Mathematical modelling of operational stability of sowing machines’ mechanical systems

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.139846

Keywords:

motion stability, differential equation, coulter system, perturbed state

Abstract

This study addresses the construction of mathematical models for the operational stability of mechanical systems in agricultural seeders. The objects of research are the coulter systems of seeders with a support-packer roller and direct sowing planters, which are the disc working bodies of most sowing machines. The complexity in mathematical modeling of systems stability is due to a significant number of factors whose values are of variable and random character. To model them, it is proposed to explore the stability of systems based on their control parameters: lengths and angles of inclination, installation height of nodes and parts of a seeder, etc. The endogenous and exogenous parameters that include the following: step at sowing, soil surface depth and its properties, dimensions and weight of seeds, etc., are fixed at preset limits, in accordance with agricultural conditions. Difficulties in solving such systems of differential equations and obtaining the analytical solutions are explained by the condition for an inverse problem: the forces that act on a system must by in a constant equilibrium. The proposed modeling of system stability is based on the Lyapunov second method, which implies the construction and investigation of functions of perturbed motion at variable control parameters. We have established expressions for determining the stage of asymptotic stability of the system, which are characterized by the magnitude of time and distance that are required to return it to the unperturbed state. The obtained resulting mathematical expressions allowed us to establish significant factors: the length of a hitch, the rigidity of a spring, the inclination angle of a hitch, distance to the point of fastening a spring rod, which define the perturbed path of the coulter system. The result of modeling is the obtained damping character of the perturbed motion of the examined systems, as well as the established dependences of perturbed path of coulter systems on the above-specified parameters.

To test the adequacy of the derived mathematical expressions for determining the stability of sowing machines, to refine the ranges in the variation of significant parameters, we carried out an experimental research. We employed the procedure for a multi-factorial experiment. As a result, with the help of the developed modelling method and based on the experiment conducted, we determined the rational parameters for working bodies of sowing machines of different types, which could be applied for efficient operation and in the design process of similar machines.

Author Biographies

Olena Mogilnay, Institute of Vegetable and Melons, NAAS of Ukraine Instytutska str., 1, v. Selektsiyne, Kharkiv region, Ukraine, 62478

PhD, Director

Vladimir Paschenko, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 62001

Doctor of Technical Sciences, Professor

Department of Technology Systems Optimization named after T. P. Yevsyukova

Sergei Kharchenko, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 62001

Doctor of Technical Sciences, Associate Professor

Department of Technology Systems Optimization named after T. P. Yevsyukova

Vladimir Domashenko, Akhtyrskiy college of the Sumy National Agrarian University Sumska str., 46, Okhtyrka, Ukraine, 42700

Director

Kostiantyn Siedykh, Kharkiv National Agricultural University named after V. V. Dokuchayev Dokuchaevske-2, Kharkiv region, Kharkiv district, Ukraine, 62483

