A Study of Roughness and Non-Newtonian Effects in Lubricated Contacts

This article is concerned with the simulation of a lubricated contact considering the fluid to be non-Newtonian of the Maxwell type. Severe operating conditions lead to very small surface-to-surface distances. In this situation it is necessary to take roughness effects into account. A popular method consists in averaging the film thickness following Patir and Cheng (ASME J. Lubr. Technol., 100, pp. 12–17, 1978), or more recently Wang et al. (Tribol. Trans., 45(1), pp. 1–10, 2000), with good reported results compared with experimental data. To overcome certain limitations that become apparent at very small film thickness, notably when the roughness is two-dimensional, in 1995 Jai (Math. Modell. Numer. Anal., 29(2), pp. 199–233, 1995) introduced a new technique based on a rigorous homogenization theory in the case of compressible fluid flow. This procedure was further mathematically developed by Buscaglia and Jai (Math. Probl. Eng., 7(4), pp. 355–377, 2001) and applied to tribological problems by Jai and Bou-Saı¨d (ASME J. Tribol., 124, pp. 327–355, 2002). In this paper, we propose a similar homogenized approach in the case of non-Newtonian fluids to avoid numerical problems which are often encountered in other approaches. Results in the homogenized roughness case are obtained and compared with direct numerical solutions.