A mathematical model of the rear-trailed top harvester and an evaluation of its motion stability

J. Olt¹*, V. Bulgakov², H. Beloev³, V. Nadykto⁴, Ye. Ihnatiev⁴, O. Dubrovina² M. Arak¹, M. Bondar² and A. Kutsenko²

¹Estonian University of Life Sciences, Institute of Technology, 56 Kreutzwaldi Str., EE 51006 Tartu, Estonia
²National University of Life and Environmental Sciences of Ukraine, 15 Heroiv Oborony Str., UA 03041 Kyiv, Ukraine
³University of Ruse “Angel Kanchev”, 5, Studentska Str., BG 7017 Ruse, Bulgaria
⁴Dmytro Motornyi Tavria State Agrotechnological University, 18B Khmelnytsky Ave, UA 72310 Melitopol, Zaporozhye Region, Ukraine
*Correspondence: jyri.olt@emu.ee

Abstract:

Improving the quality of sugar beet harvesting to a great extent depends on the first operation in the process, which involves cutting and harvesting sugar beet tops. This technological process is performed with the use of either the haulm harvesting modules of beet harvesters or top harvesting machines as separate agricultural implements, which are aggregated with a tractor. At the same time, front-mounted harvesters are as widely used as trailed asymmetric implements, in which case the aggregating tractor moves on the already harvested area of the field. The purpose of this work is to determine the optimal design and kinematic parameters that would improve the stability in the performance of the technological process of harvesting sugar beet tops by means of developing the basic theory of the plane-parallel motion performed by the rear-trailed asymmetric top harvester. As a result of the analytical study, an equivalent scheme has been composed, on the basis of which a new computational mathematical model has been developed for the plane-parallel motion of the asymmetric top harvester in the horizontal plane on the assumption that the connection between the wheeled tractor and the rear-trailed top harvester is made in the form of a cylindrical hinge joint. Using the results of mathematical modelling, the system of linear second-order differential equations that determines the transverse movement of the centre of mass of the aggregating wheeled tractor and the rotation of its longitudinal symmetry axis by a certain angle about the said centre of mass as well as the angle of deviation of the rear-trailed asymmetric top harvester from the longitudinal symmetry axis of the tractor at an arbitrary instant of time has been obtained. The solving of the obtained system of differential equations provides for determining the stability and controllability of the motion performed by the asymmetric machine-tractor unit, when it performs the technological process of harvesting sugar beet tops.

Key words:

harvesting machine, plane-parallel motion, stability of movement, sugar beet tops

Theoretical research into the motion of combined fertilising and sowing tractor-implement unit

V. Bulgakov¹, V. Adamchuk², M. Arak³, I. Petrychenko² and J. Olt³*

¹National University of Life and Environmental Sciences of Ukraine, 15 Heroyiv Oborony Str., UA03041 Kyiv, Ukraine
²National Scientific Centre, Institute for Agricultural Engineering and Electrification, 11 Vokzalna Str., Glevaкha-1, Vasylkiv District, UA08631 Kiev Region, Ukraine
³Estonian University of Life Sciences, Institute of Technology, 56 Kreutzwaldi Str., EE51014 Tartu, Estonia
*Correspondence: jyri.olt@emu.ee

Abstract:

A mathematical model has been developed representing the motion of a seed drill combination simultaneously performing the preceding banded placement of mineral fertilisers. Such a combined unit comprises the gang-up wheeled tractor, the fertiliser distribution module behind the tractor attached to it with the use of a hitch and intended for the banded placement of mineral fertilisers and the grain drill behind the fertiliser distribution module attached to it also with the use of a hitch. For the components of this dynamic system the coordinates of their centres, their masses as well as the external forces and the reactions of the soil surface applied to them have been determined. In order to use the original dynamic equations in the form of the Lagrange equations of the second kind, the generalised coordinates and kinetic energy relations have been determined. Following the necessary transformations, a system of six differential equations of motion has been generated, which characterises the behaviour of the combined machine unit during its plane-parallel motion. In this system, two line coordinates and one angular coordinate characterise the behaviour of the propulsion and power unit (wheeled tractor), while three angular coordinates characterise the rotations of the draft gear and the centres of the machines integrated with its use.

Key words: