基于能量等效的直齿锥齿轮时变啮合刚度计算

陈思宇; 谭儒龙; 郭晓东; 张卫青; 舒锐志

doi:10.13224/j.cnki.jasp.20210095

Chinese

您当前的位置：

首页 >

文章列表页 >

基于能量等效的直齿锥齿轮时变啮合刚度计算

动力传输 | 更新时间：2025-04-07

- 基于能量等效的直齿锥齿轮时变啮合刚度计算
- Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence
- 航空动力学报 2022年37卷第2期页码：320-329
- 作者机构：
  
  重庆理工大学机械工程学院，重庆 400054
- 作者简介：
  
  陈思宇（1996-），男，硕士，主要从事智能化与数字化制造方面的研究。E⁃mail：1605510003@qq.com
  谭儒龙（1987-），男，副教授，博士，研究方向为高性能机电传动技术及系统、齿轮传动。E⁃mail：rulong.tan@cqut.edu.cn
- 基金信息：
  
  国家重点研发计划项目(2018YFB2001700);国家自然科学基金资助项目(51805060;51905060)
- DOI：10.13224/j.cnki.jasp.20210095
  中图分类号：
- 稿件说明：
移动端阅览
陈思宇, 谭儒龙, 郭晓东, 等. 基于能量等效的直齿锥齿轮时变啮合刚度计算[J]. 航空动力学报, 2022,37(2):320-329.

Siyu CHEN, Rulong TAN, Xiaodong GUO, et al. Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence[J]. Journal of Aerospace Power, 2022, 37(2): 320-329.
陈思宇, 谭儒龙, 郭晓东, 等. 基于能量等效的直齿锥齿轮时变啮合刚度计算[J]. 航空动力学报, 2022,37(2):320-329. DOI： 10.13224/j.cnki.jasp.20210095.

Siyu CHEN, Rulong TAN, Xiaodong GUO, et al. Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence[J]. Journal of Aerospace Power, 2022, 37(2): 320-329. DOI： 10.13224/j.cnki.jasp.20210095.

摘要

针对直齿圆锥齿轮啮合刚度的计算问题，从微元思想出发，将变截面齿廓划分为若干等截面微段齿段，基于能量等效建立微段齿段啮合刚度计算模型，并利用积分方法获得单齿啮合刚度。此外，基于力平衡和变形协调条件进一步提出了齿轮时变啮合刚度计算模型，同时根据几何关系导出了相应传动误差计算式。利用有限元分析对解析计算模型进行了验证，并分析了误差来源。结果表明：利用该模型不仅能够将直齿锥齿轮啮合刚度计算精度保证在2%以内，还达到了快速求解的目的。

Abstract

As one of the most important dynamic excitation sources of gear system，gear time⁃varying meshing stiffness is a key parameter of gear system dynamics model. In view of the problem of calculating the meshing stiffness of straight bevel gears，the variable section tooth profile was divided into several micro⁃section tooth segments with equal section based on the idea of micro⁃element. The calculation model of meshing stiffness of micro⁃section tooth segments was established based on energy equivalent，and the single tooth meshing stiffness was obtained by using integral method. In addition，based on force balance and deformation coordination conditions，a computational model of gear time⁃varying meshing stiffness was proposed，and the corresponding formula of transmission error was derived according to geometric relations.The finite element analysis was used to verify the calculation method and analyze the error source. The results showed that the calculation accuracy of meshing stiffness of straight bevel gears can be guaranteed within 2% by using this model，and the purpose of quick solution can be achieved.

关键词

Keywords

references

王延忠 , 周元子 , 李国权 , 等 . 螺旋锥齿轮啮合刚度及参数振动稳定性研究 [J]. 航空动力学报 , 2010 , 25 （ 7 ）: 1664 ⁃ 1669 .

WANG Yanzhong , ZHOU Yuanzi , LI Guoquan , et al . Study on meshing stiffness and parametric vibration stability of spiral bevel gear [J]. Journal of Aerospace Power , 2010 , 25 （ 7 ）: 1664 ⁃ 1669 . （in Chinese）

孟宗 , 石桂霞 , 王福林 , 等 . 基于时变啮合刚度的裂纹故障齿轮振动特征分析 [J]. 机械工程学报 , 2020 , 56 （ 17 ）: 108 ‑ 115 .

MENG Zong , SHI Guixia , WANG Fulin , et al . Vibration characteristic analysis of cracked gear based on time⁃varying meshing stiffness [J]. Journal of Mechanical Engineering , 2020 , 56 （ 17 ）: 108 ⁃ 115 . （in Chinese）

WAN Zhiguo , CAO Hongrui , ZI Yanyang , et al . Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears [J]. Mechanism and Machine Theory , 2015 , 92 : 447 ⁃ 463 .

SHAO Y , CHEN Z . Dynamic features of planetary gear set with tooth plastic inclination deformation due to tooth root crack [J]. Nonlinear Dynamics , 2013 , 74 （ 4 ）: 1253 ⁃ 1266 .

樊继开 . 含裂纹齿轮的时变啮合刚度计算及裂纹辨识研究 [D]. 武汉：华中科技大学 , 2017 .

FAN Jikai . Calculation of time⁃varying meshing stiffness of cracked gear and study on crack identification [D]. Wuhan : Huazhong University of Science and Technology , 2017 . （in Chinese）

CHEN Siyu , TANG Jiuyuan , LUO Caiwang . Effects of the gear tooth modification on the nonlinear dynamics of gear transmission system [J]. Advanced Materials Research , 2010 , 905 （ 198 ）: 2764 ⁃ 2769 .

