Mathematical Modeling of the Process of Grinding Materials

Based on knowledge of thermodynamic flows and driving forces of the crushing process and the application of the principle of minimum entropy production a dependence for determining the size of particles resistant to crushing was obtained and verified using experimental results on grinding corundum in a planetary mill. To model the kinetics of grinding, an integrodifferential equation for the balance of the number of particles by linear dimensions was obtained, where the probability of particle crushing was determined from the physicochemical essence of the thermodynamic crushing flows. The results of calculating the density of the distribution function of the number of particles and the change in the average size of corundum particles during grinding over time are presented, which agree well with the experimental data. Optimal modes for carrying out the process of grinding corundum in a planetary mill to obtain particles of a given size have been found.