Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

Abstract

Gas foil bearings (GFBs) find 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 shaft 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 strips. 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 paper 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 Cholesky decomposition of the stiffness matrix representing the top foil and bump strips is performed off-line 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 journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential wavy-like minimum film thickness profile. The 1D top foil model is recommended 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.

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

“…Sagging occurs when the hydrodynamic film pressure causes a top foil deflection between bumps. The phenomenon was thoroughly investigated using both beam theory considerations [14] as well as analytical 2D plate theory [3,21] and FE-based models [22,28,29,34,36]. Here, a periodic expression, based on simple beam theory, approximates the sagging effect analytically and is added to the foil flexibility originally given by Wallowit and Anno [31].…”

The Effect of Area Contact on the Static Performance of Multileaf Foil Bearings

“…Its local deformation influences the bearing performance and must be considered in the analytical models. San Andres and Kim (17) used the 2D shell anisotropic structure and 1D beam-like structure for the top foil deformation. The 1D finite element model was recommended due to its best comparison to the experimental data and low computational cost.…”

Simulation of Static Performance of Air Foil Bearings Using Coupled Finite Element and Computational Fluid Dynamics Techniques

“…They use this model in Ref. [4], while they modeled the top foil using ID and 2D finite elements. They mentioned that both advancements significantly increase the computational efficiency.…”