Investigation of the whirling motion and rub/impact occurrence in a 16-pole rotor active magnetic bearings system with constant stiffness

TLDR: In this article, a 16-pole rotor active magnetic bearing system with constant stiffness is considered and the equations of motion are derived to show the asymmetry between the rotor's horizontal and vertical displacements.

Abstract: In this paper, the weight of the rotor is considered in a 16-pole rotor active magnetic bearing system with constant stiffness. The equations of motion are derived to show the asymmetry between the rotor’s horizontal and vertical displacements. Accordingly, the rotor may exhibit forward, backward, intermediate, or hybrid whirls. The possibility to overcome the backward whirl and to symmetrize the rotor’s motion again is discussed. Also, the rotor may rub/impact with the stator legs depending on the values of the adopted system parameters. The multiple-scales method is utilized to extract the approximate solutions of the studied model and to analyze its nonlinear dynamics and the aforementioned whirls. The discussion is enhanced by different analytical plots such as the rotor’s responses to its eccentricity $$f$$ and rotation speed $$\varOmega $$ . Numerical validation is carried out to demonstrate how these analytical plots describe precisely the nonlinear dynamical behavior of the whole system. Finally, whirl orbit maps are plotted to simulate the real-life motion of the rotor at different whirls and at rub/impact occurrence.