An Approximate Analytic Solution of the One-Dimensional Foil Bearing Problem

Abstract

Approximate solutions are found to the one-dimensional steady-state foil bearing problem in which a longitudinally translating, flexible tensioned sheet of material rides on a thin film of entrained air as it wraps around a fixed cylinder. The approximate solutions use the first few terms of a scaled, exponential power series and minimize the squared residual in the governing differential equation. The solutions are simple, compare well with more exact solutions, and provide excellent starting points for more sophisticated, iterative solution algorithms.