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Based on the minimum energy principle of magnetization stable state, this paper presents a definition of three-dimensional (3-D) hysteresis operator by analyzing the magnetization state of the magnetic particles. The direction determination rule of magnetization is given in detail. The critical surface equation of the hysteresis operator is described in the space sphere coordinate system according to the modeling principle of the hybrid vector hysteresis model. The magnetization process of the hysteresis operator is studied under the alternating and rotational magnetic field, respectively. Moreover, a 3-D isotropic hysteresis model is initiatively established, and the hysteresis properties of soft magnetic composite (SMC) material are simulated and compared with the experimental results. This study lays a foundation to build the 3-D hybrid vector hysteresis model and simulate the 3-D magnetic properties.

Three-Dimensional Magnetic Hysteresis Modeling Based on Vector Hysteresis Operator