Nonlinear Dynamics

, Volume 85, Issue 1, pp 365–374 | Cite as

A frictional contact finite element for wheel/rail dynamic simulations

  • S. H. Ju
Original Paper


The main purpose of this paper is to develop a simple-model moving wheel/rail contact element, so that the sticking, sliding, and separation modes of the wheel/rail contact can be appropriately simulated. In the proposed finite element, the wheel and rail are simulated using the cubic-spline contact element, and a power function normal stiffness and a constant horizontal stiffness are connected to the cubic-spline contact stiffness. The three-dimensional (3D) contact finite element analysis for a realistic wheel and rail was used to accurately model the wheel/rail contact stiffness. The validated examples show that the proposed nonlinear moving wheel element can simulate the complicated sliding, sticking, and separation contact problems with good accuracy. The complicated contact modes, including the multiple contact situation between wheel flange and rail side, can also be simulated accurately. Moreover, the computer memory and CPU time required to achieve this are much less than needed with the 3D finite element contact model.


Contact Cubic spline Derailment Finite element analysis Moving contact element Rail Wheel 



This study was supported by the National Science Council, Republic of China, under contract number: NSC97-2221-E-006-116-MY3.


  1. 1.
    Lin, Y.H., Trethewey, M.W.: Finite element analysis of elastic beams subjected to moving dynamic loads. J. Sound Vib. 136(2), 323–342 (1990)CrossRefGoogle Scholar
  2. 2.
    Fryba, L.: Vibration of Solids and Structures Under Moving Load. Thomas Telford, London (1999)CrossRefMATHGoogle Scholar
  3. 3.
    Bowe, C.J., Mullarkey, T.P.: Wheel–rail contact elements incorporating irregularities. Adv. Eng. Softw. 36(11–12), 827–837 (2005)CrossRefGoogle Scholar
  4. 4.
    Sun, Y.Q., Dhanasekar, M., Roach, D.: A three-dimensional model for the lateral and vertical dynamics of wagon-track systems. Proc. Inst. Mech. Eng., Part F J. Rail Rapid Transit 217(1), 31–45 (2003)CrossRefGoogle Scholar
  5. 5.
    Ju, S.H., Lin, H.D., Hsueh, C.C., Wang, S.L.: A simple finite element model for vibration analyses induced by moving vehicles. Int. J. Numer. Method Eng. 68(12), 1232–1256 (2006)CrossRefMATHGoogle Scholar
  6. 6.
    Xiao, X.B., Wen, Z.F., Jin, X.S., Sheg, X.Z.: Effects of track support failures on dynamic response of high speed tracks. Int. J. Nonlinear Sci. Numer. Simul. 8(4), 615–630 (2007)CrossRefGoogle Scholar
  7. 7.
    Rathod, C., Shabana, A.A.: Geometry and differentiability requirements in multibody railroad vehicle dynamic formulations. Nonlinear Dyn. 47(1–3), 249–261 (2007)MATHGoogle Scholar
  8. 8.
    Dinh, V.N., Kim, K.D., Warnitchai, P.: Simulation procedure for vehicle–substructure dynamic interactions and wheel movements using linearized wheel–rail interfaces. Finite Elem. Anal. Des. 45(5), 341–356 (2009)CrossRefGoogle Scholar
  9. 9.
    Recuero, A.M., Escalona, J.L., Shabana, A.A.: Finite-element analysis of unsupported sleepers using three-dimensional wheel–rail contact formulation. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn. 225(2), 153–165 (2011)Google Scholar
  10. 10.
    Yang, Y.B., Lin, B.H.: Vehicle–bridge interaction analysis by dynamic condensation method. J. Struct. Eng.-ASCE 121(11), 1636–1643 (1995)CrossRefGoogle Scholar
  11. 11.
    Au, F.T.K., Wang, J.J., Cheung, Y.K.: Impact study of cable-stayed railway bridges with random rail irregularities. Eng. Struct. 24(5), 529–541 (2002)CrossRefGoogle Scholar
  12. 12.
    Kwark, J.W., Choi, E.S., Kim, Y.J., Kim, B.S., Kim, S.I.: Dynamic behavior of two-span continuous concrete bridges under moving high-speed train. Comput. Struct. 82(4–5), 463–474 (2004)CrossRefGoogle Scholar
