Modelling Cavitation in (Elasto)Hydrodynamic Lubrication

In this chapter we will present a derivation of a mathematical model describing how cavitation influences the pressure distribution in a thin lubricant film between two moving surfaces. The main idea in the derivation is to first describe the influence of cavitation on the mass flow and thereafter using a conservation law for the mass. This leads to a nonlinear system with two complementary variables: one is the pressure distribution and the other is related to the density, i.e. a nonlinear complementarity problem (NLCP). The proposed approach is used to derive a mass conserving cavitation model considering that density, viscosity and film thickness of the lubricant depend on the pressure. To demonstrate the applicability and evaluate the proposed model and the suggested numerical implementation, a few model problems are analysed and presented.