The differential equation of root movement during its vibration excavation from soil

Abstract

Goal. To improve the productivity and quality of digging sugar beetroots by substantiating the rational design and kinematic parameters of the vibrating digging working body. Methods. Theoretical research uses methods of higher mathematics, in particular the integration of differential equations, and theoretical mechanics — the basic law of dynamics of a material point. Results. An equivalent scheme of force interaction of a root with working surfaces of vibrating digging working body is made, on the basis of which a new calculated mathematical model of vibration extraction of beetroot from the soil is constructed. The solution of this system of differential equations on the PC made it possible to build the basic graphical relationships between the structural and kinematic parameters of this process. Conclusions. New analytical dependences of velocity and root movement in time in the direction of translational motion of the vibrating digging working body taking into account its constructive and kinematic parameters are obtained. With the help of PC, the dependences of speed and movement of a root in time at its movement upwards in the course of extraction from soil taking into account constructive and kinematic parameters of the vibrating digging working body are constructed. During the calculations, it was found out that the time of extraction of a root from the soil was 0.032 s.