volume | PIER Journals

Abstract

The magnetic field distribution of an axially magnetised cylinder with elliptical profile is analytically modelled and analysed in this paper. An accurate and fast-computed semi-analytical model is developed, based on the charge model and geometrical analysis, to compute the three components of the magnetic field generated by this elliptical cylinder in three dimensional space. The accuracy of the model is verified using Finite Element Analysis. The analytical expressions are efficient for calculating the implementation of the magnetic field, taking less than one millisecond to execute on a modern PC. Using the fast-computed analytical model, the distribution of the magnetic field of an axially magnetised cylinder with different elliptical profiles is studied and compared with that of a circular cylinder. The variations in magnetic field strength of axial, azimuthal and radial components can be used in novel sensing applications. The derived analytical model can be extended to calculate the magnetic field of arc-shaped elliptical and circular cylinders with axial magnetization, which can be used in Halbach arrangements.

1. Wu, S.-T., J.-Y. Chen, and S.-H. Wu, "A rotary encoder with an eccentrically mounted ring magnet," IEEE Transactions on Instrumentation and Measurement, Vol. 63, 1907, 2014.
doi:10.1109/TIM.2014.2302243

2. Coey, J. M. D., Magnetism and Magnetic Materials, Cambridge University Press, 2009.

3. Furlani, E. P., Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications, Academic Press, 2001.

4. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Analytical calculation of the magnetic field created by permanent-magnet rings," IEEE Transactions on Magnetics, Vol. 44, 1982, 2008.
doi:10.1109/TMAG.2008.923096

5. Xu, X. N., D. W. Lu, G. Q. Yuan, Y. S. Han, and X. Jin, "Studies of strong magnetic field produced by permanent magnet array for magnetic refrigeration," Journal of Applied Physics, Vol. 95, 6307, 2004.

6. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "The three exact components of the magnetic field created by a radially magnetized tile permanent magnet," Progress In Electromagnetics Research, Vol. 88, 307-319, 2008.
doi:10.2528/PIER08112708

7. Jian, L. and K. T. Chau, "Analytical calculation of magnetic field distribution in coaxial magnetic gears," Progress In Electromagnetics Research, Vol. 92, 1-16, 2009.
doi:10.2528/PIER09032301

8. Yonnet, J.-P., S. Hemmerlin, E. Rulliere, and G. Lemarquand, "Analytical calculation of permanent magnet couplings," IEEE Transactions on Magnetics, Vol. 29, 2932, 1993.
doi:10.1109/20.280913

9. McClurg, G. O., "Magnetic field distributions for a sphere and for an ellipsoid," American Journal of Physics, Vol. 24, 496, 1956.
doi:10.1119/1.1934288

10. Rakotoarison, H. L., J. P. Yonnet, and B. Delinchant, "Using Coulombian approach for modeling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Transactions on Magnetics, Vol. 43, 1261, 2007.
doi:10.1109/TMAG.2007.892316

11. Nguyen, V. T. and T.-F. Lu, "Analytical expression of the magnetic field created by a permanent magnet with diametrical magnetization," Progress In Electromagnetics Research C, Vol. 87, 163, 2018.
doi:10.2528/PIERC18073001

12. Ravaud, R. and G. Lemarquand, "Magnetic field produced by a parallelepipedic magnet of various and uniform polarization," Progress In Electromagnetics Research, Vol. 98, 207-219, 2009.
doi:10.2528/PIER09091704

13. Nguyen, V. T. and T.-F. Lu, "Modelling of magnetic field distributions of elliptical cylinder permanent magnets with diametrical magnetization," Journal of Magnetism and Magnetic Materials, Vol. 491, 2019.
doi:10.1016/j.jmmm.2019.165569

14. Kim, W., M. Kim, and Y. Y. Kim, "Polarization of a permanent magnet to yield specific magnetic field Distribution," Journal of Applied Physics, Vol. 104, 064915-1, 2008.

15. Acevedo, M. T. M., V. D. D. Zhabon, and O. Otero, "Analytical study of the magnetic field generated by multipolar magnetic configuration," Journal of Physics: Conference Series, Vol. 687, 1, 2016.
doi:10.1088/1742-6596/687/1/012059

16. Karttenen, H., P. Kroger, H. Oja, M. Poutanen, and K. J. Donner, Fundamental Astronomy, 5th Ed., 507, Springer, 2007.
doi:10.1007/978-3-540-34144-4

17. Hideo, K., The Design, Manufacture and Application of Non-circular Gears, 1st Ed., Tokyo, Nikkan Industrial Press, 2001.

18. Bair, B. W., "Tooth profile generation and analysis of crowned elliptical gears," ASME Journal of Mechanical Design, Vol. 131, 0745031, 2009.
doi:10.1115/1.3125884

19. Chen, C. F. and C. B. Tsay, "Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth," Journal of Materials Processing Technology, Vol. 148, 226, 2004.
doi:10.1016/j.jmatprotec.2003.07.011

20. Ciarrocchi, M., V. D. Miccoli, M. Alecci, A. Sotgiu, and A. Galante, "Design of an elliptical permanent magnet for surface magnetic resonance imaging," Measurement Science and Technology, Vol. 20, 1-4, 2008.

21. Filsoufi, F., R. S. Farivar, L. Aklog, C. A. Anderson, R. H. Chen, S. Lichtenstein, J. Zhang, and D. H. Adams, "Automated distal coronary bypass with a novel magnetic coupler (MVP system)," The Journal of Thoracic and Cardiovascular Surgery, Vol. 127, 185, 2004.
doi:10.1016/j.jtcvs.2003.04.005

22. Takazakura, T., T. Morita, and T. Sugiura, "Dynamical behaviour of noncontact driving cam mechanism using permanent magnets," International Journal of Applied Electromagnetics and Mechanics, Vol. 52, 169, 2016.
doi:10.3233/JAE-162036

23. Caciagli, A., R. J. Baars, A. P. Philipse, and B. W. M. Kuipers, "Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization," Journal of Magnetism and Magnetic Materials, Vol. 456, 423-432, 2018.
doi:10.1016/j.jmmm.2018.02.003

24. Strubecker, K., Vorlesungen¨uber Darstellende Geometrie, 26, Gottingen, Vandenhoeck & Ruprecht, 1967.

25. Bjork, R., "The ideal dimensions of a Halbach cylinder of finite length," Journal of Applied Physics, Vol. 109, 013915-1-6, 2011.
doi:10.1063/1.3525646

Dr. Van Tai Nguyen

Dr. Tien-Fu Lu

Dr. William Robertson

Dr. Paul Grimshaw