Structural design of 4 m telescope mount base based on topology optimization method

Fu Shixin; Zhou Chao; Cao Yuyan; Fan Lei; Han Xida

Volume 44 Issue 8

Sep. 2015

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Fu Shixin, Zhou Chao, Cao Yuyan, Fan Lei, Han Xida. Structural design of 4 m telescope mount base based on topology optimization method[J]. Infrared and Laser Engineering, 2015, 44(8): 2441-2447.

Citation:

Fu Shixin, Zhou Chao, Cao Yuyan, Fan Lei, Han Xida. Structural design of 4 m telescope mount base based on topology optimization method[J]. Infrared and Laser Engineering, 2015, 44(8): 2441-2447.

Structural design of 4 m telescope mount base based on topology optimization method

1.
Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China

Received Date: 2014-12-10
Rev Recd Date: 2015-01-13
Publish Date: 2015-08-25

Abstract

To meet the requirement for high stiffness and lightweight, topology optimization method with constraints of static displacements and first resonance frequency was studied in 4 m telescope mount base design. Firstly, mathematical model of topology optimization was built subjected to minimum compliance, with pseudo density of the finite elements as design variables, static displacements, first resonance frequency and total mass as optimization constraints. Procedure of calculating sensitivities of optimization objective was presented in detail. Furthermore, topology optimization method was applied in mount base design, based on which shape and size design were carried out. Finally, the static stiffness and dynamic behavior of the optimized structure was analyzed and checked using the finite element method. The achieved results show that total mass of mount base reduces from 27.66 t to 22.15 t, while the maximum displacement decreases from 0.037 7 mm to 0.014 mm and first resonance frequency increases from 217.1 Hz to 247.45 Hz, ie, improving static and dynamic performances with lots of mass cut, which validate the presented topology optimization method. This topology optimization method will provide efficient help to other components' design of 4m telescope mount.
- lightweight design,
- topology optimization,
- telescope mount base,
- finite element analysis,
- stiffness

References

[1]
[2]	An Yuan, Jia Xuezhi, Zhang Lei, et al. Optimizing design of CFRP based main backbone with high stiffness ratio for space camera [J]. Opt Precision Eng, 2013, 21(2): 416-422. (in Chinese)安源, 贾学志, 张雷, 等. 基于碳纤维复合材料的空间相机高比刚度主承力板优化设计[J]. 光学精密工程, 2013, 21(2): 416-422.
[3]
[4]	Sun Jingwei, Lv Tianyu, Yao Lishuang, et al. Design and assembly of transmitter-telescope[J]. Opt Precision Eng, 2014, 22(2): 369-375. (in Chinese)孙敬伟,吕天宇,姚丽双,等. 发射望远镜的设计和装调[J]. 光学精密工程, 2014, 22(2): 369-375.
[5]	Xu Xinhang, Gao Yunguo, Yang Hongbo, et al. Large-diameter fast steering mirror on rigid support technology for dynamic platform [J]. Opt Precision Eng, 2014, 22(1): 117-124. (in Chinese)徐新行, 高云国, 杨洪波, 等. 车载大口径刚性支撑式快速反射镜[J]. 光学精密工程, 2014, 22(1): 117-124.
