Non-linear vibration of an angular-misaligned rotor system with uncertain parameters

Parametric uncertainties play a significant role in the response predictions of a rotor system. In this paper, the quantification of uncertainty effects on the dynamic responses and vibration characteristics of a multi-rotor bearing system with the fault of angular misalignment is investigated. First, the motion equations of the rotor system are derived by taking into account the nonlinear supporting bearing and the displacement constraint between two rotors. The stochastic modeling with uncertainties of misalignment, damping and nonlinear support stiffness are then developed based on the polynomial chaos expansion technique in a stochastic framework, and traditional Monte-Carlo simulation is used as a comparison reference. Finally, the response statistics and dynamic behaviors of the stochastic system are demonstrated by mean and its probability density function (PDF). The results show that the super-harmonic resonance occur at the 1/2 of the critical speed due to the effect of misalignment, and as the uncertainty increases the realization amplitudes are spread over a wider band of amplitudes. Furthermore, P-bifurcation in the response PDFs is also presented in some situations.