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Research Papers

Analytical Treatment With Rigid-Elastic Vibration of Permanent Magnet Motors With Expanding Application to Cyclically Symmetric Power-Transmission Systems

[+] Author and Article Information
Shiyu Wang

Mem. ASME
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
Key Laboratory of Mechanism Theory
and Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control,
Tianjin 300072, China
e-mail: wangshiyu@tju.edu.cn

Jie Xiu

School of Electrical Engineering and Automation,
Tianjin University,
Tianjin 300072, China

Shuqian Cao

School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control,
Tianjin 300072, China

Jianping Liu

School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 12, 2012; final manuscript received November 4, 2013; published online January 16, 2014. Assoc. Editor: Yukio Ishida.

J. Vib. Acoust 136(2), 021014 (Jan 16, 2014) (13 pages) Paper No: VIB-12-1037; doi: 10.1115/1.4025993 History: Received February 12, 2012; Revised November 04, 2013

The phasing effect of the slot/magnet combination on rigid-elastic vibration is addressed by incorporating the cyclic symmetry of permanent magnet (PM) motors. Expanding research is also carried out to achieve more general findings in rotary power-transmission systems widely available in practical engineering. To these aims, model-free analysis is used to deal with the effect via superposition treatment. The results imply that the vibration induced by temporal-spatial excitation can be classified into rotational, translational, and balanced modes, all of which have rigid and elastic vibrations having specific base and/or contaminated deflections, and the elastic vibration can be of the standing, forward traveling, and backward traveling waves. These modes can be suppressed or excited depending on whether particular algebraic relationships are satisfied by slot/magnet combination, excitation order, and base and contaminated wave numbers. Since the analysis is independent of any models, specified magnetic force, and rigid-elastic vibration, analytical results regarding the expected relationships can be naturally created due to the structural and force symmetries of the PM motors. Because of this, similar results can be found for other rotary systems basically consisting of a rotary rotor and a stationary stator both having equally-spaced features, apart from the PM motors, typically including the turbine machines having fluid field and planetary gears with a mechanical contact. As an engineering application, the proposed method can serve as a fundamental tool when predicting or even suppressing the possible excitations associated with particular vibration modes in the mechanical and electrical designs of the symmetric systems. The superposition effect and analytical predictions are verified by the finite element method and strict comparisons against those from disk-shaped structures in an existing study.

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Topics: Vibration , Stators , Waves
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Figures

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Fig. 1

Schematic of a sample three-slot stator and superposition of elastic waves

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Fig. 2

Vibration modes of case I

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Fig. 3

Magnitudes and harmonics of contaminations in case I

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Fig. 4

Vibration modes of case II

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Fig. 5

Magnitudes and harmonics of contaminations in case II

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Fig. 6

Configurations of harmonic magnetic forces

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Fig. 7

Harmonic responses of case I

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Fig. 8

Harmonic responses of case II

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Fig. 9

Comparison of rotationally periodic systems, (a) bladed disk structure, (b) excitation schematic, and (c) PM motor

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Fig. 10

Cyclically symmetric systems: (a) turbine machines, (b) planetary gears, and (c) basic schematic of structure and inner excitations

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