Modelling of dynamic characteristics of tractor systems to improve stability on uneven fields

Viktor Duhanets, Pavlo Fedirko, Oleksandr Hovorov, Vitaliy Pukas, Mykola Volynkin
Abstract

The study aimed to determine the impact of the centre of mass shift, the angle of inclination of the terrain and local disturbances on the spatial stability of the transport system, with the subsequent determination of its equilibrium limit modes. The methodology was based on a combination of theoretical modelling, adaptive control and multi-level validation in a changing environment. The critical vertical displacement of the hull was found to be up to 0.15 m at an 18° tilt due to the asymmetric passage of obstacles, which confirmed the need for accurate dynamics prediction. Stability analysis has established safe roll angles of 25-30° for Ukrainian black soil (friction coefficient 0.6-0.8). The uneven load and soil moisture content (20-30%) affected stability, requiring model calibration. Hybrid methods compensated for seat vibrations by adaptively controlling the damper. Adaptive ground contact improved traction on soft ground, while nonlinear predictive steering optimised the trajectory on slopes. The expediency of the geometry of the reference plane and the position of the centre of mass when developing algorithms for stabilising agricultural machinery, given the impact on stability in variable terrain, was established. Stochastic modelling of soil disturbances was used to predict the impact of random environmental changes on the trajectory and stability of the equipment. The proposed theoretical model is suitable for the design and dynamic hull control systems, especially for operation on slopes and complex geometries. The integration of sensor systems with models ensured adaptation to real-time conditions. The practical value of the results was to improve the safety of agricultural machinery and optimise its spatial orientation on slopes by process engineers and developers of active levelling systems when designing new generation machinery

