Research Papers

Cross Wind Effects on Vehicle–Track Interactions: A Methodology for Dynamic Model Construction

[+] Author and Article Information
Lei Xu

Train and Track Research Institute,
Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail:  leix_2013@163.com

Wanming Zhai

Train and Track Research Institute,
Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 27, 2018; final manuscript received November 26, 2018; published online January 11, 2019. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 14(3), 031003 (Jan 11, 2019) (11 pages) Paper No: CND-18-1384; doi: 10.1115/1.4042142 History: Received August 27, 2018; Revised November 26, 2018

An efficient and accurate model for the dynamic assessment of vehicle-track behavior subjected to cross wind actions is developed in this paper, where the wind–vehicle–track interaction is regarded as a coupled vibration system. First, a vehicle–track interaction model is proposed by taking the hypotheses of wheel/rail rigid contact and displacement complementarity. Unlike explicit force-based methods, the vehicle-track systems are wholly coupled by interaction matrices and load vectors, which are computationally more efficient than most of the existing methods and fairly accurate in low frequency vibrations. Then, the fluctuating cross winds are simulated by the fast Fourier transform technique from spectral representations with the consideration of spatial correlation of multipoint wind time histories and vehicle movement. The unsteady cross wind forces are obtained by introducing weighting function. Finally, a modeling framework, with the coupled interactions between cross winds, vehicle, and the tracks included, is built effectively. Through the validated dynamic model, the cross wind effects on vehicle-track dynamic performance can be fully revealed. Besides, it is concluded that the dynamic performance of vehicle-track systems differs significantly in various excitation modes, i.e., average cross wind, fluctuating cross wind, and track irregularities.

Copyright © 2019 by ASME
Topics: Vehicles , Wind , Rails , Wheels
Your Session has timed out. Please sign back in to continue.


