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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	S. T. Tolmachev, A. V. Il'chenko
Formato:	article
Lenguaje:	EN RU UK
Publicado:	National Technical University "Kharkiv Polytechnic Institute" 2020
Materias:	nonlinear anisotropic medium vector magnetization characteristics energy potential reciprocity principle asymptotic expressions magnetic permeability tensor Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/b77896659b0345b299f7c1bd3506ab44
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b77896659b0345b299f7c1bd3506ab44
record_format	dspace
spelling	oai:doaj.org-article:b77896659b0345b299f7c1bd3506ab442021-12-02T15:27:19ZTHE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION10.20998/2074-272X.2020.2.062074-272X2309-3404https://doaj.org/article/b77896659b0345b299f7c1bd3506ab442020-04-01T00:00:00Zhttp://eie.khpi.edu.ua/article/view/2074-272X.2020.2.06/201182https://doaj.org/toc/2074-272Xhttps://doaj.org/toc/2309-3404The 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.S. T. TolmachevA. V. Il'chenkoNational Technical University "Kharkiv Polytechnic Institute"articlenonlinear anisotropic mediumvector magnetization characteristicsenergy potentialreciprocity principleasymptotic expressionsmagnetic permeability tensorElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENRUUKElectrical engineering & Electromechanics, Iss 2, Pp 40-45 (2020)
institution	DOAJ
collection	DOAJ
language	EN RU UK
topic	nonlinear anisotropic medium vector magnetization characteristics energy potential reciprocity principle asymptotic expressions magnetic permeability tensor Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	nonlinear anisotropic medium vector magnetization characteristics energy potential reciprocity principle asymptotic expressions magnetic permeability tensor Electrical engineering. Electronics. Nuclear engineering TK1-9971 S. T. Tolmachev A. V. Il'chenko THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION
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.
format	article
author	S. T. Tolmachev A. V. Il'chenko
author_facet	S. T. Tolmachev A. V. Il'chenko
author_sort	S. T. Tolmachev
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
publisher	National Technical University "Kharkiv Polytechnic Institute"
publishDate	2020
url	https://doaj.org/article/b77896659b0345b299f7c1bd3506ab44
work_keys_str_mv	AT sttolmachev thereciprocityprincipleforanonlinearanisotropicmediumwithouthysteresistheoryandpracticeofapplication AT avilchenko thereciprocityprincipleforanonlinearanisotropicmediumwithouthysteresistheoryandpracticeofapplication AT sttolmachev reciprocityprincipleforanonlinearanisotropicmediumwithouthysteresistheoryandpracticeofapplication AT avilchenko reciprocityprincipleforanonlinearanisotropicmediumwithouthysteresistheoryandpracticeofapplication
_version_	1718387225215893504

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

Ejemplares similares