Fast and reduced full-system finite element solution of elastohydrodynamic lubrication problems

Abstract

This paper presents a reduced full-system finite element solution of elastohydrodynamic lubrication (EHL) problems. It aims to demonstrate the feasibility of this approach by applying it to the simple isothermal Newtonian line contact case. However the proposed model can be extended to more complex situations. This model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, three different techniques are tested: the classical “modal reduction” and “Ritz-vector” methods and a novel “EHL-basis” method. The reduction order in the first two appears to be insufficient and a large number of degrees of freedom is required in order to attain an acceptable solution. On the other hand, the “EHL-basis” method shows up to be much more efficient, requiring only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude execution time gain with errors of the order of only 1‰ for the central and minimum film thicknesses.