Principles of tribology

Principles of Tribology Principles of Tribology Shizhu Wen Tsinghua University Beijing, China Ping Huang South China University of Technology Guangzhou, China Second Edition 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 Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions The right of Shizhu Wen and Ping Huang to be 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damages, including but not limited to special, incidental, consequential, or other damages 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 v Contents About the Authors xxi Second Edition Preface xxiii Preface xxv Introduction xxvii Part I 1.1 1.2 1.3 1.3.1 1.3.1.1 1.3.1.2 1.3.2 1.3.2.1 1.3.2.2 1.3.2.3 1.3.3 1.3.3.1 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 1.4.7 1.4.7.1 1.4.7.2 1.5 1.5.1 1.5.2 1.6 1.6.1 1.6.2 Lubrication Theory Lubrication States Density of Lubricant Viscosity of Lubricant Dynamic Viscosity and Kinematic Viscosity Dynamic Viscosity Kinematic Viscosity Relationship between Viscosity and Temperature Viscosity–Temperature Equations ASTM Viscosity–Temperature Diagram Viscosity Index 10 Relationship between Viscosity and Pressure 10 Relationships between Viscosity, Temperature and Pressure Non-Newtonian Behaviors 12 Ree–Eyring Constitutive Equation 12 Visco-Plastic Constitutive Equation 13 Circular Constitutive Equation 13 Temperature-Dependent Constitutive Equation 13 Visco-Elastic Constitutive Equation 14 Nonlinear Visco-Elastic Constitutive Equation 14 A Simple Visco-Elastic Constitutive Equation 15 Pseudoplasticity 16 Thixotropy 16 Wettability of Lubricants 16 Wetting and Contact Angle 17 Surface Tension 17 Measurement and Conversion of Viscosity 19 Rotary Viscometer 19 Off-Body Viscometer 19 Properties of Lubricants 11 vi Contents 1.6.3 Capillary Viscometer 19 References 21 2.1 2.1.1 2.1.2 2.1.2.1 2.1.2.2 2.2 2.2.1 2.2.2 2.2.2.1 2.2.2.2 2.2.3 2.2.3.1 2.2.3.2 2.2.3.3 2.3 2.3.1 2.3.1.1 2.3.1.2 2.3.2 2.3.2.1 2.3.2.2 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.5 22 Reynolds Equation 22 Basic Assumptions 22 Derivation of the Reynolds Equation 23 Force Balance 23 General Reynolds Equation 25 Hydrodynamic Lubrication 26 Mechanism of Hydrodynamic Lubrication 26 Boundary Conditions and Initial Conditions of the Reynolds Equation 27 Boundary Conditions 27 Initial Conditions 28 Calculation of Hydrodynamic Lubrication 28 Load-Carrying Capacity W 28 Friction Force F 28 Lubricant Flow Q 29 Elastic Contact Problems 29 Line Contact 29 Geometry and Elasticity Simulations 29 Contact Area and Stress 30 Point Contact 31 Geometric Relationship 31 Contact Area and Stress 32 Entrance Analysis of EHL 34 Elastic Deformation of Line Contacts 35 Reynolds Equation Considering the Effect of Pressure-Viscosity 35 Discussion 36 Grubin Film Thickness Formula 37 Grease Lubrication 38 References 40 Numerical Methods of Lubrication Calculation 3.1 3.1.1 3.1.1.1 3.1.1.2 3.1.2 3.1.2.1 3.1.2.2 3.1.3 3.1.3.1 3.1.3.2 3.1.3.3 3.1.3.4 3.2 3.2.1 3.2.1.1 3.2.1.2 Basic Theories of Hydrodynamic Lubrication 41 Numerical Methods of Lubrication 42 Finite Difference Method 42 Hydrostatic Lubrication 44 Hydrodynamic Lubrication 44 Finite Element Method and Boundary Element Method 48 Finite Element Method (FEM) 48 Boundary Element Method 49 Numerical Techniques 51 Parameter Transformation 51 Numerical Integration 51 Empirical Formula 53 Sudden Thickness Change 53 Numerical Solution of the Energy Equation 54 Conduction and Convection of Heat 55 Conduction Heat Hd 55 Convection Heat Hv 55 Contents 3.2.2 3.2.3 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.1.3 3.3.1.4 3.3.2 3.3.2.1 3.3.2.2 3.3.2.3 3.4 3.4.1 3.4.1.1 3.4.1.2 3.4.1.3 3.4.2 3.4.3 3.4.4 3.4.4.1 3.4.4.2 3.4.4.3 3.4.4.4 3.4.5 3.4.5.1 3.4.5.2 3.4.5.3 3.4.5.4 3.4.5.5 Energy Equation 56 Numerical Solution of Energy Equation 59 Numerical Solution of Elastohydrodynamic Lubrication 60 EHL Numerical Solution of Line Contacts 60 Basic Equations 60 Solution of the Reynolds Equation 62 Calculation of Elastic Deformation 62 Dowson–Higginson Film Thickness Formula of Line Contact EHL 64 EHL Numerical Solution of Point Contacts 64 The Reynolds Equation 65 Elastic Deformation Equation 66 Hamrock–Dowson Film Thickness Formula of Point Contact EHL 66 Multi-Grid Method for Solving EHL Problems 68 Basic Principles of Multi-Grid Method 68 Grid Structure 68 Discrete Equation 68 Transformation 69 Nonlinear Full Approximation Scheme for the Multi-Grid Method 69 V and W Iterations 71 Multi-Grid Solution of EHL Problems 71 Iteration Methods 71 Iterative Division 72 Relaxation Factors 73 Numbers of Iteration Times 73 Multi-Grid Integration Method 73 Transfer Pressure Downwards 74 Transfer Integral Coefficients Downwards 74 Integration on the Coarser Mesh 74 Transfer Back Integration Results 75 Modification on the Finer Mesh 75 References 76 Lubrication Design of Typical Mechanical Elements 78 4.1 4.1.1 4.1.1.1 4.1.1.2 4.1.1.3 4.1.2 4.2 4.2.1 4.2.2 4.2.2.1 4.2.2.2 4.2.2.3 4.2.2.4 4.2.3 4.3 4.3.1 4.3.2 Slider and Thrust Bearings 78 Basic Equations 78 Reynolds Equation 78 Boundary Conditions 78 Continuous Conditions 79 Solutions of Slider Lubrication 79 Journal Bearings 81 Axis Position and Clearance Shape 81 Infinitely Narrow Bearings 82 Load-Carrying Capacity 83 Deviation Angle and Axis Track 83 Flow 84 Frictional Force and Friction Coefficient 84 Infinitely Wide Bearings 85 Hydrostatic Bearings 88 Hydrostatic Thrust Plate 89 Hydrostatic Journal Bearings 90 vii viii Contents 4.3.3 4.3.3.1 4.3.3.2 4.3.3.3 4.4 4.4.1 4.4.2 4.4.3 4.5 4.5.1 4.5.2 4.5.2.1 4.5.2.2 4.5.3 4.5.3.1 4.5.3.2 4.5.3.3 4.6 4.6.1 4.6.2 4.7 4.7.1 4.7.2 4.7.3 4.8 4.8.1 4.8.1.1 4.8.1.2 4.8.1.3 4.8.2 4.9 Bearing Stiffness and Throttle 90 Constant Flow Pump 91 Capillary Throttle 91 Thin-Walled Orifice Throttle 92 Squeeze Bearings 92 Rectangular Plate Squeeze 93 Disc Squeeze 94 Journal Bearing