Development of calculation mathematical model of the asymmetric haulm-harvesting unit

Goal. Development of the main provisions of the theory of plane-parallel motion of an asymmetric haulm-harvesting unit, which will allow further numerical modeling on a PC of its optimal kinematic and design parameters, which will increase the stability of the technological process of sugar beet harvesting. Methods. During the study, methods were used to build computational mathematical models of agricultural machines and machine units, based on theoretical mechanics, higher mathematics, and the basics of the theory of automatic control. The transformations and simplifications of the obtained differential equations of motion are aimed at their further use for numerical calculations on the PC. Results. As a result of the analytical study, an equivalent scheme was constructed, based on which a calculated mathematical model of the plane-parallel motion of an asymmetric haulm-harvesting unit in the horizontal plane was developed, provided that the wheel tractor and rear trailer coupling is connected by a cylindrical hinge. According to the results of mathematical modeling, a new system of linear differential equations of the second order is obtained, which describes the transverse movement of the center of mass of a wheeled tractor and rotation of its longitudinal axis of symmetry by a certain angle around the specified center of mass, as well as the angle of deviation of the trailed haulm-harvesting unit from the longitudinal axis of symmetry of the tractor at any time. Conclusions. An equivalent scheme is constructed, based on which the calculated mathematical model of plane-parallel motion in the horizontal plane of the asymmetric haulm-harvesting unit is developed. A new system of linear differential equations of the second order is obtained, which describes the transverse displacement of the center of mass of the wheeled tractor, as well as the angle of deviation of the trailed haulm-harvesting unit from the longitudinal axis of the tractor at any time. Based on the obtained system of differential equations it is possible to study the stability of the asymmetric haulm-harvesting machine-tractor unit when performing the technological process of sugar beet harvesting.