An Averaging Technique for the Analysis of Rough Surface High Bearing Number Gas Flows

Earlier analytical solutions by White (1980, 1983, 1992, 1993) included Couette effects, transverse diffusion, and mass storage in a model lubrication equation for narrow width wavy surface high bearing number gas films. The model lubrication equation did not include longitudinal diffusion effects due to the high bearing number restriction. Crone et al. (1991), however, reported numerical solutions of the full Reynolds equation for a gimbal mounted slider subject to wavy surface roughness. The first objective of this work is to reconcile the differences observed between the reported results of White and those of Crone et al. for moving and stationary roughness. The second objective is to describe how to best apply what appears to be a universal property of a high bearing number gas film subjected to a rough surface. Each solution of the model lubrication equation by White (1980, 1983, 1992, 1993) produced a product term based on local gas pressure and clearance (Z = Ph) that is independent of roughness details but which is dependent on the statistical properties of the roughness. In the present work, this characteristic is treated as a universal property of all high bearing number rough surface gas films. The product variable Z = Ph is introduced into the generalized full lubrication equation, and the resulting lubrication equation is ensemble averaged before a solution is attempted. This removes the short length and time scale effects due to the surface roughness. Solution of the ensemble averaged equation for Z(x, y, t) then follows by standard analytical or numerical methods. The unaveraged pressure is then given by P(x, y, t) = Z(x, y, t)/h(x, y, t) and the ensemble averaged or mean pressure at a point is computed from P_m(x, y, t) = Z(x, y, t)E(1/h(x, y, t)), where E(1/h) represents the ensemble average of 1/h. Using this technique, numerical solutions of the full generalized lubrication equation based on kinetic theory were obtained for a low flying gimbal mounted slider. Results indicate that the nominal flying height increases and the minimum flying height decreases as surface roughness increases.