Nonlinear dynamics of a misaligned and eccentric rotor system with three base motions

Misalignment and eccentricity are common major faults in rotor systems, which significantly affect vibration characteristics of rotor systems. This study aims to investigate dynamic responses of a coupling-misaligned and eccentric rotor system supported by four ball bearings with cubic nonlinear contact stiffness under three base motions, i.e., base rolling, pitching, and hovering motions, contributing to a deeper understanding of vibration characteristics of rotor dynamic systems in space transportation equipment. Equations of motion of the rotor system under base motions are derived by using the Lagrangian method. The incremental harmonic balance method is used to obtain periodic solutions of the rotor system under base motions, and the Floquet theory along with the precise Hsu's method is employed to analyze stability of periodic solutions and their bifurcations. It is found that vibration intensity of the rotor system is not always aggravated under the effect of a base motion load, and it can even be suppressed in some conditions. Nevertheless, response characteristics at even multiples of the shaft rotation frequency for the misalignment fault remain significant, and these fault characteristics are consistent with those observed when the base is fixed. In addition, base motions affect the amplitude of the constant vibration response in frequency domain, leading to the deviation of disk center trajectories. Disk center trajectories shift direction varies with base motion types, potentially causing rotor-stator rubbing impacts at different locations. Furthermore, it is found that nonlinear behaviors of the rotor system change with base motions, including differences in bifurcation types and rotation speeds corresponding to bifurcations. These findings provide theoretical support for the structural design and fault diagnosis of transportation equipment that frequently undergoes spatial motions, such as aircraft engines.