Finite Element Solution for the Rarefied Gas Lubrication Problem

Abstract

This paper is useful in analyzing the performance of finite-width-air bearings in the rarefied gas region, using a newly developed finite element method. The linearized Boltzmann equation was solved by numerical iteration and a pressure equation was obtained, coupled with a continuous equation. The finite element method was developed for solving the pressure equation. The results were compared with a two moment approximate solution for the Boltzmann equation, which corresponds to the conventional slip flow analysis developed by Burgdorfer. An analysis of tapered flat slider flying characteristics in the rarefied gas regime, e.g., when the inverse Knudsen number in the trailing edge = 1, showed that the present exact solution for the Boltzmann equation was different from the two moment approximate solution by more than 10 percent in load capacity value, when the dimensionless load was not so large as when it is used for actual slider design.