Study of the dynamic vertical interaction of multi-axle rolling stock with railway track

  • Asel Abdullayeva orcid

    School of Transport Engineering and Logistics named after M. Tynyshpayev, Satbayev University, Almaty 050013, Kazakhstan

  • Aidos Toktamyssov

    School of Transport Engineering and Logistics named after M. Tynyshpayev, Satbayev University, Almaty 050013, Kazakhstan

  • Gabit Bakyt orcid

    Department of Rolling Stock, Mukhametzhan Tynyshbayev ALT University, Almaty 050012, Kazakhstan

  • Muslim Aikumbekov orcid

    School of Transport Engineering and Logistics named after M. Tynyshpayev, Satbayev University, Almaty 050013, Kazakhstan

  • Amandyk Yelshibekov orcid

    Department of Transport Equipment and Technologies, Saken Seifullin Kazakh Agrotechnical University, Astana 010011, Kazakhstan

  • Ayaulym Abylkhanova

    School of Transport Engineering and Logistics named after M. Tynyshpayev, Satbayev University, Almaty 050013, Kazakhstan

Article ID: 4460
Keywords: railway track, vertical and lateral forces, mechanical modelling, high-speed operation, dynamic characteristics

Abstract

The continuous growth in the demand for increased capacity of the existing railway network of the Republic of Kazakhstan, particularly in regions bordering the Russian Federation and China, makes the issue of improving the operational safety of heavy-haul freight trains with increased mass and length especially relevant. The introduction of heavy trains represents a complex engineering and operational task that involves the use of more powerful locomotives, increased axle loads, reconstruction of track infrastructure and power supply systems, and the improvement of transportation technologies. In addition, higher train speeds combined with increasing freight traffic intensity require improvements in the strength and stability of the railway track structure. The technical policy of Kazakhstan Temir Zholy is aimed at a full transition to continuously welded track constructed on reinforced-concrete foundations. Edge stresses arising from rail bending and torsion under vertical and horizontal loads from rolling stock are among the key parameters determining rail strength. It is well known that the half-sum of the edge stresses characterizes the vertical impact on the track, whereas their half-difference represents the horizontal impact (lateral force). These parameters also reflect the influence of force moments generated by lateral loads and by the displacement of the conventional center of the wheel-rail contact patch relative to the rail head.

Published
2026-07-27
How to Cite
Abdullayeva, A., Toktamyssov, A., Bakyt, G., Aikumbekov, M., Yelshibekov, A., & Abylkhanova, A. (2026). Study of the dynamic vertical interaction of multi-axle rolling stock with railway track. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4460

References

[1]Zhai W, Wang K, Cai C. Fundamentals of vehicle–track coupled dynamics. Vehicle System Dynamics. 2009; 47(11): 1349–1376. doi: 10.1080/00423110802621561

[2]Xia H, Zhang N, Guo W. Dynamic Analysis of Train–Bridge System Subjected to Crosswinds. In: Dynamic Interaction of Train-Bridge Systems in High-Speed Railways: Theory and Applications. Springer; 2018. pp. 291–349. doi: 10.1007/978-3-662-54871-4_6

[3]Knothe Kl, Grassie SL. Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies. Vehicle System Dynamics. 1993; 22(3–4): 209–262. doi: 10.1080/00423119308969027

[4]Nielsen JCO, Igeland A. Vertical dynamic interaction between train and track – influence of wheel and track imperfections. Journal of Sound and Vibration. 1995; 187(5): 825–839. doi: 10.1006/jsvi.1995.0566

[5]Abdullayev S, Bakyt G, Kamzina A, et al. Dynamic Interaction of the TE-33A Diesel Locomotive and the Track in a Curve with a Radius of 600 Meters. International Journal of Mechanical Engineering and Robotics Research. 2024; 13(2): 205–212. doi: 10.18178/ijmerr.13.2.205-212

[6]Zhai WM, Wang KY, Lin JH. Modelling and experiment of railway ballast vibrations. Journal of Sound and Vibration. 2004; 270(4–5): 673–683. doi: 10.1016/S0022-460X(03)00186-X

[7]Ribeiro D, Calçada R, Brehm M, et al. Train–Track–Bridge Dynamic Interaction on a Bowstring-Arch Railway Bridge: Advanced Modeling and Experimental Validation. Sensors. 2023; 23(1): 171. doi: 10.3390/s23010171

[8]Abdullayev S, Bakyt G, Kamzina A, et al. Interaction of the TE33a Diesel Locomotive and the Railway Track on Curved Section with Radius 290 m. Communications - Scientific letters of the University of Zilina. 2023; 25(4): B315–B326. doi: 10.26552/com.C.2023.069

[9]Shi Z, Wang K, Zhang D, et al. Experimental investigation on dynamic behaviour of heavy-haul railway track induced by heavy axle load. Transport. 2019; 34(3): 351–362. doi: 10.3846/transport.2019.10325

