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A mathematical description of the movement of caryopses in the composition of the components of grain material (CGM) on the surface of a stepped vibrating feeder is given when CGM is introduced into the aspiration channel of the separator under the action of vibrations on the CGM. The trajectories of movement of grains on the surface of the vibrating feeder with different sizes were obtained. The obtained equation of the movement of seeds under the action of vibrations makes it possible to determine the dependence of the speed of movement of the material in the CGM layer on a number of factors: the geometric parameters of the vibrating feeder, the angle of material feeding, the initial kinematic mode of the grain material, the indicator of the kinematic mode of the vibrating feeder, and the friction coefficient of the CGM. The process of movement of grain material on the stepped surface of the vibrating feeder has been substantiated, which makes it possible to determine the rational parameters of introducing the CGM into the aspiration channel of the separator and uniform distribution in the channel with the subsequent possibility of its fractionation. The dependence of the function of the flow rate of grain material on the stepped surface of the vibrating feeder is obtained, which makes it possible to determine the parameters of the distribution of grain material over the sectional area of the aspiration channel of the separator. The estimation of the absolute speed of grain material movement on the stepped surface of the vibrating feeder is made on the basis of a mathematical model constructed by hydrodynamic analogy, which in turn predetermines the analysis of the recombination of caryopses along the thickness of the vibrated layer of grain material. According to the established mathematical models, graphical dependences of the absolute speed of movement on time, the trajectories of the array of particles, the calculated trajectories of particles of grain material, which are fed into the pneumatic channel under initial conditions, were built.

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.

Development of a mathematical model and calculated analytical dependencies for determining the trajectories and parameters of grain movement in a vibro-fluidized layer of grain material components under the action of a pulsating air flow. They are based on the methods of deterministic mathematical modeling and theoretical mechanics based on the equations of motion of a material point at a variable air flow speed and the action of a pulsating air flow. Theoretical studies were carried out using the methods of mathematical analysis and modeling. The research results were processed using elements of the theory of probability and mathematical statistics using software packages; to determine the rational parameters of the process, the method of statistical experiment planning was used. A mathematical description of the motion of the grain material particles in a combined vibration-air separator under the action of a pulsating air flow of variable speed is given. The trajectories of motion of particles with different sizes are obtained. The obtained equation of motion of a particle under the influence of a pulsating air flow makes it possible to determine the dependence of the speed of movement of the material in a vibro-fluidized layer of grain material on a number of factors: the geometric parameters of the sieve-free sieve, the feed angle of the material, the initial kinematic mode of the material, the index of the kinematic mode of the sieve-free sieve, as well as the coefficient of windage of the grain. On the basis of theoretical studies, the possibility of separating particles of grain material into fractions according to aerodynamic properties with vibropneumatic loading of grain into the channel has been determined. The use of a pulsating air flow as a separating carrier, and taking into account the deflecting forces, made it possible to significantly increase the splitting of the trajectories and the criterion for dividing the grain into fractions.