空间引力波望远镜主镜组件结构设计及热稳定性分析

房思俊,李博宏,何斌,等. 空间引力波望远镜主镜组件结构设计及热稳定性分析[J]. 光电工程,2024,51(2): 230157. doi: 10.12086/oee.2024.230157
引用本文: 房思俊,李博宏,何斌,等. 空间引力波望远镜主镜组件结构设计及热稳定性分析[J]. 光电工程,2024,51(2): 230157. doi: 10.12086/oee.2024.230157
Fang S J, Li B H, He B, et al. Design and thermal stability analysis of primary mirror assembly for space-borne gravitational wave telescope[J]. Opto-Electron Eng, 2024, 51(2): 230157. doi: 10.12086/oee.2024.230157
Citation: Fang S J, Li B H, He B, et al. Design and thermal stability analysis of primary mirror assembly for space-borne gravitational wave telescope[J]. Opto-Electron Eng, 2024, 51(2): 230157. doi: 10.12086/oee.2024.230157

空间引力波望远镜主镜组件结构设计及热稳定性分析

  • 基金项目:
    国家重点研发计划(2021YFC2202202,2021YFC2202204,2022YFC2203801)
详细信息
    作者简介:
    *通讯作者: 范磊,fanlei6@mail.sysu.edu.cn
  • 中图分类号: O439

Design and thermal stability analysis of primary mirror assembly for space-borne gravitational wave telescope

  • Fund Project: Project supported by National Key Research and Development Program of China (2021YFC2202202, 2021YFC2202204, 2022YFC2203801)
More Information
  • 针对空间引力波探测对望远镜系统提出的皮米级稳定性和λ/30波前误差的应用需求,提出了一种光机集成分析与优化方法。首先开展了主镜侧支撑点位置分析和支撑结构拓扑优化;然后基于并联Bipod连杆支撑的柔度矩阵,建立了各结构参数的评价函数,并通过Matlab分析初步确定柔性支撑尺寸参数取值范围;最后,搭建了光机集成仿真平台对结构进一步优化。结果表明,系统一阶频率为392.43 Hz,重力和温度载荷下主镜面形变化优于λ/60;在10 μK/Hz1/2的空间热扰动下,主镜组件尺寸稳定性在10 pm/Hz1/2水平。

  • Overview: Space gravitational wave detection missions typically consist of three identical satellites, with two laser links between the satellites at an angle of sixty degrees forming a Michelson interferometer. The arm length changes are measured using high-precision inter-satellite laser interferometry. As a key component of the inter-satellite laser interferometry system, the telescope system needs to have picometer-level optical path stability, a wavefront error of λ/30, and stray light less than 10−10 of the transmitted power. To meet the requirements of space gravitational wave detection for the telescope system, an optical and mechanical integrated analysis and optimization method is proposed to design and optimize the primary mirror and its supporting structure. The off-axis parabolic primary mirror adopts the side three-point support method, and the influence of the support point position on the mirror surface shape and the rigid body displacement under gravity conditions has been studied. Optimization of the size of the triangular lightweighting holes on the primary mirror has been performed, and density-based topology optimization has been used to optimize the support backplate while ensuring that the first-order mode of the primary mirror component remains essentially unchanged. The flexural matrix of the primary mirror component supported by a parallel bipod linkage structure was derived based on spinor theory, and an evaluation function for the support structure was established. The size parameter range of flexible support was preliminarily determined by Matlab analysis. A optical-mechanical integrated simulation platform is set up to optimize the parameters of the support structure using a weighted sum method to convert the multi-objective optimization problem into a single-objective optimization problem. The results showed that the first-order frequency of the primary mirror component system was 392.43 Hz. Under gravity and temperature loads, the deformation of the primary mirror surface was better than λ/60, the translational rigid body displacement was better than 2.5 μm, and the rotational rigid body displacement was better than 0.5 μrad, all of which met the design specifications. Under space thermal disturbance of 10 μK/Hz1/2, the size stability of the primary mirror component, represented by the displacement of the central point of the mirror, was at a level of 10 pm/Hz1/2.

