Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

TLDR

The study examines how differential schemes and mesh density affect EHL film thickness using a full numerical solution with a semi‑system approach. Numerical cases spanning central film thicknesses from hundreds of nanometers to a few nanometers were used to assess solution variations across different schemes and mesh sizes. When the film is thick, scheme and mesh effects are negligible, but for ultra‑thin films (<10–20 nm) they become significant, with the 1st‑order backward scheme yielding the largest thickness.

Abstract

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.