4.5.3.2 Superimposition Method of Pressures 101
4.5.3.3 Superimposition Method of Carrying Loads 101
4.6 Gas Lubrication Bearings 102
4.6.1 Basic Equations of Gas Lubrication 102
4.6.2 Types of Gas Lubrication Bearings 103
4.7 Rolling Contact Bearings 106
4.7.1 Equivalent Radius R 107
4.7.2 Average Velocity U 107
4.7.3 Carrying Load Per Width W /b 107
4.8 Gear Lubrication 108
4.8.1 Involute Gear Transmission 109
4.8.1.1 Equivalent Curvature Radius R 110
4.8.1.2 Average Velocity U 111
4.8.1.3 Load Per Width W /b 112
4.8.2 Arc Gear Transmission EHL 112
4.9 Cam Lubrication 114
References 116
5 Special Fluid Medium Lubrication 118
5.1 Magnetic Hydrodynamic Lubrication 118
5.1.1 Composition and Classification of Magnetic Fluids 118
5.1.2 Properties of Magnetic Fluids 119
5.1.2.1 Density of Magnetic Fluids 119
5.1.2.2 Viscosity of Magnetic Fluids 119
5.1.2.3 Magnetization Strength of Magnetic Fluids 120
5.1.2.4 Stability of Magnetic Fluids 120
5.1.3 Basic Equations of Magnetic Hydrodynamic Lubrication 121
5.1.4 Influence Factors on Magnetic EHL 123
5.2 Micro-Polar Hydrodynamic Lubrication 124
5.2.1 Basic Equations of Micro-Polar Fluid Lubrication 124
5.2.1.1 Basic Equations of Micro-Polar Fluid Mechanics 124
5.2.1.2 Reynolds Equation of Micro-Polar Fluid 125
5.2.2 Influence Factors on Micro-Polar Fluid Lubrication 128
5.2.2.1 Influence of Load 128
5.2.2.2 Main Influence Parameters of Micro-Polar Fluid 129
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5.3 Liquid Crystal Lubrication 130
5.3.1 Types of Liquid Crystal 130
5.3.1.1 Tribological Properties of Lyotropic Liquid Crystal 131
5.3.1.2 Tribological Properties of Thermotropic Liquid Crystal 131
5.3.2 Deformation Analysis of Liquid Crystal Lubrication 132
5.3.3 Friction Mechanism of Liquid Crystal as a Lubricant Additive 136
5.3.3.1 Tribological Mechanism of 4-pentyl-4′-cyanobiphenyl 136
5.3.3.2 Tribological Mechanism of Cholesteryl Oleyl Carbonate 136
5.4 Electric Double Layer Effect in Water Lubrication 137
5.4.1 Electric Double Layer Hydrodynamic Lubrication Theory 138
5.4.1.1 Electric Double Layer Structure 138
5.4.1.2 Hydrodynamic Lubrication Theory of Electric Double Layer 138
5.4.2 Influence of Electric Double Layer on Lubrication Properties 142
6 Lubrication Transformation and Nanoscale Thin Film Lubrication 147
6.1 Transformations of Lubrication States 147
6.1.1 Thickness-Roughness Ratio𝜆 147
6.1.2 Transformation from Hydrodynamic Lubrication to EHL 148
6.1.3 Transformation from EHL to Thin Film Lubrication 149
6.2 Thin Film Lubrication 152
6.2.1 Phenomenon of Thin Film Lubrication 153
6.2.2 Time Effect of Thin Film Lubrication 154
6.2.3 Shear Strain Rate Effect on Thin Film Lubrication 157
6.3 Analysis of Thin Film Lubrication 158
6.3.1 Difficulties in Numerical Analysis of Thin Film Lubrication 158
6.3.2 Tichy’s Thin Film Lubrication Models 160
6.3.2.1 Direction Factor Model 160
6.3.2.2 Surface Layer Model 161
6.3.2.3 Porous Surface Layer Model 161
6.4 Nano-Gas Film Lubrication 161
6.4.1 Rarefied Gas Effect 162
6.4.2 Boundary Slip 163
6.4.2.1 Slip Flow 163
6.4.2.2 Slip Models 163
6.4.2.3 Boltzmann Equation for Rarefied Gas Lubrication 165
6.4.3 Reynolds Equation Considering the Rarefied Gas Effect 165
6.4.4 Calculation of Magnetic Head/Disk of Ultra Thin Gas Lubrication 166
6.4.4.1 Large Bearing Number Problem 167
6.4.4.2 Sudden Step Change Problem 167
6.4.4.3 Solution of Ultra-Thin Gas Lubrication of Multi-Track Magnetic Heads 167
References 169
7 Boundary Lubrication and Additives 171
7.1 Types of Boundary Lubrication 171
7.1.1 Stribeck Curve 171
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7.1.2 Adsorption Films and Their Lubrication Mechanisms 172
7.1.2.1 Adsorption Phenomena and Adsorption Films 172
7.1.2.2 Structure and Property of Adsorption Films 174
7.1.3 Chemical Reaction Film and its Lubrication Mechanism 177
7.1.3.1 Additives of Chemical Reaction Film 178
7.1.3.2 Notes for Applications of Extreme Pressure Additives 178
7.1.4 Other Boundary Films and their Lubrication Mechanisms 179
7.1.4.1 High Viscosity Thick Film 179
7.1.4.2 Polishing Thin Film 179
7.1.4.3 Surface Softening Effect 179
7.2 Theory of Boundary Lubrication 179
7.2.1 Boundary Lubrication Model 179
7.2.2 Factors Influencing Performance of Boundary Films 181
7.2.2.1 Internal Pressure Caused by Surface Tension 181
7.2.2.2 Adsorption Heat of Boundary Film 182
8 Lubrication Failure and Mixed Lubrication 190
8.1 Roughness and Viscoelastic Material Effects on Lubrication 190
8.1.1 Modifications of Micro-EHL 190
8.1.2 Viscoelastic Model 191
8.1.3 Lubricated Wear 192
8.1.3.1 Lubricated Wear Criteria 193
8.1.3.2 Lubricated Wear Model 193
8.1.3.3 Lubricated Wear Example 193
8.2 Influence of Limit Shear Stress on Lubrication Failure 195
8.2.1 Visco-Plastic Constitutive Equation 195
8.2.2 Slip of Fluid–Solid Interface 196
8.2.3 Influence of Slip on Lubrication Properties 196
8.3 Influence of Temperature on Lubrication Failure 200
8.3.1 Mechanism of Lubrication Failure Caused by Temperature 200
8.3.2 Thermal Fluid Constitutive Equation 201
8.3.3 Analysis of Lubrication Failure 202
8.4 Mixed Lubrication 203
References 207
Part II Friction and Wear 209
9 Surface Topography and Contact 211
9.1 Parameters of Surface Topography 211
9.1.1 Arithmetic Mean Deviation R a 211
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9.1.2 Root-Mean-Square Deviation (RMS)𝜎 or R q 211
9.1.3 Maximum Height Rmax 212
9.1.4 Load-Carrying Area Curve 212
9.1.5 Arithmetic Mean Interception Length of Centerline S ma 212
9.1.5.1 Slope ̇z aoṙz q 213
9.1.5.2 Peak Curvature C a or C q 213
9.2 Statistical Parameters of Surface Topography 213
9.2.1 Height Distribution Function 214
9.2.2 Deviation of Distribution 215
9.2.3 Autocorrelation Function of Surface Profile 216
9.3 Structures and Properties of Surface 217
9.4 Rough Surface Contact 219
9.4.1 Single Peak Contact 219
9.4.2 Ideal Roughness Contact 220
9.4.3 Random Roughness Contact 221
9.4.4 Plasticity Index 223
References 223
10 Sliding Friction and its Applications 225
10.1 Basic Characteristics of Friction 225
10.1.1 Influence of Stationary Contact Time 226
10.1.2 Jerking Motion 226
10.1.3 Pre-Displacement 227
10.2 Macro-Friction Theory 228
10.2.1 Mechanical Engagement Theory 228
10.2.2 Molecular Action Theory 229
10.2.3 Adhesive Friction Theory 229
10.2.3.1 Main Points of Adhesive Friction Theory 230
10.2.3.2 Revised Adhesion Friction Theory 232
10.2.4 Plowing Effect 233
10.2.5 Deformation Energy Friction Theory 235
10.2.6 Binomial Friction Theory 236
10.3 Micro-Friction Theory 238
10.3.1 “Cobblestone” Model 238
