超轻空间相机主支撑背板的优化设计
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摘要
针对某空间相机超轻和高热稳定性的要求,设计一体化的背板结构,使得支撑背板既是整机主承力板,又是主反射镜支撑背板;采用具有高比刚度、高热稳定性的SiC作为背板材料,通过施加最小尺寸约束的变密度拓扑优化,确定支撑板背部筋的布置;建立以第二代非支配排序遗传算法为优化算法的多目标优化模型,集成反射镜面形误差和背板质量,完成背板的尺寸优化设计,背板质量仅为0.591 kg,筋厚的最小值为2.1 mm;最后利用有限元分析对优化结果进行动、静力学性能分析。结果表明:在5℃温升载荷下,反射镜组件镜面面形方均根为0.158 nm,具有良好的热稳定性;在X向重力载荷作用下(与光轴垂直方向/面形检测方向),镜面面形的方均根为1.169 nm,峰谷值为5.403 nm;反射镜组件的一阶固有频率为397 Hz,镜面边缘随机振动响应(RMS)小于16g,满足空间应用。
According to the requirements of ultra-light and high thermal stability of a space camera, an integrated backplate structure is designed so that the supporting backplate is not only the backplate of the main mirror, but also the main bearing plate of the space camera. The SiC with high specific stiffness and high thermal stability is used as the backplate material. The layout of back ribs is determined by the variable density topology optimization with the addition of a minimum size constraint. The size optimization design is completed by a multi-objective optimization model with Non-dominated Sorting Genetic Algorithm II(NSGA-II), integrating the mirror surface shape and the mass of the backplate. The mass of the backplate is only 0.591 kg and the minimum rib thickness is 2.1 mm. The dynamic and static performances of the optimization results are finally analyzed by the finite element analysis. The results show that the root-mean-square value of the mirror shape in the mirror assembly is 0.158 nm under a temperature rising load of 5 °C, which means good thermal stability. The root-mean-square value of the mirror shape is 1.169 nm and the peak to valley value is 5.403 nm under the X-direction gravity load(the direction perpendicular to the optical axis/the direction of detecting surface shape). The first-order intrinsic frequency of the mirror assembly is 397 Hz and the random vibration response value of the sampling point of the mirror edge is less than 16g. These mean the requirements for space application are satisfied.
According to the requirements of ultra-light and high thermal stability of a space camera, an integrated backplate structure is designed so that the supporting backplate is not only the backplate of the main mirror, but also the main bearing plate of the space camera. The SiC with high specific stiffness and high thermal stability is used as the backplate material. The layout of back ribs is determined by the variable density topology optimization with the addition of a minimum size constraint. The size optimization design is completed by a multi-objective optimization model with Non-dominated Sorting Genetic Algorithm II(NSGA-II), integrating the mirror surface shape and the mass of the backplate. The mass of the backplate is only 0.591 kg and the minimum rib thickness is 2.1 mm. The dynamic and static performances of the optimization results are finally analyzed by the finite element analysis. The results show that the root-mean-square value of the mirror shape in the mirror assembly is 0.158 nm under a temperature rising load of 5 °C, which means good thermal stability. The root-mean-square value of the mirror shape is 1.169 nm and the peak to valley value is 5.403 nm under the X-direction gravity load(the direction perpendicular to the optical axis/the direction of detecting surface shape). The first-order intrinsic frequency of the mirror assembly is 397 Hz and the random vibration response value of the sampling point of the mirror edge is less than 16g. These mean the requirements for space application are satisfied.
引文
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[16] Peng X R. A comparative study on models of structural stiffness optimization problems[J]. Journal of Hunan City University (Natural Science Edition), 2016, 25(1): 1-4. 彭细荣. 结构刚度优化问题模型比较研究[J]. 湖南城市学院学报(自然科学版), 2016, 25(1): 1-4.
[17] Kr?del M, Zauner C. Extreme stable and complex structures for optomechanical applications[J]. Proceedings of SPIE, 2015, 9574: 95740G.
[18] Xiao X W, Xiao D, Lin J G, et al. Overview on multi-objective optimization problem research[J]. Application Research of Computers, 2011, 28(3): 805-808, 827. 肖晓伟, 肖迪, 林锦国, 等. 多目标优化问题的研究概述[J]. 计算机应用研究, 2011, 28(3): 805-808, 827.
[19] Huang Q T, Gao Q, Yu J C. FEM analysis of ultra thin mirror supporting structure effect on surface deformation in gravity field[J]. Proceedings of SPIE, 2006, 6148: 61480W.
[19] Huang Q, Gao Q, Yu J. FEM analysis of ultra thin mirror supporting structure effect on surface deformation in gravity field[C]. 2nd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Large Mirrors and Telescopes, 2006: 61480W.
[20] Li F, Ruan P, Zhao B C. Study on the surface deformation of flat reflector under gravity load[J]. Acta Photonica Sinica, 2005, 34(2): 272-275. 李福, 阮萍, 赵葆常. 重力作用下平面反射镜变形研究[J]. 光子学报, 2005, 34(2): 272-275.
[21] Chen Z, Zhang R, Chen Z, et al. Experiment and modal analysis on the primary mirror structure of Space Solar Telescope[J]. Proceedings of SPIE, 2006, 6265: 62654B.
[2] Fu S X, Zhou C, Cao Y Y, et al. Structural design of 4 m telescope mount base based on topology optimization method[J]. Infrared and Laser Engineering, 2015, 44(8): 2441-2447. 付世欣, 周超, 曹玉岩, 等. 基于拓扑优化的4 m望远镜底座结构设计[J]. 红外与激光工程, 2015, 44(8): 2441-2447.