Keywords

acceleration, grip coefficient, field testing, stabilisation, adaptive control

Suggested citation
Duhanets, V., Fedirko, P., Hovorov, O., Pukas, V., & Volynkin, M. (2025). Modelling of dynamic characteristics of tractor systems to improve stability on uneven fields. Machinery & Energetics, 16(2), 159-174. https://doi.org/10.31548/machinery/2.2025.159
References
  1. Abdul Manaf, M.Z., Hudha, K., Samin, P.M., & Bakar, S.A. (2023). Modelling and verification of a 12-DOF tractor-semitrailer longitudinal model for load transfer analysisInternational Journal of Heavy Vehicle Systems, 30(5), 525-559.
  2. Adamchuk, V., Bulgakov, V., Nadykto, V., Ihnatiev, Y., & Olt, J. (2016). Theoretical research into the power and energy performance of agricultural tractorsAgronomy Research, 14(5), 1511-1518.
  3. Ahmadian, M., Chen, Y., & Zhang, Z. (2024). Emergency collision avoidance maneuvers of multi-trailer articulated heavy vehicles. Vehicle System Dynamics, 62(11), 2837-2860. doi: 10.1080/00423114.2024.2305292.
  4. Bekker, M.G. (1962). Mechanics of off-the-road locomotion. Proceedings of the Institution of Mechanical Engineers: Automobile Division, 16(1), 9-16. doi: 10.1243/PIME_AUTO_1962_000_009_02.
  5. Belloni, M., Vignati, M., Sabbioni, E., & Cutini, M. (2023). Characterization of vertical dynamics of a multi-purpose tractor with static and dynamic experimental tests. Retrieved from https://saemobilus.sae.org/papers/characterization-vertical-dynamics-a-multi-purpose-tractor-static-dynamic-experimental-tests-2023-01-0177.
  6. Bulgakov, V., Aboltins, A., Adamchuk, V., Kuvachov, V., Pascuzzi, S., Kyurchev, V., Rucins, A., & Nesvidomin, V. (2024). Investigation of wide span vehicle technological part movement stability. Engineering for Rural Development, 23, 522-530. doi: 10.22616/ERDev.2024.23.TF099.
  7. Bulgakov, V., Adamchuk, V., Nozdrovický, L., & Ihnatiev, Y. (2017). Theory of vibrations of sugar beet leaf harvester front-mounted on universal tractor. Acta Technologica Agriculturae, 20(4), 96-103. doi: 10.1515/ata-2017-0019.
  8. Carabin, G., Becce, L., Mandler, A., Nicolosi, F., & Mazzetto, F. (2024). Experimental validation of the influence of obstacles on tractor rollover stability. In R. Berruto, M. Biocca, E. Cavallo, M. Cecchini, S. Failla & E. Romano (Eds.), Safety, health and welfare in agriculture and agro-food systems (pp. 153-163). Cham: Springer. doi: 10.1007/978-3-031-63504-5_15.
  9. Chi, Y., Mao, L., Wang, X., Pang, S., & Yang, Y. (2024). Three-dimensional numerical simulation and experimental validation of airborne ground-penetrating radar based on CNCS-FDTD method under undulating terrain conditions. Scientific Reports, 14(1), article number 22156. doi: 10.1038/s41598-024-73375-y.
  10. Dai, D., Chen, D., Mao, X., Zhang, Y., Li, Y., Wang, S., & Zhang, B. (2023). Design and performance analysis of indoor calibration device for the force-measuring system of the tractor three-point hitch. International Journal of Agricultural and Biological Engineering, 16(3), 47-54. doi: 10.25165/j.ijabe.20231603.7455.
  11. Dong, Y., Yan, D., & Feng, X. (2023). Stability of tracked vehicles on soft grounds under multidirectional loading conditions. Canadian Geotechnical Journal, 60(11), 1743-1755. doi: 10.1139/cgj-2022-0532.
  12. Duan, L., Kang, K., Chen, S., Du, Z., Zhang, L., Liu, Z., Yang, F., & Wang, Z. (2025). Analysis and verification of a slope steering model of TRVs in hilly and mountainous environments. Agronomy, 15(1), article number 147. doi: 10.3390/agronomy15010147.
  13. García, J.M., Yánez, P., & Martínez, J.E. (2023). Evaluation of navigability in skid-steer mobile robots with passive trailers moving on sloping terrain. Revista Iberoamericana de Automática e Informática Industrial, 20(1), 13-24. doi: 10.4995/riai.2022.17161.
  14. Gong, X., Tao, G., Qiu, R., Zang, Z., Zhang, S., & Gong, J. (2024). Terrain-aware spatio-temporal trajectory planning for ground vehicles in off-road environment. In Proceedings of the 10th international conference on electrical engineering, control and robotics (pp. 200-207). Guangzhou: IEEE. doi: 10.1109/EECR60807.2024.10607329.
  15. Hamersma, H.A., van Aswegen, J.C., Guthrie, A.G., & Els, P.S. (2024). UAV-based three-dimensional rough terrain modelling. In Proceedings of the 21st international and 12th Asia-Pacific regional conference of the international society for terrain-vehicle systems (pp. 163-169). Ferrara: ISTVS. doi: 10.56884/TK3ZX342.
  16. Han, S., Yoon, K., Park, G., & Huh, K. (2024). Robust lane keeping control for tractor with multi-unit trailer under parametric uncertainty. IEEE Transactions on Intelligent Vehicles, 9(1), 2333-2347. doi: 10.1109/TIV.2023.3272655.
  17. Hassan, H., Sahib, B., Krehel, R., & Kočiško, M. (2017). Increase of accuracy of geometric forms of surfaces ground by a grinding wheel of various grain sizes. Advances in Mechanical Engineering, 9(8). doi: 10.1177/1687814017726006.
  18. Hrushetskyi, S., Oleksiyko, S., & Tykhy, M. (2024). Modern running system of management of agricultural machinery. International Science Journal of Engineering & Agriculture, 3(6), 61-74. doi: 10.46299/j.isjea.20240306.06.
  19. Huseynov, H. (2024). New trends in mechanical engineering technology. Advances in Science and Technology, 148, 257-263. doi: 10.4028/p-XvVNq0.
  20. Ismayilzada, M., Safarova, T., Novruzova, U., & Abbasova, S. (2025). Innovative technologies in the production of agricultural machinery to improve the efficiency of agribusinesses. Scientific Horizons, 28(5), 78-89. doi: 10.48077/scihor5.2025.79.
