631.26

screw-conveyor mixer; direct flow screw mixer; rotary casing; loose mixture; kinematics of the flow of bulk goods; equations of motion, drag body of bulk material.

The model of mixtures movement in screw conveyors-mixers with rotating body is considered in this paper. It is shown that the process of mixing the mixture occurs more intensively in the mode of operation, in which the load is lifted by rotating casing into the upper part of the conveyor, from where part of it spirals down, and part of it crumbles. above the shaft and enters another cell formed by adjacent turns of the screw operating body. At the same time, the mixture is shoveled and distributed along the length, which ensures high smoothing capacity of the mixer conveyor. To establish the kinematic parameters of the mixer conveyor in the cylindrical coordinate system, the equilibrium equation of the separate element of the mixture, which is acted upon by the reaction forces from the rotating body and the screw operating body, was considered. Ranges of values of the angular velocities of the shroud rotation, at which the stationary movement of the bulk cargo into the dumping zone occurs, were determined. Dependencies to determine the kinematic parameters of the mixer, which ensure the operating modes of the mixer under the condition of the specified quality of mixing were obtained.

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2. Rohatynskyi R.M., Gevko I.B., Lyashuk O.L., Gud V.Z., Dyachun A.E., Melnychuk A.L., Slobodian L.M. Promising screw conveyors: designs, calculation, research. Ternopil, 2019. 212 p. [in Ukrainian]
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4. Dheeraj M., Abhishek S., Harsh P., Ram D., Jyeshtharaj B., Shankar S. A review of granular flow in screw feeders and conveyors // Powder Technology. 2020. Vol. 366. P. 369‑381.
5. Hewko B.M., Popovich P.V., Diachun A.Y., Lyashuk O.L., Liubachivskyi R.O. The study of bulk material kinematics in a screw conveyor-mixer // INMATEH: Agricultural engineering. Bucharest/Romania, 2015. Vol. 47. No. 3. P. 156‑163.
6. Rohatynskyi R., Gevko I., Diachun A, Lyashuk O., Skyba O., Melnychuk A. Feasibility study of improving the transport performance by means of screw conveyors with rotary casings // Acta Technologica Agriculturae. Nitra, Slovaca Universitas Agriculturae Nitriae, 2019.  4/2019. P. 141‑146.
7. Hu, G., Chen, J., Jian, B., Wan, H., Liu, L. Modeling and simulation of transportation system of screw conveyors by the discrete element method. // 2010 International Conference on Mechanic Automation and Control Engineering, MACE 2010, Article number5536244. P. 927‑930.
8. 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). 2010. Vol. 10, No. 5/6.
9. Aca Jovanović, Lato Pezo, Sanja Stanojlović, Nenad Kosanić, Ljubinko Lević. Discrete element modelling of screw conveyor-mixers // Hem. Ind. 2015. 69 (1). P. 95–101.
10. Liqing S. Xiaodi Z. Qingliang Z., Kuidong G., Kao J., Jiawei Z. Application of a screw conveyor with axial tilt blades on a shearer drum and investigation of conveying performance based on DEM // Particuology. 2022 Vol. 61. P. 91‑102.
11. Gud V.Z. Synthesis of mixers with screw working bodies // Journal "Nature Management Engineering". Kharkiv, 2020. Issue 1(15). P. 66 72. [in Ukrainian]
12. Gud V.Z., Klendiy V.M., Shust I.M. Research results of the telescopic screw conveyor // Agricultural machines. Lutsk, 2019. Issue 42. P. 12-20. [in Ukrainian]
13. Hud V., Rogatynskyi R., Hevko I., Lyashuk O., Huryk O., Рік A. Research on resonant oscillations of the telescopic screw – granular media system caused by external periodic forces // INMATEH - Agricultural Engineering. 2020, Vol. 60 Issue 1. P. 29-36.