10.3.2 Oscillator Models 240
10.3.2.1 Independent Oscillator Model 240
10.3.2.2 Composite Oscillator Model 241
10.4.4 Influence of Surface Film 245
10.5 Other Friction Problems and Friction Control 246
10.5.1 Friction in Special Working Conditions 246
10.5.1.1 High Velocity Friction 246
10.5.1.2 High Temperature Friction 246
10.5.1.3 Low Temperature Friction 247
10.5.1.4 Vacuum Friction 247
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10.5.2 Friction Control 247
10.5.2.1 Method of Applying Voltage 247
10.5.2.2 Effectiveness of Electronic Friction Control 248
10.5.2.3 Real-Time Friction Control 249
References 250
11 Rolling Friction and its Applications 252
11.1 Basic Theories of Rolling Friction 252
11.1.1 Rolling Resistance Coefficient 252
11.1.2 Rolling Friction Theories 254
11.1.2.1 Hysteresis Theory 255
11.1.2.2 Plastic Deformation Theory 256
11.1.2.3 Micro Slip Theory 257
11.1.3 Adhesion Effect on Rolling Friction 258
11.1.4 Factors Influencing Rolling Friction of Wheel and Rail 260
11.1.5 Thermal Analysis of Wheel and Rail 262
11.1.5.1 Heat Transferring Model of Wheel and Rail Contact 262
11.1.5.2 Temperature Rise Analysis of Wheel and Rail Contact 264
11.1.5.3 Transient Temperature Rise Analysis of Wheel for Two-Dimensional Thermal
Shock 268
11.1.5.4 Three-Dimensional Transient Analysis of Temperature Rise of Contact 269
11.1.5.5 Thermal Solution for the Rail 270
11.2 Applications of Rolling Tribology in Design of Lunar Rover 271
11.2.1 Foundations of Force Analysis for Rigid Wheel 271
11.2.1.1 Resistant Force of Driving Rigid Wheel 271
11.2.1.2 Driving Force and Sliding/Rolling Ratio of the Wheel 274
11.2.2 Mechanics Model of a Wheel on a Soft Surface 275
11.2.2.1 Wheel Sinkage 276
11.2.2.2 Soil Deformation and Stress Model 276
11.2.2.3 Interaction Force between Wheel and Soil 277
11.2.3 Dynamic Analysis of Rolling Mechanics of Lunar Rover with Unequal Diameter
Wheel 278
11.2.3.1 Structure with Unequal Diameter Wheel 278
11.2.3.2 Interaction model of wheel and soil 278
11.2.3.3 Model and Calculation of Movement for Unequal Diameter Wheel 280
12.1.1.2 Molecular and Mechanical Wear 283
12.1.1.3 Corrosive and Mechanical Wear 283
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12.2.2 Factors Influencing Abrasive Wear 286
12.2.3 Mechanism of Abrasive Wear 289
12.3 Adhesive Wear 290
12.3.1 Types of Adhesive Wear 291
12.3.1.1 Light Adhesive Wear 291
12.3.1.2 Common Adhesive Wear 291
s ≤ c 296
12.3.4.3 Instantaneous Temperature Criterion 297
12.3.4.4 Scuffing Factor Criterion 298
12.4 Fatigue Wear 298
12.4.1 Types of Fatigue Wear 298
12.4.1.1 Superficial Fatigue Wear and Surface Fatigue Wear 298
12.4.1.2 Pitting and Peeling 299
12.4.2 Factors Influencing Fatigue Wear 300
12.4.2.1 Load Property 300
12.4.2.2 Material Property 302
12.4.2.3 Physical and Chemical Effects of the Lubricant 302
12.4.3 Criteria of Fatigue Strength and Fatigue Life 303
12.4.3.1 Contact Stress State 303
12.4.3.2 Contact Fatigue Strength Criteria 304
12.4.3.3 Contact Fatigue Life 306
12.5 Corrosive Wear 307
12.5.1 Oxidation Wear 307
12.5.2 Special Corrosive Wear 309
12.5.2.1 Factors Influencing the Corrosion Wear 309
13.1.2.1 Hard Phase Bearing Mechanism 316
13.1.2.2 Soft Phase Bearing Mechanism 316
13.1.2.3 Porous Saving Oil Mechanism 316
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13.1.2.4 Plastic Coating Mechanism 317
13.2 Wear Process Curve 317
13.2.1 Types of Wear Process Curves 317
13.2.2 Running-In 317
13.2.2.1 Working Life 318
13.2.2.2 Measures to Improve the Running-in Performance 319
13.3 Surface Quality and Wear 320
13.3.1 Influence of Geometric Quality 321
13.3.2 Physical Quality 323
13.4 Theory of Adhesion Wear 324
13.5 Theory of Energy Wear 325
13.6 Delamination Wear Theory and Fatigue Wear Theory 327
13.6.1 Delamination Wear Theory 327
13.6.2 Fatigue Wear Theory 329
14 Anti-Wear Design and Surface Coating 337
14.1 Selection of Lubricant and Additive 337
14.1.4 Seal and Filter 341
14.2 Matching Principles of Friction Materials 343
14.2.1 Material Mating for Abrasive Wear 343
14.2.2 Material Mating for Adhesive Wear 344
14.2.3 Material Mating for Contact Fatigue Wear 345
14.2.4 Material Mating for Fretting Wear 345
14.2.5 Material Mating for Corrosion Wear 345
14.3.2 Design of Surface Coating 354
14.3.2.1 General Principles of Coating Design 354
14.3.2.2 Selection of Surface Plating Method 354
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14.4 Coating Performance Testing 355
14.4.1 Appearance and Structure 355
14.4.1.1 Coating Appearance 355
14.4.1.2 Measurement of Coating Thickness 355
14.4.1.3 Determination of Coating Porosity 355
14.4.2 Bond Strength Test 356
14.4.2.1 Drop Hammer Impact Test 356
14.4.2.2 Vibrator Impact Test 356
14.4.2.3 Scratch Test 357
14.4.2.4 Broken Test 357
14.4.2.5 Tensile Bond Strength Test 357
14.4.2.6 Shear Bond Strength Test 357
14.4.2.7 Measurement of Internal Bond Strength of Coating 358
15.1.2 Commonly Used Friction and Wear Testing Machines 364
15.1.3 EHL and Thin Film Lubrication Test 365
15.1.3.1 EHL and Thin Film Lubrication Test Machine 365
15.1.3.2 Principle of Relative Light Intensity 366
15.2 Measurement of Wear Capacity 368
15.3 Analysis of Friction Surface Morphology 373
15.3.1 Analysis of Surface Topography 373
15.3.2 Atomic Force Microscope (AFM) 374
15.3.3 Surface Structure Analysis 375
15.3.4 Surface Chemical Composition Analysis 377
15.3.4.1 Energy Spectrum Analysis 377
15.3.4.2 Electron Probe Micro-Analysis (EPMA) 377
15.4 Wear State Detection 378
15.4.1 Ferrography Analysis 378
15.4.2 Spectral Analysis 379
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17.2.3 Friction of Closed-Die Forging 418
17.2.4 Lubrication and Wear 418
17.3 Drawing Tribology 421
17.3.1 Friction and Temperature 421
17.3.2 Lubrication 422
17.3.2.1 Establishment of Hydrodynamic Lubrication 423
17.3.2.2 Hydrodynamic Lubrication Calculation of Drawing 424
17.3.3 Wear of Drawing Die 424
17.3.3.1 Wear of Die Shape 424
17.3.3.2 Wear Mechanism 425
17.3.3.3 Measures to Reduce Wear 425
17.3.4 Anti-Friction of Ultrasound in Drawing 427
17.4 Rolling Tribology 429
17.4.1 Friction in Rolling 429
17.4.1.1 Pressure Distribution and Frictional Force 429
17.4.1.2 Friction Coefficient of Rolling 430
18.1 Mechanics Basis for Soft Biological Tissue 437
18.1.1 Rheological Properties of Soft Tissue 437
18.1.2 Stress–Strain Curve Analysis 437
18.1.3 Anisotropy Relationships 439
18.2 Characteristics of Joint Lubricating Fluid 440
18.2.1 Joint Lubricating Fluid 440
18.2.2 Lubrication Characteristics of Joint Fluid 441
18.3 Lubrication of Human and Animal Joints 443
