A new method for the calculation of the Campbell diagram of a foil-air bearing rotor model

Campbell diagrams (describing free linearised vibration) of rotor/foil-air bearing (FAB) systems are currently based on the linearised force coefficients (FC) method, which eliminates the air film and foil state variables from the eigenvalue analysis. Individual modes of FC-based Campbell diagrams have not been verified by transient nonlinear dynamic analysis (TNDA) at low amplitudes and significant discrepancies between FC and TNDA stability predictions have been reported. This paper introduces a new method that avoids the FC method by extracting the Campbell diagram directly from the nonlinear state-space model. Through appropriate scaling of the eigenvectors and the application of a minimum journal amplitude criterion, it is found that the multitude of eigenvalues/eigenvectors of the state Jacobian could be filtered to extract the relevant modes. Where appropriate, a maximum damping criterion should also be applied. Each extracted mode is precisely verified using TNDA with mode-specific initial conditions. The methodology is successfully applied to a symmetric rigid rotor on single-pad FABs with the pad modelled by the simple equivalent foundation model. The simulation results correlate well with observations reported in an independent study that used a more advanced foil model but was restricted to TNDA (no Campbell diagram).