Towards a complete numerical description of lubricant film dynamics in ball bearings

In this article, we propose a framework for a detailed finite element analysis of elastohydrodynamic lubrication in ball bearings. Our contribution to this field is twofold. First, we present a fully monolithic ALE method for the treatment of fluid---structure interaction. For the lubricant, we use the full Navier---Stokes equations in combination with a pressure-dependent viscosity law and include thermal effects. Second, we introduce a novel method for a fully implicit treatment of the evolution of the lubricants' free surface using Nitsches method. This allows for arbitrarily large time steps independent of the spatial discretization. Despite the variety of numerical challenges present in this application, such as anisotropy and extreme values of pressure, our approach for the first time shows robustness up to high rotational speeds as required in industrial applications. We describe the numerical ingredients we use in detail and present numerical results that validate our approaches and demonstrate its capabilities.