小型反射镜柔性镜座柔度分析

Flexibility analysis of mirror flexible lens seat

为了进行小型反射镜柔性镜座的柔度研究。首先利用伴随变换建立柔性镜座的柔度矩阵,推导出轴向、侧向某方向柔度分别为9.58×10-8m/N、1.38×10-8m/N,并用有限元分析软件MSC.Patran/Nastra仿真得到轴向柔度1.00×10-8m/N、侧向柔度1.33×10-8m/N。之后假设镜座与模拟镜之间连接处柔度矩阵为6×6对角阵。将此矩阵组合至镜座柔度理论模型中,得到侧向柔度关于连接处柔度矩阵对角线元素的表达式。通过对侧向柔度实验数据进行非线性拟合得到其数值,并计算出其正交方向与轴向柔度分别为4.039×10-7m/N、2.20×10-7m/N与实测值4.136×10-7m/N、2.25×10-7m/N比较,分别相差9%、2%,证明了简化的正确性与方法的可行性。本文利用优化的方法对柔度实验数据进行了非线性拟合,避开了可能的各向异性等具体的物理性质,直接在数学上建立其柔度模型,同时,对工程中类似问题的求解提供了指导;本文对于柔性镜座的分析对于项目之后的分析与装调也有重要意义。

In order to study mirror flexible lens seat＇ s flexibility, the flexibility matrix of fexible lens seat is estab- lished by the adjoint transformation,the obtained axial and lateral flexibilities are 9. 58 ×10^-8m/N and 1.38 ×10^-8 m/N respectively, and the simulated axial and lateral flexibilities are 1.00 ×10^-8 m/N and 1.33 ×10^-8 m/N by using the finite element analysis software ANSYS. Assuming the flexibility matrix that locate between lens seat and simula- tion is 6 ~ 6 diagonal matrix, the matrix combination is applied to a mirror seat theory model,the expression of lateral flexibility about diagonal elements is gotten. The experimental data of lateral flexibility is nonlinear fitted, and its val- ues are gotten,and the calculated axial and lateral flexibilities are 4. 039×10^-7m/N and 2. 20×10^-7m/N respective- ly. The difference between the analyzing results and the measured values are 9% and 2%. The flexibility experimental data is nonlinear fitted by using the optimized method, and the method avoids the physical properties such as anisotro- py. The flexibility model is established directly in the mathematical model, and it provides a reference for solving the similar problems in project.