On study of plane-parallel movement of sowing machine-tractor unit
Keywords:
посівний машинно-тракторний агрегат, Lagrange equation, motion, sowing machine-tractor unitAbstract
The paper substantiates the method of studying the plane-parallel movement of the sowing machine-tractor unit (MTA) through the formation of equations of dynamics using Lagrange equations of the II kind. Theoretical studies were carried out on the example of a sowing machine-tractor unit as part of an all-wheel drive tractor of the classic layout Belarus-1025 manufactured by MTZ and a seeder Vega-8 W Profi manufactured by PJSC "Elworthy" (Kropyvnytskyi). Tractor of a classic layout, all-wheel drive, with front steered wheels. as well as discard factors that complicate mathematical modeling and do not affect the calculation. The following assumptions were introduced: the plane-parallel motion of the unit was considered; in the process of compiling the mathematical model, the deferent (plane-parallel movement of the unit in the plane XOZ) and roll (plane-parallel movement of the unit in the plane YOZ) were not taken into account; the processes that occur in the hydraulic steering drive were not taken into account; the processes that occur in the transmission are not taken into account; the dynamic characteristics of the engine were not taken into account during acceleration and braking of the unit; the skeletons of the sections are absolutely solid, and the entire aggregate is symmetrical with respect to the longitudinal plane; rolling resistance forces are considered constant; lateral forces on the tires are limited by the grip of the wheels on the road. The rolling resistance of the wheels of the tractor and seeder is calculated depending on the vertical load on the corresponding wheel. When compiling a mathematical model, the case of movement along a curved trajectory is used, which corresponds to the actual trajectory of the sowing units in the field. In the process of movement, the front and rear wheels of the tractor are the drivers. The position of the tractor-seeder system will be determined by four generalized coordinates: the projection of the velocity of the tractor's center of mass on the x-axis; projection of the velocity of the center of mass of the tractor on the y-axis; the angle of rotation of the tractor frame around the vertical axis; the angle of rotation of the seeder frame around the vertical axis. To bring the equations of MTA dynamics to the Cauchy form and the numerical solution of the SLAR system, the mathematical software package MatLab 2021a was used by the Kramer method. The developed mathematical model allows you to study the dynamics (movement) of the elements of the sowing MTA in the longitudinally parallel plane and determine the influence of geometric parameters of the unit on its dynamics, oscillations of elements around a rectilinear trajectory and stability of motion.
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