Calculation of the optimum parameters of a gyrating crusher for rock crushing

Optimization of operating parameters and modeling of the operation of equipment for the processing and preparation of products of mining plants is an urgent task. Crushers are often used as such equipment. Single-roll gyratory crushers can be used directly in mines for rock crushing. In this paper, using a differential equation, the optimal parameters of such a crusher are calculated. The paper shows that the form of the cheek of the working chamber, which is rational from the point of view of productivity, is the arc of a logarithmic spiral. The obtained mathematical models make it possible to determine the performance of the crusher and the rotational speed of its main working body. Thus, models and expressions were obtained for calculating the kinematic components of the loads on the crusher roll. Using the concept of fuzzy («fuzzy») sets, multi-criteria optimization of the parameters of the working chamber was performed: the eccentricity and the central angle of the beginning of the cheek profile. Due to the optimal choice of the profile of the working chamber and the angular coordinates of the installation of fixed jaws, a decrease in the coefficients of variation of the kinematic components of the loads on the working body is achieved: the moment – by 1.67 times, the radial load – by 1.2 times.

Kondrakhin V. P., Konyukhov V. Yu., Polyakova A. S., Moiseeva E. E., Boyko A. А. Calculation of the optimum parameters of a gyrating crusher for rock crushing. MIAB. Mining Inf. Anal. Bull. 2023;(11-1):88-101. [In Russ]. DOI: 10.25018/0236_1493_2023_111_0_88.

V.P. Kondrakhin, Scientific Department, Kh. Ibragimov Complex Institute of Russian Academy of Sciences, 364906, Grozny, Russia, e-mail: vkondrakhin52@mail.ru,
V.Yu. Konyukhov, Cand. Sci. (Eng.), Professor, Assistant Professor, Irkutsk National Research Technical University, 664074, Irkutsk, Russia, e-mail: konyukhov_vyu@mail.ru,
A.S. Polyakova¹, Cand. Sci. (Eng.), Senior Lecturer, e-mail: Polyakova_nasty@mail.ru, ORCID ID: 0000-0003-1035-4403,
E.E. Moiseeva¹, Cand. Sci. (Econ.), Assistant Professor,Head of Chair, e-mail: mee.05@mail.ru,
A.А. Boyko¹, Cand. Sci. (Econ.), Assistant Professor, e-mail: boiko@sibsau.ru, Siberian Federal University, 660041, Krasnoyarsk, Russia, Artificial Intelligence Technology Scientific and Education Center, Bauman Moscow State Technical University, 105005, Moscow, Russia, ORCID ID: 0000-0001-7185-2890,
¹ Reshetnev Siberian State University of Science and Technology, 660037, Krasnoyarsk, Russia.

V.P. Kondrakhin, e-mail: vkondrakhin52@mail.ru.

1. Zinovieva O. M., Kolesnikova L. A., Merkulova A. M., Smirnova N. A. On the issue of assessing the ecological condition of the environment to achieve sustainable development of coal-mining regions of Russia. Sustainable Development of Mountain Territories. 2023, vol. 15, no. 1, pp. 35—43. [In Russ]. DOI: 10.21177/1998-4502-2023-15-1-35-43.

2. Rylnikova M. V., Angelov V. A., Turkin I. S. Distinctive features of technological and design solutions on disposal of waste of ore mining and processing in a worked-out area. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2015, no. 2, pp. 59—66. [In Russ].

3. Rybak Ya., Khairutdinov M. M., Kongar-Suryun Ch. B., Tyulyaeva Yu. S. Resource-saving technologies for development of mineral deposits. Sustainable Development of Mountain Territories. 2021, vol. 13, no. 3, pp. 406—415. [In Russ]. DOI: 10.21177/1998-4502-2021-13-3-406-415.

4. Gutarevich V. O., Martyushev N. V., Klyuev R. V., Kukartsev V. A., Kukartsev V. V., Iushkova L. V., Korpacheva L. N. Reducing oscillations in suspension of mine monorail track. Applied Sciences. 2023, vol. 13, no. 8, article 4671. DOI: 10.3390/app13084671.

5. Bosikov I. I., Klyuev R. V., Savchenko I. A., Kukartsev V. V., Kukartsev V. A., Tynchenko Y. A. Modeling and complex analysis of the topology parameters of ventilation networks when ensuring fire safety while developing coal and gas deposits. Fire. 2023, vol. 6, no. 3, article 95. DOI: 10.3390/fire6030095.

