Магнитные свойства многокомпонентных гетерогенных сред с двоякопериодической структурой

Abstract

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.

Heterogeneous media have a widerange of practical applications. Media with a doubly periodicstructure (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 restrictionson the number of phases, their geometry, concentration, and magnetic properties. Based on the theory of elliptic functions andsecondary 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 withoutspecifying 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.