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Transport Problems

Silesian University of Technology

Subject: Economics, Transportation, Transportation Science & Technology


eISSN: 2300-861X



VOLUME 14 , ISSUE 4 (December 2019) > List of articles


Oleksandr PSHINKO / Liudmyla URSULYAK * / Serhii KOSTRYTSIA / Yevhen FEDOROV / Anzhela SHVETS

Keywords : mathematical modelling, the parameters of the longitudinal profile, regulating braking, longitudinal forces of impact and quasistatic character, braking distances

Citation Information : Transport Problems. Volume 14, Issue 4, Pages 161-172, DOI:

License : (CC BY 4.0)

Received Date : 05-March-2018 / Accepted: 11-October-2019 / Published Online: 08-December-2019



The main objective of the simulation is to study the effect caused by the parameters of the longitudinal profile on the maxima of longitudinal forces in freight trains of increased length during adjustment braking and running-out. To decrease the number of numerical experiments, some empirical formulae for estimating the maximum longitudinal forces during the motion of freight trains along the track with various configurations of its longitudinal profile's gradient changes have been obtained for the first time. Comparison of those forces with the permitted values, from the point of view of the railway stock strength and eventual vehicle derailment, has been performed. As a result of numerical integration of the system of non-linear differential equations of train motion for the considered driving modes, the values of the greatest longitudinal shock and quasi-static forces, as well as the dependence of the latter on the train length, initial braking velocity, on the algebraic difference of gradients and the length of the horizontal area that separates two gradients with opposite signs are estimated. The proposed mathematical model and methodology can be applied during standardization of the longitudinal profile's parameters from the point of view of the freight traffic safety for the trains of various length.

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1. Wu, Q. & Spiryagin, M. & Cole, C. Longitudinal train dynamics: an overview. Vehicle System Dynamics. 2016. No. 54 (12). Р. 1688-1714. DOI:10.1080/00423114.2016.1228988

2. Wu, Q. & Luo, Sh. & Cole, C. Longitudinal dynamics and energy analysis for heavy haul trains.  J. Mod. Transport. 2014. No. 22(3). Р. 127-136. DOI:10.1007/s40534-014-0055-x

3. Qi, Zh. & Huang, Zh. & Kong X. Simulation of longitudinal dynamics of long freight trains in positioning operations. Journal Vehicle System Dynamics International Journal of Vehicle Mechanics and Mobility. 2012. Vol. 50. No. 9. Р. 1409-1433. DOI: org/10.1080/00423114.2012.661063

4. Chang, Ch. & Guo, G. & Wang, J. & Ma, Y. Study on longitudinal force simulation of heavy-haul train. Vehicle System Dynamics. 2017. Vol. 55. No. 4. Р. 571-582. DOI: 10.1080/00423114.2016.1269183

5. Wang, X. & Tang, T. & He, H. Optimal control of heavy haul train based on approximate dynamic programming. Advances in mechanical engineering. 2017. Vol. 9, No. 4. P. 1-15. DOI: 10.1177/1687814017698110

6. Lin, X. & Wang, Q. & Wang, P. & Sun, P. & Feng, X. The Energy-Efficient Operation Problem of a Freight Train Considering Long-Distance Steep Downhill Sections. Energies. 2017. No. 10 (6), Р. 1-26. DOI:10.3390/en10060794

7. Frilli, A. & Meli, E. & Nocciolini, D. & Pugi, L. & Rindi, A. Object oriented simulation of longitudinal trair dynamics efficient tools to optimize sustainability and efficiency of railway systems. In: AEIT International Annual Conference, 14-16 Oct. 2015, Naples, Italy. 2015. DOI:10.1109/AEIT.2015.7415257

8. Васильев, А.С. & Болдырев, А.П. & Кеглин, Б.Г. & Гуров А.М. Исследование продольной нагруженности грузовых вагонов, оснащенных фрикционными поглощающими аппаратами нового исполнения, при переходных режимах движения поїзда. Вестн. Брянск. гос. техн. ун-та. 2014. No. 1 (41). Р. 12-17. [In Russian: Vasilev, A.S. & Boldyrev, A.P. & Keglin, B.G. & Gurov, A.M. (2014). Research of freight car's longitudinal loading equipped new frictional absorbing devices. Bulletin of Bryansk State Technical University.]