6. Malorodov V. G., Mizin V. A., Kondrakhin V. P., Olkhovsky O. V. Single-roll crusher. Patent of Ukraine no. 51700, priority dated 10/13/98, published 12/16/2002, bull. no. 12.

7. Abramkin N. I., Mansurov P. A., Kuzina A. V., Levkin Yu. M. Justification of the roll crusher calculation parameters, taking into account the use of spar screen surface. Sustainable Development of Mountain Territories. 2023, vol. 15, no. 2, pp. 473—481. [In Russ]. DOI: 10.21177/1998-4502-2023-15-2-473-481.

8. Kondrakhin V. P., Martyushev N. V., Klyuev R. V., Sorokova S. N., Efremenkov E. A., Valuev D. V., Mengxu Q. Mathematical modeling and multi-criteria optimization of design parameters for the gyratory crusher. Mathematics. 2023, vol. 11, article 2345. DOI: 10.3390/math 11102345.

9. Djokoto S. S., Karimi H. R. Modeling and simulation of a High-Pressure Roller Crusher for silicon carbide production. Proceeding of the International Conference on Electrical Power Quality and Utilisation (EPQU). 2011, pp. 1—6. DOI: 10.1109/EPQU.2011.6128963.

10. Johansson M., Evertsson M. A time dynamic model of a high-pressure grinding rolls crusher. Minerals Engineering. 2019, vol. 132, pp. 27—38. DOI: 10.1016/j.mineng.2018.12.008.

11. Efremenkov E. A., Shanin S. A., Martyushev N. V. Development of an algorithm for computing the force and stress parameters of a cycloid reducer. Mathematics. 2023, vol. 11, article 993. DOI: 10.3390/math11040993.

12. Lieberwirth H., Hillmann P., Hesse M. Dynamics in double roll crushers. Minerals Engineering. 2017, vol. 103, pp. 60—66. DOI: 10.1016/j.mineng.2016.08.009.

13. Bello S., Bajela G., Lamidi S., Oshinlaja S. Design and fabrication of pneumatic can crushing machine. International Journal of Advances in Scientific Research and Engineering. 2020, vol. 6, pp. 154—161. DOI: 10.31695/IJASRE.2020.33914.

14. Chakule R., Patil S., Talmale P. Design and development of can crushing machine. Asian Journal of Engineering and Applied Technology. 2020, vol. 9, pp. 25—28. DOI: 10.51983/ ajeat-2020.9.1.1082.

15. Bahre K., Krohm R. Continuous operation crushing machine, 2023. Retrieved from: https://www.researchgate.net/publication/255043528_Continuous-operation_crushing_machine.

16. Kurbanov X., Yadgarov S., Turdiev A., Amanov Z. Development of a technological image of a stone crushing machine. International Journal of Innovative Technology and Exploring Engineering. 2020, no. 9, pp. 313—315. DOI: 10.35940/ijitee.E2197.039520.

17. Pacana A., Siwiec D., Bednarova L., Sofranko M., Vegsöova O., Cvoliga M. Influence of natural aggregate crushing process on crushing strength index. Sustainability. 2021, vol. 13, article 8353. DOI: 10.3390/su13158353.

18. Rajan B., Singh D. Understanding influence of crushers on shape characteristics of fine aggregates based on digital image and conventional techniques. Construction and Building Materials. 2017, vol. 150, pp. 833—843.

19. Bengtsson M., Hulthen E., Evertsson C. M. Size and shape simulation in a tertiary crushing stage, a multi objective perspective. Minerals Engineering. 2015, vol. 77, pp. 72—77. DOI: 10.1016/j.mineng.2015.02.015.

20. Ostroukh A., Surkova N., Varlamov O., Chernenky V., Baldin A. Automated process control system of mobile crushing and screening plant. Journal of Applied Engineering Science. 2018, vol. 16, pp. 343—348.

21. Cleary P. W., Sinnott M. D., Morrison R. D., Cummins S., Delaney G. W. Analysis of cone crusher performance with changes in material properties and operating conditions using DEM. Minerals Engineering. 2017, vol. 100, pp. 49—70. DOI: 10.1016/j.mineng.2016.10.005.

