Recently, articulated buses with a capacity of 150-200 people have been increasingly used in passenger transportation. The overall length of such buses is limited to 18.5 meters. It is explained by the need to meet regulatory requirements for maneuverability.
In Ukraine, the Road Traffic Rules allow the total length of a road train to be 22 meters. With this length, the passenger capacity of the articulated bus increases significantly, but the issues of maneuverability and stability of such buses remain open. Preliminary studies have shown that even a bus with a total length of 18.75 m with an unmanageable trailer axle does not meet the requirements of regulatory documents for maneuverability. Using a self-aligning trailer axle meets the requirements for maneuverability even with an articulated bus length of up to 20.0 m. Still, the question of the stability of such a bus remains open. Using a specified mathematical model of a two-link road train adapted for an articulated bus with a self-aligning trailer axle, the stability indicators of an articulated bus in different driving modes were determined. It is shown that the critical velocity of the articulated bus with the blocked wheels of the trailer's self-aligning axle was 31.87 m/s, which significantly exceeds the maximum velocity of the bus. In the presence of a perturbation, the pattern of changes in the lateral and angular velocities of the articulated bus during the transition process at a velocity of 6 m/s is damped by a logarithmic law, which indicates the stability of the articulated bus movement. When the velocity is increased to 12 m/s, the pattern of changes in lateral and angular velocities also dampens. Still, there are more intense oscillations, which at a velocity of 14 m/s become divergent, leading to a loss of stability of the articulated bus. Similar results were obtained when the rotation of the articulated bus was 90 degrees. Thus, the maximum velocity of the articulated bus with unlocked wheels of the trailer's self-aligning axle should not exceed 14 m/s. When this velocity is reached, the wheels of the self-aligning axis should lock.
It determines the field of application of the self-aligning trailer axle on articulated buses. For driving at higher velocities, fundamentally new control systems for the bus control and the articulated bus trailer are needed.
1. Hnatov, A. V., Arhun, Sh. V., & Ulyanets, O. A. (2017). Elektromobili - maibutnie, iake vzhe nastalo [Electric cars - the future that has already arrived]. Avtomobil i elektronika. Suchasni tekhnolohii [Automobile and Electronics. Modern Technologies], 11, 24-28 (in Ukrainian).
2. Sakhno, V. P., Murovanyi, I. S., Sharai, S. M., & Kotenko, A. S. (2024). Porizhni analiz sharnirno-zchlenovanykh avtobusiv za manevrenistiu [Comparative analysis of articulated buses for maneuverability]. Suchasni tekhnolohii v mashynobuduvanni i na transporti [Modern Technologies in Mechanical Engineering and Transport], 2, 197-207. DOI: 10.36910/automash.v2i23.1542 (in Ukrainian).
https://doi.org/10.36910/automash.v2i23.1542
3. Arhun, Sh. (2019). Elektrobusy - perspektyvnyi miskyi transport Kharkova [Electric buses - a promising urban transport of Kharkiv]. Avtomobilnyi transport [Automotive Transport], 44, 59-65. DOI: 10.30977/АТ.2219-8342.2019.44.0.59 (in Ukrainian).
https://doi.org/10.30977/AT.2219-8342.2019.44.0.59
4. Sakhno, V. P., Mayak, M. M., & Kotenko, A. S. (2024). Do porivnialnoi otsinky sharnirno-zchlenovanykh avtobusiv z riznymy sylovymy ustanovkamy [Comparative assessment of articulated buses with different power units]. Suchasni tekhnolohii v mashynobuduvanni i na transporti [Modern Technologies in Mechanical Engineering and Transport], 2, 197-207. DOI 10.36910/automash.v2i23.1542 (in Ukrainian).
5. Sakhno, V. P., Sharai, S. M., Murovanyi, I. S., & Chovcha, I. V. (2022). Do vyznachennia stiikosti rukhu trylankovykh avtopoizdiv [On the determination of movement stability of three-link road trains]. Suchasni tekhnolohii v mashynobuduvanni ta transporti [Modern Technologies in Mechanical Engineering and Transport], 1(18), 155-167. DOI: 10.36910/automash.v1i18.772 (in Ukrainian).
https://doi.org/10.36910/automash.v1i18.772
6. Zinko, R., Lanets, O., & Skvarok, Y. (2023). Modeling of three-link road trains. In IOP Conference Series: Materials Science and Engineering (pp. 012027). IOP Publishing. DOI 10.1088/1757-899X/1277/1/012027 (in English).
https://doi.org/10.1088/1757-899X/1277/1/012027
7. De Felice, A., Mercantini, M., & Sorrentino, S. (2021). Stability analysis of articulated bus in straight-ahead running manoeuvre. Journal of Applied and Computational Mechanics, 7(3), 1649-1662. DOI: 10.22055/JACM.2021.36566.2869 (in English).
