延续算法在简单轨道客车系统分岔中的应用  

Continuation method and its application in bifurcation of a railway passenger car system with simple rails

作　　者：高学军[1] 李映辉[2] 乐源[2] 

机构地区：[1]成都理工大学环境与土木工程学院,成都610059 [2]西南交通大学力学与工程学院,成都610031

出　　处：《振动与冲击》2012年第20期177-182,共6页Journal of Vibration and Shock

基　　金：牵引动力国家重点实验室开放课题(TPL1106);国家自然科学基金项目(11072204;11102030;10902092);中央高校基本科研业务费专项资金;成都理工大学高层次人才科研启动项目(HK0034)

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。By taking a railway passenger car system as a studying object,the vehicle was simplified as a multiple-rigid-body system composed of one carboy,two bogie frames,four wheel sets,and primary and secondary suspensions.The rails were modeled as discrete rigid bodies with lateral stiffness and damping,moving forward with their corresponding wheel sets.Moreover,the interaction forces between the wheels and the rails in rolling contact mainly included creep forces and the flange forces.The continuation methods for stationary solutions and periodic solutions to ordinary differential equations for a similar vehicle system were presented.Then,the continuation method was empleyed to study the lateral bifurcation behavior of the railway passenger car system running on a straight track with simple rails.Meanwhile,the numerical results were compared with those of the traditional vehicle system having the same suspension components but no rails.The study results showed that the bifurcation diagrams of the two models resemble each other in the investigated speed range;two Hopf bifurcation points,from which two unstable periodic solutions sub-critically bifurcate,are found in a small speed range;the difference is that the values of two Hopf bifurcation points 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 but no rails;the higher values are mainly related to the lateral stiffness of rails.

关 键 词：稳定性 分岔 延续算法 简单轨道 客车系统 

分 类 号：O322[理学—一般力学与力学基础] U260.11[理学—力学]