轮轨冲击振动系统非线性动力学特性分析
金洋，李万祥，张红兵
（兰州交通大学 机电工程学院，甘肃 兰州 730070）
摘要：当车辆通过轨道的局部不平顺时，轮轨间将产生大小突变且具有随机性的作用力，使车辆垂向系统的动态响应发生较大变化，这会影响车辆与轨道部件的疲劳寿命、影响车辆行驶的平稳性，还会导致车辆振动加剧。为分析当轮轨间发生冲击振动时车辆垂向减振系统的动态特性，通过建立一种垂向轮轨冲击振动系统物理数学模型，将动力学方程处理为无量纲形式，利用定步长四阶R-K数值方法求解该冲击振动系统响应，并将轮轨垂向冲击位置作为系统的Poincaré映射界面，结合分岔图、相图、时域响应对该系统在不同的无量纲激振频率下的分岔形式进行了分析，通过数值仿真，分析了系统通过余维二Hopf-Flip分岔、倍周期分岔向混沌运动转迁的过程，为车辆减振设计中的混沌预测和控制提供参考依据。
关键词：轮轨冲击振动；Poincaré映射；Hopf-Flip分岔；混沌
中图分类号：O322；U260.11+1 文献标志码：A doi：10.3969/j.issn.1006-0316.2024.06.007
文章编号：1006-0316 (2024) 06-0044-10
Analysis of Nonlinear Dynamic Characteristics of Wheel-Rail Impact Vibration System
JIN Yang，LI Wanxiang，ZAHNG Hongbing
( School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China )
Abstract：When the vehicle passes through the local irregularities on the track, a force with sudden and random variations occurs between the wheel and rail, which causes a large change to the dynamic response of the vertical system of the vehicle, which affects the fatigue life of both the vehicle and the track components and the smooth operation of the vehicle, escalating the vehicle vibration. In order to analyze the dynamic characteristics of the vertical vibration damping system of the vehicle when the impact vibration occurs between the wheel and rail, this paper establishes a physical and mathematical model of the vertical wheel-rail impact vibration system, in which the dynamic equations are transformed into dimensionless forms, and the response of the impact vibration system is solved through the fourth-order R-K numerical method with fixed step size. And the vertical impact position of wheel and rail is considered as the Poincaré mapping interface of the system, the bifurcation forms of the system under different dimensionless excited frequencies are analyzed by employing the bifurcation diagrams, phase diagrams and the time domain response. Through the numerical simulation, the process of the system transitioning to chaotic motion through codimension-two Hopf-Flip bifurcation and period-doubling bifurcation is analyzed, which provides a reference for the chaos prediction and control in the vehicle vibration reduction design.
Key words：wheel-rail impact vibration；Poincaré map；Hopf-Flip bifurcation；chaos
———————————————
收稿日期：2023-08-30
基金项目：中央引导地方科技发展资金（22ZY1QA005）
作者简介：金洋（1998－），男，甘肃武威人，硕士研究生，主要研究方向为非线性振动，E-mail：631504731@qq.com；李万祥（1972－），男，甘肃天水人，硕士，副教授，主要研究方向为机械振动理论。
（兰州交通大学 机电工程学院，甘肃 兰州 730070）
摘要：当车辆通过轨道的局部不平顺时，轮轨间将产生大小突变且具有随机性的作用力，使车辆垂向系统的动态响应发生较大变化，这会影响车辆与轨道部件的疲劳寿命、影响车辆行驶的平稳性，还会导致车辆振动加剧。为分析当轮轨间发生冲击振动时车辆垂向减振系统的动态特性，通过建立一种垂向轮轨冲击振动系统物理数学模型，将动力学方程处理为无量纲形式，利用定步长四阶R-K数值方法求解该冲击振动系统响应，并将轮轨垂向冲击位置作为系统的Poincaré映射界面，结合分岔图、相图、时域响应对该系统在不同的无量纲激振频率下的分岔形式进行了分析，通过数值仿真，分析了系统通过余维二Hopf-Flip分岔、倍周期分岔向混沌运动转迁的过程，为车辆减振设计中的混沌预测和控制提供参考依据。
关键词：轮轨冲击振动；Poincaré映射；Hopf-Flip分岔；混沌
中图分类号：O322；U260.11+1 文献标志码：A doi：10.3969/j.issn.1006-0316.2024.06.007
文章编号：1006-0316 (2024) 06-0044-10
Analysis of Nonlinear Dynamic Characteristics of Wheel-Rail Impact Vibration System
JIN Yang，LI Wanxiang，ZAHNG Hongbing
( School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China )
Abstract：When the vehicle passes through the local irregularities on the track, a force with sudden and random variations occurs between the wheel and rail, which causes a large change to the dynamic response of the vertical system of the vehicle, which affects the fatigue life of both the vehicle and the track components and the smooth operation of the vehicle, escalating the vehicle vibration. In order to analyze the dynamic characteristics of the vertical vibration damping system of the vehicle when the impact vibration occurs between the wheel and rail, this paper establishes a physical and mathematical model of the vertical wheel-rail impact vibration system, in which the dynamic equations are transformed into dimensionless forms, and the response of the impact vibration system is solved through the fourth-order R-K numerical method with fixed step size. And the vertical impact position of wheel and rail is considered as the Poincaré mapping interface of the system, the bifurcation forms of the system under different dimensionless excited frequencies are analyzed by employing the bifurcation diagrams, phase diagrams and the time domain response. Through the numerical simulation, the process of the system transitioning to chaotic motion through codimension-two Hopf-Flip bifurcation and period-doubling bifurcation is analyzed, which provides a reference for the chaos prediction and control in the vehicle vibration reduction design.
Key words：wheel-rail impact vibration；Poincaré map；Hopf-Flip bifurcation；chaos
———————————————
收稿日期：2023-08-30
基金项目：中央引导地方科技发展资金（22ZY1QA005）
作者简介：金洋（1998－），男，甘肃武威人，硕士研究生，主要研究方向为非线性振动，E-mail：631504731@qq.com；李万祥（1972－），男，甘肃天水人，硕士，副教授，主要研究方向为机械振动理论。
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