基于Kahan方法的磁流变抛光凸元件几何特性分析  

Analysis of geometric characteristics of magnetorheological polishing convex elements based on Kahan method

作　　者：杨航 佘娜 张云飞[2] 黄文[2] 贾阳 YANG Hang;SHE Na;ZHANG Yun-fei;HUANG Wen;JIA Yang(College of Engineering,Zunyi Normal University,Zunyi 563006,China;Institute of Mechanical Engineering,China Academy of Engineering Physics,Mianyang 621900,China;Wuhan Optoelectronic National Laboratory,Huazhong Optoelectronic Technology Research Institute,Wuhan 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：《激光与红外》2022年第2期266-272,共7页Laser & Infrared

基　　金：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);遵义市科技局科技研发项目(遵市科合HZ字[2020]21号);贵州省基础研究计划项目(黔科合基础-ZK[2021]一般272)资助。

摘　　要：凸光学元件在磁流变抛光区域的几何特性对制造高精度、高表面完整性光学元件有重要影响,凸光学元件曲率、嵌入深度与角度的变化将引起磁流变抛光区域压力场的变化。为了研究凸光学元件不同的曲率、嵌入深度与嵌入角度下抛光区域的压力场,首先通过建立磁流变抛光过程中压力模型,对抛光区域的压力进行分析;其次基于Kahan数值方法建立了多场耦合积分的快速计算方法。最后,计算凸光学元件在不同曲率、嵌入深度及角度下得到磁流变抛光区域压力场分布,研究凸元件在磁流变抛光区域受几何特性影响的工艺规律;得出结论:在磁流变抛光过程中通过改变凸光学元件曲率、相同曲率下的嵌入深度以及角度的情况下,当加工凸元件曲率增大时,磁流变抛光区域压力场会随之增大;当凸元件曲率一定、嵌入深度逐渐变深时,磁流变抛光区域压力场会增大;当凸元件曲率一定、嵌入角度增加时,磁流变抛光区域压力场会随角度先增大再减小。The geometric characteristics of the convex optical element in the magnetorheological polishing area have an important influence on the manufacture of high-precision and high surface integrity optical elements.Variations in curvature,embedding depth and angle of the convex optical element will cause the change of pressure field in the magnetorheological polishing area.In order to study the pressure field of the polishing area under different curvatures,embedding depths and embedding angles of convex optical elements,the pressure in the polishing area was analyzed firstly by establishing a pressure model during the magnetorheological polishing process.Secondly,a fast calculation method for multi-field coupled integral was established based on the Kahan numerical method.Finally,the pressure field distribution of the magnetorheological polishing area is obtained by calculating the convex optical element under different curvatures,embedding depths and angles,and the process law of the convex element affected by the geometric characteristics in the magnetorheological polishing area is studied.It is concluded that in the polishing process,by changing the curvature of the convex optical element,the embedding depth and the angle under the same curvature,when the curvature of the processed convex element increases,the pressure field of the magnetorheological polishing area will increase accordingly;when the curvature of the convex element is constant and the embedding depth gradually deepens,the pressure field of the magnetorheological polishing area will increase;when the curvature of the convex element is constant and the embedding angle increases,the pressure field of the magnetorheological polishing area will increases and then decreases with the angle.

关 键 词：Kahan方法 磁流变抛光 压力场 凸光学元件 几何特性 

分 类 号：O435[机械工程—光学工程]