Mathematical Model of Contacting Freeform Surface Contour Measurement

QIU Gu-feng; YU Jing-chi; HUANG Qi-tai; NI Ying; WANG Yi

doi:10.3788/OPE.20132111.2813

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Mathematical Model of Contacting Freeform Surface Contour Measurement

更新时间：2020-08-12

- Mathematical Model of Contacting Freeform Surface Contour Measurement
- Optics and Precision Engineering Vol. 21, Issue 11, Pages: 2813-2820(2013)
- 作者机构：
  
  苏州大学现代光学研究所,江苏苏州,215006
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20132111.2813
  CLC： TB92;TH72
- Received：26 March 2013，
  
  Revised：15 May 2013，
  
  Published Online：22 November 2013，
  
  Published：15 November 2013
- 稿件说明：
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仇谷烽, 余景池, 黄启泰, 倪颖, 王毅. 接触式三坐标测量自由曲面的数据处理模型[J]. 光学精密工程, 2013,21(11): 2813-2820

CHOU Gu-Feng, TU Jing-Che, HUANG Qi-Tai, NI Ying, WANG Yi. Mathematical Model of Contacting Freeform Surface Contour Measurement[J]. Editorial Office of Optics and Precision Engineering, 2013,21(11): 2813-2820
仇谷烽, 余景池, 黄启泰, 倪颖, 王毅. 接触式三坐标测量自由曲面的数据处理模型[J]. 光学精密工程, 2013,21(11): 2813-2820 DOI： 10.3788/OPE.20132111.2813.

CHOU Gu-Feng, TU Jing-Che, HUANG Qi-Tai, NI Ying, WANG Yi. Mathematical Model of Contacting Freeform Surface Contour Measurement[J]. Editorial Office of Optics and Precision Engineering, 2013,21(11): 2813-2820 DOI： 10.3788/OPE.20132111.2813.

摘要

为了能够在接触式自由曲面轮廓测量过程中放宽对工件位置调整的要求并提供高精度的测量结果，本文运用最小二乘法的基本原理，提出了一个可通过测量数据拟合出一个最佳位置放置参数的数学模型。该模型能同时校正自由曲面放置时存在的绕X、Y、Z轴的微小旋转量及沿X、Y、Z方向上的微小偏离量所造成的测量误差。大量数学模拟结果表明，该模型在恢复上述误差源上具有很高的精度，可精确地恢复1 cm以下的偏心和0.1以下的旋转量。对一实际自由曲面的测量结果表明，该模型可靠有效，为接触式三坐标测量自由曲面轮廓提供了宽松的镜子放置条件，同时提供了可靠的测量结果。其分析数据的基本原理对其它非接触式的自由曲面的轮廓测量同样具有较高的参考价值。

Abstract

To unwind the requirement of a freeform surface for the position adjustment and to provide high precision measurement results in a high precision contacting freeform surface contour measurement

this paper proposes a mathematical model based on the least square method. The model can fit the measured dada to obtain optimized position parameters. After analysis of possible causes for the measurement error of Coordinate Measuring Machine(CMM)

the model can be used to correct the errors caused by the rotation in the X

Z axes and the eccentricity in the X

Z direction that exist in the positioning of freeform surface. By mathematical simulations

it is proved that this model achieves high precision in correction of the errors for eccentricity less than 1 cm and inclination less than 0.1 and shows a very reliable and effective result. It provides loose workpiece positioning conditions

high precision and reliable measurement results. The analysis principles proposed also offer a reference for other contacting freeform surface contour measurement methods.

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references

XIONG Z H, LI Z X. Error compensation of workpiece localization [C]. Proceedings of 2001 IEEE International Conference on Robotics and Automation, 2001：2249-2254.[2]杨钦，徐永安，翟红英,等. 计算机图形学[M]. 北京：清华大学出版社，2005.YANG Q,XU Y A,ZHAI H Y. Computer Graphics [M]. Beijing: Tsinghua University Press,2005. （in Chinese)[3]李全胜,成晔,张伯鹏. 光学自由曲面计算机控制加工中的形面检测研究[J ]. 光学精密工程,1999 ,7 (3): 89-96.LI Q SH,CHENG Y,ZHANG B P. Study on profile measuring in computer controlled fabrication of optical freeform surf ace [J]. Opt. Precision Eng.,1999 ,7 (3 ): 89-96. (in Chinese)[4]杜建军,高栋,孔令豹. 光学自由曲面误差评定中匹配方法的研究[ J ]. 光学精密工程, 2006, 14(1): 133-135.DU J J, GAO D, KONG L B. Study of matching methods for error evaluation of optical freeform surface [J]. Opt. Precision Eng., 2006, 14 (1) : 133-135. (in Chinese)[5]李圣怡,陈善勇,戴一帆. 自由曲面光学器件检测技术[ J ]. 纳米技术与精密工程, 2005, 3 (2) : 132-133.L I SH Y, CHEN SH Y, DAI Y F. Inspection of free2form optics[J]. Nano. Precision Eng., 2005, 3(2) : 132-133. (in Chinese)[6]仇谷烽,郭培基,解滨,等.接触式非球面轮廓测量的数据处理模型[J].光学精密工程,2007,15(4):492-498.QIU G F，GUO P J，XIE B, et al.. Mathematical model of contacting aspheric surface contour measurement [J].Opt. Precision Eng.,2007,15(4):492-498.(in Chinese)[7]王东霞，温秀兰，赵艺兵,等.基于CAD模型引导测量的自由曲面定位及轮廓度误差评定[J].光学精密工程，2012,20(12):2720-2727.WANG D X,WEN X L, ZHAO Y B. Localization and profile error evaluation of freeform surface based on CAD model-directed measurement[J] .Opt. Precision Eng., 2012,20(12):2720-2727. (in Chinese)

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