18.3.1 Performance of Human Joint 444
18.3.2 Joint Lubricating Fluid 445
18.3.3 Lubrication Mechanism of Joint 446
18.4 Friction and Wear of Artificial Joint 447
18.4.1 Friction and Wear Test 447
18.4.2 Wear of Artificial Joint 448
18.4.2.1 Experimental Method and Apparatus 449
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19.1.1 Working Conditions in Space 453
19.1.2 Features of Space Tribology Problems 455
19.2 Analysis of Performances of Space Tribology 456
19.2.1 Starved Lubrication 456
19.2.2 Parched Lubrication 456
19.2.3 Volatility Analysis 458
19.2.4 Creeping 460
19.3 Space Lubricating Properties 462
19.3.1 EHL Characteristics of Space Lubricant 462
19.3.2 Space Lubrication of Rolling Contact Bearing 463
20.2 Tribological Analysis Technique for MEMS 467
20.2.1 Measurement of Micro/Nano-Frictional Force 467
20.2.2 Stick-Slip Phenomenon 470
20.2.3 Measurement of Micro Adhesive Force 473
20.2.4 Factors Influencing Surface Analysis 473
20.2.4.1 Normal Load 473
20.2.4.2 Temperature 478
20.2.4.3 Sliding Velocity 483
20.3 Tribological Study of a Micro Motor 484
20.3.1 Lubrication of Micro Motor 486
20.3.2 Measurement of Frictional Force 487
20.3.3 Influence Factors 488
20.3.3.1 Intermittent Time 488
20.3.3.2 Humidity 489
20.3.3.3 Hydrodynamic Film and Boundary Film 490
20.4 Wear Analysis of MEMS 491
20.4.1 Mechanism of Micro Wear 492
20.4.2 Micro Wear of Monocrystalline Silicon 494
20.4.3 Micro Wear of Nickel Titanium Shape Memory Alloy 496
Trang 1721.1.3.2 Types of Molecular Films 514
21.1.3.3 Influence of External Field 515
21.2 Green Lubricant 516
21.2.1 Introduction of Green Lubricants 517
21.2.1.1 Harmfulness of petroleum products 517
21.2.1.2 Harmfulness of Waste Oil 517
21.2.1.3 Harmfulness of Waste Gas 517
21.2.1.4 Green Basis Oils, Lubricating Oil and Additives 517
21.2.2 Development of Green Lubricating Oil for Refrigeration 518
21.3.2 Friction-Induced Noise of Wheel-Rail 524
21.3.3 Friction-Induced Noise of Rolling Contact Bearing 526
21.3.3.1 Sources of Noise 526
21.3.3.2 Influence Factors of Noise 527
21.4 Remanufacturing and Self-Repairing 528
21.4.1 Remanufacturing 529
21.4.1.1 Laser Remanufacturing Technology 529
21.4.1.2 Electric Brush Plating Technology 530
21.4.1.3 Nano Brush Plating Technology 530
21.4.1.4 Supersonic Spray Coating Technology 530
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About the Authors
Wen Shizhuis a member of the Chinese Academy of Sciences and professor of the Department
of Precision Instruments and Technology, Tsinghua University He is the honorary director
of the State Key Laboratory of Tribology His research interests include: elastohydrodynamiclubrication, thin film lubrication, mechanisms of control of friction and wear, nano-tribologyand micro machine design He was born in Feng County of Jiangxi Province in 1932, and grad-uated in 1955 in Tsinghua University He has received 19 national or ministerial prizes for hisdistinguished research achievements, including: second prize in the National Natural ScienceAwards; third prize in the National Technology Invention Awards; 2004 award for Teaching &
Research of Tsinghua University; and the Science and Technology Achievement Award of the
Ho Leung and Ho Lee Foundation in 2002
Huang Ping is professor of the School of Mechanical and Automotive Engineering, SouthChina University of Technology He was born in Qiqihar City, Heilongjiang Province in 1957
He graduated from the Department of Engineering Mechanics, Tsinghua University obtaininghis PhD degree in 1989, and worked in the State Key Laboratory of Tribology of TsinghuaUniversity for seven years He now serves as the director of the Design and Equipment Institute
of South China University of Technology He has published seven books and more than 160articles He won second prize in the National Natural Science Awards, third prize in theNational Invention Awards and more than seven other provincial and ministerial scientificand technological progress awards He won the national famous teacher award in 2011
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Second Edition Preface
This edition of Principles of Tribology, based on the first edition, is formed by revising the
inad-equacies of the original edition and its being improved in response to the hotspots of recenttribology research Since the book was first published, the readers have offered various sugges-tions and opinions, and given the developments in tribology research, we thought it necessary
to make this revision of the book
Although one important task for this edition was to make some error corrections, it retainsthe basic framework of the first edition, with 21 chapters in three parts
Also, in response to the rapid development of high-speed railways and the implementation
of the lunar exploration project in China, rolling friction has become more important, so it isbrought into a separate chapter (11) Although in the previous version, rolling friction was men-tioned as a typical phenomenon of friction, we only gave some basic definitions In Chapter 11,
we give more detail on rolling friction definitions, rolling friction theories and stick-slip nomena in rolling friction, as well as contact and heat generation of rolling friction betweenwheel and rail In fact, rolling friction exists widely in transportation, automobile, machinerymanufacturing, production and daily life, and it has functions which cannot be substituted bysliding friction
phe-Another new area of content in this edition is tribology research in MEMS(micro-electromechanical system) covered in Chapter 20 This includes the application
of atomic force microscopy in tribology of MEMS, micro motor tribology research and microanalysis of wear mechanisms This content is focused on recent tribology research and therapid development of MEMS
Also, ecological tribology, a hot topic in tribology research, has been introduced inChapter 21 This chapter includes zero friction and superlubrication, green lubricating oil,friction-induced noise and its control, plus remanufacturing technologies and self-repairingtechnology Ecological tribology research will become an important research direction for thefuture
Of course, the new content is far more than just rolling friction, MEMS tribology and greentribology, but limited space here precludes more detailed coverage of the additions We hopethat the contents of the book will be more systematic and accurate in this edition
We present our most sincere thanks to our colleagues and graduate students for their siastic support, and to all the others who have provided help and made a contribution to thedevelopment of tribology research in general and this edition in particular