Squeeze 94 Dynamic Bearings 96 Reynolds Equation of Dynamic Journal Bearings 96 Simple Dynamic Bearing Calculation 98 A Sudden Load 98 Rotating Load 99 General Dynamic Bearings 100 Infinitely Narrow Bearings 100 Superimposition Method of Pressures 101 Superimposition Method of Carrying Loads 101 Gas Lubrication Bearings 102 Basic Equations of Gas Lubrication 102 Types of Gas Lubrication Bearings 103 Rolling Contact Bearings 106 Equivalent Radius R 107 Average Velocity U 107 Carrying Load Per Width W /b 107 Gear Lubrication 108 Involute Gear Transmission 109 Equivalent Curvature Radius R 110 Average Velocity U 111 Load Per Width W /b 112 Arc Gear Transmission EHL 112 Cam Lubrication 114 References 116 Special Fluid Medium Lubrication 5.1 5.1.1 5.1.2 5.1.2.1 5.1.2.2 5.1.2.3 5.1.2.4 5.1.3 5.1.4 5.2 5.2.1 5.2.1.1 5.2.1.2 5.2.2 5.2.2.1 5.2.2.2 118 Magnetic Hydrodynamic Lubrication 118 Composition and Classification of Magnetic Fluids 118 Properties of Magnetic Fluids 119 Density of Magnetic Fluids 119 Viscosity of Magnetic Fluids 119 Magnetization Strength of Magnetic Fluids 120 Stability of Magnetic Fluids 120 Basic Equations of Magnetic Hydrodynamic Lubrication 121 Influence Factors on Magnetic EHL 123 Micro-Polar Hydrodynamic Lubrication 124 Basic Equations of Micro-Polar Fluid Lubrication 124 Basic Equations of Micro-Polar Fluid Mechanics 124 Reynolds Equation of Micro-Polar Fluid 125 Influence Factors on Micro-Polar Fluid Lubrication 128 Influence of Load 128 Main Influence Parameters of Micro-Polar Fluid 129 Contents 5.3 5.3.1 5.3.1.1 5.3.1.2 5.3.2 5.3.3 5.3.3.1 5.3.3.2 5.4 5.4.1 5.4.1.1 5.4.1.2 5.4.2 5.4.2.1 5.4.2.2 5.4.2.3 5.4.2.4 Liquid Crystal Lubrication 130 Types of Liquid Crystal 130 Tribological Properties of Lyotropic Liquid Crystal 131 Tribological Properties of Thermotropic Liquid Crystal 131 Deformation Analysis of Liquid Crystal Lubrication 132 Friction Mechanism of Liquid Crystal as a Lubricant Additive 136 Tribological Mechanism of 4-pentyl-4′ -cyanobiphenyl 136 Tribological Mechanism of Cholesteryl Oleyl Carbonate 136 Electric Double Layer Effect in Water Lubrication 137 Electric Double Layer Hydrodynamic Lubrication Theory 138 Electric Double Layer Structure 138 Hydrodynamic Lubrication Theory of Electric Double Layer 138 Influence of Electric Double Layer on Lubrication Properties 142 Pressure Distribution 142 Load-Carrying Capacity 143 Friction Coefficient 144 An Example 144 References 145 6.1 6.1.1 6.1.2 6.1.3 6.2 6.2.1 6.2.2 6.2.3 6.3 6.3.1 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3 6.4 6.4.1 6.4.2 6.4.2.1 6.4.2.2 6.4.2.3 6.4.3 6.4.4 6.4.4.1 6.4.4.2 6.4.4.3 147 Transformations of Lubrication States 147 Thickness-Roughness Ratio 𝜆 147 Transformation from Hydrodynamic Lubrication to EHL 148 Transformation from EHL to Thin Film Lubrication 149 Thin Film Lubrication 152 Phenomenon of Thin Film Lubrication 153 Time Effect of Thin Film Lubrication 154 Shear Strain Rate Effect on Thin Film Lubrication 157 Analysis of Thin Film Lubrication 158 Difficulties in Numerical Analysis of Thin Film Lubrication 158 Tichy’s Thin Film Lubrication Models 160 Direction Factor Model 160 Surface Layer Model 161 Porous Surface Layer Model 161 Nano-Gas Film Lubrication 161 Rarefied Gas Effect 162 Boundary Slip 163 Slip Flow 163 Slip Models 163 Boltzmann Equation for Rarefied Gas Lubrication 165 Reynolds Equation Considering the Rarefied Gas Effect 165 Calculation of Magnetic Head/Disk of Ultra Thin Gas Lubrication 166 Large Bearing Number Problem 167 Sudden Step Change Problem 167 Solution of Ultra-Thin Gas Lubrication of Multi-Track Magnetic Heads 167 References 169 Boundary Lubrication and Additives 7.1 7.1.1 Types of Boundary Lubrication 171 Stribeck Curve 171 Lubrication Transformation and Nanoscale Thin Film Lubrication 171 ix x Contents 7.1.2 7.1.2.1 7.1.2.2 7.1.3 7.1.3.1 7.1.3.2 7.1.4 7.1.4.1 7.1.4.2 7.1.4.3 7.2 7.2.1 7.2.2 7.2.2.1 7.2.2.2 7.2.2.3 7.2.3 7.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 Adsorption Films and Their Lubrication Mechanisms 172 Adsorption Phenomena and Adsorption Films 172 Structure and Property of Adsorption Films 174 Chemical Reaction Film and its Lubrication Mechanism 177 Additives of Chemical Reaction Film 178 Notes for Applications of Extreme Pressure Additives 178 Other Boundary Films and their Lubrication Mechanisms 179 High Viscosity Thick Film 179 Polishing Thin Film 179 Surface Softening Effect 179 Theory of Boundary Lubrication 179 Boundary Lubrication Model 179 Factors Influencing Performance of Boundary Films 181 Internal Pressure Caused by Surface Tension 181 Adsorption Heat of Boundary Film 182 Critical Temperature 183 Strength of Boundary Film 184 Lubricant Additives 185 Oily Additives 185 Tackifier 186 Extreme Pressure Additives (EP Additives) 187 Anti-Wear Additives 187 Other Additives 187 References 189 190 Roughness and Viscoelastic Material Effects on Lubrication 190 Modifications of Micro-EHL 190 Viscoelastic Model 191 Lubricated Wear 192 Lubricated Wear Criteria 193 Lubricated Wear Model 193 Lubricated Wear Example 193 Influence of Limit Shear Stress on Lubrication Failure 195 Visco-Plastic Constitutive Equation 195 Slip of Fluid–Solid Interface 196 Influence of Slip on Lubrication Properties 196 Influence of Temperature on Lubrication Failure 200 Mechanism of Lubrication Failure Caused by Temperature 200 Thermal Fluid Constitutive Equation 201 Analysis of Lubrication Failure 202 Mixed Lubrication 203 References 207 8.1 8.1.1 8.1.2 8.1.3 8.1.3.1 8.1.3.2 8.1.3.3 8.2 8.2.1 8.2.2 8.2.3 8.3 8.3.1 8.3.2 8.3.3 8.4 Lubrication Failure and Mixed Lubrication Part II Friction and Wear 209 Surface Topography and Contact 211 9.1 9.1.1 Parameters of Surface Topography 211 Arithmetic Mean Deviation Ra 211 Contents 9.1.2 9.1.3 9.1.4 9.1.5 9.1.5.1 9.1.5.2 9.2 9.2.1 9.2.2 9.2.3 9.3 9.4 9.4.1 9.4.2 9.4.3 9.4.4 Root-Mean-Square