A comparison of modal analyses of foil-air bearing rotor systems using two alternative linearisation methods

When applied to the free vibration (modal) analysis of foil-air bearing rotor systems, the classical linear force coefficients method (LFCM) can be regarded as an indirect form of linearisation that eliminates the air film and foil state variables.
Research into its accuracy has been limited to its predictive ability for the instability onset speed compared against the low amplitude response of the nonlinear system. Two recent studies highlighted issues that artificially inflated the method
discrepancies reported previously. This paper verifies the LFCM on a series of cases and identifies indisputable ones where it gives misleading results. A novel robust procedure is devised for the LFCM computation of Campbell diagrams and modal stability plots. A first-ever study of the accuracy of the LFCM’s modal analysis capability is carried out using as benchmark the recently developed direct linearisation method. In contradiction to a recent study, the LFCM results did not exhibit a systematic error as the foil compliance increases, though it is not excluded that such an error may occur in other situations. The two cases identified where the LFCM gave misleading predictions relate to pad flutter with top foil detachment and half engine order whirl modes attributed to the air film.