Research Papers

Use of ANCF Surface Geometry in the Rigid Body Contact Problems: Application to Railroad Vehicle Dynamics

[+] Author and Article Information
Martin B. Hamper

Department of Mechanical
and Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
e-mail: mhampe3@uic.edu

Cheng Wei

Department of Aerospace Engineering,
Harbin Institute of Technology,
Harbin, Heilongjiang 150001, China
e-mail: weicheng@hit.edu.cn

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 October 4, 2013; final manuscript received April 11, 2014; published online January 12, 2015. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 10(2), 021008 (Mar 01, 2015) (12 pages) Paper No: CND-13-1241; doi: 10.1115/1.4027442 History: Received October 04, 2013; Revised April 11, 2014; Online January 12, 2015

In the analysis of multibody system (MBS) dynamics, contact between two arbitrary rigid bodies is a fundamental feature in a variety of models. Many procedures have been proposed to solve the rigid body contact problem, most of which belong to one of the two categories: offline and online contact search methods. This investigation will focus on the development of a contact surface model for the rigid body contact problem in the case where an online three-dimensional nonconformal contact evaluation procedure, such as the elastic contact formulation—algebraic equations (ECF-A), is used. It is shown that the contact surface must have continuity in the second-order spatial derivatives when used in conjunction with ECF-A. Many of the existing surface models rely on direct linear interpolation of profile curves, which leads to first-order spatial derivative discontinuities. This, in turn, leads to erroneous spikes in the prediction of contact forces. To this end, an absolute nodal coordinate formulation (ANCF) thin plate surface model is developed in order to ensure second-order spatial derivative continuity to satisfy the requirements of the contact formulation used. A simple example of a railroad vehicle negotiating a turnout, which includes a variable cross-section rail, is tested for the cases of the new ANCF thin plate element surface, an existing ANCF thin plate element surface with first-order spatial derivative continuity, and the direct linear profile interpolation method. A comparison of the numerical results reveals the benefits of using the new ANCF surface geometry developed in this investigation.

