Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

Abstract

The object of this study is the grinding process in a tumbling mill when the mechanism of destruction by abrasion is implemented, which is caused by the mechanism of shear loading. The abrasive effect due to the impulse interaction during the mutual chaotic movement of granular particles in the shear layer of loading, characterized by the granular temperature, is taken into account. The task solved was determining the parameters of the shear interaction, which is caused by the difficulties of modeling and complexity of the hardware analysis of behavior of the internal loading in the mill. A mathematical model was built based on data visualization for the abrasion grinding mechanism. The power of the shear interaction forces was taken as an analog of the grinding performance. The initial shear characteristic was considered to be the average value of the shear velocity gradient in the central averaged normal section of the shear layer. The impact on productivity of the granular temperature and mass fraction of the shear layer and loading turnover was taken into account. The effect of rotation speed on performance was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative particle size of 0.0104. The maximum value of the energy and productivity of grinding by abrasion was established at the relative speed of rotation ψω=0.55–0.6. The results have made it possible to establish a rational speed when grinding by abrasion, ψω=0.5–0.6. This value is smaller in comparison with grinding by crushing ψω=0.55–0.65 and breaking ψω=0.75–0.9. The established effect is explained by the detected activation of the chaotic quasi-thermodynamic movement of particles of the shear layer at slow rotation. The model built makes it possible to predict rational technological parameters of the energy-saving process of fine grinding in a tumbling mill by abrasion