Nonlinear stability analysis of a flexible rotor-bearing system by numerical continuation

Abstract

A rotor supported by hydrodynamic bearings may undergo unstable motion and may exhibit several nonlinear phenomena in the vicinity of the critical stability speed. This paper presents a stability analysis of a flexible rotor supported by journal bearings using a nonlinear dynamic model and a short bearing approximation. Numerical continuation is applied to determine the boundaries of stability and the bifurcations of the limit cycles. Nonlinear phenomena such as jumping motion and bi-stability domain are predicted. An extended stability chart has also been determined including the domains of stable oscillatory motion. The investigation also includes the effect of rotor flexibility and bearing characteristics on the stability boundaries and on the safe operating speed range. For a selected range of bearing parameters, two Hopf bifurcation regions are found for high rotor stiffness, three regions for low stiffness and four bifurcation regions in transition between high and low stiffness. It has also been found that the stable operating speed range decreases with rotor flexibility and bearing parameter.