Deviation (RMS) 𝜎 or Rq 211 Maximum Height Rmax 212 Load-Carrying Area Curve 212 Arithmetic Mean Interception Length of Centerline Sma Slope ż a or ż q 213 Peak Curvature Ca or Cq 213 Statistical Parameters of Surface Topography 213 Height Distribution Function 214 Deviation of Distribution 215 Autocorrelation Function of Surface Profile 216 Structures and Properties of Surface 217 Rough Surface Contact 219 Single Peak Contact 219 Ideal Roughness Contact 220 Random Roughness Contact 221 Plasticity Index 223 References 223 10 Sliding Friction and its Applications 225 10.1 10.1.1 10.1.2 10.1.3 10.2 10.2.1 10.2.2 10.2.3 10.2.3.1 10.2.3.2 10.2.4 10.2.5 10.2.6 10.3 10.3.1 10.3.2 10.3.2.1 10.3.2.2 10.3.2.3 10.3.3 10.4 10.4.1 10.4.2 10.4.3 10.4.4 10.5 10.5.1 10.5.1.1 10.5.1.2 10.5.1.3 10.5.1.4 Basic Characteristics of Friction 225 Influence of Stationary Contact Time 226 Jerking Motion 226 Pre-Displacement 227 Macro-Friction Theory 228 Mechanical Engagement Theory 228 Molecular Action Theory 229 Adhesive Friction Theory 229 Main Points of Adhesive Friction Theory 230 Revised Adhesion Friction Theory 232 Plowing Effect 233 Deformation Energy Friction Theory 235 Binomial Friction Theory 236 Micro-Friction Theory 238 “Cobblestone” Model 238 Oscillator Models 240 Independent Oscillator Model 240 Composite Oscillator Model 241 FK Model 242 Phonon Friction Model 242 Sliding Friction 243 Influence of Load 243 Influence of Sliding Velocity 244 Influence of Temperature 245 Influence of Surface Film 245 Other Friction Problems and Friction Control 246 Friction in Special Working Conditions 246 High Velocity Friction 246 High Temperature Friction 246 Low Temperature Friction 247 Vacuum Friction 247 212 xi 524 Principles of Tribology object are subjected to the action of the frictional force F on their interface After substituting the variables into the force balance equations, we can obtain k1 (v0 t − x1 ) = F + m1 ẍ −F = k2 x2 + mL ẍ + c2 ẋ (21–4) or ẍ = − k1 k F(|ẋ − ẋ |) ẋ + v0 t − m1 m1 m1 ẍ = − c2 k F(|ẋ − ẋ |) ẋ − x − m2 m2 m2 (21–5) The above differential equations can easily be solved by the method of differential calculus We assume that the initial state of the system is as shown in Figure 21.8, where k and k are in the natural states, and m1 and m2 are stationary When the velocity is v0 and if the driving force on m1 is not large enough to overcome the static friction force between m1 and m2 , m1 has no relative motion to m2 Therefore, the two objects are in the “stick” stage If m1 starts to move relatively to m2 because the driving force on m1 begins to be larger than the frictional force, the load on the spring k begins to be reduced, that is, the system is in the “slip” stage At this stage, the driving force will gradually drop When the driving force on m1 drops to less than the dynamic frictional force, it will be in the second “stick” stage This again causes the driving force to increase until the second “slip” stage starts So this continues to alternate By the above simple qualitative analysis, it can be seen that when the relative velocity v is equal to zero, the motion is determined by the frictional force, but when the relative velocity v is not equal to zero, it is determined by the relationship of the frictional force and the velocity v, that is, F = f (v) 21.3.2 Friction-Induced Noise of Wheel-Rail A train often makes a screaming sound while it moves along the rails The friction-induced noise level is about 120 dB with the frequency of 4000–8000 Hz As a typical example, the noise spectrums of a train travelling along a railway track with a radius of curvature of 193 m are represented in Figure 21.9 Research on the forces and motion between the wheels and the train frame through a corner showed that for a railway gauge of l.435 m, if the radius of the railway is less than 500 m, there Figure 21.8 Frictional-mechanical system model [13] Ecological Tribology Figure 21.9 Noise spectrums of wheel-rail [14] will be a lateral sliding between wheel and rail For the train velocity of 15 m/s and a radius of 200–500 m, the lateral sliding velocity vt is in the range of 0.1–0.3 m/s The lateral slip and interfacial friction will bring about stick-slip of the wheel-rail system to cause the vibration Then, noise will be induced After analyzing the causes of noise in the frictional-mechanical system, another important task is to reduce it The noise can be thought as the “output loss” caused by the tribo system The following method describing a friction-induced noise system can be used to study the correlations between the parameters of noise Then, the parameters can be modified to reduce the noise sources According to the contents in Section 21.3.1, the noise induced by friction can be written as Z = f (X, S) where, Z is noise volume; X are the working parameters; S are the structural parameters X and S are vectors There are several sub-factors in each of them as follows 1) Working parameters X = {W , V , T}: W is the load (or vehicle weight), V is the velocity (train velocity, lateral sliding velocity or etc.) and T is temperature (depending on the current season) 2) Structural parameters S = {A, P, R}: A is the type elements including (1) wheel type, (2) track type and (3) environmental conditions P is the performance elements including the materials of wheel and rail, the geometrical designs of the wheel-rail and the geometries of the railway R is the relationship elements including all the tribo relationships of (1), (2) and (3) of A As an example, if we want to modify the sub-parameter A, it can be seen that (1) and (2) are mostly fixed by the standard of the train wheel-rail system Neither of them can be changed easily Therefore, the noise can only be limited by directly controlling (3) the environmental conditions, which are the noise sources on the interface during a friction process Experience