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能量法计算齿根具有裂纹的齿轮啮合刚度

于耀庭 何芝仙 时培成

于耀庭, 何芝仙, 时培成. 能量法计算齿根具有裂纹的齿轮啮合刚度[J]. 机械科学与技术, 2021, 40(5): 716-720. doi: 10.13433/j.cnki.1003-8728.20200117
引用本文: 于耀庭, 何芝仙, 时培成. 能量法计算齿根具有裂纹的齿轮啮合刚度[J]. 机械科学与技术, 2021, 40(5): 716-720. doi: 10.13433/j.cnki.1003-8728.20200117
YU Yaoting, HE Zhixian, SHI Peicheng. Calculation of Gear Mesh Stiffness of Cracked Dedendum via Energy Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(5): 716-720. doi: 10.13433/j.cnki.1003-8728.20200117
Citation: YU Yaoting, HE Zhixian, SHI Peicheng. Calculation of Gear Mesh Stiffness of Cracked Dedendum via Energy Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(5): 716-720. doi: 10.13433/j.cnki.1003-8728.20200117

能量法计算齿根具有裂纹的齿轮啮合刚度

doi: 10.13433/j.cnki.1003-8728.20200117
基金项目: 

国家自然科学基金项目 51575001

详细信息
    作者简介:

    于耀庭(1993-), 硕士研究生, 研究方向为机械系统动力学, MaxPainkiller@163.com

    通讯作者:

    何芝仙, 教授, 硕士生导师, 博士, hzx@ahpu.edu.cn

  • 中图分类号: TH123.3

Calculation of Gear Mesh Stiffness of Cracked Dedendum via Energy Method

  • 摘要: 计算齿根具有裂纹的齿轮啮合刚度是求解含裂纹的齿轮传动系统动力学问题的基础。提出一种计及齿根裂纹表面自由能的计算齿轮啮合刚度的能量方法,该法将法向力作用下裂纹齿轮的弹性势能视为无裂纹齿轮的弹性势能与裂纹产生过程中释放的裂纹表面自由能之和。裂纹表面自由能通过裂纹应力强度因子与能量释放率之间的关系获得,齿根裂纹应力强度因子用权函数法求解。计算结果表明:齿根裂纹对齿轮啮合刚度影响很大;随着裂纹长度增加,裂纹齿轮啮合刚度减小,其求解结果与ANSYS软件计算结果一致。
  • 图  1  含齿根边缘裂纹的轮齿

    图  2  能量法示意图

    图  3  轮齿受力图

    图  4  有限宽板条边缘裂纹力学模型

    图  5  齿顶法向作用力下齿根边缘裂纹应力强度因子

    图  6  不同齿根裂纹长度下的齿轮啮合刚度

    表  1  参考载荷作用下裂纹应力强度因子多项式系数

    γ0 γ1 γ2 γ3 γ4 γ5 γ6 γ7
    1.121 5 -2.748 5 23.024 -108.34 282.21 -403.49 296.69 -88.319
    下载: 导出CSV

    表  2  齿轮几何参数及材料属性

    参数 数值 参数 数值
    弹性模量/GPa 200 齿宽/mm 20
    泊松比 0.3 齿顶高系数 1.0
    齿数 55/55 顶隙系数 0.25
    模数/mm 5 重合度 1.77
    压力角/(°) 20
    下载: 导出CSV

    表  3  能量法与有限元法刚度值对比

    啮合点半径/mm 能量法/(N·m-1) 有限元法/(N·m-1) 相对误差/%
    142.5 1.664×108 1.620×108 2.71
    141.5 1.964×108 1.948×108 0.81
    140.5 2.297×108 2.310×108 -0.54
    139.5 2.660×108 2.678×108 -0.66
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-01-05
  • 刊出日期:  2021-05-01

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