621.867.4

vertical screw conveyors, loose cargo, continuous medium, helical coordinate system, strain rates, stresses, kinematics of the flow loose cargo.

The article considers the model of transporting bulk cargo by flow by vertical high-speed screw conveyors. The peculiarities of mutual movement of cohesive and fine cargoes, in particular, in the conditions of their layer-by-layer movement, are revealed. To analyze the stress-strain state of bulk cargo in the conditions of screw conveying, a special helical coordinate system was used, which made it possible to significantly simplify the solution of the problem. The dependences for describing the shape of the helical surface that restricts the flow of cargo under the condition of incomplete filling of the working space, the volume of the elementary sector of the flow and its center of gravity are derived. The use of the model of layer-by-layer material motion is substantiated, and the distribution of linear and angular velocities of particles in the flow and, accordingly, centrifugal forces is determined. It is shown that for vertical high-speed conveyors, the motion of the flow as a whole and its individual particles retains the laws of helical transporting, which makes it possible to use the model of a material particle with the given parameters to calculate the design and operating modes of the conveyor.

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13. Rogatynskyi R., Dmytriv O., Dmytriv D., Grubenyuk M. (2019). Doslidzhennia potoku vantazhu v hvyntovykh konveierakh [Studying the flow of the cargo in the screw conveyors]. Materialy ХХІ naukovoi konferentsii TNTU im. I. Puliuia (Tern., 16–17 May 2019.). P. 32–33. [In Ukrainian].

1.  John V. (2016). The Oseen equations. Finite element methods for incompressible flow problems (Vol. 51, pp. 243–300). Cham: Springer Series in Computational Mathematics. Doi: https://doi.org/10.1007/978-3-319-45750-5_5.
2.   Williams J. R., O'Connor, R. (December 1999). Discrete element simulation and the contact problem. Archives of Computational Methods in Engineering. 6 (4): 279–304. CiteSeerX 10.1.1.49.9391 doi:10.1007/BF02818917.
3.   Hu G., Chen J., Jian B., Wan H., Liu L. 2010. Modeling and simulation of transportation system of screw conveyors by the discrete element method. 2010 International Conference on Mechanic Automation and Control Engineering, MACE2010, Article number5536244. P. 927–930.
4.   Justin W Fernandez, Paul W. Cleary, William Mcbride, Effekt of screw desing on hopper draw dawn by a horizontal screw feeder. Seventh International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia. 2009. 9–11. Decem. Р. 1–6.
5.   Philip J. Owen, Paul W. Cleary. Screw conveyor performance: comparison of discrete element modelling with laboratory experiments. Progress in Computational Fluid Dynamics. An International Journal (PCFD). Vol. 10. No. 5. 2010. Р. 327–333.
6.   Gevko B. M., Danylchenko M. Mekhanizmy z hvyntovymy prystroyamy [Mechanisms with screw devices]. Lviv, Svit, 1993. 208 р. [Іn Ukrainian].
7.   Grigor'yev A. M. [Screw Conveyors]. Moskva: Mashinostroenie, 1972. 184 p. [In Russian].
8.   Lyashuk O. L., Rogatynska O. R., Serilko D. L. Modelling of the vertical screw conveyer loading. INMATEH: Agricultural engineering. Bucharest, Romania. 2015. Vol. 45. No. 1, P. 87–94.
9.   Roberts A. W.  (1999) The influence of granular vortex motion on the volumetric performance of enclosed screw conveyors. Powder Technol. 104. 1999. P. 56–67.
10. Liu N., Liang C., Liu D., Ma J., Lu D., Li B ., Luo D. (2023). The axial force model optimization and dynamic characteristics of shear-friction force in screw. Chemical Engineering Research and Design. Volume 189. January 2023. P. 272–281.
11. Gevko B. M., Rogatynskyi R. M. Gevko, B.M. Vintovyye podayushchiye mekhanizmy sel'skokhozyaystvennykh mashin. Screw Feeding Mechanisms of Agricultural Machines. Lviv: Vyshcha shkola, 1989. 176 p. [Іn Ukrainian].
12. Loveykin V. S., Rogatynska O. R. Vybir ratsionalʹnykh parametriv ta rezhymiv roboty vertykalʹnykh hvyntovykh konveyeriv [Choice of rational parameters and modes of operation of vertical screw conveyors]. Zbirnyk naukovykh pratsʹ Vinnytsʹkoho derzhavnoho ahrarnoho universytetu. 2005. No. 23. P. 181–195. [Іn Ukrainian].
13. Rogatynskyi R., Dmytriv O., Dmytriv D., Grubenyuk M. (2019). Doslidzhennia potoku vantazhu v hvyntovykh konveierakh [Studying the flow of the cargo in the screw conveyors]. Materialy ХХІ naukovoi konferentsii TNTU im. I. Puliuia (Tern., 16–17 May 2019.). P. 32–33. [In Ukrainian].