基于力矩促动器的镜面半主动光学支撑系统集成优化设计

张奔雷; 杨飞; 王富国; 卢保伟

doi:10.37188/CO.2022-0121

基于力矩促动器的镜面半主动光学支撑系统集成优化设计

doi: 10.37188/CO.2022-0121

张奔雷^{1, 2,},
杨飞^1, ,,
王富国¹,
卢保伟^{1, 2}

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春130033
2.
中国科学院大学, 北京100049

基金项目: 吉林省科技发展计划（No. 20210402065GH）；中国科学院青年创新促进会优秀会员（No. Y202053）；中国科学院国际伙伴计划（No. 181722KYSB20200001）；国家自然科学基金（No. 11973040）

详细信息

作者简介:
张奔雷（1997—），男，山东曹县人，硕士研究生，2019年于中原工学院获得学士学位，主要从事大口径地基望远镜光机结构优化设计方面的研究。E-mail：zhangbenleiii@163.com

杨　飞（1982—），男，博士，研究员，博士生导师，2009年于中国科学院长春光学精密机械与物理研究所获得硕士学位，2017年于长春理工大学获得博士学位，现主要从事大口径光学工程技术的光机系统研究。E-mail：yangflying@163.com

中图分类号: TH751
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出版历程
- 收稿日期: 2022-06-11
- 修回日期: 2022-06-28
- 网络出版日期: 2022-08-03

Integrated optimization design of mirror semi-active support system based on Warping Harness

ZHANG Ben-lei^{1, 2
,},
YANG Fei^{1
, ,},
WANG Fu-guo¹,
LU Bao-wei^{1, 2}

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Supported by Science and Technology Development Program of Jilin Province (No. 20210402065GH); Excellent Member of Youth Innovation Promotion Association, CAS (No. Y202053); International Partnership Program of the Chinese Academy of Sciences (No. 181722KYSB20200001); National Natural Science Foundation of China (NSFC) (No. 11973040)

More Information

Corresponding author: yangflying@163.com

摘要

摘要:
基于半主动光学技术的半主动支撑，通过力矩促动器(Warping Harness, WH)弹簧叶片将校正力转换为校正力矩，对由重力、温度等误差源引入的镜面低阶像差进行校正。针对利用传统经验设计反射镜时存在的设计缺陷，提出一种反射镜支撑系统优化设计新方法，即结合结构尺寸优化和经验设计的镜面支撑系统综合设计优化方法，并建立一套基于WH 的半主动镜面支撑系统。首先，按照经验公式设计了支撑系统初始结构；设计了一款L形镂空式WH弹簧叶片，并对其开展了非线性分析及疲劳分析，确定叶片厚度为2 mm、寿命为1.2×10⁶次。然后，通过优化镜面支撑点位置、三角板柔节位置、支撑系统柔性件关键尺寸参数，将光轴竖直及水平状态下镜面RMS值由119 nm和106 nm分别降至13.3 nm和4.8 nm；1 °C温差状态下镜面面形差由2.8 nm降至1.9 nm；一阶谐振频率由80 Hz提升至130 Hz。最后，采用提出的方法对半主动支撑系统的校正能力进行验证。结果表明：本套半主动支撑系统对镜面离焦、初级像散、初级慧差、初级球差的校正率最高可达99%，且校正后各像差幅值均小于1 nm；室温自重状态下对镜面面形RMS值校正率最高可达46.5%；温升10°C情况下的校正率为31.28%。
- 支撑系统 /
- 集成优化 /
- 半主动光学 /
- 力矩促动器 /
- 低阶像差
Abstract:
The semi-active support is based on the semi-active optical technology, and the correction force is converted into a correction torque through a Warping Harness(WH) spring blade to correct the mirror low-order aberration introduced by error sources such as gravity and temperature. Aiming at the defects of traditional empirical design of mirrors, a new optimal design method for a mirror support system is proposed, that is, a comprehensive design optimization method of mirror support system based on structural size optimization combined with empirical design, and a set of semi-active mirror support systems based on WH is established. Firstly, the initial structure of the support system is designed according to the empirical formula; an L-shaped hollow WH spring blade is designed, and the nonlinear analysis and fatigue analysis are carried out to determine that the blade thickness is 2 mm and the service life is 1.2×10⁶ times. Then, the RMS value of the mirror surface in the vertical and horizontal states of the optical axis was reduced from 119 nm and 106 nm to 13.3 nm and 4.8 nm by optimizing the position of the mirror support point, the position of the triangular plate flexure joint, and the key dimension parameters of the support system’s flexible parts; under the state of 1 °C temperature difference, the specular aberration is reduced from 2.8 nm to 1.9 nm; the first-order resonance frequency is increased from 80 Hz to 130 Hz. Finally, this method is used to verify the correction ability of the semi-active support system. The results show that the correction rate of the semi-active support system for mirror defocus, primary astigmatism, primary coma and primary spherical aberration can reach up to 99%. The amplitude of each aberration is less than 1 nm; the correction rate of the RMS value of the mirror’s surface shape can reach up to 46.5% under it′s own weight state at room temperature, and the correction rate is 31.28%.
- support system /
- integration optimization /
- semi-active optics /
- Warping Harness /
- low-order aberrations