Li, T. , Yu, M. , Zhang, J. , and Zhang, W. , 2015, “ A Fast Equilibrium State Approach to Determine Interaction Between Stochastic Cross Winds and High-speed Vehicles,” J. Wind Eng. Ind. Aerodyn., 143, pp. 91–104. [CrossRef]
Zhao, X. , and Li, Z. , 2011, “ The Solution of Frictional Wheel-Rail Rolling Contact With a 3D Transient Finite Element Model: Validation and Error Analysis,” Wear, 271(1–2), pp. 444–452. [CrossRef]
Vermeulen, P. J. , and Johnson, K. L. , 1964, “ Contact of Non-Spherical Bodies Transmitting Tangential Forces,” ASME J. Appl. Mech., 31(2), pp. 338–340. [CrossRef]
Sladkowski, A. , and Sitarz, M. , 2005, “ Analysis of Wheel-Rail Interaction Using FE Software,” Wear, 258(7–8), pp. 1217–1223. [CrossRef]
Wanming, Z. , 2015, Vehicle-Track Coupled Dynamics, 4th ed., Science Press, Beijing, China.
Cai, C. , He, Q. , Zhu, S. , Zhai, W. , and Wang, M. , 2019, “ Dynamic Interaction of Suspension-Type Monorail Vehicle and Bridge: Numerical Simulation and Experiment,” Mech. Syst. Signal Process., 118, pp. 388–407. [CrossRef]
Zeng, Z.-P. , Liu, F.-S. , Lou , P., Zhao, Y.-G. , and Peng, L.-M. , 2016, “ Formulation of Three-Dimensional Equations of Motion for Vehicle-Sab Track-Bridge Interaction System and Its Application to Random Vibration Analysis,” Appl. Math. Modell., 40(11–12), pp. 5891–5929. [CrossRef]
Yang, Y. B. , Chang, C. H. , and Yau, J. D. , 1999, “ An Element for Analysing Vehicle-Bridge Systems Considering Vehicle's Pitching Effect,” Int. J. Numer. Method Eng., 46(7), pp. 1031–1047. [CrossRef]
Garg, V. K. , and Dukkipati, R. V. , 1984, Dynamics of Railway Vehicle Systems, Academic Press, New York.
Iwnicki, S. , 2006, Handbook of Railway Vehicle Dynamics, Taylor & Francis, London.
Zhu, S. Y. , Yang, J. Z. , Yan, H. , Zhang, L. Q. , and Cai, C. B. , 2015, “ Low Frequency Vibration Control of Floating Slab Tracks Using Dynamic Vibration Absorbers,” Veh. Syst. Dyn., 53(9), pp. 1296–1314. [CrossRef]
Götz, G. , and Polach, O. , 2018, “ Verification and Validation of Simulations in a Rail Vehicle Certification Context,” Int. J. Rail Transp., 6(2), pp. 83–100. [CrossRef]
Kouroussis, G. , Vogiatzis, K. E. , and Connolly, D. P. , 2018, “ Assessment of Railway Ground Vibration in Urban Area Using In-Situ Transfer Mobilities and Simulated Vehicle-Track Interaction,” Int. J. Rail Transp., 6(2), pp. 113–130. [CrossRef]
Shabana, A. A. , and Sany, J. R. , 2001, “ A Survey of Rail Vehicle Track Simulations and Flexible Multibody Dynamics,” Nonlinear Dyn., 26(2), pp. 179–210. [CrossRef]
Davenport, A. G. , 1964, “ Note on the Distribution of the Largest Value of a Random Function With Application to Gust Loading,” Proc. Inst. Civ. Eng., 28(2), pp. 187–196. https://www.icevirtuallibrary.com/doi/10.1680/iicep.1964.10112
Balzer, L. A. , 1977, “ Atmospheric Turbulence Encountered by High-Speed Ground Transport Vehicles,” J. Mech. Eng. Sci., 19(5), pp. 227–235. [CrossRef]
Simiu, E. , and Scanlan, R. , 1986, Wind Effects on Structures, Wiley-Interscience Publication, New York.
Cooper, R. , 1984, “ Atmospheric Turbulence With Respect to Moving Ground Vehicles,” J. Wind Eng. Ind. Aerodyn., 17(2), pp. 215–238. [CrossRef]
Baker, C. J. , 1991, “ Ground Vehicles in High Cross Winds—Part I: Steady Aerodynamic Forces,” J. Fluids Struct., 5(1), pp. 69–90. [CrossRef]
Baker, C. J. , 1991, “ Ground Vehicles in High Cross Winds—Part II: Unsteady Aerodynamic Forces,” J. Fluids Struct., 5(1), pp. 91–111. [CrossRef]
Sterling, M. , Baker, C. , Bouferrouk, A. , ONeil, H. , Wood, S. , and Crosbie, E. , 2009, “ An Investigation of the Aerodynamic Admittances and Aerodynamic Weighting Functions of Vehicles,” J. Wind Eng. Ind. Aerodyn., 97(11–12), pp. 512–522. [CrossRef]
Baker, C. J. , 2010, “ The Simulation of Unsteady Aerodynamic Cross Wind Forces on Vehicles,” J. Wind Eng. Ind. Aerodyn., 98(2), pp. 88–99. [CrossRef]
Li, Y. , Hu, P. , Xu, Y.-L. , Zhang, M. , and Liao, H. , 2014, “ Wind Loads on a Moving Vehicle-Bridge Deck System by Wind-Tunnel Model Test,” Wind Struct., 19(2), pp. 145–167. [CrossRef]
Bocciolone, M. , Cheli, F. , Corradi, R. , Muggiasca, S. , and Tomasini, G. , 2008, “ Cross Wind Action on Rail Vehicles: Wind Tunnel Experimental Analyses,” J. Wind Eng. Ind. Aerodyn., 96(5), pp. 584–610. [CrossRef]
Tomasini, G. , Giappino, S. , and Corradi, R. , 2014, “ Experimental Investigation of the Effects of Embankment Scenario on Railway Vehicle Aerodynamic Coefficients,” J. Wind Eng. Ind. Aerodyn., 131, pp. 59–71. [CrossRef]
