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Numerical Calculation of Lubrication: Methods and Programsby Ping Huang
Synopses & ReviewsPublisher Comments:Focusing on basic lubrication problems this book offers specific engineering applications. The book introduces methods and programs for the most important lubrication problems and their solutions. It is divided into four parts. The first part is about the general solving methods of the Reynolds equation, including solutions of Reynolds equations with different conditions and their discrete forms, such as a steadystate incompressible slider, journal bearing, dynamic bearing, gas bearing and grease lubrication. The second part gives the ‘energy equation solution’. The third part introduces methods and programs for elastohydrodynamic lurbication, which links the Reynolds equation with the elastic deformation equation. The final part presents application lubrication programs used in engineering.
With an emphasis on clear explanations, the text offers a thorough understanding of the numerical calculation of lubrication for graduate students on tribology and engineering mechanics courses, with more detailed materials suitable for engineers. This is an accessible reference for senior undergraduate students of tribology and researchers in thinfilm fluid mechanics. Synopsis:This book describes basic lubrication problems and specific engineering applications. It focuses on the Reynolds equation, illustrating solutions with different conditions and discrete forms, such as dynamic bearing or grease lubrication. Thermal fluid lubrication problems are addressed by combining the Reynolds and energy equation solution, while the topic of elastohydrodynamic lubrication illustrates a combination of programs, join solution methods, and the Reynolds equation. Additional programs address lubrication for different parts with specific design, such as the magnetic hard disk/head and its steadystate design.
Synopsis:Focuses on basic lubrication problems and offers specific engineering applications. The book is divided into four parts. The first part is Reynolds equation solution, which includes solutions of Reynolds equations with the different conditions and the discrete forms, such as the steadystate incompressible slider, journal bearing, dynamic bearing, gas bearing and grease lubrication. The second part is energy equation solution. The form of the discrete energy equations and the temperatureviscosity equations are given first. Then, thermal fluid lubrication problems are solved, combined with the Reynolds and the energy equation. In elastohydrodynamic lubrication, the elastic deformation equations are given first. Then, the pressureviscosity and temperatureviscosity equation are also introduced. Then the joint solution methods and programs combined with the Reynolds equation and the elastic deformation equation are introduced. The programs include the isothermal and thermal elastohydrodynamic lubrications and grease elastohydrodynamic lubrication. In the final part, the lubrication programs include the herringbone groove bearing lubrication of micro motor and its optimization design, the super thin gas film lubrication for the magnetic hard disk/head and its steadystate design.
About the AuthorPing Huang, South China University of Technology, Guangzhou, China
Table of ContentsPreface xv
Part 1 NUMERICAL METHOD FOR REYNOLDS EQUATION 1 1 Reynolds Equation and its Discrete Form 3 1.1 General Reynolds Equation and Its Boundary Conditions 3 1.1.1 Reynolds Equation 3 1.1.2 Definite Condition 3 1.1.3 Computation of Lubrication Performances 5 1.2 Reynolds Equations for Some Special Working Conditions 6 1.2.1 Slider and Thrust Bearing 6 1.2.2 Journal Bearing 7 1.2.3 Hydrostatic Lubrication 8 1.2.4 Squeeze Bearing 9 1.2.5 Dynamic Bearing 9 1.2.6 Gas Bearing 10 1.3 Finite Difference Method of Reynolds Equation 10 1.3.1 Discretization of Equation 11 1.3.2 Difference Form of Reynolds Equation 12 1.3.3 Iteration of Differential Equation 13 1.3.4 Iteration Convergence Condition 13 2 Numerical Method