Averaged Reynolds Equation Extended to Gas Lubrication Possessing Surface Roughness in the Slip Flow Regime: Approximate Method and Confirmation Experiments

Abstract

The average film thickness theory is extended to gas lubrication possessing surface roughness in the slip flow regime. A simplified averaged Reynolds equation is derived and its applicability is confirmed through comparing with experiments. This averaging equation makes use of the mixed average film thickness defined as Havem = αHm + (1 − α)Hmˆ, where m = 1, 2 and 3; α indicates the mixing ratio; and H¯ and Hˆ denote the arithmetically and harmonically averaged film thicknesses. The experiments were performed using computer flying heads having precisely photolithography-fabricated longitudinal, transverse or checkered pattern roughnesses under submicron spacing conditions. From the excellent agreement obtained between the calculated and experimental results, it can be concluded that the assumption that velocity slippage occurs along the surface even if roughnes is present is justified, and that the approximate method is applicable for determining the surface roughness effects in the slip flow regime.