TSI HS RST, 2008, “ Technical Specification for Interoperability Relating to the ‘Rolling Stock' Sub-System of the Trans-European High-Speed Rail System,” Official Journal of the European Union L847132, Directive 2008/232/CE.
EN, 2010, “ Railway Applications-Aerodynamics—Part 6: Requirements and Test Procedures for Cross Wind Assessment,” CEN, Brussels, Belgium, Standard No. EN 14067-6.
Cheli, F. , Corradi, R. , and Tomasini, G. , 2012, “ Cross Wind Action on Rail Vehicles: A Methodology for the Estimation of the Characteristic Wind Curves,” J. Wind Eng. Ind. Aerodyn., 104–106, pp. 248–255. [CrossRef]
Xu, Y. L. , and Ding, Q. S. , 2006, “ Interaction of Railway Vehicles With Track in Cross-Winds,” J. Fluids Struct., 22(3), pp. 295–314. [CrossRef]
Suzuki, M. , Tanemoto, K. , and Maeda, T. , 2003, “ Aerodynamic Characteristic of Vehicle/Vehicles Under Cross Winds,” J. Wind Eng. Ind. Aerodyn., 91(1–2), pp. 209–218. [CrossRef]
Baker, C. , 2013, “ A Framework for the Consideration of the Effects of Cross Winds on Vehicles,” J. Wind Eng. Ind. Aerodyn., 123, pp. 130–142. [CrossRef]
Yan, N. , Chen, X. , and Li, Y. , 2018, “ Assessment of Overturning Risk of High-Speed Vehicles in Strong Cross Winds Using Spectral Analysis Approach,” J. Wind Eng. Ind. Aerodyn., 174, pp. 103–118. [CrossRef]
Carrarini, A. , 2007, “ Reliability Based Analysis of the Cross Wind Stability of Railway Vehicles,” J. Wind Eng. Ind. Aerodyn., 95(7), pp. 493–509. [CrossRef]
Wetzel, C. , and Proppe, C. , 2010, “ On Reliability and Sensitivity Methods for Vehicle Systems Under Stochastic Cross Wind Loads,” Veh. Syst. Dyn., 48(1), pp. 79–95. https://www.tandfonline.com/doi/abs/10.1080/00423110903183917
Yu, M. , Zhang, J. , Zhang, K. , and Zhang, W. , 2015, “ Cross Wind Stability Analysis of a High-Speed Vehicle Based on Fuzzy Random Reliability,” Proc. Inst. Mech. Eng. Part F, 229(8), pp. 875–887. [CrossRef]
Dorigatti, F. , Sterling, M. , Baker, C. J. , and Quinn, A. D. , 2015, “ Cross Wind Effects on the Stability of a Model Passenger Vehicle—A Comparison of Static and Moving Experiments,” J. Wind Eng. Ind. Aerodyn., 138, pp. 36–51. [CrossRef]
Hecjmann, A. , Kurzeck, B. , Bünte, T. , and Loose, S. , 2014, “ Considerations on Active Control of Cross Wind Stability of Railway Vehicles,” Veh. Syst. Dyn., 52(6), pp. 759–775. https://www.tandfonline.com/doi/abs/10.1080/00423114.2014.901539
Thomas, D. , Berg, M. , and Stichel, S. , 2010, “ Measurements and Simulations of Rail Vehicle Dynamics With Respect to Overturning Risk,” Veh. Syst. Dyn., 48(1), pp. 97–112. https://www.tandfonline.com/doi/abs/10.1080/00423110903243216
Diedrichs, B. , Ekequist, M. , Stichel, S. , and Tengstrand, H. , 2004, “ Quasi-Static Modelling of Wheel-Rail Reactions Due to Crosswind Effects for Various Types of High-Speed Rolling Stock,” Proc. Inst. Mech. Eng., Part F, 218(2), pp. 134–148. https://journals.sagepub.com/doi/10.1243/0954409041319614
Proppe, C. , and Zhang, X. , 2014, “ Risk Assessment for Crosswind Stability of Vehicles on Exposed Sites,” PAMM. Proc. Appl. Math. Mech., 14(1), pp. 769–770. https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201410367
Zeng, Q. , Lou, P. , and Xiang, J. , 2002, “ The Principle of Total Potential Energy With Stationary Value in Elastic System Dynamics and Its Application to the Analysis of Vibration and Dynamic Stability,” J. Huazhong Univ. Sci. Technol. (Urban Sci. Ed.), 19(1), pp. 1–8. http://www.doc88.com/p-292203190710.html
Xu, L. , Chen, X. M. , Li, X. W. , and He, X. L. , 2018, “ Development of a Railway Wagon-Track Interaction Model: Case Studies on Excited Tracks,” Mech. Syst. Signal Process., 100, pp. 877–898. [CrossRef]
Kalker, J. J. , 1982, “ A Fast Algorithm for the Simplified Theory of Rolling Contact,” Veh. Syst. Dyn., 11(1), pp. 1–13. https://www.tandfonline.com/doi/abs/10.1080/00423118208968684
Brigham, E. O. , 1988, The Fast Fourier Transform and Its Applications, Prentice Hall, Englewood Cliffs, NJ.
Deodatis, G. , 1996, “ Simulation of Ergodic Multivariate Stochastic Processes,” J. Eng. Mech., ASCE, 122(8), pp. 778–787. [CrossRef]
Cao, Y. H. , Xiang, H. F. , and Zhou, Y. , 2000, “ Simulation of Stochastic Wind Velocity Field on Long-Span Bridges,” J. Eng. Mech., 126(1), pp. 1–6. [CrossRef]
Xu, L. , and Zhai, W. , 2018, “ An Advanced Vehicle-Slab Track Interaction Model Considering Rail Random Irregularities,” J. Vib. Control, 24(19), pp. 4592–4603. [CrossRef]
Xu, L. , Zhai, W. , and Gao, J. , 2017, “ A Probabilistic Model for Track Random Irregularities in Vehicle/Track Coupled Dynamics,” Appl. Math. Modell., 51, pp. 145–158. https://www.sciencedirect.com/science/article/pii/S0307904X17304195


