volume | PIER Journals

Abstract

This paper deals with the magnet pole shape design for the minimization of cogging torque in permanent magnet synchronous machines (PMSM). New shapes of permanent magnet are proposed. The magnet shape is modeled analytically by a set of stacked and well dimensioned layers relatively to the height and opening angle. The final shape of magnet is configured by using three models in view of obtaining lower magnitude of cogging torque. A 2-D exact analytical solution of magnetic ﬁeld distribution taking into account the shape of magnet, the irregular mechanical thickness of air-gap and semi-closed stator slots is established. The influence of motor's parameters such as the number of stator slots per pole and per phase and PM's magnetization on cogging torque is discussed. Analytical results are validated by the static finite-element method (FEM).

1. Boughrara, K., B. Ladghem Chikouche, R. Ibtiouen, D. Zarko, and O. Touhami, "Analytical analysis of slotted air-gap surface mounted permanent-magnet synchronous motor with magnet bars magnetized in shifting direction," IEEE Trans. Magn., Vol. 45, No. 2, 747-758, Feb. 2009.
doi:10.1109/TMAG.2008.2008751 Google Scholar

2. Laskaris, K. I. and A. G. Kladas, "Permanent-magnet shape optimization effects on synchronous motor performance," IEEE Trans. Ind. Elect., Vol. 58, No. 9, 3776-3783, Sep. 2011.
doi:10.1109/TIE.2010.2093481 Google Scholar

3. Ashabani, M., Y. Abdel-Rady, and I. Mohamed, "Multiobjective shape optimization of segmented pole permanent-magnet synchronous machines with improved torque characteristic," IEEE Trans. Magn., Vol. 47, No. 4, 795-804, Apr. 2011.
doi:10.1109/TMAG.2010.2104327 Google Scholar

4. Pang, Y., Z. Q. Zhu, and Z. J. Feng, "Cogging torque in cost-effective surface-mounted permanentmagnet machines," IEEE Trans. Magn., Vol. 47, No. 9, 2269-2276, Sep. 2011.
doi:10.1109/TMAG.2011.2147326 Google Scholar

5. Islam, R., I. Husain, A. Fardoun, and K. McLaughlin, "Permanent-magnet synchronous motor magnet designs with skewing for torque ripple and cogging torque reduction," IEEE Trans. Ind. Appl., Vol. 45, No. 1, 152-160, Jan./Feb. 2009.
doi:10.1109/TIA.2008.2009653 Google Scholar

6. Shin, P. S., S. H. Woo, and C. S. Koh, "An optimal design of large scale permanent magnet pole shape using adaptive response surface method with latin hypercube sampling strategy," IEEE Trans. Magn., Vol. 45, No. 3, 1214-1217, Mar. 2009.
doi:10.1109/TMAG.2009.2012565 Google Scholar

7. Chabchoub, M., I. B. Salah, G. Krebs, R. Neji, and C. Marchand, "PMSMcogging torque reduction: Comparison between different shapes of magnet," First International Conference of Renewable Energies and Vehicular Technology, 206-211, 2012.
doi:10.1109/REVET.2012.6195272 Google Scholar

8. Oh, S., S. Min, and J. Hong, "Air gap flux density waveform design of surface-mounted permanent magnet motor considering magnet shape and magnetization direction," IEEE Trans. Magn., Vol. 49, No. 5, 2393-2396, May 2013.
doi:10.1109/TMAG.2013.2246142 Google Scholar

9. Guemes, J. A., A. M. Iraolagoitia, J. I. Del Hoyo, and P. Fernandez, "Torque analysis in permanent-magnet synchronous motors: A comparative study," IEEE Trans. Energy Convers., Vol. 26, No. 1, 55-63, Mar. 2011.
doi:10.1109/TEC.2010.2053374 Google Scholar

10. Sung, S. J., S. J. Park, and G. H. Jang, "Cogging torque of brushless DC motors due to the interaction between the uneven magnetization of a permanent magnet and teeth curvature," IEEE Trans. Magn., Vol. 47, No. 7, 1923-1928, Jul. 2011.
doi:10.1109/TMAG.2011.2120599 Google Scholar

11. Tudorache, T. and I. Trifu, "Permanent-magnet synchronous machine cogging torque reduction using a hybrid model," IEEE Trans. Magn., Vol. 48, No. 10, 2627-2632, Oct. 2012.
doi:10.1109/TMAG.2012.2198485 Google Scholar

