In this article, a new mathematical model of a major hysteresis loop and a simple procedure for the formation of first-order and higher-order reversal curves are proposed. The applicability of the model has been tested by comparison with measured results, obtained with electrical steel and ferrite cores, and simulation results obtained with the Preisach model. Very good agreement has been found between simulated and measured major and minor hysteresis loops, as well as first-order and higher-order reversal curves.

The first of this two-part article illustrates the state-of-the-art in soft magnetic materials characterization starting with very early developments and giving a retrospective view of research carried out in this field. One famous measurement setup is the Epstein frame, named after Josef Epstein. Around 1900, he published a German article about “The magnetic testing of laminated steel”. As it is highly likely interesting to researchers worldwide, the authors reconsidered his contributions in English language. Consequently, the most common measurement setups are introduced. Besides the Epstein frame, these are the single sheet tester and setups analyzing ring-shaped specimens. These setups allow for a 1-D characterization of the material, while it usually features anisotropic properties and cross-coupling of the magnetization axes. For this reason, 2-D and even 3-D setups are considered and presented here. This article provides a thorough introduction to the field of material characterization. It is the basis for modeling the material characteristics, which is presented in the second part, which also includes recent developments for considering manufacturing impact. It is of particular interest when dealing with mass-produced electric machines. Eventually, these articles shall constitute valuable references for both engineers new to this field as well as experienced researchers.

The first part of this two-part article is about a retrospective view of material characterization, starting with the work of J. Epstein around the year 1900 and respective basic explanations. Consequently, the work presented herein is about the current state-of-the-art, recent developments, and future trends in characterization of ferromagnetic materials. Modeling is in fact a type of characterization, in a phenomenological and mathematical sense, and therefore it is treated with due attention in this article. Quantifying the properties of soft magnetic materials retains significant scientific attention. Thanks to new optimization techniques and advances in numerical evaluation, modern electromagnetic devices feature high utilization. Classical models exhibit assumptions that do not allow modern machine or device characterization with high accuracy. In this manuscript, typically applied techniques and recent incremental improvements, as well as newly developed models are introduced and discussed. Moreover, the significant impact of manufacturing on the materials’ characteristics and its quantification is illustrated. Within this article, a broad overview of the state-of-the-art as well as recent advances and future trends in soft magnetic material characterization is presented. Thus, it is a valuable reading for beginners and experts, from academia and industry alike.

The aim of this paper is to present a comprehensive approach to analyse and interpret power loss in ferromagnetic materials with particular attention devoted to excess power loss. Experimental results obtained with an Epstein frame and toroidal core made of electrical steel are presented in the paper, including quasistatic and dynamic hysteresis loops. According to the time waveforms of the measured magnetic field and magnetic flux density, an instantaneous power loss is calculated for the quasistatic and dynamic case. Moreover, the instantaneous power loss due to eddy current is calculated, as well as the instantaneous excess power loss and excess magnetic field. This excess magnetic field is compared to the excess magnetic field calculated by Bertotti?s model. Analysis and discussion of the results obtained is given in the paper.