Investigation of the whirling motion and rub/impact occurrence in a 16-pole rotor active magnetic bearings system with c
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ORIGINAL PAPER
Investigation of the whirling motion and rub/impact occurrence in a 16-pole rotor active magnetic bearings system with constant stiffness Ali Kandil
Received: 25 August 2020 / Accepted: 2 November 2020 Ó Springer Nature B.V. 2020
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 X. 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.
A. Kandil (&) Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt e-mail: [email protected]; [email protected]
Keywords 16-Pole rotor AMBs Forward whirl Backward whirl Intermediate whirl Hybrid whirl Rub/impact occurrence
1 Introduction Active magnetic bearing (AMB) is a promising technology which has the attention of many researchers since it overcomes the most crucial problem of energy dissipation, i.e., friction. The idea can be epitomized in supporting a rotor via magnetic levitation without any physical contact or mechanical wear. In some cases, the weight of the rotor may cause an unbalance leading to unwanted vibrations. Enormous number of research papers focused on the control process of rotor AMB. Ji et al. [1] reduced the dynamics of a rigid rotor which was suspended by AMBs to a simpler form using center manifold theory and normal form method. The studied system exhibited an existence of saddle node, saddle connection, and Hopf bifurcations by local bifurcation analyses in the vertical direction. Ji and Hansen [2] considered nonlinearities and both fundamental and internal resonance conditions in the same system which exhibited a variety of interesting phenomena. These phenomena were bifurcation, jump, sensitivity to initial conditions, coexistence of multiple solutions, and amplitude-modulated motions. Ji [3, 4] studied the
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A. Kandil
effect of time-delayed feedback control in both a simple magnetic bearing system and a Jeffcott rotor with an additional magnetic bearing located at the di
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