has shown that spraying some phosphate solution on the rail, can significantly suppressed the noise From simulating a stick-slip process, it is known that the stick-slip effect depends on the velocity gradient Therefore, in order to clarify the possibility of eliminating 525 526 Principles of Tribology the noise caused by stick-slip, and the optimum conditions of the rail surface treatment, some research had carried on the stick-slip tests in the laboratory as follows [14] A plate and a ball of the actual wheel-rail materials was used in the simulation test under the working conditions similar to the actual ones, that is, pH = 50 × 107 N/m2 and v = 0.02–0.2 m/s The test results showed that noise is obviously influenced by surface treatment Through a surface treatment, although the static friction coefficient f s drops slightly, the dynamic friction coefficient f d can be increased significantly Therefore, their difference Δf = f s − f d drops If the difference is small enough, the stick-slip effect can be greatly reduced so that the friction-induced noise can be significantly controlled The typical results for the stick-slip effect before and after carrying out the surface treatment are shown in Figure 21.10 Through the systematic research, it has been found that phosphate solution can be prepared for the practical purpose of reducing friction-induced noise The solution should be sprayed on the rail in a timely way in order to effectively reduce the noise which is caused by stick-slip of the wheel-rail system 21.3.3 Friction-Induced Noise of Rolling Contact Bearing 21.3.3.1 Sources of Noise Rolling contact bearings are often the main noise sources in machines Friction and vibration are the main causes of the bearing noise, and they often affect each other Vibration will increase friction, and vice versa Therefore, both of them will amplify the bearing noise The main cause of noise noise in a sliding bearing is poor lubrication, which increases the friction between the shaft surface and the bearing surfaces In order to reduce the noise of a sliding bearing, a thick oil film should be maintained between the two frictional surfaces Because the noise level of a sliding bearing is much less than that of a rolling contact bearing, only the noise of rolling contact bearings is dealt with here [15] The poor lubrication of a rolling contact bearing is mainly caused by geometric errors and poor surface quality of the bearing parts Geometric errors may bring about radial runout and vibration Because the inner ring, the outer ring and the rolling bodies are now generally machined to ultra-high precision, the noise of a rolling contact bearing due to geometric errors has been significantly reduced However, the effect of the geometric error cannot be completely eliminated Figure 21.10 Influence of surface treatment on stick-slip [14] Ecological Tribology High-level noise may also be caused by resonant frequencies during operation Even though a rolling contact bearing has no surface imperfections, no geometric errors and a very low surface roughness, the vibration may still be induced due to inherent elastic deformation affecting the assembly clearances between the rolling elements and the raceways In the contact area, elastic deformation of the raceways and the rolling bodies is generated by the load The elastic deformation is maximum if there is only one rolling body at the bottom, as shown in Figure 21.11a, but elastic deformation is minimum if the distances between the two rolling bodies relative to the load vertex are equal, as shown in Figure 21.11b Therefore, this vibration frequency is equal to the number of rolling elements passing through a fixed point of the outer raceway per time Obviously, the noise of a rolling contact bearing is related to the friction of the parts of the bearing The surface damage caused by wear and tear is seriously harmful to the smooth motion so as to increase the vibration Any damage of the bearing can bring about significant vibration and noise When a rolling contact bearing is correctly installed and operating, its surface damage is mainly caused by plastic deformation and wear, particularly due to the contact fatigue 21.3.3.2 Influence Factors of Noise 1) Influence of bearing types: Rolling elements are the main components that cause friction-induced noise in a rolling contact bearing If the shapes of the rolling bodies are different, the relative motions between them and the inner rollway or the outer rollway are different This will result in different kinds of noise levels Comparison tests have been carried out for types 32220/P5 and 32218/P5 tapered roller bearings, types 6220 and 6218 deep-groove ball bearings and types 7220AC and 7218AC angular-contact ball bearings on the front and rear spindles of a C6150 lathe The experimental results are shown in Table 21.12 The noise levels of the ball bearings are nearly dBA lower than those of the tapered roller bearings Therefore, in order to reduce the noise of the rolling contact bearing, ball bearings should preferably be chosen if other requirements can been met 2) Influence of cage accuracy: The bearing cage is often made of low carbon steel plate When a rolling contact bearing is running, the friction between the rolling bodies and the cage is sliding friction with impacts, so that a high noise level will be created The experiments showed that reducing the gap between the cage and the rolling bodies can reduce about dBA of the bearing noise level In addition, the cages of high velocity and high precision bearings are in the form of a solid structure and are usually made of phenolic adhesive plaster, bronze or aluminum alloy These bearings have significantly lower noise 3) Influence of pre-tightening force: Setting the pre-tightening force can usually improve the rigidity of the support for the bearings