Vasiliev V. Mathematical modeling of flat solid units movement along an inclined roller conveyor in a homogeneous medium // Resources and Technology. 2026. №4, Vol. 23. P. 21‒46.

Mathematical modeling of flat solid units movement along an inclined roller conveyor in a homogeneous medium

Vasiliev
Vladimir Viktorovich

Ph. D. in engineering, associate professor, Voronezh State Agrarian Universitynamed after Emperor Peter the Great, vasiliev.vladimir87@mail.ru

Key words:
flat solid unit; inclined roller conveyor; mathematical simulation

Summary: A mathematical model of flat solid units movement along an inclined roller conveyor in a homogeneous medium is presented, which takes into account all the main resistances that have a direct impact on the movement of a flat solid unit along the conveyor. In particular, formulas are obtained for calculating the final speed of a flat solid unit movement along an inclined roller conveyor, the distance traveled by a flat solid unit, and the relationship between the instantaneous speed of a flat solid unit movement along a roller conveyor and its coordinate is established. To implement this mathematical model, a computer program has been developed that allows the results of the simulation to be presented in the form of graphical dependencies. The graphical dependencies obtained during the simulation process provide an opportunity to study the influence of the parameters of the inclined roller conveyor, its canting angle, as well as the parameters of the flat solid units and the physical properties of the wood, on the speed and duration of the solid units movement along the roller conveyor. The program also provides calculation of the traveled distance at which flat solid units will reach the specified speed, and determination of the traveled distance from the duration of the descent. The study of the effect of the inclined roller conveyor length and its canting angle on the final speed of movement of flat solid units and the total duration of their descent, calculated with the mathematical model, allowed us to obtain graphical dependencies of the final speed of flat solid units movement on the inclined roller conveyor and the total duration of their descent on the length of the roller conveyor and its angle of inclination. The above dependencies show that as the length of the roller conveyor increases, the final speed of the flat units and the duration of their descent increase according to a quadratic function. As the canting angle of the roller conveyor increases, the final speed of the flat units increases, and the duration of their descent decreases. An analysis of the obtained graphical dependencies of the final speed of flat solid units movement along an inclined roller conveyor and the total duration of their descent on the length of the conveyor and its canting angle showed that the flat solid unit made according to patent No. 2777676 of the Russian Federation has the highest final speed of movement, and the duration of its descent along the inclined roller conveyor is shorter than the duration of descent of flat solid units made according to patents No. 210485 of the Russian Federation and No. 2777676 of the Russian Federation, due to the higher rolling force caused by the design features of the flat solid unit (RF Patent No. 2777676).

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Mathematical modeling of flat solid units movement along an inclined roller conveyor in a homogeneous medium