Effects of approximations regarding stress and temperature profiles on the solution in thermal elastohydrodynamically lubricated line contacts

Abstract

The assumptions of both a Couette flow dominance and a quadratic temperature profile across the film are commonly used in the analysis of thermal non-Newtonian elastohydrodynamic lubrication. In such calculations, the conduction across the film and the energy dissipation are assumed to be the main phenomena in the prediction of temperature rise. Consequently the gradients of the physical properties across the film as well as the reverse flow and the heat convection in all directions are assumed to have no or little impact on the general characteristics of the temperature profiles and therefore can be neglected. The objective of this paper is to assess the quality of these approximations. A comparison between both the simplified and the complete non-Newtonian thermal approach is made for the line contact problem. The complete solution is based upon the resolution of a two-dimensional energy equation, which is fully coupled with the non-Newtonian Reynolds equation. The analysis reveals some local discrepancies between both the simplified and the complete solutions. These differences are clearly visible at the inlet of the contact where a bump in the temperature profiles disappears in the simplified approach. The results also show a significant difference in the levels of temperature predicted within the high-pressure region between the simplified and complete approach. In regard to the friction coefficient, the simplified calculation forecasts a lower coefficient than that obtained with the complete formulation.