  13. 13.
    Xia, H., Zhang, N.: Dynamic analysis of railway bridge under high-speed train. Comput. Struct. 83(23–24), 1891–1901 (2005)CrossRefGoogle Scholar
  14. 14.
    Xia, H., Han, Y., Zhang, N., Guo, W.W.: Dynamic analysis of train–bridge system subjected to non-uniform seismic excitations. Earthq. Eng. Struct. Dyn. 35(12), 1563–1579 (2006)Google Scholar
  15. 15.
    Auersch, L.: The excitation of ground vibration by rail traffic: theory of vehicle–track–soil interaction and measurements on high-speed lines. J. Sound Vib. 284(1–2), 103–132 (2005)CrossRefGoogle Scholar
  16. 16.
    Xi, S., Andreas, P.A.: Measurement and modeling of normal contact stiffness and contact damping at the meso scale. Trans. ASME 127(1), 52–60 (2005)CrossRefGoogle Scholar
  17. 17.
    Lei, X., Zhang, B.: Analyses of dynamic behavior of track transition with finite elements. J. Vib. Control 17(11), 1733–1747 (2011)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Gupta, S., Degrande, G., Lombaert, G.: Experimental validation of a numerical model for subway induced vibrations. J. Sound Vib. 321(3–5), 786–812 (2009)CrossRefGoogle Scholar
  19. 19.
    Connolly, D., Giannopoulos, A., Forde, M.C.: Numerical modelling of ground borne vibrations from high speed rail lines on embankments. Soil Dyn. Earthq. Eng. 46, 13–19 (2013)CrossRefGoogle Scholar
  20. 20.
    Seo, J.H., Sugiyama, H., Shabana, A.: Three-dimensional large deformation analysis of the multibody pantograph/catenary systems. Nonlinear Dyn. 42(2), 199–215 (2005)CrossRefMATHGoogle Scholar
  21. 21.
    Tanabe, M., Matsumoto, N., Waku, H., Sogabe, M., Okuda, H.: A simple and efficient numerical method for dynamic interaction analysis of a high-speed train and railway structure during an earthquake. J. Comput. Nonlinear Dyn. 3(4), Article Number 041002 (2008)Google Scholar
  22. 22.
    Dinh, V.N., Kima, K.D., Warnitchai, P.: Dynamic analysis of three-dimensional bridge–high-speed train interactions using a wheel–rail contact model. Eng. Struct. 31(12), 3090–3106 (2009)CrossRefGoogle Scholar
  23. 23.
    Nishimura, K., Terumichi, Y., Morimura, T., Sogabe, K.: Development of vehicle dynamics simulation for safety analyses of rail vehicles on excited tracks. J. Comput. Nonlinear Dyn. 4(1), Article Number 011001 (2009)Google Scholar
  24. 24.
    Li, Q., Xu, Y.L., Wu, D.J., Chen, Z.W.: Computer-aided nonlinear vehicle–bridge interaction analysis. J. Vib. Control 16(12), 1791–1816 (2010)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Ju, S.H.: A simple finite element for nonlinear wheel/rail contact and separation simulations. J. Vib. Control 20(3), 330–338 (2014)CrossRefGoogle Scholar
  26. 26.
    Pombo, J., Ambrosio, J.: An alternative method to include track irregularities in railway vehicle dynamic analyses. Nonlinear Dyn. 68(1–2), 161–176 (2012)CrossRefGoogle Scholar
  27. 27.
    Antolin, P., Zhang, N., Goicolea, J.M., Xia, H., Astiz, M., Oliva, J.: Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways. J. Sound Vib. 332(5), 1231–1251 (2013)CrossRefGoogle Scholar
  28. 28.
    Kouroussis, G., Verlinden, O.: Prediction of railway ground vibrations: accuracy of a coupled lumped mass model for representing the track/soil interaction. Soil Dyn. Earthq. Eng. 69, 220–226 (2015)CrossRefGoogle Scholar
  29. 29.
    Montenegro, P.A., Neves, S.G.M., Calcada, R.: Wheel–rail contact formulation for analyzing the lateral train–structure dynamic interaction. Comput. Struct. 152, 200–214 (2015)CrossRefGoogle Scholar
  30. 30.
    Ju, S.H.: A cubic–spline contact element for frictional contact problems. J. Chin. Inst. Eng. 21(2), 119–128 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Cheng-Kung UniversityTainan CityTaiwan, ROC

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