CLC number: U270.1+1

On-line Access: 2013-06-03

Received: 2012-11-28

Revision Accepted: 2013-04-29

Crosschecked: 2013-05-16

Cited: 6

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Li Zhou, Zhi-yun Shen. Dynamic analysis of a high-speed train operating on a curved track with failed fasteners[J]. Journal of Zhejiang University Science A, 2013, 14(6): 447-458.

@article{title="Dynamic analysis of a high-speed train operating on a curved track with failed fasteners",

author="Li Zhou, Zhi-yun Shen",

journal="Journal of Zhejiang University Science A",

volume="14",

number="6",

pages="447-458",

year="2013",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1200321"

}

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%T Dynamic analysis of a high-speed train operating on a curved track with failed fasteners

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%A Zhi-yun Shen

%J Journal of Zhejiang University SCIENCE A

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%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A1200321

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T1 - Dynamic analysis of a high-speed train operating on a curved track with failed fasteners

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A1 - Zhi-yun Shen

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PB - Zhejiang University Press & Springer

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DOI - 10.1631/jzus.A1200321

**Abstract: **A high-speed train-track coupling dynamic model is used to investigate the dynamic behavior of a high-speed train operating on a curved track with failed fasteners. The model considers a high-speed train consisting of eight vehicles coupled with a ballasted track. The vehicle is modeled as a multi-body system, and the rail is modeled with a Timoshenko beam resting on the discrete sleepers. The vehicle model considers the effect of the end connections of the neighboring vehicles on the dynamic behavior. The track model takes into account the lateral, vertical, and torsional deformations of the rails and the effect of the discrete sleeper support on the coupling dynamics of the vehicles and the track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. The train model couples with the track model by using a Hertzian contact model for the wheel/rail normal force calculation, and the nonlinear creep theory by Shen et al. (

**
**

1. Introduction

Since the early 1970s, many theoretical models have been developed to predict the behavior of railway vehicle and track systems (Knothe and Grassie,

The coupled vehicle/track models can characterize many basic phenomena, and they are widely used to understand the behavior of the railway system dynamics. Among the existing dynamic models of railway vehicle coupled with a track, most were used to deal with vehicle/track vertical interaction problems in relatively low frequency ranges (Nielsen and Igeland,

In addition, many vehicle-bridge interaction and train-track-bridge coupling models were developed to investigate the railway system dynamics. In these studies, the train was usually modeled as a series of moving loads or an improved multi-rigid-body system. When dealing with the bridge structure, two kinds of numerical methods were widely used. One is the finite element method (FEM), and the other is the component mode synthesis method (substructure approach). Owing to its high accuracy and versatility, the FEM is extensively used to investigate the dynamic response of a bridge structure under moving vehicles (Frýba,

Most of the dynamic models developed in the above studies consider only a single vehicle coupled with the track or bridge, which ignores the influence of inter-vehicle connections on the dynamics of trains. While some of them consider multiple vehicles, the inter-vehicle connection model was still neglected. Furthermore, almost all the existing dynamic models considering multiple vehicles are based on the assumption that the track is regarded as a rigid track or a nearly rigid track. These models cannot take the track support stiffness variation along the track into account. In the present paper, a 3D-coupled train/track dynamic model, considering the various discrete supports by sleepers and track support stiffness, is introduced to analyze the effect of train speed and broken fasteners on a curved track on the dynamic behavior of the train and the track when the high-speed train passes over the curved track with the failed fasteners at different speeds. The proposed model considers an eight-vehicle train coupled with a three-layer ballasted track. In the model, each vehicle is modeled as a multi-body system, and rails are assumed to be Timoshenko beams supported by the discrete sleepers. The vehicle model considers the effect of the inter-vehicle connections on the dynamic behavior of the neighboring vehicles. The rail supports are assumed to move backward at a constant speed to simulate the vehicle running forward along the track at the same speed. The dynamic behavior analysis includes the wheel/rail forces and the derailment coefficients consisting of

2. Model of vehicle/track

Since the vehicle system contains many differential equations and the detailed derivation of the equations is tedious (which is ignored here), the equations of motion are expressed as

The deformation of rails is described by the Timoshenko beam theory, including the bending and torsion. Using the modal synthesis method and normalized shape functions of the Timoshenko beam, the fourth-order partial differential equations of rails are converted into second-order ordinary equations as follows:

for the lateral bending motion:

for the vertical bending motion,

and for the torsional motion,

In Eqs. (

The sleeper in the present model is treated as an Euler-Bernoulli beam with free-free ends in the vertical direction, while as a lumped mass for its lateral motion (Fig.

According to Newton’s Second Law, the lateral rigid motion of the sleeper can be written as

The ballast bed is replaced by equivalent rigid ballast bodies in this calculation model, and only the vertical motion of each ballast body is taken into account. The vertical motion equations of ballast bodies

The model developed by Shen et al. (

3. Numerical results and discussion

Fig.

Compared to the normal condition, the maximum lateral force on the high rail increases by about 10%, 83%, and 113% in the cases, respectively, where the fastener failure occurs on the low rail, high rail, and both high and low rails of the curved track. Meanwhile, the minimum lateral force on the low rail decreases by about 66%, 92%, and 125%, respectively, as indicated in Figs.

Figs.

Note that the maximum wheelset loading reduction in the case of five disabled fasteners occurring on the high rail is larger than that occurring on both high and low rails. Furthermore, the difference of wheelset loading reduction between the normal case and the case of five disabled fasteners occurring on the low rail is very minor. This phenomenon is much concerned with the high-speed train negotiating a curved track with the deficient super-elevation. In the present analysis case where the train speed is 350 km/h and the radius of the curved track is 7000 m, the super-elevation of 150 mm is truly undersized. In this situation, the wheel loading of the wheelsets are not symmetrical, and this asymmetrical load condition results in a train dynamic response being much related to the contact behaviour of the high rail and left wheels. When the high-speed train negotiates the curved track with disabled fasteners occurring on the high rail, the asymmetrical rail support state worsens the interaction of the wheel and the high rail.

Fig.

Fig.

Fig.

In Fig.

4. Conclusions

* Project supported by the National Natural Science Foundation of China (No. U1134202), the National Basic Research Program (973) of China (No. 2011CB711103), and the Program for Changjiang Scholars and Innovative Research Team in University (Nos. IRT1178 and SWJTU12ZT01), China © Zhejiang University and Springer-Verlag Berlin Heidelberg 2013

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