Global dynamic characteristics of a piecewise smooth rotor/stator rubbing system with high speed

Abstract

In this paper the global dynamic characteristics of a piecewise smooth rotor/stator rubbing system with high speed, which significantly differs from those of a low-speed system, are explored by numerical simulation and theoretical analysis. A sigmoid function is utilized to smoothen the governing equations, enabling the derivation and validation of bifurcation diagrams, as well as corresponding orbits, full spectra and Poincaré sections for both periodic and quasi-periodic motions. Additionally, the frequency relations of the quasi-periodic motions are determined. Based on the stability analysis of the periodic solutions, the presence of Hopf bifurcation boundaries, which indicate ‘jump’ phenomena between periodic and quasi-periodic motions, along with saddle-node bifurcation boundaries, is confirmed. Consequently, the global dynamic characteristics are obtained by the evolution of equilibrium solutions. Notably, zero-Hopf bifurcation is identified for the first time in the rotor/stator rubbing system with high speed. The work also reveals deep insights into the interactive effect of parameters on the dynamic characteristics of the smoothening model.