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[7]	San Xiaogang, Sun Ning, Zhuo Renshan, et al. Design of supporting structure for primary mirror of large aperture theodolite [J]. Opt Precision Eng, 2013, 21(12): 3111-3117. (in Chinese)伞晓刚, 孙宁, 卓仁善, 等. 大口径光电经纬仪主反射镜支撑结构设计[J]. 光学精密工程, 2013, 21(12): 3111-3117.
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[9]	Fan Lei, Zhang Jingxu, Wu Xiaoxia, et al. Optimum design of edge-lateral support for large-aperture lightweight primary mirror[J]. Opt Precision Eng, 2012, 20(10): 2207-2213. (in Chinese)范磊, 张景旭, 吴小霞, 等. 大口径轻量化主镜边缘侧向支撑的优化设计[J]. 光学精密工程, 2012, 20(10): 2207-2213.
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[14]	Mlejnek H P, Schirrmacher R. An engineering approach to optimal material distribution and shape finding [J]. Computer Methods in Applied Mechanics and Engineering, 1993, 106: 1-26.
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[16]	Bendsoe M P, Sigmund O. Material interpolations in topology optimization[J]. Archive of Applied Mechanics, 1999, 69:635-654.
[17]	Park K S, Lee J H, Youn S H. Lightweight mirror design method using topology optimization [J]. Optical Engineering, 2005, 44(5): 053002-1-053002-6.
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[19]	Liu Shutian, Hu Rui, Zhou Ping, et al. Topologic optimization for configuration design of web-skin-type ground structure based large-aperture space mirror[J]. Opt Precision Eng, 2013, 21(7): 1803-1810. (in Chinese)刘书田, 胡瑞, 周平, 等. 基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法[J]. 光学精密工程, 2013, 21(7): 1803-1810.
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[21]	Li Yuan, Jiao Mingyin, Chang Weijun, et al. Lightweight topological optimization design of scanning mirror [J]. Infrared and Laser Engineering, 2011, 40(7): 1294-1298. (in Chinese)李元, 焦明印, 常伟军, 等. 扫描反射镜轻量拓扑优化设计[J]. 红外与激光工程, 2011, 40(7): 1294-1298.
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[26]	Wang Yongxian, Wang Bing, Ren Jianyue, et al. Improvement of carbon fiber support structure and topology optimization design of space camera [J]. Infrared and Laser Engineering, 2009, 38(4): 702-724. (in Chinese)王永宪,王兵,任建岳,等. 空间相机碳纤维支撑结构改进及拓扑优化设计[J]. 红外与激光工程, 2009, 38(4): 702-724.
[27]
[28]	Cao Diansheng. Topology optimization of scanning mirror of UV to near-infrared hyperspectral detector [J]. Infrared and Laser Engineering, 2014, 43(11): 3813-3819. (in Chinese)曹佃生. 紫外-近红外高光谱探测仪扫描镜拓扑优化设计[J]. 红外与激光工程,2014, 43(11): 3813-3819.
[29]	Qi Guang, Xu Yanjun, Liu Bingqiang. Lightweight structure design for SiC/Al supporting plate of space mirror [J]. Infrared and Laser Engineering, 2014, 43(7): 2214-2218. (in Chinese)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.
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[31]	Maeda Y, Nishiwaki S, Izui K, et al. Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes [J]. Int J Numer Methods Eng, 2006, 67: 597-628.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Structural design of 4 m telescope mount base based on topology optimization method

1. Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China

Received Date: 2014-12-10

Rev Recd Date: 2015-01-13

Publish Date: 2015-08-25

Key words:

Abstract: To meet the requirement for high stiffness and lightweight, topology optimization method with constraints of static displacements and first resonance frequency was studied in 4 m telescope mount base design. Firstly, mathematical model of topology optimization was built subjected to minimum compliance, with pseudo density of the finite elements as design variables, static displacements, first resonance frequency and total mass as optimization constraints. Procedure of calculating sensitivities of optimization objective was presented in detail. Furthermore, topology optimization method was applied in mount base design, based on which shape and size design were carried out. Finally, the static stiffness and dynamic behavior of the optimized structure was analyzed and checked using the finite element method. The achieved results show that total mass of mount base reduces from 27.66 t to 22.15 t, while the maximum displacement decreases from 0.037 7 mm to 0.014 mm and first resonance frequency increases from 217.1 Hz to 247.45 Hz, ie, improving static and dynamic performances with lots of mass cut, which validate the presented topology optimization method. This topology optimization method will provide efficient help to other components' design of 4m telescope mount.

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Reference (31)

[1]
[2]	An Yuan, Jia Xuezhi, Zhang Lei, et al. Optimizing design of CFRP based main backbone with high stiffness ratio for space camera [J]. Opt Precision Eng, 2013, 21(2): 416-422. (in Chinese)安源, 贾学志, 张雷, 等. 基于碳纤维复合材料的空间相机高比刚度主承力板优化设计[J]. 光学精密工程, 2013, 21(2): 416-422.
[3]
[4]	Sun Jingwei, Lv Tianyu, Yao Lishuang, et al. Design and assembly of transmitter-telescope[J]. Opt Precision Eng, 2014, 22(2): 369-375. (in Chinese)孙敬伟,吕天宇,姚丽双,等. 发射望远镜的设计和装调[J]. 光学精密工程, 2014, 22(2): 369-375.
[5]	Xu Xinhang, Gao Yunguo, Yang Hongbo, et al. Large-diameter fast steering mirror on rigid support technology for dynamic platform [J]. Opt Precision Eng, 2014, 22(1): 117-124. (in Chinese)徐新行, 高云国, 杨洪波, 等. 车载大口径刚性支撑式快速反射镜[J]. 光学精密工程, 2014, 22(1): 117-124.
[6]
[7]	San Xiaogang, Sun Ning, Zhuo Renshan, et al. Design of supporting structure for primary mirror of large aperture theodolite [J]. Opt Precision Eng, 2013, 21(12): 3111-3117. (in Chinese)伞晓刚, 孙宁, 卓仁善, 等. 大口径光电经纬仪主反射镜支撑结构设计[J]. 光学精密工程, 2013, 21(12): 3111-3117.
[8]
[9]	Fan Lei, Zhang Jingxu, Wu Xiaoxia, et al. Optimum design of edge-lateral support for large-aperture lightweight primary mirror[J]. Opt Precision Eng, 2012, 20(10): 2207-2213. (in Chinese)范磊, 张景旭, 吴小霞, 等. 大口径轻量化主镜边缘侧向支撑的优化设计[J]. 光学精密工程, 2012, 20(10): 2207-2213.
[10]
[11]
[12]	Bendsoe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 71: 197-224.
[13]
[14]	Mlejnek H P, Schirrmacher R. An engineering approach to optimal material distribution and shape finding [J]. Computer Methods in Applied Mechanics and Engineering, 1993, 106: 1-26.
[15]
[16]	Bendsoe M P, Sigmund O. Material interpolations in topology optimization[J]. Archive of Applied Mechanics, 1999, 69:635-654.
[17]	Park K S, Lee J H, Youn S H. Lightweight mirror design method using topology optimization [J]. Optical Engineering, 2005, 44(5): 053002-1-053002-6.
[18]
[19]	Liu Shutian, Hu Rui, Zhou Ping, et al. Topologic optimization for configuration design of web-skin-type ground structure based large-aperture space mirror[J]. Opt Precision Eng, 2013, 21(7): 1803-1810. (in Chinese)刘书田, 胡瑞, 周平, 等. 基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法[J]. 光学精密工程, 2013, 21(7): 1803-1810.
[20]
[21]	Li Yuan, Jiao Mingyin, Chang Weijun, et al. Lightweight topological optimization design of scanning mirror [J]. Infrared and Laser Engineering, 2011, 40(7): 1294-1298. (in Chinese)李元, 焦明印, 常伟军, 等. 扫描反射镜轻量拓扑优化设计[J]. 红外与激光工程, 2011, 40(7): 1294-1298.
[22]
[23]
[24]	Xu Wei, Wu Qingwen, Zhai Yan, et al. Optimal design and analysis of long circular reflector subassembly in the space optical remote sensor [J]. Infrared and Laser Engineering, 2013, 42(3): 752-757. (in Chinese)徐炜, 吴清文, 翟岩, 等. 空间光学遥感器长圆形反射镜组件优化设计与分析[J]. 红外与激光工程, 2013, 42(3): 752-757.
[25]
[26]	Wang Yongxian, Wang Bing, Ren Jianyue, et al. Improvement of carbon fiber support structure and topology optimization design of space camera [J]. Infrared and Laser Engineering, 2009, 38(4): 702-724. (in Chinese)王永宪,王兵,任建岳,等. 空间相机碳纤维支撑结构改进及拓扑优化设计[J]. 红外与激光工程, 2009, 38(4): 702-724.
[27]
[28]	Cao Diansheng. Topology optimization of scanning mirror of UV to near-infrared hyperspectral detector [J]. Infrared and Laser Engineering, 2014, 43(11): 3813-3819. (in Chinese)曹佃生. 紫外-近红外高光谱探测仪扫描镜拓扑优化设计[J]. 红外与激光工程,2014, 43(11): 3813-3819.
[29]	Qi Guang, Xu Yanjun, Liu Bingqiang. Lightweight structure design for SiC/Al supporting plate of space mirror [J]. Infrared and Laser Engineering, 2014, 43(7): 2214-2218. (in Chinese)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.
[30]
[31]	Maeda Y, Nishiwaki S, Izui K, et al. Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes [J]. Int J Numer Methods Eng, 2006, 67: 597-628.

Structural design of 4 m telescope mount base based on topology optimization method

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