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超大口径弯月镜支撑点布局-刚度-校正力联合优化

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文章导航 > 光电工程 > 2020 Vol. 47 > No. 8 > 190551

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习兴华，张超杰，胡海飞，等. 超大口径弯月镜支撑点布局-刚度-校正力联合优化[J]. 光电工程，2020，47(8)：190551. doi: 10.12086/oee.2020.190551
引用本文: 习兴华，张超杰，胡海飞，等. 超大口径弯月镜支撑点布局-刚度-校正力联合优化[J]. 光电工程，2020，47(8)：190551. doi: 10.12086/oee.2020.190551
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Xi X H, Zhang C J, Hu H F, et al. Layout-stiffness-correction force joint optimization of support system for ultra-large thin meniscus mirror[J]. Opto-Electron Eng, 2020, 47(8): 190551. doi: 10.12086/oee.2020.190551
Citation: Xi X H, Zhang C J, Hu H F, et al. Layout-stiffness-correction force joint optimization of support system for ultra-large thin meniscus mirror[J]. Opto-Electron Eng, 2020, 47(8): 190551. doi: 10.12086/oee.2020.190551
shu

超大口径弯月镜支撑点布局-刚度-校正力联合优化

    • 1.

      长春工业大学机电工程学院，吉林 长春 130012

    • 2.

      中国科学院长春光学精密机械与物理研究所，吉林 长春 130033

    • 3.

      吉林大学机械与航空航天工程学院，吉林 长春130025

  • 基金项目:
    国家自然科学基金资助项目(11873007)；中央引导地方科技发展基金(202002035JC)
详细信息
    作者简介:
  • 习兴华(1994-)，男，硕士研究生，主要从事空间光学遥感器结构优化设计方面的研究。E-mail：1973038493@qq.com
    • 通讯作者: 关英俊(1978-)，男，博士，教授，博士生导师，主要从事空间光学遥感器结构优化设计方面的研究。E-mail：gyj5460@sohu.com

  • 中图分类号: TH751; TH74

Layout-stiffness-correction force joint optimization of support system for ultra-large thin meniscus mirror

    • 1.

      School of Mechanical and Electrical Engineering, Changchun University of Technology, Changchun, Jilin 130012, China

    • 2.

      Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China

    • 3.

      School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin 130025, China

  • Fund Project: Supported by National Natural Science Foundation of China (11873007) and Central Guiding Local Science and Technology Development Fund (202002035JC)
More Information

    摘要

  • 在超大口径原位加工与检测中，目前多采用被动式Whiffletree液压支撑系统(原位支撑)，而该类支撑单元的轴向刚度存在较大差异性，会显著影响轻薄型反射镜的面形精度。为解决这一问题，研究了主动型原位支撑的支点布局、单元刚度和主动校正力的联合优化方法。首先，针对支撑单元刚度差异，提出了支撑刚度、支点位置的分级布局优化方法，获得了支撑系统的初始优化解; 其次，结合模式定标法和最小二乘法，进行了支撑点主动力校正，以获得支撑面形的最终优化解; 最后，结合具体案例的数字仿真试验，验证了方法的有效性。结果表明：对于4 m弯月型轻薄反射镜，仅被动支撑下，分级布局优化后，60点方案面形精度RMS值由150.6 nm减少到32.9 nm，78点方案面形精度RMS值由45.2 nm减少到22.6 nm，优化效果显著; 进一步经主动校正后，60点方案和78点方案面形精度RMS值分别为14.6 nm和6.9 nm，均满足面形精度RMS值小于λ/40(λ=632.8 nm)的指标要求; 最终选取60点轴向支撑方案。通过对支点布局、支撑刚度和校正力进行联合优化，可以大幅增加原位支撑系统的适用性、灵活性，降低实施难度。

    Passive hydraulic support units (PHSUs) are frequently used in the in-situ fabrication and testing (in-situ support). However, the difference in PHSUs' stiffness will affect the mirror surface figure, especially for those thin meniscus mirrors. In order to solve this problem, the joint optimization method of layout, stiffness and active correction is studied. Firstly, for the difference of PHUS' stiffness, a hierarchical layout optimization method for support stiffness and support position is proposed to obtain the initial optimization solution of the support system. Then, the mode calibration method and the least square method is used for active correction of support system to obtain the final optimized solution of the mirror surface figure. Finally, the effectiveness of the method is verified by a numerical simulation experiment with specific cases. The results show that, for 4 m thin meniscus mirror, after layout optimization, with the hydraulic passive support system, the root mean square (RMS) of the mirror surface errors of 60 point axial support system is reduced from 150.6 nm to 32.9 nm, and the RMS value of the mirror surface errors of 78 point axial support system is reduced from 45.2 nm to 22.6 nm. The optimization effect is remarkable. After active correction, the RMS value of the mirror surface errors of 60 point axial support system is 14.6 nm, and it is 6.9 nm for 78 point axial support system. The requirement of the RMS value of the mirror surface error is less than λ/40 (λ=632.8 nm). The support systems meet the requirement. Finally, the 60 point axial support system was selected. Through the joint optimization of layout, stiffness and active correction for supporting points, it can greatly increase the applicability, flexibility and reduce the difficulty of implementation for the in-situ support system.

