1 Basic equations of elastohydrodynamic lubrication
1.1 Basic equations
1.1.1 One-dimensional Reynolds equation of elastohydrodynamic lubrication
1.1.2 Two-dimensional Reynolds equation of EHL
1.1.3 EHL Reynolds equation with two direction velocities
1.1.4 Time-dependent EHL Reynolds equation
1.2 Film thickness equation without elastic deformation
1.2.1 Film thickness equation in line contact
1.2.2 Film thickness equation in point contact
1.2.3 Film thickness equation in ellipse contact
1.3 Surface elastic deformation
1.3.1 One-dimensional elastic deformation equation
1.3.2 Two-dimensional elastic deformation equation
1.4 Viscosity and density equations varying with pressure and temperature
1.4.1 Viscosity equations
1.4.2 Density equation
1.5 Load balancing condition
1.5.1 Load balancing equation
1.5.2 Numerical calculation of load balancing
1.6 Finite difference method of Reynolds equation
1.6.1 Discretization of equation
1.6.2 Different forms of Reynolds equation
1.6.3 Iteration of differential equation
1.6.4 Iteration convergence condition
2 Numerical calculation method and program of elastic deformation 21
2.1 Numerical method and program of elastic deformation in line contact 21
2.1.1 Equations of elastic deformation
2.1.2 Numerical method of elastic deformation
2.1.3 Calculation diagram and program
2.1.4 Example
2.2 Numerical method and program for elastic deformation in point contact
2.2.1 Equation of elastic deformation
2.2.2 Numerical method for elastic deformation in point contact
2.2.3 Calculation diagram
2.2.4 Program
2.2.5 Example
2.3 Numerical method and program of elastic deformation in ellipse contact
2.3.1 Contact geometry
2.3.2 Contact pressure and contact zone
2.3.3 Calculation program
2.3.4 Calculation results
2.4 Calculation of elastic deformation with multigrid integration technique
2.4.1 Principle of multigrid integration
2.4.2 Calculation programs and examples
3 Numerical calculation method and program for energy equation
3.1 Energy equation
3.1.1 One-dimensional energy equation
3.1.2 Two-dimensional energy equation
3.2 Numerical method and program for thermal hydrodynamic lubrication
3.2.1 One-dimensional thermal hydrodynamic lubrication
3.2.2 Two-dimensional thermal hydrodynamic lubrication
4 Numerical calculation method and program for isothermal EHL in line contact
4.1 Basic equations and nondimensional equations
4.1.1 Basic equations
4.1.2 Nondimensional equations
4.1.3 Discrete equations
4.2 Numerical calculation method and program
4.2.1 Iteration method
4.2.2 Program and example
5 Newton–Raphson method and programs to solve EHL problems in line contact
5.1 Basic equations
5.2 Newton–Raphson iteration method
5.2.1 Coefficient matrix
5.2.2 Calculation of variables in equations
5.3 Numerical method and program of Newton–Raphson method
5.3.1 Coefficient treatment in nonlubricated region
5.3.2 Determination of ρeHe
5.3.3 Determination and correction of initial rigid film thickness
5.3.4 Calculation program
5.3.5 Example
6 Numerical calculation method and program for isothermal EHL in point contact
6.1 Basic equations for isothermal EHL in point contact
6.1.1 Basic equations
6.1.2 Nondimensional equations
6.2 Numerical calculation method and program
6.2.1 Differential equations
6.2.2 Iteration method
6.2.3 Calculation diagram
6.2.4 Calculation program
6.2.5 Example
7 Numerical calculation method and programs of multigrid method for isothermal EHL
7.1 Basic principles of multigrid method
7.1.1 Grid structure
7.1.2 Equation discrete
7.1.3 Restriction and extension
7.2 Nonlinear full approximation scheme of multigrid method
7.2.1 Parameter transformation downwards
7.2.2 Correction of lower grid parameters
7.2.3 Parameter transformation upwards