Huang Ping
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Preface
The formation and development of tribology as a practical subject is closely related to therequirements of social production and the progress of science and technology so that itsresearch styles and research areas have been continuously evolving
In the early 18th century, Amontons and Coulomb proposed the classic formulas of slidingfriction after carefully studying a large number of friction tests and experiments This was theearly research style of tribology, based on experience
At the end of the 19th century, Reynolds revealed the mechanism of viscous fluids ing to bearing lubrication to derive the famous equation of the hydrodynamic lubrication: theReynolds equation, which laid the theoretical foundation of lubrication Therefore, it created anew research style based on continuum mechanics
accord-In the 20th century, due to production development, tribology research fields were furtherexpanded During the period, Hardy proposed the boundary lubrication theory, which wasbased on physical and chemical adsorption films of polar molecules of the lubricant on thesurface This promoted studies of lubricants and additives Tomlinson explained the cause ofsolid sliding friction from the viewpoint of energy conversion in molecular motion Further-more, Bowden and Tabor established the adhesion friction theory based on the plowing effect
These achievements not only expanded the range of tribology, but prompted it to become adiscipline involving mechanics, materials science, thermal physics and physical-chemistry, so
as to create a multidisciplinary research style
In 1965, the British Ministry of Education and Science published the report Tribology and
Research This was the first time that tribology had been defined as the science of the frictionprocess Since then, tribology as a separate discipline has been paid wide attention by industryand academia wordwide, and tribology research has entered a new period of development
With in-depth theoretical and applied research, it is recognized that in order to effectivelyrealize the potential of tribology in the economy, research has to evolve from the macro to themicro scale, from quality to quantity, from the static to dynamic and from single discipline tomultidiscipline At the same time, tribological research has gradually extended from the anal-ysis of tribological phenomena to the analysis and control of them, or even to the control oftribological properties on a target In addition, tribology research in the past mainly focused onequipment maintenance, but it has now changed to innovative design of mechanical products
Modern science and technology, especially information science, materials science andnano-technology, plays a significant role in pushing the development of tribology For example,because of the rapid development of computer science and numerical analysis, many complextribological phenomena have been solved quite accurately with quantitative analysis There-fore, the numerical methods used in lubrication simulation have pushed lubrication theory
to consider a number of practical factors influencing the design of modern machinery Asanother example, the electron microscope and micro-analytical instruments are now widelyused for the analysis of worn surfaces to provide useful tools in studying the wear mechanism
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xxvi Preface
At the same time, the development of materials science has developed many new materialsand surface treatment technologies so as to greatly promote research on the wear mecha-nism The fields of modern wear have extended from metal materials to non-metallic materials,including ceramics, polymers and composites Surface treatment technologies using physical,chemical and mechanical methods to modify the material properties of the surface have beenthe most rapidly developing area of tribology in recent years
The development of nano-technology has generated a series of new disciplines, includingmicro- or nano-tribology It occurs because tribological phenomena are closely related
to the micro-structural changes and the dynamic behaviors of the surface and interface
Nano-tribology provides a new style from the macro to the atomic and molecular scales toreveal the mechanisms of friction, wear and lubrication so as to establish the relationshipbetween the macroscopic properties and the micro structures of the material These are thebasic tribology mechanisms The emergence of nano-tribology shows that tribology study hasentered a new stage
Furthermore, tribology is an interdisciplinary subject closely connected with other disciplines
to form a new research field, which has distinctive features Chemical tribology, biologicaltribology and ecological tribology appearing in recent years may become hot fields in futuretribological research
This book is based on the Chinese version previously published by Tsinghua University Press,which achieved recognition for its excellence as a scientific work by gaining a National BookAward
In the book, we try as far as possible to reflect the whole picture of modern tribology andintroduce new areas of tribological research and development trends Obviously, the new areascurrently are not yet well-known, so we will give a brief exposition for the reader to promotedevelopment of these areas For the classical contents of tribology, we try to clearly state thebasis of knowledge
Because the scope of tribology is wide and the nature of a book is essentially limited, somedefects or deficiencies may exist and we therefore welcome criticisms and corrections fromreaders
During the writing of the book, we have cited many researches of scholars both domesticand international We present our most sincere thanks to them as well as to the colleagues andgraduate students at Tsinghua University for their enthusiastic support, help and contribution
to the development of tribology research and to this book
Huang Ping
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Introduction
This book is a compilation of the current developments in the tribology research of the authorsand their co-workers over a long period It is a systematic presentation of tribology fundamen-tals and their applications It also presents the current state and development trends in tribologyresearch
