Modelling Flows in Lubrication

This chapter introduces the reader to lubrication theory and describes the governing equations, models and methods that can be used to simulate various types of lubricated systems. It starts with an introduction to the tribological contact and to the different lubrication regimes. The basis for the classical lubrication theory is then given and thereafter follows a presentation of how to obtain the Reynolds equation by means of scaling and asymptotic analysis of the Navier–Stokes equations. After having obtained the Reynolds equation, a quite elaborate presentation of cavitation algorithms is given. It includes discretisation and presents the analytical solution for a pocket bearing as a benchmark model problem. Then, the concept of homogenisation of surface roughness is introduced. This starts from the simplest iso-viscous and incompressible case, expands to include compressibility with a constant bulk modulus constitutive relation and then also addresses the case of ideal gases. Thereafter, the relation between homogenised coefficients and the Patir and Cheng flow factors is described and finally it is shown how to incorporate the effect of mixed lubrication into the model.