Theoretical study of the flight range of sugar beet chaff when it is mowed by a chaff harvesting machine

Abstract

Goal. To justify the rational design parameters and modes of operation of the developed design of the unloading mechanism of the sugar beet harvester, which ensure high productivity and uniformity of sugar beet spread over the surface of the beet field as an organic fertilizer. Methods. To conduct theoretical research, methods of mathematical modeling, higher mathematics, theoretical mechanics, methods of compiling computer programs and numerical calculations on a PC, as well as analysis of the obtained graphic dependencies were used. Results. In order to justify the rational parameters and modes of operation of the unloading mechanism of the newly designed chaff harvesting machine developed by us, a mathematical model of the chaff particle movement after its departure from the discharge nozzle of the specified mechanism before reaching the field surface was built. The obtained system of differential equations describes the flight of a particle of mowed hickory at an arbitrary moment of time, taking into account the speed of its departure from the discharge nozzle, the influence of the air flow and air resistance, which takes into account the translational speed of the movement of the unit across the field, as well as the speed and direction of the wind. Solving the resulting system of differential equations on a PC made it possible to determine the rational design and kinematic parameters of the unloa-ding mechanism, which ensure the necessary initial speed of departure of the chaff particles from the discharge nozzle, and, therefore, the required range and uniformity of the chaff spread over the field. Conclusions. A mathematical model of the movement of a chaff particle after its departure from the outlet of the discharge mechanism of the chaff harvesting machine was built, taking into account its translational movement, as well as the influence of the wind on the flight trajectory of the chaff. The solution of the resulting system of nonlinear differential equations of motion of a sedge particle using a PC made it possible to calculate the range of the sedge’s flight after it left the discharge nozzle and reached the field surface. As the calculations show, the dependence of the flight range of the particle on time t is close to exponential, and in time t = 0.5 s the flight range reaches 0.72 m. With a further increase in time t, the flight range of the particle practically does not change. At the same time, the flight speed of the particle of the string along the Oy axis during the time t = 0.5 s intensively decreases from 22 ms–1 to zero and does not change during its further movement. During the time t = 0.12 s, the particle of the straw rises up due to the kinetic energy of the particle’s departure from the discharge nozzle (initial speed V0). At t > 0.12 s, the particle begins to move downward according to a linear law and reaches the surface of the field (z =–2 m) in time t = 1.85 s. During the time t = 0.4 s, the velocity of the particle along the Oz axis decreases intensively from 12 ms–1 to –1.3 ms–1, then remains constant until the particle reaches the surface of the field. At negative values of this speed, the particle of the hen starts to move down and reaches the surface of the field.