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

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.

Copyright © 2014 by ASME
Topics: Vibration , Stators , Waves
Your Session has timed out. Please sign back in to continue.


Huang, B., and Hartman, A., 1997, “High Speed Ten Pole/Twelve Slot DC Brushless Motor With Minimized Net Radial Force and Low Cogging Torque,” U.S. Patent No. 5,675,196.
Tang, R. Y., 1997, Modern Permanent Magnet Machines: Theory and Design, Mechanical Industry Press, Beijing.
Hwang, S. M., Eom, J. B., Jung, Y. H., Lee, D. W., and Kang, B. S., 2001, “Various Design Techniques to Reduce Cogging Torque by Controlling Energy Variation in Permanent Magnet Motors,” IEEE Trans. Magn., 37(4), pp. 2806–2809. [CrossRef]
Williams, M. M., Zariphopoulos, G., and Macleod, D. J., 1994, “Performance Characteristics of Brushless Motor Slot/Pole Configurations,” Incremental Motion Control Systems and Devices Symposium (IMCSD 94), San Jose, CA, June 14–16, pp. 145–153.
Zhu, Z. Q., and Howe, D., 2000, “Influence of Design Parameters on Cogging Torque in Permanent Magnet Machines,” IEEE Trans. Energy Convers., 15(4), pp. 407–412. [CrossRef]
Hanselman, D. C., 1997, “Effect of Skew, Pole Count and Slot Count on Brushless Motor Radial Force, Cogging Torque and Back EMF,” IEE Proc.: Electr. Power Appl., 144(5), pp. 325–330. [CrossRef]
Hwang, C. C., Wu, M. H., and Cheng, S. P., 2006, “Influence of Pole and Slot Combinations on Cogging Torque in Fractional Slot PM Motors,” J. Magn. Magn. Mater., 304(1), pp. e430–e432. [CrossRef]
Chen, S. X., Low, T. S., Lin, H., and Liu, Z. J., 1996, “Design Trends of Spindle Motors for High Performance Hard Disk Drives,” IEEE Trans. Magn., 32(5), pp. 3848–3850. [CrossRef]
Bi, C., Jiang, Q., and Lin, S., 2005, “Unbalanced-Magnetic-Pull Induced by the EM Structure of PM Spindle Motor,” 8th International Conference on Electrical Machines and Systems (ICEMS 2005), Nanjing, China, September 27–29, pp. 183–187. [CrossRef]
Song, Z. H., Han, X. Y., Chen, L. X., and Tan, R. Y., 2007, “Different Slot/Pole Combination Vibro-Acoustics of Permanent Magnet Synchronous Motor,” Micro Motor, 40(12), pp. 11–14. [CrossRef]
Huo, M. N., Wang, S. Y., Xiu, J., and Cao, S. Q., 2013, “Effect of Magnet/Slot Combination on Triple-Frequency Magnetic Force and Vibration of Permanent Magnet Motors,” J. Sound Vib., 332(22), pp. 5965–5980. [CrossRef]
Rahman, B. S., and Lieu, D. K., 1991, “The Origin of Permanent Magnet Induced Vibration in Electric Machines,” ASME J. Vibr. Acoust., 113(4), pp. 476–481. [CrossRef]
Chen, Y. S., Zhu, Z. Q., and Howe, D., 2006, “Vibration of PM Brushless Machines Having a Fractional Number of Slots Per Pole,” IEEE Trans. Magn., 42(10), pp. 3395–3397. [CrossRef]
Wang, S. Y., Xu, J. Y., Xiu, J., Liu, J. P., Zhang, C., and Yang, Y. H., 2011, “Elastic Wave Suppression of Permanent Magnet Motors by Pole/Slot Combination,” ASME J. Vibr. Acoust., 133(2), p. 024501. [CrossRef]
Jang, G. H., and Lieu, D. K., 1991, “The Effect of Magnet Geometry on Electric Motor Vibration,” IEEE Trans. Magn., 27(6), pp. 5202–5204. [CrossRef]
Chang, S. C., and Yacamini, R., 1996, “Experimental Study of the Vibrational Behaviour of Machine Stators,” IEE Proc.: Electr. Power Appl., 143(3), pp. 242–250. [CrossRef]
Long, S. A., Zhu, Z. Q., and Howe, D., 2001, “Vibration Behavior of Stators of Switched Reluctance Motors,” IEE Proc.: Electr. Power Appl., 148(3), pp. 257–264. [CrossRef]
