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