Study and assessment of railroad wheel-climb formulations and assumptions

Abstract

In railroad wheel climb ${L \mathord{\left/ {\vphantom {L V}} \right. \kern-0pt} V}$ derailment criteria, it is assumed that the direction of the relative velocity of the flange-contact point in its totality is downward, leading to an upward friction force along the wheel flange profile. That is, the longitudinal component of the relative velocity of the flange-contact point is assumed negligible. It is further assumed that the climb progresses along a flange profile, and consequently, the flange-contact point trajectory is defined by the flange profile curve or a straight line. This paper examines these two basic assumptions by developing a three-dimensional wheel climb model that relaxes the assumptions used in deriving the planar ${L \mathord{\left/ {\vphantom {L V}} \right. \kern-0pt} V}$ ratio. The results obtained show that, in case of flange contact at a large angle of attack, there is a nonzero longitudinal velocity component of the wheel flange-contact point, and the trajectory of this point is not, in general, defined by the flange profile or a straight line. Consequently, the phenomenon of wheel climb at a large angle of attack is three-dimensional, demonstrating the need for further investigations of the derailment criteria based on planar analysis.

Keywords

Wheel climb / ${L \mathord{\left/ {\vphantom {L V}} \right. \kern-0pt} V}$ ratio / Nadal’s limit / Wheel/rail flange contact / Non-generalized coordinates

References

[1] Wang W, Li GX. Development of a simulation model of a high-speed vehicle for a derailment mechanism. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2010, 224(2): 103-113

[2] Zeng J, Wu P. Study on the wheel/rail interaction and derailment safety. Wear, 2008, 265: 1452-1456

[3] Shabana AA, Ling H (2023) Spatial dynamic formulation of the L/V ratio and mechanics of wheel climb. Nonlinear Dyn 111(16):14731–14750

[4] Shabana AA. Nadal’s formula and high speed rail derailments. J Comput Nonlinear Dyn, 2012, 7: 41003-1-41003-8

[5] Blader FB. “A Review of Literature and Methodologies in the Study of derailment Caused by Excessive Forces at the Wheel/Rail Interface”, AAR Report R-717, 1990, Washington, D.C., Association of American Railroads

[6] Elkins J, Wu H (2000) New criteria for flange climb derailment. In: IEEE/ASME Joint Rail Conference. Newark, pp 1–7

[7] Marquis B, Grief R (2011) Application of Nadal limit in the prediction of wheel climb derailment. In: Proceedings of the ASME/ASCE/IEEE 2011 Joint Rail Conference. Pueblo, Paper # JRC2011-56064, March 16–18

[8] Shust WC, Elkins JA, Kalay JA et al (1997) Wheel climb derailment tests using AAR’s track loading vehicle. Association of American Railroads Report R-910, Washington D.C.

[9] Wu H, Elkins JA (1999) Investigation of wheel flange climb derailment criteria. Association of American Railroads Report R-931, Washington D.C.

[10] Wilson N, Shu X, Kramp K (2004) Effect of independently rolling wheels on flange climb derailment. In: Proceedings of the ASME International Mechanical Engineering Congress. Anaheim, pp 21–27

[11] Weinstock H (1984) Wheel climb derailment criteria for evaluation of rail vehicle safety. Report No. 84-WA/RT-1, John A. Volpe National Transportation Systems Center, Cambridge

[12] Matsudaria T (1963) Dynamics of high speed rolling stock. RTRI Quarterly Reports 7(1): 45–97

[13] Koci HH, Swenson CA (1978) Locomotive wheel loading—A system approach. General Motors Electromotive Division, LaGrange

[14] Nadal MJ (1908) Locomotives á vapeur. Collection Encyclopédie Scientifique, Bibliotéque de Mécanique Appliquée et Génie, Vol. 186, Paris

[15] Shabana AA, Sany JR. An augmented formulation for mechanical systems with non-generalized coordinates: application to rigid body contact problems. Nonlinear Dyn, 2001, 24(2): 183-204

[16] Shabana A (2021) Mathematical foundation of railroad vehicle systems: geometry and mechanics. John Wiley & Sons, Chichester

[17] O’Shea JJ, Shabana AA (2016) Analytical and numerical investigation of wheel climb at large angle of attack. Nonlinear Dyn 83(1):555–577

[18] O’Shea JJ, Shabana AA (2017) Further investigation of wheel climb initiation: Three-point contact. Proc Inst Mech Eng Part K J Multi Body Dyn 231(1):121–132

