1. State key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China 2. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
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.
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.
Fig.1Tooth 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.1Parameters of double-circular-arc tooth profile
Fig.2Diagram of tooth thickness deviation
Fig.3Schematic diagram of theoretical M-value for tooth profile of flexspline
Fig.4Schematic 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.2Factors and levels of harmonic gear manufacturing error
Fig.5Meshing 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.3Material physical performance parameters of harmonic gear
Fig.6Stress nephogram of flexpline ring gear
Fig.7Effect of M-value deviation of flexspline on stress of flexspline tooth observation point
Fig.8Effect of M-value deviation of circular spline on stress of flexspline tooth observation point
Fig.9Effect of cam long half axis deviation on stress of flexspline tooth observation point
Fig.10Effect of cam short half axis deviation on stress of flexspline tooth observation point
Fig.11Response surface of M-value deviation of flexspline and circular spline on stress of flexspline tooth observation point
Fig.12Response surface of M-value deviation of flexspline and cam long half axis deviation on stress of flexspline tooth observation point
Fig.13Response surface of M-value deviation of circular spline and cam long half axis deviation on stress of flexspline tooth observation point
Fig.14Adjustment curves of cam long half axis by four kinds of solutions
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