Grahic Jump Location
Fig. 1

Vehicle-track systems: (a) side view and (b) end view

Grahic Jump Location
Fig. 2

Wind turbulence at space–time field (top) and the wind speed with respect to a moving vehicle (bottom)

Grahic Jump Location
Fig. 3

Spectral comparisons between simulation and target: (a) autospectrum at wind velocity point 1, (b) autospectrum at wind velocity point 10, and (c) cross-spectrum of fluctuating winds between points 1 and 10

Grahic Jump Location
Fig. 4

Modeling framework for wind–vehicle–track interactions

Grahic Jump Location
Fig. 5

Mode of excitation input

Grahic Jump Location
Fig. 6

Time domain track irregularity and its PSD sets [47]

Grahic Jump Location
Fig. 7

Comparison between this model and Zhai et al. under excitation of fluctuating wind forces: (a) car body lateral acceleration, (b) car body vertical acceleration, (c) car body lateral displacement, and (d) car body vertical displacement

Grahic Jump Location
Fig. 8

Car body lateral vibrations under mode of excitations: (a) car body lateral displacement and (b) car body lateral acceleration

Grahic Jump Location
Fig. 9

Wheel-axle force (a) and wheel-rail vertical force (b)

Grahic Jump Location
Fig. 10

Rail lateral displacement (a) and vertical displacement (b)

Grahic Jump Location
Fig. 11

PSD of car body acceleration under different excitations: (a) car body lateral acceleration and (b) car body vertical acceleration

Grahic Jump Location
Fig. 12

PSD of wheel-rail forces: (a) wheel-axle force and (b) wheel-rail vertical force

Grahic Jump Location
Fig. 13

Maximum acceleration of the car body under various excitations: (a) lateral acceleration and (b) vertical acceleration

Grahic Jump Location
Fig. 14

Wheel-rail vertical force: (a) minimum value at the windward side and (b) maximum value at the leeward side

Grahic Jump Location
Fig. 15

Maximum rail displacement: (a) lateral displacement and (b) vertical displacement at the windward side

Grahic Jump Location
Fig. 16

Maximum displacement of the track slab: (a) lateral displacement and (b) vertical displacement



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In