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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.