MATHEMATICAL MODELING OF THE MAGNETIC FIELD OF HIGH-GRADIENT MAGNETIC SEPARATORS WITH A DOUBLE-PERIODIC MATRIX STRUCTURE

A detailed justification of the method of calculating local and effective characteristics of magnetic filters of the matrix structure of high-gradient magnetic separators is given. It is shown that under the assumption of a doubly-periodic structure of the matrix and the plane-parallel character of the field, it allows to significantly expand the possibilities of existing methods due to the absence of significant restrictions on the geometric and physical parameters of the ferromagnetic elements of the matrix and their concentration. The method is based on the integral equation relative to the magnetization vector of the elements of the main parallelogram of periods. The doubly-periodic nature of the solution is automatically provided by the construction of the integral operator kernel, and unlike differential methods, there is no need to set boundary conditions. Within the framework of the linear formulation, clear criteria of similarity are formulated for the effective and local characteristics of the field, in particular for isolines of magnetic forces. The functional possibilities of the method are illustrated by the results of computational experiments on the examples of matrices with different geometric characteristics of the elements. According to the results of computational experiments, the complex and unpredictable distribution of magnetic forces even in matrixes of elements of simple geometry is illustrated. In particular, the calculations confirmed the hypothetical assumption regarding the existence of periodic bifurcation points in which there are no magnetic forces. These points are the centers of zones with negligible magnetic forces, which should be taken into account when calculating the extraction capacity of the matrix. Specific examples illustrate the method of determining the potential zone of extraction of weakly magnetic materials, in which the values of magnetic forces exceed their minimum permissible level, taking into account technological limitations. References 20, figures 5, table 1. © Видавець Інститут електродинаміки НАН України, 2025 Це стаття відкритого доступу за ліцензією CC BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.uk