Issue №3, Vol. 19
Il'yushenko D., Lokshtanov B., Orlov V., Kunickaya O., Pelyukhov R., SHvecova V. Mathematical description of the process of bulk material movement in horizontal continuous drums // Resources and Technology. 2022. №3, Vol. 19. P. 57‒68.



DOI: 10.15393/j2.art.2022.6403

Mathematical description of the process of bulk material movement in horizontal continuous drums

Il'yushenko
   Dmitrij 		St. Petersburg State Forest Engineering University named after S. M. Kirov, dilium@yandex.ru
Lokshtanov
   Boris 		Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny, blokshtanov@mail.ru
Orlov
   Vitaly 		Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny, artictvetal1987@gmail.com
Kunickaya
   Olga 		Arctic State Agrotechnological University, ola.ola07@mail.ru
Pelyukhov
   Roman 		Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny, cocucka007@rambler.ru
SHvecova
   Viktoriya 		Saint Petersburg State University of Architecture and Civil Engineering, vikt.schvetzova2012@yandex.ru
Key words:
drum
loose material
dynamic slope angle
caving line		 Summary: The article considers the process of moving a single particle in a bulk medium, which partially fills a horizontally placed rotating drum of continuous action. As the degree of the bulk material filling in the drum (filling segment) at the inlet to the drum is greater than that at the outlet of the drum, an inclined plane of bulk material is formed, through which the particle moves along the longitudinal axis of the drum. The mathematical description of the process of the bulk material particles moving in a horizontal rotating drum is given. It is established that the process of motion of a particle is pulsating. The process is described by the equation of a particle rise along a circle (along the cylinder) together with the filling segment and by the equation of a particle motion along a rupture plane. It is found that during one period of rupture the particle moves along the drum axis along the surface of the rupture plane by the value of the next section, in which the degree of filling will decrease and the origin of coordinates of particle motion will change. Parameters of the rupture plane depend on material properties (dynamic rupture angle), on degree of the drum filling with the material at the inlet and outlet, on the length of the drum. The spatial line of a particle rupture located on the surface of the rupture plane is described mathematically. In the article the formulas describe the trajectories of the bulk material particles movement in the drum and the drawings visually demonstrate these trajectories. Mathematical description of the process and calculations justify the optimal filling of the drum with bulk material. The authors propose the design of the drums to ensure optimal conditions for bulk material treatment. The research was performed within the framework of the scientific school «Innovative developments in the field of logging industry and forestry».

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