On some aspects of numerical solutions of thin-film and mixed elastohydrodynamic lubrication

Abstract

Numerical solution of the thin-film and mixed elastohydrodynamic lubrication (EHL) is of great importance to the study of lubrication transition and breakdown, as well as surface failures caused by contact. However, in this region, converged and accurate numerical solutions become difficult, and effects of computational mesh density and differential schemes appear to be more significant. Also, there is currently a debate on how surface contact should be defined and analysed, and whether it is indeed possible to model contact through a grid-converged solution of the EHL equation system. This paper presents a set of analysed sample cases with different computational meshes, different cut-off values for handling contact, on different levels of central film thickness, from several hundred nanometres down to zero. Based on the results, some key issues are discussed (such as whether the contact can be modelled with the Reynolds equation system, how a contact should be defined and analysed, how computational meshes should be selected and managed, what the reasonable and satisfactory convergence accuracy should be, and so on). In addition, a progressive mesh densification (PMD) method is presented and compared with the multi-grid (MG) method. It is demonstrated that the PMD method may be able to significantly reduce computing time. On the other hand, the MG method may be good for thick-film cases with smooth surfaces or low frequency roughness, but is not desirable for the ultra-thin film and mixed EHL, especially when moderate and high frequency surface roughness is involved.