Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

Abstract

The derivation of fast, reliable, and accurate modeling procedures for the solution of thermal elastohydrodynamic lubrication problems is a topic of significant interest in the Tribology community. In this paper, a novel model order reduction technique is introduced for the analysis of thermal elastohydrodynamic lubrication problems. The method uses static condensation to reduce the size of the linear elasticity part within the overall matrix system, followed by a splitting algorithm to avoid the burden of solving a semi-dense matrix system. The results reveal the exactness of the proposed methodology, which does not introduce any additional model-reduction approximations to the overall solution. They also reveal the reduction in computational times, which is in the order of 10–20% for line contacts, while it is in excess of 50% for circular contacts. The robustness of the proposed method is displayed by using it to model some relatively highly loaded contacts whose numerical solution is known to be rather challenging.