Scientific analysis of mathematical models of charge motion in grinding chambers of various-type mills

The analysis of the kinematics of grinding media and design schemes of the process of interaction of grinding media with the crushed material is carried out. The classification of models of grinding media motion is carried out and the advantages of mathematical and computer modeling of processes occurring in grinding chambers of mills of various types are revealed. The features of modeling the movement of grinding media for each type of mill are indicated. The advantages and disadvantages of using the finite element method in modeling the movement of grinding media in a drum mill are revealed. The results of studies on modeling the distribution of balls by size inside the grinding chamber of a drum mill, the angular speed of rotation of the drum, as well as their effect on power consumption, loading movement and segregation of balls in a laboratory mill are presented. The dependences of the frequency and velocity of energy dissipation on the energy of collision of grinding media with the lining at different values of the grinding chamber filling coefficient with grinding media are presented. The architecture of the dispatching system for the grinding process was reviewed, including a digital twin of the mill and an automatic alarm detection module. The process of modeling a dynamic portrait of ball loading in the grinding chamber of a vibrating mill is considered, the trajectories of balls in the grinding chamber are described, and the loading is divided into dynamic zones. The advantages and disadvantages of applying modeling methods to a specific type of mill are analyzed.

Dmitrak Iu. V., Kravtsov A. A., Adamova L. S., Kutuev R. R., Tsiganov A. E. Scientific analysis of mathematical models of charge motion in grinding chambers of varioustype mills. MIAB. Mining Inf. Anal. Bull. 2025;(9-1):55-74. [In Russ]. DOI: 10.25018/0236_ 1493_2025_91_0_55.

The study was supported by the Russian Science Foundation, Grant No. 25-67-00009, https://rscf.ru/project/25-67-00009/.

Iu.V. Dmitrak¹, Dr. Sci. (Eng.), Professor, Chief Researcher, Head of Department, e-mail: dmitrak@yandex.ru,
A.A. Kravtsov¹, Junior Researcher, e-mail: havok.08@mail.ru,
L.S. Adamova¹, Junior Researcher, e-mail: Adamovamila16@yandex.ru,
R.R. Kutuev², Chief Designer, e-mail: kutuev.globaltest@yandex.ru,
A.E. Tsiganov², Design Engineer, e-mail: cyganov@globaltest.ru,
¹ Institute of Comprehensive Exploitation of Mineral Resources RAS, 111020, Moscow, Russia,
² LLC GlobalTest, 607185, Sarov, Russia.

Iu.V. Dmitrak, e-mail: dmitrak@yandex.ru.

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