[10]Lamprea-Pineda AC, Connolly DP, Hussein MFM. Beams on elastic foundations – A review of railway applications and solutions. Transportation Geotechnics. 2022; 33: 100696. doi: 10.1016/j.trgeo.2021.100696

[11]Yang Z, Zhang P, Moraal J, et al. An experimental study on the effects of friction modifiers on wheel–rail dynamic interactions with various angles of attack. Railway Engineering Science. 2022; 30(3): 360–382. doi: 10.1007/s40534-022-00285-y

[12]Zakeri JA, Xia H, Fan JJ. Dynamic responses of train-track system to single rail irregularity. Latin American Journal of Solids and Structures. 2009; 6(2): 143–160.

[13]Fröhling RD, Hettasch G. Wheel-Rail Interface Management: A Rolling Stock Perspective. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2010; 224(5): 491–497. doi: 10.1243/09544097JRRT339

[14]Zhai W. Two simple fast integration methods for large-scale dynamic problems in engineering. International Journal for Numerical Methods in Engineering. 1996; 39(24): 4199–4214. doi: 10.1002/(SICI)1097-0207(19961230)39:24%3C4199::AID-NME39%3E3.0.CO;2-Y

[15]Chen C, McDowell GR. An investigation of the dynamic behaviour of track transition zones using discrete element modelling. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2016; 230(1): 117–128. doi: 10.1177/0954409714528892

[16]Johansson A, Nielsen JCO. Out-of-round railway wheels—wheel-rail contact forces and track response derived from field tests and numerical simulations. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2003; 217(2): 135–146. doi: 10.1243/095440903765762878

[17]Touati M, Lamdouar N, Tajani C. Dynamic Behavior of a Railway Track Under a Moving Wheel Load Modelled as a Sinusoidal Pulse. Communications in Mathematics. 2023; 32(1): 10774. doi: 10.46298/cm.10774

[18]Wu TX. On the railway track dynamics with rail vibration absorber for noise reduction. Journal of Sound and Vibration. 2008; 309(3–5): 739–755. doi: 10.1016/j.jsv.2007.07.049

[19]Lundqvist A, Dahlberg T. Railway track stiffness variations – consequences and countermeasures. In: Proceedings of the 19th IAVSD Symposium of Dynamics of Vehicles on Roads and Tracks; 28 August–2 September 2005; Milano, Italy.

[20]Kaewunruen S, Sresakoolchai J, Zhou Z. Sustainability-Based Lifecycle Management for Bridge Infrastructure Using 6D BIM. Sustainability. 2020; 12(6): 2436. doi: 10.3390/su12062436

[21]Rempelos G, Ognibene G, Le Pen L, et al. Railway Track Deterioration Models: A Review of the State of the Art. Transportation Geotechnics. 2024; 49: 101377. doi: 10.1016/j.trgeo.2024.101377

[22]Gao L, Luo L, Lu D, et al. Dynamic Response of Railway Subgrade Under Train Load and Freeze–Thaw Action. Applied Sciences. 2025; 15(4): 1735. doi: 10.3390/app15041735

[23]Solonenko VG, Musayev JS, Makhmetova NM, et al. Dynamic Analysis of Railway Vehicle–Track Interaction: Modeling Elastic–Viscous Track Properties and Experimental Validation. Applied Sciences. 2025; 15(13): 7152. doi: 10.3390/app15137152

[24]Ma W, Xu Z, Luo S, et al. Influence of Wheel Axle Stiffness Character to the Wheel/Rail Dynamic Contact on the Straight Track. Transport. 2013; 30(1): 24–32. doi: 10.3846/16484142.2013.819035

[25]Zhang D, Zhai W, Wang K. Dynamic interaction between heavy-haul train and track structure due to increasing axle load. Australian Journal of Structural Engineering. 2017; 18(3): 190–203. doi: 10.1080/13287982.2017.1363126

[26]Lei X, Zhang B. Influence of Track Stiffness Distribution on Vehicle and Track Interactions in Track Transition. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2010; 224(6): 592–604. doi: 10.1243/09544097JRRT318

[27]Kargarnovin MH, Younesian D. Dynamics of Timoshenko beams on Pasternak foundation under moving load. Mechanics Research Communications. 2004; 31(6): 713–723. doi: 10.1016/j.mechrescom.2004.05.002

[28]Polepally G, Neridu S, Pasupuleti VDK, et al. Experimental and Numerical Investigation of Axial Load Capacity for Box-type Railway Bridges. Procedia Structural Integrity. 2024; 52: 487–505. doi: 10.1016/j.prostr.2023.12.049

[29]Zhai W, Stichel S, Ling L. Train–track coupled dynamics problems in heavy-haul rail transportation. Vehicle System Dynamics. 2025; 63(7): 1187–1240. doi: 10.1080/00423114.2025.2494834