7.2.4 V and W loops
7.3 Key factors to solve EHL problem with multigrid method
7.3.1 Iteration methods
7.3.2 Relaxation factors selection
7.4 Program for EHL in line contact with multigrid method
7.4.1 Specification of program
7.4.2 Calculation program
7.4.3 Example
7.5 Program for EHL in point contact with multigrid method
7.5.1 Specification of program
7.5.2 Calculation program
7.5.3 Example
8 Numerical calculation method and program for isothermal EHL in ellipse contact
8.1 Basic equation
8.1.1 Reynolds equation
8.1.2 Film thickness equation
8.1.3 Viscosity–pressure equation
8.1.4 Density–pressure equation
8.1.5 Load balancing equation
8.2 Calculation program
8.2.1 Calculation diagram
8.2.2 Calculation program
8.2.3 Example
9 Numerical calculation method and program for isothermal EHL in elliptical contact with two-dimensional velocities
9.1 Basic equations
9.2 Velocity treatment
9.3 Numerical calculation method and program
9.3.1 Flowchart
9.3.2 Program
9.3.3 Example
10 Numerical calculation method and program for thermal EHL
10.1 Basic equations for thermal EHL
10.1.1 Thermal EHL in line contact
10.1.2 TEHL in point contact
10.2 Viscosity and temperature across film thickness
10.2.1 Calculation of fluid velocity field
10.2.2 Continuity equation
10.2.3 Energy equation
10.2.4 Temperature boundary conditions
10.2.5 Calculation of linear equation set
10.2.6 Program to calculate temperature
10.3 Numerical calculation method and program for TEHL in line contact
10.3.1 Flowchart
10.3.2 Program
10.3.3 Example
10.4 Numerical calculation method and program for TEHL in point contact
10.4.1 Flowchart
10.4.2 Calculation program
10.4.3 Example
11 Numerical calculation method and program for grease EHL
11.1 Basic equations of grease EHL
11.2 Numerical calculation and program for isothermal grease EHL
11.2.1 Line contact problem
11.2.2 Point contact problem
11.3 Numerical calculation method and program for thermal GEHL
11.3.1 Line contact problem
11.3.2 Point contact problem
12 Numerical calculation method and program for EHL considering effect of electric double layer
12.1 Structure of electric double layer
12.2 Reynolds equation considering EDL effect
12.2.1 Modified Reynolds equation
12.2.2 Expression of electroviscosity
12.3 Calculation program and example
12.3.1 Calculation program
12.3.2 Example
13 Numerical calculation method and program for time-dependent EHL in line contact
13.1 Time-dependent EHL Reynolds equation
13.1.1 Nondimensional Reynolds equation
13.1.2 Discrete Reynolds equation
13.2 Numerical calculation method and program
13.2.1 Iteration method
13.2.2 Calculation diagram
13.2.3 Calculation program
13.2.4 Example
14 Numerical calculation method and program for isothermal EHL with rough surface
14.1 Film thickness equation with surface roughness
14.2 Calculation of rough surface EHL problem with Newton–Raphson method
14.2.1 Sine roughness
14.2.2 Single depression
14.3 EHL solution with random roughness in line contact
14.3.1 Description of program
14.3.2 Calculation program
14.3.3 Example
14.4 EHL solution with random roughness in point contact
14.4.1 Description of program
14.4.2 Calculation program
14.4.3 Example
14.5 Random roughness generation program
15 Numerical calculation method and program for micropolar fluid EHL
15.1 Reynolds equation of micropolar fluid EHL
15.1.1 Basic equations
15.1.2 Reynolds equation
15.2 Calculation program for EHL of micropolar fluid in line contact
15.2.1 Description of program
15.2.2 Calculation program
15.2.3 Example
15.3 Calculation program for EHL with micropolar fluid in point contact
15.3.1 Calculation program
15.3.2 Example
References
Index
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