双驱动补偿压弯的椭圆镜有限元分析

Elliptic mirror finite element analysis of double drive compensated bending

为满足同步辐射光束线对相关光学元件的技术需求,设计了双驱动四点滚柱压弯机构。通过有限元仿真分析实现高精度大尺寸光学镜面的非等力矩椭圆柱面压弯。以外形尺寸为1200 mm×70 mm×50 mm的反射镜为研究对象,基于物距26.5 m、像距13 m及掠入射角2.8 mrad,根据理论椭圆面形方程与梁变形弯矩方程计算出施加在压弯镜两端的不等力矩。利用有限元软件对双驱动四点压弯机构进行仿真分析,在重力补偿力矩存在情况下,分别对聚焦镜进行单点补偿、双点补偿、三点补偿以及四点补偿的有限元分析,得到与理论计算相对应的仿真补偿面形结果。模拟施加两端的不等力矩将面形误差从单点补偿时的0.81μrad降低到四点补偿下的0.075μrad,对应理论面形误差0.013μrad,最大程度可以降低原误差的95.96%,证实四点式双驱动机构通过多点补偿可以对椭圆压弯面形误差产生有效减小的趋势,且减小趋势不断平缓。证明该机构在多点补偿下对大尺寸椭圆镜压弯精度的提高具有可行性和有效性,对同步辐射光束线压弯技术有重要的理论指导作用与意义。

[Background]In order to meet the technical requirements of synchrotron radiation beamlines for related optical components,a double-drive four-point roller bending mechanism is designed.[Purpose]This study aims to implement an unequal moment elliptical cylinder bending of high-precision large-size optical mirror through finite element analysis(FEA)simulation.[Methods]First of all,a reflector with an external dimension of 1200 mm×70 mm×50 mm was taken as the research object.Based on the object distance of 26.5 m,the image distance of 13 m and the grazing incidence angle of 2.8 mrad,the pressure applied to the bending moment was calculated according to the theoretical ellipse shape equation and the beam deformation bending moment equation.Then,the FEA software was employed to simulate and analyze the double-drive four-point bending mechanism.The focusing mirror was subjected to single-point compensation,double-point compensation,three-point compensation and four-point compensation in the presence of gravity compensation torque.Finally,the simulation compensation surface results obtained by FEA were compared with the theoretical calculation results.[Results]The simulated application of unequal torque at both ends reduces the surface shape error from 0.81μrad under single-point compensation to0.075μrad under four-point compensation,reducing 95.96%of the original error to the greatest extent.It can effectively reduce the elliptical bending surface shape error with theoretical value of 0.013μrad,and the decreasing trend is gradually gentle.[Conclusions]This study indicates that the double drive compensated bending mechanism is feasible and effective to improve the bending accuracy of large-scale elliptical mirrors under multi-point compensation,and has important theoretical guiding role and significance for the bending technology of synchrotron radiation beamlines.