A comprehensive dynamic model to investigate the stability problems of the rotor–bearing system due to multiple excitations

Abstract

In this paper, a comprehensive dynamic model is proposed to analyze the dynamic behaviors of the rotor–bearing system. Three types of excitation including the bearing waviness, the unbalanced force and the finite number of balls (varying compliance effect) are considered. Based on the extended Jones–Harris model with five degrees of freedom, the load distribution and then the stiffness of the angular contact ball bearing are obtained theoretically. After introducing the three types of excitation into the model, the bearing stiffness matrix becomes time-varying and many parametric frequencies are found due to the multiple excitations. Then, the stability problems of the parametrically excited rotor–bearing system are investigated utilizing the discrete state transition matrix method (DSTM). The simple instability regions arising from the translational and the angular motions are analyzed respectively. The effects of the amplitude and the initial phase angle of the bearing waviness, the rotor eccentricity, the bearing preload and the damping of the rotating system on the instability regions are discussed thoroughly. It is shown that the waviness amplitudes have significant influences on the instability regions, while the initial phase angles of the waviness almost have no effect on the instability regions. The rotor eccentricity just affects the widths of the instability regions. The increasing of the bearing preload only shifts the positions of the instability regions. Damping could reduce the instability regions but it could not diminish the regions completely.