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计及短周期误差的直齿轮副近周期运动及其辨识

刘鹏飞 朱凌云 苟向锋 石建飞 金国光

刘鹏飞, 朱凌云, 苟向锋, 石建飞, 金国光. 计及短周期误差的直齿轮副近周期运动及其辨识. 力学学报, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
引用本文: 刘鹏飞, 朱凌云, 苟向锋, 石建飞, 金国光. 计及短周期误差的直齿轮副近周期运动及其辨识. 力学学报, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
Liu Pengfei, Zhu Lingyun, Gou Xiangfeng, Shi Jianfei, Jin Guoguang. Neighboring periodic motion and its identification for spur gear pair with short-period errors. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
Citation: Liu Pengfei, Zhu Lingyun, Gou Xiangfeng, Shi Jianfei, Jin Guoguang. Neighboring periodic motion and its identification for spur gear pair with short-period errors. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556

计及短周期误差的直齿轮副近周期运动及其辨识

doi: 10.6052/0459-1879-21-556
基金项目: 国家自然科学基金(51365025), 天津市自然科学基金(18JCYBJC88800, 19JCZDJC38700)和天津市研究生科研创新项目(2020YJSB067)资助项目
详细信息
    作者简介:

    苟向锋, 教授, 主要研究方向: 机械系统动力学. E-mail: 20150022@tiangong.edu.cn

  • 中图分类号: TH132, O322

NEIGHBORING PERIODIC MOTION AND ITS IDENTIFICATION FOR SPUR GEAR PAIR WITH SHORT-PERIOD ERRORS

  • 摘要: 齿轮副中的齿距偏差等短周期误差使系统出现复杂的周期运动, 影响齿轮传动的平稳性. 将该类复杂周期运动定义为近周期运动, 采用多时间尺度Poincaré映射截面对其进行辨识. 为研究齿轮副的近周期运动, 引入含齿距偏差的直齿轮副非线性动力学模型, 并计入齿侧间隙与时变重合度等参数. 采用变步长4阶Runge-Kutta法数值求解动力学方程, 由所提出的辨识方法分析不同参数影响下系统的近周期运动. 根据改进胞映射法计算系统的吸引域, 结合多初值分岔图、吸引域图与分岔树状图等研究了系统随扭矩与啮合频率变化的多稳态近周期运动. 研究结果表明, 齿轮副中的短周期误差导致系统的周期运动变复杂, 在微观时间尺度内, 系统的Poincaré映射点数呈现为点簇形式, 系统的点簇数与实际运动周期数为宏观时间尺度的Poincaré映射点数. 短周期误差导致系统在微观时间尺度内的吸引子数量增多, 使系统运动转迁过程变复杂. 合理的参数范围及初值范围可提高齿轮传动的平稳性. 该辨识与分析方法可为非线性系统中的近周期运动研究奠定理论基础.

     

  • 图  1  含短周期误差的齿轮系统的复杂周期运动[23]

    Figure  1.  Complex periodic motions of gear systems with short-period errors [23]

    图  2  随刚度波动幅值变化的直齿轮副动力学特性[10]

    Figure  2.  Dynamics characteristics of spur gear pair via stiffness fluctuation amplitude [10]

    图  3  齿轮副简化物理模型

    Figure  3.  Simplified physical model of gear pair

    图  4  随刚度波动幅值变化的直齿轮副多时间尺度分岔图

    Figure  4.  Bifurcation diagrams of the spur gear pair with different time scales via stiffness fluctuation amplitude

    图  5  随扭矩变化的直齿轮副多时间尺度分岔图

    Figure  5.  Bifurcation diagrams of the spur gear pair with different time scales via torque

    图  6  随啮合频率变化的直齿轮副多时间尺度分岔图

    Figure  6.  Bifurcation diagrams of the spur gear pair with different time scales via meshing frequency

    图  7  系统随扭矩变化的多初值分岔图及TLE谱

    Figure  7.  Multi-initial values bifurcation diagrams and TLE spectrums of system via F

    图  8  系统随扭矩变化的吸引域

    Figure  8.  Basin of attraction of system via F

    图  9  系统随扭矩变化的分岔树状图

    Figure  9.  Bifurcation dendrogram of system via F

    图  10  系统随啮合频率变化的多初值分岔图及TLE谱

    Figure  10.  Multi-initial values bifurcation diagrams and TLE spectrums of system via ω

    图  13  系统随啮合频率变化的分岔树状图

    Figure  13.  Bifurcation dendrogram of system via ω

    图  11  系统随啮合频率变化的吸引域

    Figure  11.  Basin of attraction of system via ω

    图  12  系统随啮合频率变化的相图与Poincaré映射图

    Figure  12.  Phase portraits and Poincaré maps of system via ω

    表  1  齿轮参数

    Table  1.   Parameters of a spur gear pair

    ParametersPinionGear
    precision grade6 GM6 GM
    module/mm55
    number of teeth2126
    下载: 导出CSV

    表  2  主动轮齿距偏差值(Np =21)

    Table  2.   Pitch deviation values of the pinion (Np =21)

    a1234567
    ΔFpt1(a)
    /μm
    01.943.75.095.96.35.9
    a891011121314
    ΔFpt1(a)
    /μm
    5.093.71.940−1.94−3.7−5.09
    a15161718192021
    ΔFpt1(a)
    /μm
    −5.9−6.3−5.9−5.09−3.7−1.940
    下载: 导出CSV

    表  3  从动轮齿距偏差值(Ng =26)

    Table  3.   Pitch deviation values of the gear (Ng =26)

    b1234567
    ΔFpt2(b)
    /μm
    01.743.374.75.96.66.9
    b891011121314
    ΔFpt2(b)
    /μm
    6.86.35.394.112.570.87−0.87
    b15161718192021
    ΔFpt2(b)
    /μm
    −2.57−4.11−5.39−6.3−6.8−6.9−6.6
    b2223242526
    ΔFpt2(b)
    /μm
    −5.9−4.79−3.37−1.740
    下载: 导出CSV

    表  4  从动轮齿距偏差值(Ng =13)

    Table  4.   Pitch deviation values of the gear (Ng =13)

    b1234567
    ΔFpt2(b)
    /μm
    03.56.0676.063.50
    b8910111213
    ΔFpt2(b)
    /μm
    −3.5−6.06−7−6.06−3.50
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-29
  • 录用日期:  2022-01-22
  • 网络出版日期:  2022-01-23
  • 刊出日期:  2022-03-18

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