Studies on machine noise sources have shown that Figure 21.11 Elastic deformation of rolling contact bearing [15] (a) (b) 527 528 Principles of Tribology Table 21.12 Comparisons of noise levels of different types of bearings, dBA [15] 32220/P5 6220 7220AC Noise level (dBA) 32218/P5 6218 7218AC Main shaft spindle rotation 81 72 72 Total machine operation 81.4 81 81 top sleeve spring (a) (b) Figure 21.12 Pre-tightening structure of rolling contact bearing using springs [15] if the bearing pre-tightening force is too large, the bearing noise level will increase by about dB and the bearing temperature will increase also However, if there is no pre-tightening force, that is, if a gap exists, the noise level will increase by 2dB Therefore, in order to control the noise of the bearing, the pre-tightening force should be controlled to a reasonable value An axial pre-tightening structure can ensure that the bearings experience a normal pre-tightening force [15] As shown in Figure 21.12, the springs on the circumference have been used to make the axial force uniform on the inner ring and the outer ring of the bearing Because the bearing always runs under an adjustable pre-tightening force, noise can be kept to a very low level all the time 4) Influence of bearing accuracy: Generally speaking, the higher the accuracy of the bearing, the lower the noise Table 21.13 gives experimental data for a pair of roller contact bearings 32220 and 32218 with combinations of different accuracies in the inner ring, the outer ring and the rollers at a speed of 1250 rpm It can be seen that if the accuracy of the rollers is increased by one grade, the noise of the bearings will decrease 7–10 dBA Therefore, the roller precision is one of the main factors affecting bearing noise 21.4 Remanufacturing and Self-Repairing Remanufacturing is a method of reducing the material loss Furthermore, if certain special additives are put into lubricants, a worn surface can be repaired by itself during working; this is, referred to as self-repairing In the following, these two technologies are introduced briefly Ecological Tribology Table 21.13 Effects of different combinations of precisions on noise [15] Inner ring precision Outer ring precision P4 Roller precision Sound level dBA P4 Ultra-precision machining with first level precision 69.5 P4 P4 Common machining with second level precision 76 P5 P5 Ultra-precision machining with first level precision 70 P5 P5 Common machining with second level precision 80–81 21.4.1 Remanufacturing Most mechanical parts that fail so through surface damage, such as wear, corrosion and high temperature oxidation Local damage of a surface often causes a part to fail or even the whole machine Therefore, improving surface properties is an effective way to prolong the service life of equipment, save resources and reduce environmental pollution The aim of surface engineering is to prepare a functional surface layer using various methods to greatly improve the properties of the surface The thickness of the layer is generally from just a few microns to a few millimeters – a small percentage of the structure size However, it enables the part to have high resistance to abrasion, corrosion and/or high temperature The average efficiency increase of surface engineering technology is to 20 times Surface engineering can directly and locally enforce, repair and protect important parts from rapid failure or recover the use of failed parts According to reports, tens of billions RMB have been saved in manufacturing industries in China through application of surface engineering since the 1980s Furthermore, there are growing problems of waste disposal and resource shortage due to rapid development For example, it was estimated that about 700 million of cars were abandoned in 2015 in China, and more than 200 million electronic products, such as computers, televisions, air conditioners and refrigerators, were abandoned in 2015 in China, about half the total waste electronic products for the whole world In order to alleviate the shortage of resources, reduce environment pollution due to waste products and utilize waste materials effectively, remanufacturing engineering became a hot topic at the end of the twentieth century Remanufacturing technology uses advanced processing methods to recover waste products so that it will regain its original technical performance, and be able to work again and thus prolong the service life of the part If a mechanical part has become worn or corroded, the most widely used repair methods are surface coating or heat-treating It is reported that the life of the overflowing parts, such as blades, of a turbine can increase 3–5 times after being repaired by the flame spray welding technology with oxygen acetylene turbine [16] Furthermore, by using the plasma spraying technology to repair a truck part, the wear-resistance of its surface can be improved about 1.4–8.3 times, more than that of new products, while the repair cost is only 10–12% of its original price There are many different remanufacturing technologies, just a few of which are introduced here due to space limitations 21.4.1.1 Laser Remanufacturing Technology The lLaser remanufacturing is a new repair technology, which combines laser cladding, material science and various other techniques, to make a broken or worn part regain its original 529 530 Principles of Tribology Figure 21.13 Main process flow of laser remanufacturing dimensions and performance, so as to reach or even exceed the original product specification The core of the laser remanufacturing technology is laser cladding, which refers to putting a cladding material on the surface of the matrix and melting it with high energy density laser to form a highly strengthened thin layer so as to repair the worn part and improve its surface properties The processing flow of laser