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The purpose of this paper is to use a new rational approach for the design of some magnetic couplings. Our method is based on the association of analytical models and an exact global optimization algorithm named IBBA and developed by the third author. The analytical model presented in this paper is more sophisticated than those previously dealt using IBBA. Therefore, some under and over estimating functions have been constructed for those particular problems of design in order to improve the convergence of IBBA. Some optimal results highlight the efficiency of this approach.