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 Rec (1)(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(lambda) determinates the stability of linear system, and the sign of Rec (1)(0) determines the property of Hopf bifurcation with Rec (1)(0)> 0 for supercritical and Rec (1)(0)< 0 for subcritical.