9. Ceraolo, M. & Lutzemberger, G. & Frilli, A. & Pugi L. Regenerative braking in high speed railway applications: Analysis by different simulation tools. In: Environment and Electrical Engineering (EEEIC): IEEE 16th International Conference. Florence, Italy, 2016. Р. 1-5. DOI:10.1109/EEEIC.2016.7555474

10. Wei, W. & Hu, Y. & Wu, Q. & Zhao, X. & Zhang, J. & Zhang, Y. An air brake model for longitudinal train dynamics studies. Vehicle System Dynamics. 2017. Vol. 55. No. 4. Р. 517-533. DOI:10.1080/00423114.2016.1254261

11. Serajian, R. & Mohammadi, S. & Nasr, A. Influence of train length on in-train longitudinal forces during brake application. Vehicle System Dynamics. 2018. DOI:10.1080/00423114.2018.1456667

12. Pugi, L. & Rindi, A. & Ercole, A.G. & Palazzolo, A. & Auciello, J. & Fioravanti, D. & Ignesti, M. Preliminary studies concerning the application of different braking arrangements on Italian freight trains. Vehicle System Dynamics. 2011. No. 49 (8). P. 1339-1365. DOI:10.1080/00423114.2010.505291

13. Blochinas, E. & Dailydka, S. & Lingaitis, L. & Ursuliak, L. Nestacionarieji ir kvazistatiniai geležinkelio traukinių judčjimo režimai. Vilnius: Technika. 2015. 167 p. [In Lithuanian: Blochinas, E. & Dailydka, S. & Lingaitis, L. & Ursuliak, L. Nonstationary and quasi-static modes of railway train movement. Vilnius: Technika]

14. Varazhun, I. & Shimanovsky, A. & Zavarotny, A. Determination of Longitudinal Forces in the Cars Automatic Couplers at Train Electrodynamic Braking. In: Proceedings of the 9th international scientific conference Transbaltica-2016. May 7-8, 2016. Vilnius. No. 134. Р. 415421. DOI:10.1016/j.proeng.2016.01.032

15. Shabana, A.A. & Aboubakr, A.K. & Ding L. Use of the non-inertial coordinates in the analysis of train longitudinal forces. Journal of Computational and Nonlinear Dynamics. 2012. No. 7(1).  Р. 1–10. doi: 10.1115/1.4004122

16. Stewart, M. F. & Punwani, S.K. & Andersen, D.R. & Booth, G.F. & Singh, S.P. & Prabhakaran A. Simulation of Longitudinal Train Dynamics: Case Studies Using the Train Energy and Dynamics Simulator (TEDS). In: Joint Rail Conference. San Jose, California, USA, 2015. Р. V001T02A011. DOI:10.1115/JRC2015-5760 2015

17. Блохин, Е.П. & Железнов, К.И. & Урсуляк, Л.В. Вычислительный комплекс для решения задач безопасности и устойчивости движения подвижного состава железных дорог. Наука и прогресс транспорта. Вестник Днепропетровского национального университета железнодорожного транспорта. 2007. No. 18. P. 106-114. [In Russian: Blokhin, Y.P. & Zheleznov, K.I. & Ursuljak, L.V. Computing complex for solving problems of safety and stability of the movement of rolling stock of railways. Bulletin of the Dnipropetrovsk National University of Railway Transport]

18. Myamlin, S. & Dailidka, S. & Neduzha, L. Mathematical Modeling of a Cargo Locomotive. In: Proc. of 16th Intern. Conf. Transport Means. Kaunas, 2012. Р. 310-312.

19. Гребенюк, П.Т. & Долганов, А.Н. & Некрасов, О.А. & etc. Правила тяговых расчетов для поездной работы. Москва: Транспорт. 1985. 287 p. [In Russian: Grebenyuk, P.T., & Dolganov, A.N. & Nekrasov, O.A. & et al. Rules of traction for train work. Moscow: Transport]

20. Урсуляк, Л.В. & Вайчиунас, Г. & Романюк, Я.Н. & Петренко, В. & Степченкова, Е.С.  О форме кривой наполнения тормозных цилиндров в грузовых поездах. Наука и прогресс транспорта. Вестник Днепропетровского национального университета железнодорожного транспорта. 2016. No. 2 (62). P. 165-173. DOI:10.15802/stp2016/67346. [In Russian: Ursuljak, L.V. & Vaiciunas, G. & Romanyuk, Ya.N. & Petrenko, V. & Stepchenkova, E.S. About Waveform of Braking Cylinder Filling in Freight Cars. Bulletin of the Dnipropetrovsk National University of Railway Transport]

21. DSTU 7598:2014. Вагони вантажні. Загальні вимоги до розрахунків та проектування нових і модернізованих вагонів колії 1520 мм (несамохідних). Київ:  ДП «УкрНДНЦ». 158 p.  [In Ukrainian: Freight wagons. General requirements for the calculation and design of new and modernized wagons of 1520 mm gauge (non-self-propelled). Kiev: State Enterprise "UkrNDNTS"]