A Dynamic Model for Dissipative Structures used in Bump-Type Foil Bearings

Abstract

A gas bearing of bump-type foil comprises an underlying structure made of one or several strips of corrugated sheet metal covered by a top foil surface. The fluid film pressure thus needs to be coupled with the behavior of this structure for obtaining the equivalent bearing characteristics. The dynamic model of the bump-type foil structure is then of capital importance. The approach presented in this article is an extension of a previously presented static model considering the structure as a multidegree of freedom system. The continuous corrugated sheet is considered as a discrete one with two nodes and three degrees of freedom for each bump that are linked by linear springs. The hereby presented dynamic model is based on the time-domain integration of the elastic structure under a given load variation. Its efficiency is conditioned by the ability to deal with the discontinuities contained in the nonlinear Coulomb friction model. In order to avoid these numerical difficulties, the Coulomb friction forces are regularized by using Petrov's model (Petrov and Ewins (1)). The present work introduces the results obtained for a single bump and for strips made of several bumps. Stick-slip and hysteresis curves for a single bump under an oscillatory load are first presented. The dissipated energy per cycle and the load-deflection ratio variations in the function of the pressure excitation amplitude and of the friction coefficient are compared to the previous finite element results and exhibit good correlation. Then the case of a strip constituted of six bumps is analyzed and the resulting hysteresis loop is compared to the experimental results published by Ku (2). The two curves correlate well and validate the dynamic structural model.