Vibrations in engineering and technology

Veselovska Nataliia Rostyslavіvna – Doctor  of  Engineering,  Professor,  Head  of  the  Department  of Machines and Equipment of Agricultural Production of Vinnitsa National Agrarian University (3 Soniachna St., Vinnytsia, Ukraine, 21008, e-mail: wnatalia@ukr.net).

Shargorodskyi Serhiy Anatoliyovych - candidate of technical sciences, associate professor of the Department of "Machines and Equipment for Agricultural Production" of the Vinnytsia National Agrarian University (Sonyachna St., 3, Vinnytsia, 21008, Ukraine, e-mail: serganatsharg@gmail.com).

Burlaka Serhii Andriyovych - Doctor of Philosophy, senior lecturer of the Department of "Technological Processes and Equipment of Processing and Food Production" of the Vinnytsia National Agrarian University (Sonyachna St., 3, Vinnytsia, 21008, Ukraine, e-mail: ipserhiy@gmail.com).

Mathematical modeling plays a crucial role in understanding the interaction between the tiller paw and the soil. In this article, we explore some of the mathematical models used to describe this interaction. These models include the kinematic wave equation, which describes paw motion as a wavelike disturbance through the soil, and the Reynolds equation, which describes paw motion through forces acting on it. Also discussed are the soil deformation equations, Froude number, and Mohr-Coulomb failure criterion, which describe soil deformation, the relative importance of inertial and gravity forces, and soil shear strength, respectively. Using these equations, we can better understand the various physical and mechanical forces that play an important role in the interaction between the tiller foot and the soil, leading to improved design and performance of tillers.

The use of these mathematical models provides a more complete understanding of the complex interaction of the cultivator paw with the soil. They help predict the behavior of the soil under different conditions and give insight into how to optimize the cultivator design for better performance. This knowledge can be used to develop new cultivator designs, resulting in more efficient and effective tillage. In summary, mathematical modeling is a vital tool for understanding the interaction between the tiller paw and the soil, providing valuable information on how to improve tillage efficiency and effectiveness.

In addition, the mathematical models discussed in this paper can be used to improve our understanding of soil mechanics, which is critical for a variety of applications, including agriculture, construction, and environmental protection. By improving our understanding of the interaction between the tiller paw and the soil, we can develop more efficient and effective tillage methods that will lead to better yields, improve soil condition and reduce soil erosion. Ultimately, the development of accurate and reliable mathematical models of tiller-soil interactions will play a key role in the sustainable use and management of our valuable soil resources.

1. Ivanov M.I., Rutkevych V.S., Kolisnyk O.M., Lisovoy I.O. (2019). Research of the influence of the parameters of the block-portion separator on the adjustment range of speed of operating elements. INMATEH - Agricultural Engineering. Vol. 57/1. P. 37–44. [in English].

2. Rutkevych V.S. (2018). Development of mulchers branch of fruit trees between the rows of an intensive garden. Tekhnika, enerhetyka, transport APK. № 3 (102). C. 22–27. [in English].

3. Sysolin P.V., Salo V.M., Kropivnyy V.M. (2001). Silʹsʹkohospodarsʹki mashyny: teoretychni osnovy, konstruktsiya, proektuvannya: Pidruchnyk dlya studentiv vyshchykh navchalʹnykh zakladiv zi spetsialʹnosti “Mashyny ta obladnannya silʹsʹkohospodarsʹkoho vyrobnytstva” Kn.1: Mashyny dlya rilʹnytstva. K.: Urozhay, 384 c. [in Ukrainian].

4. Burlaka S.A. (2022). Alhorytm funktsionuvannya mashynno-traktornoho ahrehatu z vykorystannyam systemy zhyvlennya zi zmishuvachem palyv. Khmelʹnytsʹkoho natsionalʹnoho universytetu. S. 140-145. [in Ukrainian].

5. Hunʹko I. V., Burlaka S. A. (2022). Matematychne modelyuvannya roboty systemy zhyvlennya dyzelʹnoho dvyhuna pratsyuyuchoho na biopalyvi z droselʹnym rehulyuvannya skladu palyvnoyi sumishi. The scientific heritage. 2020. No50. S. 34–39. [in Ukrainian].

6. Patil M.K., Palanichamy M.S. (1988). A mathematical model of tractor-occupant system with a new seat suspension for minimization of vibration response. Applied Mathematical Modelling. Vol. 12, Issue 1. Pp. 63–71. [in English].

7. Rutkevych V., Kupchuk I., Yaropud V., Hraniak V., Burlaka S. (2022). Numerical simulation of the liquid distribution problem by an adaptive flow distributor. Przegląd Elektrotechniczny. № 2 (98). P. 64–69. [in English].

8. Mikulina M.O. (2018). Analitychne doslidzhennya tekhniko-ekonomichnykh pokaznykiv ornykh ahrehativ. Visnyk Sumsʹkoho Natsionalʹnoho Ahrarnoho Universytetu, seriya «Mekhanizatsiya ta avtomatyzatsiya vyrobnychykh protsesiv», No 10-34. 90 s. [in Ukrainian].

9. Sereda L.P., Rutkevych V.S., Zinyev M.V. (2018). Doslidzhennya matematychnoyi modeli hidropryvoda sehmentno-palʹtsevoho rizalʹnoho aparata kosarky. Tekhnika, enerhetyka, transport APK. № 1 (100). C. 111–123. [in Ukrainian].

10. Rutkevych V.S. (2018). Matematychne modelyuvannya roboty hidravlichnoho pryvoda sektsiy shyrokozakhvatnoho kulʹtyvatora z poslidovnym spratsyuvannyam hidrotsylindriv. Tekhnika, enerhetyka, transport APK. № 2 (101). C. 37–47. [in Ukrainian].

11. Kravchuka V.I., Hrytsyshyna M.I., Kovalya S.M. (2004). Suchasni tendentsiyi rozvytku konstruktsiy silʹsʹkohospodarsʹkoyi tekhniky. K.: Ahrarna nauka. 396 s. [in Ukrainian].

12. Bulgakov V., Olt J., Kuvachov V. et al. (2020). A theoretical and experimental study of the traction properties of agricultural gantry systems. Agraarteadus: Journal of Agricultural Science. No XXXI (1). R. 10–16. [in English].