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Technical Brief

Elliptic Motions and Control of Rotors Suspending in Active Magnetic Bearings

[+] Author and Article Information
Xiao-Dong Yang, Hua-Zhen An, Ying-Jing Qian, Wei Zhang, Ming-Hui Yao

Beijing Key Laboratory of Nonlinear Vibrations and
Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing, China 100124

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 23, 2015; final manuscript received May 10, 2016; published online June 2, 2016. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 11(5), 054503 (Jun 02, 2016) (8 pages) Paper No: CND-15-1449; doi: 10.1115/1.4033659 History: Received December 23, 2015; Revised May 10, 2016

The nonlinear dynamics of rotors suspending in the active magnetic bearings (AMBs) with eight pole pairs are investigated. The nonlinear governing equations of two degree-of-freedom (2DOF) are obtained considering the rotor with proportional–derivative (PD) controller. By studying the conservative free vibrations of the general 2DOF nonlinear systems, three types of motions are found, namely, in-unison modal motions, elliptic modal motions, and quasi-periodic motions. The method of multiple scales is used to obtain the amplitude-phase portrait to demonstrate the three types of motions by introducing the energy ratios and phase differences. It is found that in-unison modal motions do not exist due to the symmetry feature of the rotors in the AMBs. The effect of the PD controller and damping to the vibration suppression is discussed by the idea of the rolled-up amplitude-phase portrait.

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Figures

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Fig. 1

Principle of rotor–AMB

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Fig. 2

Cross section diagram of the rotor in the AMB

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Fig. 3

The amplitude-phase portrait for different conditions: (a) stable in-unison and none elliptic motions, (b) stable in-unison and unstable elliptic motions, (c) stable elliptic and none in-unison motions, (d) stable elliptic and unstable in-unison motions, and (e) stable in-unison and stable elliptic motions

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Fig. 4

The time histories and phase trajectories for different motions: (a) in-unison modal motions, (b) elliptic modal motions, and (c) quasi-periodic motions

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Fig. 5

The amplitude-phase portrait for the rotor in AMB

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Fig. 6

The vibration suppression effect of the damping and control coefficients presented by roll-up amplitude-phase portraits and time histories: (a) the effect of the damping, (b) the effect of the proportional gain coefficient, and (c) the effect of the derivative gain coefficient

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