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轮对非线性动力学系统蛇行运动的解析解

史禾慕 曾晓辉 吴晗

史禾慕, 曾晓辉, 吴晗. 轮对非线性动力学系统蛇行运动的解析解. 力学学报, 2022, 54(7): 1807-1819 doi: 10.6052/0459-1879-22-003
引用本文: 史禾慕, 曾晓辉, 吴晗. 轮对非线性动力学系统蛇行运动的解析解. 力学学报, 2022, 54(7): 1807-1819 doi: 10.6052/0459-1879-22-003
Shi Hemu, Zeng Xiaohui, Wu Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1807-1819 doi: 10.6052/0459-1879-22-003
Citation: Shi Hemu, Zeng Xiaohui, Wu Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1807-1819 doi: 10.6052/0459-1879-22-003

轮对非线性动力学系统蛇行运动的解析解

doi: 10.6052/0459-1879-22-003
基金项目: 国家自然科学基金(11672306, 51805522), 中国科学院先导项目(XDB22020101), 国家重点研发计划课题(2016YFB1200602)和大连理工大学海岸和近海工程国家重点实验室开放基金(LP21V1)资助
详细信息
    作者简介:

    曾晓辉, 研究员, 主要研究方向: 工程结构系统动力学、海洋工程力学、车辆系统动力学. E-mail: zxh@imech.ac.cn

  • 中图分类号: U270.1+1

ANALYTICAL SOLUTION OF THE HUNTING MOTION OF A WHEELSET NONLINEAR DYNAMICAL SYSTEM

  • 摘要: 在对铁路车辆系统的极限环幅值和非线性临界速度进行分析时通常采用数值方法, 不便于研究其随系统参数的变化规律. 轮对系统保留了影响车辆系统动力学性能的几个关键要素: 如轮轨几何非线性约束、轮轨接触蠕滑关系和悬挂系统等, 可以反映铁路车辆系统蛇行运动的本质特性. 轮对系统自由度少、参数少, 可以采用解析方法进行分析. 本文选取合适的特征量把轮对非线性动力学方程无量纲化, 得到了带有小参数的两自由度微分方程; 采用多尺度方法对该方程进行了解析求解; 给出了轮对系统极限环幅值的解析表达式并对其稳定性进行了判定; 给出了轮对系统的分岔速度解析表达式, 并进而获得系统的非线性临界速度的解析表达式. 在对得到的解析解用数值结果进行验证后, 用得到的解析解进行了系统参数影响分析. 传统的分岔图计算方法(如降速法、路径跟踪法等)需对微分方程进行大量数值积分计算方可求解系统的非线性临界速度值, 而通过本文获得的解析表达式可直接给出系统的非线性临界速度值和极限环幅值, 便于研究轮对系统动力学特性随参数的变化规律,进行快速方案比对和筛选, 为转向架结构优化设计提供参考.

     

  • 图  1  轮对模型示意图

    Figure  1.  Schematic diagram of the wheelset model

    图  2  tan(δRθ) − tan(δL + θ) 随轮对横摆变化关系

    Figure  2.  tan(δRθ) − tan(δL + θ) varies with the lateral displacement of wheelset

    图  3  本研究结果与文献[20]结果对比

    Figure  3.  Comparison of results between this paper and Ref. [20]

    图  4  时间历程曲线与相平面内相轨迹

    Figure  4.  Time-history curves and phase trajectories in the phase plane

    图  5  x1x2的频谱图

    Figure  5.  Frequency spectra of x1 and x2

    图  6  fh对应的时间历程曲线

    Figure  6.  Time-history curves corresponding to fh

    图  7  摄动解与数值积分结果对比

    Figure  7.  Comparison between perturbation solution and numerical integration

    图  8  摄动解计算分岔图和数值积分结果对比

    Figure  8.  Comparison of bifurcation diagrams calculated by perturbation solution and numerical integration

    图  9  Vnλ的关系曲线

    Figure  9.  Relationship between the Vn with λ

    图  10  VnKx的关系曲线

    Figure  10.  Relationship between the Vn with Kx

    图  11  不同Kx值对应系统的分岔图

    Figure  11.  Bifurcation diagram of the system with different Kx

    图  12  不同λ值对应系统的分岔图

    Figure  12.  Bifurcation diagram of the system with different λ

    A1  轮对参数

    A1.   Wheelset parameters

    ParametersValue
    m/kg2000
    J/(kg·m2)980
    Kx/(MN·m−1)3.0
    Ky/(MN·m−1)7.48
    b/m0.7465
    l/m1.0
    r0/m0.43
    f11/MN1.5232
    f22/MN1.4019
    δ0/(N·m−1)3.4158 × 105
    δ1/(N·m−3)2.0053 × 1010
    δ2/(N·m−5)5.7054 × 1014
    λ0.05
    g/(m·s−2)9.80
    V
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-12-30
  • 录用日期:  2022-03-02
  • 网络出版日期:  2022-03-03
  • 刊出日期:  2022-07-15

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