    • Overview

  • Overview: With the increasing requirements for the sensitivity, resolution and angle of view of space telescopes, the aperture of space mirror are getting bigger and bigger, which greatly increases the difficulty of mirror fabrication support. For the space mirror in the in-situ fabrication and testing, besides the influence of other factors such as temperature, the self-weight deformation has a great influence on mirror surface figure. And the larger the aperture and the higher the precision, the more difficult the support is. The self-weight deformation is mainly affected by factors such as the number of support points, the position of the support points and the stiffness of the support unit. Passive hydraulic support units (PHSUs) are frequently used in the in-situ fabrication and testing. However, some studies have found that the number of supporting units of large-aperture mirrors is too large, resulting in a large difference in the stiffness of each group of hydraulic support units, and has a great influence on mirror surface figure. It has become a hidden danger affecting the accuracy of in-situ fabrication and testing. In order to reduce the number of supporting units and increase the accuracy of the supporting surface, the joint optimization method of layout, stiffness and active correction is studied. Firstly, for the difference of PHUS' stiffness, a hierarchical layout optimization method for support stiffness and support position is proposed to obtain the initial optimization solution of the support system. Then, the mode calibration method and the least square method is used for active correction of support system to obtain the final optimized solution of the mirror surface figure. Finally, the effectiveness of the method is verified by a numerical simulation experiment with specific cases. The results show that, for 4 m thin meniscus mirror, after layout optimization, with the hydraulic passive support system, the root mean square (RMS) of the mirror surface errors of 60 point axial support system is reduced from 150.6 nm to 32.9 nm, and the RMS value of the mirror surface errors of 78 point axial support system is reduced from 45.2 nm to 22.6 nm. The optimization effect is remarkable. After active correction, the RMS value of the mirror surface errors of 60 point axial support system is 14.6 nm, and it is 6.9 nm for 78 point axial support system. The requirement of the RMS value of the mirror surface error is less than λ/40 (λ=632.8 nm). The support systems meet the requirement. Finally, the 60 point axial support system was selected. Through the joint optimization of layout, stiffness and active correction for supporting points, it can greatly increase the applicability, flexibility and reduce the difficulty of implementation for the in-situ support system.

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  • 图 1  支撑系统优化流程图

    Figure 1.  Optimization flow for support system

    下载: 全尺寸图片 幻灯片

    图 2  两种方案轴向支撑点布局示意图。

    Figure 2.  Schematic diagram of axial layout of two schemes.

    下载: 全尺寸图片 幻灯片

    图 3  反射镜前20阶模态振型

    Figure 3.  The first twenty vibration modes of the mirror

    下载: 全尺寸图片 幻灯片

    图 4  主动校正后面形。

    Figure 4.  Mirror deformations after active corrections.

    下载: 全尺寸图片 幻灯片

    表 1  各支撑方案自重变形下面形精度

    Table 1.  The mirror surface RMS values of each support system from the gravity

    Support points 60 66 78 84
    RMS/nm 78.3 74.1 39.3 39.2
    下载: 导出CSV

    表 2  60点轴向支撑系统布局优化结果

    Table 2.  Results of layout optimization for 60 point axial support system

    60points K1/(N/mm) K2/(N/mm) K3/(N/mm) K4/(N/mm) R1/mm R2/mm R3/mm R4/mm PV/nm RMS/nm
    Before 2002 1918 1978 1935 465 910 1315 1780 633.0 150.6
    After 1978 1918 2002 1890 471 921 1355 1818 169.0 32.9
    下载: 导出CSV

    表 3  78点轴向支撑系统布局优化结果

    Table 3.  Results of layout optimization for 78 point axial support system

    78 points K1/(N/mm) K2/(N/mm) K3/(N/mm) K4/(N/mm) K5/(N/mm) R1/mm R2/mm R3/mm R4/mm R5/mm PV/nm RMS/nm
    Before 1890 2002 1918 1978 1935 425 775 1125 1475 1825 300.0 45.2
    After 1935 1978 2002 1918 1890 412 756 1135 1468 1826 120.6 22.6
    下载: 导出CSV

    表 4  60点支撑方案模式定标计算结果

    Table 4.  Results of mode calibration for 60 point axial support system

    Mode F1max/N F2max/N F3max/N F4max/N SRMS/nm
    1 -0.5 1.3 -3.2 5.6 1000
    2 -0.2 -2.1 5.9 15.5 1000
    3 0.1 -3.1 -14.5 40.1 999
    4 -0.04 -4.2 -27.2 90.4 1000
    5 0.007 4.7 -39.0 -126.6 1000
    6 1221.0 693.85 66.9 -701.9 999
    7 185.8 233.5 117.9 -137.4 999
    8 -156.2 257.0 -180.2 115.51 999
    9 -305.6 69.4 181.9 -94.1 999
    10 -0.2 4.2 69.8 -312.9 1000
    11 48.7 341.2 376.7 -148.7 1000
    12 -609.3 163.4 392.8 -136.8 999
    13 -0.08 -3.33 94.7 492.5 999
    14 21.3 -74.7 -646.8 200.4 999
    15 708.1 -510.3 614.5 -179.8 999
    16 502.3 -705.9 436.0 -99.1 999
    17 -0.6 1.7 124.2 723.5 1000
    18 -7.5 -438.9 1080.0 -268.2 1000
    19 625.2 934.3 -741.2 -147.4 999
    20 -1578.0 1157.3 -506.9 -91.1 999
    下载: 导出CSV
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收稿日期:  2019-09-19
修回日期:  2020-01-09
刊出日期:  2020-08-01

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