THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION

THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION

The construction of the correct vector material equations for nonlinear anisotropic soft magnetic materials remains one of the main reserves for increasing the accuracy of mathematical models in solving magnetostatic problems in the field formulation. The aim of the work is to establish asymptotic e...

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Date:2020
Main Authors: Tolmachev, S. T., Il'chenko, A. V.
Format: Article
Language:English
Ukrainian
Published: National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2020
Subjects:
nonlinear anisotropic medium
vector magnetization characteristics
energy potential
reciprocity principle
asymptotic expressions
magnetic permeability tensor
621.318.13
Online Access:http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06
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Journal Title:Electrical Engineering & Electromechanics

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Electrical Engineering & Electromechanics
id eiekhpieduua-article-201159
record_format ojs
institution Electrical Engineering & Electromechanics
baseUrl_str
datestamp_date 2020-04-21T20:42:19Z
collection OJS
language English
Ukrainian
topic nonlinear anisotropic medium
vector magnetization characteristics
energy potential
reciprocity principle
asymptotic expressions
magnetic permeability tensor
621.318.13
spellingShingle nonlinear anisotropic medium
vector magnetization characteristics
energy potential
reciprocity principle
asymptotic expressions
magnetic permeability tensor
621.318.13
Tolmachev, S. T.
Il'chenko, A. V.
THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
topic_facet нелинейная анизотропная среда
векторные характеристики намагничивания
энергетический потенциал
принцип взаимности
асимптотические выражения
тензор магнитной проницаемости
621.318.13
nonlinear anisotropic medium
vector magnetization characteristics
energy potential
reciprocity principle
asymptotic expressions
magnetic permeability tensor
621.318.13
format Article
author Tolmachev, S. T.
Il'chenko, A. V.
author_facet Tolmachev, S. T.
Il'chenko, A. V.
author_sort Tolmachev, S. T.
title THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
title_short THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
title_full THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
title_fullStr THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
title_full_unstemmed THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
title_sort reciprocity principle for a nonlinear anisotropic medium without hysteresis: theory and practice of application
title_alt ПРИНЦИП ВЗАИМНОСТИ ДЛЯ НЕЛИНЕЙНОЙ АНИЗОТРОПНОЙ СРЕДЫ БЕЗ ГИСТЕРЕЗИСА: ТЕОРИЯ И ПРАКТИКА ПРИМЕНЕНИЯ
description The construction of the correct vector material equations for nonlinear anisotropic soft magnetic materials remains one of the main reserves for increasing the accuracy of mathematical models in solving magnetostatic problems in the field formulation. The aim of the work is to establish asymptotic expressions for the reciprocity principle, which is a fundamental property of reversible magnetization processes of nonlinear anisotropic media, and to use the obtained results to optimize the computational process when constructing the vector magnetization characteristic and differential permeability tensor. The potentiality property of the magnetic flux density vector B in H-space is used. The main result of the paper is an illustration, using concrete examples, of an alternative method for calculating vector magnetization characteristics for one of the orthogonal families. In order to eliminate the instrumental error and ensure maximum accuracy and reliability of the obtained results, the exact characteristics for the components of the vector magnetization characteristic obtained by differentiating a special analytical expression for the potential were used as initial ones. The principle of reciprocity, by virtue of its universal nature, makes a significant contribution to the theory of nonlinear anisotropic media in the hysteresis-free approximation. Asymptotic expressions for the reciprocity principle are obtained for the first time. The performed computational experiments on the construction of vector characteristics based on the known magnetization characteristics in one of the directions confirm almost complete coincidence with the exact values obtained analytically. The use of asymptotic expressions for the reciprocity principle not only greatly simplifies computational processes for determining the orthogonal magnetization characteristics, but also implements the calculation of differential permeability tensors for arbitrary field values. The proposed method can be implemented in applications for calculating the magnetic field in devices with nonlinear anisotropic magnetically soft materials, primarily with cold rolled sheet electrical steels, which are most used in electrical engineering.
publisher National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
publishDate 2020
url http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06
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spelling eiekhpieduua-article-2011592020-04-21T20:42:19Z THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION ПРИНЦИП ВЗАИМНОСТИ ДЛЯ НЕЛИНЕЙНОЙ АНИЗОТРОПНОЙ СРЕДЫ БЕЗ ГИСТЕРЕЗИСА: ТЕОРИЯ И ПРАКТИКА ПРИМЕНЕНИЯ Tolmachev, S. T. Il'chenko, A. V. нелинейная анизотропная среда векторные характеристики намагничивания энергетический потенциал принцип взаимности асимптотические выражения тензор магнитной проницаемости 621.318.13 nonlinear anisotropic medium vector magnetization characteristics energy potential reciprocity principle asymptotic expressions magnetic permeability tensor 621.318.13 The construction of the correct vector material equations for nonlinear anisotropic soft magnetic materials remains one of the main reserves for increasing the accuracy of mathematical models in solving magnetostatic problems in the field formulation. The aim of the work is to establish asymptotic expressions for the reciprocity principle, which is a fundamental property of reversible magnetization processes of nonlinear anisotropic media, and to use the obtained results to optimize the computational process when constructing the vector magnetization characteristic and differential permeability tensor. The potentiality property of the magnetic flux density vector B in H-space is used. The main result of the paper is an illustration, using concrete examples, of an alternative method for calculating vector magnetization characteristics for one of the orthogonal families. In order to eliminate the instrumental error and ensure maximum accuracy and reliability of the obtained results, the exact characteristics for the components of the vector magnetization characteristic obtained by differentiating a special analytical expression for the potential were used as initial ones. The principle of reciprocity, by virtue of its universal nature, makes a significant contribution to the theory of nonlinear anisotropic media in the hysteresis-free approximation. Asymptotic expressions for the reciprocity principle are obtained for the first time. The performed computational experiments on the construction of vector characteristics based on the known magnetization characteristics in one of the directions confirm almost complete coincidence with the exact values obtained analytically. The use of asymptotic expressions for the reciprocity principle not only greatly simplifies computational processes for determining the orthogonal magnetization characteristics, but also implements the calculation of differential permeability tensors for arbitrary field values. The proposed method can be implemented in applications for calculating the magnetic field in devices with nonlinear anisotropic magnetically soft materials, primarily with cold rolled sheet electrical steels, which are most used in electrical engineering. Рассмотрены теоретические и практические аспекты построения векторных материальных уравнений нелинейных анизотропных сред. Показано, что используемые методы учета магнитных свойств даже в безгистерезисном приближении не всегда удовлетворяют требованиям полноты и математической строгости. Подтверждена эффективность энергетического подхода к построению векторных характеристик магнитного состояния таких сред. Особое внимание уделено принципу взаимности как фундаментальному свойству обратимых процессов намагничивания. Установлены новые асимптотические выражения для принципа взаимности и на численных примерах показана их эффективность при построении векторной модели магнитной среды без использования энергетического потенциала.  National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2020-04-21 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06 10.20998/2074-272X.2020.2.06 Electrical Engineering & Electromechanics; No. 2 (2020); 40-45 Электротехника и Электромеханика; № 2 (2020); 40-45 Електротехніка і Електромеханіка; № 2 (2020); 40-45 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06/201182 http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06/201183 Copyright (c) 2020 S. T. Tolmachev, A. V. Il'chenko https://creativecommons.org/licenses/by-nc/4.0

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