Nonlinear dynamic analysis of supercritical and subcritical Hopf bifurcations in gas foil bearing-rotor systems

The Hopf bifurcation behavior is an important issue for the nonlinear dynamic analysis of gas foil bearing (GFB)-rotor systems. However, there is a lack of detailed study on different types of Hopf bifurcation and their corresponding characteristics for GFB-rotor systems. This paper is intended to provide a clear and systematic insight into the nonlinear dynamic characteristics of GFB-rotor systems with a supercritical or a subcritical Hopf bifurcation. The onset speed (OS) of instability (i.e., the bifurcation point) for the system is calculated by the linear stability analysis. The periodic solution of the system before or after the bifurcation point is obtained by the shooting method, and its stability is assessed by the Floquet multipliers. The shock stability and the unbalanced response characteristics of the GFB-rotor system with a supercritical or a subcritical Hopf bifurcation are presented. A GFB-rotor system with a supercritical Hopf bifurcation shows better dynamic characteristics than a system with a subcritical Hopf bifurcation. The parameter analysis reveals that the aspect ratio and the foil stiffness of the GFBs have obvious effects on the Hopf bifurcation type, while the loss factor has a relatively small effect. It is remarkable that although a lower foil stiffness increases the OS of instability, the actual speed limit would probably decrease as the Hopf bifurcation changes from a supercritical to a subcritical type. This can contribute to an understanding of the necessity of studies on actual available operating speed based on nonlinear analysis rather than conventional linear analysis for the bearing design.