基于信赖域狗腿法的非球面抛光后置处理方法  

Aspherical Finishing Post Processing Method Based on Trust Region Dogleg Method

作　　者：杨航 赵功[2] 张强 汪玉兰 黄文[2] 何建国[2] 贾阳 Yang Hang;Zhao Gong;Zhang Qiang;Wang Yulan;Huang Wen;He Jianguo;Jia Yang(College of Engineering,Zunyi Normal University,Zunyi,Guizhou 563006,China;Institute of Mechanical Manufacturing Technology,China Academy of Engineering Physics,Mianyang,Sichuan 621900,China;Wuhan National Laboratory for Optoelectronics,Huazhong Research Institute of Electro-Optical Technology,Wuhan,Hubei 430073,China)

机构地区：[1]遵义师范学院工学院,贵州遵义563006 [2]中国工程物理研究院机械制造工艺研究所,四川绵阳621900 [3]华中光电技术研究所武汉光电国家实验室,湖北武汉430073

出　　处：《激光与光电子学进展》2020年第5期217-224,共8页Laser & Optoelectronics Progress

基　　金：贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]249);贵州省科技计划(黔科合LH字[2017]7084,黔科合平台人才[2018]5784);国家“高档数控机床与基础制造装备”科技重大专项“巨型激光装置光学元件超精密制造系统示范工程”课题资助(2017ZX04022001)。

摘　　要：提出利用信赖域狗腿法解决通用非球面光学元件抛光后置求解的强非线性问题。基于低序体表示和齐次变换方法建立适用于任意非球面面形和任意轨迹抛光的正向运动学模型;基于信赖域狗腿法建立强非线性正向运动学模型的数值优化求解方法,获得相应的逆向运动学数值结果;对逆向运动学数值求解结果进行处理得到各轴控制量,用于抛光后置处理。对一初始面形均方根值为0.037λ的离轴非球面采用光栅线进行4轮抛光,采用螺旋线进行5轮抛光,加工元件的面形收敛到均方根值为0.012λ,总收敛效率达到!"#$"%,表明所提后置处理方法是正确的,能够用于非球面加工。This paper proposes to use the trust region dogleg method to solve the high nonlinearity problem of post finishing of general aspheric optical components.Firstly,based on the low-order body representation and the homogeneous transformation method,a forward kinematic model suitable for any aspherical surface shape and arbitrary path is established.Then,a strong nonlinear forward kinematic model is established based on the trust region dogleg method.The numerical optimization method is used to obtain the corresponding inverse kinematics numerical results.Finally,the inverse kinematics numerical solution results are processed to obtain the control values of each axis for post processing.For an off-axis aspheric surface with an initial surface shape of root mean square 0.037λ,after four rounds of finishing with a raster line path planning and five rounds of finishing with a spiral path planning,the surface shape of the processed component converges to root mean square 0.012λ,and the total convergence efficiency reaches! "#$" %,indicating that the proposed post-processing method is correct and can be used for aspheric processing.

关 键 词：光学制造 非球面制造 信赖域方法 狗腿法 后置处理 

分 类 号：O435[机械工程—光学工程]