Numerical modelling of compliant foil structure in gas foil bearings: Comparison of four top foil models with and without radial injection

Abstract

In the literature, there exists no consensus on a best practice for modelling the compliant foil structure of Gas Foil Bearings (GFBs). This paper focuses on the top foil modelling and its original contribution to the modelling problem is a comparison of steady state analysis efficiency, and transient and steady state accuracy between four top foil models with and without gas injection. The bump foil is modelled using the Simple Elastic Foundation Model (SEFM), and the four top foil models are (a) neglecting the top foil, i.e. the foil structure is modelled as a basic SEFM, (b) Euler–Bernoulli (EB) beam elements, (c) non-curved shell elements, and (d) curved shell elements. The theoretical analysis is carried out using a multi-domain numerical model and exemplified using a rigid rotor supported by three-pad GFBs. Comparing steady state journal eccentricities, low discrepancies are seen between almost all investigated models. However, the basic SEFM is found to be insufficient for cases with injection. Using the curved model as a benchmark, it is found that the predictions of steady state journal eccentricities, transient response, and eigenvalues made by the model with non-curved shell elements are less accurate than those of the model with EB beam elements. Thus, despite a higher degree of simplification, the model with EB beam elements is found to be both more computationally efficient as well as more accurate for steady state analysis when compared to the model with non-curved shell elements. While the radial foil deformation for the curved model exhibits dependency on the axial coordinate, this dependency is significantly overestimated by the model using non-curved shell elements. This is most pronounced for the case without injection, and it could explain the inferiority of the model using non-curved shell elements for estimating steady state journal eccentricities. A stress analysis indicates that this is caused by the non-curved shell element model not accounting for the membrane stresses in the top foil.