On the bifurcations of a rigid rotor response in squeeze-film dampers

Abstract

The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the response of a rigid rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter ( B), gravity parameter ( W), spring parameter ( S) and unbalance parameter ( U), on the bifurcations of the rotor response are investigated. Spring parameter ( S) values between 0 and 1 are considered. A spring parameter value of S=0 represents the special case of dampers without centering springs. With the exception of the case S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of B, W and U irrespective of the value of S. Period-doubling and secondary Hopf bifurcations which occurred for low values of S (⩽0.3) were not observed for the higher values S⩾0.5. For very low stiffness values ( S<0.1), a period-3 solution that formed a closed bifurcation curve consisting of a pair of saddle-nodes, was found. Period-doubling cascades of the period-1 and period-3 orbits, boundary crisis and type 3 intermittency are the routes to chaos for this system. This study also revealed that combination values of gravity and spring parameters although resulting in similar values of the static eccentricity ratio exhibited remarkably different bifurcation behavior. The possibility of bifurcation phenomena arising from the interactions between large rotor imbalance forces and fluid-film forces in cavitated dampers, occurring in industrial rotating machinery, cannot be de-emphasized.