Imbalance Response and Stability of Eccentric Squeeze-Film-Damped Nonlinear Rotor Bearing Systems

Abstract

Solutions for the imbalance response and stability of squeeze-film-damped nonlinear rotor bearing systems are presented. The rotor imbalance response is approximated by a trigonometric series whose coefficients are determined using a collocation method together with a nonlinear least squares regression. To improve numerical efficiency, the number of nonlinear equations for iterative solution is reduced to that corresponding to the number of nonlinear supports. A linear polynomial predictor is used to provide initial values for the iteration and, to ensure continuity through critical points, an arc-length continuation algorithm is used. To investigate the stability of the solution, the Floquet transition matrix method is used with an approximate transition matrix computed using a rectangular ripple method. Numerical examples are given for an eccentric squeeze-film-damper-mounted rigid rotor.