Development of calculating process for elasto-hydrodynamic spot contact by p-FEM

Abstract

Rolling-sliding machines such as gears, cams and followers, and bearings, which are often subjected to high loads, high speeds and high slip conditions when not only the pressure distribution in the lubricant and variation of the viscosity due to pressure is a question but the surface deformation to calculate the sub-surface stress field. To analyse the tribological conditions of the contact surfaces, after Osborne Reynolds (1886), who presented the theory of hydrodynamic lubrication and the governing partial differential equation for the pressure field, the generalized Reynolds equation was developed by Dowson (1962). Although several methods have been already developed for solving EHD problems, the solution of the highly nonlinear problem is still quite challenging. Unfortunately, only few solutions were published based on FEM despite it permits the using of polynomial approximation for powerful calculation of the generalized Reynolds equation without smooth mesh. However, applying rough mesh, the end of the contact can locate far from the boundaries of the elements. This fact makes to be important to manage the cavitation inside elements. So the development of a p-version FEM model for calculating the film shape, the pressure and temperature distribution and its implementation to commercial software seems to be timely. For this reason, special lubricant film element can be developed for such problems where pressure and film thickness can be handled as independent element variables in the generalized Reynolds equation and determined incrementally by fully coupling the hydrodynamic and the solid mechanic problem.