A Comparison of Homogenization and Direct Techniques for the Treatment of Roughness in Non-Newtonian-Modified Reynolds Equation: Numerical Results

This article is concerned with the simulation of a lubricated contact in severe running conditions considering the fluid as Non-Newtonian of Maxwell type. To overcome some limitations that become apparent at very small film thickness, notably when the roughness is two-dimensional, Jai in 1995 introduced a new technique based on a rigorous homogenization theory in the case of compressible fluid flow. This procedure was mathematically developed by Jai [1] and Buscaglia and Jai [2], and applied to tribological problems by Jai and Bou-Sai¨d [3]. The theoretical developments have been presented and discussed elsewhere [6] of this work and we present here some numerical results obtained from the homogenized technique. The obtained results were discussed and compared with the direct methods of calculation, and seem to us valid for a definitive validation of this method said about homogenization. These results have been compared to the exact solution obtained from a numerical simulation. By direct inspection it is clear that the symmetry predicted by the homogenization method is not present in the exact solution which qualitatively agrees with the homogenized solution.