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Preface xv <p>Part 1 NUMERICAL METHOD FOR REYNOLDS EQUATION 1</p> <p><b>1 Reynolds Equation and its Discrete Form 3</b></p> <p>1.1 General Reynolds Equation and Its Boundary Conditions 3</p> <p>1.1.1 Reynolds Equation 3</p> <p>1.1.2 Definite Condition 3</p> <p>1.1.3 Computation of Lubrication Performances 5</p> <p>1.2 Reynolds Equations for Some Special Working Conditions 6</p> <p>1.2.1 Slider and Thrust Bearing 6</p> <p>1.2.2 Journal Bearing 7</p> <p>1.2.3 Hydrostatic Lubrication 8</p> <p>1.2.4 Squeeze Bearing 9</p> <p>1.2.5 Dynamic Bearing 9</p> <p>1.2.6 Gas Bearing 10</p> <p>1.3 Finite Difference Method of Reynolds Equation 10</p> <p>1.3.1 Discretization of Equation 11</p> <p>1.3.2 Difference Form of Reynolds Equation 12</p> <p>1.3.3 Iteration of Differential Equation 13</p> <p>1.3.4 Iteration Convergence Condition 13</p> <p><b>2 Numerical Method and Program for Incompressible and Steady Lubrication of One-dimensional Slider 17</b></p> <p>2.1 Basic Equations 17</p> <p>2.1.1 Reynolds Equation 17</p> <p>2.1.2 Boundary Conditions 18</p> <p>2.1.3 Continuity Equation 18</p> <p>2.2 Numerical Method for Incompressible and Steady Lubrication of One-dimensional Slider 18</p> <p>2.2.1 Discrete Reynolds Equation 19</p> <p>2.3 Calculation Program for Incompressible and Steady Lubrication of One-dimensional Slider 20</p> <p>2.3.1 Introduction 20</p> <p>2.3.2 Calculation Diagram 21</p> <p>2.3.3 Calculation Program 21</p> <p>2.3.4 Calculation Results 24</p> <p><b>3 Numerical Method and Program for Incompressible and Steady Lubrication of Two-dimensional Slider 25</b></p> <p>3.1 Basic Equations 25</p> <p>3.2 Discrete Reynolds Equation 26</p> <p>3.3 Calculation Program for Incompressible and Steady Lubrication of Two-dimensional Slider 27</p> <p>3.3.1 Introduction 27</p> <p>3.3.2 Calculation Diagram 27</p> <p>3.3.3 Calculation Program 28</p> <p>3.3.4 Calculation Results 31</p> <p><b>4 Numerical Method and Program for Incompressible and Steady Lubrication of Journal Bearing 33</b></p> <p>4.1 Basic Equations 33</p> <p>4.1.1 Axis Position and Clearance Shape 33</p> <p>4.1.2 Reynolds Equation 34</p> <p>4.2 Numerical Method for Incompressible and Steady Lubrication of Journal Bearing 35</p> <p>4.2.1 Dimensionless Reynolds Equation 35</p> <p>4.2.2 Discrete Form of Reynolds Equation 36</p> <p>4.3 Calculation Program for Incompressible and Steady Lubrication of Journal Bearing 37</p> <p>4.3.1 Calculation Diagram 37</p> <p>4.3.2 Calculation Program 38</p> <p>4.3.3 Calculation Results 40</p> <p><b>5 Numerical Method and Program for Incompressible Squeeze Lubrication 41</b></p> <p>5.1 Basic Equation 41</p> <p>5.2 Numerical Method and Program for Rectangular Plane Squeeze 42</p> <p>5.2.1 Basic Equations 42</p> <p>5.2.2 Numerical Method 42</p> <p>5.2.3 Calculation Diagram 43</p> <p>5.2.4 Calculation Program 44</p> <p>5.2.5 Calculation Results 47</p> <p>5.3 Numerical Method and Program for Disc Squeeze 47</p> <p>5.3.1 Basic Equations 47</p> <p>5.3.2 Numerical Method 48</p> <p>5.3.3 Calculation Diagram 48</p> <p>5.3.4 Calculation Program 49</p> <p>5.3.5 Calculation Results 52</p> <p>5.4 Numerical Method and Program for Journal Bearing Squeeze 52</p> <p>5.4.1 Basic Equations 52</p> <p>5.4.2 Numerical Method 54</p> <p>5.4.3 