MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE
Heterogeneous media have a wide range of practical applications. Media with a doubly periodic structure (matrices of high-gradient magnetic separators, etc.) occupy an important place. Their study is usually based on experimental and approximate methods and is limited to simple two-phase systems. Th...
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| Дата: | 2020 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English Ukrainian |
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National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine”
2020
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| Онлайн доступ: | http://eie.khpi.edu.ua/article/view/2074-272X.2020.1.05 |
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| Назва журналу: | Electrical Engineering & Electromechanics |
Репозитарії
Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-195840 |
|---|---|
| record_format |
ojs |
| institution |
Electrical Engineering & Electromechanics |
| collection |
OJS |
| language |
English Ukrainian |
| topic |
двоякопериодическая гетерогенная среда интегральное уравнение вектор намагниченности поле напряженности тензор магнитной проницаемости высокоградиентная сепарация матрица магнитные силы 621.3.013.22 517.968 doubly periodic heterogeneous medium integral equation magnetization vector strength field homogenization problem magnetic permeability tensor polygradient separation matrix magnetic forces 621.3.013.22 517.968 |
| spellingShingle |
двоякопериодическая гетерогенная среда интегральное уравнение вектор намагниченности поле напряженности тензор магнитной проницаемости высокоградиентная сепарация матрица магнитные силы 621.3.013.22 517.968 doubly periodic heterogeneous medium integral equation magnetization vector strength field homogenization problem magnetic permeability tensor polygradient separation matrix magnetic forces 621.3.013.22 517.968 Tolmachev, S. T. Bondarevskyi, S. L. Il'chenko, A. V. MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| topic_facet |
двоякопериодическая гетерогенная среда интегральное уравнение вектор намагниченности поле напряженности тензор магнитной проницаемости высокоградиентная сепарация матрица магнитные силы 621.3.013.22 517.968 doubly periodic heterogeneous medium integral equation magnetization vector strength field homogenization problem magnetic permeability tensor polygradient separation matrix magnetic forces 621.3.013.22 517.968 |
| format |
Article |
| author |
Tolmachev, S. T. Bondarevskyi, S. L. Il'chenko, A. V. |
| author_facet |
Tolmachev, S. T. Bondarevskyi, S. L. Il'chenko, A. V. |
| author_sort |
Tolmachev, S. T. |
| title |
MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| title_short |
MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| title_full |
MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| title_fullStr |
MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| title_full_unstemmed |
MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE |
| title_sort |
magnetic properties of multicomponent heterogeneous media with a doubly periodic structure |
| title_alt |
МАГНИТНЫЕ СВОЙСТВА МНОГОКОМПОНЕНТНЫХ ГЕТЕРОГЕННЫХ СРЕД С ДВОЯКОПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ |
| description |
Heterogeneous media have a wide range of practical applications. Media with a doubly periodic structure (matrices of high-gradient magnetic separators, etc.) occupy an important place. Their study is usually based on experimental and approximate methods and is limited to simple two-phase systems. The development of universal and accurate methods of mathematical modelling of electrophysical processes in such environments is an urgent task. The aim of the paper is to develop a method for calculating local and effective parameters of a magnetostatic field with minimal restrictions on the number of phases, their geometry, concentration, and magnetic properties. Based on the theory of elliptic functions and secondary sources, an integral equation is formulated with respect to the magnetization vector of the elements of the main parallelogram of the periods. The calculated expressions for the complex potential, field strength, and components of the effective magnetic permeability tensor are obtained. The results of a series of computational experiments confirming the universality and effectiveness of the method are presented. As an example of a practical application, a detailed study of the field of the magnetic forces of the matrix is carried out: the lines of magnetic isodine and potential extraction areas for a complex version of the matrix are constructed. Within the framework of the developed method, the calculation of local and effective field characteristics is carried out by solving the field problem in the field of an arbitrary parallelogram of periods without specifying boundary conditions on its sides with a comprehensive consideration of significant interdependent factors. The practical value of the method is to create new opportunities for improving the technical characteristics of electrophysical devices for which the universality and accuracy of calculating local and effective field characteristics is decisive. An algorithm for optimizing the characteristics of the separator is proposed. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
