Numerical Simulation of the Elastohydrodynamic Reynolds-Rod Model for Lubrication of Rough Surfaces

Abstract

In this work, the numerical simulation of a micro-elastohydrodynamic process is performed. More precisely, we consider a journal bearing device whose bearing is formed by a rough elastic layer which reinforces a rigid structure. The mechanical problem is governed by a system of variational inequalities for the lubricant pressure and the elastic bearing displacement. The numerical algorithm is based on a fixed point iteration between the elastic and hydrodynamic parts of the problem, a duality method to deal with the unilateral constraints and appropriate finite elements discretizations. Nevertheless, to obtain accurate approximations of the involved magnitudes, the required number of mesh points increases (and so the computational cost) as the periodic roughness frequence tends to infinity. In order to overcome this computational drawback when simulating rapidly oscillating roughness, limit models associated to different amplitude-frequence rates have been deduced in [7]. Hence, in the present work, appropriate numerical methods are also proposed for this representative limit models. Moreover, the computed pressures, bearing displacements and hydrodynamic loads illustrate the theoretical convergences stated in [7].