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TECHNICAL PAPERS

Numerical Procedure for the Simulation of Wheel/Rail Contact Dynamics

[+] Author and Article Information
Ahmed A. Shabana, Marcello Berzeri

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7022

Jalil R. Sany

Center for Automated Mechanics, 5242 W. Cermak Rd., Cicero, IL 60804

J. Dyn. Sys., Meas., Control 123(2), 168-178 (Mar 28, 2000) (11 pages) doi:10.1115/1.1369109 History: Received March 28, 2000
Copyright © 2001 by ASME
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References

Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Kalker, J. J., 1990, Three-dimensional elastic bodies in rolling contact, Kluwer Academic, Dordrecht/Boston/London.
Vermeulen,  P. J., and Johnson,  K. L., 1964, “Contact of nonspherical bodies transmitting tangential forces,” ASME J. Appl. Mech., 31, pp. 338–340.
Kalker,  J. J., 1982, “A fast algorithm for the simplified theory of rolling contact,” Veh. Syst. Dyn., 5, pp. 317–358.
Kalker,  J. J., 1996, “Book of Tables for the Hertzian Creep-Force Law,” Technical Report, Department of Applied Analysis. Delft University of Technology, Delft, The Netherlands.
De Pater,  A. D., 1988, “The geometric contact between track and wheel-set,” Veh. Syst. Dyn., 17, pp. 127–140.
Fisette,  P., and Samin,  J. C., 1994, “A wheel/rail contact model for independent wheels,” Arch. Appl. Mech., 64, pp. 180–191.
Shabana, A. A., and Sany, J. R., 2001, “An Augmented Formulation for Mechanical Systems with Non-Generalized Coordinates: Application to Rigid Body Contact Problems,” Journal of Nonlinear Dynamics, Vol. 24, No. 2, pp. 183–204.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice-Hall, Englewood Cliffs, NJ.
Shabana, A. A., 1998, Dynamics of Multibody Systems, Second Edition, Cambridge University Press, Cambridge, UK.
Berzeri, M., 2000, Ph.D. thesis, Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL.
Shabana, A. A., 2001, Computational Dynamics, Second Edition, J. Wiley, New York.
Ahlberg, J. H., Nilson, E. N., and Walsh, J. L., 1967, The Theory of Splines and Their Applications, Academic Press, New York.
Shikin, E. V., and Plis, A. I., 1995, Handbook on Splines for the User, CRC Press, Boca Raton, FL.
Garg, V. K., and Dukkipati, R. V., 1984, Dynamics of Railway Vehicle Systems, Academic Press, Orlando, FL.
Love, A. E., 1927, A Treatise on the Mathematical Theory of Elasticity, 4th Edition, Dover.
Knothe,  K., and Böhm,  F., 1999, “History of stability of railway and road vehicles,” Veh. Syst. Dyn., 31, pp. 283–323.

Figures

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Global and local positions of the contact point Pk
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Surface of revolution of the wheel
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Definition of the rail surface by translation of a two-dimensional curve
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The surface parameter θ of the cylindrical surface of the wheel at three different configurations
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Scheme for the generation of a two-layer and a three-layer spline
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The measured profile of a wheel
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First derivative of the curve y(x) as obtained from an interpolating spline and from a smoothing process
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Second derivative of the curve y(x) as obtained from an interpolating spline and from a smoothing process
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Coefficient m obtained using tabulated values and Eq. (38)
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Coefficient n obtained using tabulated values and Eq. (38)
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The wheelset with cylindrical wheels
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Creepage coefficients at the right wheel
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Contact forces at the right wheel
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Creepage coefficients at the right wheel when the wheelset is subjected to a lateral motion constraint
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Lagrange multipliers associated with the vertical contact constraints when the wheelset is subjected to a lateral motion constraint
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Forces at the right wheel when the wheelset is subjected to a lateral motion constraint
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External forces applied to the wheelset
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Creepage coefficients at the right wheel
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Lateral displacement of the wheelset and surface parameters s1 for the right wheel and s2 for the right rail
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Forces at the right wheel
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Angular accelerations of the wheelset with respect to the global axes
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Contacts between the right wheel and the right rail at time t=2.85 s
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Vertical displacement of the wheelset
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Angular accelerations of the wheelset with respect to the global axes
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Forces at the left wheel
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Contacts between the left wheel and the left rail at time t=0.34 s

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