Моделювання сходження сипкого матеріалу з відцентрового конусного дискового дозатора

Abstract

Aim. Development of an analytical model and study of particle movement on the surface of a conical disk rotary dispenser-mixer of bulk material. Method. The particle, which is placed on the conical disk, is subjected to gravity directed vertically downwards, the pressure force of the vertical component of the bulk component. The force of the normal reaction of the surface of the conical disk is directed perpendicular to the cone generating line of the dispenser disk at a given point where the material particle is located. Cartesian coordinate system. The x-axis is directed along the generator line from the vertex, the y-axis is perpendicular to the x-axis and z-axis and is directed towards the rotation of the disk, and the z-axis is directed vertically upwards. The centrifugal force vector is directed along the radius. The Coriolis force is directed tangentially perpendicular to the x-axis in the opposite direction to the direction of rotation of the disk. The friction force, as the resulting force vector, is directed in the opposite direction from the direction of movement of the particle on the disk due to the centrifugal force. The force of friction of the particle on the surface of the disk decomposes into normal and radial projections. Considering an elementary particle as a material point, the differential equation of motion in vector form. Projecting the vector equality on the X and Y axis, we obtain a system of differential equations of particle motion. The numerical Runge-Kutta solution using the rkfixed function in the MathCad environment was used to solve the differential equations. Results. The speed and trajectory of the particles of bulk material depends on the angle of the conical disk and the frequency of its rotation. As the angle of the cone generating line increases, the duration of movement of the particle on the surface of the cone and the distance of movement decreases. The smoothness of movement is determined by the angle between the velocity vectors vx and vy. Smooth change of the direction of the vector of the resulting speed makes it possible to increase the accuracy of dosing the material and increases the discreteness. Scientific novelty. For the first time, a system of differential equations of motion of a material particle on a conical dispenser of centrifugal type was obtained, which takes into account the distribution of particle friction forces on the disk surface on normal and radial projections and their solution by the Runge-Kutta numerical method. Practical value. The application of the obtained system of differential equations and the algorithm of their solution makes it possible to model the design and technological parameters of the disk conical centrifugal dispenser of bulk materials.