光学元件挠性支撑结构广义建模及优化设计

摘要

A mechanical and a parameter optimization model for flexure support structure of optical components were proposed to allow the flexure structure meet simultaneously the requirements of the stiffness for optical component position and the compliance for temperature adaptability . Meanwhile , the corresponding modeling method was investigated . As this flexure structure was consisted of several identical flexure parts ,it was simplified into an indeterminate beam structure ,and the radical stiffness and tangential stiffness were derived using the virtual work principle .Then ,by assuming optical components for the rigid body ,the whole stiffness of the flexure support structure was derived based on the force equilibrium and its compatible deformation , and the correction factor was introduced to compensate the error caused by the rigid assumption .Finally ,the total strain energy of the flexure structure was taken as the objective function ,and the collaborative optimization model was derived considering the geometrical pattern and parameters simultaneously . By introducing the integral variables ,the whole stiffness of the structure was simplified into a linear combination of the integral variable and discrete stiffness ,and the harmonic terms were eliminated .The whole stiffness model was verified by the simulation and experiment , and the experiment results are highly in agreement with the simulation results .A lens mounting was taken for an example ,the optimization method of the flexure mounting structure was verified .The finite element simulation results show that the surface precision of the lens has been improved by 23% .%建立了挠性支撑结构的力学模型及优化设计模型，以使光学元件挠性支撑结构同时满足元件定位的刚度要求和温度适应性的柔度要求，同时给出了相应的建模方法。考虑挠性支撑结构是由圆周对称分布的挠性单元组成的，故将挠性单元简化为超静定梁结构，应用虚功原理推导了挠性单元的径向及切向刚度。然后，假设光学元件为刚性体，根据力平衡条件及变形协调条件，推导了挠性支撑结构的整体刚度，并引入修正因子补偿了刚体假设带来的误差。最后，以挠性支撑结构总变形能为目标函数，推导了同时考虑挠性支撑结构几何构形及参数的协同优化设计模型，通过引入了整型变量将结构整体刚度简化为整型变量和离散刚度的线性组合，从而使优化模型中不含有谐波函数项。基于数值仿真和实验对结构刚度模型进行了验证，结果显示：实验、仿真和理论计算结果一致。此外，以透镜支撑为例，验证了挠性支撑结构的优化设计方法，有限元分析结果表明，透镜面形精度较初始设计提高了23％。