MATHEMATICAL MODELING OF OPERATING CONDITIONS OF THE ROD GRINDING LOAD IN THE CASCADE MODE OF ORE GRINDING

Abstract

The factors affecting the wear of the grinding load in the cascade mode of ore grinding are identified. Among them are sliding, impact, rolling on the abrasive, abrasion and crushing of the abrasive, applied force, and applied displacement speed. The modeling was performed as part of the development of the topic "Optimization of open-cycle rod mills productivity for ore and finished product with minimal energy and material overruns", which is part of the scientific theme of the Central Ukrainian National Technical University. The topic of the article is relevant. The aim of the work is to develop a criterion for assessing the wear of the rod loading of a tumbling mill in the form of a mathematical model by analyzing the effect of influencing factors. The methods used are analysis, comparison, mathematical modeling, the theory of ore grinding in rod mills, decomposition and composition, methods of the theory of resistance to wear, methods of the theory of wear of metal bodies in interaction with a loose abrasive. The research was carried out on the example of the МСЦ-35-55 rod mill, which is currently used at iron ore processing plants. It is most characterized by a cascade mode of operation, in which the ore is destroyed mainly by crushing and abrasion. An optimized rod loading with three rod diameters is used. In this mode of operation, the smallest diameter rods are pushed to the drum wall, and the largest ones are concentrated in the central area of its cross section. In a rod mill, the grinding media is formed by enlarged zones with rods of approximately the same diameter, which allows it to be considered as one-dimensional. The bulk of the rods is pressed against the drum wall motionless, and the ore trapped in the lower zone moves to the upper mark, from where it rolls down in a cascade. The grinding media movement speed on the natural slope of the rods is in the range of 2.12...2.5 m/s. It was found that all the factors affecting the grinding media wear affect the rods of different diameters almost equally. Therefore, it can be argued that rods of different diameters operate under almost identical conditions. Under such conditions, the main operating factor is the area of contact between the grinding media and the abrasive in the form of crushed ore, which is recommended as a criterion for evaluating the wear of the rods. A criterion for evaluating the wear of the grinding media in the form of a mathematical model has been proposed. Prospect for further research is simulation modeling of the wear of the rod grinding media in specific types of tumbling mills.