Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab

Dongjiang Cao; Peng Shang; Yang Zhao

doi:10.16578/j.issn.1004.2539.2022.05.014

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Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab

Design· Calculation | 更新时间：2022-09-24

- Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab
- Journal of Mechanical Transmission Vol. 46, Issue 5, Pages: 100-107(2022)
- 作者机构：
  
  1.庆安集团有限公司，陕西西安 710077
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2022.05.014
  CLC：
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曹东江,尚鹏,赵阳.基于Matlab的渐开线变位直齿轮时变啮合刚度计算分析[J].机械传动,2022,46(05):100-107.

Cao Dongjiang,Shang Peng,Zhao Yang.Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab[J].Journal of Mechanical Transmission,2022,46(05):100-107.
曹东江,尚鹏,赵阳.基于Matlab的渐开线变位直齿轮时变啮合刚度计算分析[J].机械传动,2022,46(05):100-107. DOI： 10.16578/j.issn.1004.2539.2022.05.014.

Cao Dongjiang,Shang Peng,Zhao Yang.Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab[J].Journal of Mechanical Transmission,2022,46(05):100-107. DOI： 10.16578/j.issn.1004.2539.2022.05.014.

摘要

考虑齿轮真实的渐开线及过渡曲线方程，对齿轮进行精确建模，推导并利用Weber能量法计算了变位齿轮变形量，推导了刚度计算中涉及的载荷角, $β_{j}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34760994&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34760991&type=,2.53999996,4.48733330,、压力角, $α_{k}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34758961&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34758957&type=,3.21733332,3.72533321,、旋转角, $t a n α_{k}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34758972&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34758967&type=,8.38199997,3.80999994,同载荷点坐标, $X_{M j}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761006&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761004&type=,4.40266657,3.72533321,的映射关系，根据齿轮重合度，计算了齿轮啮合周期中单、双对齿轮交替啮合的区段边界；在此基础上，考虑齿轮副综合啮合效应，求解出齿轮副综合时变刚度。通过Matlab GUI编程，实现了齿轮参数化建模设计与齿轮时变刚度计算的有机结合。研究结果为进一步进行变位齿轮动力学研究提供了重要支撑。

Abstract

Considering the real involute and transition curve equation of gears，an accurate model of gears is conducted. The deformation of modified gear is deduced and calculated by Weber energy method. The mapping relationships of load angle , $β_{j}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34760994&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34760991&type=,2.53999996,4.48733330,，pressure angle , $α_{k}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761010&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761009&type=,3.21733332,3.72533321,，rotation angle tan , $α_{k}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761010&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761009&type=,3.21733332,3.72533321, and coordinate , $X_{M j}$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761006&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34761004&type=,4.40266657,3.72533321, of load point are deduced. According to the contact ratio of gears，the alternate meshing section boundary of single and double pairs of gear in meshing cycle is calculated. On this basis，the comprehensive meshing effect of gear pair has been taken into consideration in solving the comprehensive time-varying stiffness of gear pair. The combination of gear parametric modeling design and gear time-varying stiffness calculation is realized by Matlab GUI programming. The results provide important support for further research on gear dynamics.

关键词

Weber能量法时变啮合刚度Matlab重合度

Keywords

Weber energy methodTime-varying meshing stiffnessMatlabContact ratio

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