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Research Papers

Use of Finite Element and Finite Segment Methods in Modeling Rail Flexibility: A Comparative Study

[+] Author and Article Information
Martin B. Hamper

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

Antonio M. Recuero

Department of Mechanical and Materials Engineering,  University of Seville, Seville, 41004, Spainamrecuero@us.es

José L. Escalona

Department of Mechanical and Materials Engineering,  University of Seville, Seville, 41004, Spainescalona@us.es

Ahmed A. Shabana

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

J. Comput. Nonlinear Dynam 7(4), 041007 (Jun 21, 2012) (11 pages) doi:10.1115/1.4006728 History: Received June 20, 2011; Revised December 14, 2011; Published June 21, 2012; Online June 21, 2012

Safety requirements and optimal performance of railroad vehicle systems require the use of multibody system (MBS) dynamics formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. The first method is based on the floating frame of reference (FFR) formulation which allows for the use of a detailed finite element mesh with the component mode synthesis technique in order to obtain a reduced order model. In the second method, the flexible body is modeled as a finite number of rigid elements that are connected by springs and dampers. This method, called finite segment method (FSM) or rigid finite element method, requires the use of rigid MBS formulations only. In the third method, the FFR formulation is used to obtain a model that is equivalent to the FSM model by assuming that the rail segments are very stiff, thereby allowing the exclusion of the high frequency modes associated with the rail deformations. This FFR/FS model demonstrates that some rail movement scenarios such as gauge widening can be captured using the finite element FFR formulation. The three procedures FFR, FSM, and FFR/FS will be compared in order to establish differences among them and analyze the specific application of the FSM to modeling track flexibility. Convergence of the methods is analyzed. The three methods proposed in this investigation for modeling the movement of three-dimensional tracks are used with a three-dimensional elastic wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail deformations. Several conclusions will be drawn in view of the results obtained in this investigation.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Frames of reference in finite segment method

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Figure 4

Suspended wheelset model

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Figure 5

Track model used in numerical example

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Figure 6

First lateral mode shape using FSM and FEM models (solid line, FS, dashed line, FE)

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Figure 7

Vertical displacement at centroid of each FS at 27.5 m (dotted line: 5 FS, dashed line: 16 FS, solid line: 50 FS)

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Figure 8

Lateral displacement at centroid of each FS at 27.5 m (dotted line: 5 FS, dashed line: 16 FS, solid line: 50 FS)

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Figure 9

Vertical displacements at contact location 27.5 m (solid line: FS, dashed line: FFR (FS), dotted-dashed line: FFR (FE))

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Figure 10

Lateral displacements at contact location 27.5 m (solid line: FS, dashed line: FFR (FS), dotted-dashed line: FFR (FE))

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Figure 11

Vertical displacements at contact location 25.5 m (solid line: FS, dashed line: FFR (FS), dotted line: FFR (FE, 14 Modes), dotted-dashed line: FFR (FE, 30 Modes))

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Figure 12

Temporal evolution of the vertical displacement at the location 27.5 m (solid line: FS, dashed line: FFR (FS), dotted-dashed line: FFR (FE))

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Figure 13

Normal force using the three FS models (5 FS, 16 FS, 50 FS)

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Figure 14

Normal force using the three methods (FS, FFR (FS), FFR (FE))

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Figure 15

Lateral creepage in the flexible stretch (solid line: FS (16 FS), dotted-dashed line: FFR (FE))

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Figure 16

Longitudinal creepage in the flexible part (solid line: FS (16 FS), dotted-dashed line: FFR (FE))

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Figure 17

Lateral contact force in the flexible part (solid line: FS (16 FS), dotted-dashed line: FFR (FE))

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Figure 18

Longitudinal contact force in the flexible part (solid line: FS (16 FS), dotted-dashed line: FFR (FE))

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Figure 19

Normal contact force using spherical joints (solid line: FS (16 FS), dotted-dashed line: FS (16 FS, Spher.), dashed line: FE)

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Figure 20

Wheelset velocity using spherical joints (solid line: FS (16 FS), dotted-dashed line: FS (16 FS, Spher.), dashed line: FE)

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Figure 1

Definition of reference frames

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Figure 2

Definition of the surface parameters

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