Bifurcation\instability forms of high speed railway vehicles

The China high speed railway vehicles of type CRH2 and type CRH3, modeled on Japanese high speed Electric Multiple Units (EMU) E2 series and Euro high speed EMU ICE3 series possess different stability behaviors due to the different matching relations between bogie parameters and wheel profiles. It is known from the field tests and roller rig tests that, the former has a higher critical speed while large limit cycle oscillation appears if instability occurs, and the latter has lower critical speed while small limit cycle appears if instability occurs. The dynamic model of the vehicle system including a semi-carbody and a bogie is established in this paper. The bifurcation diagrams of the two types of high speed vehicles are extensively studied. By using the method of normal form of Hopf bifurcation, it is found that the subcritical and supercritical bifurcations exist in the two types of vehicle systems. The influence of parameter variation on the exported function Rec1(0) in Hopf normal form is studied and numerical shooting method is also used for mutual verification. Furthermore, the bifurcation situation, subcritical or supercritical, is also discussed. The study shows that the sign of Re(λ) determinates the stability of linear system, and the sign of Rec1(0) determines the property of Hopf bifurcation with Rec1(0)>0 for supercritical and Rec1(0)<0 for subcritical.

[1]  Jun Xiang,et al.  Numerical study on the restriction speed of train passing curved rail in cross wind , 2009 .

[2]  Utz von Wagner,et al.  Nonlinear Dynamic Behaviour of a Railway Wheelset , 2009 .

[3]  J. K. Hedrick,et al.  A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis , 1983 .

[4]  Oldrich Polach,et al.  Comparability of the non-linear and linearized stability assessment during railway vehicle design , 2006 .

[5]  Chapman Frederick Dendy Marshall.  A history of British railways down to the year 1830 , 1971 .

[6]  Hans True,et al.  Dynamics of a Rolling Wheelset , 1993 .

[7]  V K Garg,et al.  Dynamics of railway vehicle systems , 1984 .

[8]  Y. Kuznetsov.  Elements of applied bifurcation theory (2nd ed.) , 1998 .

[9]  M. A. Lohe,et al.  On the application of a numerical algorithm for Hopf bifuraction to the hunting of a wheelset , 1984, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10]  H. Nijmeijer,et al.  Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .

[11]  Sen-Yung Lee,et al.  Nonlinear Analysis on Hunting Stability for High-Speed Railway Vehicle Trucks on Curved Tracks , 2005 .

[12]  Jing Zeng,et al.  Stability Analysis of High Speed Railway Vehicles , 2004 .

[13]  A. Wickens.  The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels , 1965 .

[14]  Carsten Knudsen,et al.  Non-linear dynamic phenomena in the behaviour of a railway wheelset model , 1991 .

[15]  Yuan Yue,et al.  The “resultant bifurcation diagram” method and its application to bifurcation behaviors of a symmetric railway bogie system , 2012 .

[16]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[17]  Yung-Chang Cheng,et al.  Hunting stability analysis of high-speed railway vehicle trucks on tangent tracks , 2005 .

[18]  Mehdi Ahmadian,et al.  Hopf Bifurcation and Hunting Behavior in a Rail Wheelset with Flange Contact , 1998 .

[19]  Ch. Kaas-Petersen.  Chaos in a railway bogie , 1986 .

[20]  J. J. Kalker,et al.  A Fast Algorithm for the Simplified Theory of Rolling Contact , 1982 .

[21]  O Polach,et al.  On non-linear methods of bogie stability assessment using computer simulations , 2006 .

[22]  H. True.  On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics , 1999 .

[23]  Yoshihiro Suda.  High Speed Stability and Curving Performance of Longitudinally Unsymmetric Trucks with Semi-active Control , 1994 .

[24]  Christian Kaas-Petersen,et al.  A Bifurcation Analysis of Nonlinear Oscillations in Railway Vehicles , 1983 .

[25]  Krzysztof Zboinski,et al.  Self-exciting vibrations and Hopf's bifurcation in non-linear stability analysis of rail vehicles in a curved track , 2010 .

[26]  Hans True,et al.  RAILWAY VEHICLE CHAOS AND ASYMMETRIC HUNTING , 1992 .

[27]  Mehdi Ahmadian,et al.  Effect of System Nonlinearities on Locomotive Bogie Hunting Stability , 1998 .

[28]  K. Johnson,et al.  Contact of Nonspherical Elastic Bodies Transmitting Tangential Forces , 1964 .