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We propose an approach to solve the coupled problem of the magnetic field penetration into soft ferromagnets and a frequency dependent magnetic hysteresis. The magnetic field diffusion is related to the macroscopic eddy currents. The hysteresis model is related to the microscopic eddy currents derived from the magnetic domain wall movements, and is responsible for the frequency dependence of hysteresis loops. In this paper, based on a lumped model and fractional derivative operators, we demonstrate that it is possible to replace the coupled diffusion/dynamic hysteresis in a simplest formulation using fractional operators. Such a formulation can be solved easily. Instead of solving a 1D problem of diffusion, we show here that a lumped model with appropriate fractional time derivative operator can be an exact formulation of the problem. In addition, we confirm that the model is using experimental available information, obtained by standard single sheet tester measuring bench (the tangential surface excitation field, and the cross section average induction). [ABSTRACT FROM AUTHOR]

This paper reviews the use of the fractional derivative operators for the dynamic magnetization of ferromagnetic specimens. Magnetic behaviors in ferromagnetic specimens are strongly nonlinear and frequency dependent. Magnetism has an atomic origin but the magnetic behavior as observed at the human scale is highly affected by phenomena occurring at larger scales. Under the influence of an external magnetic field, the homogeneity of a ferromagnetic sample magnetization is linked to the excitation dynamics. Models and simulations in this domain are strongly needed, as they provide theoretical explanations and allow us to anticipate complex phenomena, difficult to observe in a practical way. On the one hand, such multi-scale dynamical behaviors can hardly be taken into account with the usual mathematical operators. On the other hand, correct simulation results on large frequency bandwidths can be obtained using fractional derivative operators. The use of fractional derivatives can be envisaged through different approaches: Lump models based on time fractional differential equations is one option, and fractional anomalous diffusion equations is another. In this manuscript, these two methods are detailed and compared. Theoretical results are compared to experimental ones, and conclusions and perspectives are drawn such as possible improvements. [ABSTRACT FROM AUTHOR]

• Magnetic losses are simulated under alternating and rotational magnetization. • Fractional derivatives are used for the dynamical contribution. • The simulation method relies on eight parameters. • The losses reduction at Bsat under rotational magnetization is correctly simulated. The performance of electromagnetic devices like motors and transformers is dictated by their efficiency of magnetic energy conversion, and the adequate modeling of this efficiency is essential in device design processes. However, a universal model that yields satisfactory results for this process under both alternating and rotating magnetic fields has yet to be developed. The present work addresses this issue by extending a previously proposed vector dry-friction modeling method to include frequency dependence using fractional derivative operators. The resulting vector model relies on eight parameters that can be adjusted to fit a wide range of experimental data, and thereby provides accurate estimations of magnetic losses over broad frequency bandwidths under both alternating and rotating magnetic fields. The model provides excellent agreement with the commonly observed reduction in magnetic losses when approaching saturation under low frequency rotating excitations, and further includes overshadowing with eddy current loss as the frequency increases. The accuracy and universality of the model are demonstrated under both alternating and rotational magnetization conditions based on comparisons with experimental results. [ABSTRACT FROM AUTHOR]

• Magnetic behaviors are simulated under alternating and rotational magnetization. • The Bergqvist dry-friction model and the multiscale model are combined. • Predictions of the behavior under high amplitude rotating magnetization are obtained. • Highly anisotropic FeSi Go electrical steel is simulated and characterized. Vector quantities and tensorial properties rule the magnetization mechanisms in ferromagnetic materials. Every ferromagnetic material is anisotropic to some degree in its magnetic response, so this anisotropy has to be considered for a general model. In this study, a multiscale approach based on a statistical description of the magnetic domain distribution and the knowledge of the crystallographic texture is used to predict the anhysteretic behavior along an arbitrary space direction. Combined with the vector Bergqvist dry-friction hysteresis model, qualitatively reliable simulation results are obtained under alternating and rotational magnetization. FeSi 3% grain-oriented (FeSi GO) electrical steel is chosen as study material: FeSi GO are widespread so that extensive data are available and strongly anisotropic, forcing the model toward the "worst-case" scenario from the viewpoint of anisotropy. Moreover, under high excitation of rotational magnetization, losses drop due to the disappearance of the magnetic domains. This behavior is represented correctly by the proposed simulation method. In such conditions, the magnetization behavior is led mainly by the anhysteretic behavior, strengthening the predictive ability of the proposed model. In this manuscript, comparisons between simulations and measurements under many amplitudes of alternating and rotational magnetization for different levels of imposed excitation or magnetization are provided and used to validate the simulation method. [ABSTRACT FROM AUTHOR]