A finite element approach to model thin films in circular EHD contacts

Lubrication of machine elements such as gears and bearings appears to be essential for the good functioning of a mechanical system. In many applications, the pressure generated within tribological interfaces is high enough to induce elastic deformations at the surface of the contacting bodies. This lubrication regime is known as ElastoHydroDynamic (EHD) Lubrication. It involves a strong coupling between fluid mechanics, solid mechanics and lubricant rheology which makes the problem highly non-linear. So far, most of the numerical studies of lubricated contacts were carried out by using finite difference1, 2 or finite volume3 methods. More recently, CFD4 approach has been proposed to solve Navier-Stokes equations. The use of finite elements was limited to the case of journal bearings operating under hydrodynamic regime5, 6. In this work, we present a new approach for the numerical study of EHD circular contact using the finite element method (FEM) to solve the Reynolds equation, Boussinesq’s theory to calculate the elastic deformation of the surfaces and various physical laws to account the lubricant rheological behavior (WLF, Doolittle, Carreau). The advantage of choosing FEM is the availability of finite elements packages which permits to reduce the time spent in implementation and adapting the method to tribological applications. We use a multiphysics FEM software to solve the EHD circular contact and to obtain numerical results under broader operating conditions than those imposed during experiments. To reduce calculation time, we introduced multigrid method for solving the Reynolds equation and multi-integration technique for the elastic problem.