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Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (12): 2289-2297    DOI: 10.3785/j.issn.1008-973X.2019.12.005
Mechanical and Energy Engineering     
Influence law of manufacturing error on harmonic gear stress
Qian CHEN1(),Jun-yang LI1,*(),Jia-xu WANG1,2,Qian-qian JIANG1,Ting TANG1
1. State key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China
2. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
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Abstract  

The experiment was designed based on the response surface theory to study the influence about various manufacturing errors of harmonic gears on the tooth surface stress and wear of the flexspline. A four-factor response surface model was adopted, which includes the span value (M-value) deviation of the flexspine, the M-value deviation of the circular spline, the long half axis deviation, and the short half axis deviation of the wave generator. Then corresponding harmonic gear models were established for finite element simulation analysis, respectively. The experimental results show that the cam long half axis deviation is most sensitive to the stress on the flexspline tooth, the M-value deviation of the flexspline and the M-value deviation of the circular spline less, and the cam short axis deviation sensitivity the least. Four kinds of error compensation schemes were proposed for different deviations of the gears of the circular spline and the flexspline, which may occur during the manufacturing process, to improve the meshing condition and the accuracy retention. That is, the long half axis of the cam can be reduced when the M-values of the flexspline and the circular spline are both negative deviation, or positive and negative deviation respectively; the long half axis of the cam can be increased when the M-values of the flexspline and the circular spline are both positive deviation, or negative and positive deviation respectively.



Key wordsharmonic gear transmission      double-circular-arc tooth profile      manufacturing error      finite element      response surface method     
Received: 02 March 2019      Published: 17 December 2019
CLC:  TH 132.43  
Corresponding Authors: Jun-yang LI     E-mail: 957772748@qq.com;lijunyang1982@sina.com
Cite this article:

Qian CHEN,Jun-yang LI,Jia-xu WANG,Qian-qian JIANG,Ting TANG. Influence law of manufacturing error on harmonic gear stress. Journal of ZheJiang University (Engineering Science), 2019, 53(12): 2289-2297.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.12.005     OR     http://www.zjujournals.com/eng/Y2019/V53/I12/2289


制造误差对谐波齿轮应力的影响规律

为研究谐波齿轮各种制造误差对柔轮齿面应力与磨损情况的影响,根据响应面思想,设计实验,采用四因素响应面模型,分析柔轮跨距值(M值)偏差、刚轮M值偏差、波发生器长半轴偏差及短半轴偏差,分别建立相应谐波齿轮模型,并进行有限元仿真分析. 实验结果表明,凸轮长半轴偏差对柔轮齿上应力敏感度最大,柔轮、刚轮M值偏差次之,凸轮短半轴偏差敏感度最小;针对在制造加工时可能出现的刚轮与柔轮齿廓不同偏差情况提出4种误差补偿方案,即当柔轮、刚轮M值均为负偏差或分别为正偏差、负偏差时减小凸轮长半轴,当柔轮、刚轮M值均为正偏差或分别为负偏差、正偏差时增大凸轮长半轴,以此改善啮合情况并提高精度保持性.


关键词: 谐波齿轮传动,  双圆弧齿廓,  制造误差,  有限元,  响应面法 
Fig.1 Tooth profile of flexspline with double-circular-arc tooth profile
符号 意义 符号 意义
${h^{\rm{*}}_{\rm{a}}}$ 齿顶高系数 $\gamma $ 公切线倾角
${h^{\rm{*}}_{\rm{f}}}$ 齿根高系数 $t$ 齿根壁厚
$h$ 全齿高 ${X_{\rm{a}}}$ 凸齿圆心移距量
${\rho _{\rm{a}}}$ 凸圆弧齿廓半径 ${Y_{\rm{a}}}$ 凸齿圆心偏移量
${\rho _{\rm{f}}}$ 凹圆弧齿廓半径 ${X_{\rm{f}}}$ 凹齿圆心移距量
${Y_{\rm{f}}}$ 凹齿圆心偏移量 m 柔轮模数
kt 齿厚比 ? ?
Tab.1 Parameters of double-circular-arc tooth profile
Fig.2 Diagram of tooth thickness deviation
Fig.3 Schematic diagram of theoretical M-value for tooth profile of flexspline
Fig.4 Schematic diagram of theoretical M-value for tooth profile of circular spline
水平编码 δ1/mm δ2/mm δ3/mm δ4/mm
?2 ?0.050 ?0.050 ?0.050 ?0.050
?1 ?0.025 ?0.025 ?0.025 ?0.025
0 0 0 0 0
1 0.025 0.025 0.025 0.025
2 0.050 0.050 0.050 0.050
Tab.2 Factors and levels of harmonic gear manufacturing error
Fig.5 Meshing of harmonic gear finite element analysis (FEA) model
部件 材料 E/GPa μ ρ/(kg·m?3)
柔轮 30CrMnSiA 196 0.3 7 750
刚轮 45 210 0.269 7 850
波发生器 45 210 0.269 7 850
Tab.3 Material physical performance parameters of harmonic gear
Fig.6 Stress nephogram of flexpline ring gear
Fig.7 Effect of M-value deviation of flexspline on stress of flexspline tooth observation point
Fig.8 Effect of M-value deviation of circular spline on stress of flexspline tooth observation point
Fig.9 Effect of cam long half axis deviation on stress of flexspline tooth observation point
Fig.10 Effect of cam short half axis deviation on stress of flexspline tooth observation point
Fig.11 Response surface of M-value deviation of flexspline and circular spline on stress of flexspline tooth observation point
Fig.12 Response surface of M-value deviation of flexspline and cam long half axis deviation on stress of flexspline tooth observation point
Fig.13 Response surface of M-value deviation of circular spline and cam long half axis deviation on stress of flexspline tooth observation point
Fig.14 Adjustment curves of cam long half axis by four kinds of solutions
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