CHEN Siyu , TANG Jiuyuan , LUO Caiwang , et al . Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction [J]. Mechanism and Machine Theory , 2011 , 46 （ 4 ）: 466 ⁃ 478 .

PIMSARN M , KAZEROUNIAN K . Efficient evaluation of spur gear tooth mesh load using pseudo interference stiffness estimation method [J]. Mechanism and Machine Theory , 2002 , 37 （ 8 ）: 769 ⁃ 786 ．

常乐浩 , 刘更 , 郑雅萍 , 等 . 一种基于有限元法和弹性接触理论的齿轮啮合刚度改进算法 [J]. 航空动力学报 , 2014 , 29 （ 3 ）: 682 ⁃ 688 .

CHANG Lehao , LIU Geng , ZHENG Yaping , et al . A modified method for determining mesh stiffness of gears based on finite element method and elastic contact theory [J]. Journal of Aerospace Power , 2014 , 29 （ 3 ）: 682 ⁃ 688 . （in Chinese）

王刚强 . 修形斜齿轮啮合刚度解析模型与系统振动特性研究 [D]. 重庆：重庆大学 , 2018 .

WANG Gangqiang . An analytical model for the meshing stiffness of helical gears with modification and system vibration characteristics [D]. Chongqing : Chongqing University , 2018 . （in Chinese）

魏冰阳 , 杨建军 , 聂少武 . 差曲面拓扑的齿轮啮合刚度计算与承载接触分析 [J]. 航空动力学报 , 2019 , 34 （ 12 ）: 2745 ⁃ 2752 .

WEI Bingyang , YANG Jianjun , NIE Shaowu . Calcution of gear meshing stiffness and loaded tooth contact analysis based on ease⁃off surface topology [J]. Journal of Aerospace Power , 2019 , 34 （ 12 ）: 2745 ⁃ 2752 . （in Chinese）

唐进元 , 蒲太平 . 基于有限元法的螺旋锥齿轮啮合刚度计算 [J]. 机械工程学报 , 2011 , 47 （ 11 ）: 23 ⁃ 29 .

TANG Jinyuan , PU Taiping . Meshing stiffness calculation of spiral bevel gears based on finite element method [J]. Journal of Mechanical Engineering , 2011 , 47 （ 11 ）: 23 ⁃ 29 . （in Chinese）

ALSHYYAB A , KAHRAMAN A . Non⁃linear dynamic analysis of a multi⁃mesh gear train using multi⁃term harmonic balance method:period⁃one motions [J]. Journal of Sound and Vibration , 2005 , 284 （ 1 ）: 151 ⁃ 172 .

马辉 , 逄旭 , 宋溶泽 , 等 . 基于改进能量法的直齿轮时变啮合刚度计算 [J]. 东北大学学报（自然科学版） , 2014 , 35 （ 6 ）: 863 ⁃ 866,884 .

MA Hui , PENG Xu , SONG Rongze , et al . Calculation of time⁃varying mesh stiffness of straight gear based on improved energy method [J]. Journal of Northeastern University （Natural Science Edition） , 2014 , 35 （ 6 ）: 863 ⁃ 866,884 . （in Chinese）

CHEN Zaigang , SHAO Yimin . Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack [J]. Mechanism and Machine Theory , 2013 , 62 : 63 ⁃ 74 .

CHEN Zaigang , SHAO Yimin . Mesh stiffness of an internal spur gear pair with ring gear rim deformation [J]. Mechanism and Machine Theory , 2013 , 69 : 1 ⁃ 12 .

CHEN Zaigang , ZHOU Ziwei , ZHAI Wanming , et al . Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations [J]. Mechanism and Machine Theory , 2020 , 149 : 103838.1 ⁃ 103838.17 .

MENNEM R C . Parametrically excited vibrations in spiral bevel geared systems [D]. West Lafayette,US : Purdue University , 2004 .

MARAMBEDU K R . Development of a procedure for the analysis of load distribution,stresses and transmission error of straight bevel gears [D]. Columbus,US : Ohio State University , 2009 .

陈霞 . 直齿锥齿轮修形方法研究 [D]. 武汉：华中科技大学 , 2006 .

CHEN Xia . Research on the tooth modification methods of the straight bevel gear [D]. Wuhan : Huazhong University of Science and Technology , 2006 . （in Chinese）

CHAARI F , FAKHFAKH T , HADDAR M . Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness [J]. European Journal of Mechanics:A/Solids , 2008 , 28 （ 3 ）: 461 ‑ 468 .

孙庆华 . 直齿锥齿轮渐开线齿形起测点的展开角计算 [J]. 计量技术 , 1995 （ 9 ）: 7 ⁃ 9 .

SUN Qinghua . Calculation of expand angle of measuring point of ininvolute tooth profile of spurbevel gears [J]. Metrology Science and Technology , 1995 （ 9 ）: 7 ⁃ 9 . （in Chinese）

谭儒龙 . 共轭曲线锥齿轮研究 [D]. 重庆 : 重庆大学 , 2016 .

TAN Rulong . Research on conjugated curve bevel gears [D]. Chongqing : Chongqing University , 2016 . （in Chinese）

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

直齿锥齿轮低安装误差敏感性设计与实验验证

无螺栓后挡板与叶片接触压力的分析

基于自适应MOMEDA滚动轴承故障特征提取方法

与发动机匹配的旁路式双喉道气动矢量喷管数值模拟研究

考虑多源不确定性的复合材料风扇叶片高周疲劳失效概率评估