Mathematical modelling of oscillations of a machine for cutting tops of root crops

Abstract

High-quality cutting of root crop tops at the root ensures both a high yield and determines the condition of the root crops before they are extracted from the soil. Therefore, the search for conditions that will ensure this is an important and urgent problem for the production of these crops. The purpose of this research was to determine, through an analytical study, the optimal parameters of a new design of a machine for harvesting root crop tops, which is mounted in front of an aggregating tractor and performs oscillatory movements in the longitudinal-vertical plane. Methods related to the modelling of complex dynamic systems consisting of an aggregating tractor and a front-mounted machine, the development and solution of the final form of differential equations of oscillatory motion and computer modelling of the oscillatory process were used. According to the developed equivalent scheme, a new differential equation of angular vibrations of the machine was solved in the final form. In addition, numerical modelling was performed on a PC, which allowed constructing graphical dependencies of the machine’s turning angle φ at different speeds V of its forward movement and values of the c stiffness coefficient and μ damping coefficient of the pneumatic tyres of the copying wheels, and at different values of the unevenness of the soil surface and the main design parameters of the machine. It was established that with an increase V from 1.5 m·s-1 to 2.5 m·s-1, the amplitude of oscillations of the machine’s turning angle φ increased from 0.88° to 1.18°. However, at V 1.5 m·s-1, the duration of the transient process is 0.22 s, and at a speed of 2.5 m·s-1, this figure is already 0.14 s, i.e., a decrease of 36%. The positive amplitude of oscillations φ of the machine’s steering angle reaches 1.2°, and the negative amplitude does not exceed 0.3°, i.e., the oscillation range is insignificant. In the range of values considered V, preference should be assigned to its higher value. The structural and kinematic parameters of the system examined were determined using computer simulation. The presented method of mathematical modelling of the oscillatory process can be used in the research of any machines that are hitched in front of the aggregating tractors