volume | PIER Journals

Abstract

In this paper, the computation of forces and torques mutually applied between a helical toroidal magnet and a magnet shaped like an angular plane sector is illustrated. The evaluation considers the magnetostatic field hypothesis. The main aim of this study is to furnish a tool for performing fast and accurate evaluation of forces and torques based on the method of the magnetic charges with reference to helical toroidal magnetic systems. The particular geometry of the case study concerns the development of unconventional configurations of electrical machines. These configurations should reduce the magnetic flux changing during the machine operation. A small change of the magnetic flux reduces all the losses associated to the flux variation. The illustrated model for the computation of forces and moments also represents a starting point for a reliable analytical numerical evaluation of the external/internal actions applied to parts of other kinds of helical toroidal systems as stellarator and similar ones.

1. Vanoost, D., H. De Gersem, J. Peuteman, G. Gielen, and D. Pissoort, "Nonlinear magnetostatic finite element formulation for models with radial symmetry," IEEE Transactions on Magnetics, Vol. 50, No. 50, Febraury 2014. Google Scholar

2. Stumberger, B., G. Stumberger, D. Dolinar, A. Hamler, and M. Trlep, "Evaluation of saturationand ˇ cross-magnetization effects in interior permanent-magnet synchronous motor," IEEE Transactions on Industry Applications, Vol. 39, No. 5, 1264-1271, September/October 2003.
doi:10.1109/TIA.2003.816538 Google Scholar

3. Stumberger, B., G. Stumberger, and D. Dolinar, "Analysis of cross-saturation effects in a ˇ linear synchronous reluctance motor performed by finite elements method and measurements," Proceedings of 12th International Conference on Power Electronics and Motion Control, EPE-PEMC 2006, IEEE Conferences Publications, 2006. Google Scholar

4. Ruoho, S. and A. Arkkio, "Partial demagnetization of permanent magnets in electrical machines causedby an inclined field," IEEE Transactions on Magnetics, Vol. 44, No. 7, 1773-1778, July 2008.
doi:10.1109/TMAG.2008.921951 Google Scholar

5. Fratila, R., A. Benabou, A. Tounzi, and J. C. Mipo, "Nonlinear modeling of magnetization loss in permanent magnets," IEEE Transactions on Magnetics, Vol. 48, No. 11, 2957-2960, November 2012.
doi:10.1109/TMAG.2012.2193878 Google Scholar

6. Muscia, R., "Symmetry of magnetostatic fields generated by toroidal helicoidal magnets," IEEE Transactions on Magnetics, Vol. 51, No. 10, 7002614, October 2015. Google Scholar

7. Brouver, L., S. Caspi, D. Robin, and W. Wan, "3D toroidal field multipoles for curved accelerator magnets," Proceedings of PAC 2013, 907-909, Pasadena, CA, USA, 2013. Google Scholar

8. He, Y., Z. Yang, W. Ba, X. Zhang, G. Zhuang, X. Hu, Y. Pan, and Z. Liu, "Calculation of the poloidal magnetic field configuration for the J-TEXT tokamak," IEEE Transactions on Applied Superconductivity, Vol. 20, No. 3, 1840-1843, 2010.
doi:10.1109/TASC.2010.2043520 Google Scholar

9. Maviglia, F., R. Albanese, M. De Magistris, P. J. Lomas, S. Minucci, F. G. Rimini, A. C. C. Sips, and P. C. De Vries, "Electromagnetic models of plasma breakdown in the JET tokamak," IEEE Transactions on Magnetics, Vol. 50, No. 2, Febraury 2014.
doi:10.1109/TMAG.2013.2282351 Google Scholar

10. Jin, C. G., T. Yu, Y. Zhao, Y. Bo, C. Ye, J. S. Hu, L. J. Zhuge, S. B. Ge, X. M. Wu, H. T. Ji, and J. G. Li, "Helicon plasma discarge in a toroidal magnetic field of the tokamak," IEEE Transactions on Plasma Science, Vol. 39, No. 11, 3103-3107, November 2011.
doi:10.1109/TPS.2011.2161344 Google Scholar

11. Albanese, R., G. Artaserse, F. Maviglia, F. Piccolo, and F. Sartori, "Identification of vertical instabilities in the JET tokamak," IEEE Transactions on Magnetics, Vol. 44, No. 6, June 2008. Google Scholar

12. Albanese, R., M. De Magistris, R. Fresa, F. Maviglia, and S. Minucci, "Numerical formulations for accurate magnetic field flow tracing in fusion tokamaks," Proceedings of the 9th International Conference on Computation in Electromagnetics (CEM 2014), 2014. Google Scholar

