Generalization of the Classical Method for Calculating Dynamic Hysteresis Loops in Grain-Oriented Electrical Steels

Abstract

We have studied the ability of two one-dimensional (1-D) time-stepping models, both based on the concept of magnetic viscosity, to reproduce dynamic loops and losses in grain-oriented (GO) electrical steels under arbitrary magnetization regimes. We found that GO steels (0.3 mm thick) can be modeled quite accurately at magnetizing frequencies up to 200 Hz by a thin sheet representation, which is applied to a bulk material. At higher frequencies, acceptable results can be obtained through a finite-difference solver of a 1-D penetration equation whose applicability to GO steels can be explained in terms of domain wall bowing. Because of the inertial effect introduced by the magnetic viscosity, the average error in the loss prediction is reduced from 40% for the conventional classical method to 5% for the methods we studied. We demonstrated the accuracy of the models using two GO steels whose losses and -characteristics were measured by computer-controlled Epstein and single-sheet testers.

On physical aspects of the Jiles-Atherton hysteresis models

“…4(a), dynamic loops predicted by the DHM-B are a good first approximation of those obtained experimentally (a method 22,23 of improving the DHM-B will be mentioned at the end of this section). On the contrary, the dynamic loops in Fig.…”

“…Under these conditions, the loss separation (8) is equivalent to the field separation 22,23 HðtÞ ¼ H hyst ðtÞ þ H clas ðtÞ þ H exc ðtÞ;…”

AC loss density component in electrical steel sheets

“…p. 401, 428], [40,41]. The dynamic component of the effective field may be derived from a viscous-type equation proposed originally by Zirka et al [55][56][57][58][59][60]. Zirka's approach combined with the recently developed modification of the Jiles-Atherton model [42] yielded a remarkably good agreement between the model and the experiment in recent descriptions of dynamic minor loops in electrical steels [43,44].…”

“…It should be remarked that the original Zirka's approach was applied to describe the 'excess' loss component only, what was the possible reason for the introduction of specific approximations for dynamic magnetic conductivity function in different parts of the hysteresis loop [57][58][59][60]. In [43,44] all loss components due to eddy currents were lumped together and approximations like those revealed in [57][58][59][60] were found unnecessary.…”

Magnetic field computation in a non-oriented sheet cross-section considering the hysteresis phenomenon

“…Several approaches have been suggested to study the magnetic phenomena in silicon-iron alloys. We mention for instance those of Bertotti [3], Bertotti and Mayergoyz [4], and Zirka et al [5,6]. To optimize the sheet characteristics of silicon-iron alloys, such as reduction in magnetic losses and taking into account the skin effect, it is necessary to compute the magnetic field and the distribution of the magnetic flux density in the sheet cross-section in the dynamic mode.…”