Abstract
Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g., reaction fields and losses, remain approximately the same. This article presents a peculiar case where the physical nature of the problem and the type of governing mathematical equations change upon homogenization. We consider a stratified nonlinear magnetic and conducting medium, where a low-frequency excitation induces eddy currents. It is shown that this eddy current problem becomes, upon homogenization, mathematically equivalent to a magnetostatic one and takes eddy currents into account via a complex-valued nonlinear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -curve. The homogenization procedure is demonstrated for a cylindrical laminated iron core. High accuracy of homogenization, even for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local</i> loss distribution, is demonstrated.
Highlights
E FFECTIVE medium theory is well known as an indispensable tool for studying various types of composites [1], [2]: a fine-scale heterostructure with material parameters rapidly varying in space is replaced with a homogeneous sample in such a way that its reaction fields and/or relevant energies are approximately the same [3]
One side of a trade-off for eddy current problems in laminated cores is the harmonic balance approximation (HBA), well established in applied electromagnetic analysis, with reliable results reported in the literature [18], [19], [20]
The eddy current problem examined in this paper changes its physical nature upon homogenization, when a stratified nonlinear magnetic medium is replaced with an effective homogeneous one
Summary
E FFECTIVE medium theory (homogenization) is well known as an indispensable tool for studying various types of composites [1], [2]: a fine-scale heterostructure with material parameters rapidly varying in space is replaced with a homogeneous sample in such a way that its reaction fields and/or relevant energies are approximately the same [3]. Stratified magnetic structures composed of thin insulationcoated conducting magnetic sheets are considered Such laminated stacks are commonly used in magnetic cores to reduce eddy current losses. The novelty of the paper is not in the use of complex permeability per se but rather in the role this permeability plays in homogenization: its real and imaginary parts provide a fit to the physically measurable properties (reaction fields and losses) of the laminated core. The homogenized model yields accurate eddy current losses and reaction fields
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