Multi-objective Topological Optimization of Primary Mirror of Laser Communication Terminal
-
摘要: 为提高激光通信主镜的质量,针对激光通信终端主镜进行优化设计。基于多目标拓扑优化和折衷规划法的理论,建立了一种考虑多工况结构刚度和质量最小化的多目标优化数学模型。利用Optistruct求解器对主镜进行优化设计,得到主镜新模型。对主镜结构进行详细设计和有限元分析,分析在主镜光轴水平和竖直工况时的镜面变形。结果表明主镜轻量化率为55.3%,与优化前相比主镜光轴竖直时主镜面形精度有较大提高,满足激光通信中对主镜性能指标的要求。与不同轻量化主镜结构进行对比,该方法得到的结构面形精度更高,验证了该方法的可行性。Abstract: To improve the quality of a laser communication terminal, the paper studies the optimization of its primary mirror. Based on the multi-objective topological optimization theory and the compromise programming method, it establishes the mathematical model of multi-objective topological optimization, with the multiple stiffness conditions and the weight minimization considered. The Optistruct software is used to optimize the primary mirror and its new model is obtained, which is reconstructed and analyzed with the finite element analysis. The deformation of the mirror surface is analyzed in the horizontal and vertical conditions of the primary mirror. The results show that the lightweight ratio of the primary mirror reaches 55.3% and that its surface figure in the vertical condition is larger than the original model, satisfying requirements for the primary mirror for laser communication. Compared with different structures of the lightweight primary mirror, the surface figure of the multi-objective topological optimized primary mirror is larger, thus verifying the feasibility of the optimization method.
-
表 1 单目标优化结果
C1min 4.722×10-5 C1max 3.497×10-4 C2min 1.47×10-5 C2max 8.365×10-5 Vmin 0.01 Vmax 1 表 2 主镜优化前后结果对比
质量/kg 工况1 工况2 PV/nm RMS/nm PV/nm RMS/nm 初始值 20.8 12.65 2.60 2.00 0.40 优化值 9.3 9.58 2.33 2.14 0.31 减少量 55.3% 24.3% 10.4% -7% 22.5% 表 3 不同轻量化形式结构对比
质量/kg 工况1 工况2 PV/nm RMS/nm PV/nm RMS/nm 三角形 10.5 12.52 2.58 2.24 0.41 扇形 9.5 13.15 2.86 2.32 0.44 拓扑优化结构 9.3 9.58 2.33 2.14 0.31 -
[1] 闫勇, 金光, 杨洪波.空间反射镜结构轻量化设计[J].红外与激光工程, 2008, 37(1):97-101 doi: 10.3969/j.issn.1007-2276.2008.01.023Yan Y, Jin G, Yang H B. Lightweight structural design of space mirror[J]. Infrared and Laser Engineering, 2008, 37(1):97-101(in Chinese) doi: 10.3969/j.issn.1007-2276.2008.01.023 [2] 刘婷毓.1.23m SiC轻量化主镜柔性支撑技术的研究[D].长春: 中国科学院研究生院(长春光学精密机械与物理研究所, 2012Liu T Y. Research on flexure mounts for a 1.23m SiC lightweight primary mirror[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2012(in Chinese) [3] 范磊.2m级地基望远镜SiC主镜轻量化设计及支撑技术研究[D].中国科学院研究生院(长春光学精密机械与物理研究所), 2013Fan L. Research on the lightweight design and support of the 2m-SiC primary mirror for ground-based telescope[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2013(in Chinese) [4] 郭中泽, 张卫红, 陈裕泽.结构拓扑优化设计综述[J].