[19] Khulief YA, Shabana AA (1986) Impact responses of multi-body systems with consistent and lumped masses. J Sound Vib 104(2):187–207

[20] Khulief YA, Shabana AA (1986) Dynamics of multibody systems with variable kinematic structure. J Mech Transm Autom Des 108(2):167–175

[21] Iwnicki SD, Parkinson H, Stow JM (1999) Assessing railway vehicle derailment potential using neural networks. The Rail Technology Unit, Manchester Metropolitan University

[22] Goodall RM, Iwnicki SD (2026) Non-linear dynamic techniques v. equivalent conicity methods for rail vehicle stability assessment. The Dynamics of Vehicles on Roads and on Tracks Supplement to Vehicle System Dynamics. CRC Press, Boca Raton

[23] Chen G, Zhai W, Zuo H (2001) Safety management of track irregularities of 250 km/h high-speed railway. Journal of Southwest Jiaotong University 14(5): 495–499 (in Chinese)

[24] Wang K, Zhai W, Cai C (2001) Lateral stability analysis of cars on resilient track structure. Rolling Stock 39(7): 1–4 (in Chinese)

[25] Montenegro PA, Carvalho H, Ribeiro D et al (2021) Assessment of train running safety on bridges: a literature review. Eng Struct 241:112425

[26] Cole C, McClanachan M, Spiryagin M et al (2012) Wagon instability in long trains. Veh Syst Dyn 50(sup1):303–317

[27] Eslami Z, Ghousi R, Ghanbari H (2025) A data-driven framework for railroad accident analysis based on the CRISP-DM and association rule mining: Empirical evidence from the federal railroad administration (2020–2024). Results Eng 27:106825

[28] Kwak S-L (2012) A comparative study on railway accident safety statistics among nations and other transportation modes. J Korean Soc Railw 15(2):193–198

[29] Kaeeni S, Khalilian M, Mohammadzadeh J (2018) Derailment accident risk assessment based on ensemble classification method. Saf Sci 110:3–10

[30] Oh K, Yoo M, Jin N, et al (2022) A review of deep learning applications for railway safety. Appl Sci 12(20):10572

[31] Bulduk N, Metin M (2025) A novel measurement-based computational method for real-time distribution of lateral wheel–rail contact forces. Machines 13(12):1105

[32] Lai J, Xu J, Chen Y et al (2023) Evaluation of dynamic derailment in a railway switch considering the longitudinal impacts caused by vehicle retarder. Proc Inst Mech Eng Part F J Rail Rapid Transit 237(6):806–817

[33] Bae H-U, Moon J, Lim S-J et al (2020) Full-scale train derailment testing and analysis of post-derailment behavior of casting bogie. Appl Sci 10(1):59

[34] Lai J, Xu J, Wang P et al (2021) Numerical investigation on the dynamic behaviour of derailed railway vehicles protected by guard rail. Veh Syst Dyn 59(12):1803–1824

[35] Xu J, Wang J, Wang P, Chen J, Gao Y, Chen R, Xie K. Study on the derailment behaviour of a railway wheelset with solid axles in a railway turnout. Veh Syst Dyn, 2020, 58: 123-143

[36] Lai J, Xu J, Liao T, et al (2022) Investigation on train dynamic derailment in railway turnouts caused by track failure. Eng Fail Anal 134:106050

[37] Liu B, Rismantab-Sany J, Vollebregt E (2025) Effects of conformal wheel/rail contact modelling on the dynamic responses of a wheelset. Veh Syst Dyn:1–24

[38] Vollebregt E (2021) Detailed wheel/rail geometry processing with the conformal contact approach. Multibody Syst Dyn 52(2):135–167

[39] Pascal J-P, Sany JR (2019) Dynamics of an isolated railway wheelset with conformal wheel–rail interactions. Veh Syst Dyn 57(12):1947–1969

[40] Bosso N, Magelli M, Zampieri N (2022) Simulation of wheel and rail profile wear: a review of numerical models. Railw Eng Sci 30(4):403–436

[41] Bosso N, Magelli M, Zampieri N (2021) Development and validation of a new code for longitudinal train dynamics simulation. Proc Inst Mech Eng Part F J Rail Rapid Transit 235(3):286–299

[42] Wu Q, Spiryagin M, Cole C (2016) Longitudinal train dynamics: an overview. Veh Syst Dyn 54(12):1688–1714

[43] Schmid R, Micić Batka V, Pospischil F (2026) Prud’homme criterion: a review of its application in railway vehicle approval. Int J Rail Transp 14(1):1–16

RIGHTS & PERMISSIONS

The Author(s)

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.