LAUSR

This article presents a new analytical model for a permanent magnet that is particularly useful for calculating the magnetic force between two permanent magnets in a magnetic spring. The new model treats a single magnet as a pair of parallel magnetically charged surfaces, which we call dual-charged surfaces (DCSs). With the model, the force between two magnets is treated as the interaction of four charged surfaces, which can be calculated analytically as a function of magnets’ geometry and magnetization. This new model overcomes a major problem of other commonly used analytical models (dipole and point charge models) that predict infinitely large repulsive force when the separation distance between two magnets approaches zero and allows accurate calculation of the repulsive force in both near and far fields. The model is verified with experiments and finite element method (FEM) simulations through demonstrating correct prediction on the magnetic force versus separation over a wide range of the separation distance. With the root-mean-square deviation (RMSD) as a measure of the model accuracy, the DCS model is shown to have better accuracy over the Gilbert model (based on a pair of point charges), the Ampere model (based on a pair of dipoles), and the fitted polynomial method.