Calculation Diagram 54</p> <p>5.4.4 Calculation Program 55</p> <p>5.4.5 Calculation Results 60</p> <p><b>6 Numerical Method and Program for Dynamic Bearing 61</b></p> <p>6.1 Basic Equations 61</p> <p>6.2 Numerical Method for Trace of Journal Center 65</p> <p>6.2.1 Introduction 65</p> <p>6.2.2 Calculation Steps 66</p> <p>6.3 Calculation Program for Dynamic Journal Bearing 67</p> <p>6.3.1 Introduction 67</p> <p>6.3.2 Calculation Diagram 67</p> <p>6.3.3 Calculation Program 68</p> <p>6.3.4 Calculation Results 82</p> <p><b>7 Numerical Method and Program for Gas Lubrication 85</b></p> <p>7.1 Basic Equations 85</p> <p>7.1.1 General Reynolds Equation of Gas Lubrication 85</p> <p>7.2 Numerical Method of Gas Lubrication 86</p> <p>7.2.1 Basic Equations of Steady and Isothermal Gas Lubrication 86</p> <p>7.2.2 Numerical Method 87</p> <p>7.3 Calculation Program for Gas Lubrication 88</p> <p>7.3.1 Calculation Program and Solutions of One-Dimensional Gas Lubrication 88</p> <p>7.3.2 Numerical Program and Solutions of Two-Dimensional Gas Lubrication 91</p> <p>7.3.3 Numerical Program and Solutions of Journal Bearing Gas Lubrication 94</p> <p><b>8 Numerical Method and Program for Rarefied Gas Lubrication 97</b></p> <p>8.1 Basic Equations 97</p> <p>8.2 Numerical Method of Rarefied Gas Lubrication 99</p> <p>8.2.1 Rarefied Gas Lubrication Model 99</p> <p>8.2.2 Treatment of the Ultra-Thin Gas Film Lubrication Equation 100</p> <p>8.3 Discretization and Iteration of Modified Reynolds Equation 101</p> <p>8.3.1 Discrete Equation 101</p> <p>8.3.2 Iteration Method 101</p> <p>8.4 Calculation Program for Rarefied Gas Lubrication of Slider 102</p> <p>8.4.1 Procedures Introduction 102</p> <p>8.4.2 Calculation Diagram 102</p> <p>8.4.3 Calculation Program 102</p> <p>8.4.4 Calculation Results 106</p> <p><b>9 Numerical Method and Program for One-dimensional Grease Lubrication 107</b></p> <p>9.1 Basic Equations 107</p> <p>9.1.1 Introduction 107</p> <p>9.1.2 Constitutive Equations of Grease 108</p> <p>9.1.3 Reynolds Equation 109</p> <p>9.2 Numerical Method of One-Dimensional Grease Lubrication 109</p> <p>9.3 Calculation Program of One-Dimensional Grease Lubrication 110</p> <p>9.3.1 Calculation Diagram 110</p> <p>9.3.2 Calculation Program 111</p> <p>9.3.3 Calculation Results 113</p> <p><b>Part 2 NUMERICAL METHOD FOR ENERGY EQUATION 115</b></p> <p><b>10 Energy Equation and its Discrete Form 117</b></p> <p>10.1 Basic Equations 117</p> <p>10.1.1 Simplified Energy Equation 118</p> <p>10.1.2 Boundary Conditions 118</p> <p>10.1.3 Numerical Method 119</p> <p>10.2 Influence of Temperature on Lubricant Performance 120</p> <p>10.2.1 Viscosity–Temperature Equation 120</p> <p>10.2.2 Density–Temperature Equation 120</p> <p>10.3 Numerical Method for Thermal Hydrodynamic Lubrication 121</p> <p>10.3.1 Methods and Program for One-dimensional Thermal Hydrodynamic Lubrication 121</p> <p>10.3.2 Numerical Method and Program for Two-dimensional Thermal Hydrodynamic Lubrication 124</p> <p><b>11 Numerical Method and Program for Incompressible and Steady Thermal Hydrodynamic Lubrication of Journal Bearing 131</b></p> <p>11.1 Basic Equations 131</p> <p>11.1.1 Reynolds Equation 131</p> <p>11.1.2 Energy Equation 132</p> <p>11.1.3 Viscosity–Temperature Equation 132</p> <p>11.2 Numerical Method 132</p> <p>11.2.1 