Vector Model for Losses in Non-Oriented Steel sheets

The presence of two-dimensional (2D) magnetization processes in devices and electrical machines calls for the development of vector model for loss prediction. Starting from the Del Vecchio-Charap work [2], we developed a static model able to reproduce the 2D evolution of magnetization in soft non-oriented steel sheets: the most interesting case for applications. The material is assimilated to an ensemble of biaxial grains, each associated with a hysteron having two orthogonal easy axes. In each of them, the field driven irreversible switch of magnetization between the easy directions (Barkhausen jump: BJ) is governed by the value of local coercive field (about ten times smaller than the anisotropy fields); the ensemble of all these BJs accounts for the domain wall displacement. After the BJ, the local magnetization is brought to its energy minimum by the antagonism between anisotropy and Zeeman energy, so determining the reversible magnetization component. Domain wall reversible processes (bending) are not considered, whereas the role of macroscopic and internal demagnetizing fields is accounted for. The system average magnetization is obtained after integrating the outputs of single hysterons, each weighted by probability density functions suitably characterizing the material properties (i.e.: grain orientations, coercive and anisotropy fields). We have been able to reproduce the loss vs. polarization W(Jp) evolution in several non-oriented materials, subjected to alternating and rotating fields. In particular, under circular induction, the W drop at high Jp was always found, without introducing “ad hoc” fitting functions. It is remarkable that the outlined approach can be extended to systems magnetized in dynamic conditions. [1] C. Appino, C. Ragusa, and F. Fiorillo, “Can rotational magnetization be theoretically assessd?”, IJAEM 44 (20144), 355-370 [2] R.M. Del Vecchio, S. H. Charap, “Two dimensional hysteresis model”, IEEE Trans. Mag. 20 (1984), 1437-1439