The efficient computation of the nonlinear dynamic response of a foil–air bearing rotor system

Abstract

The foil–air bearing (FAB) enables the emergence of oil-free turbomachinery. However, its potential to introduce undesirable nonlinear effects necessitates a reliable means for calculating the dynamic response. The computational burden has hitherto been alleviated by simplifications that compromised the true nature of the dynamic interaction between the rotor, air film and foil structure, introducing the potential for significant error. The overall novel contribution of this research is the development of efficient algorithms for the simultaneous solution of the state equations. The equations are extracted using two alternative transformations: (i) Finite Difference (FD); and (ii) a novel arbitrary-order Galerkin Reduction (GR) which does not use a grid, considerably reducing the number of state variables. A vectorized formulation facilitates the solution in two alternative ways: (i) in the time domain for arbitrary response via implicit integration using readily available routines; and (ii) in the frequency domain for the direct computation of self-excited periodic response via a novel Harmonic Balance (HB) method. GR and FD are cross-verified by time domain simulations which confirm that GR significantly reduces the computation time. Simulations also cross-verify the time and frequency domain solutions applied to the reference FD model and demonstrate the unique ability of HB to correctly accommodate structural damping.