Viktor Kravets, Volodymyr Samusia, Dmytro Kolosov, Kostiantyn Bas, Serhii Onyshchenko. Discrete mathematical model of travelling wave of conveyor transport

Details
Parent Category: Geo-Technical Mechanics, 2020
Category: Geo-Technical Mechanics, 2020, № 154

Geoteh. meh. 2020, 154, 112-120

https://doi.org/10.1051/e3sconf/202016800030

DISCRETE MATHEMATICAL MODEL OF TRAVELLING WAVE OF CONVEYOR TRANSPORT

1Viktor Kravets, 1Volodymyr Samusia, 1Dmytro Kolosov, 1Kostiantyn Bas, 1Serhii Onyshchenko

National Technical University "Dnipro Polytechnic" of the Ministry of Education and Science of Ukraine

Language: English

Abstract. A mathematical model of a travelling wave in a matrix form is constructed. A degree of discreteness of the travelling wave and corresponding steps in phase and length are introduced. Asymmetric, unified matrices are compiled, which represent a generalized travelling wave, depending on a degree of discreteness. A generalized, dimensionless travelling wave is transformed into a required one with dimensions by specified technical parameters: amplitude and wavelength that is realized. A dependency of coordinates of points of a plane discrete travelling wave and discrete phase angles is established. A dependency of angular (phase) velocity and velocity of the travelling wave, which corresponds to the known results, is established. The presented matrix mathematical model is considered as an initial stage of technical possibility to realize a continuous travelling wave in a discrete form when developing a new type of transportation – wave transport.

REFERENCES

1. Kulikova, D.V., Pavlychenko, A.V. (2016). Estimation of ecological state of surface water bodies in coal mining region as based on the complex of hydrochemical indicators. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (4), 62-70

2. Kolesnik, V.Ye., Pavlichenko, A.V., Buchavy, Yu.V. (2016). Determination of dynamic parameters of dust emission from a coal mine fang. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2), 81-87

3. Bulat, A., Voloshyn, O., Ponomarenko, S., Gubenko, D. (2013). New-generation technique and technology for leakage tests. Annual Scientific-Technical Colletion - Mining of Mineral Deposits 2013, 1-4. https://doi.org/10.1201/b16354-2

4. Bondarenko, A.O., Naumenko, R.P. (2019). Comprehensive solution of recycling waste from stone processing industry. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (4), 96-101. https://doi.org/10.29202/nvngu/2019-4/14

5. Dryzhenko, A., Shustov, A., Moldabayev, S. (2017). Justification of parameters of building inclined trenches using belt conveyors. International Multidisciplinary Scientific GeoConference Surveying Geology and Mining Ecology Management, SGEM, 17, (13), 471-478. https://doi.org/10.5593/sgem2017/13/S03.060

6. Ropyak, L., Schuliar, I., Bohachenko, O. (2016). Influence of technological parameters of centrifugal reinforcement upon quality indicators of parts. Eastern-European Journal of Enterprise Technologies, 1, 5(79). https://doi.org/10.15587/1729-4061.2016.59850

7. Bazhenov, V.A., Gulyar, A.I., Piskunov, S.O., Andrievskii, V.P. (2013). Design life assessment of the blade root of a gas turbine unit under thermomechanical loading. Strength of Materials, 45(3), 329-339. https://doi.org/10.1007/s11223-013-9463-0

8. Sladkowski, A.V., Kyrychenko, Y.O., Kogut, P.I., Samusya, V.I., Kolosov, D.L., (2019). Innovative designs of pumping deep-water hydrolifts based on progressive multiphase non-equilibrium models. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2), 51-57. https://doi.org/10.29202/nvngu/2019-2/6

9. Pivnyak, G., Samusia, V., Oksen, Y., Radiuk, M. (2015). Efficiency increase of heat pump technology for waste heat recovery in coal mines. New Developments in Mining Engineering 2015: Theoretical and Practical Solutions of Mineral Resources Mining, 1-4. https://doi.org/10.1201/b19901-2

10. Krasovskiy, P., Tsyplenkov, D., Nesterova, O., (2013). Operating dynamics of parameters and technical losses in the components of power supply systems. Energy Efficiency Improvement of Geotechnical Systems - Proceedings of the International Forum on Energy Efficiency, 113-120. https://doi.org/10.1201/b16355-15

