Continuation Method and Its Application in Bifurcation of aRailway Passenger Car System with Simple Rails

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (20) : 177-182.

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Continuation Method and Its Application in Bifurcation of aRailway Passenger Car System with Simple Rails

GAO Xue-jun1, LI Ying-hui2 , Yue Yuan2

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Abstract

By taking a railway passenger car system as the research object, the vehicle is simplified as a multiple rigid body
system composed of one carboy, two bogie frames, four wheel sets, and primary and secondary suspensions. The rails are modeled as
discrete rigid bodies with lateral stiffness and damping, and moved forward with their corresponding wheel sets. Moreover, the
interaction forces between the wheels and the rails in rolling contact mainly include creep forces and the flange forces. The methods
for the continuation of the stationary solutions and periodic solutions of ordinary differential equations for similar vehicle system are
presented. Then the continuation method is applied to study the lateral bifurcation behavior of the railway passenger car system
running on a straight track with simple rails. Meanwhile, the numerical results are compared with that of the traditional vehicle system
which has the same suspension components but no rails. Research results show that the bifurcation diagram of the two models are
resemble in the investigated speed range. And two Hopf bifurcation points, from which two unstable periodic solutions sub-critically
bifurcated, are found in small speed range. The difference is the values of two Hopf bifurcation speeds and the critical speed of the
vehicle system with simple rails are all slightly higher than the corresponding values of the traditional vehicle system with the same
suspension components. However, the values of the bifurcation speed are mainly related to the lateral stiffness of rails.

Key words

stability / bifurcation / continuation method / simple rails / railway passenger car system

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GAO Xue-jun;LI Ying-hui;Yue Yuan. Continuation Method and Its Application in Bifurcation of aRailway Passenger Car System with Simple Rails[J]. Journal of Vibration and Shock, 2012, 31(20): 177-182