Direct and Inverse Solutions for Elastohydrodynamic Lubrication of Finite Porous Journal Bearings

Abstract

In this paper a numerical solution for the elastohydrodynamic lubrication of a finite porous journal bearing is presented. The Brinkman–extended Darcy model was applied within the porous layer to incorporate the viscous shear stresses into the analysis. A simple elastic model is used to describe the elastic deformation of the liner. An inverse model is introduced to estimate the permeability parameter and/or the eccentricity ratio from experimentally obtained pressure data. As experimental measurements were not conducted, these data were simulated numerically. It consists of a direct solution for the pressure, for given parameters (permeability parameter and/or the eccentricity ratio), to which a normally distributed random error is added. The least-squares optimization technique is used to solve the proposed inverse problem. A unique solution was obtained for one-parameter estimation. The two-parameter estimation case, however, leads to multiple solutions lying on a constant load line.