The application of the bilinear foil model to three-pad foil air bearings in rotordynamic analysis including reduced order modelling

Foil air bearings (FABs) are the mainstay of oil-free turbomachinery technology which is undergoing rapid expansion. A rotor system using such bearings is a nonlinear multi-domain dynamical system comprising the rotor, the air films and the foil structures. Multi-pad (segmented) FABs offer opportunity for enhanced stability performance but are naturally more computationally challenging than single (360 degrees) pad FABs. Their analysis has been limited to a simple model that ignores the detachment of the top foil from the underlying foil. Although a correction can be applied for the rotor vibration, the actual top foil deflection cannot be predicted. Additionally, reduced order modelling techniques have so far not been applied to such bearings. This paper presents the nonlinear and linearised dynamic analyses of three-pad FAB rotor systems considering foil detachment and using both Galerkin Reduction (GR) and Finite Difference (FD) to model the air film. Various models for the force distribution on the top foil are considered for use within a bilinear foil model, focusing on the ability to achieve numerical convergence. GR halved the computation time for a waterfall graph, without compromising the accuracy of the prediction of the nonlinear response. The results are validated against results from the literature.