Extension of the Conducting Sheet Analogy to Externally Pressurized Gas Bearings

Abstract

Incompressible, viscous flow in narrow passages bounded by parallel surfaces yields the two-dimensional Laplace equation, ∇2 P = 0. The pressure field, load capacity, and lubricant flow of hydrostatic oil bearings can be readily determined by means of the electric analogy of the conducting sheet. The equation ∂∂xP∂P∂x + ∂∂yP∂P∂y = 0 characterizes laminar, isothermal flow of gas lubricants in otherwise geometrically identical bearings. It is shown that by means of suitable change of the dependent variable this equation can be reduced to the Laplacian form. The ensuing advantage is the extension of the conducting sheet analogy to externally pressurized thrust and journal guide bearings when the lubricant is a gas.