Performance of closed-form equations for force between cylindrical magnets over wide range of volume, aspect ratio, and force

Abstract Four types of magnets were used in this study: neodymium NdFeB (grade N35 and N52), ferrite (Y10), samarium-cobalt SmCo (XG30 2:17). They chosen to represent a wide range volumes from 0.035 19 cm 3 (540 times), radius R 1.5 12.5 mm (8 ×), length L 0.5 40 (80 aspect ratio L/R 0.051 17 (330 contact forces 0.2 250 N (over 1000 ×). The study shows that previously reported closed-form equations are valid only at large distances (small forces). At short (large forces) the calculated force diverges infinity or accuracy depends on ratio, some fail more than others. A new equation is proposed as small modification known function, which provides reasonable behaviour over whole studied range. However, unknown general practical case, because theoretical calculations do not take into account imperfections real magnets, so there no single absolute reference.