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

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.