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Technical Brief

A Simple Procedure for the Solution of Three-Dimensional Wheel/Rail Conformal Contact Problem

[+] Author and Article Information
Antonio M. Recuero

Department of Mechanical and Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
e-mail: arecuero@uic.edu

Ahmed A. Shabana

Department of Mechanical and Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
e-mail: shabana@uic.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 27, 2013; final manuscript received December 1, 2013; published online February 13, 2014. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 9(3), 034501 (Feb 13, 2014) (6 pages) Paper No: CND-13-1051; doi: 10.1115/1.4026154 History: Received February 27, 2013; Revised December 01, 2013

This paper describes a simple and efficient procedure for the treatment of conformal contact conditions with special emphasis on railroad wheel/rail contacts. The general three-dimensional nonconformal contact conditions are briefly reviewed. These nonconformal contact conditions, which are widely used in many applications because of their generality, allow for predicting online one point of contact, provided that the two surfaces in contact satisfy certain geometric requirements. These nonconformal contact conditions fail when the solution is not unique as the result of using conformal surface profiles or surface flatness, situations often encountered in many applications including railroad wheel/rail contacts. In these cases, the Jacobian matrix obtained from the differentiation of the nonconformal contact conditions with respect to the surface parameters suffer from singularity that causes interruption of the computer simulations. The singularities and the fundamental issues that arise in the case of conformal contact are discussed, and a simple and computationally efficient procedure for avoiding such singularities in general multibody systems (MBS) algorithms is proposed. In order to demonstrate the use of the proposed procedure, the wheel climb of a wheelset as the result of an external lateral force is considered as an example. In this example, the wheel and rail profiles lead to conformal contact scenarios that could not be simulated using the nonconformal contact conditions.

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References

Ayasse, J. B., and Chollet, H., 2005, “Determination of the Wheel Rail Contact Patch in Semi-Hertzian Conditions,” Veh. Syst. Dyn., 43(3), pp. 161–172. [CrossRef]
Shabana, A. A., Zaazaa, K. E., and Sugiyama, H., 2008, Railroad Vehicle Dynamics: A Computational Approach, Taylor & Francis, London.
Shabana, A. A., Zaazaa, K. E., Escalona, J. L., and Sany, J. R., 2004, “Development of Elastic Force Model for Wheel/Rail Contact Problems,” J. Sound Vib., 269, pp. 295–325. [CrossRef]
Shabana, A. A., Tobaa, M., Sugiyama, H., and Zaazaa, K. E., 2005, “On the Computer Formulations of the Wheel/Rail Contact Problem,” Nonlinear Dyn., 40, pp. 169–193. [CrossRef]
Bhaskar, A., Johnson, K. L., Wood, G. D., and Woodhouse, J., 1997, “Wheel-Rail Dynamics With Closely Conformal Contact. Part 1: Dynamic Modelling and Stability Analysis,” Proc. Inst. Mech. Eng., F J. Rail Rapid Transit, 211(1), pp. 11–26. [CrossRef]
Telliskivi, T., and Olofsson, U., 2001, “Contact Mechanics Analysis of Measured Wheel/Rail Profiles Using the Finite Element Method,” Proc. Inst. Mech. Eng., F J. Rail Rapid Transit, 215, pp. 65–72. [CrossRef]
Pombo, J., Ambrosio, J., and Silva, M., 2007, “A New Wheel-Rail Contact Model for Railway Dynamics,” Veh. Syst. Dyn., 45(2), pp. 165–189. [CrossRef]

Figures

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Fig. 1

Nonconformal contact geometry

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Fig. 2

Local conformal contact geometry

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Fig. 3

Wheel and rail surface parameterization

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Fig. 4

Two configurations before reaching conformal contact (t = 0.3 and 5.14 s)

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Fig. 5

Two conformal contact configurations (t = 6.0 and 12.0 s)

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Fig. 6

Start of rolling with rapid change in the location of the contact points

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Fig. 7

A second point of contact at the outer side of the rail before complete derailment

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Fig. 8

Lateral surface parameters for the first contact point (solid curve, s1w, dashed curve, s2r)

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Fig. 9

Lateral surface parameters for the second contact point (solid curve, s1w, dashed curve, s2r)

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Fig. 10

Normal contact forces at the contact points. (Solid curve, right contact pair, first contact point; dashed curve, right contact pair, second contact point; dotted-dashed curve, left contact pair (single contact point)).

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