ULE~?叠层反射镜二维等效建模方法研究
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摘要
ULE~?叠层反射镜是实现大口径、低面密度、高刚度空间反射镜的有效途径。为提高ULE~?叠层反射镜设计效率,文章基于蜂窝夹芯结构均质板等效理论,推导了叠层反射镜二维等效模型建模方法,利用有限元法计算二维等效模型自由模态频率,对比详细模型计算结果,验证等效模型计算精度,并结合设计实例验证该二维等效模型在叠层反射镜优化设计中的有效性。分析结果表明,叠层反射镜面密度大于40kg/m~2时,二维等效模型模态频率计算误差优于4%,满足优化设计精度要求。文章提出的叠层反射镜二维等效建模方法大幅缩减叠层反射镜有限元模型规模,实现叠层反射镜有限元模型高度参数化,有效提高了叠层反射镜设计效率。
ULE~? stacked-core mirror technology provides an effective way to make space mirrors with large aperture, low areal density and high stiffness. In order to improve the design efficiency and accuracy for ULE~? stacked-core mirrors, a 2D equivalent modeling method is derived based on equivalent plate theory for sandwich structure in this paper. The finite element method is used to calculate the free modal frequency of the 2D equivalent model, and then the results are compared with those obtained by detailed model to verify the accuracy of the equivalent method. The validity of the 2D equivalent model in the optimization design of the stacked-core mirror is verified by a simulation example. The results show that the frequency error of 2D equivalent model is less than 4% when the areal density of the stacked-core mirror is greater than 40 kg/m~2,which can satisfy the requirements of the mirror design optimization. The 2D equivalent method proposed in the paper can greatly reduce the scale of the finite element model and increase the parameterization level highly,thus effectively improving the design efficiency for the stacked-core mirrors.
ULE~? stacked-core mirror technology provides an effective way to make space mirrors with large aperture, low areal density and high stiffness. In order to improve the design efficiency and accuracy for ULE~? stacked-core mirrors, a 2D equivalent modeling method is derived based on equivalent plate theory for sandwich structure in this paper. The finite element method is used to calculate the free modal frequency of the 2D equivalent model, and then the results are compared with those obtained by detailed model to verify the accuracy of the equivalent method. The validity of the 2D equivalent model in the optimization design of the stacked-core mirror is verified by a simulation example. The results show that the frequency error of 2D equivalent model is less than 4% when the areal density of the stacked-core mirror is greater than 40 kg/m~2,which can satisfy the requirements of the mirror design optimization. The 2D equivalent method proposed in the paper can greatly reduce the scale of the finite element model and increase the parameterization level highly,thus effectively improving the design efficiency for the stacked-core mirrors.
引文
[1]刘韬.国外静止轨道大口径反射成像技术发展综述[J].航天返回与遥感,2016,37(5):1-9.LIU Tao.An Overview of Development of Foreign Large Aperture Reflection Imaging Technology on Geostationary Orbit[J].Spacecraft Recovery&Remote Sensing,2016,37(5):1-9.(in Chinese)
[2]SABIA R,EDWARDS M J,VANBROCKLIN R,et al.Corning 7972 ULE Material for Segmented and Large Monolithic Mirror Blanks[C]//SPIE Astronomical Telescopes+Instrumentation.International Society for Optics and Photonics,2006.
[3]STAHL H P.Advanced Mirror Technology Development for Very Large Space Telescopes[C]//American Astronomical Society Meeting.Baltimore,MD:American Astronomical Society Meeting Abstracts#223,2011.
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[7]宫辉,连华东.大口径双拱型SiC反射镜背部构型初步研究[J].航天返回与遥感,2010,31(4):32-37.GONG Hui,LIAN Huadong.Preliminary Study on Backside Structure of Large-aperture Double-arch SiC Mirror[J].Spacecraft Recovery&Remote Sensing,2010,31(4):32-37.(in Chinese)
[8]VANDERPLAATS G N.Numerical Optimization Techniques for Engineering Design:With Application[J].Computer Aided Optimal Design:Structural and Mechanical Systems,2005,27(4):197-239.