Discrete Reynolds Equation 132</p> <p>11.2.2 Discrete Energy Equation 133</p> <p>11.2.3 Temperature–Viscosity Equation 133</p> <p>11.3 Calculation Program 133</p> <p>11.3.1 Calculation Diagram 133</p> <p>11.3.2 Calculation Program 134</p> <p>11.3.3 Calculation Results 138</p> <p><b>Part 3 NUMERICAL METHOD FOR ELASTIC DEFORMATION AND THERMAL ELASTOHYDRODYNAMIC LUBRICATION 141</b></p> <p><b>12 Numerical Method and Program for Elastic Deformation and Viscosity–Pressure Equation 143</b></p> <p>12.1 Basic Equations of Elastic Deformation 143</p> <p>12.1.1 Film Thickness Equation 143</p> <p>12.1.2 Elastic Deformation Equation 143</p> <p>12.2 Numerical Methods and Programs of Elastic Deformation 145</p> <p>12.2.1 Numerical Method and Program of Elastic Deformation Equation in Line Contact 145</p> <p>12.2.2 Numerical Method and Program of Elastic Deformation Equation in Point Contact 148</p> <p>12.3 Viscosity–Pressure and Density–Pressure Equations 155</p> <p>12.3.1 Viscosity–Pressure Relationship 155</p> <p>12.3.2 Viscosity–Pressure–Temperature Relationship 156</p> <p>12.3.3 Density–Pressure Relationship 156</p> <p><b>13 Numerical Method and Program for EHL in Line Contact 159</b></p> <p>13.1 Basic Equations 159</p> <p>13.2 Numerical Method 160</p> <p>13.2.1 Dimensionless Equations 160</p> <p>13.2.2 Discrete Equations 161</p> <p>13.2.3 Iterative Method 162</p> <p>13.2.4 Selection of Iterative Methods 163</p> <p>13.2.5 Relaxation Factors 164</p> <p>13.3 Calculation Program 164</p> <p>13.3.1 Calculation Diagram 164</p> <p>13.3.2 Calculation Program 165</p> <p>13.3.3 Calculation Results 171</p> <p><b>14 Numerical Method and Program for EHL in Point Contact 173</b></p> <p>14.1 Basic Equations 173</p> <p>14.2 Numerical Method 174</p> <p>14.2.1 Dimensionless Equations 174</p> <p>14.2.2 Discrete Equations 175</p> <p>14.3 Calculation Program 176</p> <p>14.3.1 Calculation Diagram 176</p> <p>14.3.2 Calculation Program 177</p> <p>14.3.3 Calculation Results 186</p> <p><b>15 Numerical Method and Program for Grease EHL in Line Contact 187</b></p> <p>15.1 Basic Equations 187</p> <p>15.1.1 Reynolds Equation 187</p> <p>15.1.2 Film Thickness Equation 187</p> <p>15.1.3 Viscosity–Pressure Equation 188</p> <p>15.1.4 Density–Pressure Equation 188</p> <p>15.2 Numerical Method 188</p> <p>15.2.1 Dimensionless Equations 188</p> <p>15.2.2 Discrete Equations 189</p> <p>15.3 Calculation Program 189</p> <p>15.3.1 Calculating Diagram 189</p> <p>15.3.2 Calculation Program 190</p> <p>15.3.3 Calculation Results 199</p> <p><b>16 Numerical Method and Program for Grease EHL in Point Contact 201</b></p> <p>16.1 Basic Equations 201</p> <p>16.1.1 Reynolds Equation 201</p> <p>16.1.2 Film Thickness Equation 201</p> <p>16.1.3 Elastic Deformation Equation 202</p> <p>16.1.4 Viscosity–Pressure Equation 202</p> <p>16.1.5 Density Equation 202</p> <p>16.2 Numerical Method 202</p> <p>16.2.1 Dimensionless Equations 202</p> <p>16.2.2 Discrete Equations 203</p> <p>16.3 Calculation Program 204</p> <p>16.3.1 Calculation Diagram 204</p> <p>16.3.2 Calculation Program 205</p> <p>16.3.3 Calculation Results 214</p> <p><b>17 Numerical Method and Program for Thermal EHL in Line Contact 215</b></p> <p>17.1 Basic Equations 215</p> <p>17.1.1 Reynolds Equation 215</p> <p>17.1.2 Energy Equation 215</p> <p>17.1.3 