A computational efficient general wheel-rail contact detection method


The development and implementation of an appropriate methodology for the accurate geometric description of track models is proposed in the framework of multibody dynamics and it includes the representation of the track spatial geometry and its irregularities The wheel and rail surfaces are parameterized to represent any wheel and rail profiles obtained from direct measurements or design requirements A fully generic methodology to determine, online during the dynamic simulation, the coordinates of the contact points, even when the most general three dimensional motion of the wheelset with lespect to the rails is proposed This methodology is applied to study specific issues in railway dynamics such as the flange contact problem and lead and lag contact configurations A formulation for the description of the normal contact forces, which result from the wheel-rail interaction, is also presented The tangential creep forces and moments that develop in the wheel-rail contact area are evaluated using Kalker linear theory, Heuristic force method, Polach formulation The methodology is implemented in a general multibody code The discussion is supported through the application of the methodology to the railway vehicle ML95, used by the Lisbon metro company

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  1. Andersson, E, Berg, M and Stichel, S, 1998,Rail Vehicle Dynamics, Fundamentals and Guidelines, Royal Institute of Technology (KTH), Stockholm, Sweden

  2. Berzeri, M, Sany, J and Shabana, A, 2000, Curved Track Modeling Using the Absolute Nodal Coordinate Formulation, Technical Report MBS00-4-UIC, Department of Mechanical Engineering, University of Illinois, Chicago

  3. De Boor, C A, 1978,Practical Guide to Splines, Springer-Verlag, New York, New York

  4. Gaig, V and Dukkipati, R, 1984,Dynamics of Railway Vehicle Systems, Academic Press, New York, New York

  5. Kalker, J, 1996,Book of Tables for the Hertzian Creep-Force Law, Report of the Faculty of Technical Mathematics and Informatics No 96–61, Delft University of Technology, Delft, The Netherlands

  6. Kalker, J, 1979, “The Computation of Thiee- Dimensional Rolling Contact with Dry Friction,”Numerical Methods in Engineering, 14(9), pp 1293–1307

    MATH  Article  Google Scholar 

  7. Kalker, J, 1990,Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Dordrecht, The Netherlands

  8. Kik, W and Piotrowski, Fast, J A, 1996, “Approximate Method to Calculate Normal Load at Contact Between Wheel and Rail and Creep Forces During Rolling,”2nd Mini Conference on Contact Mechanics and Wear of Rail/Wheel System, TU Budapest, Budapest, Hungary

  9. Lankarani, H M and Nikiavesh, P E, 1994, “Continuous Contact Force Models for Impact Analysis in Multibody Systems,”Nonlinear Dynamics, 5, pp 193–207

    Google Scholar 

  10. Polach, O, 1999, “A fast Wheel-Rail Forces Calculation Computer Code,”Vehicle System Dynamics, Sup 33, pp 728–739

    Google Scholar 

  11. Pombo, J and Ambrosio, J, 2003, “A General Track Model for Rail Guided Vehicles Dynamics,”VII Congresso de Mecanica Aplicada e Computacional, April 14–16, Evora, Portugal, pp 47–56a

    Google Scholar 

  12. Pombo, J and Ambrosio, J, 2003b, “A Wheel- Rail Contact Model for Rail Guided Vehicles Dynamics,”ECCOMAS Conference Multibody 2003 -Advances in Computational Multibody Dynamics, July 1–4, Lisbon, Portugal

  13. Pombo, J and Ambrosio, J, 2001, “General Spatial Curve Joint for Rail Guided Vehicles Kinematics and Dynamics,”Multibody Systems Dynamics, 9, No 237–264

    Article  Google Scholar 

  14. Shabana, A, Berzeri, M and Sany, J, 2003c, “Numerical Procedure for the Simulation of Wheel/Rail Contact Dynamics,”Journal of Dynamic Systems Measurement and Control-Transactions of the Asme, 123(2), pp 168–178

    Article  Google Scholar 

  15. Shen, Z, Hedrick, J and Elkins, J, 1983, “Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis,”Proc of 8th IAVSD Symp on Dynamics of Vehicles on Road and Tracks, Cambridge, Massachussetts pp 591–605

    Google Scholar 

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Correspondence to João Pombo or Jorge Ambrosio.

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Pombo, J., Ambrosio, J. A computational efficient general wheel-rail contact detection method. J Mech Sci Technol 19, 411–421 (2005). https://doi.org/10.1007/BF02916162

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Key Words

  • Railway Dynamics
  • Multibody Dynamics
  • Contact Mechanics
  • Rail-Wheel Contact