Vol. 91
Latest Volume
All Volumes
PIERC 148 [2024] PIERC 147 [2024] PIERC 146 [2024] PIERC 145 [2024] PIERC 144 [2024] PIERC 143 [2024] PIERC 142 [2024] PIERC 141 [2024] PIERC 140 [2024] PIERC 139 [2024] PIERC 138 [2023] PIERC 137 [2023] PIERC 136 [2023] PIERC 135 [2023] PIERC 134 [2023] PIERC 133 [2023] PIERC 132 [2023] PIERC 131 [2023] PIERC 130 [2023] PIERC 129 [2023] PIERC 128 [2023] PIERC 127 [2022] PIERC 126 [2022] PIERC 125 [2022] PIERC 124 [2022] PIERC 123 [2022] PIERC 122 [2022] PIERC 121 [2022] PIERC 120 [2022] PIERC 119 [2022] PIERC 118 [2022] PIERC 117 [2021] PIERC 116 [2021] PIERC 115 [2021] PIERC 114 [2021] PIERC 113 [2021] PIERC 112 [2021] PIERC 111 [2021] PIERC 110 [2021] PIERC 109 [2021] PIERC 108 [2021] PIERC 107 [2021] PIERC 106 [2020] PIERC 105 [2020] PIERC 104 [2020] PIERC 103 [2020] PIERC 102 [2020] PIERC 101 [2020] PIERC 100 [2020] PIERC 99 [2020] PIERC 98 [2020] PIERC 97 [2019] PIERC 96 [2019] PIERC 95 [2019] PIERC 94 [2019] PIERC 93 [2019] PIERC 92 [2019] PIERC 91 [2019] PIERC 90 [2019] PIERC 89 [2019] PIERC 88 [2018] PIERC 87 [2018] PIERC 86 [2018] PIERC 85 [2018] PIERC 84 [2018] PIERC 83 [2018] PIERC 82 [2018] PIERC 81 [2018] PIERC 80 [2018] PIERC 79 [2017] PIERC 78 [2017] PIERC 77 [2017] PIERC 76 [2017] PIERC 75 [2017] PIERC 74 [2017] PIERC 73 [2017] PIERC 72 [2017] PIERC 71 [2017] PIERC 70 [2016] PIERC 69 [2016] PIERC 68 [2016] PIERC 67 [2016] PIERC 66 [2016] PIERC 65 [2016] PIERC 64 [2016] PIERC 63 [2016] PIERC 62 [2016] PIERC 61 [2016] PIERC 60 [2015] PIERC 59 [2015] PIERC 58 [2015] PIERC 57 [2015] PIERC 56 [2015] PIERC 55 [2014] PIERC 54 [2014] PIERC 53 [2014] PIERC 52 [2014] PIERC 51 [2014] PIERC 50 [2014] PIERC 49 [2014] PIERC 48 [2014] PIERC 47 [2014] PIERC 46 [2014] PIERC 45 [2013] PIERC 44 [2013] PIERC 43 [2013] PIERC 42 [2013] PIERC 41 [2013] PIERC 40 [2013] PIERC 39 [2013] PIERC 38 [2013] PIERC 37 [2013] PIERC 36 [2013] PIERC 35 [2013] PIERC 34 [2013] PIERC 33 [2012] PIERC 32 [2012] PIERC 31 [2012] PIERC 30 [2012] PIERC 29 [2012] PIERC 28 [2012] PIERC 27 [2012] PIERC 26 [2012] PIERC 25 [2012] PIERC 24 [2011] PIERC 23 [2011] PIERC 22 [2011] PIERC 21 [2011] PIERC 20 [2011] PIERC 19 [2011] PIERC 18 [2011] PIERC 17 [2010] PIERC 16 [2010] PIERC 15 [2010] PIERC 14 [2010] PIERC 13 [2010] PIERC 12 [2010] PIERC 11 [2009] PIERC 10 [2009] PIERC 9 [2009] PIERC 8 [2009] PIERC 7 [2009] PIERC 6 [2009] PIERC 5 [2008] PIERC 4 [2008] PIERC 3 [2008] PIERC 2 [2008] PIERC 1 [2008]
2019-04-02
A New Approximation for Calculating the Attraction Force in Cylindrical Permanent Magnets Arrays and Cylindrical Linear Single-Axis-Actuator
By
Progress In Electromagnetics Research C, Vol. 91, 213-225, 2019
Abstract
New accurate approximation is proposed using integral expressions for evaluating the magnetic force between cylindrical permanent magnet arrays. The magnetic field distribution is calculated analytically by using Coulombian model. In this paper, every cylindrical magnet is divided into elementary cuboidal magnets.The accuracy can be controlled by regulating the value of elementary cuboidal permanent magnets ``N''. The approximation can also be used to calculate the force interaction in the cylindrical linear single-axis-actuator. We confirm the validity of magnetic force calculation by comparing it with other methods and measurements. The calculation results are in very good agreement with measured values, which indicates the feasibility of our approximation.
Citation
Naamane Mohdeb, Hicham Allag, and Tarik Hacib, "A New Approximation for Calculating the Attraction Force in Cylindrical Permanent Magnets Arrays and Cylindrical Linear Single-Axis-Actuator," Progress In Electromagnetics Research C, Vol. 91, 213-225, 2019.
doi:10.2528/PIERC19010804
References

