An Improved Magnetic Charge Model for Force Calculations Between Permanent Magnets Considering Relative Permeability

The magnetic charge model is a powerful tool for calculating the interaction forces between permanent magnets. This model enables the analytical or semi-analytical derivation of mathematical expressions for the interaction forces, thereby significantly reducing the computational time required compared to finite element modeling (FEM). However, the classical magnetic charge model has a clear limitation; it assumes a relative permeability of 1 for each magnet to simplify mathematical derivations. Since the actual relative permeabilities of permanent magnets are greater than 1, this assumption inevitably leads to non-negligible modeling errors. This article proposes a new method for calculating interaction forces between permanent magnets, which takes their relative permeabilities into account. The key to this improved method lies in determining the actual magnetic polarization of each magnet under the magnetic field created by all magnets in space. This challenge is addressed jointly by the linear demagnetization model of permanent magnets and the magnetic field expressions derived from the classical magnetic charge model. Both FEM and experimental results indicate that the improved model significantly reduces the force calculation errors compared to the classical model. Moreover, the improved model allows further enhancement of modeling accuracy by subdividing the magnets into smaller elements. Additionally, this model retains the fast computational speed of the classical model, making it highly suitable for the analysis and optimization of magneto-mechanical devices based on permanent magnets.