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中心距偏差对微线段齿轮系统的动力学特性影响研究

徐锐 黄康 张靖 汪久根

徐锐,黄康,张靖, 等. 中心距偏差对微线段齿轮系统的动力学特性影响研究[J]. 机械科学与技术,2021,40(9):1338-1346 doi: 10.13433/j.cnki.1003-8728.20200223
引用本文: 徐锐,黄康,张靖, 等. 中心距偏差对微线段齿轮系统的动力学特性影响研究[J]. 机械科学与技术,2021,40(9):1338-1346 doi: 10.13433/j.cnki.1003-8728.20200223
XU Rui, HUANG Kang, ZHANG Jin, WANG Jiugeng. Influence of Center Distance Deviation on Dynamic Characteristics of Micro-segment Gear System[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(9): 1338-1346. doi: 10.13433/j.cnki.1003-8728.20200223
Citation: XU Rui, HUANG Kang, ZHANG Jin, WANG Jiugeng. Influence of Center Distance Deviation on Dynamic Characteristics of Micro-segment Gear System[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(9): 1338-1346. doi: 10.13433/j.cnki.1003-8728.20200223

中心距偏差对微线段齿轮系统的动力学特性影响研究

doi: 10.13433/j.cnki.1003-8728.20200223
基金项目: 国家自然科学基金项目(51775156)、安徽工程大学引进人才科研启动基金项目(2019YQQ005)、安徽高校协同创新项目(GXXT-2019-048)及安徽工程大学校级科研项目(Xjky2020008)
详细信息
    作者简介:

    徐锐(1985−),讲师,博士,研究方向为机械传动与齿轮动力学,xuruixr2006@163.com

    通讯作者:

    张靖,正高级工程师,博士,tony.zhang@foxmail.com

  • 中图分类号: TH113

Influence of Center Distance Deviation on Dynamic Characteristics of Micro-segment Gear System

  • 摘要: 为了提高微线段齿轮的应用性,从中心距偏差的角度对微线段齿轮的动力学特性进行了研究。依据微线段齿轮齿廓构型原理,基于齿轮啮合关系推导了其齿廓数学模型;采用离散化TCA(齿面接触分析)方法计算了微线段齿轮的传动误差,分析了不同中心距偏差对渐开线和微线段齿轮的传动误差和侧隙的影响;通过建立微线段齿轮动力学模型,分析了渐开线和微线段齿轮在不同载荷、转速下中心距偏差对动态响应的影响。结果表明:微线段齿轮比渐开线齿轮对中心距偏差更为敏感;在低速轻载工况下,渐开线齿轮的动力学特性更好,在载荷较大的工况下,尤其是在中高速重载工况下,当中心距偏差被控制在一定范围内时,微线段齿轮具有更好的动态特性。
  • 图  1  微线段齿轮与渐开线齿轮齿廓对比图

    图  2  微线段齿条齿廓构造原理

    图  3  微线段齿轮齿廓构造过程

    图  4  离散化TCA原理图

    图  5  传动误差计算示意图

    图  6  中心距偏差对渐开线齿轮传动误差的影响

    图  7  中心距偏差对微线段齿轮传动误差的影响

    图  8  微线段齿轮啮合线

    图  9  直齿轮副扭转振动模型

    图  10  微线段齿轮有限元模型

    图  11  微线段与渐开线齿轮时变啮合刚度

    图  12  $\varOmega\; {\rm{ = }}\;0.2,T = 100\;{\rm{N \cdot m}}$工况下的动态响应

    图  13  $\varOmega\; {\rm{ = }}\;0.5,T = 500\;{\rm{N \cdot m}}$工况下的动态响应

    图  14  $\varOmega \;{\rm{ = }}\;0.5,T = 1\;000\;{\rm{N \cdot m}}$工况下的动态响应

    图  15  $\varOmega\; {\rm{ = }}\;1,T = 1\;000\;{\rm{N \cdot m}}$工况下的动态响应

    表  1  渐开线齿轮参数

    参数及单位数值参数及单位数值
    模数/mm 3 齿根圆/mm 82.5
    齿数 30 齿宽/mm 30
    压力角/(°) 20 中心距/mm 90
    齿顶圆直径/mm 96
    下载: 导出CSV

    表  2  微线段齿轮参数

    参数及单位数值参数及单位数值
    模数/mm3齿顶圆/mm96
    齿数30齿根圆/mm82.5
    初始压力角/(°)20齿宽/mm30
    初始压力角增量/(°)0.00065中心距/mm90
    初始基圆半径/mm400000
    下载: 导出CSV

    表  3  传动误差拟合结果

    中心距偏
    差/mm
    拟合函数$e(\bar t)$
    0.02$\begin{array}{l} {\rm{0} }{\rm{.008\;682 - 2} }{\rm{.098} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 1} }{\rm{.268} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 5} }{\rm{.838} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{cos(2} }\omega { {\bar t) + 2} }{\rm{.838} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 6} } } }{\rm{sin(2} }\omega { {\bar t)} }- \\ {\rm{ 1} }{\rm{.565} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 3} }{\rm{.223} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$
    0.04$\begin{array}{l} {\rm{0} }{\rm{.010\;8 - 7} }{\rm{.231} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 2} }{\rm{.31} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 9} }{\rm{.287} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{cos(2} }\omega { {\bar t) + 1} }{\rm{.999} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{sin(2} }\omega { {\bar t)} }- \\ {\rm{ 2} }{\rm{.424} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 5} }{\rm{.257} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$
    0.06$\begin{array}{l} {\rm{0} }{\rm{.012\;73 - 4} }{\rm{.469} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 3} }{\rm{.094} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 1} }{\rm{.197} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{cos(2} }\omega { {\bar t) - 8} }{\rm{.21} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{sin(2} }\omega { {\bar t)} }+ \\ {\rm{ 1} }{\rm{.031} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 6} }{\rm{.024} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$
    下载: 导出CSV

    表  4  两种方法得到的侧隙对比

    中心距偏差$\Delta a$/mm侧隙$b$/mm侧隙变化值$\Delta b$/mm
    计算公式离散化TCA计算公式离散化TCA
    00.04700.046500
    0.020.06070.06030.01370.0138
    0.040.07440.07390.02740.0274
    0.060.08810.08750.04110.0410
    下载: 导出CSV

    表  5  中心距偏差对微线段齿轮副侧隙的影响

    中心距偏差$\Delta a$/mm侧隙$b$/mm侧隙变化值$\Delta b$/mm
    00.04810
    0.020.05090.0028
    0.040.05310.0050
    0.060.05460.0065
    下载: 导出CSV
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  • 收稿日期:  2020-01-11
  • 刊出日期:  2021-10-18

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