[9]凯斯·B·道尔,维克托·L·基恩伯格,格雷戈里·J·迈克尔斯.光机集成分析[M].连华东,王小勇,徐鹏,译.北京:国防工业出版社,2015.DOYLE K B,GENBERG V L,MICHELS G J.Integrated Optomechanical Analysis[M].LIAN Huadong,WANG Xiaoyong,XU Peng,translated.Beijing:National Defend Industry Press,2015.(in Chinese)
[10]YODER P.Opto-mechanical Systems Design,Fourth Edition,Volume 2:Design and Analysis of Large Mirrors and Structures[M].CRC Press,2015.
[11]蒋权,杨洪波,李宗轩,等.光学小卫星蜂窝主承力板的设计与测试[J].红外与激光工程,2016,45(12):242-249.JIANG Quan,YANG Hongbo,LI Zongxuan,et al.Design and Experiment of Honeycomb Sandwich Plate of Optical Small Satellite[J].Infrared and Laser Engineering,2016,45(12):242-249.(in Chinese)
[12]刘健,周春燕.长厚比对正六边形铝蜂窝夹层板等效板模型动力学计算精度的影响[J].复合材料学报,2016,33(8):1838-1847.LIU Jian,ZHOU Chunyan.Influence of Length-thickness Ratio on Dynamics Calculation Accuracy of Equivalent Plate Model of Hexagonal Aluminum Honeycomb Sandwich Plate[J].Acta Materiae Compositae Sinica,2016,33(8):1838-1847.(in Chinese)
[13]张铁亮,丁运亮,金海波.蜂窝夹层板结构等效模型比较分析[J].应用力学学报,2011,28(3):275-282.ZHANG Tieliang,DING Yunliang,JIN Haibo.Comparative Analysis of Equivelent Models for Honeycomb Sandwich Plates[J].Chinese Journal of Applied Mechanics,2011,28(3):275-282.(in Chinese)
[14]谭陆洋,王栋,李林,等.光学小卫星主载荷承力结构的多工况优化设计[J].红外与激光工程,2017,46(12):272-278.TAN Luyang,WANG Dong,LI Lin,et al.Multi-condition Optimization Design of Main Load Bearing Structure of Optical Small Satellite[J].Infrared and Laser Engineering,2017,46(12):272-278.(in Chinese)
[15]富明慧,徐欧腾,陈誉.蜂窝芯层等效参数研究综述[J].材料导报,2015,29(5):127-134.FU Minghui,XU Outeng,CHEN Yu.An Overview of Equivalent Parameters of Honeycomb Cores[J].Materials Review,2015,29(5):127-134.(in Chinese)
[16]LUCA G,ALDO S.Dynamic Modeling of Honeycomb Sandwich Panel[J].Archive of Applied Mechanics,2007,11(11):779-793.
[17]CHENG Q H,LEE H P,LU C.A Numerical Analysis Approach for Evaluating Elastic Constants of Sandwich Structures with Various Cores[J].Composite Structures,2006,74(2):226-236.
[18]GENBERG V L,MICHELS G J.Using Integrated Models to Minimize Environmentally Induced Wavefront Error in Optomechanical Design and Analysis[C]//SPIE Optics Engineering+Applications.San Diego,California,2017.
[19]杨佳文,黄巧林.大口径反射镜结构参数优化设计[J].中国空间科学技术,2011,31(4):77-83.YANG Jiawen,HUANG Qiaolin.Optimized Design of Structure Parameters for Large-aperture Mirrors[J].Chinese Space Science and Technology,2011,31(4):77-83.(in Chinese)
[20]XIAO G,ZHU Z.Friction Materials Development by Using DOE/RSM and Artificial Neural Network[J].Tribology International,2010,43(1):218-227.
