Structural optimization for the design of an ultra-lightweight SiC mirror with a diameter of 500 mm
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摘要: 为满足超轻量化光学系统近衍射极限的性能要求，利用先进的CAE仿真与现代高性能SiC制作工艺，研究Φ500 mm SiC反射镜的超轻量化反射镜结构。首先，通过对比现有反射镜常用材料和制作工艺，选取反射镜材料。针对圆形对称反射镜结构特性，采用全等刚度设计，结合集成优化方法，设计反射镜结构形式。同时，采用背部支撑结构，完成反射镜组件结构设计。仿真结果表明：主镜质量小于5 kg，面密度小于20 kg/m2。3个方向自重变形下及4 ℃温升工况下的面形误差（RMS值）均优于λ/50；主镜组件的一阶谐振频率不小于120 Hz，动态响应分析表明最薄弱处应力小于100 MPa。满足反射镜设计要求，轻量化效果显著，结构稳定可靠。Abstract: To meet the performance requirements of ultra-lightweight Φ500 mm-reflector optical system in near diffraction limit, the structure of the reflector is studied using advanced CAE simulation and modern high-performance SiC fabrication technology. Firstly, mirror materials were selected by comparing the common materials and manufacturing processes of existing mirrors. Then, with regards to the structural characteristics of circular symmetrical reflectors, the structure of proposed reflector was designed based on integrated optimization of the full stiffness method. Finally, the reflector assembly was designed with a back-support structure. The simulation results show that the mass of proposed primary mirror is less than 5 kg and the surface density is less than 20 kg/m2. The surface errors (RMS value) of the three directions of dead weight deformation at 4 ℃ temperature rise are less than λ/50. The first-order resonance frequency of the primary mirror assembly is no less than 120 Hz and the stress at the weakest point as measured by dynamic response analysis is less than 100 MPa. The structural optimization of the mirror meets its design requirements, with a remarkable lightweight effect and a structure that is both stable and reliable.
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图 10 主镜组件前6阶振型图。（a）~（f）分别是1~6阶振型
Figure 10. The first six order mode shapes of the subassembly. (a)~(f) are the 1st to 6th modes in order
图 11 Y向（a）和Z向（b）加速度频率响应曲线
Figure 11. Acceleration frequency response curves in (a) Y and (b) Z directions
图 14 重力方向翻转180°后镜面干涉仪检测图
Figure 14. Mirror interferogram inspection results by gravity fliping 180°
表 1 优化结果
Table 1. Optimized results
Variable Domain Original Optimized 1/mm 2≤(1)≤2.5 3 2 2/ mm 2≤(2)≤2.5 4 2 3/ mm 2≤(3)≤5 5 4 4/ mm 5≤(4)≤20 10 15 5/ mm 2≤(5)≤4 4 3 6/ mm −10≤(6)≤50 0 25 7/ mm −30≤(7)≤20 0 −6 8/ mm −50≤(8)≤20 0 −48 Mass/kg − 8.763 3.26 $ {\mathrm{R}\mathrm{M}\mathrm{S}}_{Y} $/nm − 5.436 6.368 $ {\mathrm{R}\mathrm{M}\mathrm{S}}_{Z} $/nm − 25.784 4.421 
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表 2 反射镜组件面形精度分析结果
Table 2. Analysis results of mirror surface precision
载荷工况 PV/nm RMS/nm 转角/″ 线位移/μm 重力_X 27.565 4.672 0.886 4.864 重力_y 27.564 4.663 0.873 5.135 重力_Z 22.433 3.876 0.007 1.358 4 ℃温升 10.282 1.468 − −
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表 3 主镜组件前6阶模态分析结果
Table 3. The first 6-order modal analysis results of primary mirror subassembly
阶数 频率/Hz 振型 1 140.366 Rotate along Y-axis 2 145.386 Rotate along X-axis 3 218.985 Rotate along Z-axis 4 359.664 Move along Z-axis 5 478.532 Move along Y-axis 6 658.369 Move along X-axis
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表 4 反射镜组件特性扫频结果
Table 4. Test results of characteristic frequency for mirror subassembly
Order Frequency/Hz Libration form 1 142.29 Y-axis 2 147.68 X-axis 3 320.10 Z-axis
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