and Program for Incompressible and Steady Lubrication of Onedimensional Slider 17 2.1 Basic Equations 17 2.1.1 Reynolds Equation 17 2.1.2 Boundary Conditions 18 2.1.3 Continuity Equation 18 2.2 Numerical Method for Incompressible and Steady Lubrication of Onedimensional Slider 18 2.2.1 Discrete Reynolds Equation 19 2.3 Calculation Program for Incompressible and Steady Lubrication of Onedimensional Slider 20 2.3.1 Introduction 20 2.3.2 Calculation Diagram 21 2.3.3 Calculation Program 21 2.3.4 Calculation Results 24 3 Numerical Method and Program for Incompressible and Steady Lubrication of Twodimensional Slider 25 3.1 Basic Equations 25 3.2 Discrete Reynolds Equation 26 3.3 Calculation Program for Incompressible and Steady Lubrication of Twodimensional Slider 27 3.3.1 Introduction 27 3.3.2 Calculation Diagram 27 3.3.3 Calculation Program 28 3.3.4 Calculation Results 31 4 Numerical Method and Program for Incompressible and Steady Lubrication of Journal Bearing 33 4.1 Basic Equations 33 4.1.1 Axis Position and Clearance Shape 33 4.1.2 Reynolds Equation 34 4.2 Numerical Method for Incompressible and Steady Lubrication of Journal Bearing 35 4.2.1 Dimensionless Reynolds Equation 35 4.2.2 Discrete Form of Reynolds Equation 36 4.3 Calculation Program for Incompressible and Steady Lubrication of Journal Bearing 37 4.3.1 Calculation Diagram 37 4.3.2 Calculation Program 38 4.3.3 Calculation Results 40 5 Numerical Method and Program for Incompressible Squeeze Lubrication 41 5.1 Basic Equation 41 5.2 Numerical Method and Program for Rectangular Plane Squeeze 42 5.2.1 Basic Equations 42 5.2.2 Numerical Method 42 5.2.3 Calculation Diagram 43 5.2.4 Calculation Program 44 5.2.5 Calculation Results 47 5.3 Numerical Method and Program for Disc Squeeze 47 5.3.1 Basic Equations 47 5.3.2 Numerical Method 48 5.3.3 Calculation Diagram 48 5.3.4 Calculation Program 49 5.3.5 Calculation Results 52 5.4 Numerical Method and Program for Journal Bearing Squeeze 52 5.4.1 Basic Equations 52 5.4.2 Numerical Method 54 5.4.3 Calculation Diagram 54 5.4.4 Calculation Program 55 5.4.5 Calculation Results 60 6 Numerical Method and Program for Dynamic Bearing 61 6.1 Basic Equations 61 6.2 Numerical Method for Trace of Journal Center 65 6.2.1 Introduction 65 6.2.2 Calculation Steps 66 6.3 Calculation Program for Dynamic Journal Bearing 67 6.3.1 Introduction 67 6.3.2 Calculation Diagram 67 6.3.3 Calculation Program 68 6.3.4 Calculation Results 82 7 Numerical Method and Program for Gas Lubrication 85 7.1 Basic Equations 85 7.1.1 General Reynolds Equation of Gas Lubrication 85 7.2 Numerical Method of Gas Lubrication 86 7.2.1 Basic Equations of Steady and Isothermal Gas Lubrication 86 7.2.2 Numerical Method 87 7.3 Calculation Program for Gas Lubrication 88 7.3.1 Calculation Program and Solutions of OneDimensional Gas Lubrication 88 7.3.2 Numerical Program and Solutions of TwoDimensional Gas Lubrication 91 7.3.3 Numerical Program and Solutions of Journal Bearing Gas Lubrication 94 8 Numerical Method and Program for Rarefied Gas Lubrication 97 8.1 Basic Equations 97 8.2 Numerical Method of Rarefied Gas Lubrication 99 8.2.1 Rarefied Gas Lubrication Model 99 8.2.2 Treatment of the UltraThin Gas Film Lubrication Equation 100 8.3 Discretization and Iteration of Modified Reynolds Equation 101 8.3.1 Discrete Equation 101 8.3.2 Iteration Method 101 8.4 Calculation Program for Rarefied Gas Lubrication of Slider 102 8.4.1 Procedures Introduction 102 8.4.2 Calculation Diagram 102 8.4.3 Calculation Program 102 8.4.4 Calculation Results 106 9 Numerical Method and Program for Onedimensional Grease Lubrication 107 9.1 Basic Equations 107 9.1.1 Introduction 107 9.1.2 Constitutive Equations of Grease 108 9.1.3 Reynolds Equation 109 9.2 Numerical Method of OneDimensional Grease Lubrication 109 9.3 Calculation Program of OneDimensional Grease Lubrication 110 9.3.1 Calculation Diagram 110 9.3.2 Calculation Program 111 9.3.3 Calculation Results 113 Part 2 NUMERICAL METHOD FOR ENERGY EQUATION 115 10 Energy Equation and its Discrete Form 117 10.1 Basic Equations 117 10.1.1 Simplified Energy Equation 