Modeling of Evolution of Shape of Ductile Metal Disk for Isotropic Bombardment

摘要

This work is devoted to a calculation of formation time of a toroidal shape of a flat piece of ductile metal in enrichment of minerals. Gold grains occurring in nature, in most cases, originally have a form of a flat plate (the scaly form). Continuous bombardment of the surface of a piece of gold with surrounding grains of sand during the enrichment of ores in various jigging. separation, and crusher devices results in the piece assuming a toroidal shape. When separating, the shape of the grains in the form of a torus is considered to be the most effective. Therefore, the problem of calculation of the formation time of the toroidal shape of the piece of gold is urgent. In this paper, we propose a physical model for the formation of the toroidal shape of the piece of ductile metal, in which an isotropic, homogeneous flow of particles deforming a plane body (disk) is introduced. Based on the proposed physical model, a mathematical model of evolution of the surface under deformation of a body was developed. A first-order differential equation is obtained with respect to the deformable surface, which is solved by the Runge-Kutta method. As a result of the study, the dependence of the deformed surface on the time was determined.