[21]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究[J].航空学报,2006,27(1):55-61.GUO Qintao,ZHANG Lingmi,FEI Qingguo.Response Surface Method and Its Experimental Design for Deterministic Computer Simulation[J].Acta Aeronauticaet Astronautica Sinica,2006,27(1):55-61.(in Chinese)
[22]李宗轩,邢利娜,解鹏.视频空间相机Φ330mm口径主镜组件设计[J].光子学报,2016,45(7):12-17.LI Zongxuan,XING Lina,XIE Peng.Design of theΦ330 mm Primary Mirror Assembly of Spaceborne Video Camera[J].Acta Photonica Sinica,2016,45(7):12-17.(in Chinese)
[23]包奇红,沙巍,陈长征,等.空间Si C反射镜背部中心支撑特性[J].光子学报,2017,46(2):22-31.BAO Qihong,SHA Wei,CHEN Changzheng,et al.Characteristics of Rear Support in Centre for Space SiC Mirror[J].Acta Photonica Sinica,2017,46(2):21-31.(in Chinese)
[2]SABIA R,EDWARDS M J,VANBROCKLIN R,et al.Corning 7972 ULE Material for Segmented and Large Monolithic Mirror Blanks[C]//SPIE Astronomical Telescopes+Instrumentation.International Society for Optics and Photonics,2006.
[3]STAHL H P.Advanced Mirror Technology Development for Very Large Space Telescopes[C]//American Astronomical Society Meeting.Baltimore,MD:American Astronomical Society Meeting Abstracts#223,2011.
[4]EGERMAN R,MATTHEWS G,WYNN J,et al.The Current and Future State-of-the-art Glass Optics[C]//Astro2010:The Astronomy and Astrophysics Decadal Survey.2009.
[5]STAHL H P.Advanced Mirror Technology Development(AMTD)Project:Overview and Year Four Accomplishments[C]//SPIE Astronomical Telescopes+Instrumentation.Edinburgh,United Kingdom,2016.
[6]刘红.低面密度叠层蜂窝低膨胀玻璃质反射镜研制技术[C]//第三届空间光学与遥感应用论坛.北京:北京空间机电研究所,2017.LIU Hong.Manufacturing Technology of Low Area Density Stacked-core Mirror Using Low Expansion Glass[C]//The Third Space Optics and Remote Sensing Applications Forum.Beijing:Beijing Institute of Space Mechanics&Electricity,2017.(in Chinese)
[7]宫辉,连华东.大口径双拱型SiC反射镜背部构型初步研究[J].航天返回与遥感,2010,31(4):32-37.GONG Hui,LIAN Huadong.Preliminary Study on Backside Structure of Large-aperture Double-arch SiC Mirror[J].Spacecraft Recovery&Remote Sensing,2010,31(4):32-37.(in Chinese)
[8]VANDERPLAATS G N.Numerical Optimization Techniques for Engineering Design:With Application[J].Computer Aided Optimal Design:Structural and Mechanical Systems,2005,27(4):197-239.
[9]凯斯·B·道尔,维克托·L·基恩伯格,格雷戈里·J·迈克尔斯.光机集成分析[M].连华东,王小勇,徐鹏,译.北京:国防工业出版社,2015.DOYLE K B,GENBERG V L,MICHELS G J.Integrated Optomechanical Analysis[M].LIAN Huadong,WANG Xiaoyong,XU Peng,translated.Beijing:National Defend Industry Press,2015.(in Chinese)
[10]YODER P.Opto-mechanical Systems Design,Fourth Edition,Volume 2:Design and Analysis of Large Mirrors and Structures[M].CRC Press,2015.
