SUBHARMONIC AND QUASI-PERIODIC MOTIONS OF AN ECCENTRIC SQUEEZE FILM DAMPER-MOUNTED RIGID ROTOR

When a squeeze-film damper is operated eccentrically, the nonlinear da mper forces are no longer radially symmetric and subharmonic and quasi -periodic vibrations may be excited by the rotor unbalance. In this st udy, the unbalance response of a rigid rotor, supported on an eccentri c squeeze film damper, is first approximated by a harmonic series whos e coefficients are determined by the collocation method, together with a nonlinear least-square regression. The stability of the resulting p eriodic solution is then examined using the Floquet transition matrix method. For sufficiently large values of the unbalance and the damper static radial misalignment, it is shown that the approximate harmonic motion loses its stability and bifurcates into a stable subharmonic mo tion and a quasi-periodic motion at speeds above twice the system crit ical speed. This analytical finding is verified by a numerical integra tion in forms of the Poincare map, the rotor trajectory, the bifurcati on diagram, and the power spectrum. It is suggested that stability ana lysis and numerical integration should always be incorporated into an approximate analytical method to achieve an adequate approximation. Th e results of this study show that the introduction of squeeze-film dam pers may give rise to the undesirable nonsynchronous vibrations, which limits the maximum speed al which dampers should be used.