摘要
为探究含有频变刚度定位节点的轮对系统横向失稳问题,分析频变刚度定位节点的“频变”机理,建立具有非线性轮轨接触关系的轮对横向动力学模型,利用Hopf分岔的发生条件得到系统分岔点,并利用中心流形定理和范式理论判断系统分岔类型,研究频变刚度节点参数对系统Hopf分岔点、分岔类型的影响规律。结果表明:相较于节点中的刚度k_(s),刚度k_(c)对系统分岔行为的影响更大,随着刚度k_(c)的增大,系统临界速度先增大,达到最大值后,再缓慢减小;增大阻尼c会显著提高系统的临界速度,同时更容易使系统发生超临界Hopf分岔;对于高维系统,通过中心流行定理降维,再利用范式理论判断系统Hopf分岔类型,该方法利于编程计算,适用于多参数、大范围的参数选择。
In order to investigate the lateral instability of wheelset systems with frequency varying stiffness positioning nodes,through analysis of the frequency variation mechanism of such nodes and development of a lateral dynamic model with non-linear wheel-rail contact relationships,this study identified the bifurcation points of the system using the occurrence conditions of Hopf bifurcation,and determined the types of system bifurcation by using the centre manifold theory and the normal forms.Furthermore,the effects of the node parameters on the Hopf bifurcation points and types were studied.The results show that compared with the stiffness k_(s)in the nodes,the stiffness k_(c)exerts a more significant influence on the bifurcation behavior of the system.With increasing stiffness k_(c),the critical speed of the system initially increases,and thendecreases slowly after reaching the maximum.Increasing the damping of c significantly increases the critical speed of the system and concurrently enhances the likelihood of supercritical Hopf bifurcation.For multi-dimensional systems,the method first reduces dimensionality through the centre manifold theory,and subsequently determines the system Hopf bifurcation types by using the normal forms.This method facilitates programming calculation,and is well-suited for multi-parameter and large-range parameter selection scenarios.
作者
徐坤
雒耀祥
XU Kun;LUO Yaoxiang(R&D Center,Baoji CRRC Times Engineering Machinery Co.,Ltd.,Xi’an 710000,China)
出处
《铁道学报》
北大核心
2025年第11期83-92,共10页
Journal of the China Railway Society
基金
国家重点研发计划(2023YFB2304004)。
关键词
频变刚度
定位节点
轮对系统
稳定性
HOPF分岔
frequency varying stiffness
positioning nodes
wheelset system
stability
Hopf bifurcation
