延续算法在简单轨道客车系统分岔中的应用

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (20) : 177-182.

论文

延续算法在简单轨道客车系统分岔中的应用

高学军1，李映辉2，乐源2

作者信息 +

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

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

Author information +

文章历史 +

摘要

以铁道客车系统为研究对象，将轨上车辆简化成包括车体、构架、轮对等刚体和一二系悬挂的多刚体动力学系统；
轨下只考虑钢轨并将其视为随各个轮对一起向前运动，具有一定横向刚度和阻尼的离散刚体；轮轨之间则考虑轮轨滚动接触
蠕滑力和轮缘力。讨论类似车辆系统运动微分方程组定常解、周期解延续计算的方法，并应用该方法对包含有简单轨道的客
车系统运行直线轨道上的横向运动分岔问题进行研究，同时也与相同悬挂条件下，不考虑钢轨的传统车辆动力学模型计算结
果进行对比。研究表明：在车辆速度变化范围内，两种模型的分岔曲线相似，都是在相差不大的速度下出现两个Hopf分岔点
并从这两点以亚临界方式分岔出不稳定的周期解曲线，不同的是考虑简单轨道的车辆系统两个Hopf分岔点值和临界速度值都
要比同等悬挂条件下传统车辆动力学模型的计算结果稍高些，而高出的程度则主要与钢轨的横向刚度大小有关。

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.

导出引用

高学军;李映辉;乐源. 延续算法在简单轨道客车系统分岔中的应用[J]. 振动与冲击, 2012, 31(20): 177-182

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