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  • 图 1  望远镜系统示意图。(a) 望远镜光学系统[6];(b) 主镜组件

    Figure 1.  Schematic diagram of the telescope system. (a) Telescope optical system; (b) Primary mirror assembly

    图 2  主镜轻量化模型。(a) 支撑点布局;(b) 筋板参数;(c) 镜面厚度

    Figure 2.  Primary mirror lightweight model. (a) Support point layout; (b) Rib plate parameters; (c) Mirror thickness

    图 3  不同重力方向下支撑顶角与面形和刚体位移关系。(a) X方向重力作用;(b) Y方向重力作用

    Figure 3.  Relation between top angle of support and surface shape and rigid body displacement under different gravity directions. (a) Gravity force in the X-direction; (b) Gravity force in the Y-direction

    图 4  背板拓扑优化结果。(a)初始背板;(b) 拓扑结果;(c) 优化后背板

    Figure 4.  Topology optimization results of the backplane. (a) Initial backplane; (b) Topological result; (c) Optimized backplane

    图 5  梁单元应力应变示意

    Figure 5.  Stress-strain diagram of the beam element

    图 6  柔性支腿参数

    Figure 6.  Parameters of the flexible legs

    图 7  单个Bipod柔性支撑示意

    Figure 7.  Schematic diagram of a single Bipod flexible support

    图 8  主镜组件柔性支撑示意

    Figure 8.  Schematic diagram of primary mirror’s flexible support

    图 9  结构参数对评价函数影响

    Figure 9.  Influence of structural parameters on the evaluation function

    图 10  主镜组件结构变形。(a)有限元模型;(b)重力工况;(c) 温度工况;(d) 叠加工况

    Figure 10.  The structure of the primary mirror assembly is deformed. (a) Finite element model; (b) Gravity condition; (c) Temperature condition; (d) Superposition condition

    图 11  主镜面形误差。(a)重力工况;(b) 温度工况;(c) 叠加工况

    Figure 11.  Surface error of the primary mirror. (a) Gravity condition; (b) Temperature condition; (c) Superposition condition

    图 12  主镜组件结构尺寸稳定性。(a) 环境温度波动;(b) 结构尺寸稳定性

    Figure 12.  Structural stability of primary mirror assembly. (a) Temperature stability of the environment; (b) Dimensional stability of structure

    表 1  主镜组件材料属性

    Table 1.  Properties of primary mirror component materials

    MatericalsZerodur4J36TC4
    Density/(g·cm3)2.538.904.44
    Poisson ratio0.240.250.34
    Young's modulus /GPa90.3141109
    CTE/(10−6·K−1)0.010.659.10
    Thermal conductivity/(W·m−1·K−1)1.3113.76.8
    下载: 导出CSV

    表 2  主镜轻量化筋参数

    Table 2.  The parameters of the lightweight primary mirror

    NameEdge thicknessRoof thicknessRib thicknessRib spacing
    Parmhcehpmljinlju
    Range/mm[6, 10][7, 9][4, 7][54, 66]
    Value/mm88560
    下载: 导出CSV

    表 3  参数优化结果

    Table 3.  The parameters of the lightweight primary mirror

    Parml1l2l3l4t1t2w1w2
    Range/mm[6, 10][5, 14][5, 14][1, 4][1, 3][0.5, 2][8, 14][8, 14]
    Value/mm8962211010
    下载: 导出CSV

    表 4  主镜组件模态分析

    Table 4.  Modal analysis of primary mirror components

    Mode 1Mode 2Mode 3Mode 4Mode 5Mode 6
    Frequency/Hz392.43394.83722.33770.50927.36994.01
    下载: 导出CSV

    表 5  主镜组件分析结果

    Table 5.  Primary mirror component analysis results

    TXTYTZRXRYRMS
    Requirement≤5 μm≤5 μm≤5 μm≤2.5 μrad≤2.5 μrad15 nm
    G−4.91 nm−1.59 μm−2.404 nm −36.3 nrad6.64 nrad5.47 nm
    T−0.423 nm−1.84 nm−0.714 μm−83.8 nrad21.9 nrad3.63 nm
    G+T−5.34 nm−1.60 μm−0.717 μm−0.120 μrad28.6 nrad3.61 nm
    下载: 导出CSV
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出版历程
收稿日期:  2023-06-30
修回日期:  2023-10-09
录用日期:  2023-10-10
刊出日期:  2024-02-29

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