118 10.1.2 Boundary Conditions 118 10.1.3 Numerical Method 119 10.2 Influence of Temperature on Lubricant Performance 120 10.2.1 Viscosity–Temperature Equation 120 10.2.2 Density–Temperature Equation 120 10.3 Numerical Method for Thermal Hydrodynamic Lubrication 121 10.3.1 Methods and Program for Onedimensional Thermal Hydrodynamic Lubrication 121 10.3.2 Numerical Method and Program for Twodimensional Thermal Hydrodynamic Lubrication 124 11 Numerical Method and Program for Incompressible and Steady Thermal Hydrodynamic Lubrication of Journal Bearing 131 11.1 Basic Equations 131 11.1.1 Reynolds Equation 131 11.1.2 Energy Equation 132 11.1.3 Viscosity–Temperature Equation 132 11.2 Numerical Method 132 11.2.1 Discrete Reynolds Equation 132 11.2.2 Discrete Energy Equation 133 11.2.3 Temperature–Viscosity Equation 133 11.3 Calculation Program 133 11.3.1 Calculation Diagram 133 11.3.2 Calculation Program 134 11.3.3 Calculation Results 138 Part 3 NUMERICAL METHOD FOR ELASTIC DEFORMATION AND THERMAL ELASTOHYDRODYNAMIC LUBRICATION 141 12 Numerical Method and Program for Elastic Deformation and Viscosity–Pressure Equation 143 12.1 Basic Equations of Elastic Deformation 143 12.1.1 Film Thickness Equation 143 12.1.2 Elastic Deformation Equation 143 12.2 Numerical Methods and Programs of Elastic Deformation 145 12.2.1 Numerical Method and Program of Elastic Deformation Equation in Line Contact 145 12.2.2 Numerical Method and Program of Elastic Deformation Equation in Point Contact 148 12.3 Viscosity–Pressure and Density–Pressure Equations 155 12.3.1 Viscosity–Pressure Relationship 155 12.3.2 Viscosity–Pressure–Temperature Relationship 156 12.3.3 Density–Pressure Relationship 156 13 Numerical Method and Program for EHL in Line Contact 159 13.1 Basic Equations 159 13.2 Numerical Method 160 13.2.1 Dimensionless Equations 160 13.2.2 Discrete Equations 161 13.2.3 Iterative Method 162 13.2.4 Selection of Iterative Methods 163 13.2.5 Relaxation Factors 164 13.3 Calculation Program 164 13.3.1 Calculation Diagram 164 13.3.2 Calculation Program 165 13.3.3 Calculation Results 171 14 Numerical Method and Program for EHL in Point Contact 173 14.1 Basic Equations 173 14.2 Numerical Method 174 14.2.1 Dimensionless Equations 174 14.2.2 Discrete Equations 175 14.3 Calculation Program 176 14.3.1 Calculation Diagram 176 14.3.2 Calculation Program 177 14.3.3 Calculation Results 186 15 Numerical Method and Program for Grease EHL in Line Contact 187 15.1 Basic Equations 187 15.1.1 Reynolds Equation 187 15.1.2 Film Thickness Equation 187 15.1.3 Viscosity–Pressure Equation 188 15.1.4 Density–Pressure Equation 188 15.2 Numerical Method 188 15.2.1 Dimensionless Equations 188 15.2.2 Discrete Equations 189 15.3 Calculation Program 189 15.3.1 Calculating Diagram 189 15.3.2 Calculation Program 190 15.3.3 Calculation Results 199 16 Numerical Method and Program for Grease EHL in Point Contact 201 16.1 Basic Equations 201 16.1.1 Reynolds Equation 201 16.1.2 Film Thickness Equation 201 16.1.3 Elastic Deformation Equation 202 16.1.4 Viscosity–Pressure Equation 202 16.1.5 Density Equation 202 16.2 Numerical Method 202 16.2.1 Dimensionless Equations 202 16.2.2 Discrete Equations 203 16.3 Calculation Program 204 16.3.1 Calculation Diagram 204 16.3.2 Calculation Program 205 16.3.3 Calculation Results 214 17 Numerical Method and Program for Thermal EHL in Line Contact 215 17.1 Basic Equations 215 17.1.1 Reynolds Equation 215 17.1.2 Energy Equation 215 17.1.3 Film Thickness Equation 216 17.1.4 Elastic Deformation Equation 216 17.1.5 Roelands Viscosity–Pressure–Temperature Equation 216 17.1.6 Density–Pressure–Temperature Equation 217 17.2 Numerical Method 217 17.2.1 Dimensionless Equations 217 17.2.2 Discrete Equations 218 17.3 Calculation Program 220 17.3.1 Calculation Diagram of Multigrid Method 220 17.3.2 Calculation Diagram of Temperature 221 17.3.3 Calculation Program 222 17.3.4 Calculation Results 236 18 Numerical Method and Program for Thermal EHL in Point Contact 237 18.1 Basic Equations 237 18.1.1 Reynolds Equation 237 18.1.2 Energy Equation 237 18.1.3 Film Thickness