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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
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Design and thermal stability analysis of primary mirror assembly for space-borne gravitational wave telescope
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Abstract
In order to meet the application requirements of pimi-level stability and λ/30 wavefront error in space gravitational wave detection, an optical and mechanical integrated analysis and optimization method is proposed. Firstly, the position analysis of the support points on the main mirror side and the topology optimization of the support structure were carried out. Then, based on the flexibility matrix of parallel Bipod linkage support, the evaluation function of each structure parameter is established, and the value range of flexible support size parameters was preliminarily determined by Matlab analysis. Finally, an integrated optical and mechanical simulation platform was built to further optimize the structure.The results show that the first-order frequency of the system is 392.23 Hz, and the deformation of the primary mirror surface deformation under gravity and temperature loads is better than λ/60. Under thermal disturbances in a space environment of 10 μK/Hz1/2, the dimensional stability of the primary mirror component is at a level of 10 pm/Hz1/2. -
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References
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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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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
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Figure 1.
Schematic diagram of the telescope system. (a) Telescope optical system; (b) Primary mirror assembly
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Figure 2.
Primary mirror lightweight model. (a) Support point layout; (b) Rib plate parameters; (c) Mirror thickness
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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
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Figure 4.
Topology optimization results of the backplane. (a) Initial backplane; (b) Topological result; (c) Optimized backplane
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Figure 5.
Stress-strain diagram of the beam element
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Figure 6.
Parameters of the flexible legs
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Figure 7.
Schematic diagram of a single Bipod flexible support
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Figure 8.
Schematic diagram of primary mirror’s flexible support
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Figure 9.
Influence of structural parameters on the evaluation function
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Figure 10.
The structure of the primary mirror assembly is deformed. (a) Finite element model; (b) Gravity condition; (c) Temperature condition; (d) Superposition condition
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Figure 11.
Surface error of the primary mirror. (a) Gravity condition; (b) Temperature condition; (c) Superposition condition
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Figure 12.
Structural stability of primary mirror assembly. (a) Temperature stability of the environment; (b) Dimensional stability of structure
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