Mathematical model of the lateral traction of the tractor

Abstract

The issues of the course stability of the movement of the agricultural tractor aggregate acquire the greatest urgency in the plowing, since an additional unfolding moment arises on the plow (due to the geometry of its working surfaces), which can lead the tractor aside from rectilinear movement. The operator often has to correct the movement of the machine, which contributes to rapid fatigue and, as a result, a decrease in productivity. The development of a mathematical model of the tractor's motion under the influence of an external eccentric load on the hook will allow to determine the limiting value of the shearing force. The drift of the tractor under the influence of external forces (without participation from the side of the driver) is a passive turn, which currently lacks sufficient attention in the theory of the curvilinear movement of the caterpillar tractor, since the theory of rotation is usually aimed at examining the active movement (under the driving influence of the driver ). The drift is a set of controlled rectilinear motion and uncontrolled shear under the action of the lateral component of force on the hook. Considering the low operating speeds of the tractor, it is possible to compile a quasistatic model of curvilinear motion in the drift, which consists of: differential equations of motion and equilibrium conditions of external forces with limiting friction. As a result of solving the system of presented equations, trajectories of the tractor's motion are obtained under different load on the hook. The model allows: to study the trajectory of motion on various ground backgrounds; find the optimal ratio of the weight of the tractor and the forces of resistance; to study the influence of the parameters of the working element (the attachment point of the plow and the angle of inclination of the plow surface) on the characteristics of motion.