On the effects of the temperature profile approximation in thermal Newtonian solutions of elastohydrodynamic lubrication line contacts

The assumptions of a quadratic temperature profile and mean viscosity across the film, which are frequently used in the analysis of thermal elastohydrodynamic lubrication (EHL), are examined acid discussed. Two different approaches for solving the thermal EHL problem are compared for line contact conditions, namely (a) a one-dimensional model based upon both the assumption of a quadratic temperature profile and the adoption of the mean physical properties across the film and (b) a two-dimensional model which includes changes in temperature and physical properties of a lubricant across the film and which takes into account the conditions of reverse flow and heat convection across the film occurring at the inlet region. A multi-grid algorithm is implemented to solve these two conditions. The temperature profile and the general solutions in the conjunction obtained in both approaches are compared. For the one-dimensional model, results reveal that temperature peaks just prior to the inlet of the conjunction. This feature is not apparent in the two-dimensional model and results in lower values in film thickness and larger frictional coefficients than in the two-dimensional model. In the high-pressure region, both equations yield almost the same mean temperature.