[11]蒋权,杨洪波,李宗轩,等.光学小卫星蜂窝主承力板的设计与测试[J].红外与激光工程,2016,45(12):242-249.JIANG Quan,YANG Hongbo,LI Zongxuan,et al.Design and Experiment of Honeycomb Sandwich Plate of Optical Small Satellite[J].Infrared and Laser Engineering,2016,45(12):242-249.(in Chinese)
[12]刘健,周春燕.长厚比对正六边形铝蜂窝夹层板等效板模型动力学计算精度的影响[J].复合材料学报,2016,33(8):1838-1847.LIU Jian,ZHOU Chunyan.Influence of Length-thickness Ratio on Dynamics Calculation Accuracy of Equivalent Plate Model of Hexagonal Aluminum Honeycomb Sandwich Plate[J].Acta Materiae Compositae Sinica,2016,33(8):1838-1847.(in Chinese)
[13]张铁亮,丁运亮,金海波.蜂窝夹层板结构等效模型比较分析[J].应用力学学报,2011,28(3):275-282.ZHANG Tieliang,DING Yunliang,JIN Haibo.Comparative Analysis of Equivelent Models for Honeycomb Sandwich Plates[J].Chinese Journal of Applied Mechanics,2011,28(3):275-282.(in Chinese)
[14]谭陆洋,王栋,李林,等.光学小卫星主载荷承力结构的多工况优化设计[J].红外与激光工程,2017,46(12):272-278.TAN Luyang,WANG Dong,LI Lin,et al.Multi-condition Optimization Design of Main Load Bearing Structure of Optical Small Satellite[J].Infrared and Laser Engineering,2017,46(12):272-278.(in Chinese)
[15]富明慧,徐欧腾,陈誉.蜂窝芯层等效参数研究综述[J].材料导报,2015,29(5):127-134.FU Minghui,XU Outeng,CHEN Yu.An Overview of Equivalent Parameters of Honeycomb Cores[J].Materials Review,2015,29(5):127-134.(in Chinese)
[16]LUCA G,ALDO S.Dynamic Modeling of Honeycomb Sandwich Panel[J].Archive of Applied Mechanics,2007,11(11):779-793.
[17]CHENG Q H,LEE H P,LU C.A Numerical Analysis Approach for Evaluating Elastic Constants of Sandwich Structures with Various Cores[J].Composite Structures,2006,74(2):226-236.
[18]GENBERG V L,MICHELS G J.Using Integrated Models to Minimize Environmentally Induced Wavefront Error in Optomechanical Design and Analysis[C]//SPIE Optics Engineering+Applications.San Diego,California,2017.
[19]杨佳文,黄巧林.大口径反射镜结构参数优化设计[J].中国空间科学技术,2011,31(4):77-83.YANG Jiawen,HUANG Qiaolin.Optimized Design of Structure Parameters for Large-aperture Mirrors[J].Chinese Space Science and Technology,2011,31(4):77-83.(in Chinese)
[20]XIAO G,ZHU Z.Friction Materials Development by Using DOE/RSM and Artificial Neural Network[J].Tribology International,2010,43(1):218-227.
[21]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究[J].航空学报,2006,27(1):55-61.GUO Qintao,ZHANG Lingmi,FEI Qingguo.Response Surface Method and Its Experimental Design for Deterministic Computer Simulation[J].Acta Aeronauticaet Astronautica Sinica,2006,27(1):55-61.(in Chinese)
[22]李宗轩,邢利娜,解鹏.视频空间相机Φ330mm口径主镜组件设计[J].光子学报,2016,45(7):12-17.LI Zongxuan,XING Lina,XIE Peng.Design of theΦ330 mm Primary Mirror Assembly of Spaceborne Video Camera[J].Acta Photonica Sinica,2016,45(7):12-17.(in Chinese)
[23]包奇红,沙巍,陈长征,等.空间Si C反射镜背部中心支撑特性[J].光子学报,2017,46(2):22-31.BAO Qihong,SHA Wei,CHEN Changzheng,et al.Characteristics of Rear Support in Centre for Space SiC Mirror[J].Acta Photonica Sinica,2017,46(2):21-31.(in Chinese)