并联结构轴系回转误差建模及装配优化

董一鸣; 江波; 李翔宇; 谢友金; 吕涛; 阮萍

doi:10.37188/CO.2023-0171

并联结构轴系回转误差建模及装配优化

doi: 10.37188/CO.2023-0171

董一鸣^{1, 2, 3,},
江波^{1, 3, ,},
李翔宇^{1, 3},
谢友金^{1, 3},
吕涛^{1, 3},
阮萍^{1, 3}

1.
中国科学院西安光学精密机械研究所光电跟踪与测量技术研究室, 陕西西安 710119
2.
中国科学院大学光电学院, 北京 100049
3.
中国科学院空间精密测量技术重点实验室, 陕西西安 710119

基金项目: 国家自然科学基金青年基金项目（No. 12103081）

详细信息

作者简介:
江　波（1981—），男，湖北武汉人，博士，正高级工程师，2015年于中国科学院大学获得工学博士学位，主要从事光电测控技术、微小位移及角度驱动技术、同步辐射技术等方面的研究。E-mail：ilysay@opt.ac.cn

中图分类号: TH745
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出版历程
- 收稿日期: 2023-09-28
- 录用日期: 2023-11-24
- 网络出版日期: 2024-01-16

Rotary error modeling and assembly optimization of parallel structure shafting

DONG Yi-ming^{1, 2, 3
,},
JIANG Bo^{1, 3
, ,},
LI Xiang-yu^{1, 3},
XIE You-jin^{1, 3},
LV Tao^{1, 3},
RUAN Ping^{1, 3}

1.
Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
CAS Key Laboratory of Space Precision Measurement Technology, Xi’an 710119, China

Funds: Supported by National Natural Science Foundation for Young Scientists of China (No. 12103081)

More Information

Corresponding author: ilysay@opt.ac.cn

摘要

摘要:
为提高光电经纬仪等二维转台的轴系运动精度，本文基于雅可比旋量理论建立了一种可考虑零件结构误差及其耦合放大效应的数学模型。针对“一端固定、一端游动”的轴系结构，提出了局部并联结构的分析方法。通过数值仿真分析，获得了各零件结构误差对轴系运动精度的影响以及最优的轴系装配方案。光学口径为650 mm的光电经纬仪的装调结果表明：装配优化后的轴系运动精度较优化前提高了32.1%。所构造的轴系运动精度模型及优化方法，为指导光电经纬仪等二维转台的轴系装调以及公差设计提供了一定的理论根据。
- 光学测量 /
- 二维转台 /
- 轴系运动模型 /
- 光电经纬仪 /
- 装配优化
Abstract:
In order to improve the shafting motion accuracy of two-dimensional turntables such as photoelectric theodolites, we establish a mathematical model considering both the structural error of parts and the coupling amplification effect based on Jacobian-Torsor theory. Aiming at a shafting structure with one fixed end and one swimming, an analysis method of partial parallel structure was proposed. Through numerical simulation analysis, the impact of each part’s structural errors on the motion accuracy of the shafting and the optimal shafting assembly scheme were obtained. The results of assembly and adjustment of a photoelectric theodolite with an optical diameter of 650 mm show that the motion accuracy of assembly optimized the shaft system improved by 32.1%. The precision model and optimization method of shafting motion provide a theoretical basis for the shafting adjustment and tolerance design of two-dimensional turntables such as photoelectric theodolites.
- optical measurement /
- two-dimensional turntable /
- shafting motion model /
- photoelectric theodolite /
- assembly optimization

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图 1 运动误差示意图

Figure 1. Diagram of motion error

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图 2 局部并联结构示意图

Figure 2. Diagram of local parallel structure

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图 3 轴系结构与回转误差测量

Figure 3. Shaft structure and rotary error measurement

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图 4 PSO收敛曲线

Figure 4. PSO convergence curve

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图 5 敏感性分析

Figure 5. Sensitivity analysis

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图 6 几何量测量

Figure 6. Geometric measurement

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图 7 轴颈跳动

Figure 7. Journal runout

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图 8 优化三维曲面图

Figure 8. Optimized 3D surface

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图 9 装配误差补偿

Figure 9. Assembly error compensation

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表 1 俯仰轴系几何误差及编号

Table 1. Geometric deviation items and numbers of elevation axle

零件名	坐标系	误差项	编号
固定端轴承	o₁	δ(x), δ(y), δ(z), θ(y), θ(z)	1, 2, 3, 4, 5
固定端轴套	o₂	δ(x), δ(y), δ(z), θ(y), θ(z)	6, 7, 8, 9, 10
固定端法兰	o₃	δ(x), δ(y), δ(z), θ(y), θ(z)	11, 12, 13, 14, 15
游动端法兰	o₄	δ(x), δ(y), δ(z), θ(y), θ(z)	16, 17, 18, 19, 20
游动端轴承	o₅	δ(y), θ(z)	21, 22
游动端轴套	o₆	δ(x), δ(y), δ(z), θ(y), θ(z)	23, 24, 25, 26, 27

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表 2 轴系运动模型参数

Table 2. Shafting motion model parameters

参数名	数值
E₁	[±0.005, ±0.020, ±0.020, 0, ±9.696×10⁻⁶, ±9.696×10⁻⁶]
E₂	[±0.005, ±0.005, ±0.005, 0, ±9.696×10⁻⁶, ±9.696×10⁻⁶]
E₃	[±0.005, ±0.005, ±0.005, 0, ±9.696×10⁻⁶, ±9.696×10⁻⁶]
E₄	[±0.010, ±0.010, ±0.010, 0, ±8.242×10⁻⁶, ±8.242×10⁻⁶]
E₅	[0 ±0.010, ±0.010, 0, 0, 0]
E₆	[±0.005, ±0.020, ±0.020, 0, ±9.696×10⁻⁶, ±9.696×10⁻⁶]
L₁	250 mm
L₂	1100 mm
L₃	200 mm
L₄	150 mm

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表 3 测量结果

Table 3. Measurement results

转角 /rad	跳动量 /μm	顺时针			逆时针
转角 /rad	跳动量 /μm	X/″	Y/″	$ \sqrt{X^{2}+Y^{2}} $	X/″	Y/″	$ \sqrt{X^{2}+Y^{2}} $
0	0	0	0	0	0.5	0.2	0.54
0.52	4	1.7	1.5	2.27	1.9	0.8	2.06
1.05	3	2.2	1.7	2.78	3	1.5	3.35
1.57	5	2.8	1.6	3.22	3.3	1.2	3.51
2.09	2	2.3	0.3	2.32	2.6	−0.1	2.60
2.62	3	1.6	0.2	1.61	1.5	0.5	1.58
3.14	5	0.6	1.9	1.99	0.7	2.1	2.21
3.67	10	1.3	3.3	3.55	1	3.1	3.26
4.19	9	2.1	3.3	3.91	1.9	3	3.55
4.71	7	2.3	2	3.05	2.5	1.7	3.02
5.24	4	1.1	1	1.49	1	0.3	1.04
5.76	1	−0.1	−0.3	0.32	0.1	−0.1	0.14
6.28	1	0.4	−0.1	0.41	0.4	−0.1	0.42

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