Thermal elastohydrodynamic analysis of circular contacts Part 1: Newtonian model

Abstract

Solutions of the thermal elastohydrodynamically lubricated point contact problems are presented for both low and high Peclet number conditions. The surface temperatures are calculated using the full expression of the moving heat source equation given by Carslaw and Jaeger. Of interest is the potential of the method to predict solutions for pure sliding conditions in which one surface velocity is zero. The energy equation is treated as a two-dimensional problem by approximating the variation in temperature across the film with a quadratic profile. To solve the strongly non-linear set of equations which govern the problem a relaxation scheme is proposed which takes advantage of the weak coupling between the Reynolds equation and energy equation in the high-pressure region of the contact. The iterative process corresponds to a two-stage process in which pressure and temperature are relaxed independently. The numerical scheme provides a stable and fast convergence and has the added advantage of allowing the isothermal relaxation schemes for pressure previously developed to be reused.