Abstract

There are still significant challenges in accurate positioning of optical freeform surfaces on the machine tool and the measurement instrument, due to the high accuracy requirement and their complex shapes. This paper proposes a fiducial-aided on-machine positioning method (FAOPM) that combines the on-machine measurement and off-machine measurement to precisely position optical freeform surfaces during the precision manufacturing cycle including rough machining, fine machining, measurement, and error compensation. The FAOPM makes use of fiducials, which are firstly measured in coordinate measuring machine with nanometric accuracy to generate a fiducial-aided computer aided design (FA-CAD) of the designed optical surface, then the developed on-machine measuring device obtains the accurate positions of the fiducials after remounting in the machining coordinate system. Finally, the relative position of the workpiece is identified so that the associated cutting paths and compensation tool path can be easily generated. Several optical freeform surfaces were experimentally machined to prove the capability of the proposed method. The results indicate that the positions of the workpiece during the precision manufacturing and measurement cycle were precisely achieved and the form accuracy of the optical freeform surfaces was remarkable improved based on the FAOPM.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Compensation strategy for machining optical freeform surfaces by the combined on- and off-machine measurement

Xiaodong Zhang, Zhen Zeng, Xianlei Liu, and Fengzhou Fang
Opt. Express 23(19) 24800-24810 (2015)

Model-based self-optimization method for form correction in the computer controlled bonnet polishing of optical freeform surfaces

Zhong-Chen Cao, Chi Fai Cheung, and Ming Yu Liu
Opt. Express 26(2) 2065-2078 (2018)

Highly efficient machining of non-circular freeform optics using fast tool servo assisted ultra-precision turning

Zexiao Li, Fengzhou Fang, Xiaodong Zhang, Xianlei Liu, and Huimin Gao
Opt. Express 25(21) 25243-25256 (2017)

References

  • View by:
  • |
  • |
  • |

  1. F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
    [Crossref]
  2. W. Lee, S. To, and C. Cheung, Design and advanced manufacturing technology for freeform optics, (The Hong Kong Polytechnic University).
  3. W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
    [Crossref]
  4. F. Niehaus, S. Huttenhuis, and A. Pisarski, “Fabrication and measurement of freeform surfaces using an integrated machining platform,” in Freeform Optics, (Optical Society of America, 2013), FW1B. 4.
  5. S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” in SPIE Astronomical Telescopes + Instrumentation, (International Society for Optics and Photonics, 2010), 773908–773908–773910.
  6. W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
    [Crossref]
  7. S. Moriyasu, Y. Yamagata, H. Ohmori, and S. Morita, “Probe type shape measuring sensor, and NC processing equipment and shape measuring method using the sensor,” (Google Patents, 2003).
  8. F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
    [Crossref]
  9. H. Ohmori, Y. Watanabe, W. M. Lin, K. Katahira, and T. Suzuki, “An ultraprecision on-machine measurement system,” in Key Engineering Materials, (Trans Tech Publ, 2005), 375–380.
  10. W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
    [Crossref]
  11. W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
    [Crossref]
  12. X. Zhang, Z. Zeng, X. Liu, and F. Fang, “Compensation strategy for machining optical freeform surfaces by the combined on- and off-machine measurement,” Opt. Express 23(19), 24800–24810 (2015).
    [Crossref] [PubMed]
  13. X. Zhang, L. Jiang, and G. Zhang, “Novel method of positioning optical freeform surfaces based on fringe deflectometry,” CIRP Ann.- Manuf. Tech. (2017).
  14. X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
    [Crossref]
  15. L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
    [Crossref]
  16. L. Shaw and A. Weckenmann, “Automatic registration method for hybrid optical coordinate measuring technology,” CIRP Ann.- Manuf. Tech. 60(1), 539–542 (2011).
    [Crossref]
  17. C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
    [Crossref]
  18. M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
    [Crossref]
  19. Y. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Comput. Aided Des. 36(13), 1395–1417 (2004).
    [Crossref]
  20. K. Medicus, J. D. Nelson, and M. Brunelle, “The need for fiducials on freeform optical surfaces,” in Optical System Alignment, Tolerancing, and Verification Ix, J. Sasian and R. N. Youngworth, eds. (Spie-Int Soc Optical Engineering, Bellingham, 2015).
  21. M. Brunelle, J. Yuan, K. Medicus, and J. D. Nelson, “Importance of Fiducials on Freeform Optics,” in Optifab 2015, J. L. Bentley and S. Stoebenau, eds. (Spie-Int Soc Optical Engineering, Bellingham, 2015).
  22. Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
    [Crossref]
  23. S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
    [Crossref]
  24. D. Li, C. F. Cheung, M. Ren, L. Zhou, and X. Zhao, “Autostereoscopy-based three-dimensional on-machine measuring system for micro-structured surfaces,” Opt. Express 22(21), 25635–25650 (2014).
    [Crossref] [PubMed]
  25. S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
    [Crossref]
  26. A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
    [Crossref]
  27. E. Olesch, C. Faber, R. Krobot, R. Zuber, and G. Häusler, “Quantitative Deflectometry Challenges Interferometry,” in Fringe2013:7th International Workshop on Advanced Optical Imaging and Metrology, W. Osten, ed. (Springer Berlin Heidelberg, Berlin, Heidelberg, 2014), pp. 907–910.
  28. N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
    [Crossref]
  29. S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
    [Crossref]
  30. G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
    [Crossref]
  31. S. Zhang and S. To, “The effects of spindle vibration on surface generation in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 71, 52–56 (2013).
    [Crossref]
  32. G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
    [Crossref]
  33. S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
    [Crossref]

