Semi-analytical prediction of the periodic vibration in a sliding bearing–rotor​ system

As for studying the sub-harmonic and super-harmonic periodic motions, eigenvalue dynamics and period-doubling bifurcation tree of the nonlinear rotor system, an implicit discrete mapping method is applied to a nonlinear sliding bearing–rotor system. The nonlinear term of the rotor system is triggered by the oil film forces of the sliding bearing at both ends. In order to accurately reveal the dynamic characteristics of the system, in this paper, a thirteen-parameter polynomial oil film force model is proposed. It considers the effects of displacement and velocity on the oil film force. And, the discrete mapping method used in this paper is a semi-analytical tool for solving equations with high precision. Consequently, continuous eigenvalue diagrams and bifurcation trees of periodic solutions from Period-1 to Period-4 motions of the nonlinear rotor system are obtained. For verification, numerical simulations are completed. Numerical and semi-analytical results are compared in time–history displacement, velocity and trajectories. Furthermore, the active feedback controller is carried out to improve the stability of the system.