# Mathematical modelling of oscillatory movements cleaner of the heads of root cultures from remains on the root

• 1 Institute of Mechanics and Automation of Agricultural Production of the National Academy of Agrarian Sciences of Ukraine, Ukraine

## Abstract

Harvesting root crops still poses a challenging problem for the agricultural mechanization industry. Even though the technology of separate harvesting of tops and roots has undoubted advantages, the quality of the final product, i.e. roots, depends significantly on the accuracy of cutting tops from their heads to the roots and the thoroughness of their final cleaning from residues. One of the ways to solve this problem is to create improved constructions of peelers and their further testing, experimental and theoretical studies to determine their optimal structural and kinematic parameters. To implement the above, a new mathematical model was constructed, the study of which made it possible to assess the influence of the construction parameters of the root crop head cleaner from the residues of tops on the root on the indicators of its oscillatory process in the longitudinal-vertical plane when moving along uneven soil surfaces. Numerical calculations of the obtained mathematical model were carried out on a PC using the PTC Mathcad 15 software environment and the previously determined input numerical parameters. The amplitude-frequency and phase-frequency characteristics were constructed, which made it possible to determine the optimal parameters of this oscillatory system. Based on the mathematical modelling performed, the influence of irregularities in the longitudinal profile of the soil surface on the angular oscillations of the cleaner, as well as the influence of different values of the stiffness coefficient c and the damping coefficient μ of its two copy wheels, as well as the length l, or the longitudinal coordinate of their placement on the cleaner frame, was first of all determined. The mathematical modelling of the oscillatory movements of the cleaner made it possible to establish that the value of the stiffness coefficient c of the pneumatic tires of its trailing wheels should be not less than 315 kNm–1, which is ensured by the air pressure in its tires, which should be equal to 135 kPa. In addition, it has been established that the change in the value of the coefficient μ of damping of the tires of the cleaner’s tracking wheels should be in the following range 350…1350 Nsm–1 and this parameter does not affect the amplitude and phase frequency characteristics of oscillations under the influence of oscillations of the ordinates of the longitudinal profile of field surface irregularities in the frequency range 0…24 s–1. Also, the influence of oscillations of the longitudinal profile ordinates of the field in the specified frequency range of 0…24 s–1 depends little on the change in the value of the longitudinal coordinate l of the location of its tracing wheels. Therefore, the placement of the tracing wheels on the frame should be determined based on the constructional features of the cleaner.

## References

1. Bulgakov V.M., Adamchuk V.V., Nadykto V.T., Budzanivskyi M.I. Dynamics of oscillations of the root crop head cleaner from the residues of tops on the root – Bulletin of Agricultural Science, 2023, № 2, pp. 43-52.
2. Bulgakov V.M. Beet harvesting machines. Monograph. – Kyiv: Agrarian Science, 2011. – 352 p.
3. Directions and methods of development of working bodies of agricultural machines. Kyiv: Agrarian Science, 2001. – 280 p.
4. Kainuma H., Aoki J., Suzuki T. Et al. Development of potato haulm remover (Part 1) – state of potatoes at harvest and the effects of different haulm removal methods on potato quality. Journal of the Japanese Society of Agricultural Machinery, 2013. Volume 75. Issue 6. рр. 434-439.
5. Hevko, R., Brukhanskyi, R., Flonts, I., Synii, S., Klendii, O. Advances in Methods of Cleaning Root Crops // Bulletin of the Transilvania University of Braşov. Series II. – Braşov: Transilvania University Press Braşov (Romania) – Vol. 11 (60) No. 1 – 2018. – pp. 127-138.
6. Wang F. Optimization and field experiment of an adjustable device for sugar beet digger. International Journal of Agricultural and Biological Engineering, 2021. Volume 14. No. 6. рр. 68-74. DOI 10.25165/J.IJABE.20211406.6667.
7. Titiwa K.P. et al. Development of potato (Solanum Tuberosum L.) haulm cutter. IOP Conference Series: Earth and Environmental Science, 2019. Volume 301. 012009. doi:10.1088/1755- 1315/301/1/012009.
8. Ignatiev E.I. Theoretical modelling of the oscillatory movement of the root crop head cleaner mounted on an integrated plowing tractor. Mechanization and electrification of agriculture: national collection, Glevakha, 2017. Issue 4 (103). рр. 47-56.
9. Bulgakov V.M., Holovach I.V., Ruzhylo Z.V., Ignatiev E.I., Adamchuk O.V., Trokhanyak O.M. Theory and technical means for harvesting sugar beet tops: monograph, 2021. Kyiv: Agrarian Science. – 212 р.
10. Bulgakov V.M., Adamchuk V.V., Kurchev V.M., Nadykto V.T., Ignatiev E.I. Root crop head cleaner. Patent of Ukraine No. 115942, IPC A01D 23/02. Applied for on September 07, 2016; published on January 10, 2018. Bulletin № 1.
11. Bulgakov V.M., Adamchuk V.V., Golovach I.V., Nadykto V.T., Ignatiev E.I. Experimental studies of a two-shaft root crop head cleaner. Bulletin of Agrarian Science, 2022. №7. рр. 53-61.
12. Acosta E. C., Aguilar J.J.C., Aguilar J.J.C., Carrillo J.A.C., Garcia J.M.V., Fernandez J.P., Vargas M.G.A. Modeling of Tire Vertical Behavior Using a Test Bench. IEEE Access, 2020. Volume 8. pp. 106531-106541. DOI 10.1109/ACCESS. 2020. 3000533.
13. Deng L., Yan W., Zhu Q. Vehicle impact on the deck slab of concrete box-girder bridges due to damaged expansion. Journal of Bridge Engineering, 2016. Volume 21. № 2. – 13 p. ID 06015006.
14. Friedl R., Mangerig I. Dynamic amplification of bridge-expansion-joints considering roughness induced vehicle vibrations. Procedia Engineering, 2017. Volume 199. рр. 2651-2656.
15. Zheng E., Zhong X., Zhu R., Xue J., Cui S., Gao H. et al. Investigation into the vibration characteristics of agricultural wheeled tractor-implement system with hydro-pneumatic suspension on the front axle. Journal of Terramechanics, 2019. Volume 186. рр. 14-33.
16. Yoo H., Oh J., Chung W-J., Han H-W., Kim J-T., Park Y-J., et al. Measurement of stiffness and damping coefficient of rubber tractor tires using dynamic cleat test based on point contact model. International Journal of Agricultural and Biological Engineering, 2021. Volume 14(1). рр. 157-164.
17. Bulgakov, V., Adamchuk, V., Arak, M., Nadykto, V., Kyurchev, V., Olt, J. Theory of vertical oscillations and dynamic stability of combined tractor-implement unit. Agronomy Research, 2016. Volume 14. Issue 3. рр. 689-710.