K. Y. WANG ET AL.

156

wagon should be 61 km/h. However, according to the

code for design of railway line [20], it is prescribed that

the maximum negotiation speed of a freight truck on this

curved track is 65 km/h. Moreover, the practical opera-

tion experience also proves the fact that the negotiation

speed usually reaches 65 km/h on this curved track. Thus,

when a freight vehicle passes through this curved track

with a speed of 65 km/h, the nonlinear critical speed of

the vehicle should be more than 76.4 km/h. That is to say,

the lateral stability of this type vehicle cannot meet the

real requirement for the curved track, and the hunting

motion appears usually.

Furthermore, compared with the results in paper [17]

that the nonlinear critical speed of this heavy-haul vehi-

cle on a tangent track is 134 km/h, it can be concluded

that the nonlinear critical speed of a vehicle on a curved

track is lower than that on a tangent track. In other words,

the performance of the lateral stability on a curved track

is worse than that on a tangent track.

6. Conclusions

1) Due to effects of various factors such as the large

conicity, the excitation of the lateral shift and the wheel-

set angle of attack, the hunting motion appears easily

when a heavy-haul vehicle negotiates a curved track at a

low speed. Under this situation of the hunting motion,

there are two stable limit cycles relative to the track cen-

terline, as is different with the phenomenon on a tangent

track where there is one stable limit cycle.

2) The nonlinear critical speed of the heavy-haul vehi-

cle on the curved track can be calculated by the SRM. As

for the curved track with a radius of 600 m and a su-

perelevation of 55 mm, the nonlinear critical speed of the

heavy-haul vehicle is 76.4 km/h, which is lower than the

speed on the tangent track.

3) Finally, for the curved track, much attention should

be paid to the lateral stability, as well as the running

safety.

7. Acknowledgements

The authors wish to acknowledge the support and moti-

vation provided by National Natural Science Foundation

of China (51075340) and Tong Education Foundation for

Young Teachers in the Higher Education Institutions

(121075) and Program for Innovation Research Team in

University in China (No. IRT1178).

REFERENCES

[1] R. R. Huilgol, “Hopf-Friedrichs Bifurcation and the

Hunting of a Railway Axle,” Quarterly Journal Applica-

tion Mathematics, Vol. 36, 1978, pp. 85-94.

[2] T. Hans and K. Petersen, “A Bifurcation Analysis of

Nonlinear Oscillation in Railway Vehicles,” Proceeding

of the 8th IAVSD Symposium, Cambridge, 15-19 August

1983, pp. 320-329.

[3] K. Petersen, “Chaos in a Railway Bogie,” Acta Me-

chanica, Vol. 61, No. 1-4, 1986, pp. 91-107.

[4] R. V. Dukkipati, “Lateral Stability Analysis of a Railway

Truck on Roller Rig,” Mechanism and Machine Theory,

Vol. 36, No. 2, 2001, pp. 189-204.

doi:10.1016/S0094-114X(00)00017-3

[5] R. V. Dukkkipati and S. N. Swamy, “Lateral Stability and

Steady State Curving Performance of Unconventional

Rail Tracks,” Mechanism and Machine Theory, Vol. 36,

No. 5, 2001, pp. 577-587.

doi:10.1016/S0094-114X(01)00006-4

[6] S. Y. Lee and Y. C. Cheng, “Hunting Stability Analysis

of High-Speed Railway Vehicle Trucks on Tangent

Tracks,” Journal of Sound and Vibration, Vol. 282, No.

3-5, 2005, pp. 881-898. doi:10.1016/j.jsv.2004.03.050

[7] Y. C. Cheng and S. Y. Lee, “Nonlinear Analysis on Hunt-

ing Stability for High-Speed Railway Vehicle Trucks on

Curved Tracks,” Journal of Vibration and Acoustics, Vol.

127, No. 4, 2005, pp. 324-332. doi:10.1115/1.1924640

[8] S. Y. Lee and Y. C. Cheng, “Influences of the Vertical

and the Roll Motions of Frames on the Hunting Stability

of Trucks Moving on Curved Tracks,” Journal of Sound

and Vibration, Vol. 294, No. 3, 2006, pp. 441-453.

doi:10.1016/j.jsv.2005.10.025

[9] W. Zhai and X. Sun, “A Detailed Model for Investigating

Vertical Interaction between Railway Vehicle and Track,”

Vehicle System Dynamics, Vol. 23, No. 1, 1994, pp. 603-

615. doi:10.1080/00423119308969544

[10] W. M. Zhai, K. Y. Wang and C. B. Cai, “Fundamentals of

Vehicle-Track Coupled Dynamics,” Vehicle System Dy-

namics, Vol. 47, No. 11, 2009, pp. 1349-1376.

doi:10.1080/00423110802621561

[11] W. M. Zhai and K. Y. Wang, “Lateral Interactions of Trains

and Tracks on Small-Radius Curves: Simulation and Ex-

periment,” Vehicle System Dynamics, Vol. 44, No. 1,

2006, pp. 520-530. doi:10.1080/00423110600875260

[12] E. C. Slivsgaard, “On the Interaction between Wheels and

Rails in Railway Dynamics,” Ph.D. Dissertation, Techni-

cal University of Denmark, Copenhagen, 1995.

[13] F. Xia, “The Dynamics of the Three-Piece-Freight-Truck,”

Ph.D. Dissertation, Technical University of Denmark,

Copenhagen, 2002.

[14] G. Chen and W. M. Zhai, “A New Wheel/Rail Spatially

Dynamic Coupling Model and Its Verification,” Vehicle

System Dynamics, Vol. 41, No. 4, 2004, pp. 301-322.

doi:10.1080/00423110412331315178

[15] Z. Shen, J. Hedrick and J. Elkins, “A Comparison of Al-

ternative Creep Force Models for Rail Vehicle Dynamic

Analysis,” Proceeding of the 8th IAVSD Symposium,

Cambridge, 15-19 August 1983, pp. 591-605.

[16] W. M. Zhai and K. Y. Wang, “Lateral Hunting Stability

of Railway Vehicles Running on Elastic Track Struc-

tures,” Journal of Computational and Nonlinear Dynam-

ics, Transactions of the ASME, Vol. 5, No. 4, 2010, pp.

1-9.

Copyright © 2012 SciRes. JTTs