A Non-Iterative Method to Solve for Magnetic Fields, Forces, and Torques Due to Permanent Magnets with Non-Unity Relative Permeability

Although the majority of common permanent magnet materials have relative permeabilities between 1.05 and 1.3, they are often modelled analytically with the assumption of unity relative permeability. While this greatly simplifies analysis, it introduces modelling errors, leading to overestimates of magnetic fields, forces, and torques. This paper presents a new method for modelling interactions between magnets with non-unity relative permeabilities assuming constant uniform remanence magnetisation and permeability. In contrast to other methods which use an iterative approach, this methodology requires calculating magnetic field information only once, leading to a considerable reduction in computational effort. Based on a triangular surface mesh, this method permits the calculation for any magnetic geometry and for magnetic systems with arbitrarily many magnets. Verification is performed using finite element simulations, with the proposed method showing high accuracy and speed.