MATHEMATICAL MODELLING OF THE VOLUME OF THE CAPTURED SLURRY DOSE BY THE FEEDER CURL WHEN THE COORDINATE SYSTEM IS ROTATED

Abstract

At concentrators in Ukraine in the first stages of ore preparation ore grinding capacity can be significantly reduced due to pulsations of material in the drum of the ball mill during the loading of ore, sands of the spiral classifier, water and balls. In the process of analysing recent studies and publications, it was found that practically solutions have been found to prevent the occurrence of pulsations during the loading of feed ore, water and balls into the mill. However, the same cannot be said for the loading of spiral classifier sands. Given that the article is focused on solving the problem of loading the sands of a mechanical spiral classifier into a ball mill, its topic is relevant. This research was carried out within the framework of the development of scientific topics of the Central Ukrainian National Technical University. The purpose of the work is to establish the possibility of adjusting the snail feeder to the process of capturing pulp doses in the receiving device by rotating the curl coordinate system. The methods of comparison, analysis, theory of ball mills, theory of grinding materials, theory of automatic control, mathematical modelling, analytical geometry, theory of plane curves, theory of definite integrals were used in the research process. It has been proven that sand flow can strongly influence the condition of the pulp in the ball mill. The snail feeder, dividing the discharge of the spiral classifier can alleviate the situation, but it is itself a source of excitation of possible pulp oscillations in the ball mill. In the process of the study the longitudinal areas of the captured pulp dose in the old coordinate system and in the new (rotated by the angle φ) coordinate system were determined, which are respectively equal to 0.002059 conditional square unit and 0.001449 conditional square unit. Since the longitudinal area fully characterises the captured pulp dose, judgements can be made on the basis of the data obtained. The individual data show that the volume of the captured dose when the coordinate system is rotated by 10° is significantly less compared to that without rotation. The reduction in the volume of captured dose by the curl when the coordinate system is rotated is 29.63 %, which is significant. This will negatively affect the feeder performance and lead to overconsumption of electricity for pulp transport. So, in the process of the conducted researches it has been established that it is inexpedient to adjust the snail feeders by rotation of the coordinate system. It is necessary to develop an original approach of curl profile formation and the phase of its beginning establishment to ensure optimal parameters of the snail feeder. The prospect of further research is the development of such an approach of curl profile formation and justification of its installation relative to the mill feed throat.