Tseng, J. G., and Wickert, J. A., 1994, “On the Vibration of Bolted Plate and Flange Assemblies,” ASME J. Vibr. Acoust., 116(4), pp. 469–473. [CrossRef]
Kim, M., Moon, J., and Wickert, J. A., 2000, “Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures,” ASME J. Vibr. Acoust., 122(1), pp. 62–68. [CrossRef]
Chang, J. Y., and Wickert, J. A., 2000, “Response of Modulated Doublet Modes to Travelling Wave Excitation,” J. Sound Vib., 242(1), pp. 69–83. [CrossRef]
Chang, J. Y., and Wickert, J. A., 2002, “Measurement and Analysis of Modulated Doublet Mode Response in Mock Bladed Disks,” J. Sound Vib., 250(3), pp. 379–400. [CrossRef]
Wu, X. H., and Parker, R. G., 2006, “Vibration of Rings on a General Elastic Foundation,” J. Sound Vib., 295(1–2), pp. 194–213. [CrossRef]
Kim, H., and Shen, I. Y., 2009, “Ground-Based Vibration Response of a Spinning, Cyclic, Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects,” ASME J. Vibr. Acoust., 131(2), p. 021007. [CrossRef]
Kim, H., Khalid, N. T., and Shen, I. Y., 2009, “Mode Evolution of Cyclic Symmetric Rotors Assembled to Flexible Bearings and Housing,” ASME J. Vibr. Acoust., 131(5), p. 051008. [CrossRef]
Wang, S. Y., Xiu, J., Xu, J. Y., Liu, J. P., and Shen, Z. G., 2010, “Prediction and Suppression of Inconsistent Natural Frequency and Mode Coupling of a Cylindrical Ultrasonic Stator,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 224(9), pp. 1853–1861. [CrossRef]
Kumar, A., and Krousgrill, C. M., 2012, “Mode-Splitting and Quasi-Degeneracies in Circular Plate Vibration Problems: The Example of Free Vibrations of the Stator of a Traveling Wave Ultrasonic Motor,” J. Sound Vib., 331(26), pp. 5788–5802. [CrossRef]
Parker, R. G., 2000, “A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration,” J. Sound Vib., 236(4), pp. 561–573. [CrossRef]
Wang, S. Y., Huo, M. N., Zhang, C., Liu, J. P., Song, Y. M., Cao, S. Q., and Yang, Y. H., 2011, “Effect of Mesh Phase on Wave Vibration of Spur Planetary Ring Gear,” Eur. J. Mech. A/Solids, 30(6), pp. 820–827. [CrossRef]
Ouyang, H. J., 2011, “Moving-Load Dynamic Problems: A Tutorial (With a Brief Overview),” Mech. Syst. Signal Process., 25(6), pp. 2039–2060. [CrossRef]
Chen, D. L., Wang, S. Y., Xiu, J., and Liu, J. P., 2011, “Physical Explanation on Rotational Vibration Via Distorted Force Field of Multi-Cyclic Symmetric Systems,” 13th World Congress in Mechanism and Machine Science (IFToMM’11), Guanajuato, Mexico, June 19–25.
Kahraman, A., 1994, “Natural Modes of Planetary Gear Trains,” J. Sound Vib., 173(1), pp. 125–130. [CrossRef]
Nicolet, C., Ruchonnet, N., and Avellan, F., 2006, “One-Dimensional Modeling of Rotor Stator Interaction in Francis Pump-Turbine,” 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, October 17–21.
Dai, J. C., Hu, Y. P., Liu, D. S., and Long, X., 2011, “Modelling and Characteristics Analysis of the Pitch System of Large Scale Wind Turbines,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 225(3), pp. 558–567. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Vibration modes of case I

Grahic Jump Location
Fig. 3

Magnitudes and harmonics of contaminations in case I

Grahic Jump Location
Fig. 4

Vibration modes of case II

Grahic Jump Location
Fig. 5

Magnitudes and harmonics of contaminations in case II

Grahic Jump Location
Fig. 6

Configurations of harmonic magnetic forces

Grahic Jump Location
Fig. 7

Harmonic responses of case I

Grahic Jump Location
Fig. 8

Harmonic responses of case II

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In