Optimum geometry analyses for rectangular "hard" magnet pairs

Optimum-geometry calculations have been performed for rectangular "hard" magnet pairs of both two- and three-dimensional geometries. The optimum magnet dimensions were sought to maximize repulsion force and stiffness for specified values of pole separation and lateral offset. Two types of optimization were carried out: 1) constrained, in which force and stiffness were maximized for fixed magnet volume, and 2) unconstrained, in which the magnet dimensions were unrestricted, with the objective functions then force and stiffness per unit volume. In contrast to previous work, function maxima were found using numerical optimization techniques. The results include several theoretically limiting cases for the force or stiffness available from rectangular ideal-magnet pairs, together with the corresponding optimum geometries.