高精度光学平板在三点支撑下自重变形的研究
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摘要
影响高精度光学元件重要的因素之一是支撑结构。主要研究了在三点支撑下,自重变形量与口径和厚度的关系。采用数值分析、有限元法(FEM)模型与实验验证相结合的方法完成对三点支撑下自重变形量的研究。采用薄板理论推导了在三点支撑下,重力变形与口径、厚度的关系;采用有限元法分析了一系列不同厚度、不同口径的平面镜自重变形大小;利用实验验证了模型的正确性。在薄板理论模型基础上,完善了自重变形与不同材料、口径、厚度、形状的变形函数,为快速计算出三点支撑下的自重变形提供理论依据。
Support structure is one of the most important factor of high- precision optical components. The relationship between the gravity deformation and caliber and thickness under three-point support is studied. The combination of numerical analysis, finite element method(FEM) and experimental validation is used to complete support under its own gravity deformation of three-point support. Firstly, using sheet theoretical to derivate the relationship between the gravity deformation and caliber, thickness under three-point support; and then, using the FEM analysis of the gravity deformation plane mirror size in a range of different thicknesses and calibers. Finally,the correctness of the model is validated by experiment. Under the basic of the sheet theoretical, the relationship between the gravity deformation and material, caliber, thickness and form is established completely, and it provides theoretical basis for quickly work out the gravity deformation under three-point support.
Support structure is one of the most important factor of high- precision optical components. The relationship between the gravity deformation and caliber and thickness under three-point support is studied. The combination of numerical analysis, finite element method(FEM) and experimental validation is used to complete support under its own gravity deformation of three-point support. Firstly, using sheet theoretical to derivate the relationship between the gravity deformation and caliber, thickness under three-point support; and then, using the FEM analysis of the gravity deformation plane mirror size in a range of different thicknesses and calibers. Finally,the correctness of the model is validated by experiment. Under the basic of the sheet theoretical, the relationship between the gravity deformation and material, caliber, thickness and form is established completely, and it provides theoretical basis for quickly work out the gravity deformation under three-point support.
引文
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18 Wang Baoxu.Optomechanical Structure Design and Analysis for Large Aperture Reference Spherical Lens[D].Beijing:University of Chinese Academy of Sciences,2010,37(8):2029-2034.汪宝旭.大口径球面标准镜头光机结构设计与分析[D].北京:中国科学院大学,2012:30-45.
19 Zhang Yanwei,Su Dongqi,Sui Yongxin,et al..Absolute testing of rotationally asymmetric surface deviation with the method of rotationaveraging and compensation[J].Chinese J Lasers,2014,41(7):0708007.张艳微,苏东奇,隋永新,等.基于旋转平均补偿算法的旋转非对称面形绝对检测[J].中国激光,2014,41(7):0708007.
20 Miao Erlong,Zhang Jian,Gu Yongqiang,et al..Measurement error analysis of high precision Fizeau interferometer for lithography projection objective[J].Chinese J Lasers,2010,37(8):2029-2034.苗二龙,张建,谷勇强,等.用于光刻投影物镜检测的高精度菲佐干涉仪误差分析[J].中国激光,2010,37(8):2029-2034.
2 Wu Qingwen,Lu E,Wa Jiaqi,et al..Study on the surface figure changes of primary mirror centerally supported under gravity load[J].Optics and Precision Engineering,1996,4(4):23-28.吴清文,卢锷,王家骐,等.自重作用下中心支撑主反射镜面形变化研究[J].光学精密工程,1996,4(4):23-28.
3 Zhang Dejiang,Liu Liren,Xu Rongwei,et al..Finite element analysis for wavefront error of lenses induced by gravity[J].Acta Optica Sinica,2005,25(4):538-541.张德江,刘立人,徐荣伟,等.透镜自重变形引起波像差的有限元分析[J].光学学报,2005,25(4):538-541.
4 P R Yoder.Opto-Mechanical Systems Design[M].Boca Raton:The Chemical Rubber Company Press,2006:460-461.
5 Cho M K,Price R S,Moon I K.Optimization of the ATST primarymirror support system[C].SPIE,2006,6273:63731E.
6 Fan Lili,Zhang Jingxu,Jiang Hao,et al..Design of the primary mirror supportof equatorial telescope[J].Infrared and Laser Engineering,2011,40(3):476-479.范李立,张景旭,姜皓,等.极轴式望远镜主镜支撑设计[J].红外与激光工程,2011,40(3):476-479.