There are 21 chapters, consisting of three parts: I: lubrication theory and lubricationdesign, II: friction and wear mechanism and control, III: applied tribology Beside the classicaltribology contents, it also covers interdisciplinary areas of tribology The book mainly focuses
on the regularities and characteristics of tribological phenomena in engineering Furthermore,
it presents basic theories, numerical analysis methods and experimental measuring techniques
as well as the applications of tribology
The book is intended to be used as a textbook for senior-level or graduate-level studentsmajoring in mechanical engineering or in related subjects in universities and colleges It canalso serve as a valuable reference for engineers and technicians in machine design and tribologyresearch
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1
Part I Lubrication Theory
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1 Properties of Lubricants
Many fluids serve as lubricants in industry Among them, oil and grease are the most commonlyused Air, water and liquid metals are also used as special lubricants; for example, liquid sodium
is often used as a lubricant in nuclear reactors In some situations, solid lubricants, such asgraphite, molybdenum disulfide or polytetrafluoroethylene (PTFE) can also be used In this firstchapter we will discuss the viscosity and density of lubricants, as they are the two importantphysical properties associated with lubrication
In lubrication theory, the most important physical property of a lubricant is its viscosity, themost important factor in determining the lubrication film thickness In hydrodynamic lubrica-tion, the lubricant film thickness is proportional to the viscosity, while in elastohydrodynamiclubrication it is proportional to the viscosity to the powers 0.7 Although in boundary lubrica-tion the viscosity does not directly influence the film thickness, the oil packages formed betweenpeaks and valleys of roughness will carry part of the load Therefore lubricant viscosity is closelyrelated to its load-carrying capacity
Furthermore, viscosity is also an important factor influencing the frictional force
A high-viscosity lubricant not only causes a lot of friction loss, but also produces a lot
of heat, which make cooling control difficult Because temperature rise caused by frictioncan lead to failure of the lubricant film, the surface will be worn increasingly Therefore, areasonable viscosity is required for practical lubrication
The performance of elastohydrodynamic lubrication (EHL) also depends on the cal characteristics of a lubricant In point or line contacts, an EHL film is very thin, less thanone micro-meter, but the pressure is very high, up to 1 GPa And, because the contact area
rheologi-is often very small, the shear rate may be higher than 107s–1 such that the passing time isvery short, less than 10–3s Therefore, a friction process is always accompanied by high tem-perature For such conditions, the properties of a lubricant are quite different from those of
a Newtonian fluid In such cases, therefore, it is necessary to study the rheological ties of lubricants Experiments show that although the film thickness formula derived from theNewtonian fluid model is usually applied to the elastohydrodynamic lubrication, the frictionalforce and temperature calculated by a Newtonian fluid model will cause a large error There-fore, in thermo-elastohydrodynamic lubrication (TEHL), more realistic non-Newtonian fluidmodels should be used These belong to a lubricant rheology study which will not only help usunderstand the lubrication mechanism more deeply but also has major significance in energyconservation and improvement in the life of mechanical elements
proper-1.1 Lubrication States
The purpose of lubrication is to form a lubricant film to separate the friction surfaces to carry
a load with a low shear stress to reduce friction and wear of materials A lubricant film can be
Trang 25Formation method of
Hydrodynamic lubrication
between friction surfaces forms a dynamic lubricant film
For surface contacts in high speed situations such as journal bearings
pressure fluid form a lubricant film between friction surfaces
For surface contacts in low speed situations such as journal bearings and guides
Elastohydrodynamic lubrication
lubrication
For point or line contacts in high speed situations, such
as gears and rolling bearing
lubrication
For point or line contacts in low speed and high precision situations, such as precision rolling contact bearing
reaction such as adsorption between lubricant molecules and metal surfaces
For low speed situations, such as journal bearings
adsorbed film, etc.
For no lubrication or self-lubricating friction pairs
a liquid, a gas or a solid According to the mechanisms of lubricant film formation, lubricationstates can be divided into the following six basic types: (1) hydrodynamic lubrication; (2) hydro-static lubrication; (3) elastohydrodynamic lubrication; (4) thin film lubrication; (5) boundarylubrication; and (6) dry friction The features of the lubrication states are listed in Table 1.1
A lubrication state has its typical film thickness However, we cannot determine the cation state simply and accurately based on the thickness alone because the surface roughnessalso needs to be considered Figure 1.1 lists the thickness orders of different lubricant films androughnesses Only when a lubricant film thickness is high enough is it possible to form a fullfilm that will completely lubricate to avoid the peaks of the two rough surfaces contacting eachother If several lubrication states exist at the same time, this is known as mixed lubrication, asshown in Figure 1.2
lubri-It is often inconvenient to determine a lubrication state based on lubricant film thicknessbecause film thickness measurement is difficult For convenience, the friction coefficient can
Figure 1.1 Lubricant film thickness and
roughness height.
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Figure 1.2 Typical friction coefficients of the lubrication states.
Figure 1.3 Stribeck curve of a journal bearing.
also be used to determine a lubrication state Figure 1.2 presents some typical friction cients corresponding to the lubrication states
coeffi-With varying working conditions, one lubrication state may transform into another Figure 1.3gives a typical Stribeck curve of a journal bearing The curves indicate the transformation oflubrication states corresponding with the working conditions Here, the dimensionless bearingparameter (𝜂U/p) reflects the working conditions, where 𝜂 is the lubricant viscosity, U is the
sliding velocity and p is the average pressure (carrying load per unit area).