2018 (1)

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

2015 (1)

2014 (4)

D. Li, C. F. Cheung, M. Ren, L. Zhou, and X. Zhao, “Autostereoscopy-based three-dimensional on-machine measuring system for micro-structured surfaces,” Opt. Express 22(21), 25635–25650 (2014).
[Crossref] [PubMed]

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
[Crossref]

G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
[Crossref]

2013 (2)

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

S. Zhang and S. To, “The effects of spindle vibration on surface generation in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 71, 52–56 (2013).
[Crossref]

2012 (3)

S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
[Crossref]

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

2011 (1)

L. Shaw and A. Weckenmann, “Automatic registration method for hybrid optical coordinate measuring technology,” CIRP Ann.- Manuf. Tech. 60(1), 539–542 (2011).
[Crossref]

2010 (4)

C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
[Crossref]

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

2007 (5)

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
[Crossref]

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

2004 (1)

Y. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Comput. Aided Des. 36(13), 1395–1417 (2004).
[Crossref]

2000 (1)

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

1998 (1)

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Aoki, J.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Arai, Y.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Araki, T.

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Bi, Q.

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

Borchardt, B.

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Buttress, J.

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Chen, F. J.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Cheng, K.

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

Cherukuri, H.

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Cheung, C.

C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
[Crossref]

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

Cheung, C. F.

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

D. Li, C. F. Cheung, M. Ren, L. Zhou, and X. Zhao, “Autostereoscopy-based three-dimensional on-machine measuring system for micro-structured surfaces,” Opt. Express 22(21), 25635–25650 (2014).
[Crossref] [PubMed]

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Chiu, W. M.

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Dutterer, B.

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Estler, W. T.

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Evans, C.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Fan, Y. F.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Fang, F.

X. Zhang, Z. Zeng, X. Liu, and F. Fang, “Compensation strategy for machining optical freeform surfaces by the combined on- and off-machine measurement,” Opt. Express 23(19), 24800–24810 (2015).
[Crossref] [PubMed]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Gao, W.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Glover, F.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Goel, G.

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Gu, P.

Y. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Comput. Aided Des. 36(13), 1395–1417 (2004).
[Crossref]

Huang, H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Huang, N.

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

Hwang, J. H.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Ibaraki, S.

S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
[Crossref]

Iritani, T.

S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
[Crossref]

Jiang, X.

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
[Crossref]

Ju, B.-F.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Kelly, J.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Kiyono, S.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Kong, L.

