Numerical Calculation of Elastohydrodynamic Lubrication

Ping Huang South China University of Technology, China

• Introduction xiPreface xiiiNomenclature xvii1 Basic equations of elastohydrodynamic lubrication 11.1 Basic equations 11.1.1 One-dimensional Reynolds equation of elastohydrodynamic lubrication 11.1.2 Two-dimensional Reynolds equation of EHL 31.1.3 EHL Reynolds equation with two direction velocities 31.1.4 Time-dependent EHL Reynolds equation 41.2 Film thickness equation without elastic deformation 41.2.1 Film thickness equation in line contact 41.2.2 Film thickness equation in point contact 51.2.3 Film thickness equation in ellipse contact 51.3 Surface elastic deformation 61.3.1 One-dimensional elastic deformation equation 61.3.2 Two-dimensional elastic deformation equation 61.4 Viscosity and density equations varying with pressure and temperature 71.4.1 Viscosity equations 71.4.2 Density equation 91.5 Load balancing condition 101.5.1 Load balancing equation 101.5.2 Numerical calculation of load balancing 111.6 Finite difference method of Reynolds equation 151.6.1 Discretization of equation 151.6.2 Different forms of Reynolds equation 171.6.3 Iteration of differential equation 181.6.4 Iteration convergence condition 182 Numerical calculation method and program of elastic deformation 212.1 Numerical method and program of elastic deformation in line contact 212.1.1 Equations of elastic deformation 212.1.2 Numerical method of elastic deformation 222.1.3 Calculation diagram and program 232.1.4 Example 252.2 Numerical method and program of elastic deformation in point contact 272.2.1 Equation of elastic deformation 272.2.2 Numerical method for elastic deformation in point contact 282.2.3 Calculation diagram 292.2.4 Program 302.2.5 Example 312.3 Numerical calculation method and program for elastic deformation in ellipse contact 332.3.1 Contact geometry 332.3.2 Contact pressure and contact zone 362.3.3 Calculation program 382.3.4 Calculation results 442.4 Calculation of elastic deformation with multigrid integration technique 442.4.1 Principle of multigrid integration 442.4.2 Calculation programs and examples 493 Numerical calculation method and program for energy equation 613.1 Energy equation 613.1.1 One-dimensional energy equation 623.1.2 Two-dimensional energy equation 623.2 Numerical method and program for thermal hydrodynamic lubrication 643.2.1 One-dimensional thermal hydrodynamic lubrication 643.2.2 Two-dimensional thermal hydrodynamic lubrication 684 Numerical calculation method and program of isothermal EHL in line contact 754.1 Basic equations and Nondimensional equations 754.1.1 Basic equations 754.1.2 Nondimensional equations 764.1.3 Discrete equations 774.2 Numerical calculation method and program 784.2.1 Iterative method 784.2.2 Program and example 795 Newton–Raphson method and programs to solve EHL problems in line contact 875.1 Basic equations 875.2 Newton–Raphson iterative method 885.2.1 Coefficient matrix 885.2.2 Calculation of variables in equations 895.3 Numerical method and program of Newton–Raphson 905.3.1 Coefficient treatment in nonlubricated region 905.3.2 Determination of ρeHe 905.3.3 Determination and correction of initial rigid film thickness 915.3.4 Calculation Program 915.3.5 Example 966 Numerical calculation method and program of isothermal EHL in point contact 996.1 Basic equations of isothermal EHL in point contact 996.1.1 Basic equations 996.1.2 Nondimensional equations 1006.2 Numerical calculation method and program 1016.2.1 Differential equations 1016.2.2 Iteration method 1026.2.3 Calculation diagram 1026.2.4 Calculation program 1066.2.5 Example 1117 Numerical calculation method and programs of multigrid method for isothermal EHL 1137.1 Basic principles of multigrid method 1137.1.1 Grid structure 1137.1.2 Equation discrete 1147.1.3 Restriction and extension 1147.2 Nonlinear full approximation scheme of multigrid method 1167.2.1 Parameter transformation downwards 1167.2.2 Correction of lower grid