It should be noted that methods of studying lubrication states may vary For hydrodynamiclubrication and hydrostatic lubrication, theories of viscous fluid mechanics and heat transfer arenecessarily used to analyze pressure and temperature distributions As for elastohydrodynamiclubrication, elastic deformation of the contact surfaces and the rheological properties of lubri-cants must be added, while for boundary lubrication the perspectives of physical and chemicalknowledge will help us understand the mechanisms of formation and failure of a boundary film
For dry friction, the main task is to avoid wear and tear Therefore, its study involves materialscience, elastic and plastic mechanics, heat transfer, physical chemistry and so on
1.2 Density of Lubricant
The density is one of the most common physical properties of a lubricant A liquid lubricant
is usually considered to be incompressible, and its thermal expansion is ignored so that thedensity is considered as a constant Generally, the density of 20∘C is considered the standard
In Table 1.2, the standard densities of some basic lubricants are given
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6 Principles of Tribology
Table 1.2 Standard densities of some basic lubricants.
Hydroxymethyl-phenyl diphenyl phosphate
The density of a lubricant is actually the function of pressure and temperature Under someconditions, such as in the elastohydrodynamic lubrication state, the density of a lubricantshould be considered to be variable
The volume of lubricant is reduced with increase of pressure, so that its density increases
The relationship of density and pressure can be expressed as follows:
where C is the compression coefficient; V is the volume of lubricant; M is the mass of lubricant.
The following well-known density equation is available:
where𝜌0and𝜌 p are the densities at pressures p0and p respectively.
The desirable C can be obtained from the following expression:
where𝜂 is the viscosity, mPa⋅s, and C is a constant, m2/N
Conveniently, the following density and pressure relationship is often used in lubricationanalysis:
where p is the pressure, GPa.
The influence of temperature on density is due to thermal expansion, which increases thelubricant volume in order to decrease the density If the thermal expansion coefficient of alubricant is𝛼 T, then
where 𝜌 T is the density at temperature T; 𝜌0 is the density at temperature T0; 𝛼 T is theconstant,∘C–1
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Usually,𝛼 T can be expressed in the following way If the viscosity of a lubricant is less than
3000 mPa⋅s (i.e 1g𝜂 ≤ 3.5), then
1.3.1 Dynamic Viscosity and Kinematic Viscosity
Viscosity is the capability of a fluid to resist shear deformation When a fluid flows on a solid face, due to adhesion to the solid surface and the interaction between the molecules of the fluid,shear deformation of the fluid exists Therefore, viscosity is the measurement of the resistance
sur-of the internal friction sur-of a fluid
1.3.1.1 Dynamic Viscosity
Newton first proposed the viscous fluid model He considered that a fluid flow consists of many
very thin layers The adjacent layers slide relatively, as shown in Figure 1.4, where h is the ness, U is the velocity of the moving surface, A is the area of the surface and F is the drawing
thick-force Due to viscous friction within layers of the fluid, movement is transferred from one layer
to the next Because of viscosity, relative sliding between the layers results in shear stress, that
is, friction within the fluid The movement is transferred to the adjacent layer such that thefaster layer is decelerated, but the slower layer is accelerated This forms a velocity difference
If the surfaces A and B are parallel to each other, the distribution of the velocity u is linear, as
dx
dz =
d dz
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8 Principles of Tribology
Figure 1.5 Viscosity definition.
From the above equation, we can see that the shear rate is equal to the gradient of the fluidflow velocity across the film thickness Therefore, Newton’s viscosity law can be written as
𝜏 = 𝜂 du
where𝜂 is the defined as the fluid dynamic viscosity.
Dynamic viscosity is the ratio of shear stress to shear rate In the international system of units(SI), the unit of dynamic viscosity is N⋅s/m2or Pa⋅s, as shown in Figure 1.5
In the CGS system often used in engineering, the dynamic viscosity unit is dyne⋅s/cm2or
P (Poise)
1 P = 1 dyne•s∕cm2=0.1 N•s∕m2=0.1 Pa•s (1.11)Because P is too large, 1% P or cP (centipoise) is often used
If the imperial system is used, the unit of dynamic viscosity is Reyn
The unit of kinematic viscosity in SI is m2/s, and in the CGS system of units it is the Stoke (St),
1 St = 102mm2/s = 10–4m3/s Because St is too large, cSt (centi St) is more commonly used inpractice; 1 cSt = 1 mm2/s
As the densities of common mineral oils are usually in the range of 0.7–1.2 g/cm3, choosingthe typical mineral oil density equal to 0.85 g/cm3, the following approximation can be conve-niently used in engineering
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1.3.2 Relationship between Viscosity and Temperature
Viscosity of lubricants varies significantly with temperature Generally, the higher the viscosity,the more sensitive the lubricant is to changes in temperature
From a molecular viewpoint, fluid is composed of a large number of randomly movingmolecules so that the viscosity of fluid is the result of gravitational forces and momentum of themolecules The gravitational forces between the molecules significantly vary with the distancebetween molecules, while the momentum depends on velocity As temperature rises, both theaverage molecular motion and average molecular distance of the fluid increase This causesthe momentum of molecules to increase, but the gravitational forces to decrease Therefore,the viscosity of a liquid drops sharply with the increase of temperature and this significantlyaffects lubrication
In order to accurately determine the lubrication performance, thermal analysis should becarried out to find out the variation of viscosity Temperature calculation therefore becomes animportant part of lubrication analysis The influence of temperature on gas viscosity is com-monly neglected although the viscosity of gas usually increases slightly with increase of tem-perature
A lot of research into the relationships between viscosity and temperature has been carriedout and, as a result, a number of formulas have been put forward Some formulas are summaries
of empirical data To use these formulas, we must carefully consider their usage limitations
where 𝜂0 is the viscosity under temperature T0; 𝜂 at temperature T; 𝛽 is the
viscosity–temperature coefficient, approximately equal to 0.03 1/∘C; m = 1, 2, …; 𝜃 is
the temperature of “infinite viscosity” and for a standard mineral oil,𝜃 is desirably equal to
95∘C; a, s and b are constants.
In the above equations, the Reynolds viscosity–temperature equation is more convenient to
be used, but the Vogel viscosity–temperature equation is more accurate
1.3.2.2 ASTM Viscosity–Temperature Diagram
ASTM (American Society for Testing and Materials) suggests using viscosity index(VI) to describe the viscosity–temperature relationship and giving their correspondingviscosity–temperature diagram
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10 Principles of Tribology
Figure 1.6 ASTM diagram.
Then, Equation 1.19 becomes
The advantage of Equation 1.20 is that only two viscosities at the corresponding temperatures
need to be measured in order to determine the constants A and B Then a straight line can be
plotted to find other viscosities at any temperature
For a typical mineral oil, an ASTM diagram is very effective Furthermore, the viscosity angle
in the diagram can be used as an index to evaluate the viscosity–temperature feature of alubricant
Equation 1.21
VIsof some lubricating oils are given in Table 1.3
As the larger the VI, the less the variation of viscosity with temperature, a lubricating oil with
a large VI possesses a good viscosity–temperature property.