14. Dmytriv D.V., Dmytriv O.R., Dmytrotsa V.L., Grubenyuk M.V., Tsapyk R.P. Two-shaft screw conveyors-mixers. // Collection of abstracts of reports of the International scientific and technical conference dedicated to the memory of Professor Gevka Bohdan Matviyovych "Problems of the theory of design and manufacture of transport and technological machines", September 23-24, 2021. T.: FOP Palyanitsa VA, 2021. P. 74–75. [in Ukrainian]
15. Fenglei Q., Theodore J. H. Mark Mba W. Numerical study of particle mixing in a lab-scale screw mixer using the discrete element method // Powder Technology. 2017. Vol. 308. P. 334‑345.
16. Milada P., Lato P., Aca  J., Anja T., Ljubiša A., Biljana L., Predrag K. Discrete element model of particle transport and premixing action in modified screw conveyors. Powder Technology. 2018. Vol. 336. P. 255-264.
17. Lato P., Aca J., Milada P., Radmilo Č., Biljana L. Modified screw conveyor-mixers – Discrete element modeling approach // Advanced Powder Technology. 2015. Vol. 26, Issue 5,  P. 1391-1399.
18. Yu.V. Naumenko Fundamentals of the theory of operating modes of drum mills: monograph. Rivne: Publishing House SPD Zelent O.I., 2009. 282 p. [in Ukrainian]
19. Dyachun A.E., Lyashuk O.L., Kotyk R.M., Mykhailiuk V.P., Gandziy V.S. Study of the kinematics of loose material in a screw conveyor-mixer with a rotating casing and a corrugated screw // Bulletin of the Kharkiv National Technical University of Agriculture. 2019. Issue 198. P. 233-243. [in Ukrainian]
20. Rogatynskyi R., Hevko I., Diachun A., Rogatynska O., Melnychuk A. The cargo movement model by the screw conveyor surfaces with the rotating casing // Scientific Journal of TNTU. Tern.: TNTU, 2018. Vol 92. No 4. P. 34–41.
21. Dyachun A.E., Dmytriv O.R., Gevko B.R., Koval S.O., Tsapyk R.P. Experimental automated installation of a screw conveyor with a rotating casing for mixing loose materials // Promising technologies and devices. Lutsk, 2024. Issue 24. P. 38-44. [in Ukrainian]
22. Rohatynskyi R.M., Gevko I.B., Dmytriv D.V., Gud, V.Z., Dmytriv O.R. Modeling of mixing of components by screw conveyors-mixers // Agricultural machines. 2020. Issue 45. P. 84-93. [in Ukrainian]

1. Gevko B.M., Danylchenko M.G. Mechanisms with screw devices. Lviv: Svit, 1993. 208 p. [in Ukrainian]
2. Rohatynskyi R.M., Gevko I.B., Lyashuk O.L., Gud V.Z., Dyachun A.E., Melnychuk A.L., Slobodian L.M. Promising screw conveyors: designs, calculation, research. Ternopil, 2019. 212 p. [in Ukrainian]
3. Lyashuk O.L., Rohatynska O.R., Peleshok T.M., Lyubachivskyi R.O. Study of the process of transportation of bulk cargo by inclined screw conveyors // Bulletin of TNTU. T.: TNTU, 2015. Volume 79. No. 3. P. 137-143. [in Ukrainian]
4. Dheeraj M., Abhishek S., Harsh P., Ram D., Jyeshtharaj B., Shankar S. A review of granular flow in screw feeders and conveyors // Powder Technology. 2020. Vol. 366. P. 369‑381.
5. Hewko B.M., Popovich P.V., Diachun A.Y., Lyashuk O.L., Liubachivskyi R.O. The study of bulk material kinematics in a screw conveyor-mixer // INMATEH: Agricultural engineering. Bucharest/Romania, 2015. Vol. 47. No. 3. P. 156‑163.
6. Rohatynskyi R., Gevko I., Diachun A, Lyashuk O., Skyba O., Melnychuk A. Feasibility study of improving the transport performance by means of screw conveyors with rotary casings // Acta Technologica Agriculturae. Nitra, Slovaca Universitas Agriculturae Nitriae, 2019.  4/2019. P. 141‑146.
