Mathematical model of the caterpillar tractor side drive during plowing

The questions 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 motion. The tractor driver often has to correct the movement of the tractor, which contributes to its quick fatigue and, as a result, a decrease in the productivity of the work. 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 withdrawal of the tractor under the influence of external forces (without participation from the tractor driver) is a passive turn, which currently is not paid enough attention in the theory of the curvilinear motion of the caterpillar tractor, since the theory of rotation is usually directed to the studies of active movement (under the control action of the tractor operator). 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 during withdrawal, which consists of differential equations of motion and equilibrium conditions of external forces in the event of 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 developed mathematical model allows: to study the trajectory of motion on various soil backgrounds; find the optimal ratio of the weight of the tractor and the drag force on the hook; 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.