Modeling the Effect of Compressive Stress on Hysteresis Loop of Grain-Oriented Electrical Steel

Abstract

Modeling of hysteresis loops may be useful for the designers of magnetic circuits in electric machines. The present paper focuses on the possibility to apply the Harrison model to describe hysteresis loops of grain-oriented electrical steel subject to compressive stress. The model extension is achieved by introduction of an additional term into the equation that describes irreversible magnetization process. The extension term does not include a product of stress and magnetization, as could be anticipated from Sablik’s theory, applicable, e.g., to the Jiles–Atherton model. The present contribution points out the fundamental differences between the two aforementioned modeling approaches, which are based on different philosophies despite some apparent similarities. The modeling results are in a qualitative agreement with the experimental results obtained from a single sheet tester for a representative commercially available grain-oriented electrical steel grade 0.27 mm thick.

An Alternative Formulation of the Harrison Model

“…As pointed out earlier, the reduced field strength h modeled with the original Harrison description rarely reaches values close to zero; for example, for Fe-Si electrical steels, the maximal value h crit is around 0.498 [8] since the reduced temperature t ∼ = 293/1043 = 0.281 [10]. Our goal was to find out a functional dependence which would behave qualitatively like the one given with (3) yet able to reach h = 1 within the bounds m ∈ −1; 1 .…”

“…The present contribution is inspired by an excellent review work published recently [5]. It extends several concepts which have been mentioned in the previous publications [6][7][8][9]. The fundamental concept of the paper is to modify the Harrison model of ferromagnetism to make it more useful for engineering purposes.…”

“…The outcome of hysteresis loops with realistic shapes were obtained by summing field strength contributions corresponding to the irreversible and reversible re-magnetization processes, cf. [10] or Figure 3 in [8]. The concept of the present paper is to introduce a weighted summation from several elementary irreversible hysteresis operators and, thus, to treat the elementary Harrison unit as a generalized stop operator [5,25,26].…”

The Effects of Sheet Thickness and Excitation Frequency on Hysteresis Loops of Non-Oriented Electrical Steel

“…This corresponds to the so-called forward model, cf. [ 15 ]. In this case, it is natural to speak of hysteresis in terms of a lagged response between H and B.…”

“…On the other hand, the conditions for material characterization in accordance with international standards assume a specific waveform shape of the system output quantity (for soft magnetic materials polarization is practically equal to induction, the difference in values usually does not exceed a fraction of a percent), and thus it requires the inversion of the computation chain, cf. [ 15 ]. Therefore, a conclusion may be drawn that hysteresis models used to describe the measurement results should have magnetic induction as their input.…”