remanufacturing is shown in Figure 21.13 21.4.1.2 Electric Brush Plating Technology The anode of the power source is connected to the brush plating pen, and the cathode of the power source is connected to the part The plating pen usually uses high purity fine graphite as the anode material and the graphite block is wrapped in a layer of cotton and anti-wear polyester cotton During plating, the pen is dipped in the plating bath and moved on the surface of the work-piece at a certain relative speed, and under an appropriate pressure The plating metal ions diffuse into the surface of the work-piece under the action of the electric field, and they deposit on the surface to form a coating When the coating has grown thick enough, the worn part has been repaired 21.4.1.3 Nano Brush Plating Technology The nano brush plating technology was developed from traditional electric brush plating It adds nano particles with certain specific properties into the brush plating solution so as to obtain a composite brush plating solution During plating, the nano particles, under the action of the electric field or the clamping force of the complex ions, deposit metal ions onto the surface to form a coating Because the nano particles disperse into the composite coating, they can improve the performance of the surface 21.4.1.4 Supersonic Spray Coating Technology The supersonic spray coating technology use an electric arc formed on the end of a wire to melt the wire and, through a Laval nozzle, to accelerate the melted wire into a fine supersonic airflow to spray the surface of the work-piece to form a coating It has advantage such as high strength, low porosity and low surface roughness In addition, before determining whether a worn part can be repaired or not, many other tasks should be carried out at the very beginning The steps of the remanufacturing processing Ecological Tribology Figure 21.14 Remanufacturing routine routine are given in Figure 21.14, where the steps belonging to remanufacturing or traditional manufacturing have been divided 21.4.2 Self-Repairing The self-repairing technology is a method for adding special additives into a lubricant and, through the action of friction, to repair a worn part Therefore, the additive is the key to realizing self-repair Usually, nano copper powder is used as the additive to repair the worn surfaces of mechanical parts under the condition of friction The diameter of the nano copper particles is usually 20–80 nm and 0.5% of the base oil Before it is used, ultrasonic vibration should be applied for about 60 to disperse the powder uniformly in the lubricant For example, the wear of the cylinder and the piston of an automobile engine will increase with increased mileage When the wear gap reaches a certain value, the performance of the engine will be seriously reduced If adding some appropriate repair additives into the engine lubricating oil, the worn parts can be self-repaired as the engine works In their studies, Jiang et al used a copper type additive to repair the surface [17] The recovered height H has been estimated by calculation, as shown in Figure 21.15a Their experimental results showed that the frictional force decreased with running time increasing, as shown in Figure 21.15b These results meant that the sealing performance of the cylinder had been improved Therefore, the service life of the cylinder was prolonged The mechanisms of a self-repair additive can be classified into two kinds as follows 21.4.2.1 Spreading Film Under the action of affinity between the additive molecules and the metal surface, the additive molecules show polarity under the action of friction They spread to the microcosmic surface of the friction pair to form a spreading film, which is of anti-friction and wear-resistance 21.4.2.2 Eutectic Film Under the condition of boundary lubrication, the local high temperature caused by friction will prompt the additive particles to combine with worn particles to form some small eutectic spheres They may form a protective film with a lubrication function on the contact surface Therefore, self-repair is achieved This film will fill in the micro valleys of the worn surface so as to improve its sealing performance, reduce the frictional force and prolong the life of the 531 532 Principles of Tribology Figure 21.15 Experiment and calculation results of self-repairing [17] parts The nanoparticles of some metals or metal alloys can achieve the mechanism of this theory Under conditions of a certain temperature and pressure, the surface experiences intensive friction and plastic deformation during a friction process The nanoparticles adsorbed on the friction surface will interact with the plastically deformed surface If the temperature of the surface is high enough, the intensity of nanoparticles will decrease to form a eutectic film with the microscopic particles of the metal surface It fills in the micro valleys of the surface to form a repair film It should be pointed out that self-repairing is a dynamic process because it must occur under the friction condition With increasing friction and temperature, the film may increase but the normal wear also exists The repair film is also worn at the same time, even during the self-repairing process, so the repaired thickness will be limited, and it is impossible to compensate completely for the worn volume while the wear process and the self-repairing process are balanced References Luo Jianbin, Shi Bing, Qian Linmao et al., (1997) Recent advances and mechanism discus- sion of superlubrication, Journal of Tsinghua University (Sci & Tech), 37(11): 104–109 Kapitza, P (1938) Viscosity of Liquid Helium below the 𝜆-Point, Nature, 141: 74–74 (08 January 1938) doi:10.1038/141074a0 Kubota, M., Obata, T and Ishiguro, R., Superfluidity and quantized vortex studies under rotation up to Hz at mK and Hz at sub-mK