Abstract
Magnetic losses in a laminated ferromagnetic core have been studied for years. However, magnetization mechanisms are complex, and the ideal model is still lacking. Classic resolution in the time domain combines a 1D magnetic diffusion equation with a viscosity-based magneto dynamic material law (first-order differential equation). This simultaneous resolution has already been solved by matrix inversion: the diffusion equation temporal term is replaced by its differential equation expression. It leads to a fast solution but overestimates the excess losses linked to the dynamic of the magnetic domains wall motions. Improved material laws using power operators have alternatively been tested. However, it is impossible to regroup the magnetic field terms on the same side of the final equation, and the resolution can only go through complex iterative methods (fixed point, Newton-Raphson). In this study, we propose to combine a fractional diffusion equation and a fractional viscosity-based magneto dynamic differential equation. Matrix resolution is possible, such as an accurate simulation of the dynamic behavior by adjusting the fractional order. The space term of the diffusion equation being solved by space discretization, the combined resolution leads to local information (excitation and induction fields). The number of dynamic parameters is limited but large enough for excellent simulation results.
Highlights
An accurate evaluation of the conversion law is mandatory in the design of new electromagnetic devices
Seventy years later (1952), Polivanov,13 followed by Pry, and Bean,14 proposed the first qualitative models for the magnetization mechanisms. These theories remained prevalent for many years up to Bertotti’s Statistical Theory of Losses (STL), which is still nowadays the most used method to evaluate the ferromagnetic losses in electromagnetic conversions
In Ref. 12, the combined resolution is obtained using the iterative Newton-Raphson method associated with the TriDiagonalMatrix Algorithm (TDMA)
Summary
Paper published as part of the special topic on 15th Joint MMM-Intermag Conference. AFFILIATIONS ELyTMaX UMI 3757, CNRS–Université de Lyon–Tohoku University, International Joint Unit, Tohoku University, Sendai, Japan
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
