Coupling Strategies for Finite Element Modeling of Thermal Elastohydrodynamic Lubrication Problems

This paper investigates coupling strategies for finite element modeling (FEM) of thermal elastohydrodynamic lubrication (TEHL) problems. The TEHL problem involves a strong coupling between several physics: solid mechanics, fluid mechanics, and heat transfer. Customarily, this problem is split into two parts (elastohydrodynamic (EHD) and thermal) and the two problems are solved separately while an iterative procedure is established between their respective solutions. This weak coupling strategy involves a loss of information, as each problem is not made intimately aware of the evolution of the other problem's solution during the resolution procedure. This typically leads to slow convergence rates. The current work offers a full coupling strategy for the TEHL problem, i.e., both the EHD and thermal parts are solved simultaneously in a monolithic system. The system of equations is generated from a finite element discretization of the governing field variables: hydrodynamic pressure, solids elastic deformation, and temperature. The full coupling strategy prevents any loss of information during the resolution procedure leading to very fast convergence rates (solution is attained within a few iterations only). The performance of the full coupling strategy is compared to that of different weak coupling strategies. Out of simplicity, only steady-state line contacts are considered in this work. Nevertheless, the proposed methodology, results, and findings are of a general nature and may be extrapolated to circular or elliptical contacts under steady-state or transient conditions.