Anisotropic hysteresis representation of steel sheets based on a vectorization technique applied to Jiles-Atherton model

Hysteresis model of soft magnetic material enables an accurate estimation of the losses in electrical application. In rotating machine, the flux distribution can magnetize many directions of the iron core. The combination of the rotational and the alternating flux density appears between the slot and the yoke region. Even if the alternating flux density appears in the middle of each tooth, the magnetic properties varies with the magnetized direction with respect to the rolling direction. Whereas the losses strictly increases with the amplitude of an alternating flux density, the hysteresis loss presents a maximum under rotational flux density condition. Although this phenomenon is properly described by the coherent rotation of the domains at the microscopic scale, the macroscopic representation of the material should represent this specific feature. In this article, a general vectorization technique is applied to the Jiles-Atherton model of hysteresis. The anisotropic anhysteresis behavior is derived from the analysis of a cubic crystal. This anhysteresis model drives the coherent rotation of the hysteresis model. Even if the model parameters are identified with alternating flux condition, the rotational flux density can be predicted properly.