INVESTIGATION OF THE MOVEMENT OF A MATERIAL PARTICLE ALONG STRAIGHT-LINE AND CURVILINE BLADES ON A HORIZONTAL DISK ROTATING AROUND A VERTICAL AXIS

Abstract

The study of the movement of material particles along a horizontal disc with orthogonally attached blades during its rotation around a vertical axis is the theoretical basis for the design of dispersing bodies of mineral fertilizers.The movement of a particle along the rectilinear blades of a horizontal disk rotating around a vertical axis has been thoroughly investigated. Of the curved vanes, we considered a vane in which the profile has the shape of a logarithmic spiral. But it is also important to find a blade profile that would satisfy these conditions based on the given initial conditions.The purpose of the article is to find a profile of a curved vane that would meet the specified requirements for the movement of a particle along this vane during rotation of a horizontal disk around a vertical axis.When rotating a disk with a curved blade, the particle performs a complex movement: transferred due to the rotation of the disk and relative along the blade. To compile the differential equations of motion, it is necessary to find the vector of absolute acceleration, which includes three components: acceleration in translational motion, acceleration in relative motion, and Coriolis acceleration.The generalized differential equations of particle motion along rectilinear and curved vanes are derived. A comparative analysis of the kinematic parameters of motion for different shapes of blades was made.It was established that with the same angular velocity of rotation of the disk and the same initial conditions, the shape of the curved blade significantly affects the absolute velocity of the particle at the time of its exit from the disk. With the shape of the blade, in which there is no pressure of the particle on it, the absolute speed of the particle is minimal. As the pressure, which is constant along the entire length of the blade, increases, its profile gradually changes, approaching the radial direction, and the absolute speed of the particle increases. However, the maximum absolute speed that can be obtained due to the curved profile of the blade under the condition of constant pressure on it is proportional to the particle speed for rectilinear blades. Under the condition of the same pressure of the particle on the blade at different angular velocities of rotation of the disk, the profiles of the blades will be different, but the absolute speeds of the particle at the time of its exit from the disk will be the same.