First International Conference on Rail Transportation,
Fundamentals of Vehicle-track Coupled Dynamics12pt font, Arial, Bold, Left Justified
Wanming ZHAI1, Kaiyun WANG1 and ChenbiaoCIA1 9pt font, Arial, Bold
1.Train and Track Research Institute, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China 9pt font, Arial, Italics
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Abstract(9pt font, Arial, Bold):The first section of the paper should be a single paragraph abstract outlining the aims, scope and conclusion of the paper. While no word limit is imposed, authors should aim for an abstract length of between 100 and 250 words. 9pt font, Times New Roman
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First International Conference on Rail Transportation,
1 Introduction 10.5ptFont, Arial, Bold, first letter in capital.
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The classical theory of railway vehicle dynamics (Wickens, 2003; Grag and Dukkipati, 1984) usually focuses on the railway vehicle itself as the analysis object without consideration of the dynamic behavior of the track system which supports the vehicle, i.e. the track structure is assumed to be a rigid base. In fact, the railway track is a typical elastic structure with damping. Vibrations of the vehicle can be transmitted to the track via the wheel-rail contact and excite vibrations of the elastic track structure, which can in reverse influence the vibrations of the vehicle not only in vertical direction but in lateral direction as well. Therefore, the vibrations of a vehicle and a track are essentially coupled with each other.
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2 Theoretical model
A vehicle-track coupled model is the theoretical foundation for analysing the vehicle-track interaction. During the last decade, a series of vehicle-track system models have been established for various research purposes. A vertical and lateral coupling model for a freight car with three-piece bogies and a ballasted track was published in an early paper by the author in 1996 (Zhai, 1996).A similar model for the vertical and lateral dynamics of the wagon-track system was presented by Sun et al in 2003(Sun et al, 2003). This paper will present a three-dimensional coupled model for typical passenger coaches and tracks including the non-ballasted slab track.
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2.1 Three-dimensional vehicle-track coupled model Times New Roman, 9pt Font, Bold, Italics
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Figures 1-3 illustrate the various components of the three-dimensional vehicle-track model, in which subsystems describing the vehicle and the track are spatially coupled by the wheel-rail interface.
Fig. 1 Three-dimensional vehicle-track coupled model (elevation)Times New Roman, 9pt Font, Bold, left justified
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In the vehicle sub-model, the car body is supported on two double-axle bogies at each end. The bogie frames are linked with the wheelsets through the primary suspensions and linked with the car body through the secondary suspensions..….
2.2 Equations of motion
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2.2.1 Equations of motion of vehicle subsystem
By using the system of coordinates moving along the track with vehicle speed, the equations of motion of the vehicle subsystem can be easily derived according to D’Alembert’s principle, which can be described in form of second order differential equations in the time domain:
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(1)
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where……
3 System excitation
As we know, the vehicle-track coupled vibrations are mainly excited by irregularities on the surfaces of wheels and rails. Generally, there are two types of geometric irregularities existing at the wheel-rail system. The one type is specific irregularities such as the wheel flat, the out-of-round wheel, the dipped rail-joint, and the rail corrugation, etc., which has been widely discussed in the literature(Zhu et al. 2015a, b)....
Table 1 gives the values of these parameters for the CR speed-raised railway lines such as theBeijing―Shanghai line.Figure 12 compares the CR track spectrum with the AAR track spectra. It can be seen from figure 12(a) that the rail vertical profile irregularities of the CR track track spectrum with the AAR track spectra. It can be seen from figure 12(a) that the rail vertical profile irregularities of the CR track spectrum are usually located between those of the AAR 5th class spectrum and 6th class spectrum……
First International Conference on Rail Transportation,
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Table 1 Values of parameters of the Chinese railway mainline track spectrum.Times New Roman, 9pt Font, Bold, left justified
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First International Conference on Rail Transportation,
Parameter / A / B / C / D / E / F / GLeft rail vertical / 1.1029 / -1.4709 / 0.5941 / 0.8480 / 3.8016 / -0.2500 / 0.0112
Right rail vertical / 0.8581 / -1.4607 / 0.5848 / 0.0407 / 2.8428 / -0.1989 / 0.0094
Left rail alignment / 0.2244 / -1.5746 / 0.6683 / -2.1466 / 1.7665 / -0.1506 / 0.0052
Right rail alignment / 0.3743 / -1.5894 / 0.7265 / 0.4353 / 0.9101 / -0.0270 / 0.0031
Cross-level / 0.1214 / -2.1603 / 2.0214 / 4.5089 / 2.2227 / -0.0396 / 0.0073
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8. Conclusions
A framework has been systematically presented in this paper for investigating the overall dynamics of the vehicle-track system. A three-dimensional vehicle-track coupled model has been established, in which the vehicle subsystem and the track subsystem are coupled through a spatial wheel-rail coupling model that considers the rail vibrations in vertical, lateral and torsional directions.
Acknowledgement
This work was supported by the National Key Basic Research Program of China (973 Program) (Grant No. 2013CB036202).
References
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Garg, V.K.,and Dukkipati, R.V.(1984).“Dynamics of Railway Vehicle Systems.” Academic Press, Canada.
Sun, Y.Q., Dhanasekar, M.,and Roach, D.(2003).“A three-dimensional model for the lateral and vertical dynamics of wagon-track systems.” Journal of Rail and Rapid Transit. 217,31-45.
Wickens, A.H. (2003).“Fundamentals of Rail Vehicle Dynamics: Guidance and Stability. ”Swets & Zeitlinger Publishers.
Zhai, W.M., Cai, C.B.,and Guo, S.Z. (1996).“Coupling model of vertical and lateral vehicle/track interactions.” Vehicle System Dynamics, 26(1), 61-79.
Zhu, S., Cai, C., and Spanos, P.D., (2015a). “A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle – slab track systems.” Journal of Sound Vibration, 335, 304-320.
Zhu, S., Yang, J., Yan, H., Cai, C., and Zhang, L., (2015b). “Low-frequency vibration control of floating-slab tracks using dynamic vibration absorber.” Vehicle System Dynamics, 2015, 53(9): 1296-1314.