Nonlinear vibration and stability analysis of a flexible rotor supported on angular contact ball bearings

Flexible rotor systems supported by angular contact ball bearings display very complicated nonlinear behavior due to clearance and nonlinear Hertzian contact force. In this paper, a nonlinear vibration theoretical model for a flexible rotor-bearing system is derived in which the dynamic model of the shaft element, disk, coupling, nonlinear contact deformations and forces of the ball bearing are established. Nonlinear responses and orbits analysis of a flexible rotor angular contact ball bearing system are studied using the numerical integration method and maximal Lyapunov exponent. Bifurcation and stability of periodic motion of the flexible rotor-bearing system are studied using the continuation-shooting method and Floquet multipliers. Influences of initial contact angles, unbalance, damping factor, axial preloads, bending moments, stiffness ratio and rotating speed on stability and the bifurcation of periodic motion of the rotor-bearing system are analyzed. Finally, the theoretical model for a flexible rotor-bearing system is experimentally verified.