Mathematical modeling and research of the work of the grain combine harvester cleaning system

•The coordinates of the nodal points of the sieve mill were determined.•Plans for their speeds and acceleration of motion were constructed.•The authors propose to use the methods of two-phase flows “gas - particles”. The purpose of this study is a mathematical description of the structural and technological parameters of the air-sieve cleaning of the grain pile for the implementation of a simulation model of the technological process of the cleaning system of a grain combine harvester. The method is given for determining the coordinate of the nodal points of a sieve mill to calculate their speed of movement, as well as to study structural and technological parameters. As a result, the following were determined: the coordinates of the nodal points of the sieve mill of the cleaning system of the combine harvester, their speed and movement acceleration; a mathematical model of the operation of the sieve mill of the combine harvester cleaning system has been developed; the Froude number for the sieve mill Fr = 5.3 is the ratio between the forces of inertia and gravity, in the field of which movement occurs; experimental measurements of the speed of the air flow on the surface of the sieve mill for the existing structures of the cleaning system of modern combine harvesters amounted to 3.75 … 10.2 m / s, which are necessary for the implementation of mathematical models of a complete description of the technological process of cleaning system in the combine harvester using methods of two-phase flow mechanics.