| publishDate |
2020 |
| url |
http://eie.khpi.edu.ua/article/view/2074-272X.2020.1.05 |
| work_keys_str_mv |
AT tolmachevst magneticpropertiesofmulticomponentheterogeneousmediawithadoublyperiodicstructure AT bondarevskyisl magneticpropertiesofmulticomponentheterogeneousmediawithadoublyperiodicstructure AT ilchenkoav magneticpropertiesofmulticomponentheterogeneousmediawithadoublyperiodicstructure AT tolmachevst magnitnyesvojstvamnogokomponentnyhgeterogennyhsredsdvoâkoperiodičeskojstrukturoj AT bondarevskyisl magnitnyesvojstvamnogokomponentnyhgeterogennyhsredsdvoâkoperiodičeskojstrukturoj AT ilchenkoav magnitnyesvojstvamnogokomponentnyhgeterogennyhsredsdvoâkoperiodičeskojstrukturoj |
| first_indexed |
2024-06-01T14:39:27Z |
| last_indexed |
2024-06-01T14:39:27Z |
| _version_ |
1800670038659694592 |
| spelling |
eiekhpieduua-article-1958402020-02-25T19:53:23Z MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE МАГНИТНЫЕ СВОЙСТВА МНОГОКОМПОНЕНТНЫХ ГЕТЕРОГЕННЫХ СРЕД С ДВОЯКОПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ Tolmachev, S. T. Bondarevskyi, S. L. Il'chenko, A. V. двоякопериодическая гетерогенная среда интегральное уравнение вектор намагниченности поле напряженности тензор магнитной проницаемости высокоградиентная сепарация матрица магнитные силы 621.3.013.22 517.968 doubly periodic heterogeneous medium integral equation magnetization vector strength field homogenization problem magnetic permeability tensor polygradient separation matrix magnetic forces 621.3.013.22 517.968 Heterogeneous media have a wide range of practical applications. Media with a doubly periodic structure (matrices of high-gradient magnetic separators, etc.) occupy an important place. Their study is usually based on experimental and approximate methods and is limited to simple two-phase systems. The development of universal and accurate methods of mathematical modelling of electrophysical processes in such environments is an urgent task. The aim of the paper is to develop a method for calculating local and effective parameters of a magnetostatic field with minimal restrictions on the number of phases, their geometry, concentration, and magnetic properties. Based on the theory of elliptic functions and secondary sources, an integral equation is formulated with respect to the magnetization vector of the elements of the main parallelogram of the periods. The calculated expressions for the complex potential, field strength, and components of the effective magnetic permeability tensor are obtained. The results of a series of computational experiments confirming the universality and effectiveness of the method are presented. As an example of a practical application, a detailed study of the field of the magnetic forces of the matrix is carried out: the lines of magnetic isodine and potential extraction areas for a complex version of the matrix are constructed. Within the framework of the developed method, the calculation of local and effective field characteristics is carried out by solving the field problem in the field of an arbitrary parallelogram of periods without specifying boundary conditions on its sides with a comprehensive consideration of significant interdependent factors. The practical value of the method is to create new opportunities for improving the technical characteristics of electrophysical devices for which the universality and accuracy of calculating local and effective field characteristics is decisive. An algorithm for optimizing the characteristics of the separator is proposed. Изложен метод расчета магнитостатического поля в двоякопериодической гетерогенной среде. Сформулировано интегральное уравнение относительно вектора намагниченности элементов среды. Расчет характеристик поля осуществляется путем решения полевой задачи в области основного параллелограмма периодов без задания граничных условий на его сторонах. Получены расчетные выражения для напряженности поля и тензора магнитной проницаемости. Приведены результаты вычислительных экспериментов, подтверждающих универсальность и эффективность метода. Проведено детальное исследование поля магнитных сил матрицы высокоградиентного магнитного сепаратора. Метод открывает новые возможности повышения технических характеристик электрофизических устройств, для которых универсальность и точность расчета локальных и эффективных характеристик поля является определяющей. National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” 2020-02-21 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/2074-272X.2020.1.05 10.20998/2074-272X.2020.1.05 Electrical Engineering & Electromechanics; No. 1 (2020); 29-38 Электротехника и Электромеханика; № 1 (2020); 29-38 Електротехніка і Електромеханіка; № 1 (2020); 29-38 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/2074-272X.2020.1.05/196656 http://eie.khpi.edu.ua/article/view/2074-272X.2020.1.05/196657 Copyright (c) 2020 S. T. Tolmachev, S. L. Bondarevskyi, A. V. Il'chenko https://creativecommons.org/licenses/by-nc/4.0 |