Analytical investigation in the impact interaction of a vibration digger with the body of the root during its extraction from the soil

Abstract

Goal. To substantiate rational constructive and kinematic parameters of the vibrating digger at its shock interaction with the root of sugar beet under the condition of its undamaging during digging from the soil. Methods. Theoretical research was conducted using the basic principles of higher mathematics and theoretical mechanics, in particular the theory of impact. Numerical calculations and graphical dependencies were obtained using a PC based on the developed and standard programs. Results. The shock interaction of the vibrating digging working body with the body of the sugar beet root at one point (asymmetric impact) is considered. Based on the developed equivalent scheme and application of the general theory of impact, a mathematical model of the impact interaction of the vibrating digger of the beet harvester with the body of the root, which is firmly connected with dry and hard soil, is built. Analytical expressions are obtained to determine the shock impulse, as well as the maximum allowable frequency of oscillations of the working body and reduced to the point of impact of its mass, provided that the root is not damaged. Based on analytical expressions, calculations were performed on a PC and graphical dependencies were created of the maximum allowable oscillation frequency of the vibrating digger and reduced to the point of impact of its mass on the amplitude of oscillations and translational velocity for a wide range of values of these parameters. Conclusions. With the increasing frequency of vibration of the vibrating digger in the range of 7.5–20.3 Hz and the speed of translational movement in the range of 1.4–2.2 m/s the value of the reduced to the point of impact of its mass tends to decrease and varies within 1.51–0.63 kg with an amplitude of oscillations of 0.016 m. The maximum allowable frequency of oscillations of the vibrating digger with increasing amplitude of its oscillations decreases sharply, the same as with the increasing speed of translational motion. Thus, for the consolidated mass of the vibrating digger 1.5 kg and the depth of its motion in the soil 0.10 m with increasing amplitude of oscillations in the range of 0.008–0.024 m and the speed of translational movement in the range of 1.4–2.2 m/s the maximum allowable frequency varies between 15.7–4.0 Hz. For the depth of motion of the vibrating digging working body 0.08 m, it varies in the range of 33.0–10.0 Hz.