Establishment of effective parameters for grinding mineral raw materials in a vibrating mill with multi-frequency vibroimpact excitation of the grinding chamber

Abstract The mathematical model of a vibrating mill with multi-frequency vibroimpact excitation of the grinding chamber and distributed parameters of the technological medium has been studied. It has been established that the impact interactions of the technological medium with the top surface of the grinding chamber lead to a significant increase in the number of impact interactions between the grinding bodies compared to the modes without impact interaction. At the same time, the sums of the maximum values of impact reactions and the sums of the maximum values of the increase in the kinetic energy of the grinding bodies increase during the period of forced excitation. In the range of changes in the distance from the free surface of the technological medium to the top surface of the grinding chamber in modes with impact interactions of the technological medium with the surface of the chamber, there are rational values of them at which the largest number of impact interactions between the grinding bodies occurs, the largest sum of force reactions of impact interaction and kinetic energy of bodies during the period of forced excitation of the mill. In this case, the most effective grinding of mineral raw materials occurs.