Journals →  Obogashchenie Rud →  2015 →  #6 →  Back

THEORY OF PROCESSES
ArticleName The theory of gradient vibratory segregation effect as applied to screening process
DOI 10.17580/or.2015.06.04
ArticleAuthor Blekhman I. I., Blekhman L. I., Vasilkov V. B., Yakimova K. S.
ArticleAuthorData

REC «Mekhanobr-tekhnika» (Russia); Institute of Problems of Mechanical Engineering, Russian Academy of
Sciences (Russia):

Blekhman I. I., Doctor of Physical and Mathematical Sciences, Professor, Head of Laboratory, iliya.i.blekhman@gmail.com

Blekhman L. I., Ph. D. in Engineering Sciences, Leading Researcher, liblekhman@yandex.ru

Vasilkov V. B., Doctor of Engineering Sciences, Leading Researcher, vlvasilkov@yandex.ru

Yakimova K. S., Ph. D. in Engineering Sciences, Leading Researcher, yakimova_ks@npkmt.spb.ru

Abstract

The results of the theoretical studies on loose material mixture vibratory gradient segregation condition, discovered by the authors, are reported. A mathematical model of separation devices, based on application of this effect, is presented. The model is a diffusion equation that takes into account a deterministic factor’s effect, e.g., force of gravity. The equation is solved subject to the appropriate initial conditions and boundary conditions. The established relationships correspond to the known empirical dependence (damped exponential curve) of fine size fraction average concentration upon screen longitudinal coordinate. With that, dependence of quantity in exponent upon main parameters was revealed. Earlier this index had been determined through experimental data. The established formulae reflect the main factor providing for development of new high-capacity vibratory screens, distinguished by intensive sieving process through screening media (sieves) installed on side walls and employing more intensive vibration (with acceleration amplitude of about 10 g and over). These formulae also permit to estimate effects of geometric parameters and, to some extent, vibration parameters, upon process rate in the separation devices in question.
The authors are indebted to L. А. Vaisberg for effectual assistance and significant comments in implementation of this work.
The work was performed with the financial aid from the Ministry of Education and Science of the Russian Federation (the Project No. 14.576.21.0015; unique identifier RFMEFI57614X0015).

keywords Loose medium, separation, vibration, gradient segregation, theory elements, deterministic and stochastic factors, screening surface
References

1. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B. Gradient vibratory segregation in loose materials size classification processes. Obogashchenie Rud = Mineral Processing, 2015, No. 5, pp. 20–24.
2. Proc. of the IUTAM Symposium on segregation in granular flows held in Cape May, NJ, USA, June 5–10, 1999, Ed. 1, Dordrecht (The Netherlands), Kluwer Academic Publishers, 2000, 348 p.
3. Kudrolli A. Size separation in vibrated granular matter. Reports on Progress in Physics, 2004, Vol. 67, pp. 209–247. URL: http://physics.clarku.edu/~akudrolli/rpp4_3_R01.pdf.
4. Vaisberg L. A., Kartavyy A. N., Korovnikov A. N. Proseivayushchie poverkhnosti grokhotov. Konstruktsii, materially, opyt primeneniya (Deck plates of screens. Designs, materials, application experience). St. Petersburg, VSEGEI Publishing House, 2005, 252 pp.
5. Blekhman I. I. Teoriya vibratsionnykh protsessov i ustroystv. Vibratsionnaya mekhannika i vibratsionnaya tekhnika (The theory of vibration processes and devices. Vibrational mechanics and vibration technique). St. Petersburg, «Ore and Metals» Publishing House, 2013, 640 pp.
6. Arsentev V. A., Blekhman I. I., Blekhman L. I., Vasilkov V. B., Feoktistov A. Yu., Yakimova K. S. Loose material classification under vibratory segregation conditions — device, modeling, experiment. Obogashchenie Rud = Mineral Processing, 2010, No. 5, pp. 13–16.
7. Arsentev V. A., Vaisberg L. A., Ustinov I. D. Trends in development of lawwater-consumption technologies and machines for finely ground mineral materials processing. Obogashchenie Rud = Mineral Processing, 2014, No. 5, pp. 3–9.
8. Van der Vaart K., Gajjar P., Epely-Chauvin G., Andreini N., Gray J. M. N. T., Ancey C. Underlying Asymmetry within Particlesize Segregation. Physical Review Letters, 2015, Vol. 114, Iss. 23. DOI: 10.1103/PhysRevLett.114.238001. URL: http://arxiv.org/abs/1501.06879.
9. Yi Fan, Schlick C. P., Umbanhowar P. B., Ottino J. M., Lueptow R. M. Modeling size segregation of granular materials: the roles of segregation, advection and diffusion. J. of Fluid Mechanics, 2014, Vol. 741, pp. 252–279.
10. Vaisberg L. А., Demidov I. V., Ivanov K. S. Mechanics of granular media under vibration action: the methods of description and mathematical modeling. Obogashchenie Rud = Mineral Processing, 2015, No. 4, pp. 21–31.
11. Nepomnyashchiy E. A. Vibrational separation of bulk mixtures as a stochastic process. Izvestiya Leningradskogo elektrotekhnicheskogo instituta (LETI), 1960, Iss. 41, pp. 109–118.
12. Nepomnyashchiy E. A. To the theory of bulk mixtures self-sorting. Izvestiya Leningradskogo elektrotekhnicheskogo instituta (LETI), 1961, No. 46, pp. 217–227.
13. Nepomnyashchiy E. A. The mathematical description of the bulk materials separation kinetics. Trudy VNIIZ, 1967, Iss. 61–62, pp. 59–66.
14. Karmazin V. V., Rakhimov S. N. Researches conducted in STC «Mining Modular Units» of segregation of gold from waste products of gold mining. Gorny informatsionno-analiticheskiy byulleten (nauchno-teknicheskii zhurnal) = Mining Informational and Analytical Bulletin (Scientific and Technical Journal), 2009, Vol. 14, No. 12, pp. 163–170.
15. Radzhabov M. M. Sovershenstvovanie tekhniki i tekhnologii izvlecheniya melkogo i tonkogo zolota na osnove vibratsionnogravitatsionnoy kontsentratsii (Improvement of techniques and technology of fine and thin gold extraction based on vibrational and gravity concentration). Avtoref. dis. … kand. tekhn. nauk (Author's abstract of Dissertation … of Ph. D. in Engineering Sciences), Moscow, Moscow State Mining University, 2013, 20 pp.
16. Andreev E. E., Tikhonov O. N. Droblenie, izmelchenie i podgotovka syrya k obogashcheniyu. Uchebnik (Crushing, grinding and preparation of raw material for enrichment. Textbook). St. Petersburg, SPSMI (TU), 2007, 439 pp.
17. Nadutyy V. P., Lapshin E. S. Veroyatnostnyye protsessy vibratsionnoy klassifikatsii mineralnogo syrya (Stochastic processes of mineral raw materials vibrational classification). Kiev, Naukova dumka, 2005, 180 pp.
18. Perov V. A. Results of the screening process research in mineral processing. Trudy VNIIZ, 1963, Iss. 42, pp. 319–325.

Language of full-text russian
Full content Buy
Back