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This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is radial. Such a configuration corresponds to a passive magnetic bearing. The magnetic force exerted between ring permanent magnets is determined by using the Coulombian model. The expressions obtained are semianalytical and we show that it is not possible to find an exact analytical expression of the force between two ring permanent magnets. Then, thanks to these semianalytical calculations, the ring dimensions are optimized in order to have a great force or a great stiffness. Moreover, we show that the relative position of the rings for which the force is the strongest depends on the air gap dimension. This result is new because the curvature effect is taken into account in this paper. We can say that such semianalytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite-element method. Moreover, semianalytical expressions have a low computational cost whereas the finite-element method has a high one. Thereby, as shown in this paper, such calculations allow an easy optimization of quadripolar lenses or devices using permanent magnets.
Date of Publication: Sept. 2009