Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient

Abstract

A 1.5-order modified Reynolds equation for solving the ultra-thin film gas lubrication problem is derived by using an accurate higher-order slip-flow model. This model features two key differences from the current second-order slip-flow model. One is the involvement of an accommodation coefficient for momentum. The other is that the coefficient of the second-order slip-flow term is 4/9 times smaller than that for the current model. From the physical consideration of momentum transfer, the accommodation coefficient is found to have no affect on the second-order slip-flow term. Numerical calculations using the 1.5-order modified Reynolds equation are performed. The results are compared with those obtained using three kinds of currently employed modified Reynolds equations: those employing the first- and second-order slip-flow models and those utilizing the Boltzmann equation. These comparisons confirm that the present modified Reynolds equation provides intermediate characteristics between those derived from the first- and second-order slip-flow models, and produces an approximation closer to the exact solution resulting from the Boltzmann-Reynolds equation.