Lecturer

Department of technical supply of agroindustrial production

References

  1. Schoen, Н. et. al. (1998). Die Landwirtschaft: Lehrbuch fuer Landwirtschaftsschuhlen. Bd. 3. Landtechnik, Bauwesen. Muenchen: BLV-Verl.-Ges., 576.
  2. Pashchenko, V. F., Kornienko, S. I. (2016). Nauchnye osnovy processov obrabotki pochvy v sisteme racional'nogo vozdelyvaniya zernovyh i ovoshchnyh kul'tur. Kharkiv: TOV «Planeta print», 320.
  3. Kornienko, S., Pashenko, V., Melnik, V., Kharchenko, S., Khramov, N. (2016). Developing the method of constructing mathematical models of soil condition under the action of a wedge. Eastern-European Journal of Enterprise Technologies, 5 (7), 34–43. doi: https://doi.org/10.15587/1729-4061.2016.79912
  4. Kornienko, S. I. et. al. (2016). Ekonomiko-ekolohichni zasady ratsionalnoho formuvannia ta vykorystannia mashynno-traktornoho parku. Kharkiv, 178.
  5. Aduov, M. A., Kapov, S. N., Nukusheva, S. A., Rakhimzhanov, M. R. (2014). Components of coulter tractive resistance for subsoil throwing about seeds planting. Life Sci J., 11 (5s), 67–71.
  6. Goryachkin, V. P. (1968). Sobranie sochineniy. Vol. 2. Moscow: Kolos, 455.
  7. Vasilenko, P. M. (1954). Elementy teorii ustoychivosti dvizheniya pricepnyh s.-h. mashin i orudiy. Sb. nauchn. tr. po zemledel'cheskoy mekhanike, 2, 79–93.
  8. Kushnarev, A., Shevchenko, I., Dyuzhaev, V., Kushnarev, S. (2008). Mekhanika vzaimodeystviya rabochih organov na uprugoy podveske s pochvoy. Tekhnika APK, 8, 22–25.
  9. Hukov, Ya. S. (1999). Obrobitok gruntu. Tekhnolohiya i tekhnika. Kyiv: NoraPrint, 280.
  10. Tishchenko, L., Kharchenko, S., Kharchenko, F., Bredykhin, V., Tsurkan, O. (2016). Identification of a mixture of grain particle velocity through the holes of the vibrating sieves grain separators. Eastern-European Journal of Enterprise Technologies, 2 (7 (80)), 63–69. doi: https://doi.org/10.15587/1729-4061.2016.65920
  11. Lyapunov, A. M. (1956). Sobranie sochineniy. Vol. 2. Moscow: AN SSSR, 263.
  12. Malkin, I. G. (1966). Teoriya ustoychivosti dvizheniya. Moscow: Nauka, 530.
  13. Sokolov, V. M. (1962). Elementy teorii ustoychivosti dvizheniya soshnikov. Traktory i sel'hozmashiny, 3, 31–34.
  14. Shiryaev, A. M. (1966). Vliyanie mikrorel'efa polya na ustoychivost' hoda diskovogo soshnika v pochve. Zapiski LSKhI, 109, 106–114.
  15. Adamchuk, V., Bulgakov, V., Gorobey, V. (2016). Theory of two-disc anchor opener of grain drill. Scientific proceedings i international scientific conference "CONSERVING SOILS AND WATER", 71–73.
  16. Turan, J., Višacki, V., Sedlar, A., Pantelić, S., Findura, P., Máchal, P., Mareček, J. (2015). Seeder with Different Seeding Apparatus in Maize Sowing. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (1), 137–141. doi: https://doi.org/10.11118/actaun201563010137
  17. Altikat, S., Celik, A., Gozubuyuk, Z. (2013). Effects of various no-till seeders and stubble conditions on sowing performance and seed emergence of common vetch. Soil and Tillage Research, 126, 72–77. doi: https://doi.org/10.1016/j.still.2012.07.013
  18. Conceição, L. A., Barreiro, P., Dias, S., Garrido, M., Valero, C., da Silva, J. R. M. (2015). A partial study of vertical distribution of conventional no-till seeders and spatial variability of seed depth placement of maize in the Alentejo region, Portugal. Precision Agriculture, 17 (1), 36–52. doi: https://doi.org/10.1007/s11119-015-9405-x
  19. Savinych, P. A., Kurbanov, R., Kuboń, M., Kamionka, J. (2015). Stability of semi-mounted sod seeder motion. Agricultural Engineering, 3 (155), 101–108. doi: http://doi.org/10.14654/ir.2015.155.140
  20. Pashchenko, V. F., Kim, V. V. (2010). Metodika postroeniya matematicheskih modeley ustoychivosti funkcionirovaniya mekhanicheskih sistem. Kharkiv, 114.
  21. Roslavcev, A. V. (2003). Teoriya dvizheniya tyagovo-transportnyh sredstv. Moscow: UMC «Triada», 171.
  22. Allen, H. P. (1981). Direct Drilling and Reduced Cultivations. Farming Press Limited, Suffolk, UK, 210.

Downloads

Published

2018-07-31

How to Cite

Mogilnay, O., Paschenko, V., Kharchenko, S., Domashenko, V., & Siedykh, K. (2018). Mathematical modelling of operational stability of sowing machines’ mechanical systems. Eastern-European Journal of Enterprise Technologies, 4(1 (94), 37–46. https://doi.org/10.15587/1729-4061.2018.139846

Issue

Vol. 4 No. 1 (94) (2018): Engineering technological systems

Section

Engineering technological systems

License

Copyright (c) 2018 Olena Mogilnay, Vladimir Paschenko, Sergei Kharchenko, Vladimir Domashenko, Kostiantyn Siedykh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.