[3] Zhang L, Ke S L, Li L, et al. Multi-objective integrated optimization design of Φ210 mm ultra-light SiC mirror[J]. Acta Photonica Sinica, 2017, 46(12): 1222001. 张雷, 柯善良, 李林, 等. Φ210 mm超薄超轻SiC反射镜多目标集成优化设计[J]. 光子学报, 2017, 46(12): 1222001.
[4] Kihm H, Moon I K, Yang H S, et al. 1-m lightweight mirror design using genetic algorithm[J]. Proceedings of SPIE, 2012, 8415: 841514.
[5] Genberg V L, Michels G J. Using integrated models to minimize environmentally induced wavefront error in optomechanical design and analysis[J]. Proceedings of SPIE, 2017, 10371: 103710I.
[6] Riva M, Moschetti M. Integrated optomechanical structural optimization through coupling of sensitivity matrixes[J]. Proceedings of SPIE, 2016, 10012: 100120D.
[7] Qi G, Xu Y J, Liu B Q. Lightweight structure design for SiC/Al supporting plate of space mirror[J]. Infrared and Laser Engineering, 2014, 43(7): 2214-2218. 齐光, 许艳军, 刘炳强. 空间相机反射镜SiC/Al支撑板轻量化结构优化设计[J]. 红外与激光工程, 2014, 43(7): 2214-2218.
[8] Li Z X, Xing L N, Xie P. Design of the Φ330 mm primary mirror assembly of spaceborne video camera[J]. Acta Photonica Sinica, 2016, 45(7): 0722003. 李宗轩, 邢利娜, 解鹏. 视频空间相机Φ330 mm口径主镜组件设计[J]. 光子学报, 2016, 45(7): 0722003.
[9] Hu J N, Dong J H, Zhou P W. Parametric design of flexure supporting for optical space remote sensor primary mirror[J]. Acta Optica Sinica, 2016, 36(11): 1128001. 胡佳宁, 董吉洪, 周平伟. 空间光学遥感器主镜柔性支撑的参数化设计[J]. 光学学报, 2016, 36(11): 1128001.
[10] Li H X, Ding Y L, Zhang H W. Support system study of rectangular mirror[J]. Acta Optica Sinica, 2015, 35(5): 0523002. 李海星, 丁亚林, 张洪文. 矩形反射镜结构支撑技术研究[J]. 光学学报, 2015, 35(5): 0523002.
[11] Logut D, Breysse J, Toulemont Y, et al. Light weight monolithic silicon carbide telescope for space application[J]. Proceedings of SPIE, 2005, 5962: 59621Q.
[12] Zhao R C, Bao J X, Cao Q, et al. Partition gelation casting in RB-SiC mirror billet[J]. Optics and Precision Engineering, 2017, 25(12): 111-116. 赵汝成, 包建勋, 曹琪, 等. 碳化硅反射镜镜坯分区浇注成型技术[J]. 光学精密工程, 2017, 25(12): 111-116.
[13] Bougoin M. SiC challenging parts for GAIA[J]. Proceedings of SPIE, 2017, 10565: 105652C.
[14] Zuo K T. Research of theory and application about topology optimization of continuum structure[D]. Wuhan: Huazhong University of Science and Technology, 2004: 98-104. 左孔天. 连续体结构拓扑优化理论与应用研究[D]. 武汉: 华中科技大学, 2004: 98-104.
[15] Luo Z, Chen L P, Huang Y Y, et al. Topological optimization design for continuum structures[J]. Advances in Mechanics, 2004, 34(4): 463-476. 罗震, 陈立平, 黄玉盈, 等. 连续体结构的拓扑优化设计[J]. 力学进展, 2004, 34(4): 463-476.
[16] Peng X R. A comparative study on models of structural stiffness optimization problems[J]. Journal of Hunan City University (Natural Science Edition), 2016, 25(1): 1-4. 彭细荣. 结构刚度优化问题模型比较研究[J]. 湖南城市学院学报(自然科学版), 2016, 25(1): 1-4.
[17] Kr?del M, Zauner C. Extreme stable and complex structures for optomechanical applications[J]. Proceedings of SPIE, 2015, 9574: 95740G.
[18] Xiao X W, Xiao D, Lin J G, et al. Overview on multi-objective optimization problem research[J]. Application Research of Computers, 2011, 28(3): 805-808, 827. 肖晓伟, 肖迪, 林锦国, 等. 多目标优化问题的研究概述[J]. 计算机应用研究, 2011, 28(3): 805-808, 827.
[19] Huang Q T, Gao Q, Yu J C. FEM analysis of ultra thin mirror supporting structure effect on surface deformation in gravity field[J]. Proceedings of SPIE, 2006, 6148: 61480W.
[19] Huang Q, Gao Q, Yu J. FEM analysis of ultra thin mirror supporting structure effect on surface deformation in gravity field[C]. 2nd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Large Mirrors and Telescopes, 2006: 61480W.
[20] Li F, Ruan P, Zhao B C. Study on the surface deformation of flat reflector under gravity load[J]. Acta Photonica Sinica, 2005, 34(2): 272-275. 李福, 阮萍, 赵葆常. 重力作用下平面反射镜变形研究[J]. 光子学报, 2005, 34(2): 272-275.
[21] Chen Z, Zhang R, Chen Z, et al. Experiment and modal analysis on the primary mirror structure of Space Solar Telescope[J]. Proceedings of SPIE, 2006, 6265: 62654B.