MATHEMATICAL SIMULATION OF THE MOVEMENT OF GRAIN MATERIAL ON THE SURFACE OF THE SPREADER UNDER ITS INTRODUCTION INTO THE ASPIRATION CHANNEL OF THE SEPARATOR

Abstract

Develop a mathematical model and calculated analytical dependences to determine the trajectories and parameters of grain movement on the surface of the vibrating feeder under the conditions of its introduction into the aspiration channel of the separator. They are based on the methods of mathematical modeling and theoretical mechanics with the application of the equations of motion of a material point under the variable action of vibrations. Theoretical research was conducted using mathematical analysis and modeling theory. The research results are processed using elements of probability theory and mathematical statistics using application packages. A mathematical description of the movement of grains of grain material components (GMC) on the surface of the vibrating feeder under the conditions of its introduction into the aspiration channel of the separator under the conditions of vibration on the GMC. The trajectories of grains on the surface of the vibrating feeder with different size are obtained. The obtained equation of motion of the particle under the action of vibrations allows to determine the dependence of the velocity of the material in the vibrated fluidized bed on a number of factors: geometrical parameters of the vibrating feeder, feed angle, initial kinematic mode of grain material, kinematic mode of the vibrating feeder and friction coefficient. The process of grain material movement on the flat surface of the vibrating feeder is described, which allows to determine the rational parameters of material introduction into the aspiration channel of the separator for its further fractionation. The dependence for the function of the grain flow rate on the flat surface of the vibrating feeder is obtained, which allows to determine the parameters of the grain material distribution by the cross-sectional area of the aspiration channel of the separator. The velocity of grain material on the flat surface of the vibrating feeder is estimated on the basis of a mathematical model constructed by hydrodynamic analogy, which in turn determines the analysis of grain recombination by the thickness of the vibrated liquid layer of grain material.