Optimization of Force Between Cylindrical Permanent Magnets

We calculated analytically and with the finite-element method the force between two identical coaxial cylindrical magnets for nine different magnetic materials at separations of 1, 3, 5, 7, and 9 mm and for height-to-diameter ratios between 0.1 and 2. For the analytical calculations, we assumed homogeneous magnetization. For the nonhomogeneous case, we used the finite-element method taking into consideration the magnetic flux density vs. field (B-H) curves of the materials. The results show that, similarly for cuboid magnets, the maximum force for a given volume of permanent-magnet material was achieved for a height-to-diameter ratio around 0.4 for homogeneously magnetized (ideal) permanent magnets. We also show that this is not always true for the nonhomogeneous cases. The resulting forces are dependent on the B-H curve of the magnets. As the B-H curves of the materials deviate from their ideal counterparts, the aspect ratio that yields maximum force increases.