On the stability of rotor bearing systems based on Hopf bifurcation theory

Abstract

This research is aimed to establish instability criteria for a rotor-bearing system which consists of a rotor supported by two fluid-film journal bearings. The static and dynamic characteristics of rotor-bearing systems with consideration of turbulent effects are evaluated by applying the Hopf bifurcation theory (HBT) to the equations of motion. A method is developed for predicting the stability envelope of rotor-bearing systems using HBT. Results are compared with published literature obtained using a trial-and-error method. A method based on HBT is presented for predicting the occurrence of a hysteresis phenomenon, which is observed in experimental results dealing with the instability of rotor-bearing systems. It is shown that the existence of hysteresis phenomenon is dependent on the system's operating parameters. To this end, the effect of oil viscosity on hysteresis phenomenon and its implications on the rotor-bearing instability are investigated. The results of a series of experiments illustrating the effectiveness of the prediction of the hysteresis phenomenon using HBT are also presented. Disparities in assessing the influence of inlet oil temperature on the instability threshold speed have been documented in the literature for a long time. Specifically, some papers presented evidence that lowering the inlet oil temperature tends to have a stabilizing effect, while others have shown the opposite. No clear explanation has been offered for this phenomenon. This research presents the results of a series of experiments that explain the nature of these disparities and sheds light on the influence of the inlet oil temperature on the instability of journal bearings. Using HBT, the influence of drag force on the dynamic performance of a rotor-bearing system is analyzed through including the drag force components in the equations of motion. The HBT is applied to a rotor-bearing system with a flexible shaft. The analysis reveals that rotor stiffness has pronounced effects on the instability threshold speed as well as the subcritical or supercritical bifurcation characteristics. Using the chart presented in this research, not only the instability threshold speed but also the bifurcation type can be easily predicted for a specific rotor-bearing system with any specific set of operating parameters.