双圆弧谐波传动柔轮齿形参数多目标优化设计

doi:10.13229/j.cnki.jdxbgxb20180336

摘要/Abstract

摘要：

根据刚轮和柔轮空载下连续不断啮合和“双共轭”现象能有效提高双圆弧谐波齿轮装置的啮合性能，提出了一种圆弧柔轮齿形参数的多目标优化设计方法。针对无公切线双圆弧齿廓，采用改进运动学法和精确转角关系进行共轭齿廓设计，以缩小共轭空白区间与共轭齿廓差异为优化目标，考虑共轭齿廓的存在条件，建立谐波传动多目标优化模型，进行单目标分析及多目标优化。结果表明：该优化方法可实现柔轮齿形参数的合理选择，使空载状态刚轮与柔轮啮合空白区域小于1.2°，共轭齿廓间差异在0.83 μm左右，能满足工程应用要求，保证空载连续啮合及“双共轭”传动精度。

关键词: 仪器仪表技术, 谐波传动, 双圆弧齿廓, 多目标优化, 齿形参数

Abstract:

The continuous meshing zone and "double conjugate" phenomenon of the circular spline and flexspline under no?load conditions can effectively improve the meshing performance of the double?arc harmonic gear device. For this reason, a multi?objective optimization design method of the tooth profile parameters of the double?circle flexspline is proposed. For the non?public tangential double?arc tooth profile, the conjugate tooth profile was designed by using the relationship between the improved kinematics method and the precise rotation angle. To reduce the difference between the conjugate blank area and the conjugate tooth profile as the optimization goal, a harmonic drive multi?objective optimization model was established. Considering the existence conditions of conjugate tooth profiles, single target analysis and multi?objective optimization are performed. The results show that the two objective functions increase with the increase of the radial deformation coefficient and the double circular arc inclination, and decrease with the increase of the tooth thickness ratio; Radial deformation coefficient and double circular arc inclination have the greatest influence on the two objective functions, and tooth thickness ratio has less influence on the difference of minimum conjugate tooth profile. Convex arc radius coefficient and concave arc radius coefficient have almost no effect on the minimum blank conjugate area; this optimization method can achieve a reasonable selection of parameters of the soft tooth profile, and make the freewheeling state between the circular spline and the flexspline is less than 1.2°, and the difference between the conjugate profiles is about 0.83 μm, which can meet the requirements of engineering applications. Guaranteed no?load continuous meshing interval and "double conjugate" transmission accuracy.

Key words: technology of instrument and meter, harmonic drive, double?arc tooth profile, multi?objective optimization, profile parameters

中图分类号:

TH132.43

王家序,蒋倩倩,李俊阳,韩彦峰,张雷,唐挺. 双圆弧谐波传动柔轮齿形参数多目标优化设计[J]. 吉林大学学报(工学版), 2019, 49(4): 1194-1202.

Jia⁃xu WANG,Qian⁃qian JIANG,Jun⁃yang LI,Yan⁃feng HAN,Lei ZHANG,Ting TANG. Multi⁃objective optimization design of flexspline profile parameters of double⁃arc harmonic drive[J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(4): 1194-1202.

图/表 14

图1

表1

图2

表2

表3

柔轮齿廓参数"

参数	数值/mm	参数	数值/mm
h $a *$	0.7	t ₁	0.7132
h $f *$	0.8	γ	6°
x_a	0.4001	x _f	0.2617
y_a	0.0671	y _f	0.0679
$ρ$ $a *$	1.5	$ρ$ $f *$	1.7
k _t	1.7	h	0.594

表3

图3

图4

表4

图5

图6

图7

图8

图9

表5

谐波齿轮传动多目标优化结果"

序号	w $0 *$	γ/(?)	ρ $a *$	ρ $a *$	k _t	f ₁(X)/(?)	f ₂(X)×10²/mm
1	1.0451	6	1.5791	1.6668	1.7	1.191279	0.083268
2	1.0356	7	1.6908	1.7289	1.7	1.356309	1.965230
3	1.0249	8	1.5489	1.6754	1.7	1.380993	2.961959
4	1.0131	9	1.5489	1.6753	1.7	1.266431	4.181113
5	1.0004	10	1.5390	1.6535	1.7	1.267915	5.210725
6	0.9869	11	1.5391	1.6534	1.7	1.397736	6.345894
7	0.9725	12	1.5610	1.6296	1.7	1.220946	7.208653
8	0.9575	13	1.5528	1.6194	1.7	1.206309	8.103814
9	0.9419	14	1.5791	1.6050	1.7	1.154419	8.907568
10	0.9258	15	1.5777	1.6001	1.7	1.073299	9.731521

表5

参考文献 13

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符号	意义
ρ	O ₁点矢径
r _m	变形前柔轮的中性层半径
Δφ	矢径ρ与Y ₂的夹角
β	轴Y ₁相对于轴Y ₂的转角
φ ₁	矢径ρ与轴Y的夹角
φ_F	输出端轴Y_F 相对于轴Y ₂的转角
φ	输出端轴Y_F 与轴Y的夹角
φ _w	轴Y相对于Y ₂的转角

符号	参数	符号	参数
h _a ^*	齿顶高系数	t y _a x _a y _f x _f m	齿根壁厚
h _f ^*	齿根高系数		凸齿圆心移距量
h	全齿高		凸齿圆心偏移量
ρ _a ^*	凸圆弧半径系数		凹齿圆心移距量
ρ _f ^*	凹圆弧半径系数		凹齿圆心偏移量
γ	双圆弧倾角		模数