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.

中文翻译：

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永磁体双电荷面解析模型及其在磁弹簧中的应用

本文介绍了一种新的永磁体分析模型，该模型对于计算磁性弹簧中两个永磁体之间的磁力特别有用。新模型将单个磁铁视为一对平行的磁荷表面，我们称之为双荷表面 (DCS)。在该模型中，两个磁铁之间的力被视为四个带电表面的相互作用，可以根据磁铁的几何形状和磁化强度进行分析计算。这种新模型克服了其他常用分析模型（偶极子和点电荷模型）的一个主要问题，这些模型在两个磁铁之间的分离距离接近零时预测无限大的排斥力，并允许准确计算近场和远场的排斥力。该模型通过实验和有限元方法 (FEM) 模拟进行验证，通过证明在很宽的分离距离范围内对磁力与分离的正确预测。以均方根偏差 (RMSD) 作为模型精度的度量，显示 DCS 模型比 Gilbert 模型（基于一对点电荷）、Ampere 模型（基于一对点电荷）具有更好的精度偶极子）和拟合多项式方法。