Theoretical and Numerical Investigation of Gas Lubrication Processes on the Basis of Aerodynamic Equations

Abstract

The dimensionless parameters of the complete system of Navier-Stokes equations of a compressible gas are estimated with reference to a typical gas bearing. It is found that the three-dimensional compressible boundary layer equations should be used as the determining equations for describing gas lubrication processes. After introducing certain assumptions with respect to the dimensionless parameters in the determining equations, an equation for the pressure, the generalized Reynolds equation, is obtained. Use of the spectral method of analysis makes it possible to transform the generalized Reynolds equation into a system of ordinary differential equations. An analytic solution of the entire boundary value problem is obtained for a journal bearing with fairly small eccentricity. By comparing the numerical results obtained using both the solution of the generalized Reynolds equation and the traditional theory it is possible to estimate the effect of the inertia forces, dissipation processes, and heat transfer.