Comprehensive study on the nonlinear parameter vibrations of the rotor system due to the varying compliance of ball bearing

In this paper, based on the restoring force coupling method, a novel mathematical model is established to study the VC parameter vibration responses of the ball bearing-rotor system, and both the rotor radial and tilting motions have been considered. Firstly, the steady state analysis on the stiffness fluctuation is conducted to determine the equivalent linear resonant frequencies of the nonlinear ball bearing-rotor system. Secondly, both the two-way sweep-frequency and fixed frequency-analysis are adopted to study the different transient response mechanisms of the rotor VC parameter vibrations, Finally, the results show that not only the multiple resonant responses including the super-harmonic, sub-harmonic, Hopf bifurcation and chaos are generated for the rotor parametric vibration, but also the complex internal resonance phenomenon occurs when the rotor natural frequency ratio in different radial directions is close to 1:2.