Cusp modelling of oil-film instability for a rotor-bearing system based on dynamic response

The amplitude jumps resulting from oil-film instability are catastrophic events that threaten the stable operation of rotor-bearing systems. In this study, a cusp model was established to investigate the instability boundary and the underlying catastrophe mechanism of rotor-bearing systems. The study presented a finite element model incorporating the nonlinear oil-film force of an experimental rotor-bearing system. The simulated dynamic responses related to oil-film instability, including the amplitude jump and the subsynchronous vibration during the run -up and run-down processes were in good agreement with the experimental data. According to catastrophe theory, the amplitude jump phenomenon can be described by a cusp model. To obtain the cusp model, a stepwise fitting method was proposed based on the dynamic response data. In addition, the topological transformation function, which maps the catastrophe boundaries of the nonlinear dynamic response to the cusp model, was obtained. The checkout results of the validation set confirmed the accuracy of the derived cusp model. The cusp model had upper and lower lobes, representing stable states corresponding to oil whip and no or low excitation of oil whirl, respectively, while the middle lobe represented the unstable state. The transition between these two stable states can explain the catastrophe, bistable, and hysteresis phenomena. The established cusp model can determine the instability boundary and further assist in the dynamic design and control of rotor-bearing systems.