Equation 238 18.1.4 Elastic Deformation Equation 238 18.1.5 Roelands Viscosity–Pressure–Temperature Equation 239 18.1.6 Density–Pressure–Temperature Equation 239 18.2 Numerical Method 239 18.2.1 Dimensionless Equations 239 18.2.2 Discrete Equations 241 18.3 Calculation Program 242 18.3.1 Calculation Diagram 242 18.3.2 Calculation Program 242 18.3.3 Calculation Results 261 19 Numerical Method and Program for Thermal Grease EHL in Line Contact 263 19.1 Basic Equations 263 19.1.1 Reynolds Equation 263 19.1.2 Energy Equation 264 19.1.3 Film Thickness Equation 264 19.1.4 Elastic Deformation Equation 265 19.1.5 Viscosity–Pressure–Temperature Equation 265 19.1.6 Density–Pressure–Temperature Equation 265 19.2 Numerical Method 265 19.2.1 Dimensionless Equations 265 19.2.2 Discrete Equations 267 19.3 Calculation Program 268 19.3.1 Calculation Diagram 268 19.3.2 Calculation Program 268 19.3.3 Calculation Results 287 20 Numerical Method and Program for Thermal Grease EHL in Point Contact 289 20.1 Basic Equations 289 20.1.1 Reynolds Equation 289 20.1.2 Energy Equation 290 20.1.3 Film Thickness Equation 290 20.1.4 Elastic Deformation Equation 291 20.1.5 Roelands Viscosity–Pressure–Temperature Equation 291 20.1.6 Density–Pressure–Temperature Equation 291 20.2 Numerical Method 291 20.2.1 Dimensionless Equations 291 20.2.2 Discrete Equations 293 20.3 Calculation Program 294 20.3.1 Calculation Diagram 294 20.3.2 Calculation Program 295 20.3.3 Calculation Results 310 Part 4 CALCULATION PROGRAMS FOR LUBRICATION ANALYSIS IN ENGINEERING 311 21 Lubrication Calculation Program for Herringbone Grooved Journal Bearing of Micro Motor 313 21.1 Basic Theory of Lubrication Calculation of Herringbone Groove Bearing 313 21.1.1 Journal Center Position and Film Thickness 313 21.1.2 Reynolds Equation 314 21.1.3 Boundary Conditions 315 21.1.4 Flux Calculation 316 21.1.5 Temperature Calculation 316 21.2 Program for Performance Calculation 318 21.2.1 Lubrication Performances 318 21.2.2 Calculation Program 318 21.3 Calculation Results 326 21.4 Instruction for HBFA Software Package 332 21.4.1 Package Contents 332 21.4.2 Program Installation 332 21.4.3 Program Operation 333 22 Lubrication Optimization Program of Herringbone Grooved Journal Bearing of Micro Motor 337 22.1 Method of Optimization Calculation 337 22.1.1 Requirements of Parameter Optimization 337 22.1.2 Optimization Model 337 22.1.3 Optimization Methods and Steps 338 22.2 Program Layout of Optimization Calculation 338 22.2.1 Optimization Program Diagram 338 22.2.2 Calculation Program 339 22.2.3 Parameters in Program 352 22.3 Optimization Calculation Examples 352 22.3.1 Example 1: Optimization Calculation for Static Load 352 22.3.2 Example 2: Optimization Calculation for Static Flux (Eccentricity Ratio e is Constant) 354 22.3.3 Example 3: Optimization Calculation for Static Flux (Load W is Constant) 354 22.3.4 Example 4: Optimization Calculation for Dynamic Load 354 22.3.5 Example 5: Optimization Calculation for Dynamic Flux (Eccentricity e is Constant) 354 22.3.6 Example 6: Optimization Calculation for Dynamic Flux (Load W is Constant) 355 22.4 Instructions for HBOA Software Package 355 22.4.1 Program Package 355 22.4.2 Program Execution 356 23 Calculation Program for Gas Lubrication of Hard Disk/Head in Ultra Thin Film 361 23.1 Basic Equations of Gas Lubricating Film of Hard Disk/Head 361 23.1.1 Basic Equations 361 23.1.2 Gas Film Thickness 362 23.1.3 Poiseuille Flow Rate 362 23.2 Discrete Equation and Special Treatments 363 23.2.1 Iterative Scheme Considering High Bearing Numbers 363 23.2.2 Abrupt Changes between Steps on ABS 364 23.3 Calculation Program 364 23.3.1 Calculation Diagram 364 23.3.2 Calculation Program 366 23.3.3 Calculation Results 371 24 Calculation Program of Flight Attitude of Magnetic Head 373 24.1 Search Strategy for Flight Attitude 373 24.2 Calculation Program 375 24.2.1 Program Introduction 375 24.2.2 Calculation Diagram 376 24.2.3 Calculation Program 376 24.2.4 Calculation Results 386 References 389 Index 391 What Our Readers Are 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