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We discuss the results of an international comparison regarding the measurement of magnetic power loss and apparent power between 20 Hz and 100 Hz at magnetic polarization values ranging between 1.3 T and 1.8 T in grain-oriented steel (GO) sheets using the Single Sheet Testing (SST) and Epstein methods. This exercise, carried out in the framework of the activity of Joint Working Group IEC 68/WG1-ISO/TC17/WG16, was aimed at a solid assessment of the degree of reproducibility of the SST method, under its prospective adoption in the industrial practice as a reference method for the specifications of grain-oriented alloys. Five different types of Fe-Si GO alloys were circulated among eleven different laboratories of metrological institutes and industry. The statistical analysis of the results shows close reproducibility properties of the SST and Epstein methods. It is obtained, in particular, that the power loss figures, measured by the participants at 50 Hz and the aforementioned peak polarization values are distributed around their reference value with relative standard deviation σ (P)SST = 0.88% and σ (P)Epst = 0.82% for SST and Epstein, respectively. It is obtained σ (S)SST = 2.20% and σ (S)Epst = 2.15% for the apparent power. For the industrially relevant case of polarization Jp = 1.7 T in the high-permeability P-type grades, these quantities amount to σ (P)SST = 0.48%, σ (P)Epst = 0.80%. By restricting the comparison to the European metrological laboratories (INRIM, NPL, PTB), the overall distributions narrow to σ (P)SST = 0.42%, σ (P)Epst = 0.55%, σ (S)SST = 1.19%, and σ (S)Epst = 0.82%. A qualitative interpretation of the main physical mechanisms and the measuring features underlying the lab-to-lab dispersion of the SST and Epstein results is discussed in this paper. It is concluded that the combination of good reproducibility and simple practical implementation make the SST method totally appropriate as a reference method for the definition of the material quality in the specification standards

International audience; By means of a newly developed broadband measuring setup we have overcome the usual upper limit for the test frequency, around a few hundred Hz, which is encountered in the two-dimensional characterization of magnetic steel sheets at technical inductions and we have measured the rotational losses in low-carbon steels up to 1 kHz and peak induction 1.7 T. An important piece of information is thus retrieved upon a frequency range useful to predict the performance of high-speed electrical machines. Our experiments, performed on thick (0.640 mm) laminations, have brought to light the emergence of the skin effect under rotational fields. This is revealed by an abrupt deviation of the excess loss component, calculated under the conventional loss separation procedure, from its well-known linear dependence on the square root of the frequency. A simple magnetic constitutive law under rotating induction is proposed and introduced into the electromagnetic diffusion equation, which is solved by finite elements coupled to a non-linear algorithm. The classical rotational eddy current loss, largely prevalent with respect to the hysteresis and excess loss components on approaching the kHz frequencies in low-carbon steels, is then calculated in the presence of skin effect, permitting one to achieve full analysis of the rotational losses and good predicting capability upon a broad range of frequencies and peak inductions.

We review state-of-the-art modeling of two-dimensional (2D) magnetization process in soft magnets. Emphasis is placed on the phenomenological assessment of the energy losses in steel sheets under rotational field. It is stressed that a general physically based theoretical framework, exploitable for applications in practical materials and machine cores, is not available at present. However, a rational approach to the 2D magnetic losses and their frequency dependence can be pursued. This is based on the separation between quasi-static (hysteresis) and dynamic magnetization processes and the connection with their unidirectional (scalar) counterpart. A number of vector models of the 2D quasi-static hysteresis behavior, typically residing on assessed scalar models, are discussed. They have prevalent formal-mathematical character, and, while being often helpful in numerical calculations, they leave unanswered the quest for solid physical interpretation. The dynamic magnetization process can, on the other hand, rely on a 2D phenomenological extension of the rmly established physical approach to the unidirectional scalar case provided by the statistical theory of losses. This is especially true for isotropic (i.e. nonoriented) magnetic laminations, where both rotational and elliptical flux loci can be conveniently handled. It permits one to achieve general appraisal of the experiments and flexible formulation, useful for numerical applications in machine cores