A New Bump-Type Foil Bearing Structure Analytical Model

A gas bearing of bump foil type comprises an underlying structure made of one or several strips of corrugated sheet metal covered by a top foil surface. The fluid film pressure needs to be coupled with the behavior of the structure for obtaining the whole bearing characteristics. Unlike in classical elasto-aerodynamic models, a foil bearing (FB) structure has a very particular behavior due to friction interfaces, bump interactions, and nonisotropic stiffness. Some authors have studied this complex behavior with the help of three-dimensional finite element simulations. These simulations evidenced a lack of reliable analytical models that can be easily implemented in a FB prediction code. The models found in the literature tend to overestimate the foil flexibility because most of them do not consider the interactions between bumps that are highly important. The present work then develops a model that describes the FB structure as a multidegree of freedom system of interacting bumps. Each bump includes three degrees of freedom linked with elementary springs. The stiffnesses of these springs are analytically expressed so that the model can be adjusted for any dimensions and material properties. Once the stiffness matrix of the whole FB structure is obtained, the entire static system is solved taking friction into account. Despite its relative simplicity, comparisons with finite elements simulations for various static load distributions and friction coefficients show a good correlation. This analytical model has been integrated into a foil bearing prediction code. The load capacity of a first generation foil bearing was then calculated using this structure model as well as other simplified theoretical approaches. Significant differences were observed, revealing the paramount influence of the structure on the static and dynamic characteristics of the foil bearing. Some experimental investigations of the static stiffness of the structure were also realized for complete foil bearings. The structure reaction force was calculated for a shaft displacement with zero rotation speed, using either the multidegree of freedom model or the usual stiffness formulas. The comparisons between theoretical and experimental results also tend to confirm the importance of taking into account the bump interactions in determining the response of the structure.