Mathematical Modeling and Multi-Criteria Optimization of Design Parameters for the Gyratory Crusher

Vitalii P. Kondrakhin, Nikita V. Martyushev (), Roman V. Klyuev, Svetlana N. Sorokova, Egor A. Efremenkov, Denis V. Valuev and Qi Mengxu
Additional contact information
Vitalii P. Kondrakhin: Scientific Department, Kh. Ibragimov Complex Institute of the Russian Academy of Sciences, Staropromyslovskoe Ave., 21 A, 364906 Grozny, Russia
Nikita V. Martyushev: Department of Material Science, Tomsk Polytechnic University, 30, Lenin Ave., 634050 Tomsk, Russia
Roman V. Klyuev: Technique and Technology of Mining and Oil and Gas Production Department, Moscow Polytechnic University, 33, B. Semenovskaya Str., 107023 Moscow, Russia
Svetlana N. Sorokova: Department of Mechanical Engineering, Tomsk Polytechnic University, 30, Lenin Ave., 634050 Tomsk, Russia
Egor A. Efremenkov: Department of Mechanical Engineering, Tomsk Polytechnic University, 30, Lenin Ave., 634050 Tomsk, Russia
Denis V. Valuev: Yurga Technological Institute (Branch), Tomsk Polytechnic University, 26, Leningradskaya Street, 652055 Yurga, Russia
Qi Mengxu: Technique and Technology of Mining and Oil and Gas Production Department, Moscow Polytechnic University, 33, B. Semenovskaya Str., 107023 Moscow, Russia

Mathematics, 2023, vol. 11, issue 10, 1-16

Abstract: There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times.

Keywords: first-order differential equation; Fourier series; multi-criteria optimization; fuzzy sets; single-roll gyratory crusher; working chamber; performance; kinematic components (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/10/2345/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/10/2345/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2345-:d:1149583

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().