A Comparison of Homogenization and Averaging Techniques for the Treatment of Roughness in Slip-Flow-Modified Reynolds Equation

Abstract

This article is concerned with the simulation of a magnetic storage device consisting of a flying head above a rigid rotating disk. The need to improve the transfer rate has led, at present, to very small surface-to-surface distances (air gaps). In this situation it is compulsory to take into account roughness effects. A popular method consists in averaging film-thickness from Mitsuya et al. (1989), with good reported results compared with experimental data. To overcome some limitations that become apparent at very small air gaps, notably when the roughness is two-dimensional, Jai in 1995 introduced a new technique based on a rigorous homogenization theory. Recent developments from Buscaglia and Jai (2000) have greatly reduced the computational complexity of the homogenization-based method, rendering it suitable for practical applications. We propose in this paper an original approach based on strength and rigorous mathematical model to avoid numerical problems which are usually encountered in classical approaches. The validation of the homogenization-based method is in some sense, a generalization of the film-averaging technique suitable for configurations in which some parameters of the latter (such as the Boltzmann correction factor) are not unambiguously defined.