11. Bobrov, O.V., Tsyplenkov, D.V., Grebeniuk, A.M., Kyrychenko, M.S. (2019). Justification of the optimum operation of electromechanical system for production and distribution of pressurized air. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, (2), 101-107. https://doi.org/10.29202/nvngu/2019-2/13

12. Voloshyn, O., Potapchuk, I., Zhevzhyk, O., Zhovtonoha, M. (2018). Results of the experimental research of the heat-transfer jet pressure to the rock surface during thermal reaming of the borehole. Ukrainian School of Mining Engineering: E3S Web of Conferences, 60. https://doi.org/10.1051/e3sconf/20186000024

13. Bondarenko, A.O. (2018). Modeling of interaction of inclined surfaces of a hydraulic classifier with a flow of solid particles. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (4), 13-20. https://doi.org/10.29202/nvngu/2018-4/5

14. Bazhenov, V.A., Gulyar, A.I., Piskunov, S.O., Shkryl, A.A. (2006). Life assessment for a gas turbine blade under creep conditions based on continuum fracture mechanics. Strength of Materials, 38(4), 392-397. https://doi.org/10.1007/s11223-006-0055-0

15. Belmas, I., Kolosov, D. (2011). The stress-strain state of the stepped rubber-rope cable in bobbin of winding. Technical and Geoinformational Systems in Mining: School of Underground Mining 2011, 211-214. https://doi.org/10.1201/b11586-35

16. Bondarenko, A.A. (2012). Mathematical modeling of soil dredger absorption processes in the underwater bottomhole. Metallurgical and Mining Industry, 4, (3), 149-152

17. Belmas, I., Kogut, P., Kolosov, D., Samusia, V., Onyshchenko, S. (2019). Rigidity of elastic shell of rubber-cable belt during displacement of cables relatively to drum. International Conference Essays of Mining Science and Practice: E3S Web of Conferences, 109. https://doi.org/10.1051/e3sconf/201910900005

18. Ilin, S., Adorska, L., Samusia, V., Kolosov, D., Ilina, I. (2019). Conceptual bases of intensification of mining operations in mines of Ukraine based on monitoring and condition management of mine hoisting systems. International Conference Essays of Mining Science and Practice: E3S Web of Conferences, https://doi.org/10.1051/e3sconf/201910900030

19. Bel'mas, I.V. (1993). Stress state of rubber-rope tapes during their random damages. Problemy Prochnosti i Nadezhnosti Mashin, (6), 45-48

20. Kolosov, L.V., Bel'mas, I.V. (1981). Use of electrical models for investigating composites. Mechanics of Composite Materials, 17(1), 115-119. https://doi.org/10.1007/BF00604895

21. Matsyuk, I.M., Morozova, Т.I., Shlyahov, E.М. (2017). Search of variants of assemblies of structural groups in planar linkages. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2), 65-69

22. Matsyuk, I.M., Shlyahov, E.М., Yehurnov, O.I. (2019). On applying high-class mechanisms of heavy-loaded machines. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (3), 68-73. https://doi.org/10.29202/nvngu/2019-3/6

23. Filimonikhin, G., Filimonikhina, I., Yakymenko, M., Yakimenko, S. (2017). Application of the empirical criterion for the occurrence of auto-balancing for axisymmetric rotor on two isotropic elastic supports. Eastern-European Journal of Enterprise Technologies, 2, 7(86), 51-58. https://doi.org/10.15587/1729-4061.2017.96622

24. Inkin, O., Tishkov, V., Dereviahina, N., Sotskov, V. (2018). Integrated analysis of geofiltrational parameters in the context of underground coal gasification relying upon calculations and modeling. Ukrainian School of Mining Engineering: E3S Web of Conferences, 60. https://doi.org/10.1051/e3sconf/20186000035

25. Sadovenko, I., Zahrytsenko, A., Podvigina, O., Dereviahina, N., Brzeźniak, S. (2018). Methodical and applied aspects of hydrodynamic modeling of options of mining operation curtailment. Solid State Phenomena, (277), 36-43. https://doi.org/10.4028/www.scientific.net/SSP.277.36

26. Shcherbakov, P., Tymchenko, S., Buhrym, O., Klymenko, D. (2019). Research into the crushing and grinding processes of iron ore with its simultaneous effect by mechanical load and electric field of ultra-high frequency. Ukrainian School of Mining Engineering: E3S Web of Conferences, 123. https://doi.org/10.1051/e3sconf/201912301030

