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Analysis of curvature radius adjustment capability of large aperture ULE segmented mirror
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摘要
针对未来大口径分块光学系统在轨变构重构问题，提出一种大范围曲率可调的轻量化设计方法。首先分析了压电陶瓷材料特性与热应变本构方程之间的关系，推导出压电应变可以由热应变精确等效，并根据挠性曲线方程解算出压电陶瓷变形量，由此实现对边距离为510 mm、曲率半径为9000 mm的ULE (ultra low expansion glass)分块镜参数化建模。仿真结果表明：54个交错式促动器在±20 V控制电压区间可实现分块镜曲率半径变构240.07 mm且呈高度线性变化关系。相关实验结果表明：控制电压在-25~20 V区间变化时，分块镜曲率半径变化量达223.44 mm，并且正向单位电压对应曲率半径变化量较负向大。本文提出的大范围曲率可调分块镜可为后续大口径分块光学在轨变构重构的工程化应用提供新的思路。
Abstract
In response to the on-orbit reconfiguration challenges faced by future large aperture segmented optical systems, a lightweight design method with a wide range of curvature adjustability is proposed. This study initially analyzes the relationship between the characteristics of piezoelectric ceramics and the constitutive equations of thermal strain, deducing that piezoelectric strain can be precisely equivalent to thermal strain. Based on the flexural curve equation, the deformation of piezoelectric ceramics is calculated, enabling the parameterized modeling of an ultra-low expansion (ULE) glass segmented mirror with an edge distance of 510 mm and a curvature radius of 9000 mm. Simulation results indicate that 54 interlaced actuators can achieve a curvature radius reconfiguration of 240.07 mm with a control voltage range of ±20 V, exhibiting a highly linear relationship. Experimental results further demonstrate that when the control voltage is varied between -25 V and 20 V, the change in the curvature radius of the segmented mirror reaches 233.44 mm, with the positive unit voltage corresponding to a greater change in curvature radius than the negative. The proposed method for a wide range of curvature adjustable segmented mirrors provides new insights for the engineering application of large aperture segmented optics in on-orbit reconfiguration.
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Key words:
- segmented mirror /
- curvature radius /
- piezoelectric ceramics /
- actuator /
- active control
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Overview
Overview: With the increasing trend of global space resource development and the intensification of future space warfare, particularly the establishment of the Space Force by the United States in 2018, space is poised to become a new battlefield. Future large-scale space optical facilities for military applications face greater threats of being targeted and destroyed in warfare. There is an urgent need for large optical imaging systems to enhance their resistance to damage and their ability to be reconstructed after being hit. Additionally, traditional space optical facilities have singular and non-adjustable in-orbit detection functions, which can no longer meet the growing diverse needs of users. There is an urgent need to develop a new type of reconfigurable space optical system capable of in-orbit adjustment and detection.
This paper adopts a design concept of adjustable parameters for single modules and variable shapes for multiple modules. Focusing on the problem of in-orbit reconfiguration of large-aperture segmented optical systems, we propose a lightweight design method with a wide range of curvature adjustability. We first analyzed the relationship between the characteristics of piezoelectric ceramic materials and the constitutive equation of thermal strain, deriving that piezoelectric strain can be precisely equivalent to thermal strain. Based on this, we achieved parameterized modeling of the ULE (ultra low expansion glass) segmented mirror with a side distance of 510 mm and an initial radius of curvature of 9000 mm. Simulation results show that 54 interleaved actuators can achieve a change in the radius of curvature of the segmented mirror by 240.07 mm within a control voltage range of ±20 V, exhibiting a highly linear relationship.
To fully verify the analysis results and achieve engineering application transformation, experimental results indicate that when the control voltage varies within the range of -25 V to 20 V, the change in the radius of curvature of the segmented mirror reaches 223.44 mm, with the positive unit voltage corresponding to a larger change in the radius of curvature than the negative. The proposed design method for a large-range curvature-adjustable segmented mirror has been verified through simulation and experiment to achieve a reconfiguration range of more than 100 mm in the radius of curvature. This provides new ideas for the engineering application of large-aperture segmented optics in in-orbit reconfiguration.
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图 3 简支梁增加转动弹簧边界条件
Figure 3. Schematic diagram of a simply supported beam with a rotational spring
图 4 分块镜模型图。(a) 分块镜有限元模型; (b) 分块镜三维模型
Figure 4. Segmented mirror model diagrams. (a) Finite element model; (b) Three-dimensional model
图 5 不同控制电压下的曲率半径仿真图。 (a) 5 V控制电压下dROC=−33.57 mm; (b) 10 V控制电压下dROC=−66.46 mm; (c) 15 V控制电压下dROC=−99.43 mm; (d) 20 V控制电压下dROC=−132.28 mm; (e) −5 V控制电压下dROC=27.59 mm; (f) −10 V控制电压下dROC=54.55 mm; (g) −15 V控制电压下dROC=82.61 mm; (h) −20 V控制电压下dROC=109.79 mm
Figure 5. Simulation diagrams of curvature radius under different control voltages. (a) At 5 V control voltage, dROC =−33.57 mm; (b) At 10 V control voltage, dROC =−66.46 mm; (c) At 15 V control voltage, dROC =−99.43 mm; (d) At 20 V control voltage, dROC =−132.28 mm; (e) At −5 V control voltage, dROC =27.59 mm; (f) At −10 V control voltage, dROC =54.55 mm; (g) At -15 V control voltage, dROC =82.61 mm; (h) At −20 V control voltage, dROC =109.79 mm
图 8 分块镜曲率半径实测结果。(a) 实测曲率半径变化曲线; (b) 单位控制电压对应曲率半径变化曲线
Figure 8. Measure curvature radius results of the segmented mirror. (a) Measured curves of radius of curvature variation; (b) Curves of radius of curvature variation per unit control voltage
表 1 分块镜建模相关参数
Table 1. Segmented mirror modeling parameters
Material Edge to edge Curvature radius Mirror surface thickness Actuator count Reinforcement rib thickness Edge rib thickness Actuator height ULE 510 mm 9000 mm 4 mm 54 2.5 mm 3 mm 29.6 mm 
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表 2 压电陶瓷属性参数
Table 2. Piezoelectric ceramic property parameters
Property Density
ρ/(g·cm−3)Elastic modulus
E/GPaPoisson
ratio υCTE
/(10−6·℃−1)Value 8 25 0.2 2
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表 3 不同控制电压下曲率半径变化结果
Table 3. Results of curvature radius variations under different control voltages
Control voltage/V Curvature radius/mm Curvature radius variations per unit control voltage/mm 20 8867.72 −6.61 15 8900.57 −6.63 10 8933.54 −6.65 5 8966.43 −6.71 0 9000.00 — −5 9027.59 5.52 −10 9054.55 5.46 −15 9081.61 5.44 −20 9107.79 5.39
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表 4 分块镜曲率半径测试结果
Table 4. Results of curvature radius testing for the segmented mirror
Control voltage/V Curvature radius/mm Curvature radius variations corresponding to unit control voltage/mm 20 8891.58 5.51 10 8953.82 4.80 0 9001.83 — −10 9036.19 3.44 −20 9086.40 4.23 −25 9115.02 4.53
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