Mathematical description of the grain cleaning process on the experimental facility

Machines with pneumatic systems are used to clean grain from light impurities and dust. Modern grain cleaning machines for preliminary cleaning from light impurities and dust with a pneumatic system do not fully meet the increasing requirements of modern agricultural production in terms of their performance. The article presents the principle of operation and a mathematical description that allows you to determine the main parameters of the installation. In this work, an analytical research method was used based on the analysis of differential equations describing the processes of cleaning grain from light impurities and dust. To develop a mathematical model, the method of constructing Lagrange mathematical models was applied. On the basis of this model, a number of equations were constructed that characterize: the transition of the potential energy of the grain mass into the kinetic energy of the grain flow; dynamic equation of the equilibrium fall of the grain flow; the volume flow rate of the air flow in the intergranular space, as well as an equation that makes it possible to determine the pressure loss in the air flow passing through the blinds and the average speed of the grains falling. Taking into account the above equations, a mathematical model is built in the form of a system of equations. This mathematical model makes it possible to determine the main design parameters of the new installation: the geometric dimensions of the working area, as well as energy costs for the grain cleaning process. The introduction of the developed installation at the receiving points of the elevators makes it possible to increase the efficiency of grain cleaning from light impurities and dust at low unit costs.