1.3.3 Relationship between Viscosity and Pressure
With increase of pressure, the distance between molecules of a fluid decreases such that its cosity increases Experiments show that when pressure is higher than 0.02 GPa, the viscosity
vis-of a mineral oil will obviously increase Under a pressure vis-of 1 GPa, the viscosity vis-of a mineraloil is several orders larger than at atmospheric pressure If pressure rises higher, a mineral oilmay lose some of its liquid properties and become like a wax Therefore, the viscosity–pressure
Table 1.3 VI of some lubricating oils.
Trang 32where𝜂 is the viscosity at pressure p; 𝜂0 is the viscosity at atmospheric pressure;𝛼 is the
viscosity–pressure coefficient; p0is equal to 5.1 × 10–9Pa; z is usually preferred to be equal to 0.68 for mineral oils; c is approximately equal to 𝛼/15.
Although the Barus equation is simple, the viscosity will be too large if pressure is higher than
1 GPa Therefore, the Roelands equation is more reasonable for such a situation
The viscosity–pressure coefficient𝛼 of mineral oils is around 2.2 × 10–8m2/N Some are given
in Tables 1.4 and 1.5
1.3.3.1 Relationships between Viscosity, Temperature and Pressure
When considering the influences of temperature and pressure on viscosity, the followingviscosity–temperature–pressure equations are used
Roelands 𝜂 = 𝜂0exp
{(ln 𝜂0+9.67)
[(1 + 5.1 × 10−9p)0.68×
(1.26)Although Equation 1.25 is simpler and easier in calculation, Equation 1.26 is more accurate
Spindle oil
Light machine oil
Heavy oil
Light machine oil
Heavy oil
Cylinder oil
Trang 33Non-Newtonian fluids are different from Newtonian fluids, as shown by Curves A, B and D
in Figure 1.7 A non-Newtonian fluid may present as plastic, pseudoplastic or expansive For
a pseudoplastic or expansive fluid, an index n is used to approximately describe its nonlinear
nature
where𝜂 and n are the constants; for a Newtonian fluid n = 1.
In Figure 1.7, Curve A representing plastic is known as the Bingham fluid It has a yieldstress𝜏 s When the shear stress𝜏 is less than 𝜏 s, the shear rate is equal to zero While𝜏 is
larger than𝜏 s, their relationship is
Grease is similar to a Bingham fluid However, the relationship of its shear stress and shearrate is nonlinear The formula of rheological property for lubricating greases can be expressedapproximately as
1.4.1 Ree–Eyring Constitutive Equation
The Ree–Eyring constitutive equation is the most commonly used non-Newtonian formula, asshown in Equation 1.30 Its shear rate slowly varies to infinite with the shear stress:
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Figure 1.8 Constitutive curves of some lubricants.
(1) Ree–Eyring fluid; (2) visco-plastic fluid; (3) circular fluid;
(4) temperature-dependent fluid.
where𝜏0is the characteristics stress;𝜂0is the initial viscosity
The Ree–Eyring model gives a fairly accurate description of the rheological property of somelubricants, especially for simple liquids The relationship of the shear stress𝜏 and the shear rate
̇𝛾 is similar to Curve 1 in Figure 1.8 𝜏0and𝜂0are the two rheological parameters depending onthe molecular structures of a lubricant
1.4.2 Visco-Plastic Constitutive Equation
Curve 2 in Figure 1.8 is the visco-plastic fluid model It has a limit shear stress𝜏 L The variation
of the shear stress with the shear rate is described by two straight lines
Experimental results show that the limit shear stress 𝜏 L changes with pressure andtemperature The limit shear stresses of common lubricants are between 4 × 105 and
2 × 107Pa
1.4.3 Circular Constitutive Equation
The circular constitutive model is asymptotic It is used for the non-Newtonian fluid effect asshown by Curve 3 in Figure 1.8 It has a continuous derivative, and the shear stress varying withthe shear rate converges to the limit𝜏 L The constitutive equation is
̇𝛾 = 𝜏 L 𝜏
𝜂0√𝜏2
L−𝜏2
1.4.4 Temperature-Dependent Constitutive Equation
The temperature-dependent constitutive model is shown by Curve 4 in Figure 1.8, consideringthe influence of temperature on viscosity [1] The most important feature of the model is thatafter reaching the maximum, the shear stress begins to decline slightly with increase of the shearrate The constitutive equation is
𝜏 = 𝜂0̇𝛾
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14 Principles of Tribology
where𝛼 = 2𝛽𝜂0x/𝜌cu0;𝛽 is the viscosity–temperature constant; 𝜂0is the initial viscosity; x is
the distance away from the inlet;𝜌 is the density; c is the specific heat capacity of the lubricant;
u0is the velocity of the moving surface
1.4.5 Visco-Elastic Constitutive Equation
Experiments show that when a lubricant flows through contact region with dramaticallychanged stresses, it presents some elasticity, that is, it becomes a visco-elastic fluid In EHLtheory, the most commonly used visco-elastic model is the Maxwell model or the linearvisco-elastic model, as shown in Figure 1.9 For a purely elastic material, it obeys Hooke’slaw
𝛾 e = 𝜏
de1
where𝛾 e is the elastic shear strain; G is the shear elastic modulus.
Derivate du to time t we have du = d˙e Therefore, Equation 1.34 becomes
1.4.6 Nonlinear Visco-Elastic Constitutive Equation
The friction coefficient obtained from the Maxwell model for an EHL problem is usually toolarge because of the Newtonian fluid viscosity of Equation 1.37 Therefore, a non-Newtonianconstitutive equation is given as
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where F( 𝜏) is a nonlinear function of 𝜏.
Johnson and Tevaarwerk [2] combined the Maxwell model with the Ree–Eyring model topropose the following nonlinear visco-elastic constitutive equation
If𝜏 ≪ 𝜏0, sinh𝜏/𝜏0≈𝜏/𝜏0 Then, F( 𝜏) ≈ 𝜏/𝜂0such that F( 𝜏) becomes the Newton’s viscosity
constitutive equation Therefore, Equation 1.39 becomes the linear visco-elastic constitutiveequation Johnson and Tevaarwerk summarized that the proposed model is suitable for linearand nonlinear viscous materials, linear and nonlinear elastic materials, as well as for elastic andplastic materials as shown in Figure 1.10
1.4.7 A Simple Visco-Elastic Constitutive Equation
Bair and Winer [3] proposed a simple visco-elastic model The relationship between the shearstress and the shear rate is
vibra-the functions of pressure p and temperature T, and can be determined by experiments.
In order to obtain the dimensionless form of Equation 1.40, set the dimensionless shear stress
𝜏∗=𝜏/𝜏 L, the dimensionless shear rate of ̇𝛾∗ = ̇𝛾𝜂∕𝜏 L, and we have ̇𝜏∗= (𝜂0∕G∞𝜏 L)∕(d 𝜏∕dt).
