A Numerical Solution of the Thermal Elastohydrodynamic Lubrication in an Elliptical Contact

Abstract

A numerical solution for the calculation of thickness and temperature of film and traction coefficients between heavily loaded elliptical contact is developed. To start the calculation a Hertzian pressure distribution modified at the inlet and outlet regions is assumed and the surface deformations are calculated. The Navier-Stokes equations and the energy equation are simultaneously solved by the finite difference method. The pressure distribution introduced is verified with the help of the condition of continuity and, if necessary, corrected. The dependence of the viscosity and the density of the lubricant on pressure and temperature is determined by empirical equations which are derived from experimental data. A time dependency of the viscosity is allowed for high viscosities. The distribution of temperature in the film is obtained for a selected example. The thicknesses of the oil film and the traction coefficients are compared with experimental results.