Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor

Abstract

When a squeeze-film damper is operated eccentrically, the nonlinear damper forces are no longer radially symmetric and subharmonic and quasi-periodic vibrations may be excited by the rotor unbalance. In this study, the unbalance response of a rigid rotor, supported on an eccentric squeeze film damper, is first approximated by a harmonic series whose coefficients are determined by the collocation method, together with a nonlinear least-square regression. The stability of the resulting periodic 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 motion and a quasi-periodic motion at speeds above twice the system critical speed. This analytical finding is verified by a numerical integration in forms of the Poincare´ map, the rotor trajectory, the bifurcation diagram, and the power spectrum. It is suggested that stability analysis and numerical integration should always be incorporated into an approximate analytical method to achieve an adequate approximation. The results of this study show that the introduction of squeeze-film dampers may give rise to the undesirable nonsynchronous vibrations, which limits the maximum speed at which dampers should be used.

Preload effect on nonlinear dynamic behavior of a rigid rotor supported by noncircular gas-lubricated journal bearing systems

“…In their work, the linearized Reynolds equation was solved by the finite element method and a comparative stability analysis was done. In 1994, Zhao et al [5] investigated nonlinear dynamic behavior of an eccentric squeeze film damper-mounted rigid rotor system. The authors showed that for large values of unbalance and static misalignment, the subharmonic and quasi-periodic motions generated at speeds of more than twice the system critical speed were bifurcated from the unbalance harmonic solution.…”

Application of a hybrid numerical method to the nonlinear dynamic analysis of a micro gas bearing system

“…Sykes and Holmes [5] reported experimental observations of sub-harmonic motion in squeeze film bearings and suggested that such motion was a possible precursor of chaotic motion. Zhao et al [6] investigated the sub-harmonic and quasiperiodic motions of an eccentric squeeze film dampermounted rigid rotor system. The authors showed that for large values of the rotor imbalance and static misalignment, the sub-harmonic and quasi-periodic motions generated at speeds of more than twice the system critical speed were bifurcated from the unstable harmonic solution.…”

Application of a hybrid numerical method to the bifurcation analysis of a rigid rotor supported by a spherical gas journal bearing system

“…Kim and Noah [10] analyzed the bifurcation of a modified Jeffcott rotor using the bearing clearance as the bifurcation parameter. In 1994, Zhao et al [11] investigated the subharmonic and quasi-periodic motions of an eccentric squeeze film damper-mounted rigid rotor system. The authors noted that at large unbalance and static misalignment values, the subharmonic and quasi-periodic motions generated at speeds of more than twice the system critical speed were bifurcated from the unstable harmonic solution.…”