Determination of the velocity field of the material grinding loading in a bead mill with a screw device
https://doi.org/10.46973/0201-727X_2026_1_209
Abstract
The use of bead mills is widespread in industrial enterprises for fine and ultrafine grinding of various multicomponent suspensions. The expediency and possibility of their constructive improvement are shown. The description of screw devices providing an increase in the efficiency of the material dispersion process in the mill body is given. The necessity of developing a mathematical description characterizing the operation of the bead mill of the developed design is substantiated in order to establish its rational parameters. A mathematical description has been developed for determining the longitudinal, radial and circumferential components of the velocity field of the material-grinding load in the body of a horizontal bead mill with screw devices. Studies have been conducted on the effect of the pitch of the blade screw on the values of the components of its speed, and patterns have been established that characterize the possibility of intensifying the grinding process.
About the Authors
S. I. Khanin
Belgorod State Technological University named after V. G. Shukhov (BSTU named after V. G. Shukhov)
Russian Federation
Russian Federation
Khanin Sergey Ivanovich, Chair of Mechanical Equipment, Doctor of Engineering Sciences, Professor
R. V. Zybin
Belgorod State Technological University named after V. G. Shukhov (BSTU named after V. G. Shukhov)
Russian Federation
Russian Federation
Zybin Roman Vladimirovich, Chair of Mechanical Equipment, Postgraduate Student
V. P. Voronov
Belgorod State Technological University named after V. G. Shukhov (BSTU named after V. G. Shukhov)
Russian Federation
Russian Federation
Voronov Vitaly Pavlovich, Chair of Mechanical Equipment, Candidate of Physico-Mathematical Sciences, Professor
O. S. Mordovskaya
Belgorod State National Research University named after V. G. Shukhov (BSTU named after V. G. Shukhov)
Russian Federation
Russian Federation
Mordovskaya Olga Sergeevna, Chair of Applied Informatics and Information Technologies, Candidate of Engineering Sciences, Associate Professor
References
1. Little, J. D. C. A Proof for the Queuing Formula L = λW / J. D. C. Little // Operations Research. – 1961. – Vol. 9 (3). – P. 383–387. – DOI 10.1287/opre.9.3.383.
2. Fundamentals of Queueing Theory / D. Gross, J. F. Shortle, J. M. Thompson, C. M. Harris. – 4th ed. – Hoboken : John Wiley & Sons, 2008. – 528 p. – ISBN 978-0-471-79127-0.
3. Ehrgott, M. Multicriteria Optimization / M. Ehrgott. – Berlin : Springer-Verlag, 2005. – 323 p. – ISBN 3-540-21398-8.
4. A fast and elitist multiobjective genetic algorithm: NSGA-II / K. Deb, A. Pratap, S. Agarwal, T. Meyarivan // IEEE Transactions on Evolutionary Computation. – 2002. – Vol. 6 (2). – P. 182–197. – DOI 10.1109/4235.996017.
5. Dijkstra, E. W. A note on two problems in connexion with graphs / E. W. Dijkstra // Numerische Mathematik. – 1959. – Vol. 1. – P. 269–271. – DOI 10.1007/BF01386390.
6. Introduction to Algorithms / T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein. – 3rd ed. – Cambridge, MA : MIT Press, 2009. – 1292 p. – ISBN 978-0-26253-305-8.
7. Preparata, F. P. Computational Geometry: An Introduction / F. P. Preparata, M. I. Shamos. – New York : Springer-Verlag, 1985. – 390 p. – ISBN 0-387-96131-3.
8. Algorithms and methods for solving scheduling problems and other extremum problems on large-scale graphs / S. V. Chernyshev, E. A. Cherepanov, E. V. Pankratiev, A. M. Chepovskii // Journal of Mathematical Sciences. – 2005. – Vol. 128 (6). – P. 3487–3495.
9. Birge, J. R. Introduction to Stochastic Programming / J. R. Birge, F. Louveaux. – New York : Springer, 2011. – 485 p.
10. Shapiro, A. Lectures on Stochastic Programming : Modeling and Theory / A. Shapiro, D. Dentcheva, A. Ruszczyński. – Philadelphia : SIAM, 2009. – DOI 10.1137/1.9780898718751.
11. Applications of Stochastic Programming / S. W. Wallace, W. T. Ziemba (eds.). – Philadelphia : SIAM, 2005. – 709 p. – ISBN 978-0-89871-555-2.
12. King, A. J. Modeling with Stochastic Programming / A. J. King, S. W. Wallace. – New York : Springer, 2012. – DOI 10.1007/978-0-387-87817-1.
13. Ben-Tal, A. Robust Optimization / A. Ben-Tal, L. El Ghaoui, A. Nemirovski. – Princeton, NJ : Princeton University Press, 2009. – 576 p. – ISBN 978-0-691-14368-2.
14. Kall, P. Stochastic Programming / P. Kall, S. W. Wallace. – Chichester : John Wiley & Sons, 1994. – 307 p. – ISBN 978-0-471-95108-7.
15. Martello, S. Knapsack Problems : Algorithms and Computer Implementations / S. Martello, P. Toth. – Chichester: John Wiley & Sons ; 1990. – ISBN 978-0-471-92420-3.
Review
For citations:
Khanin S.I., Zybin R.V., Voronov V.P., Mordovskaya O.S. Determination of the velocity field of the material grinding loading in a bead mill with a screw device. Vestnik Rostovskogo Gosudarstvennogo Universiteta Putej Soobshcheniya. 2026;(1):209-218. (In Russ.) https://doi.org/10.46973/0201-727X_2026_1_209
Views:
28
JATS XML
Email this article 