Calculation of field and force of Halbach arrays: Improved magnetic charge method for irregular magnetized magnets

Permanent magnets (PMs) are widely used in magnetic machinery. To better predict the performance of PMs, the magnetic field and force need to be calculated. In general applications, PMs are usually magnetized in a direction parallel to their symmetry axes, and the equivalent magnetic charge method (EMCM) can be used to calculate the corresponding magnetic field and force. However, in some particular cases, such as Halbach arrays, the magnetizing directions or shapes of PMs are irregular and cannot be modeled by the normal EMCM that is limited to the magnets with regular shapes and magnetizing directions. In this paper, an improved EMCM is proposed to calculate PMs with irregular magnetizing directions and shapes. The general rules of magnetic charge distribution are given. The standard forms for calculating magnets with irregular magnetizing directions are obtained through the orthogonal decomposition of the magnetizing direction to simplify the calculation. As an illustration, semi-analytical expressions for magnetic field and force of arc-shaped PMs with irregular magnetizing direction are obtained. Furthermore, the application of this method to calculate the 3-D magnetic field and axial magnetic force of Halbach arrays is discussed and compared with the finite element method (FEM) and experimental measurement. It shows that the improved EMCM has good accuracy and greatly reduces the time cost, which can provide reference for the structure design.