Development of an Analytical Method to Predict the Behaviour of the Magnetic Field in PM Linear Motors with Halbach Array

Marilia A Silveira, Leandro D Marques, Aly F Flores-Fiilho, Felipe Treviso


This paper describes the application of the method of separation of variables and the use of Fourier series for solving the Laplace´s and Poisson´s equations on the study and analysis of the magnetic field produced in a linear motor with Halbach array. Equations for predicting the 2D magnetic flux density distribution produced in the air gap were developed. The model was validated by means of finite element analysis and by measurements carried on a prototype of the linear motor. Theoretical results helped understand the behaviour of the magnetic flux density in the air gap and to obtain the values of the static propulsion force and normal force in such machine.


Analytical model, Fourier series, Halbach array, Laplace´s and Poisson´s equations, PM linear motor.

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Jean Baptiste Joseph Fourier, Théorie Analytique de la Chaleur. Paris: F. Didot, 1822.

D. L. Trumper, M. E. Williams, T. H. Nguyen, "Magnet arrays for synchronous machines,`` Proc. IEEE IAS 28th Annu. Meet., pp. 9-18, 1993.

K. J.Meessen,, B. L. J. Gysen,; J. J. H. Paulides, H.; E. A. Lomonova, "Halbach permanent magnet shape selection for slotless tubular actuators,' IEEE Transaction on Magnetics, vol. 44, n. 11, pp. ,Nov. 2008.

J. R. Melcher, Continuum Electromechanics. Cambridge, MS: MIT Press, 1981.

A. F.Flores Filho, A. A.Susin , M. A. da Silveira, "An Analytical Method to Predict the Static Performance of a Planar Actuator,`` IEEE Transaction on Magnets, vol. 39, pp. 3364-3366, Sep 2003.

K. J. Binns, P. J. Lawrenson and C. W. Trowbridge, Electric and Magnetic Fields. West Sussex: John Wiley & Sons, 1992.

W. J. Kim, High-Precision Planar Magnetic Levitation. Ph.D. Thesis, Massachusetts Institute of Techonology, Cambridge, MS, 1997.

M. G. Lee, S. Q Lee, D.-G. Gweon, "Analysis of Halbach magnet array and its application to linear motor,`` Mechatronics, vol. 10, pp. 115-128, Feb 2004.

H. Allag, J-P. Yonnet, M. Latreche, "3D analytical calculation of forces between linear Halbach-type permanent-magnet arrays", Proc. 8th Int. Symp. Adv. Electromech. Motion Syst. Electric Drives Joint Symp. (ELECTROMOTION), pp. 1-6, 2009.

. F.Flores Filho, M. A. da Silveira, R. P. Homrich, "Evaluation of the normal force of a planar actuator``, IEEE Transactions on Magnetics, v. 41, pp. 4006-4008, Oct 2005



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