Tag Archives: dynamic system

1517-1529 V. Bulgakov, V. Adamchuk, V. Nadykto, O. Kistechok and J. Olt
Theoretical research into the stability of motion of the ploughing tractor-implement unit operating on the ‘push-pull’ principle
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Theoretical research into the stability of motion of the ploughing tractor-implement unit operating on the ‘push-pull’ principle

V. Bulgakov¹, V. Adamchuk², V. Nadykto³, O. Kistechok³ and J. Olt⁴*

¹National University of Life and Environmental Sciences of Ukraine, 15, Heroyiv Oborony Str., UA 03041 Kyiv, Ukraine
²National Scientific Centre, Institute for Agricultural Engineering and Electrification, 11, Vokzalna Str., Glevaкha-1, Vasylkiv District, UA 08631 Kiev Region, Ukraine
³Tavria State Agrotechnological University, 18, B. Khmelnytsky Ave., UA 72312 Melitopol, Zaporozhye region, Ukraine
⁴Estonian University of Life Sciences, Institute of Technology, Kreutzwaldi 56, EE51014 Tartu, Estonia
*Correspondence: jyri.olt@emu.ee

Abstract:

The reduction of power consumption in the ploughing operations can be achieved by way of improving the grip properties of the implement-carrying tractors, which is facilitated by setting up ploughing units for operation on the ‘push-pull’ principle. The aim of the current research is to substantiate the set-up and parameters of the ploughing unit with a front-mounted plough basing on the theoretical investigation of the stability of its motion in the horizontal plane. The methods of research include obtaining the amplitude- and phase-frequency response characteristics of the dynamic system in order to analyse the stability of its motion under the action of external statistically random perturbations. Also, the methods of software development and PC-based numerical computation are applied. The results of the study prove that the increase of the ploughing unit’s travel speed results in the considerable rise of the gain of the amplitude of the tractor’s heading angle oscillation in response to the oscillation of the angular displacement of the front-mounted plough in the horizontal plane. The phase-frequency response displays the same behaviour, changing substantially together with the unit’s travel speed. Raising the coefficient of resistance to tyre slip of the tractor’s rear wheels from 100 to 130 kPa and the front wheels from 140 to 175 kPa results in a minor decrease of the amplitude of oscillation of the tractor’s heading angle φ. The ploughing unit has the best response to the input effect, i.e. the oscillation of the front-mounted plough’s angular displacement βp, when it operates using the 1+5 combination. The increase of the number of front-mounted plough bodies from 1 to 3 results in the substantial growth of the tractor’s heading angle oscillation amplitude. Taking into account the way, in which the ploughing unit as a dynamic system responds to the input perturbance, the increase of its travel speed can be restricted not by the condition of its motion stability, but solely by the agrotechnical requirements applied to such a process operation as ploughing. The ploughing unit’s motion stability substantially improves in case of higher air pressure in the tyres on the tractor’s front and rear wheels. This effect is especially pronounced in the perturbance oscillation frequency range (0…1.5 s–1) that covers the main part of its dispersion.

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689–710 V. Bulgakov, V. Adamchuk, M. Arak, V. Nadykto, V. Kyurchev and J. Olt
Theory of vertical oscillations and dynamic stability of combined tractor-implement unit
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Theory of vertical oscillations and dynamic stability of combined tractor-implement unit

V. Bulgakov¹, V. Adamchuk², M. Arak³, V. Nadykto⁴, V. Kyurchev⁴ and J. Olt³*

¹National University of Life and Environmental Sciences of Ukraine, 15, Heroyiv Oborony Str., UK 03041 Kyiv, Ukraine
²National Scientific Centre, Institute for Agricultural Engineering and Electrification, 11, Vokzalna Str., Glevaкha-1, Vasylkiv District, UK 08631 Kiev Region, Ukraine
³Estonian University of Life Sciences, Kreutzwaldi 56, EE51014 Tartu, Estonia
⁴Tavria State Agrotechnological University of Ukraine, Khmelnytskoho pr. 18, Melitopol, UK 72312 Zaporozhye region, Ukraine
*Correspondence: jyri.olt@emu.ee

Abstract:

 Currently, throughout the world quite extensive use is made of combined tractor-implement units, which are capable of performing several process operations in the same pass. At the same time, the state-of-the-art ploughing and general-purpose tractors that can carry as front- so rear-mounted implements and accordingly feature both the front and rear PTOs, also able to travel efficiently as forward so in reverse gear, are most suited for the performance of such operations. Authors developed and successfully tested a combined tractor-implement unit on the basis of a wheeled ploughing and general-purpose tractor, which can in one pass efficiently chop the after harvesting crop residues with a front-mounted rotary chopper and simultaneously perform tillage with a rear-mounted plough. The aim of this study is the elaboration of the theoretical basis for the process of vertical oscillation of the combined ploughing and chopping tractor-implement unit and the validation of its dynamic stability in the longitudinal and vertical plane. The research has been performed with the use of the methods of designing the analytical mathematical models of functioning of agricultural machines and machine assembly units based on the theory of tractor, the vibration theory, the theory of automatic control and dynamic stability and the methods of computer programme construction and PC-assisted numerical computation. The dynamics of the said unit have been studied basing on the analysis of the amplitude frequency characteristics of the unit as a dynamic system responding to external perturbations appearing in the form of soil surface irregularities. Following the results of the undertaken analytical study, first the equivalent schematic model of the discussed combined tractor-implement unit in the longitudinal and vertical plane was developed, the unit’s characteristic points were defined, the linear and angular displacements specified and acting forces applied. Each pneumatic-tyre wheel of the unit represented by its elastically damping model had point contacts with the soil surface irregularities defined by the respective elevations. Using the original dynamic equations in the form of the Lagrange equations of the second kind, first we defined the generalised coordinates and the formulae for the kinetic and potential energy, dissipation functions and generalised forces, then, after performing the necessary transformations, we set up the system of four differential equations, which described the motion of the dynamic system under consideration. Further, we applied the Laplace transformations to the obtained differential equation system, which provided for obtaining the system of equations in the operator form and preparing them for the representation suitable for PC-assisted numerical calculations with the use of the developed computer programme. In accordance with the numerical computation results, graphs were plotted for the amplitude and phase frequency response characteristics of the tractor’s vertical oscillations at different stiffness coefficients of its steering wheels, the amplitude frequency response characteristics of the chopper’s oscillations depending on its mass and its support wheel tyres’ stiffness coefficient as well as the characteristics of the plough’s oscillations at different stiffness coefficients of its pneumatic-tyre ground support wheel.

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