Coulombian Model for 3D Analytical Calculation of the Torque Exerted on Cuboidal Permanent Magnets with Arbitrary Oriented Polarizations

Authors

  • Hicham Allag Laboratoire de Génie Electrique de Grenoble, UMR 5269 CNRS/INPG/UJF Institut Polytechnique de Grenoble, Saint Martin d’Hères, 38402, France
  • Jean-Paul Yonnet Laboratoire de Génie Electrique de Grenoble, UMR 5269 CNRS/INPG/UJF Institut Polytechnique de Grenoble, Saint Martin d’Hères, 38402, France
  • Houssem R. E. H. Bouchekara Constantine Electrical Engineering Laboratory, LEC, Department of Electrical Engineering University of Constantine 1, 25000 Constantine, Algeria
  • Mohamed E. H. Latreche Constantine Electrical Engineering Laboratory, LEC, Department of Electrical Engineering University of Constantine 1, 25000 Constantine, Algeria
  • Christophe Rubeck Laboratoire de Génie Electrique de Grenoble, UMR 5269 CNRS/INPG/UJF Institut Polytechnique de Grenoble, Saint Martin d’Hères, 38402, France

Keywords:

Analytical calculation, coulombian approach, force, permanent magnet, torque

Abstract

This paper proposes improved analytical expressions of the torque on cuboidal permanent magnets. Expressions are valid for any relative magnet position and for any polarization direction. The analytical calculation is made by replacing polarizations by distributions of magnetic charges on the magnet poles (coulombian approach). The torque exerted on the second magnet is calculated by Lorentz force formulas for any arbitrary position. The three components of the torque are written with functions based on logarithm and arc-tangent. Results have been verified and validated by comparison with finiteelement calculation. Further, the torque can be obtained with respect to any reference point. Although these equations seem rather complicated, they enable an extremely fast and accurate calculation of the torque exerted between two permanent magnets.

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References

H. Allag and J.-P. Yonnet, “3-D analytical calculation of the torque and force exerted between two cuboidal magnets,” IEEE Trans. Magn., vol. 45, no. 10, pp. 3969-3972, Oct. 2009.

J. L. G. Janssen, J. J. H. Paulides, J. C. Compter, and E. A. Lomonova, “Threedimensional analytical calculation of the torque between permanent magnets in magnetic bearings,” IEEE Trans. Magn., 46, 1748 (2010).

H. Allag, J.-P. Yonnet, and M. E. H. Latreche, “Analytical calculation of the torque exerted between two perpendicularly magnetized magnets,” Journal of Applied Physics, 109, 07E701 (2011).

E. P. Furlani, “Formulas for the force and torque of axial couplings,” IEEE Trans. Magnetics, vol. 29, no. 5, pp. 2295-2301, Sept. 1993.

G. Akoun and J.-P. Yonnet, “3D analytical calculation of the forces exerted between two cuboidal magnets,” IEEE Trans. Magn., vol. MAG-20, no. 5, pp. 1962-1964, Sept. 1984.

J.-P. Yonnet, H. Allag, and M. E. H. Latreche, “2D and 3D analytical calculations of magnet interactions,” in Proc. MmdE Conf., Bucharest, June 15-16, 2008.

H. Allag and J.-P. Yonnet, “3D analytical calculation of interactions between perpendicularly magnetized magnets application to any magnetization direction,” Sensor Lett., vol. 7, no. 3, pp. 486-491, Aug. 2009.

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Published

2021-08-22

How to Cite

[1]
H. . Allag, J.-P. . Yonnet, H. R. E. H. . Bouchekara, M. E. H. . Latreche, and C. . Rubeck, “Coulombian Model for 3D Analytical Calculation of the Torque Exerted on Cuboidal Permanent Magnets with Arbitrary Oriented Polarizations”, ACES Journal, vol. 30, no. 04, pp. 351–356, Aug. 2021.

Issue

2015: Vol 30 Iss 4

Section

General Submission