12. Jiang, X., J. Xing, Y. Li, and Y. Lu, "Theoretical and simulation analysis of influences of stator tooth width on cogging torque of BLDC motors," IEEE Trans. Magn., Vol. 45, No. 10, 4601-4604, Oct. 2009.
doi:10.1109/TMAG.2009.2022639 Google Scholar

13. Boughrara, K., T. Lubin, R. Ibtiouen, and M. N. Benallal, "Analytical calculation of parallel double excitation and spoke-type permanent magnet motors; simplified versus exact model," Progress In Electromagnetics Research B, Vol. 47, 145-178, 2013.
doi:10.2528/PIERB12111306 Google Scholar

14. Lubin, T., S. Mezani, and A. Rezzoug, "Improved analytical model for surface mounted PM motors considering slotting effects and armature reaction," Progress In Electromagnetics Research B, Vol. 25, 293-314, 2010.
doi:10.2528/PIERB10081209 Google Scholar

15. Dubas, F. and C. Espanet, "Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect: No-load vector potential and flux density calculation," IEEE Trans. Magn., Vol. 45, No. 5, 2097-2109, May 2009.
doi:10.1109/TMAG.2009.2013245 Google Scholar

16. Wu, L. J., Z. Q. Zhu, D. A. Staton, M. Popescud, and D. Hawkins, "Comparison of analytical models of cogging torque in surface-mounted PM machines," IEEE Trans. Ind. Electron., Vol. 59, No. 6, 2414-2425, Jun. 2012.
doi:10.1109/TIE.2011.2143379 Google Scholar

17. Zarko, D., D. Ban, and T. A. Lipo, "Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance," IEEE Trans. Magn., Vol. 42, No. 7, 1828-1837, Jul. 2006.
doi:10.1109/TMAG.2006.874594 Google Scholar

18. Tavana, N. R. and A. Shoulaie, "Analysis and design of magnetic pole shape in linear permanent-magnet machine," IEEE Trans. Magn., Vol. 46, No. 4, 1000-1006, Apr. 2010.
doi:10.1109/TMAG.2009.2037951 Google Scholar

19. Jeffrey, A., Advanced Engineering Mathematics, University of Newcastle-upon-Tyne, Harcourt/Academic Press, 2002.

20. Meeker, D. C., , Finite Element Method Magnetics, Version 4.2, Apr. 2009 Build, http://www.femm.info. Google Scholar

21. Li, Y., J. Xing, T.Wang, and Y. Lu, "Programmable design of magnet shape for permanent-magnet synchronous motors with sinusoidal back EMF waveforms," IEEE Trans. Magn., Vol. 44, No. 9, 2163-2167, Sep. 2008.
doi:10.1109/TMAG.2008.2000750 Google Scholar

22. Shah, S. Q. A., T. A. Lipo, and B.-I. Kwon, "Modeling of novel permanent magnet pole shape SPM motor for reducing torque pulsation," IEEE Trans. Magn., Vol. 48, No. 11, 4626-4629, Nov. 2012.
doi:10.1109/TMAG.2012.2197188 Google Scholar

23. Jang, S.-M., H.-I. Park, J.-Y. Choi, K.-J. Ko, and S.-H. Lee, "Magnet pole shape design of permanent magnet machine for minimization of torque ripple based on electromagnetic field theory," IEEE Trans. Magn., Vol. 47, No. 10, 3586-3589, Oct. 2011.
doi:10.1109/TMAG.2011.2151846 Google Scholar

24. Chaithongsuk, S., B. Nahid-Mobarakeh, N. Takorabet, J. P. Caron, and F. Meibody-Tabar, "Optimal design of PM motors to achieve efficient flux weakening strategy in variable speed control applications," XIX International Conference on Electrical Machines — ICEM, 1-6, Rome, 2010. Google Scholar

25. Chu, W. Q. and Z. Q. Zhu, "Investigation of torque ripples in permanent magnet synchronous machines with skewing," IEEE Trans. Energy Convers., Vol. 49, No. 3, 1211-1220, Mar. 2013. Google Scholar

26. Shen, Y. and Z. Q. Zhu, "Analysis of electromagnetic performance of Halbach PM brushless machines having mixed grade and unequal height of magnets," IEEE Trans. Energy Convers., Vol. 49, No. 4, 1461-1469, Apr. 2013. Google Scholar

Dr. Ladghem-Chikouche Brahim

Dr. Kamel Boughrara

Prof. Rachid Ibtiouen