  21. Kolahi, P.M., & Nazemizadeh, M. (2023). Nonlinear dynamic modeling of tractor-trailer mobile robots with consideration of wheels inertia and their optimal point-to-point path planning. Meccanica, 58(1), 245-253. doi: 10.1007/s11012-022-01578-6.
  22. Li, Q., & Zhu, H. (2024). Performance evaluation of 2D LiDAR SLAM algorithms in simulated orchard environments. Computers and Electronics in Agriculture, 221, article number 108994. doi: 10.1016/j.compag.2024.108994.
  23. Li, Z., Yin, C., Peng, Z., Zhou, C., & Jalanezhad, M. (2024). Designing a time path tracking stabilizing controller for a tractor-trailer robot in the presence of uncertainties. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineeringdoi: 10.1177/09544070241238048.
  24. Liu, X., Wang, G., Suo, X., Du, T., Wang, W., & Zhang, C. (2025). Modeling and performance analysis of a hydraulically interconnected suspension for tri-axle mining dump trucks considering pitch-roll resistance. Journal of Mechanical Science and Technology, 39(2), 483-495. doi: 10.1007/s12206-025-0101-0.
  25. Ma, X., Xu, J., & Zhang, X. (2023). Bilateral constrained control for prosthesis walking on stochastically uneven terrain. International Journal of Mechanical Sciences, 239, article number 107896. doi: 10.1016/j.ijmecsci.2022.107896.
  26. Manoharan, A., Sharma, A., Belsare, H., Pal, K., Krishna, K.M., & Singh, A.K. (2024). Bi-level trajectory optimization on uneven terrains with differentiable wheel-terrain interaction modeldoi: 10.48550/arXiv.2404.03307.
  27. Meng, Q., Huai, Y., Wang, X., Li, Z., Zhang, R., & Nie, X. (2025). Three dimensional forest dynamic evolution based on hydraulic erosion and forest fire disturbance. Computers and Graphics, 126, article number 104152. doi: 10.1016/j.cag.2024.104152.
  28. Nadykto, V., Golub, G., Tsyvenkova, N., Kyurchev, V., Skliar, O., Skliar, R., Golub, V., & Shubenko, V. (2025). Modeling movement stability of machine-tractor units based on modular type tractor. Applied Sciences, 15(5), article number 2822. doi: 10.3390/app15052822.
  29. Puras, B., Raush, G., Freire, J., Filippini, G., Roquet, P., Tirado, M., Casadesús, O., & Codina, E. (2024). Development of a virtual telehandler model using a bond graph. Machines, 12(12), article number 878. doi: 10.3390/machines12120878.
  30. Qi, G., Yue, M., Xu, M., Zhang, L., & Liu, Y. (2025). Integrated NMPC-based vehicle stability and tracking control strategy for heavy-duty truck with road bank angle estimation. Journal of Vibration and Controldoi: 10.1177/10775463251337514.
  31. Rebrov, O.Y., Malko, M.M., Rebrova, A.O., & Yakunin, M.Ye. (2023). Method of determining reasonable tire sizes for wheeled agricultural tractors. Technical Service of Agricultural, Forestry and Transport Systems, 1, 117-125. doi: 10.20998/2078-6840.2023.1.14.
  32. Ruetenik, G.A., Jansen, J.D., Val, P., & Ylä-Mella, L. (2023). Optimising global landscape evolution models with ¹⁰Be. Earth Surface Dynamics, 11(5), 865-880. doi: 10.5194/esurf-11-865-2023.
  33. Sah, D.K., & Selekwa, M.F. (2024). Advancing autonomous backing of tractor-trailer systems: A dynamic model approach. In Proceedings of the ASME 2024 international mechanical engineering congress and exposition (article number IMECE2024-146070). Portland: American Society of Mechanical Engineers. doi: 10.1115/IMECE2024-146070.
  34. Sharma, T., & He, Y. (2024). On trade-off relationship between static and dynamic lateral stabilities of articulated heavy vehicles. Designs, 8(5), article number 103. doi: 10.3390/designs8050103.
  35. Singh, H., & Mehta, M. (2024). Development of dynamic model of tractor for vibration analysis of operator’s seat. AIP Conference Proceedings, 2962, article number 020066. doi: 10.1063/5.0192395.
  36. Tao, W., Chen, B., Zhou, L., Zheng, Z., Wu, J., & Duan, M. (2025). Design of a magnetorheological (MR) suspension damper for an agricultural tractor seat based on an adaptive neuro-fuzzy inference system (ANFIS) and active disturbance rejection control (ADRC). Mechanical Sciences, 16(1), 113-124. doi: 10.5194/ms-16-113-2025.
  37. Tong, W., Liao, K., Li, L., Gao, Z., Chen, F., & Luo, H. (2024). Optimization of the Camellia oleifera fruit harvester engine compartment heat dissipation based on temperature experiments and airflow field simulation. Agriculture, 14(9), article number 1640. doi: 10.3390/agriculture14091640.
  38. Vintoniak, V. (2024). Innovations in electronics for detecting objects in surface layers of soil: A review of methods and directions for further improvement. Technologies and Engineering, 25(3), 9-20. doi: 10.30857/2786-5371.2024.3.1.
  39. Wang, B., Gong, B., Xu, W., & Shi, X. (2024). An efficient method for modeling and evaluating the bench terrain of open-pit mines. Frontiers in Earth Science, 12, article number 1351352. doi: 10.3389/feart.2024.1351352.
  40. Wang, W.-H., Zou, T.-A., Xu, X.-J., & Xu, H.-J. (2023). Enhancing the tractive performance of unmanned vehicles using an optimised wheel-step driving system. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 237(5), 958-977. doi: 10.1177/09544070221087002.
  41. Yang, Y.-J., Jang, M.-K., & Nam, J.-S. (2024). Dynamic simulation model of miniature tracked forestry tractor for overturning and rollover safety evaluation. Agriculture, 14(11), article number 1991. doi: 10.3390/agriculture14111991.
  42. Zhou, B., Chen, S., Hu, J., You, Y., Wang, D., & Zhang, Q. (2023). Multi-body dynamics modeling and test of an articulated steering half-track tractor. International Journal of Agricultural and Biological Engineering, 16(6), 124-133. doi: 10.25165/j.ijabe.20231606.8165.