Bifurcation analysis of a flexible rotor in squeeze-film dampers with retainer springs

Abstract

Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting nonlinear behavior. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter (W), mass ratio (α) and stiffness ratio (K), on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter (Ω) between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of the gravity parameter, W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α =0.1 and K =0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α =0.4. With the exception for the case of α =0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. The numerical results presented in this work were obtained for an unbalance parameter (U) of 0.1, which is considered as the upper end of the normal unbalance range of practical rotor systems. These results provide some insights into the range of design parameters of squeeze-film dampers to ensure synchronous rotor response within a specified operating speed range.