Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.