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图 1 9个支撑点的Whiffletree支撑结构

Figure 1. Whiffletree support structure of the mirror with 9 support points

下载: 全尺寸图片幻灯片

图 2 镜面侧向定位方案

Figure 2. Lateral positioning scheme of the primary mirror

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图 3 支撑系统柔性件结构

Figure 3. Diagram structure of the flexible parts of the support system

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图 4 三角板结构设计

Figure 4. Triangle plate structure design

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图 5 镜室结构设计

Figure 5. Mirror chamber structure design

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图 6 WH弹簧叶片结构设计

Figure 6. Structure design of WH spring blade

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图 7 WH弹簧片位移线性分析

Figure 7. Linear analysis of the displacement of the WH spring blade

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图 8 WH弹簧叶片应力分析

Figure 8. Stress analysis of the WH spring blade

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图 9 支撑点位置优化前后镜面变形对比

Figure 9. Comparison of mirror deformation before and after optimization of the support point position

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图 10 3种工况下优化前（上）后（下）镜面变形图

Figure 10. Specular deformation diagrams before (top) and after (bottom) optimization under three working conditions

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图 11 镜面支撑系统三维图

Figure 11. 3D view of the mirror support system

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图 12 镜面系统有限元模型

Figure 12. Finite element model of the mirror system

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图 13 校正力与镜面像差影响分析平台

Figure 13. Correction force and mirror aberration impact analysis platform

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图 14 各校正力相对Zernike 4~11阶像差Pareto图

Figure 14. Pareto diagrams of the 4^th to 11^th order Zernike aberrations for each correction force

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图 15 半主动支撑系统俯仰过程中镜面各像差校正前后对比及校正率图

Figure 15. Comparison before and after correction and their correction rate of each aberration of the mirror surface during the pitching process of the semi-active support system

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图 16 镜面面形与俯仰角度关系图

Figure 16. The relationship between mirror surface shape and pitch angle

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图 17 俯仰过程中镜面校正前（上）后（下）云图

Figure 17. Cloud maps before (top) and after (bottom) mirror correction during pitching

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图 18 10 °C温升状态下镜面面形校正前（左）后（右）变形云图

Figure 18. Deformation cloud diagrams of the mirror’s surface shapes before (left) and after (right) correction under a 10°C temperature rise

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表 1 镜面参数

Table 1. Primary mirror parameters

参数	指标
口径d/mm	500.00
焦距f/mm	6000.00
密度(g/cm^-3)	2.53
弹性模量GPa	91.00
泊松比	0.24
热膨胀系数(10⁻⁶/K)	0.05

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表 2 各柔性件截面积计算结果

Table 2. Calculation results of the cross-sectional area of each flexible part

类别	F/N	L/mm	A_min/mm²
轴向柔性杆	12	48	0.0014
三角板柔节	50	28	0.0011
侧向柔性杆	58	42	0.0020

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表 3 支撑点位置优化结果

Table 3. Optimization results of the support point position

项目	参数
R₁/mm	68.3
R₀/mm	206.5
PV/nm	52.7
RMS/nm	12.0

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表 4 支撑柔性件结构尺寸最优解

Table 4. The optimal solution for the structural size of the supporting flexible parts

项目	参数
H/mm	2.9
R_z/mm	1.4
R_c/mm	0.5
RMS_x/nm	4.8
RMS_z/nm	13.3
RMS_t/nm	1.9

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表 5 柔性杆轴及侧向解耦结果

Table 5. Flexible rod axis and lateral decoupling results

项目	参数
R_轴/mm	1.4
R_侧/mm	0.50
S_轴轴/mm	0.00030
S_轴侧/mm	0.067
S_侧/mm	0.014
满足耦合	满足

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表 6 30 °C时镜面面形校正前后对比

Table 6. Comparison of mirror surface shapes before and after correction at 30°C

Temp_30°C	Before/nm	After/nm	correct
RMS	19.2	13.2	31.28%
Power	−13.8	−0.382	97.23%
Astig0°	−0.588	−0.0783	86.68%
Astig90°	0.0998	0.0680	31.86%
Coma0°	−0.0211	−0.0268	−27.01%
Coma90°	−0.00346	−0.0466	−1246.82%
Primary spherical	−2.43	−0.981	59.63%
Trefoil0°	−12.8	−12.4	3.13%
Trefoil90°	−1.43	−3.45	−141.26%

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表 7 镜室组件前四阶谐振频率

Table 7. The first four-order resonance frequencies of the mirror chamber assembly

阶数	1	2	3	4
频率/Hz	130.5	132.7	199.7	203.3

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