27. Sadovenko, I.A., Derevyagina, N.I. (2012). About activation potential of loess landslide massif. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2), 80-84

28. Voloshyn, O.I., Potapchuk, I.Y., Zhevzhyk, O.V. (2018). Influence of the heat-transfer stream pressure on the surface of the rock in a process of the thermal reaming of the borehole. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2), 53-59. https://doi.org/10.29202/nvngu/2018-2/6

29. Kravets, V., Sakhno, V., Bas, K., Kravets, V. (2018). Program spatial movement of high-speed vehicles. In: IOP Conf. Ser.: Mater. Sci. Eng. 383. https://doi.org/10.1088/1757-899X/383/1/012032

30. Sobko, B.Yu., Denyschenko, O.V., Lozhnikov, O.V., Kardash, V.A. (2018). The belt conveyor effectiveness at the rock haulage under flooded pit excavations. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (6), 26-32. https://doi.org/10.29202/nvngu/2018-6/4

31. Taran, I.А., Klymenko, I.Yu. (2013). Transfer ratio of double-split transmissions in case of planetary gear input. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, (6), 60-66

32. Shustov, O., Dryzhenko, A. (2016). Organization of dumping stations with combined transport types in iron ore deposits mining. Mining of Mineral Deposits, 10(2), 78-84. https://doi.org/10.15407/mining10.02.078

33. Bondarenko, A.I., Taran, I.О. (2017). Effect of antilock brake system on basic parameters of transport vehicle transmission. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, (2), 75-80

34. Kolosov, D., Dolgov, O., Bilous, O., Kolosov, A. (2015). The stress-strain state of the belt in the operating changes of the burdening conveyor parameters. New Developments in Mining Engineering 2015: Theoretical and Practical Solutions of Mineral Resources Mining, 585-590. https://doi.org/10.1201/b19901-101

35. Filimonikhin, G., Olijnichenko, L. (2015). Investigation of the possibility of balancing aerodynamic imbalance of the impeller of the axial fan by correction of masses. Eastern-European Journal of Enterprise Technologies, 5, 7(77), 30-35. https://doi.org/10.15587/1729-4061.2015.51195

36. Olshanetskii, V.E., Stepanova, L.P., Greshta, V.L., Pavlenko, D.V., Tkach, D.V. (2014). Deformation behavior of titanium VT1-0 with submicrocrystalline structure formed by the method of helical extrusion. Metal Science and Heat Treatment, 55(11-12), 603-607. https://doi.org/10.1007/s11041-014-9676-2

37. Greshta, V.L. (2017). Structural liability of sheet-rolled corrosion-resistant ferritic steels to a plastic deforming. Metallofizika i Noveishie Tekhnologii, (39), 1213-1225. https://doi.org/10.15407/mfint.39.09.1213

38. Ropyak, L.Ya., Shatskyi, I.P., Makoviichuk, M.V. (2019). Analysis of interaction of thin coating with an abrasive using one-dimensional model. Metallofizika i Noveishie Tekhnologii, 41, (5), 647-654. https://doi.org/10.15407/mfint.41.05.0647

39. Klassifikatsiya konveyerov. (2015). Retrieved from: https://www.3bhungaria.com.ua/new/178-klassifikatsiya-konvejerov-osnovnye-tipy-konvejerov-napravleniya-razvitiya-konvejerov

40. Vibratsii v tekhnike: Spravochnik. v 6-ti t./Red. soviet: V.N. Chelomey (pred.). Moskva: Mashinostroyeniye (1981). 4 Vibratsionnyye protsessy i mashiny. Pod red. E.E. Lavendela (1981)

41. Etherington, Darrell (2018). Hyperloop Transportation Technologies signs first cross-state deal in the U.S. TechCrunch. Retrived from https://techcrunch.com/2018/02/15/hyperloop-transportation-technologies-signs-first-cross-state-deal-in-the-u-s/

42. J. Orear, Physics. New York: Macmillan (1979). https://doi.org/10.1119/1.2340262

43. F.S. Crawford Jr., Waves (Berkeley Physics Course). 3 New York: McGraw-Hill (1968)

44. J.J. Stoker Water Waves: The Mathematical Theory with Applications. New Jersey: Wiley (1957)

45. Korn, G., Korn, T. (1984) Spravochnik po matematike dlya nauchnyh rabotnikov i inzhenerov. Moskva: Nauka.

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