Theoretical research of the material particle movement along the conical surface of the agricultural machine working body
Authors: Klendii M. ,   Separated subdivision of National University of Life and Environmental Sciences of Ukraine “Berezhany Agrotechnical Institute”
Published: July 2024

Purpose. To conduct theoretical studies of the movement of a particle of technological material along the inner surface of a rotary cone with a vertical axis, which carries out rotational movement and translational oscillations in order to find ways to improve grain and seed separation machines. Methods. The methods of linear algebra and differential geometry, theoretical and analytical mechanics, and computer graphics systems were used to conduct the research. Methods of numerical integration of differential equations were used to process research results, thanks to the Simulink package of the MatLab system. Results. The greatest influence on the nature of the movement of the particle of the technological material is exerted by the force of the surface reaction, because as the oscillation parameters increase, the particle may detach from the surface of the cone. During circular translational oscillations of the cone in the horizontal plane, a particle of the technological material of the material in relative motion can describe periodic trajectories between the upper and lower parallels, or slide in a circle (parallels of the cone). The second case is possible provided that the proper initial conditions of motion, which are determined analytically, are ensured. During the rotational movement of the cone, the stabilization of the movement of the particle of the technological material is impossible: it either accelerates, rising along a spiral trajectory upwards, or falls down with a large angle of inclination of the cone and insufficient angular speed of rotation. When the rotational movement of the cone and its harmonic oscillations along the axis of rotation are combined, a particle of the technological material can be detached from the surface. Conclusions 1. The peculiarities of the relative movement of a particle of technological material along the inner rough surface of a vertical cone, which carries out circular translational oscillations in the horizontal plane, rotates around its own axis or combines rotational movement around the axis and harmonic oscillations along the axis, are considered. 2. Constructed trajectories of the movement of a particle of material at different angles of inclination of the generating cone, angular speed of rotation and radius of oscillation. It was established that at large angles of inclination of the generating cone, the particle can move down, describing a spiral curve, while the decrease in pressure and speed are subject to a linear law. At an angle β of the inclination of the generating cone, a smaller angle of friction, and at small angular velocities of oscillations, the particle may not move at all. 3. Research showed that during oscillation, the pattern of particle sliding is the same for different angles β of the inclination of the generators: the particle describes a spiral trajectory, rising up the cone. Stabilization of motion does not occur: the particle either rises up or falls down due to insufficient angular velocity ω of rotation or large the elevation of the particle. 4. The presence of an oscillating component causes a variable surface reaction force. When the frequency of cone oscillations increases to w = 30 s-1, the particle detaches from the surface. Research has also shown that an increase in the amplitude of oscillations also leads to the separation of the particle from the surface. 5. The results of this study can be used in the design of separating machines used at grain processing enterprises. The prospect of these researches is to carry out theoretical calculations and build graphical dependencies to determine the trajectory of movement of process material particles with different masses, initial kinematic and dynamic characteristics. Keywords: a cone with a vertical axis, rotational motion, translational oscillations of a cone, relative motion of a particle, differential equations of motion.