Characteristics of the Nonlinear Hysteresis Loop for Rotor-Bearing Instability

Abstract

Abstract The nonlinear hysteresis loop of a journal-bearing supported rotordynamic system is characterized by the Hopf-bifurcation and Saddle-Node speeds. The nonlinearity of this system occurs in the journal-bearing fluid-film forces, and requires the imbedding of a solution for the Reynolds lubrication equation within a numerical integration scheme of the coupled motion equations in order to perform proper simulations. These show that under light bearing static load, the Saddle-Node and Hopf bifurcation coalesce to a single speed at essentially two times the self-excited vibration frequency (i.e., the lowest natural frequency). At higher bearing loads, the classical instability threshold speed (i.e., Hopf bifurcation) occurs at progressively higher rotor speeds. However, the disappearance speed (Saddle Node of the periodic orbit) of the nonlinear limit cycle occurs at progressively lower rotor speeds, asymptotically approaching approximately 1.725 times the lowest natural frequency. By adding a rotor unbalance force to the model, exploratory simulations have been made to determine the extent to which chaos signal processing in the normal speed-up or coast-down vibration of actual machines could be used to locate this lower speed bound of the instability hysteresis loop.