13. Beidler, D. C., E. Harmeyer, F. Herrnegger, J. Kisslinger, Y. Igitkhanov, and H. Wobig, "Stellarator fusion reactors — An overview," Proceedings of Toki Conference ITC12, December 2001. Google Scholar

14. Probert, P., "High-performance interpolation of stellarator magnetic fields," IEEE Transactions on Plasma Science, Vol. 39, No. 4, 1051-1054, April 2011.
doi:10.1109/TPS.2011.2105890 Google Scholar

15. Neilson, G. H., D. A. Gates, P. J., Heitzenroeder, S. C. Prager, T. Stevenson, P. Titus, M. D. Williams, and M. C. Zarnstorf, "Facilities for Quasi-Axisymmetric Stellarator research," Proceedings of 25th Symposium on Fusion Engineering (SOFE), 2013 IEEE Conferences Publications, 2013. Google Scholar

16. Imagawa, S., A. Sagara, and Y. Kozaki, "Conceptual design of magnets with CIC conductors for LHD-type reactors FFHR2m," Plasma and Fusion Research, Vol. 3, S1050, 1-5, 2008. Google Scholar

17. Rummel, T., K. Riβe, G. Ehrke, K. Rummel, A. John, T. M¨onnich, K. P. Buscer, W. H. Fietz, R. Heller, O. Neubauer, and A. Panin, "The superconducting magnet system of the stellarator wendlstein 7-X," IEEE Transactions on Plasma Science, Vol. 40, No. 3, 769-776, March 2012.
doi:10.1109/TPS.2012.2184774 Google Scholar

18. Clark, A. W., F. A. Volpe, and D. A. Spong, "Proto-circus tilted-coil tokamak-stellarator hybrid," Proceedings of 25th Symposium on Fusion Engineering (SOFE), 2013 IEEE Conferences Publications, 2013. Google Scholar

19. Dal Maso, A., Screws with curvilinear axis: A CAD analysis of coupling problems, Thesis, Supervisor: R. Muscia, Department of Engineering and Architecture, University of Trieste, Italy, 2014.

20. Chen, M., K. T. Chau, C. H. T. Lee, and C. Liu, "Design and analysis of a new axial-field magnetic variable gear using pole-changing permanent magnets," Progress In Electromagnetics Research, Vol. 153, 23-32, 2015.
doi:10.2528/PIER15072701 Google Scholar

21. Boutora, Y., N. Takorabet, and R. Ibtiouen, "Analytical model on real geometries of magnet bars of surface permanent magnet slotless machine," Progress In Electromagnetics Research B, Vol. 66, 31-47, 2016.
doi:10.2528/PIERB15121503 Google Scholar

22. Sun, X., S. Luo, L. Chen, R. Zhao, and Z. Yang, "Suspension force modelling and electromagnetic characteristics analysis of an interior bearingless permanent magnet synchronous motor," Progress In Electromagnetics Research B, Vol. 69, 31-45, 2016.
doi:10.2528/PIERB16051908 Google Scholar

23. Brown, Jr., W. F.c, "Electric and magnetic forces: A direct calculation I," Am. J. Phys., Vol. 19, 290-304, 1951.
doi:10.1119/1.1932805 Google Scholar

24. Brown, Jr., W. F., "Electric and magnetic forces: A direct calculation II," Am. J. Phys., Vol. 19, 333-350, 1951.
doi:10.1119/1.1932823 Google Scholar

25. Muscia, R., "Equivalent magnetic charge in helicoidal magnets," J. Appl. Phys., Vol. 104, 103916, 2008.
doi:10.1063/1.2975154 Google Scholar

26. Muscia, R., "Computation of the magnetic field generated by helical toroidal permanent magnets," Electromagnetics, Vol. 32, 8-30, 2012.
doi:10.1080/02726343.2012.633876 Google Scholar

27. Furlani, E. P., Permanent Magnet and Electromechanical Devices, Material, Analysis, and Applications, 136, Eq. (3.118), Academic Press, 2001.

28. Furlani, E. P., "A formula for the levitation force between magnetic disks," IEEE Transactions on Magnetics, Vol. 29, No. 6, 4165-4169, November 1993.
doi:10.1109/20.280867 Google Scholar

29. Furlani, E. P., "Formulas for the force and torque of axial coupling," IEEE Transactions on Magnetics, Vol. 29, No. 5, 2295-2301, September 1993.
doi:10.1109/20.231636 Google Scholar

30. Furlani, E. P., R. Wang, and H. Kusnadi, "A three-dimensional model for computing the torque of radial couplings," IEEE Transactions on Magnetics, Vol. 31, No. 5, 2522-2526, September 1995.
doi:10.1109/20.406554 Google Scholar

31. Mathematica 10.3, [Online] Available: http://www.wolfram.com/mathematica.

Dr. Roberto Muscia