Nonlinear and linearised analyses of a generic rotor on single-pad foil-air bearings using Galerkin Reduction with different applied air film conditions

The compressible Reynolds Equation is typically integrated within a fully-coupled dynamical foil-air bearings (FAB)-rotor system via spatial discretisation transformation e.g. Finite Difference (FD), Finite Element (FE). This paper presents a novel application of an arbitrary-order Galerkin Reduction (GR) method, which does not involve spatial discretisation, to both nonlinear and linearised analyses of rotor systems supported by single-pad FABs. The novel aspects are: application to generic flexible rotors; Jacobian-based linearisation of the GR-transformed system for the extraction of the full mode set and linear stability map; the facility to apply a pressure constraint at a circumferential location and/or the Gümbel condition. These developments are comprehensively verified on two previously considered systems by comparing alternative (GR, FD-based) simulations. The overall features of the experimental nonlinear phenomena are predicted satisfactorily. Transient nonlinear dynamic analysis (TNDA) with GR is found to be less prone to numerical divergence than with FD. For static equilibrium, stability and modal analysis (SESMA), GR is found to be over twice as fast, requiring 70-90 times less memory for saving the results.