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Analysis of Cogging Torque in Surface-Mounted Permanent Magnet Machines with Shaped Magnets

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Third Harmonic Utilization in Permanent Magnet Machines

Abstract

The third harmonic can be injected into the Sinusoidal shaped permanent magnets (PM) to improve the average torque in three-phase surface-mounted PM (SPM) machines without deteriorating the torque ripple caused by back-EMFs harmonics. However, the influence of the injected third harmonic on the cogging torque is uncertain. The aim of this chapter is to analytically derive the cogging torque in SPM machines equipped with Sinusoidal shaped (Sine-shaped) and Sinusoidal shaped with third harmonic injected (Sine+3rd-shaped) PMs, which are optimized to obtain sinusoidal and sinusoidal with third harmonic airgap flux density distributions, respectively. It is found that the cogging torque of the SPM machines with Sine-shaped PMs is negligibly small. The Sine+3rd-shaped PM can increase the amplitude of the cogging torque for the specific three-phase SPM machines with the number of slots per pole per phase (spp) equal to 0.25, 0.5 and 1. Finite element analyses are carried out on 6-slot/8-pole (spp = 0.25), 12-slot/8-pole (spp = 0.5), 24-slot/8-pole (spp = 1) and 12-slot/10-pole (spp = 0.4) SPM machines with shaped PMs to verify the analyses. A SPM machine with Sine+3rd-shaped PMs is prototyped and tested for validation.

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References

  1. Z.Q. Zhu, D. Howe, Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors. IEEE Trans. Magn. 28(2), 1371–1374 (1992)

    Article  Google Scholar 

  2. T. Ishikawa, G.R. Slemon, A method of reducing ripple torque in permanent-magnet motors without skewing. IEEE Trans. Magn. 29(2), 2028–2031 (1993)

    Article  Google Scholar 

  3. Z.Q. Zhu, D. Howe, Influence of design parameters on cogging torque in permanent magnet machines. IEEE Trans. Energy Convers. 15(4), 407–412 (2000)

    Article  Google Scholar 

  4. S.M. Hwang, J.B. Eom, Y.H. Jung, D.W. Lee, B.S. Kang, Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors. IEEE Trans. Magn. 37(4), 2806–2809 (2001)

    Article  Google Scholar 

  5. N. Bianchi, S. Bolognani, Design techniques for reducing the cogging torque in surface-mounted PM motors. IEEE Trans. Ind. Appl. 38(5), 1259–1265 (2002)

    Article  Google Scholar 

  6. Y. Yang, X. Wang, R. Zhang, T. Ding, R. Tang, The optimization of pole arc coefficient to reduce cogging torque in surface-mounted permanent magnet motors. IEEE Trans. Magn. 42(4), 1135–1138 (2006)

    Article  Google Scholar 

  7. Y. Pang, Z.Q. Zhu, Z.J. Feng, Cogging torque in cost-effective surface-mounted permanent-magnet machines. IEEE Trans. Magn. 47(9), 2269–2276 (2011)

    Article  Google Scholar 

  8. P. Zheng, J. Zhao, J. Han, J. Wang, Z. Yao, R. Liu, Optimization of the magnetic pole shape of a permanent-magnet synchronous motor. IEEE Trans. Magn. 43(6), 2531–2533 (2007)

    Article  Google Scholar 

  9. Y. Li, J.W. Xing, T.B. Wang, Y.P. Lu, Programmable design of magnet shape for permanent magnet synchronous motors with sinusoidal back EMF waveforms. IEEE Trans. Magn. 44(9), 2163–2167 (2008)

    Article  Google Scholar 

  10. S. Ruangsinchaiwanich, Z.Q. Zhu, D. Howe, Influence of magnet shape on cogging torque and back-emf waveform in permanent magnet machines, in Proceedings of International Conference on Electrical Machines and Systems, , vol. 1 (2005), pp. 284–289

    Google Scholar 

  11. A. Evans, Salient pole shoe shapes of interior permanent magnet synchronous machines, in Proceedings of 19th International Conference on Electrical Machines, Sept 2010, pp. 1–6

    Google Scholar 

  12. Y. Li, J.B. Zou, Y.P. Lu, Optimum design of magnet shape in permanent-magnet synchronous motors. IEEE Trans. Magn. 39(6), 3523–3526 (2003)

    Article  Google Scholar 

  13. K. Wang, Z.Q. Zhu, G. Ombach, Torque enhancement of surface-mounted permanent magnet machine using third-order harmonic. IEEE Trans. Magn. 50(3), 104–113 (2014)

    Article  Google Scholar 

  14. K. Wang, Z.Q. Zhu, G. Ombach, W. Chlebosz, Average torque improvement of interior permanent-magnet machine using 3rd harmonic in rotor shape. IEEE Trans. Ind. Electron. 61, 5047–5057 (2014)

    Article  Google Scholar 

  15. H.D. Lin, D. Wang, D.Z. Liu, J.Q. Chen, Influence of magnet shape on torque behavior in surface-mounted permanent magnet motors, in 17th International Conference on Electrical Machines and Systems, Hangzhou, China (2014), pp. 44–47

    Google Scholar 

  16. C.S. Koh, J.S. Seol, New cogging-torque reduction method for brushless permanent-magnet motors. IEEE Trans. Magn. 39, 3503–3506 (2003)

    Article  Google Scholar 

  17. L. Wu, W. Jin, J. Ni, J. Ying, A cogging torque reduction method for surface mounted permanent magnet motor, in Proceedings of International Conference on Electrical Machines and Systems, Seoul, Korea (2007), pp. 769–773

    Google Scholar 

  18. H. Jin, J.W. Reu, B.W. Kim, G.H. Kang, Vibration reduction of IPM-type BLDC motor using negative third harmonic elimination method of air-gap flux density. IEEE Trans. Ind. Appl. 47(3), 1300–1309 (2010)

    Article  Google Scholar 

  19. L. Zhu, S.Z. Jiang, Z.Q. Zhu, C.C. Chan, Analytical methods for minimizing cogging torque in permanent-magnet machines. IEEE Trans. Magn. 45(4), 2023–2031 (2009)

    Article  Google Scholar 

  20. Z.Q. Zhu, S. Ruangsinchaiwanich, D. Howe, Synthesis of cogging-torque waveform from analysis of a single stator slot. IEEE Trans. Ind. Appl. 42(3), 650–657 (2006)

    Article  Google Scholar 

  21. A.M. EL-Refaie, Fractional-slot concentrated-windings synchronous permanent magnet machines: Opportunities and challenges. IEEE Trans. Ind. Electron. 57(1), 107–121 (2010)

    Google Scholar 

  22. Z.Q. Zhu, A simple method for measuring cogging torque in permanent magnet machines, in Proceedings of IEEE Power Energy Society General Meeting (2009), pp. 1–4

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Kai Wang

  2. Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield, UK

    Zi-Qiang Zhu

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  1. Kai Wang
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  2. Zi-Qiang Zhu
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Correspondence to Kai Wang .

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Wang, K., Zhu, ZQ. (2019). Analysis of Cogging Torque in Surface-Mounted Permanent Magnet Machines with Shaped Magnets. In: Third Harmonic Utilization in Permanent Magnet Machines. Springer, Singapore. https://doi.org/10.1007/978-981-13-0629-7_7

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  • DOI: https://doi.org/10.1007/978-981-13-0629-7_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0628-0

  • Online ISBN: 978-981-13-0629-7

  • eBook Packages: EngineeringEngineering (R0)

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