1. Zangwill, A., Modern Electrodynamics, Cambridge University Press, 2013.

2. Reitz, J. R., F. J. Milford, and R. W. Christy, Foundations of Electromagnetic, Addison-Wesley, Wilmington, 1996.

3. Griffiths, D. J., Introduction to Electrodynamics, Pearson, Harlow, 2014.

4. Lemarquand, V. and G. Lemarquand, "Passive permanent magnet bearings for rotating shaft: Analytical calculation," Magnetic Bearings, Theory and Applications, 85-116, Sciyo Published book, October 2010.

5. Akoun, G. and J. P. Yonnet, "3D analytical calculation of the forces exerted between two cuboidal magnets," IEEE Transactions on Magnetics, Vol. 20, No. 5, 1962-1964, 1984.
doi:10.1109/TMAG.1984.1063554

6. Vokoun, D., M. Beleggia, L. Heller, and P. Sittner, "Magnetostatic interactions and forces between cylindrical permanent magnets," Journal of Magnetism and Magnetic Materials, Vol. 321, No. 22, 3758-3763, November 2009.
doi:10.1016/j.jmmm.2009.07.030

7. Vokoun, D., G. Tomassetti, M. Beleggia, and I. Stachiv, "Magnetic forces between arrays of cylindrical permanent magnets," Journal of Magnetism and Magnetic Materials, Vol. 323, No. 1, 55-60, January 2011.
doi:10.1016/j.jmmm.2010.08.029

8. Vokoun, D. and M. Beleggia, "Forces between arrays of permanent magnets of basic geometric shapes," Journal of Magnetism and Magnetic Materials, Vol. 350, 174-178, January 2014.
doi:10.1016/j.jmmm.2013.09.023

9. Ravaud, R., G. Lemarquand, S. Babic, V. Lemarquand, and C. Akeyel, "Cylindrical magnets and coils: Fields, forces and inductances," IEEE Transactions on Magnetics, Vol. 46, 3585-3590, 2010.
doi:10.1109/TMAG.2010.2049026

10. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Force and stiffness of passive magnetic bearings using permanent magnets. Part 1: Axial magnetization," IEEE Transactions on Magnetics, Vol. 45, 2996-3002, 2009.
doi:10.1109/TMAG.2009.2016088

11. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Force and stiffness of passive magnetic bearings using permanent magnets. Part 2: Radial magnetization," IEEE Transactions on Magnetics, Vol. 45, 3334-3342, 2009.
doi:10.1109/TMAG.2009.2025315

12. MacLatchy, C. S., P. Backman, and L. Bogan, "A quantitative magnetic braking experiment," American Journal of Physics, Vol. 61, No. 12, 1096-1101, 1993.
doi:10.1119/1.17356

13. Hossein Partovi, M. and E. J. Morris, "Eddy current damping of a magnet moving through a pipe," Canadian Journal of Physics, Vol. 84, 253-274, 2006.
doi:10.1139/p06-065

14. Agashe, J. S. and D. P. Arnold, "Analytical force calculations and scaling effects for cylindrical and cuboidal micro-magnets," Intermag. Conf., San Diego, CA, May 2006.