7. Hu, G., Chen, J., Jian, B., Wan, H., Liu, L. Modeling and simulation of transportation system of screw conveyors by the discrete element method. // 2010 International Conference on Mechanic Automation and Control Engineering, MACE 2010, Article number5536244. P. 927‑930.
8. 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). 2010. Vol. 10, No. 5/6.
9. Aca Jovanović, Lato Pezo, Sanja Stanojlović, Nenad Kosanić, Ljubinko Lević. Discrete element modelling of screw conveyor-mixers // Hem. Ind. 2015. 69 (1). P. 95–101.
10. Liqing S. Xiaodi Z. Qingliang Z., Kuidong G., Kao J., Jiawei Z. Application of a screw conveyor with axial tilt blades on a shearer drum and investigation of conveying performance based on DEM // Particuology. 2022 Vol. 61. P. 91‑102.
11. Gud V.Z. Synthesis of mixers with screw working bodies // Journal "Nature Management Engineering". Kharkiv, 2020. Issue 1(15). P. 66 72. [in Ukrainian]
12. Gud V.Z., Klendiy V.M., Shust I.M. Research results of the telescopic screw conveyor // Agricultural machines. Lutsk, 2019. Issue 42. P. 12-20. [in Ukrainian]
13. Hud V., Rogatynskyi R., Hevko I., Lyashuk O., Huryk O., Рік A. Research on resonant oscillations of the telescopic screw – granular media system caused by external periodic forces // INMATEH - Agricultural Engineering. 2020, Vol. 60 Issue 1. P. 29-36.
14. Dmytriv D.V., Dmytriv O.R., Dmytrotsa V.L., Grubenyuk M.V., Tsapyk R.P. Two-shaft screw conveyors-mixers. // Collection of abstracts of reports of the International scientific and technical conference dedicated to the memory of Professor Gevka Bohdan Matviyovych "Problems of the theory of design and manufacture of transport and technological machines", September 23-24, 2021. T.: FOP Palyanitsa VA, 2021. P. 74–75. [in Ukrainian]
15. Fenglei Q., Theodore J. H. Mark Mba W. Numerical study of particle mixing in a lab-scale screw mixer using the discrete element method // Powder Technology. 2017. Vol. 308. P. 334‑345.
16. Milada P., Lato P., Aca  J., Anja T., Ljubiša A., Biljana L., Predrag K. Discrete element model of particle transport and premixing action in modified screw conveyors. Powder Technology. 2018. Vol. 336. P. 255-264.
17. Lato P., Aca J., Milada P., Radmilo Č., Biljana L. Modified screw conveyor-mixers – Discrete element modeling approach // Advanced Powder Technology. 2015. Vol. 26, Issue 5,  P. 1391-1399.
18. Yu.V. Naumenko Fundamentals of the theory of operating modes of drum mills: monograph. Rivne: Publishing House SPD Zelent O.I., 2009. 282 p. [in Ukrainian]
19. Dyachun A.E., Lyashuk O.L., Kotyk R.M., Mykhailiuk V.P., Gandziy V.S. Study of the kinematics of loose material in a screw conveyor-mixer with a rotating casing and a corrugated screw // Bulletin of the Kharkiv National Technical University of Agriculture. 2019. Issue 198. P. 233-243. [in Ukrainian]
20. Rogatynskyi R., Hevko I., Diachun A., Rogatynska O., Melnychuk A. The cargo movement model by the screw conveyor surfaces with the rotating casing // Scientific Journal of TNTU. Tern.: TNTU, 2018. Vol 92. No 4. P. 34–41.
21. Dyachun A.E., Dmytriv O.R., Gevko B.R., Koval S.O., Tsapyk R.P. Experimental automated installation of a screw conveyor with a rotating casing for mixing loose materials // Promising technologies and devices. Lutsk, 2024. Issue 24. P. 38-44. [in Ukrainian]
22. Rohatynskyi R.M., Gevko I.B., Dmytriv D.V., Gud, V.Z., Dmytriv O.R. Modeling of mixing of components by screw conveyors-mixers // Agricultural machines. 2020. Issue 45. P. 84-93. [in Ukrainian]