基于有限元分析的大口径曲面棱镜胶接优化设计  

Optimization Design of Large Aperture Curved Prism Bonding Based on Finite Element Analysis

作　　者：冯军 李思远[1] 王飞橙 陈文聪 田飞飞 贾昕胤 FENG Jun;LI Siyuan;WANG Feicheng;CHEN Wencong;TIAN Feifei;JIA Xinyin(Xi'an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi'an 710119,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院西安光学精密机械研究所,西安710119 [2]中国科学院大学,北京100049

出　　处：《光子学报》2024年第11期132-146,共15页Acta Photonica Sinica

基　　金：国家自然科学基金(No.42306202)。

摘　　要：针对大口径曲面棱镜高面形精度的需求,提出了一种考虑胶固化收缩应力的胶结优化设计路线,得到了胶接优化方案。首先,根据胶体非自由固化模型,推导了胶固化应力的有限元微分方程。其次,设计了圆弧形胶斑式柔性粘结环及其框架结构。基于温度载荷法搭建了胶固化对镜面面形影响的仿真模型,并建立了等效胶收缩力关于胶体参数的响应面模型,研究了胶粘剂种类、胶体参数、粘结数量对面形的影响规律,结果表明:选用3 m-2216环氧胶、圆弧形胶斑及其柔性粘结环、在侧面6胶点胶接工况下,曲面棱镜前镜面面形PV值从0.66λ降到0.005λ、RMS值从0.15λ降到0.001λ;后镜面面形PV值从0.61λ降到0.003λ、RMS值从0.14λ降到0.001λ,曲面棱镜面形精度得到显著改善。最后,采用有限元法进行了结构力热特性分析,验证了结构设计的合理性。Aiming at the working conditions and performance requirements of large-diameter curved prisms with high face shape precision,an optimized design approach is proposed for bonding such prisms while considering the adhesive curing shrinkage stress.Based on this approach,the bonding process for large-diameter curved prisms is successfully optimized.Firstly,the finite element differential equation for the shrinkage stress during glue curing is derived based on the non-free curing model of the glue.Secondly,by applying the principles of support structure design and flexible structure design theory,a meticulously devised circular flexible bonding structure was created.The topology of the frame structure was optimized with flexibility as the primary objective while adhering to structural weight constraints,resulting in an impressive lightweight rate of 55.79%.Subsequently,a simulation and analysis model was developed to investigate the impact of adhesive curing shrinkage on mirror surface shape using the temperature loading method.The response surface model for the colloid parameters′equivalent gel contraction force was established,achieving a goodness of fit of 97.56%.It was found that the equivalent gel contraction force increased with the increase of colloid contraction rate and thickness.Additionally,the equivalent gel contraction force and the area of colloid spot exhibited different monotonous increasing and decreasing trends under varying gel contraction rates.The degree of influence of colloid contraction rate on the equivalent gel contraction force was found to be the largest,while the area of colloid spot had the least influence on the equivalent gel contraction force.The optimized parameters for the colloid were determined to be 9 mm×23 mm×0.1 mm.The study investigated the influence of adhesive type,gel parameters,and bonding quantity on the surface shape of curved prism components.The results obtained from the surface shape simulation analysis of curved prisms using three kinds of epoxy adhesives(3M-2216,

关 键 词：曲面棱镜 胶接 面形精度 响应面法 有限元仿真 结构优化 力热特性分析 

分 类 号：V461[航空宇航科学与技术—航空宇航制造工程]