temperatures, Physica B Condensed Matter, 329–333(2): 1577–1581, 2003 Shinjo, K and Hirano, M (1993) Dynamics of friction: superlubric state Surface Science 283(1-3): 473–478 Ecological Tribology Yoshizawa, H., Chen, Y.L and Israelachvili J.N (1993) Recent advances in molecular level understanding of adhesion, friction and lubrication Wear (168): 161–166 Wen, S.Z (1998) Nano tribology, Beijing: Tsinghua University Press Klein, J (1993) An experimental study of static and dynamic properties of end-attached polymer layers, Rehovot: [s.n.] Shen Jiacong, Zhang Ran, Sun Yipeng (1997) Molecular deposition film, Progress in Natural Science: National Key Laboratory of Communication, 1: 1–6 Jiang, H.J., Meng, Y.G and Wen, S.Z (1998) Study on mechanism of influence of electric 10 11 12 13 14 15 16 17 field on friction and wear characteristics of Al2 O3 /Cu Science in China (Series E), 28(6): 491–498 Thompson, P.A., Grest, G.S and Robins, M.O (1992) Phase transitions and universal dynamics in confined films Phys Rev Lett., 68: 3448–3451 Li, X.C and Yan, S.L (1999) Countermeasures of prevention and control for pollution of waste oil, Research of Renewable Resources, (3): 31–32 Wang Yonggang, Bai Xiaohua, Li Jiushen (2010) Progress in application of green lubricant and green lubricating additive, Petrochemical Industry Application, 29(6): 4–8 Moore, D.F (1975) Principles and Applications of Tribology, Pergamon Press, Oxford Jiao Dahua, Qian Desheng (1990) Control of railway environmental noise Beijing: Chinese Railway Press Zhang Jianshou, Xie Yongxu (1987) Mechanical and hydraulic noise and control, Shanghai science and Technology Press Xu B.S., Zhu, S, Ma S.N et al (2000) Applications of surface engineering and remanufacturing engineering, Materials Protection, 33(1): 1–3 Jiang B.X., Chen S.B and Dong J.X (1999) Study on Feasibility of Frictional Repairing of copper type additives, Mechanical Science and Technology, 18(3): 475–477 533 535 Index a abrasive wear 177, 233, 282, 284, 285–298, 309, 314, 324–325, 327, 330–333, 342, 343–345, 349, 364, 420, 425, 434, 449, 491 additives of lubricating oil 176, 178, 185–186, 187–188 adhesive wear 177, 235, 283–285, 290–298, 308–309, 311–312, 314–315, 320, 323, 324–325, 327, 329, 342, 344–345, 346, 364, 375, 419–420, 424, 425, 434 adhesive wear theory 324 adsorption heat of boundary film 182–183 AES 502, 507 AFM see atomic force microscopy (AFM) analysis of space tribological properties 462–465 analysis of wear failure 380–381 appearance and structure of surface coating 355–356 atomic force microscopy (AFM) 374–375, 387, 396, 398, 401, 467, 470, 473, 474, 478, 480, 484, 488, 489–490, 491, 502, 504 autocorrelation function of surface profile 216–217 b basic characteristics of friction 225–228 bead weld technique 337, 346, 347–348, 354–355 biodegradability 518–519 biodegradation 521–523 boundary condition of Reynolds equation 27–28 boundary element method 41, 49–51 boundary lubrication model 179–181, 182 boundary lubrication theory 147, 171, 179–185 brush plating 337, 350, 354–355, 530 bulging 493, 494–495, 501–507 c cam lubrication 114–116 cavitation erosion 310–312, 466 chemical absorption 173–174, 409, 461, 514 chemical reaction film 171, 177–179, 187, 188, 296, 337, 423 choice of lubricants and additives 311 circle constitutive equation 13 common surface coating methods 347–354 constant delivery pump 91 contour map 213–214 corrosion wear 178, 283, 284, 308, 309, 314, 327, 345, 379, 434, 491 creeping 460–462 curves of wear processes 311, 317–20, 322, 331, 420, 425 d density of lubricating oil 3, 5–7, 47 detection of wear states 378–380 directional factor model 160–161 double electric layer effect 118, 137–145 drawing tribology 421–429 dynamic bearing 96–102 dynamic journal bearing 96–98 dynamic viscosity 7–8, 19–20, 441–443, 463 e ecological tribology 509–532 EHL inlet analysis 34–38 elastic deformation solution 60–63, 66 elasticity theory basic of contacts 29–31 Principles of Tribology, Second Edition Shizhu Wen and Ping Huang © 2018 Tsinghua University Press Published 2018 by John Wiley & Sons Singapore Pte Ltd 536 Index elastohydrodynamic lubrication 3, 4–5, 6, 7, 11, 22, 29, 30, 60–67, 106, 108, 171, 198, 432, 444, 455, 456 electro brush plated coating 350 energy wear theory 325–327 equivalent radius of curvature 30, 106, 115 error of distribution curve 216, 217 eutectic film 531–532 extreme pressure additive 177–178, 185, 187, 188, 294, 310, 311–312, 420, 433 f fallen leave 261 fatigue wear 29, 31, 298–307, 314, 315, 317, 324, 327, 329, 331, 345, 364, 379, 420, 425, 451 fatigue wear on subsurface 298–299 fatigue wear on surface 284, 298–299, 301, 323, 342 features of space lubrication 463–465 film thickness formula of EHL 3, 64, 66–67, 108, 112, 114, 151 finite difference method 41, 42–44, 48, 134 forge tribology 412, 416–420 friction and wear of joint 447–451 friction control 247–250 friction-induced noise 509, 523–528 function of soften surface 179 function of thin polish film 179 g gas bearing 104, 167 gear lubrication 108–114 grease lubrication 38–40, 457 green lubricants 509, 516–523 h heat conduction equation 55, 56, 263 height distribution function 214–215 high stick thick film 179 hydrodynamic lubrication 3–5, 11, 22–40, 41, 42, 44–48, 56, 59, 81, 115, 118–130, 137–142, 147, 148, 152, 155, 157, 171, 198, 200, 203, 245, 423–424, 432, 433, 434, 446, 455, 491 hydrostatic bearing 88–92 hydrostatic journal bearing 90 hydrostatic thrust disk 89 i IBM wear calculation method 329–331 indentation 288, 289–290, 360, 369–371, 372, 419, 431, 433, 496, 497–499, 500–502 influence of fluid limiting shear stress on lubrication failure 195–199 influence of geometric quality on wear 321–322 influence of temperature on lubrication failure 200–203 initial condition of Reynolds equation 28 j journal bearing 5, 27, 46–47, 51, 81–88, 90, 94–97, 98, 100, 103–105, 128, 