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
[1]
丰飞, 王炜, 唐丽娜, 等 空间高精度谐波减速器的应用及其发展趋势[J]. 机械传动, 2014, 38 (10): 98- 107 FENG Fei, WANG Wei, TANG Li-na, et al Application and development trends of the space harmonic reducer with high precision[J]. Journal of Mechanical Transmission, 2014, 38 (10): 98- 107
[2]
陶孟仑, 陈阳鹏, 陈定方, 等 谐波减速器测试技术研究现状及展望[J]. 机械传动, 2018, 42 (7): 175- 180 TAO Meng-lun, CHEN Yang-peng, CHEN Ding-fang, et al Research present status and outlook of harmonic reducer testing technology[J]. Journal of Mechanical Transmission, 2018, 42 (7): 175- 180
[3]
付小月, 王伟, 王雷, 等 变刚度关节驱动器动力学特性的分析与研究[J]. 机器人, 2017, 39 (4): 466- 473 FU Xiao-yue, WANG Wei, WANG Lei, et al Analysis and study on dynamical characteristics of variable stiffness joint actuator[J]. Robot, 2017, 39 (4): 466- 473
[4]
夏田, 杨世勇, 王亚峰 谐波减速器柔轮疲劳分析[J]. 机械传动, 2017, 41 (10): 133- 135 XIA Tian, YANG Shi-yong, WANG Ya-feng Fatigue analysis of the harmonic reducer flexspline[J]. Journal of Mechanical Transmission, 2017, 41 (10): 133- 135
[5]
DENNIS L, NELSON A, ANDRE’S T Statistical analysis of the influence of tooth geometry in the performance of a harmonic drive[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37: 723
doi: 10.1007/s40430-014-0197-0
[6]
ISHIKAWA S, KIYOSAWA Y. Flexing contact type gear drive of non-profile-shifted two-circular-arc composite tooth profile: United States, US 5458023[P]. 1995–10-17.
[7]
赵建虎. 谐波传动机构柔轮的应力分布及寿命特性分析[D]. 哈尔滨: 哈尔滨工业大学, 2013: 26-34. ZHAO Jian-hu, Analysis of stress distribution and life characteristics of flexspline in harmonic drive [D]. Harbin: Harbin Institute of Technology, 2013: 26-34.
[8]
董惠敏, 李德举, 齐书学 基于正交试验和有限元分析的谐波传动柔轮杯体结构优化[J]. 机械传动, 2013, 37 (1): 34- 38 DONG Hui-min, LI De-ju, QI Shu-xue Structural optimization of the flexspline cup in harmonic drives based on orthogonal test and finite element analysis[J]. Journal of Mechanical Transmission, 2013, 37 (1): 34- 38
[9]
王家序, 周祥祥, 李俊阳, 等 杯形柔轮谐波传动三维双圆弧齿廓设计[J]. 浙江大学学报: 工学版, 2016, 50 (4): 616- 624 WANG Jia-xu, ZHOU Xiang-xiang, LI Jun-yang, et al Three dimensional profile design of cup harmonic drive with double-circular-arc common-tangent tooth profile[J]. Journal of Zhejiang University: Engineering Science, 2016, 50 (4): 616- 624
[10]
杨勇, 王家序, 周青华, 等 双圆弧谐波齿轮传动柔轮齿廓参数的优化设计[J]. 四川大学学报: 工程科学版, 2016, 48 (1): 186- 193 YANG Yong, WANG Jia-xu, ZHOU Qing-hua, et al Optimization design for flexspline tooth profile parameters of double-circular-arc harmonic drives[J]. Journal of Sichuan University: Engineering Science Edition, 2016, 48 (1): 186- 193
[11]
李奇. 不同参数对谐波减速器柔轮动态特性的影响[D]. 重庆: 重庆大学, 2016. 26-30. LI Qi. Influence of different parameters to the dynamic characteristics of the flexspline of harmonic reducer [D]. Chongqing: Chongqing University, 2016.
[12]
张雷, 杨伟超, 蒋倩倩, 等 谐波减速器核心部件结构应力分析[J]. 机械传动, 2018, 42 (12): 114- 117 ZHANG Lei, YANG Wei-chao, JIANG Qian-qian, et al Structural stress analysis of the core components of harmonic reducer[J]. Journal of Mechanical Transmission, 2018, 42 (12): 114- 117
[13]
王家序, 刘彪, 周祥祥, 等 双圆弧谐波齿轮传动齿廓设计与参数分析[J]. 四川大学学报: 工程科学版, 2016, 48 (3): 164- 170 WANG Jia-xu, LIU Biao, ZHOU Xiang-xiang, et al Double-circular-arc tooth profile design and parametric analysis of harmonic drive[J]. Journal of Sichuan University: Engineering Science Edition, 2016, 48 (3): 164- 170
[14]
王家序, 周祥祥, 李俊阳, 等 不同共轭原理的双圆弧齿廓谐波齿轮传动分析[J]. 四川大学学报: 工程科学版, 2015, 47 (5): 160- 166 WANG. Jia-xu, ZHOU Xiang-xiang, LI Jun-yang, et al Double-circular-arc tooth profile of harmonic drive analysis based on different conjugate principle[J]. Journal of Sichuan University: Engineering Science Edition, 2015, 47 (5): 160- 166
[15]
张志红, 何桢, 郭伟 在响应曲面方法中三类中心复合设计的比较研究[J]. 沈阳航空航天大学学报, 2007, 24 (1): 87- 91 ZHANG Zhi-hong, HE Zhen, GUO Wei A comparative study of three central composite designs in response surface methodology[J]. Journal of Shenyang Institute of Aeronautical Engineering, 2007, 24 (1): 87- 91
doi: 10.3969/j.issn.2095-1248.2007.01.026
[16]
张立勇, 刘新猛, 王长路, 等 径向变形量对谐波减速器啮合特性及柔轮应力的影响分析[J]. 机械传动, 2017, 41 (9): 166- 169 ZHANG Li-yong, LIU Xin-meng, WANG Chang-lu, et al Influence of radial deformation on stress of flexspline and meshing characteristic of harmonic reducer[J]. Journal of Mechanical Transmission, 2017, 41 (9): 166- 169