Film Thickness Equation 216</p> <p>17.1.4 Elastic Deformation Equation 216</p> <p>17.1.5 Roelands Viscosity–Pressure–Temperature Equation 216</p> <p>17.1.6 Density–Pressure–Temperature Equation 217</p> <p>17.2 Numerical Method 217</p> <p>17.2.1 Dimensionless Equations 217</p> <p>17.2.2 Discrete Equations 218</p> <p>17.3 Calculation Program 220</p> <p>17.3.1 Calculation Diagram of Multigrid Method 220</p> <p>17.3.2 Calculation Diagram of Temperature 221</p> <p>17.3.3 Calculation Program 222</p> <p>17.3.4 Calculation Results 236</p> <p><b>18 Numerical Method and Program for Thermal EHL in Point Contact 237</b></p> <p>18.1 Basic Equations 237</p> <p>18.1.1 Reynolds Equation 237</p> <p>18.1.2 Energy Equation 237</p> <p>18.1.3 Film Thickness Equation 238</p> <p>18.1.4 Elastic Deformation Equation 238</p> <p>18.1.5 Roelands Viscosity–Pressure–Temperature Equation 239</p> <p>18.1.6 Density–Pressure–Temperature Equation 239</p> <p>18.2 Numerical Method 239</p> <p>18.2.1 Dimensionless Equations 239</p> <p>18.2.2 Discrete Equations 241</p> <p>18.3 Calculation Program 242</p> <p>18.3.1 Calculation Diagram 242</p> <p>18.3.2 Calculation Program 242</p> <p>18.3.3 Calculation Results 261</p> <p><b>19 Numerical Method and Program for Thermal Grease EHL in Line Contact 263</b></p> <p>19.1 Basic Equations 263</p> <p>19.1.1 Reynolds Equation 263</p> <p>19.1.2 Energy Equation 264</p> <p>19.1.3 Film Thickness Equation 264</p> <p>19.1.4 Elastic Deformation Equation 265</p> <p>19.1.5 Viscosity–Pressure–Temperature Equation 265</p> <p>19.1.6 Density–Pressure–Temperature Equation 265</p> <p>19.2 Numerical Method 265</p> <p>19.2.1 Dimensionless Equations 265</p> <p>19.2.2 Discrete Equations 267</p> <p>19.3 Calculation Program 268</p> <p>19.3.1 Calculation Diagram 268</p> <p>19.3.2 Calculation Program 268</p> <p>19.3.3 Calculation Results 287</p> <p><b>20 Numerical Method and Program for Thermal Grease EHL in Point Contact 289</b></p> <p>20.1 Basic Equations 289</p> <p>20.1.1 Reynolds Equation 289</p> <p>20.1.2 Energy Equation 290</p> <p>20.1.3 Film Thickness Equation 290</p> <p>20.1.4 Elastic Deformation Equation 291</p> <p>20.1.5 Roelands Viscosity–Pressure–Temperature Equation 291</p> <p>20.1.6 Density–Pressure–Temperature Equation 291</p> <p>20.2 Numerical Method 291</p> <p>20.2.1 Dimensionless Equations 291</p> <p>20.2.2 Discrete Equations 293</p> <p>20.3 Calculation Program 294</p> <p>20.3.1 Calculation Diagram 294</p> <p>20.3.2 Calculation Program 295</p> <p>20.3.3 Calculation Results 310</p> <p><b>Part 4 CALCULATION PROGRAMS FOR LUBRICATION ANALYSIS IN ENGINEERING 311</b></p> <p><b>21 Lubrication Calculation Program for Herringbone Grooved Journal Bearing of Micro Motor 313</b></p> <p>21.1 Basic Theory of Lubrication Calculation of Herringbone Groove Bearing 313</p> <p>21.1.1 Journal Center Position and Film Thickness 313</p> <p>21.1.2 Reynolds Equation 314</p> <p>21.1.3 Boundary Conditions 315</p> <p>21.1.4 Flux Calculation 316</p> <p>21.1.5 Temperature Calculation 316</p> <p>21.2 Program for Performance Calculation 318</p> <p>21.2.1 Lubrication Performances 318</p> <p>21.2.2 Calculation Program 318</p> <p>21.3 Calculation Results 326</p> <p>21.4 Instruction for HBFA Software Package 332</p> <p>21.4.1 Package Contents 332</p> <p>21.4.2 Program Installation 