机械设计, 2007, 24(8):1-6 http://d.old.wanfangdata.com.cn/Periodical/jxsj200708001Guo Z Z, Zhang W H, Chen Y Z. An overview on the topological optimization design of structures[J]. Journal of Machine Design, 2007, 24(8):1-6(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/jxsj200708001 [5] Rozvany G I N, Querin O M, Gaspar Z, et al. Extended optimality in topology design[J]. Structural and Multidisciplinary Optimization, 2002, 24(3):257-261 doi: 10.1007/s00158-002-0235-x [6] Rozvany G I N. Traditional vs. extended optimality in topology optimization[J]. Structural and Multidisciplinary Optimization, 2009, 37(3):319-323 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=fb644461d7230c08566c8d6529751457 [7] Strömberg N. Topology optimization of structures with manufacturing and unilateral contact constraints by minimizing an adjustable compliance-volume product[J]. Structural and Multidisciplinary Optimization, 2010, 42(3):341-350 doi: 10.1007/s00158-010-0502-1 [8] 李好.改进的参数化水平集拓扑优化方法与应用研究[D].武汉: 华中科技大学, 2016Li H. Research on improved parametric level set topology optimization method and applications[D]. Wuhan: Huazhong University of Science and Technology, 2016(in Chinese) [9] 刘辛军, 李枝东, 陈祥.多工况拓扑优化问题的一种新解法-导重法[J].中国科学:技术科学, 2011, 41(7):920-928Liu X J, Li Z D, Chen X. A new solution for topology optimization problems with multiple loads:the guide-weight method[J]. Science China Technological Sciences, 2011, 54(6):1505-1514(in Chinese) [10] 张璟鑫, 梁伟, 夏洋.结构多目标拓扑优化目标函数构建方法的研究[J].中国机械工程, 2016, 27(7):899-903 doi: 10.3969/j.issn.1004-132X.2016.07.009Zhang J X, Liang W, Xia Y. Research on construction method of objective function for multi-objective topology optimization in structures[J]. China Mechanical Engineering, 2016, 27(7):899-903(in Chinese) doi: 10.3969/j.issn.1004-132X.2016.07.009 [11] 李钊, 张春光, 屈福政, 等.基于多目标满意度的履带架拓扑优化研究[J].机械科学与技术, 2015, 34(10):1488-1492 doi: 10.13433/j.cnki.1003-8728.2015.1003Li Z, Zhang C G, Qu F Z, et al. Topological optimization of crawler frame based on multi-objective satisfaction[J]. Mechanical Science and Technology for Aerospace Engineering, 2015, 34(10):1488-1492(in Chinese) doi: 10.13433/j.cnki.1003-8728.2015.1003 [12] 苗晓婷, 许泉, 刘广, 等.基于变密度法的飞行器升力面结构多目标拓扑优化设计[J].动力学与控制学报, 2014, 12(3):253-258 http://d.old.wanfangdata.com.cn/Periodical/dlxykzxb201403013Miao X T, Xu Q, Liu G, et al. Multi-objective topology optimization design method based on penalized density theory for aircraft lifting-surface[J]. Journal of Dynamics and Control, 2014, 12(3):253-258(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/dlxykzxb201403013 [13] 刘林华, 辛勇, 汪伟.基于折衷规划的车架结构多目标拓扑优化设计[J].机械科学与技术, 2011, 30(3):382-385 http://www.cnki.com.cn/Article/CJFDTotal-JXKX201103010.htmLiu L H, Xin Y, Wang W. Multi-objective topology optimization for an off-road vehicle frame based on compromise programming[J]. Mechanical Science and Technology for Aerospace Engineering, 2011, 30(3):382-385(in Chinese) http://www.cnki.com.cn/Article/CJFDTotal-JXKX201103010.htm [14] 范文杰, 范子杰, 苏瑞意.汽车车架结构多目标拓扑优化方法研究[J].中国机械工程, 2008, 19(12):1505-1508 doi: 10.3321/j.issn:1004-132X.2008.12.026Fan W J, Fan Z J, Su R Y. Research on multi-objective topology optimization on bus chassis frame[J]. China Mechanical Engineering, 2008, 19(12):1505-1508(in Chinese) doi: 10.3321/j.issn:1004-132X.2008.12.026 [15] 洪清泉, 赵康, 张攀.OptiStruct & HyperStudy理论基础与工程应用[M].北京:机械工业出版社, 2013Hong Q Q, Zhao K, Zhang P. OptiStruct & HyperStudy theoretical basis and engineering application[M]. Beijing:China Machine Press, 2013(in Chinese)