Nonlinear permanent magnets modelling with the finite element method

In order to carry out permanent-magnet calculations with the finite-element method, it is necessary to take into account the anisotropic behavior of hard magnetic materials (ferrites, NdFeB, SmCo ₅). In linear cases, the permeability of permanent magnets is a tensor. In nonlinear cases, the model uses a texture function which represents the distribution of the local easy axis of the crystallites of the magnet. This function allows a good representation of the angular dependence of the coercive field of the magnet. As a result, it is possible to express the magnetic induction B and the tensor [δB/δH] as functions of the field H and the texture parameter. This model has been implemented in the FLUX3D software, using the tensor (δB/δH) for the Newton-Raphson procedure. Three-dimensional magnetization of a ferrite magnet by a NdFeB magnet is treated as a suitable representative example. The authors analyze the results obtained for an ideally oriented ferrite magnet and a real one using a measured texture parameter