Smoothing of mid-spatial frequency errors by computer controlled surface processing
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摘要: 数控抛光已被广泛应用于光学元器件的加工制造，而抑制元件表面中频误差是加工过程中一项十分重要的内容。基于Presston方程对数控小工具抛光盘去除函数进行了建模，得到了理论化的去除函数表达式。结合去除函数，在参数化匀滑模型基础上通过建立多参数的时变理论模型，表明元件表面中频误差是随抛光过程呈指数型收敛的，其收敛效率取决于材料参数、体积去除率等抛光工艺参数。对理论模型的匀滑曲线进行了模拟分析，实现了不同工艺条件下的匀滑效率的对比。结果表明：在不同抛光盘材料的匀滑过程中，材料系数越大，其整体匀滑效率越高。同样，抛光盘体积去除率越大，对表面误差的匀滑效率也会越高。进行了一组空间周期分别为3，5，7 mm的波纹误差的匀滑实验，其结果表明，在相同的抛光参数下，具有较大空间频率的波纹匀滑效率会更高，收敛曲线下降得更快。最后对比了不同材料抛光盘匀滑效率，从实验上证实了沥青盘在波纹匀滑效率上远高于聚氨酯材料的抛光盘。Abstract: Computer Controlled Surface Processing(CCOS) technology has been widely and successfully applied to the manufacture of optical components. In typical extreme optical manufacturing engineering, smoothing the surface errors is a very important process. Based on Presston equation, the tool influence function (TIF) of polishing pad is modeled, and the theoretical expression of TIF is obtained. Based on the parametric smoothing model, a multi-parameter time-dependent theoretical model is established. The results show that the surface error of components converges exponentially with the polishing process, and the convergence efficiency depends on the polishing parameters such as material parameters and volume removal rate. The smoothing curve of the theoretical model is simulated and analyzed, and the smoothing efficiency under different technological conditions is compared. The results show that the higher the material coefficient is, the higher the overall smoothing efficiency is. Similarly, the larger the volume removal rate of the polishing pad, the higher the smoothing efficiency of the surface error. A series of smoothing experiments with 3, 5 and 7 mm ripple errors were carried out. The results show that under the same polishing parameters, the smoothing efficiency of ripple with larger spatial frequency will be higher and the convergence curve will decline faster. Finally, the smoothing efficiencies of different material are compared, and the experimental results show that the smoothing efficiency of pitch pad is much higher than that of polyurethane polishing pad.
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Key words:
- CCOS /
- tool influence function /
- smoothing model /
- material parameters /
- spatial frequency
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图 2 抛光盘半径25 mm，偏心距5 mm，公转160 r/min，自转8 r/min参数下理论去除函数
Figure 2. Theoretical TIF under the parameters of radius 25 mm, eccentricity 5 mm, revolution 160 r/min and rotation 8 r/min
图 3 抛光盘在具有波纹误差的工件表面接触示意图以及实际抛光平台
Figure 3. A pitch polishing pad contact on the workpiece with ripple error and the experiment platform
图 4 沥青抛光盘与聚氨酯抛光盘匀滑过程理论曲线对比
Figure 4. Theoretical smoothing curves of pitch pad and polyurethane pad
图 5 不同抛光盘转动参数下理论去除函数对比
Figure 5. Comparison of theoretical TIF of different rotation parameters
图 6 不同抛光盘转动参数匀滑过程理论曲线对比
Figure 6. Comparison of theoretical smoothing curves of different rotation parameters
图 7 不同空间周期波纹误差匀滑实验数据拟合曲线
Figure 7. Data points and the fitting curves of the three workpieces with different spatial-period ripple error in the smoothing experiment
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[1] Jones R A. Optimization of computer controlled polishing[J]. Applied Optics, 1977, 16(1): 218-224. doi: 10.1364/AO.16.000218 [2] Nelson J, Sanders G H. The status of the Thirty Meter Telescope project[C]//Proc of SPIE. 2008: 70121A. [3] Johns M, Mccarthy P, Raybould K, et al. Giant Magellan Telescope: Overview[C]//Proc of SPIE. 2012: 84441H. [4] Wagner R E, Shannon R R. Fabrication of aspherics using a mathematical model for material removal[J]. Applied Optics, 1974, 13(7): 1683-1689. doi: 10.1364/AO.13.001683 [5] 王毅, 倪颖, 余景池. 小型非球面数控抛光技术的研究[J]. 光学精密工程, 2007, 15(10): 1527-1533. https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200710013.htmWang Yi, Ni Ying, Yu Jingchi. Computer-controlled polishing technology for small aspheric lens. Optics and Precision Engineering, 2007, 15(10): 1527-1533 https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200710013.htm [6] Wang Zhenzhong, Peng Yunfeng, Guo Yinbiao, et al. Modeling of the static tool influence function of bonnet polishing based on FEA[J]. Int J Adv Manuf Techno, 2014, 74: 341-349. doi: 10.1007/s00170-014-6004-3 [7] Dong Zhichao, Cheng Haobo, Tam Honyuen. Modified subaperture tool influence functions of a flat-pitch polisher with reverse-calculated material removal rate[J]. Applied Optics, 2014, 53(11): 2455-2464. doi: 10.1364/AO.53.002455 [8] Nelson D G, Gould A, Klinger C, et al. Incorporating VIBE into the precision optics manufacturing process[C]//Proc of SPIE. 2011: 812613. [9] 李徐钰, 魏朝阳, 徐文东, 等. 随动压力分布下的非球面抛光去除函数[J]. 光学 精密工程, 2016, 24(12): 3061-3067. https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201612027.htmLi Xuyu, Wei Chaoyang, Xu Wendong, et al. Tool influence function in aspheric polishing under dynamic pressure distribution. Optics and Precision Engineering, 2016, 24(12): 3061-3067 https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201612027.htm [10] 王佳, 范斌, 万勇建, 等. 一种评价CCOS抛光工艺误差抑制能力的方法[J]. 光子学报, 2014, 43: 722002. https://www.cnki.com.cn/Article/CJFDTOTAL-GZXB201407035.htmWang Jia, Fan Bin, Wan Yongjian, et al. A method to evaluate the error restraint ability of CCOS process. Acta Photonica Sinica, 2014, 43: 722002 https://www.cnki.com.cn/Article/CJFDTOTAL-GZXB201407035.htm [11] Mehta A P K, Hufnagel R E. Pressure distribution under flexible polishing tools: I. Conventional aspheric optics[C]//Proc of SPIE. 1990, 1303: 178-188. [12] Mehta P K, Reid P B, Derby E A, et al. A mathematical model for optical smoothing prediction of high-spatial-frequency surface errors[C]//Proc of SPIE. 1999, 3786: 447-459. [13] Nie Xuqing, Li Shenyi, Shi Feng, et al. Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors[J]. Applied Optics, 2014, 53(6): 1020-1027. doi: 10.1364/AO.53.001020 [14] Kim D W, Park W H, An H K, et al. Parametric smoothing model for visco-elastic polishing tools[J]. Optics Express, 2010, 18(21): 22515-22526. doi: 10.1364/OE.18.022515 [15] Kim D W, Martin H, Burge J H. Control of mid-spatial-frequency errors for large steep aspheric surfaces[C]//Optical Fabrication & Testing. 2012. [16] Shu Yong, Nie Xuqing, Shi Feng, et al. Smoothing evolution model for computer controlled optical surfacing[J]. Journal of Optical Technology, 2014, 81(3): 164-167. doi: 10.1364/JOT.81.000164 -
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