C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
[Crossref]

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

Kong, L. B.

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

Lasdon, L.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Lee, J. C.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Lee, W.

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

Lee, W. B.

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Leung, T. P.

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Li, D.

Li, Y.

Y. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Comput. Aided Des. 36(13), 1395–1417 (2004).
[Crossref]

Liu, M.

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

Liu, X.

Martí, R.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Matsushita, T.

S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
[Crossref]

Nagaike, Y.

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Nakamura, Y.

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Noh, Y. J.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Ohmori, H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Park, C. H.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Phillips, S. D.

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Plummer, J.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Ren, M.

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

D. Li, C. F. Cheung, M. Ren, L. Zhou, and X. Zhao, “Autostereoscopy-based three-dimensional on-machine measuring system for micro-structured surfaces,” Opt. Express 22(21), 25635–25650 (2014).
[Crossref] [PubMed]

C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
[Crossref]

Ren, M. J.

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

Scott, P.

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
[Crossref]

Shaw, L.

L. Shaw and A. Weckenmann, “Automatic registration method for hybrid optical coordinate measuring technology,” CIRP Ann.- Manuf. Tech. 60(1), 539–542 (2011).
[Crossref]

Shibuya, A.

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Smith, S.

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Sun, C.

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

Tano, M.

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

To, S.

G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
[Crossref]

G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
[Crossref]

S. Zhang and S. To, “The effects of spindle vibration on surface generation in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 71, 52–56 (2013).
[Crossref]

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

Ugray, Z.

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Wang, S.

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

Wang, Y.

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Weckenmann, A.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

L. Shaw and A. Weckenmann, “Automatic registration method for hybrid optical coordinate measuring technology,” CIRP Ann.- Manuf. Tech. 60(1), 539–542 (2011).
[Crossref]

Whitehouse, D.

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
[Crossref]

Wilhelm, R.

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Xiao, G.

G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
[Crossref]

G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
[Crossref]

Yin, S. H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Yoshikawa, Y.

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Zeng, Z.

Zhang, G.

G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
[Crossref]

G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Zhang, S.

S. Zhang and S. To, “The effects of spindle vibration on surface generation in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 71, 52–56 (2013).
[Crossref]

Zhang, X.

X. Zhang, Z. Zeng, X. Liu, and F. Fang, “Compensation strategy for machining optical freeform surfaces by the combined on- and off-machine measurement,” Opt. Express 23(19), 24800–24810 (2015).
[Crossref] [PubMed]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Zhao, X.

Zhou, L.

Zhu, Y. J.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

CIRP Ann Manuf. Tech. (1)

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-a fresh strategy,” CIRP Ann Manuf. Tech. 56(1), 553–556 (2007).
[Crossref]

CIRP Ann.- Manuf. Tech. (3)

L. Shaw and A. Weckenmann, “Automatic registration method for hybrid optical coordinate measuring technology,” CIRP Ann.- Manuf. Tech. 60(1), 539–542 (2011).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

S. Smith, R. Wilhelm, B. Dutterer, H. Cherukuri, and G. Goel, “Sacrificial structure preforms for thin part machining,” CIRP Ann.- Manuf. Tech. 61(1), 379–382 (2012).
[Crossref]

Comput. Aided Des. (1)

Y. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Comput. Aided Des. 36(13), 1395–1417 (2004).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

M. J. Ren, C. F. Cheung, L. B. Kong, and X. Jiang, “Invariant-feature-pattern-based form characterization for the measurement of ultraprecision freeform surfaces,” IEEE Trans. Instrum. Meas. 61(4), 963–973 (2012).
[Crossref]

INFORMS J. Comput. (1)

Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

A. Shibuya, Y. Arai, Y. Yoshikawa, W. Gao, Y. Nagaike, and Y. Nakamura, “A spiral scanning probe system for micro-aspheric surface profile measurement,” Int. J. Adv. Manuf. Technol. 46(9-12), 845–862 (2010).
[Crossref]

Int. J. Mach. Tools Manuf. (7)

N. