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3D analytical calculation of the forces exerted between two cuboidal magnets
Akoun, G.   Yonnet, J.-P.  
Laboratoire d'Electrotechnique de Grenoble, Saint Martin D'Heres, France;

This paper appears in: Magnetics, IEEE Transactions on
Publication Date: Sep 1984
Volume: 20,  Issue: 5
On page(s): 1962- 1964
ISSN: 0018-9464
Current Version Published: 2003-01-06

Abstract
The interaction forces exerted between permanent magnets are used in many magneto-mechanical devices (magnetic bearings, couplings, etc...). By analytical calculation, 2D problems can be solved easily, when simple shaped magnets are used. Usually, the 3D problems are numerically computed, by using a finite element method for example. This paper presents the 3D calculation of the interaction forces exerted between two cuboidal magnets, by analytical means only. The obtained expressions are rather complicated, but a pocket programmable calculator is sufficient to the force calculation. By derivation, the analytical expressions of the stiffnesses can be easily obtained. In addition, the 3D analytical calculation allows a simple optimization of the magnet dimensions.

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