22. Dmitrak Yu. V., Atrushkevich V. A., Kubrin S. S., Adamova L. S. Evaluation of shock pulses energy in the grinding rocks process for various types of mills. Sustainable Development of Mountain Territories. 2022, vol. 14, no. 3, pp. 468—478. [In Russ]. DOI: 10.21177/19984502-2022-14-3-468-478.

23. Minasyan D. G., Eloeva A. S., Nazarov S. G., Skvortsov P. A. Comparison of the crushed material movement model in the body of vertical centrifugal mill. Sustainable Development of Mountain Territories. 2021, vol. 13, no. 1, pp. 119—124. [In Russ]. DOI: 10.21177/1998-4502-2021-13-1-119-124.

24. Adigamov R. R., Baraboshkin K. A., Mishnev P. A. Development of rolling procedures for pipes of K55 strength class at the laboratorial mill. CIS Iron and Steel Review. 2022, vol. 24, pp. 60—66. DOI 10.17580/cisisr.2022.02.09.

25. Koken E., Ozarslan A. New testing methodology for the quantification of rock crushability: Compressive crushing value. International Journal of Minerals, Metallurgy, and Materials. 2018, no. 25, pp. 1227—1236. DOI: 10.1007/s12613-018-1675-7.

26. Ershov V. A., Kondratiev V. V., Karlina A. I., Kolosov A. D., Sysoev I. A. Selection of control system parameters for production of nanostructures concentrates. Journal of Physics: Conference Series. 2018, vol. 1118, no. 1, article 012014. DOI: 10.1088/1742-6596/1118/1/012014.

27. Kondratiev V. V., Govorkov A. S., Kolosov A. D., Gorovoy V. O., Karlina A. I. The development of a test stand for developing technological operation «flotation and separation of MD2. The deposition of nanostructures MD1» produce nanostructures with desired properties. International Journal of Applied Engineering Research. 2017, vol. 12, no. 22, pp. 12373—12377.

28. Zykova A., Skeeba V., Zadkov D., Kuzkin A. Influence of W addition on microstructure and mechanical properties of Al-12% Si alloys. Materials. 2019, vol. 12, article 981. DOI: 10.3390/ma12060981.

29. Ivashutenko A., Vidayev I., Kostikov K. Influence of technological factors on structure and properties of alumina-zirconia ceramics. Advanced Materials Research. 2014, vol. 1040, pp. 845—849. DOI: 10.4028/www.scientific.net/AMR.1040.845.

30. Zeren Chen, Guoqiang Wang, Duomei Xue, Da Cui. Simulation and optimization of crushing chamber of gyratory crusher based on the DEM and GA. Powder Technology. 2021, vol. 384, pp. 36—50. DOI: 10.1016/j.powtec.2021.02.003.

31. Konyuhov V. Y., Konstantinova M. V., Gladkih A. M. Determination of restored units spectrum of equipment and development of the assembly unit repair method at industrial enterprises. Journal of Physics: Conference Series. 2019, vol. 1353, no. 1, article 012047. DOI: 10.1088/1742-6596/1353/1/012047.

32. Johansson M., Bengtsson M., Evertsson C. M., Hulthén E. A fundamental model of an industrial-scale jaw crusher. Minerals Engineering. 2017, vol. 105, pp. 69—78. DOI: 10.1016/j. mineng.2017.01.012.

33. Kondrat’ev V. V., Govorkov A. S., Lavrent’eva M. V., Sysoev I. A. Description of the heat exchanger unit construction, created in IRNITU. International Journal of Applied Engineering Research. 2016, vol. 11, no. 19, pp. 9979—9983.

34. Balanovsky A. E., Shtayger M. G. Plasma-arc surface modification of metals in a liquid medium. IOP Conference Series: Materials Science and Engineering. 2018, vol. 411, no. 1, article 012013. DOI: 10.1088/1757-899X/411/1/012013.

35. Sakawa M. Fuzzy sets and interactive multiobjective optimization. New York, Plenum Press, 1993. DOI: 10.1007/978-1-4899-1633-4.

36. Konyukhov V. Y., Permyakova D. N., Oparina T. A. Perspective for the use of industrial waste in lubricating compositions to reduce wear in friction pairs. Journal of Physics: Conference Series. 2021, vol. 2061, no. 1, article 012046. DOI: 10.1088/1742-6596/2061/1/012046.