Determining optimal parameters of the grinding media and operating parameters of the vibratory mill using multifactorial experiment designed with the simplex method

DOI: https://doi.org/10.30686/1609-9192-2026-4-68-73

Читать на русскоя языке Yu.V. Dmitrak, A.A. Kravtsov
Institute of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, Moscow, Russian Federation
Russian Mining Industry №4/ 2026 p. 68-73

Abstract: Conducting experimental research involves carrying out a large number of experiments, which is time-consuming and increases the risk of making avoidable errors. During the research, it is necessary to simultaneously determine the optimal value of the target function and ensure that a specified value of a key parameter—known in experimental design theory as a control parameter—is maintained. This article examines the application of the multivariate experimental design method in studies of the energy characteristics of the vibratory grinding process for mineral raw materials. The objective of the study is to identify the optimal values for the specific energy consumption of grinding in a vibratory mill with a minimum number of experiments and to demonstrate the efficiency of using the multivariate experimental design method. The research was conducted using the simplex planning method, with the rock grinding efficiency as the control parameter. The authors calculated the optimal operating parameters of the mill, i.e. the chamber oscillation amplitude of 3 mm, the chamber oscillation frequency of 22 Hz, the ratio of the ball diameter to the chamber diameter of 0.025, and the ratio of the core diameter to the chamber diameter of 0.2. A series of experiments was conducted on grinding 1) granite chips, 2) marble chips, and 3) gypsum based on the obtained values of the mill parameters. As a result of their research, the authors obtained data that allowed plotting graphs showing changes in the energy intensity of grinding for different rock types as a function of (1) the amplitude and frequency of the grinding chamber oscillations, (2) the ratio of the ball diameter to the chamber diameter, (3) the ratio of the ball diameter to the diameter of the core that replaces the stagnant zone in the grinding chamber.

Keywords: simplex method, grinding media, amplitude of grinding chamber oscillations, frequency of grinding chamber oscillations, stagnant zone, specific grinding energy intensity, vibration grinding

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

For citation: Dmitrak Yu.V., Kravtsov A.A. Determining optimal parameters of the grinding media and operating parameters of the vibratory mill using multifactorial experiment designed with the simplex method. Russian Mining Industry. 2026;(4):68–73. https://doi.org/10.30686/1609-9192-2026-4-68-73

Information about the article

Received: 09.03.2026

Received after peer review: 21.05.2026

Accepted for publication: 02.06.2026

Information about the authors

Yury V. Dmitrak – Doctor of Engineering Sciences, Professor, Chief Researcher, Head of the Department of Modeling and Control of Mining Systems, Institute of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, Moscow, Russian Federation; https://orcid.org/0000-0003-1278-4845; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Alexey A. Kravtsov – Junior Researcher, Department of Modeling and Control of Mining Systems, Institute of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, Moscow, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

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