Application of finite element methods to thermohydrodynamic lubrication

Abstract

Abstract A finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry. A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry. As an example, the formulations are applied to obtain numerical solutions for a three‐dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.