15. Furlani, E. P., S. Reznik, and W. Jansen, "A three-dimensional field solution for bipolar cylinders," IEEE Transactions on Magnetics, Vol. 30, No. 5, 2916-2919, IEEE, September 1994.
doi:10.1109/20.312547

16. Furlani, E. P., "Analytical analysis of magnetically coupled multipole cylinders," Journal of Physics D: Applied Physics, Vol. 33, 28-33, 2000.
doi:10.1088/0022-3727/33/1/305

17. Furlani, E. P., S. Reznik, and A. Kroll, "Journal of Physics D: Applied Physics," IEEE Transactions on Magnetics, Vol. 31, No. 1, 844-851, 1995.
doi:10.1109/20.364587

18. Ravaud, R. G., V. Lemarquand, and C. Depollier, "Analytical calculation of the magnetic field created by permanent-magnet rings," IEEE Transactions on Magnetics, Vol. 44, No. 8, 1982-1989, August 2008.
doi:10.1109/TMAG.2008.923096

19. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Discussion about the analytical calculation of the magnetic field created by permanent magnets," Progress In Electromagnetics Research B, Vol. 11, 281-297, 2009.
doi:10.2528/PIERB08112102

20. Rakotoarison, H., J. Yonnet, and B. Delinchant, "Using Coulombian approach for modelling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Transactions on Magnetics, Vol. 43, 1261-1264, April 2007.

21. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Force and stiffness of passive magnetic bearings using permanent magnets. Part 1: Axial Magnetization," IEEE Transactions on Magnetics, Vol. 45, 2996-3002, 2009.
doi:10.1109/TMAG.2009.2016088

22. Robertson, W., B. Cazzolato, and A. Zander, "A simplified force equation for coaxial cylindrical magnets and thin coils," IEEE Transactions on Magnetics, Vol. 47, 2045-2049, 2011.
doi:10.1109/TMAG.2011.2129524

23. Rovers, J., J. Jansen, J. Compter, and E. Lomonova, "Analysis method of the dynamic force and torque distribution in the magnet array of a commutated magnetically levitated planar actuator," IEEE Transactions on Industrial Electronics, Vol. 59, No. 5, 2157-2166, May 2012.
doi:10.1109/TIE.2011.2146222

24. Allag, H., J.-P. Yonnet, M. Fassenet, and M. E. H. Latrech, "3D analytical calculation of interactions between perpendicularly magnetized magnets — Application to any magnetization direction," Sensors Letters, Vol. 7, No. 3, 1-6, June 2009.
doi:10.1166/sl.2009.1094

25. Allag, H. and J.-P. Yonnet, "3-D analytical calculation of the torque and force exerted between two cuboidal magnets," IEEE Transactions on Magnetics, Vol. 45, No. 10, 3969-3972, October 2009.
doi:10.1109/TMAG.2009.2025047

26. Yonnet, J. P., H. Allag, and M. E. H. Latrech, "2D and 3D analytical calculations of magnet interactions," Proc. MmdE Conf., Bucharest, June 15–16, 2008.

27. Xu, F., X. Xu, Z. Li, and L. Chu, "Numerical calculation of the magnetic field and force in cylindrical single-axis," IEEE Transactions on Magnetics, Vol. 50, 1-6, 2014.
doi:10.1109/TMAG.2014.2329456

28. Wang, Z. and Y. Ren, "Magnetic force and torque calculation between circular coils with nonparallel axes," IEEE Transactions on Applied Superconductivity, Vol. 24, No. 4, 4901505, 2014.