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轮对非线性动力学模型稳定性和分岔特性研究

王鹏 杨绍普 刘永强 刘鹏飞 赵义伟 张兴

王鹏, 杨绍普, 刘永强, 刘鹏飞, 赵义伟, 张兴. 轮对非线性动力学模型稳定性和分岔特性研究. 力学学报, 2023, 55(2): 1-14 doi: 10.6052/0459-1879-22-469
引用本文: 王鹏, 杨绍普, 刘永强, 刘鹏飞, 赵义伟, 张兴. 轮对非线性动力学模型稳定性和分岔特性研究. 力学学报, 2023, 55(2): 1-14 doi: 10.6052/0459-1879-22-469
Wang Peng, Yang Shaopu, Liu Yongqiang, Liu Pengfei, Zhao Yiwei, Zhang Xing. Investigation of stability and bifurcation characteristics of wheelset nonlinear dynamic model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-14 doi: 10.6052/0459-1879-22-469
Citation: Wang Peng, Yang Shaopu, Liu Yongqiang, Liu Pengfei, Zhao Yiwei, Zhang Xing. Investigation of stability and bifurcation characteristics of wheelset nonlinear dynamic model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-14 doi: 10.6052/0459-1879-22-469

轮对非线性动力学模型稳定性和分岔特性研究

doi: 10.6052/0459-1879-22-469
基金项目: 国家自然科学基金(11790282, 12172235, 12072208, 52072249)和石家庄铁道大学国家重点实验室开放基金(ZZ2021-13)资助项目
详细信息
    作者简介:

    杨绍普, 教授, 主要研究方向: 车辆动力学与机械系统故障诊断. E-mail: yangsp@stdu.edu.cn

  • 中图分类号: U270.1+1

INVESTIGATION OF STABILITY AND BIFURCATION CHARACTERISTICS OF WHEELSET NONLINEAR DYNAMIC MODEL

  • 摘要: 为了探究轮对系统的横向失稳问题, 考虑了陀螺效应和一系悬挂阻尼的影响作用, 建立非线性轮轨接触关系的轮对动力学模型, 研究轮对系统的蛇行稳定性、Hopf分岔特性及迁移转化机理. 通过稳定性判据获得了轮对系统失稳临界速度. 采用中心流形定理和规范型方法对轮对动力学模型进行化简, 得到与轮对系统分岔特性相同的一维复变量方程, 理论推导求得轮对系统的第一Lyapunov系数的表达式, 根据其符号即可判断轮对系统的Hopf分岔类型. 讨论了不同参数对轮对系统Hopf分岔临界速度的影响, 探究了轮对系统的超临界、亚临界Hopf分岔域在二维参数空间的分布规律. 利用数值模拟得到轮对系统的3种典型Hopf分岔图, 验证了轮对系统超临界、亚临界Hopf分岔域分布规律的正确性. 结果表明, 轮对系统的临界速度随着等效锥度的增大而减小, 随着一系悬挂的纵向刚度和纵向阻尼的增大而增大, 随着纵向蠕滑系数的增大呈先增大后减小. 系统参数变化会引起轮对系统Hopf分岔类型发生改变, 即亚临界与超临界Hopf分岔相互迁移转化. 轮对系统Hopf分岔域在二维参数空间的分布规律对于轮对系统参数匹配和优化设计具有一定的指导意义.

     

  • 图  1  轮对系统模型

    Figure  1.  Model of wheelset system

    图  2  轮对系统特征值最大实部的变化曲线

    Figure  2.  Variation curve of the maximum real part of the eigenvalue of the wheelset system

    图  3  轮对系统的临界速度与等效锥度的关系

    Figure  3.  The relationship between critical speed and equivalent conicity

    图  4  轮对系统的临界速度与一系纵向刚度的关系

    Figure  4.  The relationship between critical speed and primary longitudinal stiffness

    图  5  轮对系统的临界速度与一系纵向阻尼的关系

    Figure  5.  The relationship between critical speed and primary longitudinal damping

    图  6  轮对系统的临界速度与纵向蠕滑系数的关系

    Figure  6.  The relationship between critical speed and longitudinal creep coefficient

    图  7  分岔类型临界线在空间${k_x}{{ - }}{k_y}$内的变化规律

    Figure  7.  Variation rule of bifurcation type critical line in parameter space ${k_x}{{ - }}{k_y}$

    图  8  分岔类型临界线空间${k_x}{{ - }}{c_x}$内的变化规律

    Figure  8.  Variation rule of bifurcation type critical line in parameter space ${k_x{ - }}{c_x}$

    图  9  分岔类型临界线在空间${c_x}{{ - }}{c_y}$内的变化规律

    Figure  9.  Variation rule of bifurcation type critical line in parameter space ${c_x}{{ - }}{c_y}$

    图  10  分岔类型临界线在空间${k_x}{{ - }}{\lambda _e}$内的变化规律

    Figure  10.  Variation rule of bifurcation type critical line in parameter space ${k_x}{{ - }}{\lambda _e}$

    图  11  $ {P_1} $位置对应的轮对系统Hopf分岔图

    Figure  11.  Hopf bifurcation diagram of wheelset system corresponding to point $ {P_1} $

    图  12  $ {P_2} $位置对应的轮对系统Hopf分岔图

    Figure  12.  Hopf bifurcation diagram of wheelset system corresponding to point $ {P_2} $

    图  13  P位置对应的轮对系统Hopf分岔图

    Figure  13.  Hopf bifurcation diagram of wheelset system corresponding to point $ P $

    表  A1  轮对系统参数

    Table  A1.   The parameters of the wheelset system

    ParameterInterpretationValueUnit
    $ m $mass of the wheelset1627kg
    $ {I_z} $yaw moment of inertia of wheelset830kg·m2
    $ {I_y} $spin moment of inertia of wheelset100kg·m2
    $ W $axle load of wheelset11.22t
    $ {r_0} $centered wheel rolling radius0.46m
    $ l $half of the swing arm1.02m
    $ a $half of the lateral distance of rolling circle0.7465m
    $ {f_{11}} $longitudinal creep coefficient1.5 × 106 N
    $ {f_{22}} $lateral creep coefficient1.5 × 106 N
    $ {f_{23}} $lateral spin creep force coefficient1000N
    $ {f_{33}} $spin creep force coefficient1000N
    $ {k_y} $primary lateral stiffness1.0MN·m−1
    $ {k_x} $primary longitudinal stiffness1.0MN·m−1
    $ {c_y} $primary lateral damping1000N·m·s−1
    $ {c_x} $primary longitudinal damping1000N·m·s−1
    $ {\lambda _e} $equivalent conicity of the wheelset0.16
    $ {\delta _1} $nonlinear wheel-rail contact control parameter−1.6 × 1011
    $ {\delta _2} $nonlinear wheel-rail contact control parameter1.6 × 1015
    下载: 导出CSV
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  • 收稿日期:  2022-10-02
  • 录用日期:  2022-11-07
  • 网络出版日期:  2022-11-08

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