Mechanisms of Destruction of Mineral Particles and Kinetic Characteristics of Ferromagnetic Bodies in Vortex Layer Devices

Identification of the mechanisms of destruction of particles of mineral components during processing in grinding devices is a scientific and practical problem, the solution of which has not yet been presented in its final form. In this paper, kinetic characteristics of ferromagnetic bodies moving under the influence of an electromagnetic field in a vortex layer apparatus are determined. A mathematical model of the motion of ferromagnetic bodies is implemented taking into account the radial inhomogeneity of the magnetic field induction. The dependence of the velocity of a ferromagnetic body on the radial coordinate for various values of the magnetic field induction and its gradient is calculated and it is shown that a ferromagnetic body can accelerate to 50 m/s. A approximate model of the disintegration of particles of a mineral component (Portland cement) as a result of their collision during processing in a vortex layer apparatus is proposed. It is found that the number of acts of disintegration for the majority of Portland cement is two, which is significantly less than the number of collisions of such particles. It has been established that the main factors influencing the destruction of particles and their activation during mechanomagnetic processing in the vortex layer apparatus are: 1) the value of magnetic induction; 2) the gradient of magnetic induction (the switching frequency of electromagnets in the vortex layer apparatus); 3) the magnetic susceptibility of the substance of the processed material. Based on the analysis of the distribution curves of mineral substance particles after crushing, zoning of the working chamber of the vortex layer apparatus is proposed: 1) the zone of mixing, grinding and activation of particles (the range of movement of ferromagnetic bodies is 0–12 m/s); 2) the zone of intensive grinding and activation of particles (the speed range is 12–50 m/s).

R.A. IBRAGIMOV¹, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
E.V. KOROLEV², Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
Sh.Kh. ZARIPOV³, Doctor of Sciences (Physics and Mathematics) (This email address is being protected from spambots. You need JavaScript enabled to view it.)

¹ Kazan State University of Architecture and Civil Engineering (1, Zelenaya Street, Kazan, 420043, Russian Federation)
² Saint Petersburg State University of Architecture and Civil Engineering (4, 2nd Krasnoarmeyskaya Street, Saint Petersburg, 190005, Russian Federation)
³ Kazan Federal University (5, Tovarishcheskaya Street, Kazan, 420097, Russian Federation)

1. Mazovendal I. Metallurgical slag-based concrete materials produced by vortex electromagnetic activation. Key Engineering Materials. 2016. Vol. 683, pp. 221–226. EDN: WQNGOX.
https://doi.org/10.4028/www.scientific.net/KEM.683.221
2. Całus D. Experimental research into the efficiency of an electromagnetic mill. Applied Sciences. 2023. No. 13. 8717. EDN: NHRQNY. https://doi.org/10.3390/ app13158717
3. Całus D., Makarchuk O., Domanowski P., Bujnowski S. A study of magnetic mill productivity. Applied Sciences. 2023. Vol. 13 (11). 6538. EDN: WCUXSK. https://doi.org/10.3390/app13116538
4. Makarchuk O., Calus D., Moroz V. Mathematical model to calculate the trajectories of electromagnetic mill operating elements. Tekhnihna Electrodynamika. 2021. No. 2, pp. 26–34. EDN: XTBVJA. https://doi.org/10.15407/techned2021.02.026
5. Коняев А.Ю., Багин Д.Н. Моделирование и исследование электромагнитных смесителей порошковых материалов // Вестник Пермского национального исследовательского политехнического университета. Электротехника, информационные технологии, системы управления. 2021. № 38. С. 129–147. EDN: DQXSPI. https://doi.org/10.15593/2224-9397/2021.2.07
5. Konyaev A.Yu., Bagin D.N. Modeling and research of electromagnetic mixers of powder materials. Vestnik of the Perm National Research Polytechnic University. Electrical engineering, information technology, control systems. 2021. No. 38, pp. 129–147. (In Russian). EDN: DQXSPI.https://doi.org/10.15593/2224-9397/2021.2.07
6. Polshchikov H., Zhukov P. Force effect of a circular rotating magnetic field of a cylindrical electric inductor on a ferromagnetic particle in process reactors. Technology Audit and Production Reserves. 2023. No. 6 (1(74)), pp. 34–40. EDN: GPXQGN. https://doi.org/10.15587/2706-5448.2023.293005
7. Milykh V.I., Shaida V.P., Yurieva O.Y. Analysis of the thermal state of the electromagnetic mill inductor with oil cooling in stationary operation modes. Electrical Engineering&Electromechanics. 2023. No. 3, pp. 12–20. EDN: HGPDES.
