Abstract
The purpose of research to formulate a mathematical description of the movement of components of grain material in pneumatic channels with artificially formed distribution of air velocity in the cross section of the channel to improve the quality of separation (trajectory divergence) of grain material components. The article considers studies of grain separation in pneumatic channels with artificially formed air velocity distribution in the cross section of the channel, to determine the rational form and parameters of material supply and options for separation of grain material into fractions. The regularities of grain motion in the form of mathematical models of the dynamics of solid particle motion in air flow are theoretically investigated and established, which differ from those known in that they take into account the action of lateral forces, material concentration, and the application of power law and artificially formed exponential air distribution law) trajectories. The solution of the system of nonlinear differential equations with initial conditions is made in the MathCad software environment in the form of grain motion trajectories in air flow, allows to calculate their motion trajectories that differ in sailing coefficients and determine rational values of pneumogravity and pneumoinertia parameters. Using the obtained dependences for the development of air separators, it is possible to determine the initial velocity of entry and direction of entry of grains into the air stream, as well as to determine the trajectories of the material in the air ducts with lower material unloading. Conclusions: 1. Theories of grain motion are theoretically investigated and established in the form of mathematical models of solid grain motion dynamics in air flow, which differ from those known in that they take into account the action of lateral forces, material concentration, and the application of power and artificial exponential law (splitting) of grain movement trajectories by 20%. 2. The solution of the system of nonlinear differential equations with initial conditions is made in the MathCad software environment in the form of grain motion trajectories in the air stream, which allows to calculate their motion trajectories differing in sailing coefficients and determine rational values of pneumogravity and pneumoinertial separators.
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