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基于改进势能法的直齿轮时变啮合刚度计算方法研究
Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method
- 机械传动 2023年47卷第2期 页码：1-7
- 作者机构：
海军航空大学 航空机械工程与指挥系（青岛校区）， 山东 青岛 266041
- 作者简介：
徐可君（1997— ），男，山东莱州人，博士研究生导师，教授；研究方向为航空发动机寿命可靠性分析与故障诊断；xukejunxuran@126.com。
- 基金信息：国家自然科学基金(11772089)
DOI：10.16578/j.issn.1004.2539.2023.02.001
中图分类号：纸质出版日期：2023-02-15，
收稿日期：2022-01-06，
修回日期：2022-03-31，
扫 描 看 全 文
徐可君,焦为,秦海勤.基于改进势能法的直齿轮时变啮合刚度计算方法研究[J].机械传动,2023,47(02):1-7.
Xu Kejun,Jiao Wei,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method[J].Journal of Mechanical Transmission,2023,47(02):1-7.
徐可君,焦为,秦海勤.基于改进势能法的直齿轮时变啮合刚度计算方法研究[J].机械传动,2023,47(02):1-7. DOI： 10.16578/j.issn.1004.2539.2023.02.001.
Xu Kejun,Jiao Wei,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method[J].Journal of Mechanical Transmission,2023,47(02):1-7. DOI： 10.16578/j.issn.1004.2539.2023.02.001.
摘要
以势能法为基础，将轮齿全齿廓分为渐开线部分和过渡曲线部分，提出一种改进的直齿轮时变啮合刚度计算方法。该方法考虑了齿根过渡曲线的参数方程，基于渐开线起始点半径、基圆半径和齿根圆半径的相对大小关系，建立了不同齿数情况下的轮齿模型，对渐开线齿廓部分的积分上限进行了修正，使得轮齿模型更为精确。对不同齿数情况下的轮齿时变啮合刚度进行计算，将改进前后方法的计算结果进行对比。结果表明，由于渐开线齿廓起始点半径和基圆半径不重合导致的计算误差会随着齿数的增加而增大；对于齿数相差较大的轮齿进行时变啮合刚度计算时，应根据齿数大小分情况进行啮合刚度计算；若用统一的轮齿模型进行计算，可能会带来较大的计算误差。参考有限元法计算结果，分析了误差产生的原因，验证了本文中所提方法的有效性。
Abstract
Based on the potential energy method
the full tooth profile of the gear teeth is divided into the involute part and the transition curve part
and an improved calculation method for the time-varying meshing stiffness of spur gears is proposed. Using this method
the parametric equation of the tooth root transition curve is considered
and based on the relative size relationship between the radius of the involute starting point
the radius of the base circle and the radius of the root circle
the tooth model with different numbers of teeth is established. A part of the integral upper limit has been corrected to make the gear tooth model more accurate. The time-varying meshing stiffness of gear teeth under different numbers of teeth is calculated
and the calculation results with this method before and after the improvement are compared. The results show that the calculation error caused by the non-coincidence of the starting point radius and the base circle radius of the involute tooth profile will increase with the increase of the number of teeth; when calculating the time-varying meshing stiffness of the teeth with a large difference in the number of teeth
the meshing stiffness calculation should be carried out according to the size of the teeth. There might be a large calculation error when the uniform gear model is used for calculation. Referring to the calculation results of the finite element method
the causes of errors are analyzed
and the effectiveness of the method proposed is verified.
关键词
改进势能法直齿轮时变啮合刚度不同轮齿模型
Keywords
Improved potential energy methodSpur gearTime-varying meshing stiffnessDifferent gear models
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