129, 148, 171–172, 296, 373, 380, 443 k kinematics viscosity 8, 9–10, 19–20 l laser 348, 529–530 liquid crystal lubrication 118, 130–137 liquid lubricant of joints 419 local thermal stable and unstable 201 lubricated wear model 190–191, 192–195 lubrication failure 54, 159, 181, 183–184, 190–207, 293, 366, 418, 433, 447, 456 lubrication of micro motor 486–487 lubrication states 3–5, 6, 39, 106, 147–152, 156, 157, 171–172, 245, 297, 329–330, 337, 364, 380, 423, 432, 434, 446, 453, 457–458, 462, 486 lunar rover 271–280 m macro friction theory 228–238 magnetic fluid lubrication 123 materials of friction pair 249 mathematical model of thin film lubrication 149, 160 measurement and exchange of viscosity 19–21 measurement of coating properties 346 measurement of wear 368–373 mechanical wear 282, 307, 322 mechanics basis of metal forming 412–416 mechanics on joints and soft tissue 445 MEMS see micro electro-mechanical system (MEMS) Index men and animal joint lubrications 437, 443–447, 451 methods and equipment of tribological experiments 363–367 micro adhesive force 473 micro contact and adhesive phenomena 387 micro electro-mechanical system (MEMS) 162, 466–507 micro friction 240, 387–393, 399, 467, 473, 474 micro frictional force 388, 389, 476 micro friction theory 238–243 micro motor 484–491 micro-polar fluid lubrication 124–130 micro slip 254, 257, 258, 259, 260 micro wear 284, 298, 314, 368, 387, 396–401, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 504, 507 milling tribology 324 mixed lubrication 4, 114, 147, 148, 149, 152, 172, 182, 190–207, 366, 419, 423, 432–434, 454, 455, 456 molecular film and boundary lubrication 401–410 molecular-mechanical wear 322 molecular polymer film 510, 513–514 monocrystalline silicon 466, 492, 493, 494–496, 501, 504, 506, 507 multi-grid integration method 68, 73–76 multi-grid level method used in lubrication problems 41 n nano film lubrication of gas 161–169 nano film lubrication of liquid 159 nonlinear visco-elastic constitutive equation 14–15 non-Newtonian properties 129, 158, 200 numerical analysis of TFL 158–160 numerical analysis of thin film lubrication 158–160 numerical method for solving ultra thin gas lubrication 166 numerical methods of Reynolds equation 41, 81 numerical solutions of elastohydrodynamic lubrication 60–67 numerical solutions of energy equation 59–60 o ordered phenomena of thin film lubrication 153–154 p parameters of surface topography 211–217 parched lubrication 453, 455–458 petroleum 136, 516, 517, 518 plowing effect 231, 233–235, 283, 284, 391–393 pre-tightening 527, 528 pseudo plastic 12, 16 p0 Us criterion 296 r Ree-Eyring constitutive equation 12–13 refrigeration 516, 518–520 remanufacturing 509, 528–531 remanufacturing and self-repairing 528–532 Reynolds equation 22–28, 35–37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 53, 54, 59, 60, 61, 62, 65, 66, 78, 81, 82, 85, 88, 89, 92, 93, 96–98, 101, 102, 103, 108, 121, 123, 124, 125, 127, 128, 138, 142, 147, 159, 160, 161, 163, 165–166, 167, 200, 424 Reynolds equation derivation 23–26, 40, 123 rigid-plastic deformation 254, 256 rolling contact bearing 4, 78, 106–108, 252, 296, 298, 306, 343, 453, 454, 463–465, 523, 526–528 rolling friction 225, 252–280, 298, 412 rolling resistant coefficient 252–254, 256 rough surface contacts 219–223 s scuffing factor criteria 298 self-repairing 509, 528–532 shape memory alloy 494 simple dynamic bearing 98–100 sinkage 273, 276, 277, 279 slider and thrust bearing 78–81 sliding friction 114, 225–250, 254, 255, 258, 263, 298, 308, 316, 327, 331, 388, 391, 415, 419, 421, 431, 471, 474, 527 sliding/rolling ratio 260, 274–275, 279, 280 slurry coating technique 349 soft surface 228, 231, 233, 275–278, 285, 291, 327, 328, 391 537 538 Index soil 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 314, 517 soil deformation 276–277 solid lubricant 3, 247, 316, 341, 346, 512 Sommerfeld boundary condition 95, 97 Sommerfeld integration 85 space tribology 453–465 spalling theory 293 spray coating 354, 355, 357, 359, 360, 361, 530 squeeze bearing 92–96 squeezing disk 94 squeezing film journal bearing 94–96 starved lubrication 456 step bearing 87, 96, 100, 169 stick-slip 186, 240, 242, 391, 392, 402, 403, 404, 467, 470–474, 512, 523, 525, 526 strength of boundary film 184–185 super dynamic friction 513 superficial structure and surface properties 303 superfluidity 509, 510–511, 514 superimposition method of carrying loads 101–102 superlubrication 242, 509–516 surface absorption 138, 326, 422, 444 surface coating 337–361, 377, 529 surface coating design 354 surface profile method 213, 368 surface quality and wear 324 surface roughness 4, 17, 147, 157, 159, 171, 172, 176, 185, 190, 203, 206, 212, 228, 236, 260, 285, 288, 290, 302, 309, 320, 321, 329, 337, 354, 359, 368, 372, 389, 409, 420, 434, 444, 445, 447, 489, 527, 530 surface tension 17–18, 122, 181–183, 188, 396, 409, 455, 456, 460, 461, 516 t TEM see transmission electronic microscope (TEM) test of surface coating performances 359 TFL and EHL testers 365 thermal analysis 9, 55, 259, 262–271 thin film lubrication 4, 142, 147–169, 207, 365–367, 514 thixotropic feature of thin film lubrication 154 thixotropy 15, 16 topographical parameters and statistics 213 topography analysis of friction surface 373–374 transformation of lubrication states transient temperature 268–269, 294 transmission electronic microscope (TEM) 373, 495, 496 two-body abrasion wear 285, 290, 425 two-dimensional profile curves 213, 214 types of boundary lubrication 171–179 u unequal diameter wheel 278–280 v variation of surface property 283–284 viscosity of fluids viscosity-pressure effect 62 w waste oil 516, 517, 518 wear calculation 282, 294, 314, 324, 329–335 wear classification 282, 283 wettability 16–18, 181, 316 wheel and rail 260–271, 525 WUns criterion 296–297 WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA