Vibrations in engineering and technology

Yaropud Vitalii – Doctor of Technical Sciences, Associate Professor, Dean of the Engineering and Technology Faculty, Vinnytsia National Agrarian University (3 Soniachna St., Vinnytsia, Ukraine, 21008, e-mail: yaropud77@gmail.com.

Tykhyy Oleksandr – Candidate for the degree of Doctor of Philosophy in specialty 133 Industrial Mechanical Engineering in Industrial Mechanical Engineering of the Department of «Machinery and Equipment for Agricultural Production» of Vinnytsia National Agrarian University (3 Sonyachna St., Vinnytsia, 21008, Ukraine, e-mail: tdsunagro@gmail.com).

The study presents an analytical investigation of an improved structural and technological design of a seeding unit equipped with a viscoelastic damping device intended to reduce dynamic oscillations and stabilize seed placement depth. A spatial hinge-linked mechanical system of the basic seeding unit is examined, its structural model is developed, and the mass-inertial, kinematic and force parameters of its main elements – including the horizontal and inclined beams, the opener shank and the gauge wheel – are determined. Based on analytical mechanics, a system of second-order Lagrange differential equations is formulated to describe the oscillatory processes, incorporating the potential and kinetic energy of the system components as well as the effects of soil reaction forces and viscous damping.

To evaluate the dynamic response of the seeding unit, numerical simulations were performed in the Wolfram Cloud environment, enabling the determination of time histories of angular and linear displacements and the identification of the oscillation characteristics, including amplitude-frequency behaviour. The results show that the implementation of a viscoelastic damper reduces oscillation amplitude, shifts resonant frequencies and decreases the system’s quality factor, thereby improving the stability of the working elements and enhancing seeding accuracy.

A second-order regression model describing the dependence of the coefficient of variation of the frame rotation angle on the damper parameters and seeder forward velocity was developed. This model enables the selection of optimal stiffness and damping values for the viscoelastic element. The obtained results may be used in the design and modernization of seeding units and serve as a basis for further research in the dynamics and vibration loading of agricultural machinery.

1. Yaropud, V. M., Hovorukha, V. B., & Datsiuk, D. A. (2023). Eksperymentalni doslidzhennia dozatora vysivnoho aparata selektsiinoi sivalky dribnonasinnievoi kultury [Experimental study of the metering device of a precision seeder for small-seeded crops]. Tekhnika, Enerhetyka, Transport APK, 3(122), 43–52. https://doi.org/10.37128/2520-6168-2023-3-5

2. Aliiev, E. B., Bezverkhnіi, P. Ye., & Aliieva, O. Yu. (2024). Vyprobuvannia udoskonalenoi systemy podachi nasinnia pnevmatychnoi sivalky tochnogo vysivu [Testing of an improved seed delivery system of a pneumatic precision seeder]. Naukovo-tekhnichnyi biuleten Instytutu oliinykh kultur NAAN, 37, 127–138. https://doi.org/10.36710/IOC-2024-37-13

3. Aliiev, E. B., & Bezverkhnіi, P. Ye. (2022). Chyselne modeliuvannia spolilniuvacha nasinnia pnevmatychnoi sivalky tochnogo vysivu [Numerical modelling of a seed decelerator in a pneumatic precision seeder]. Konstruiuvannia, vyrobnytstvo ta ekspluatatsiia silskohospodarskykh mashyn, 52, 86–98. https://doi.org/10.32515/2414-3820.2022.52.86-98

4. Yaropud, V. M., & Datsiuk, D. A. (2021). Shliakhy udoskonalennia vysivnoho aparata selektsiinoi sivalky dribnonasinnievoi kultury [Ways of improving the seeding device of a selection seeder for small-seeded crops]. Vibratsii v tekhnitsi ta tekhnolohiiakh, 1(100), 156–166. https://doi.org/10.37128/2306-8744-2021-1-15

5. Li, M., Chang, X., Gu, Y., Wang, P., & Shang, S. (2025). Design of dynamic deep-sowing system for peanut planter with double-loop feedback fuzzy PID control. Agriculture, 15(8), 808. https://doi.org/10.3390/agriculture15080808

6. Gao, Y., Yang, Y., Hu, Y., Han, X., Feng, K., Li, P., Wei, X., & Zhai, C. (2024). Study on operating vibration characteristics of different no-tillage planter row units in wheat stubble fields. Agriculture, 14(11), 1878. https://doi.org/10.3390/agriculture14111878

7. Haq, F. U., Khan, M. T., & Shah, K. (2023). Modelling and intelligent control-based damping system for smart no-till seed planter assembly. PakJET, 6(1), 23–27. https://doi.org/10.51846/vol6iss1pp13-17

8. Derkach, O. D., Makarenko, D. O., Muranov, Ye. S., & Lobodenko, A. V. (2021). Pidvyshchennia dovhovichnosti rukhomykh ziednan posivnykh mashyn vprovadzhenniam prohresyvnykh materialiv [Increasing durability of moving joints in seeding machines by introducing advanced structural materials]. Naukovyi visnyk TDATU, 11(2), 10. https://doi.org/10.37128/2520-6168-2023-4-2

9. Naumenko, M., Makarenko, D., Huridova, V., & Krutous, D. (2021). Matematyčna model vzaiemodii soshnyka posivnoho kompleksu z ґruntom za skladnykh umov ekspluatatsii [Mathematical model of interaction between the opener of a seeding complex and soil under difficult operating conditions]. Matematychne modeliuvannia, 1(44), 55–61. https://doi.org/10.31319/2519-8106.1(44)2021.235926

10. Makarenko, D. O., Derkach, O. D., Hovorukha, V. B., & Veselovska, N. R. (2023). Modernizatsiia rukhomykh ziednan sektsii posivnoho kompleksu [Modernization of movable joints of a seeding complex section]. Tekhnika, Enerhetyka, Transport APK, 123(4), 12–20. https://doi.org/10.37128/2520-6168-2023-4-2

11. Sun, S. S., Ning, D. H., Yang, J., Du, H., Zhang, S. W., & Li, W. H. (2016). A seat suspension with a rotary magnetorheological damper for heavy-duty vehicles. Smart Materials and Structures, 25, 105032. https://doi.org/10.1088/0964-1726/25/10/105032

12. Wu, S., Dou, Z., Fei, S., Shi, F., Zhang, X., Liu, Z., & Huang, D. (2025). Structural design and parameter optimization of an in-row deep fertilizer application device for maize. Agriculture, 15(18), 1934. https://doi.org/10.3390/agriculture15181934

13. Záček, J., Šebesta, K., Mohammad, H., Jenis, F., Strecker, Z., & Kubík, M. (2022). Experimental evaluation of modified Groundhook car suspension with fast magnetorheological damper. Actuators, 11, 354. https://doi.org/10.3390/act11120354

14. Kozachenko, O., Aliiev, E., & Sedykh, K. (2021). Results of investigation of the spring shank disc harrow performance. U.P.B. Sci. Bull., Series D, 83(4), 123–140.

15. Kozachenko, O. V., & Siedykh, K. V. (2020). Dynamichna model protsesu deformatsii pruzhnoi stiiky dyskatora [Dynamic model of deformation of a spring shank of a disc harrow]. Tekhnika ta Enerhetyka, 11(3), 31–39. https://doi.org/10.31548/machenergy2020.03.031

16. Sharipov, G. M., Paraforos, D. S., & Griepentrog, H. W. (2019). Validating the model of a no-till coulter assembly equipped with a magnetorheological damping system. Applied Sciences, 9(19), 3969. https://doi.org/10.3390/app9193969

17. Simionescu, P. A., & Smith, M. R. (2000). Single-valued function representations in linkage mechanism design. Mechanism and Machine Theory, 35(12), 1709–1726. https://doi.org/10.1016/S0094-114X(00)00018-5

18. Aliiev, E. B. (2023). Chyselne modeliuvannia protsesiv ahropromyslovoho vyrobnytstva: pidruchnyk [Numerical modelling of agro-industrial processes: Textbook]. Kyiv: Ahrarna Nauka. 

19. Yaropud, V. M., Aliiev, E. B., & Datsiuk, D. A. (2021). Metodyka chyselnoho modeliuvannia vysivnoho aparata selektsiinoi sivalky dribnonasinnevykh kultur [Numerical modelling method for a seeding mechanism of a selection seeder for small-seeded crops]. Machinery & Energetics, 12(3), 121–127. https://doi.org/10.31548/machenergy2021.03.121

20. Yaropud, V. M., Hovorukha, V. B., & Datsiuk, D. A. (2023). Vyprobuvannia matematychnoi modeli roboty dozatora vysivnoho aparata selektsiinoi sivalky dribnonasinnievoi kultury [Testing the mathematical model of the metering device operation of a selection seeder for small-seeded crops]. Vibratsii v Tekhnitsi ta Tekhnolohiiakh, 3(110), 52–60. https://doi.org/10.37128/2306-8744-2023-3-6 

21. Yaropud, V. M., & Datsiuk, D. A. (2023). Doslidzhennia rukhu nasinnia u rozpodilnyku vysivnoho aparata selektsiinoi sivalky dribnonasinnievykh kultur [Study of seed movement in the distributor of a seeding mechanism of a selection seeder]. Silskohospodarski mashyny, 49, 7–14. https://doi.org/10.36910/acm.vi49.945