Asymptotic Models for Ferromagnetic Materials in Eddy Current Problem
HAL (Le Centre pour la Communication Scientifique Directe)(2021)
摘要
The eddy current problem has crucial applications in the industrial field such as
inductive heating or braking of heavy vehicles. In this context, we intend to
analyze the eddy current problem for the electromagnetic field in magnetically
soft materials. These materials are used for the cores of transformers in order to
reduce the energy losses resulting from the alternating currents. The problem under consideration lies in two highly heterogeneous materials
with a common interface: we are interested to study the electromagnetic field in
a soft magnetic conducting body with a high constant permeability mu = mu−, embedded
in a magnetic dielectric medium with a constant permeability mu=mu+, in a three-dimensional
setting. Therefore, we propose to investigate the behavior of the electromagnetic field when the
magnetic permeability is “dominant” that is the ferromagnetic case.
However, in the ferromagnetic materials, we may have a small skin depth and
the amplitude of the magnetic field decays rapidly with depth inside the
magnetic conducting domain. As a result, the numerical simulation of such a
problem seems challenging although prohibitive. In order to overcome this
difficulty, we introduce for instance a small parameter epsilon, then we develop
an asymptotic approach based on a multiscale expansion. This asymptotic method was
also applied previously for highly conductive nonmagnetic materials in eddy current problem.
Therefore, we derive asymptotic models that reflect the skin effect and can be solved numerically
by using a coarse mesh.
The aim of our present work is twofold. First, we derive an asymptotic
expansion of the electromagnetic field as the parameter epsilon tends to zero when
the surface of the conducting body is smooth. Then, as an application, we
measure the magnetic skin effect by presenting the asymptotic behavior of the
characteristic depth. Finally, we compare the latter result with the previous work
corresponding to the skin effect in a bidimensional eddy current problem, when
the contrast of permeability is predominant
更多查看译文
关键词
eddy current problem,ferromagnetic materials
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要