Periodic variational Rayleigh problem of the gas-film lubrication theory

Abstract

A solution to the variational problem for a plain bearing (slider) on gas-film lubricant with periodicity conditions is considered. Using the calculus of variations, the shape of the lubricating layer providing maximum levitation force is determined. Along with the compressibility number, the parameters in the problem are the ceiling value of the profile function, and its limiting value corresponds to the results obtained by Rayleigh. Characteristics are presented for the optimum bearing in the case of different compressibility numbers.