Construction of mathematical model of particle movement by an inclined screw rotating in a fixed casing
DOI:
https://doi.org/10.15587/1729-4061.2023.288548Keywords:
force applied to a particle, differential equations of motion, cylindrical casing, angle of inclination of the screwAbstract
Screw conveyors are used to move bulk materials vertically upwards, horizontally, and at an angle to the horizon. The processes that take place when particles are moved by a screw conveyor in vertical and horizontal directions have been studied. There is a significant difference between them: for transportation in the vertical direction, the necessary conditions must be ensured (sufficient angular speed of rotation of the screw), and for horizontal transportation, the movement of the particle occurs at any angular speed of rotation of the screw. Therefore, when changing the inclination of the axis of the screw, there comes a moment when transportation becomes possible, while it was impossible in the vertical direction.
This paper considers the movement of a particle under the condition that it simultaneously contacts two surfaces: the moving surface of the screw and the stationary surface of the cylindrical casing in which the screw rotates. Their common line along which the particle slides is a helical line – the periphery of the screw. The particle slides along the helical line of the rotating screw, i.e., it is in relative motion with respect to it. At the same time, it slides along the surface of the casing, relative to which it is in absolute motion. The trajectory of the particle's absolute motion is its sliding track on the casing surface.
When constructing differential equations of the relative motion of particles, the forces applied to the particle were taken into account. The initial position was taken to be the vertical direction of the screw to transport the particle upwards. If an auger in a cylindrical casing is tilted from the vertical direction to a certain angle, then all applied forces (except the force of weight) will also tilt to this angle. On the basis of this, generalized differential equations of the relative motion of a particle during its transportation by an inclined screw were built. They made it possible to derive a generalized mathematical model of the movement of a particle by an inclined screw that rotates inside a fixed casing
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Copyright (c) 2023 Tetiana Volina, Serhii Pylypaka, Mykhailo Kalenyk, Serhii Dieniezhnikov, Viktor Nesvidomin, Iryna Hryshchenko, Yana Lytvynenko, Artem Borodai, Dmytro Borodai, Yana Borodai
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