Stability and Bifurcation of Unbalanced Response of a Squeeze Film Damped Flexible Rotor

Abstract

The stability and bifurcation of the unbalance response of a squeeze film dampermounted flexible rotor are investigated based on the assumption of an incompressible lubricant together with the short bearing approximation and the "it "film cavitation model. The unbalanced rotor response is determined by the trigonometric collocation method and the stability of these solutions is then investigated using the Floquet transition matrix method. Numerical examples are given for both concentric and eccentric damper operations. Jump phenomenon, subharmonic, and quasi-periodic vibrations are predicted for a range of bearing and unbalance parameters. The predicted jump phenomenon, subharmonic and quasi-periodic vibrations are further examined by using a numerical integration scheme to predict damper trajectories, calculate Poincare maps and power spectra. It is concluded that the introduction of unpressurized squeeze film dampers may promote undesirable nonsynchronous vibrations.

Analysis of the nonlinear dynamic response of a rotor supported on ball bearings with floating-ring squeeze film dampers

“…So far, a number of investigations into the nonlinear behaviors of rotor supported on SFD had been carried out. Zhao [3] investigated the jump phenomenon by using the collocation method, the arc-length continuation algorithm and the Levenberg-Marquardt nonlinear least squares method. Zhu [4] studied the jump phenomenon by the synchronous circular centered-orbit motion solution, numerical integration method and slow acceleration method.…”

Analysis of the Steady State Unbalance Response of Rigid Rotors on Magnetorheological Dampers: Stability, Force Transmission and Energy Dissipation

“…(26) is a periodic function of time too. According to the procedure described in Zhao et al [1994], the transition matrix H over the span of time of one period T , referred to the set of linear differential equation (26) …”

Generalized Lagrange functions and weighting coefficient formulae for the harmonic differential quadrature method

“…k ( ) can be calculated recursively by using Equations (22), (20) and (19). Hence, L kk are given explicitly as…”