Analysis of Ultra-Thin Gas Film Lubrication based on Linearized Boltzmann Equation : 1st Report, Derivation of Generalized Lubrication Equation

Abstract

A generalized lubrication equation valid for an arbitrary Knudsen number, ratio of molecular mean free path and spacing, is derived through a linearized Boltzmann equation. Numerical analysis of the equation reveals two principal results. First, a modified Reynolds equation based on first order velocity slip overestimates load carrying capacity, while the approximation equation including second order velocity slip underestimates it. Second, in the case of a high compressibility number, the difference between results from the generalized equation and the approximation equations are decreased.