Heorhii Shevchenko, Volodymyr Shevchenko, Serhii Holobokyi. Development of a mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters

Geoteh. meh. 2020, 155, 96-113

https://doi.org/10.1051/e3sconf/202016800062

  

DEVELOPMENT OF A MATHEMATICAL MODEL OF A VIBRATING POLYFREQUENCY SCREEN AS A DYNAMIC SYSTEM WITH DISTRIBUTED PARAMETERS

1Heorhii Shevchenko, 1Volodymyr Shevchenko, 2Serhii Holobokyi

1Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, 2Private join-stock company "Suha Balka"

Language: English

Abstract. A mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters has been developed. The dynamic system of solids of finite sizes was chosen as the design scheme for the screen: framework, sieves with bulk material and impactors, the contact interaction of which occurs through two-side bonds and collisions on surface areas that have elastic-damping coverings. It is shown that a change in the amplitude of the exciting force has a significant effect on the dynamics of vibration impactors of a polyfrequency vibrating. There is an amplitude value at which the impactor passes from the mode without interacting with elastic bonds to the vibro-impact mode. The impactor movements begin to change disproportionately altered by the exciting force amplitude. It is shown that the start of the impactors in the screen substantially depends on the exciting force. Changes in the amplitude of the exciting force make it possible to achieve chaotic oscillations of impactors, which in turn leads to oscillations of screen surfaces with a continuous frequency spectrum, i.e. to the operation mode of the screen, which is most appropriate for dehydration and separation of fine mineral fractions.

REFERENCES

1. Bulat, A.F., Shevchenko, G.A. (2010). Vliyanie polichastotnyh kolebaniy proseivayushchih poverhnostey vibratsionnyh grohotov na razdelenie sypuchih materialov. Scientific bulletin of the National mining university, 4, 92-97

2. Shevchenko, G.A., Shevchenko, V.G. (2015). Model vibratsionnogo polichastotnogo grohota s ogranichennym istochnikom vozbuzhdeniya. Vibration in engineering and technology, 4 (80), 105-113

3. Shevchenko, G.A., Shevchenko, V.G., Shlyakhova, M.A., Lebed, G.B. (2015). Rezonansy vibroudarnyh system. Geo-technical mechanics, 121, 28-38

4. Filippov, A.P. (2001). Kolebaniya deformiruemyh sistem. Moskva: Mashinostroenie.

5. Vorovich, I.I., Aleksandrov, V.M. (2001). Mehanika kontaktnyh vzaimodeystviy. Moskva: FIZMATLIT

6. Rzhanitsyn, A.R. (1968). Teoriya polzuchesti. Moskva: Stroyizdat.

7. Pisarenko, G.S. (1985). Obobshchennaya nelineynaya model ucheta rasseyaniya energii pri kolebaniyah. Kyiv: Naukova dumka

8. Nashif, A., Dzhouns, D., Henderson, J. (1988). Dempfirovanie kolebaniy (Vibration Damping). Moskva: Mir

9. Gulyaev, V.I., Bazhenov, V.A., Popov, S.L. (1989). Prikladnye zadachi teorii nelineynyh kolebaniy mehanicheskih system. Moskva: Vysshaya shkola

10. Kukudzhanov, V.N. (2008). Vychislitelnaya mehanika sploshnyh sred. Moskva: Izdatelstvo Fiziko-matematicheskoy literatury

11. Fletcher, K. (1988). Chislennye metody na osnove metoda Galyorkina (Numerical methods based on the Galerkin method). Moskva: Mir

12. Zenkevich, O. (1975). Metod konechnyh elementov v tehnike. Moskva: Mir

13. Holl, J., Uatt, J. (1979). Sovremennye chislennye metody resheniya obyknovennyh differentsialnyh uravneniy (Modern numerical methods for solving ordinary differential equations). Moskva: Mir

14. Hayrer, E., Nyorsett, S., Vanner, G. (1990). Reshenie obyknovennyh differentsialnyh uravneniy (Solving ordinary differential equations). Moskva: Mir

15. Arushanyan, O.B., Zaletkin, S.F. (1990). Chislennoe reshenie obyknovennyh differentsialnyh uravneniy na Fortrane. Moskva: MGU

16. Samarskiy, A.A., Vabishchevich, P.N. (2001). Additivnye shemy dlya zadach matematicheskoy fiziki. Moskva: Nauka

17. Voevodin, V.V., Voevodin, Vl.V. (2004). Parallelnye vychisleniya. Sankt- Petersburg: BHV-Peterburg

18. Zarubin, V.S., Kuvyrkin, G.N. (2008). Matematicheskie modeli mehaniki i elektrodinamiki sploshnoy sredy. Moskva: MGTU im. N.E. Baumana

19. Lavendel, E.E. (1981). Vibratsii v tehnike: spravochnik v 6 t. Vibratsionnye protsessy i mashiny. Moskva: Mashinostroenie

20. Lure, A.I. (1961). Analiticheskaya mehanika. Moskva: Gosudarstvennoe izdatelstvo fiziko-matematicheskoy literatury

21. Branets, V.N., Shmyglevskiy, I.P. (1992). Vvedenie v teoriyu besplatformennyh inertsialnyh navigatsionnyh system. Moskva: Nauka

22. Shevchenko, G.A., Bobyl’ev, A.A., Ishchuk, M.A. (2010). Obosnovanie parametrov kolebaniy sit polichastotnyh vibratsionnyh grohotov. Scientific bulletin of the National mining university, 5, 64-71

23. Bulat, A.F., Voloshin, O.I., Zhevzhik, O.V. (2013). Plasma reactor for thermochemical preparation of coal-air mixture before its burning in the furnaces. Annual Scientific-Technical Collection – Mining of Mineral Deposits, 39-44. https://doi.org/10.1201/b16354-8

24. Blyuss, B.A., Semenenko, E.V. (2005). The calculation of thermohydrodynamic parameters of pipeline transportation of polydisperse materials. Metallurgicheskaya i Gornorudnaya Promyshlennost, 1, 85-88

25. Naduty, V., Malanchuk, Z., Malanchuk, E., Korniyenko, V. (2015). Modeling of vibro screening at fine classification of metallic basalt. New Developments in Mining Engineering 2015: Theoretical and Practical Solutions of Mineral Resources Mining, 441-443. https://doi.org/10.1201/b19901-77