ОЦІНЮВАННЯ ГЕОМЕТРИЧНИХ ПАРАМЕТРІВ ПОЛЮСНОЇ СИСТЕМИ МАТРИЦІ ЕЛЕКТРОМАГНІТНОГО СЕПАРАТОРА

Purpose. The choice of the geometric dimensions ratios of system of matrix poles of electromagnetic polygradient separator to increase productivity with maintaining the reliability of extracting of ferromagnetic impurities from bulk material.Methodology. To solve the dynamic problem of motion of a ferromagnetic body in the working gap of pole system of matrix of polygradient separator under the influence of an external magnetic field the known methods of solving linear inhomogeneous differential equations are used. To confirm the reliability of obtained results the method of experimental research is used.Findings. The formulation of dynamic problem of movement of ferromagnetic body in the working gap of plate pole system of matrix of polygradient separator is carried out. Parametric equation for the trajectory of ferromagnetic body removal and a calculated relation connecting the main geometric dimensions of the system of matrix poles are obtained. The calculation results are confirmed experimentally and by operating practice of known magnetic separating devices.Originality. The mathematical description of working process of a polygradient electromagnetic separator with a plate matrix was further developed, which made it possible to obtain an analytical expression that takes into account the main geometric dimensions of the working space of matrix of separator.Practical value. Accounting of obtained analytical dependences between the length of separation zone and air gap, which characterizes the thickness of the separated material layer through which the ferromagnetic body must pass during the separation process, will ensure the necessary purity and productivity of separation.

Asymptotic Behavior of Magnetostrictive Elasticity for Microstructured Materials

According to the classical theory of Weiss, Landau, and Lifshitz, in a ferromagnetic body there is a spontaneous magnetization field m, such that ∥m∥ = τ0 = const in all points of this material Ω. In any stationary configuration, this ferromagnetic body consists of areas (Weiss domains) in which the magnetization is uniform (i.e. m = const) separated by thin transition layers (Bloch walls). Such stationary configuration corresponds to the minimum point of the magnetostrictive free energy E. We are considering an elastic magnetostrictive body in our paper. The elastic magnetostrictive free energy Eδ depends on a small parameter δ such that δ → 0. As usual, the displacement field is denoted by u. We will show that each sequence of minimizers (ui, mi) contains a subsequence that converges to a couple of fields (u0, m0). By means of a Γ-limit procedure we will show that this couple (u0, m0) is a minimizer of the new functional E0. This new functional E0 describes the magnetic-elastic properties of the body with microstructure.

Hydrogen Trapping in bcc Iron

Fundamental understanding of H localization in steel is an important step towards theoretical descriptions of hydrogen embrittlement mechanisms at the atomic level. In this paper, we investigate the interaction between atomic H and defects in ferromagnetic body-centered cubic (bcc) iron using density functional theory (DFT) calculations. Hydrogen trapping profiles in the bulk lattice, at vacancies, dislocations and grain boundaries (GBs) are calculated and used to evaluate the concentrations of H at these defects as a function of temperature. The results on H-trapping at GBs enable further investigating H-enhanced decohesion at GBs in Fe. A hierarchy map of trapping energies associated with the most common crystal lattice defects is presented and the most attractive H-trapping sites are identified.

Homogenization of composite ferromagnetic materials

The objective of this paper is to perform, by means of Γ - convergence and two-scale convergence , a rigorous derivation of the homogenized Gibbs–Landau free energy functional associated with a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the Gibbs–Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.