parameters 1167.2.3 Parameter transformation upwards 1187.2.4 V and W loops 1187.3 Key factors to solve EHL problem with multigrid method 1197.3.1 Iteration methods 1197.3.2 Relaxation factors selection 1217.4 Program of EHL in line contact with multigrid method 1227.4.1 Specification of program 1227.4.2 Calculation program 1237.4.3 Example 1337.5 Program of EHL in point contact with multigrid method 1337.5.1 Specification of the program 1337.5.2 Calculation program 1347.5.3 Example 1438 Numerical calculation method and program for isothermal EHL in ellipse contact 1458.1 Basic equation 1458.1.1 Reynolds equation 1458.1.2 Film thickness equation 1468.1.3 Viscosity–pressure equation 1468.1.4 Density–pressure equation 1478.1.5 Load balancing equation 1478.2 Calculation program 1488.2.1 Calculation diagram 1488.2.2 Calculation program 1498.2.3 Example 1579 Numerical calculation method and program of isothermal EHL in elliptical contact with two-dimensional velocities 1599.1 Basic equations 1599.2 Velocity treatment 1609.3 Numerical calculation method and program 1619.3.1 Flowchart 1619.3.2 Program 1619.3.3 Example 17110 Numerical calculation method and program for thermal EHL 17310.1 Basic equations for thermal EHL 17310.1.1 Thermal EHL in line contact 17310.1.2 TEHL in point contact 17610.2 Viscosity and temperature across film thickness 17910.2.1 Calculation of fluid velocity field 17910.2.2 Continuity equation 18110.2.3 Energy equation 18210.2.4 Temperature boundary conditions 18510.2.5 Calculation of linear equation set 18710.2.6 Program to calculate temperature 18710.3 Numerical calculation method and program for TEHL in line contact 18910.3.1 Flowchart 18910.3.2 Program 19010.3.3 Example 20110.4 Numerical calculation method and program of TEHL in point contact 20210.4.1 Flowchart 20210.4.2 Calculation program 20410.4.3 Example 21611 Numerical calculation method and program of grease EHL 21711.1 Basic equations of grease EHL 21711.2 Numerical calculation and program of isothermal grease EHL 22011.2.1 Line contact problem 22011.2.2 Point contact problem 23111.3 Numerical calculation method and program of thermal GEHL 24311.3.1 Line contact problem 24311.3.2 Point contact problem 26212 Numerical calculation method and program of EHL considering effect of electric double layer 27912.1 Structure of electric double layer 27912.2 Reynolds equation considering EDL effect 27912.2.1 Modified Reynolds equation 27912.2.2 Expression of electroviscosity 28412.3 Calculation program and example 28512.3.1 Calculation program 28512.3.2 Example 29313 Numerical calculation method and program of time-dependent EHL in line contact 29513.1 Time-dependent EHL Reynolds equation 29513.1.1 Nondimensional Reynolds equation 29513.1.2 Discrete Reynolds equation 29613.2 Numerical calculation method and program 29613.2.1 Iteration method 29613.2.2 Calculation diagram 29713.2.3 Calculation program 29713.2.4 Example 30414 Numerical calculation method and program of isothermal EHL with rough surface 30514.1 Film thickness equation with surface roughness 30514.2 Calculation of rough surface EHL problem with Newton–Raphson method 30614.2.1 Sine roughness 30614.2.2 Single depression 31114.3 EHL solution with random roughness in line contact 31714.3.1 Description of the program 31714.3.2 Calculation program 31714.3.3 Example 32114.4 EHL solution with random roughness in point contact 32214.4.1 Description of the program 32214.4.2 Calculation program 32214.4.3 Example 32614.5 Random roughness generation program 32815 Numerical calculation method and program of micropolar fluid EHL 32915.1 Reynolds equation of micropolar fluid EHL 32915.1.1 Basic equations 32915.1.2 Reynolds equation 33015.2 Calculation program of EHL of micropolar fluid in line contact 33415.2.1 Description of the program 33415.2.2 Calculation program 33415.2.3 Example 33815.3 Calculation program of EHL with micropolar fluid in point contact 33915.3.1 Calculation program 33915.3.2 Example 343References 345Index 000