Then, the dimensionless form of Equation 1.40 is
Trang 37a phenomenon is called shear thinning or pseudoplasticity, as shown in Figure 1.11 A plastic fluid usually has long chain molecules but irregular arrangements As the chains will bedirectionally arranged under shearing, the actions between adjacent layers are weakened so as
pseudo-to decrease its apparent viscosity
1.4.7.2 Thixotropy
The phenomenon that the apparent viscosity of a fluid diminishes gradually under shearing
is known as thixotropy, as shown in Figure 1.12 Thixotropy is usually reversible That is, ifshearing has stopped, the viscosity recovers, back to or close to its original value after sufficienttime For greases or thick emulsions, the effect of thixotropicity is that their structures con-tinue to be disrupted under shearing, and then self-rebuild When structural damage develops,the apparent viscosity continues to decrease When a new balance between destruction andreconstruction is established, the apparent viscosity becomes stable again
Trang 381.5.1 Wetting and Contact Angle
When a small amount of liquid contacts a solid and completely covers the solid surface, this
is called wetting If a liquid forms a spherical droplet, it is called non-wetting Usually, partialwetting phenomena exist
The phenomenon that a liquid surface automatically shrinks can be analyzed from energy
Usually, wetting can be measured by the contact angle of a liquid on a solid surface As shown
in Figure 1.13, the contact angle 𝜃 is defined as the tangent angle between the solid–liquid
interface and the liquid–gas interface at the junction point of solid, liquid and gas phases Thecontact angle𝜃 is from 0 to 180∘ for wetting to completely non-wetting Liquid with a large
contact angle𝜃 is lipophobic, while a small contact angle 𝜃 is lipophilic, that is, the adhesion
energy of a liquid is greater than its cohesive energy The magnitude of the contact angle isdetermined by the solid and liquid surface tensions or the surface free energies The surfacetension presents the work done to increase each unit area of the surface It is one of the basicphysical and chemical properties, usually presented in the unit of mN/m
Figure 1.13 shows the relationship of the contact angle and the surface tensions If 𝛾 gl,
𝛾 ls and 𝛾 sg are the surface tension of liquid–gas, solid–liquid and solid–gas respectively,then
The contact angle 𝜃 can be measured by experimental methods, such as the projection
method The gas–liquid surface tension𝛾 glcan be measured by a surface tension instrument
Then,𝛾 sg−𝛾 ls can be obtained by calculating the wetting energy (in general, 𝛾 sg and 𝛾 sl aredifficult to measure) In addition, the contact angle𝜃 is related to the solid surface roughness,
temperature and so on
1.5.2 Surface Tension
A surface tension is actually the interface energy difference of the interactions of liquid and gasphases The distances between molecules in liquid are not the same, although the summaryforce surrounding all directions of each molecule is equal to zero, the average attraction forcewill prevent them (the liquid molecules) from thermally volatilizing However, the molecules
on the liquid surface are quite different because the force of gas is much smaller than that of theliquid Furthermore, because the gas density is smaller and the distance between molecules islarger, the summary force acting on the surface molecules points toward the inside of the liquid,resulting in an increase in its energy The energy is called surface free energy As the distancebetween molecules on the surface is larger than that of the inner molecules, there is a lateralforce acting on the surface molecules, known as the surface tension
Figure 1.13 Wettability and contact angle.
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18 Principles of Tribology
Wetting of a lubricant on solid surfaces and adhesion between two solid surfaces are all related
to the surface tension
If the width of a liquid film is w, and the length increment is Δl, the free energy increment is
equal to
where ΔA is the surface area increment; 𝛾 is the surface free energy, mJ/m2.For a liquid, the surface free energy is equivalent to the surface tension and has the samedimension
There are various methods for measuring the liquid surface tension, such as the capillarymethod, the maximum bubble pressure method, the stop dripping method, the hanging dropmethod and the drop weight method The most common method is the ring method Thisinvolves lifting a ring (usually a platinum ring) away from the surface of a liquid While thering which is placed in a horizontal plane parallel to the surface of the liquid (to ensure zerocontact angle) is pulled upwards, it brings up some liquid to form a column The forces applied
on the measuring sensor include the weight of ring and the gravity of liquid, P P increases with
increase in the pulling height, but there is a limit If the pulling height is larger than the limit,the ring and the liquid surface will be separated The limit is related to the liquid surface tensionand the size of the ring if the rise of the liquid column brought up by the external force is due
to the liquid surface tension Therefore, we have
where C is the correction factor, which is the function of R/r and R3/V ; V is the volume of the
liquid brought up by the ring
The liquid surface tension generally decreases linearly with increase of temperature The face tension is also affected by pressure, but the relationship is more complex Some additives(such as surface-active agents) will significantly alter the surface tension of liquid For a fer-romagnetic fluid, its surface tension is affected by external magnetic field Table 1.6 lists thesurface tensions of some fluids at 20∘C
sur-Table 1.6 Surface tensions of some liquids (20∘C).
Liquid
Surface tension
Surface tension (mN/m)
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1.6 Measurement and Conversion of Viscosity
Viscometers are used to measure viscosity There are three types of viscometers according totheir working principles: rotary, off-body and capillary viscometers
1.6.1 Rotary Viscometer
A rotary viscometer consists of two parts filled with a liquid to be tested One part is fixedand the other rotates By measuring the shearing moment caused by the resistance of a liq-uid, the dynamic viscosity can be obtained A rotary viscometer is shown in Figure 1.14a, and acone-plate rheometer is shown in Figure 1.14b The former is composed of two concentric cylin-ders, while the latter is composed of a plane and a conical surface If the moving part rotates atdifferent speeds, the relationship of the shear stress and the shear rate can be obtained, which
is called the rhoelogical property This is very useful, especially for non-Newtonian fluid
1.6.2 Off-Body Viscometer
The most commonly used off-body viscometer is composed of a ball and a test tube filled withthe fluid to be tested In order to determine the viscosity, measure the final velocity of the fallingball As the clearance between the ball and the tube is very small, the falling ball viscometer can
be used to measure the viscosity of a gas, or of a fluid under a high pressure Another type ofoff-body viscometer consists of two vertical concentric cylinders The fluid to be tested is filledbetween them The outer cylinder is fixed, while the inner tube falls so that the viscosity can
be obtained by measuring the final falling velocity An off-body viscometer is mainly used tomeasure high-viscosity fluids
Figure 1.15 shows a relative capillary viscometer with a known constant c Measure the time for the liquid surface to drop from A to B, the kinematic viscosity of the liquid being equal to
Figure 1.14 Rotary viscometers: (a) rotational
viscometer (b) cone-plate rheometer.