Computational Analysis of Gas Foil Bearings Integrating 1D and 2D Finite Element Models for Top Foil

Gas foil bearings (GFBs) are finding widespread usage in oil-free turbo expanders, APUs and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high level vibrations, including transient rubs and severe misalignment, static and dynamic. The static load capacity and dynamic forced performance of GFBs depends largely on the material properties of the support elastic structure, i.e. a smooth foil on top of bump strip layers. Conventional models include only the bumps as an equivalent stiffness uniformly distributed around the bearing circumference. More complex models couple directly the elastic deformations of the top foil to the bump underlying structure as well as to the hydrodynamics of the gas film. This report details two FE models for the top foil supported on bump strips, one considers a 2D shell anisotropic structure and the other a 1D beam-like structure. The decomposition of the stiffness matrix representing the top foil and bump strips into upper and lower triangular parts is performed off-line and prior to computations coupling it to the gas film analysis governed by Reynolds equation. The procedure greatly enhances the computational efficiency of the numerical scheme. Predictions of load capacity, attitude angle, and minimum film thickness versus journal speed are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, but underestimate it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential profile of minimum film thickness. The 1D top foil model is to be preferred due to its low computational cost. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE top foil structural models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model. A three lobe GFB with mechanical preloads, introduced by inserting shims underneath the bump strips, is analyzed using the 1D FE structural model. Predictions show the mechanical preload enhances the load capacity of the gas foil bearing for operation at low loads and low shaft speeds. Energy dissipation, a measure of the bearing ability to ameliorate vibrations, is not affected by the preload induced. The mechanical preload has no effect on the static and dynamic forced performance of GFBs supporting large static loads.