National University of Sciences and Technology–MISIS, Moscow, Russia:

Bardovsky A. D., Professor, Doctor of Engineering Sciences, bardowski@yandex.ru
Gorbatyuk S. M., Professor, Doctor of Engineering Sciences
Gerasimova A. A., Associate Professor, Candidate of Engineering Sciences
Basyrov I. I., Assistant of Department

The article describes the studies into the process of the mill feed flow along a curved vibratory surface under the action of oriented vibrations. The differential equation of the relative movement of a grinding body in a layer of a milled material along the surface are given. The differential equation of a particle motion is obtained. The equations prove that at a certain ratio of the vibration parameters, the grinding balls of different sizes when moving upward in a milled mass have limit heights. It is found that the best size distribution of the grinding balls on the vibratory surface exists at a certain ratio of the vibration amplitude and frequency and the tangent slope of the acting face. The plotted experimental curves prove that the maximum efficiency of the process is achieved at the acting face vibration amplitude in a range of 0.6–0.8 mm and vibration frequency in a range of 48–54 Hz, and is 8–12% higher than at the amplitudes and frequencies beyond these ranges.

1. Akunov V. I., Litvinov G. P. General technical and economic indicators of counterflow jet mills. Tr. Gos. Nauchno-Issled. Inst. Tsem. Prom. 1982. No. 70. pp. 3–10.
2. Bardovskii A. D., Gerasimova A. A., Keropyan A. M. et al. Influence of the mechanical characteristics of harp screen material on screening process. Proceedings of Higher Educational Institutions. Ferrous Metallurgy. 2018. Vol. 61, No. 9. pp. 678–682.
3. Snitko S. A., Yakovchenko A. V. Influence of the Axial Reduction Conditions on the Variation in the Thickness of a Wheel Rim at the Initial Stage of Rolling. Metallurgist. 2017. Vol. 61. pp. 387–393.
4. Hodakov G. S. High milling of construction materials. Moscow : Izdatelstvo literatury po stroitelstvu, 1972. 239 p.
5. Zhang X., Baia S., Jin W., Shi Z., Yu M. et al. Simulation research on vibration separation screen of air suction jujube picking machine based on Adams. International Agricultural Engineering Journal. 2020. Vol. 29, No. 2. pp. 128–134.
6. Bardovsky A. D., Valeeva L. M., Basyrov I. I. A plant with a rotary jet grinder to produce small fractions of mineral raw material. IOP Conf. Series Materials Science and Engineering. 2020. Vol. 971. DOI: 10.1088/1757-899X/971/5/052004
7. Bardovsky A. D., Bibikov P. Ya., Deniskina T. V. Patent RF, No. 98340 Useful Model of Vibration Mill. Published: 20.10.2010.
8. Deniskina T. V. Theoretical study of the motion of grinding bodies and crushed material on a vibrating curved surface. GIAB. 2010. No. 12. pp. 203–205.
9. Astashev V. K., Pichugin K. A., Semenova E. B. Nonlinear dynamics of a vibrating machine with an electrodynamic actuator. Journal of Machinery Manufacture and Reliability. 2021. Vol. 50, No. 1. pp. 11–18.
10. Stepanenko A. I., Stepanenko A. A., Milshin O. N., Ordon S. F., Panov A. V. et al. Processing of low-grade bauxites by air separation. Nonferrous Metals and Minerals : X International Congress Proceedings. Krasnoyarsk : Nauchno-innovatsionnyi tsentr, 2018. pp. 48–54.

11. Gorbatyuk S. M., Zarapin A. Y., Chichenev N. A. Retrofit of vibrating screen of Catoca Mining Company (Angola). GIAB. 2018. No. 1. pp. 143–149.
12. Gnezdilov A. A. Implementation of resonant modes of technological vibrational machines. Bulletin of Altai State Agricultural University. 2019. No. 1(171). pp. 159–163.
13. Rumiche F., Noriega A., Lean P. et al. Metallurgical failure analysis of a welded drive beam of a vibrating screen. Engineering Failure Analysis. 2020. Vol. 118. 104936.
14. Chen Z., Tong X., Li Z. Numerical investigation on the sieving performance of elliptical vibrating screen. Processes. 2020. Vol. 8(9). 1151.
15. Blekhman I. I. Vibration Mechanics and Vibration Rheology (Theory and Applications). Moscow : Fizmatlit, 2018. 752 p.
16. Barbosa V. P., Menezes A. L., Gedraite R. et al. Vibration screening: A detailed study using image analysis techniques to characterize the bed behavior in solid–liquid separation. Minerals Engineering. 2020. Vol. 154. 106383.
17. Kobelev O., Valeeva L., Gerasimova A. Forging process flow development for plate production. Solid State Phenomena. 2021. Vol. 316. pp. 240–245.
18. Lahib M. E., Tekli J., Issa Y. B. Evaluating Fitts’ law on vibrating touchscreen to improve visual data accessibility for blind users. International Journal of Human Computer Studies. 2018. Vol. 112. pp. 16–27.
19. John Kobbina A., Emmanuel Asuming F., Joe Oteng A. Optimization Algorithms for Solving Combined Economic Emission Dispatch: A Review. Proceedings of the World Congress on Engineering and Computer Science. 2019. pp. 210–215.
20. Altshul G. M., Guskov A. M., Panovko G. Ya. Dynamics of a resonant vibrator with an equal-frequency suspension of the working body and an unbalanced vibration exciter. Obogashchenie Rud. 2022. No. 1. pp. 51–55.
21. Deniskina T. V. Influence of the shape and angle of the vibrating surface of the working body vibration mill on the quality of the finished product. GIAB. 2015. No. 8. pp. 368–372.