https://doi.org/10.20998/2074-272X.2023.3.02
8. Kazak O., Halbedel B. Correlation of the vector gradient of a magnetic field with the kinetic energy of hard magnetic milling beads in electromechanical mills. Chemie Ingenieur Technik. 2023. Vol. 95. Iss. 10, pp. 1615–1622. EDN: NWQBWH. https://doi.org/10.1002/cite.202200183
9. Ibragimov R.A., Korolev E.V., Deberdeev T.R., Leksin V.V. Structural parameters and properties of fine-grained concrete on Portland cement, activated with plasticizers in vortex layer apparatuses. ZKG International. 2018. Vol. 71. No. 5, pp. 28–35. EDN: GCPLLJ
10. Wolosiewicz-Glab M., Pieta P., Foszcz D., Ogonowski S., Niedoba T. Grinding kinetics adjustment of copper ore grinding in an innovative electromagnetic mill. Applied Sciences. 2018. No. 8. 1322. https://doi.org/10.3390/app8081322
11. Milykh V.I., Tymin M.G. A comparative analysis of the parameters of a rotating magnetic field inductor when using concentric and loop windings. Electrical Engineering and Electromechanics. 2021. No. 4, pp. 12–18. EDN: ­WYIZFS https://doi.org/10.20998/2074-272X.2021.4.02
12. Makarchuk. Analysis of interaction of forces of working elements in electromagnetic mill. Przegląd elektrotechniczny. 2019. Vol. 1 (12), pp. 64–69. EDN: ­OEXNHX https://doi.org/10.15199/48.2019.12.12
13. Makarchuk O., Całus D., Moroz V. Mathematical model to calculate the trajectories of electromagnetic mill operating elements. Technical Electrodynamics. 2021. No. 2, pp. 26–34. EDN: XTBVJA. https://doi.org/10.15407/techned2021.02.026
14. Makarchuk O., Całus D. Research of the performance indicator of an electromagnetic mill. Technical Electrodynamics. 2022. No. 1, pp. 50–57. EDN: TPSZHM. https://doi.org/10.15407/techned2022.01.050
15. Całus D. Analysis of the thermal processes in an electromagnetic mill. Energies. 2022. No. 15. EDN: ­MGBEJF. https://doi.org/10.3390/en15217899
16. Ostrowski M., Blachowski B., Bochenski M., Piernikarski D. Design of nonlinear electromagnetic energy harvester equipped with mechanical amplifier and spring bumpers. Bulletin of the Polish Academy of Sciences, Technical Sciences. 2020. Vol. 68 (6), pp. 1373–1383. EDN: ­UOEJAK. https://doi.org/10.24425/bpasts.2020.135384
17. Ogonowski S. On-line optimization of energy consumption in electromagnetic mill installation. Energies. 2021. Vol. 14 (9). 2380. EDN: PSFQNU. https://doi.org/10.3390/en14092380
18. Гурьянов Г.А., Абдеев Б.М. Прикладная модель измельчения шарообразной твердой частицы прямым ударом о недеформируемую плоскую поверхность // Вестник Пермского национального исследовательского политехнического университета. Механика. 2020. № 1. С. 32–42. EDN: QYWIMV. https://doi.org/10.15593/perm.mech/2020.1.03
18. Guryanov G.A., Abdeev B.M. Applied model of grinding a spherical solid particle with a direct blow against a non-deformable flat surface. Vestnik of the Perm National Research Polytechnic University. Mechanics. 2020. No. 1, pp. 32–42. (In Russian). EDN: QYWIMV. https://doi.org/10.15593/perm.mech/2020.1.03