7 Wang Xiangjing,Chen Jiexiang,Zhang Yi,et al..The application of APDL and UIDL in the primary mirror support optimization[J].Machinery Design&Manufacture,2009(11):86-87.王相京,陈结祥,张毅,等.APDL和UIDL在主镜支撑优化中的应用[J].机械设计与制造,2009(11):86-87.
8 Lei Jiang,Jiang Shilei,Cheng Gang.Deformation of high-accuracy photo lithographic objective lens[J].Opto-Electronic Engineering,2005,32(2):12-14.雷江,蒋世磊,程刚.高精度光刻物镜的变形研究[J].光电工程,2005,32(2):12-14.
9 Tan Fan Jiao,Qiao Yan Feng,Li Yao Bin,et al..FEM mechanical analysis for primary mirror self-weight deformation of photo-electronic theodolite[J].Optical Instruments,2007,29(6):65-68.谭凡教,乔彦峰,李耀斌,等.光电经纬仪主镜系统自重变形的有限元分析[J].光学仪器,2007,29(6):65-68.
10 Tian Wei,Wang Ping,Wang Rudong,et al..Simulation and experimental research of 193 nm projection lithography lens supporting[J].Chinese J Lasers,2012,39(8):0816002.田伟,王平,王汝冬,等.193 nm光刻投影物镜单镜支撑仿真分析及实验研究[J].中国激光,2012,39(8):0816002.
11 Slocum A.Kinematics couplings are view of design principles and application[J].Int J Mach Tools&Manuf,2010,50(4):310-327.
12 Wang Ping,Tian Wei,Wang Rudong,et al..Rotating chuck lest for removing chuck error of optical surface[J].Acta Optica Sinica,2011,31(8):0812004.王平,田伟,王汝冬,等.旋转支撑法去除元件面形测量的夹持误差[J].光学学报,2011,31(8):0812004.
13 Wang Wugui,Fu Mingfu.Advances in the research of nonlinear theory of moderately thick shells[J].Journal of Nanchang University(Engineering&Technology),2000,22(1):10-16.江五贵,扶名福.中厚板壳非线性理论的研究进展[J].南昌大学学报(工科版),2000,22(1):10-16.
14 Wang Rudong,Wang Ping,Tian Wei,et al..Design and analysis of compensation of large aperture optical element for gravity deformation[J].Chinese Optics,2011,4(3):260-264.王汝冬,王平,田伟,等.大口径光学元件重力变形补偿的设计分析[J].中国光学,2011,4(3):260-264.
15 胡企千.大型光学镜子的结构、支撑及重力变形计算方法[J].光学机械,1983,17(6):29-44.
16 Culpepper M L,Kartik M V,Dibiasio C.Design of integrated eccentric mechanisms and exact constraint fixtures for micro-level repeatability and accuracy[J].Precis Engng,2005,29(1):65-80.
17 Chen Xu,Yuan Wenquan,Feng Yutao,et al..Study of the error of the reference lens in absolute spherical testing and the thermal deformation model establishment[J].Acta Optica Sinica,2011,31(2):0212002.陈旭,袁文全,冯玉涛,等.绝对检验参考镜误差分析与热变形模型建立[J].光学学报,2011,31(2):0212002.
18 Wang Baoxu.Optomechanical Structure Design and Analysis for Large Aperture Reference Spherical Lens[D].Beijing:University of Chinese Academy of Sciences,2010,37(8):2029-2034.汪宝旭.大口径球面标准镜头光机结构设计与分析[D].北京:中国科学院大学,2012:30-45.
19 Zhang Yanwei,Su Dongqi,Sui Yongxin,et al..Absolute testing of rotationally asymmetric surface deviation with the method of rotationaveraging and compensation[J].Chinese J Lasers,2014,41(7):0708007.张艳微,苏东奇,隋永新,等.基于旋转平均补偿算法的旋转非对称面形绝对检测[J].中国激光,2014,41(7):0708007.
20 Miao Erlong,Zhang Jian,Gu Yongqiang,et al..Measurement error analysis of high precision Fizeau interferometer for lithography projection objective[J].Chinese J Lasers,2010,37(8):2029-2034.苗二龙,张建,谷勇强,等.用于光刻投影物镜检测的高精度菲佐干涉仪误差分析[J].中国激光,2010,37(8):2029-2034.