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Shabana, A. A., Zaazaa, K. E., and Sugiyama, H., 2008, Railroad Vehicle Dynamics: A Computational Approach, CRC, Boca Raton, FL.
Kassa, E., Andersson, C., and Nielsen, J. C. O., 2006, “Simulation of Dynamic Interaction Between Train and Railway Turnout,” Veh. Syst. Dyn., 44(3), pp. 247–258. [CrossRef]
Alfi, S., and Bruni, S., 2009, “Mathematical Modelling of Train-Turnout Interaction,” Veh. Syst. Dyn., 47(5), pp. 551–574. [CrossRef]
Sugiyama, H., Tanii, Y., and Matsumura, R., 2011, “Analysis of Wheel/Rail Contact Geometry on Railroad Turnout Using Longitudinal Interpolation of Rail Profiles,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 024501. [CrossRef]
Sugiyama, H., Sekiguchi, T., Matsumura, R., Yamashita, S., and Suda, Y., 2012, “Wheel/Rail Contact Dynamics in Turnout Negotiations With Combined Nodal and Non-Conformal Contact Approach,” Multibody Syst. Dyn., 27(1), pp. 55–74. [CrossRef]
Kassa, E., and Nielsen, J. C. O., 2008, “Dynamic Interaction Between Train and Railway Turnout: Full-Scale Field Test and Validation of Simulation Models,” Veh. Syst. Dyn., 46(Supplement), pp. 521–534. [CrossRef]
Schupp, G., Weidemann, C., and Mauer, L., 2004, “Modelling the Contact Between Wheel and Rail Within Multibody System Simulation,” Veh. Syst. Dyn., 41(5), pp. 349–364. [CrossRef]
Wan, C., Markine, V. L., and Shevtsov, I. Y., 2013, “Analysis of Train/Turnout Vertical Interaction Using a Fast Numerical Model and Validation of That Model,” Proc. Inst. Mech. Eng., Part F, p. 0954409713489118. [CrossRef]
Sinokrot, T., Nakhaeinejad, M., and Shabana, A. A., 2008, “A Velocity Transformation Method for the Nonlinear Dynamic Simulation of Railroad Vehicle Systems,” Nonlinear Dyn., 51, pp. 289–307. [CrossRef]
Dmitrochenko, O., and Pogorelov, D. Y., 2003, “Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn., 10, pp. 17–43. [CrossRef]
Piegl, L., and Tiller, W., 1997, The NURBS Book, 2nd ed., Springer, New York.
SINTEF ICT: Applied Mathematics, 2005, SISL: The SINTEF Spline Library Reference Manual, Version 4.4. http://www.sintef.no/upload/IKT/9011/geometri/sisl/manual.pdf
Gálvez, A., and Iglesias, A., 2010, “Particle Swarm Optimization for Non-Uniform Rational B-Spline Surface Reconstruction From Clouds of 3D Data Points,” Inform. Sci., 192, pp. 174–192. [CrossRef]
Mikkola, A., Shabana, A. A., Sanchez-Rebollo, C., and Jimenez-Octavio, J. R., 2012, “Comparison Between ANCF and B-Spline Surfaces,” Multibody Syst. Dyn., 30, 119–138. [CrossRef]
Lan, P., and Shabana, A. A., 2010, “Integration of B-Spline Geometry and ANCF Finite Element Analysis,” Nonlinear Dyn., 61, pp. 193–206. [CrossRef]
Rathod, C., Chamorro, R., Escalona, J. L., El-Sibaie, M., and Shabana, A. A., 2009, “Validation of Three-Dimensional Multi-Body System Approach for Modelling Track Flexibility,” Proc. Inst. Mech. Eng., Part F, 223, pp. 269–282. [CrossRef]
Shabana, A. A., 2012, Computational Continuum Mechanics, 2nd ed., Cambridge, Cambridge, UK.
Sinokrot, T., 2009, A New Method for Nonlinear Dynamic Modeling of Wheel/Rail Multiple Contacts, Doctoral dissertation, University of Illinois at Chicago, IL.
Shikin, E. V., and Plis, A. I., 1995, Handbook on Splines for the User, CRC, Boca Raton, FL.
Jones, A. K., 1988, “Nonrectangular Surface Patches With Curvature Continuity,” Computer-Aid. Des., 20(6), pp. 325–335. [CrossRef]
Melanz, D., Khude, N., Jayakumar, P., Leatherwood, M., and Negrut, D., 2012, “A GPU Parallelization of the Absolute Nodal Coordinate Formulation for Applications in Flexible Multibody Dynamics,” Proceedings of IDETC/CIE, Chicago, IL, Aug. 12–15.
Kreyszig, E., 1991, Differential Geometry, Dover, New York.
Kalker, J. J., 1990, Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht, Netherlands.
Vollebregt, E. A. H., 2008, “Survey of Programs on Contact Mechanics Developed by J.J. Kalker,” Veh. Syst. Dyn., 46(1), pp. 85–92. [CrossRef]
Roberson, R. E., and Schwertassek, R., 1988, Dynamics of Multibody Systems, Springer-Verlag, Berlin, Germany.
Shabana, A. A., 2010, Computational Dynamics, 3rd ed., John Wiley & Sons, Chichester, West Sussex, UK.
Shampine, L. F., and Gordon, M. K., 1975, Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W.H. Freeman, San Francisco, CA.


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Fig. 2

Linear interpolation lofted surface

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Fig. 3

ANCF thin plate element in parametric (left) and physical (right) domains

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Fig. 4

Two-element ANCF thin plate mesh

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Fig. 5

Right hand turnout diagram (Shabana et al., 2008)

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Fig. 6

ANCF Thin plate mesh with C−1 boundary

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Fig. 7

Relationship between quintic Bezier patch control points and ANCF nodal coordinates

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Fig. 8

Suspended wheelset

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Fig. 9

ANCF quintic thin plate turnout

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Fig. 10

Y coordinate of contact point on left rail

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Fig. 11

Coordinate of contact point on left rail

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Fig. 12

Trace of contact point along quintic ANCF thin plate turnout

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Fig. 13

Normal force at left contact linear interpolation versus quintic plate

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Fig. 14

Normal force at left contact cubic plate versus quintic plate




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