19. Ибрагимов Р.А., Королев Е.В. Влияние магнитного поля на гранулометрический состав портландцемента при его измельчении // Известия вузов. Строительство. 2023. № 3. С. 38–51. EDN: BFDWJK. https://doi.org/10.32683/0536-1052-2023-771-3-38-51
19. Ibragimov R.A., Korolev E.V. Influence of magnetic field on granulometric composition of Portland cement during its grinding. Izvestiya of the higher educational institutions. Construction. 2023. No. 3, pp. 38–51. (In Russian). EDN: BFDWJK. https://doi.org/10.32683/0536-1052-2023-771-3-38-51
20. Ибрагимов Р.А., Шакирзянов Ф.Р., Королев Е.В. Ударные воздействия при диспергировании минеральных материалов в аппаратах вихревого слоя // Промышленное и гражданское строительство. 2021. № 5. С. 19–25. EDN: KQAWTE. https://doi.org/10.33622/0869-7019.2021.05.19-25
20. Ibragimov R.A., Shakirzyanov F.R., Korolev E.V. Impacts during dispersion of mineral materials in vortex layer apparatuses. Promyshlennoe i grazhdanskoe stroitel’stvo. 2021. No. 5, pp. 19–25. (In Russian). EDN: ­KQAWTE. https://doi.org/10.33622/0869-7019.2021.05.19-2
21. Ибрагимов Р.А., Королев Е.В. Оценка энергозатрат на активацию минеральных компонентов в аппарате вихревого слоя // Региональная архитектура и строительство. 2025. № 1.
21. Ibragimov R.A., Korolev E.V. Assessment of energy costs for activation of mineral components in the vortex layer apparatus. Regional’naya arhitektura i stroitel’stvo. 2025. No. 1.
22. Носенко А.А., Половнева С.И. Методы и устройства для измерения удельной поверхности дисперсных материалов // Известия вузов. Прикладная химия и биотехнология. 2017. Т. 7. № 2 (21). С. 113–121. EDN: YTPLUF. https://doi.org/10.21285/2227-2925-2017-7-2-113-121
22. Nosenko A.A., Polovneva S.I. Methods and devices for measuring the specific surface of dispersed materials. Izvestiya of universities. Applied chemistry and biotechnology. 2017. Vol. 7. No. 2 (21), pp. 113–121. (In Russian). EDN: YTPLUF. https://doi.org/10.21285/2227-2925-2017-7-2-113-121
23. Воронин Н.В., Родионов Ю.В., Никитин Д.В., Филатов И.С. Определение сил воздействия на ферромагнитную частицу в процессе магнитотермического поверхностного армирования изделий из термопластичных полимеров // Вестник Тамбовского государственного технического университета. 2021. Т. 27. № 3. С. 486–496. EDN: AQPLAG. https://doi.org/10.17277/vestnik.2021.03.pp.486-496
23. Voronin N.V., Rodionov Yu.V., Nikitin D.V., Filatov I.S. Determination of impact forces on a ferromagnetic particle during magnetothermal surface reinforcement of thermoplastic polymer products. Vestnik of the Tambov State Technical University. 2021. Vol. 27. No. 3, pp. 486–496. (In Russian). EDN: AQPLAG. https://doi.org/10.17277/vestnik.2021.03.pp.486-496
24. Belyaev A., Aleshkin A., Kuts E., Shabalin V. Simulation of water flow in a cavitation reactor. Architecture and Engineering. 2023. Vol. 8. No. 1, pp. 51–59. EDN: ­QLGQNX. https://doi.org/10.23968/2500-0055-2023-8-1-51-59
25. Raghib R., Naciri I., Khalfi H. et al. Free vibration modeling in a functionally graded hollow cylinder using the Legendre polynomial approach. Architecture and Engineering. 2023. Vol. 8. No. 4, pp. 82–98. EDN: ­AJNBMP. https://doi.org/10.23968/2500-0055-2023-8-4-82-98