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Anomalous fractional diffusion equation for magnetic losses in a ferromagnetic lamination

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Abstract

During a full magnetization cycle and under a collinearity situation, the magnetic losses in a ferromagnetic are observable by plotting the average magnetic flux density or magnetization as a function of the tangent magnetic excitation. This highly frequency-dependent magnetic signature is called hysteresis cycle, and its area is equal to the energy consumed during the magnetization cycle. The physical mechanisms behind this energy conversion are complex as they interfere and take place at different geometrical scales. Microscopic Eddy currents due to domain wall variations play an important role, as well as the macroscopic Eddy currents due to the excitation field time variations and ruled by the magnetic field diffusion equation. From the literature on this topic, researchers have been proposing simulation models to reproduce and understand those complex observations. Even if all these losses contributions are physically interconnected, most of the simulation models available in the literature are based on the magnetic losses separation principle where each contribution is considered separately. Physically, the Weiss domains distribution and movements distort the diffusion process which becomes anomalous. In this article, the standard magnetic field diffusion equation is modified to take into account such anomaly. The first-order time derivation of the magnetic induction diffusion is replaced by a fractional-order time derivation. This change offers flexibility in the simulation scheme as the fractional order can be considered as an additional degree of freedom. By adjusting precisely this order, very accurate simulation results can be obtained on a very broad frequency bandwidth for the prediction of the iron losses in a ferromagnetic material.

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Funding

This study was funded by the SCAC (Service de cooperation et d’action culturelle) of the French Embassy to Cameroon. This study was funded by the National Natural Science Foundation of China (Grant No 51805298) and by the Natural Science Foundation of Shandong Province (Grant No. ZR201807090390).

Author information

Authors and Affiliations

  1. Laboratoire de Génie Electrique et Ferroélectricité – INSA de Lyon, Villeurbanne, France

    B. Ducharne & Y. A. Tene Deffo

  2. Faculty of Engineering and Technology, University of Buea, Buea, Cameroon

    Y. A. Tene Deffo

  3. Green Manufacturing R&D Laboratory, School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai, China

    B. Zhang

  4. ELyTMaX UMI 3757, CNRS – Université de Lyon – Tohoku University, International Joint Unit, Tohoku University, Sendai, Japan

    G. Sebald

Authors
  1. B. Ducharne
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  2. Y. A. Tene Deffo
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  3. B. Zhang
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  4. G. Sebald
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Correspondence to B. Ducharne.

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Ducharne, B., Deffo, Y.A.T., Zhang, B. et al. Anomalous fractional diffusion equation for magnetic losses in a ferromagnetic lamination. Eur. Phys. J. Plus 135, 325 (2020). https://doi.org/10.1140/epjp/s13360-020-00330-x

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00330-x

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