8. Dang, H. A. (2014). Determination of trajectory of articulated bus turning along curved line. Transactions on Transport Sciences, 7(1), 35. DOI: 10.2478/trans-2014-0002 (in English).
https://doi.org/10.2478/trans-2014-0002
9. The vertical motion lateral stability of road vehicle trains. Retrieved from: https://trid.trb.org/view/112747 (in English).
10. Chen, H. J., Su, W. J., & Wang, F. C. (2017). Modeling and analyses of a connected multi-car train system employing the inerter. Advances in Mechanical Engineering, 9(8), 1-13. DOI: 10.1177/1687814017701703 (in English).
https://doi.org/10.1177/1687814017701703
11. Sakhno, V. P., Polyakov, V. M., Sharai, S. M., Murovanyi, I. S., & Omelnytskyi, O. Ye. (2021). Sharnirno-zchlenovani avtobusy. Manevrenist ta stiikist [Articulated buses: Maneuverability and stability]. Lutsk: IVV LNTU. (in Ukrainian).
12. Zhang, Y., Khajepour, A., & Huang, Y. (2018). Multi-axle/articulated bus dynamics modeling: a reconfigurable approach. Vehicle System Dynamics, 56(9), 1315-1343. DOI: 10.1080/00423114.2017.1420205 (in English).
https://doi.org/10.1080/00423114.2017.1420205
13. Altafini, C. (2001). Some properties of the general n-trailer. International Journal of Control, 74(4), 409-424. DOI: 10.1080/00207170010010579 (in English).
https://doi.org/10.1080/00207170010010579
14. Emheisen, M. A., Emirler, M. T., & Ozkan, B. (2022). Lateral stability control of articulated heavy vehicles based on active steering system. International Journal of Mechanical Engineering and Robotics Research, 11(8), 575-582. DOI: 10.18178/ijmerr.11.8.575-582 (in English).
https://doi.org/10.18178/ijmerr.11.8.575-582
15. Oreh, S. T., Kazemi, R., & Azadi, S. (2012). A new desired articulation angle for directional control of articulated vehicles. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of multi-body dynamics, 226(4), 298-314. DOI: 10.1177/1464419312445426 (in English).
https://doi.org/10.1177/1464419312445426
16. Emheisen, M. A., Emirler, M. T., & Özkan, B. (2018). Active steering control of articulated heavy vehicles for improving lateral performance. In Proceedings of the 9th International Automotive Technologies Congress (pp. 771-779). Bursa, Turkey (in English).
17. Yu, Z., Xing, D., Cao, Q., & Li, S. (2016, August). Research on the stability of the semi-trailer based on neural network control. In 2016 IEEE International Conference on Mechatronics and Automation (pp. 1472-1476). Harbin, China. DOI: 10.1109/ICMA.2016.7558781 (in English).
https://doi.org/10.1109/ICMA.2016.7558781
18. Milani, S., Samim Ünlüsoy, Y., Marzbani, H., & Jazar, R. N. (2019). Semitrailer steering control for improved articulated vehicle manoeuvrability and stability. Nonlinear Engineering, 8(1), 568-581. DOI: 10.1515/nleng-2018-0124 (in English).
https://doi.org/10.1515/nleng-2018-0124
19. Bahaghighat, M. K., Kharrazi, S., Lidberg, M., Falcone, P., & Schofield, B. (2010, December). Predictive yaw and lateral control in long heavy vehicles combinations. In 49th IEEE Conference on Decision and Control (CDC) (pp. 6403-6408). Atlanta, GA, USA. DOI: 10.1109/CDC.2010.5717377 (in English).
https://doi.org/10.1109/CDC.2010.5717377
20. Vempaty, S., He, Y., & Zhao, L. (2020). An overview of control schemes for improving the lateral stability of car-trailer combinations. International journal of vehicle performance, 6(2), 151-199. DOI: 10.1504/IJVP.2020.106985 (in English).
https://doi.org/10.1504/IJVP.2020.106985
21. Timkov, O. M., Yashchenko, D. M., & Bosenko, V. M. (2010). Analitychni sposoby vyznachennia momentiv inertsii avtomobilia [Analytical methods for determining the moments of inertia of a car]. Upravlinnia proektamy, systemnyi analiz i lohistyka. Tekhnichna seriia [Project Management, Systems Analysis and Logistics. Technical Series], 7, 177-181 (in Ukrainian).