332</p> <p>21.4.3 Program Operation 333</p> <p><b>22 Lubrication Optimization Program of Herringbone Grooved Journal Bearing of Micro Motor 337</b></p> <p>22.1 Method of Optimization Calculation 337</p> <p>22.1.1 Requirements of Parameter Optimization 337</p> <p>22.1.2 Optimization Model 337</p> <p>22.1.3 Optimization Methods and Steps 338</p> <p>22.2 Program Layout of Optimization Calculation 338</p> <p>22.2.1 Optimization Program Diagram 338</p> <p>22.2.2 Calculation Program 339</p> <p>22.2.3 Parameters in Program 352</p> <p>22.3 Optimization Calculation Examples 352</p> <p>22.3.1 Example 1: Optimization Calculation for Static Load 352</p> <p>22.3.2 Example 2: Optimization Calculation for Static Flux (Eccentricity Ratio e is Constant) 354</p> <p>22.3.3 Example 3: Optimization Calculation for Static Flux (Load W is Constant) 354</p> <p>22.3.4 Example 4: Optimization Calculation for Dynamic Load 354</p> <p>22.3.5 Example 5: Optimization Calculation for Dynamic Flux (Eccentricity e is Constant) 354</p> <p>22.3.6 Example 6: Optimization Calculation for Dynamic Flux (Load W is Constant) 355</p> <p>22.4 Instructions for HBOA Software Package 355</p> <p>22.4.1 Program Package 355</p> <p>22.4.2 Program Execution 356</p> <p><b>23 Calculation Program for Gas Lubrication of Hard Disk/Head in Ultra Thin Film 361</b></p> <p>23.1 Basic Equations of Gas Lubricating Film of Hard Disk/Head 361</p> <p>23.1.1 Basic Equations 361</p> <p>23.1.2 Gas Film Thickness 362</p> <p>23.1.3 Poiseuille Flow Rate 362</p> <p>23.2 Discrete Equation and Special Treatments 363</p> <p>23.2.1 Iterative Scheme Considering High Bearing Numbers 363</p> <p>23.2.2 Abrupt Changes between Steps on ABS 364</p> <p>23.3 Calculation Program 364</p> <p>23.3.1 Calculation Diagram 364</p> <p>23.3.2 Calculation Program 366</p> <p>23.3.3 Calculation Results 371</p> <p><b>24 Calculation Program of Flight Attitude of Magnetic Head 373</b></p> <p>24.1 Search Strategy for Flight Attitude 373</p> <p>24.2 Calculation Program 375</p> <p>24.2.1 Program Introduction 375</p> <p>24.2.2 Calculation Diagram 376</p> <p>24.2.3 Calculation Program 376</p> <p>24.2.4 Calculation Results 386</p> <p>References 389</p> <p>Index 391</p>

<b>Ping Huang,</b> <i>South China University of Technology, Guangzhou, China</i>

<p>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 steady-state 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 elasto-hydrodynamic lurbication, which links the Reynolds equation with the elastic deformation equation. The final part presents application lubrication programs used in engineering.</p> <ul> <li>Provides numerical solution methodologies including appropriate software for the hydrodynamic and elasto-hydrodynamic lubrication of bearings</li> <li>Offers a clear introduction and orientation to all major engineering lubrication problems and their solutions</li> <li>Presents numerical programs for specific applications in engineering, with special topics including grease-lubricated bearings and gas bearings</li> <li>Equips those working in tribology and those new to the topic with the fundamental tools of calculation</li> <li>Downloadable programs are available at the companion website</li> </ul> <p>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 thin-film fluid mechanics.</p>

SG