大口径透镜柔性支撑结构设计与分析  

Design and Mechanical Analysis of the Flexible Mounting Structure for the Large Aperture Lens

作　　者：赵勇志[1] 曹玉岩[1] 韩西达 李玉霞[1] ZHAO Yongzhi;CAO Yuyan;HAN Xida;LI Yuxia(Changchun Institute of Optics,Fine Mechanic and Physics,Chinese Academy of Sciences,Changchun 130033)

机构地区：[1]中国科学院长春光学精密机械与物理研究所,长春130033

出　　处：《长春理工大学学报（自然科学版）》2018年第5期1-7,共7页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(11403023)

摘　　要：柔性支撑结构在透镜热变形方向上具有可控的相对自由度,环境温度变化时,柔性支撑结构能够减小透镜与支撑结构间的热应力进而提高面形精度,因而广泛应用于透镜支撑结构中。为了解决柔性支撑结构的设计及性能评价问题,对柔性支撑结构建模方法进行了深入研究。首先,根据柔性支撑结构圆周对称特性,即由圆周对称分布的圆弧形柔性单元组成,将柔性单元简化为超静定圆弧梁,推导了柔性单元的径向及切向刚度。然后,假设透镜为刚体,根据力平衡条件及变形协调条件,推导了柔性结构的整体力学模型。最后,进行了有限元仿真和实验以验证提出的柔性支撑结构力学模型,理论模型与仿真及实验结果相吻合。此外,以300mm透镜为例,分析了支撑结构几何参数对透镜面形精度的影响及透镜的热应力分布,结果表明柔性支撑结构能够有效的降低透镜与支撑结构间的温度应力,进而提高支撑性能。Flexible structures have been widely used in the mounting structure of optical lens.Since the flexible structure has controllable degree of freedom(DOF)in the direction of thermal expansion of the lens,the thermal stress between the lens and its support structure caused by temperature variation is reduced and then the surface precision of the lens can be improved.In order to design this flexible structure and evaluate its mechanical performance,the mechanical model is presented and the corresponding modeling method is investigated accordingly.At first,this flexible structure is consisted by several identical flexible elements which can be simplified into an indeterminate curved beam structure.These flexible elements are distributed symmetrically in rotational direction.The radical and tangential stiffness of the flexible element are derived.Secondly,based on the assumption that the lens is a rigid body,the whole stiffness of this flexible structure is derived according to the force equilibrium and the compatible deformation.Finally,the presented mechanical model concerning the flexible element and structure is verified by the finite element simulation and experiment.The theoretical results agree with the simulation and experimental results,which indicate that the presented mechanical model can be used to analyze the deformation of the flexible structure exactly.In addition,a lens with a diameter of 300mm was taken for an example,the influence of the geometry parameters of the flexible mounting structure on the optical precision of the lens and the thermal stress distribution were analyzed,which demonstrate the flexible mounting structure was able to alleviate the thermal stress between the lens and its mounting structure effectively and the performance of the lens was then improved.

关 键 词：柔性结构 透镜 圆弧梁 协调变形 有限元仿真 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]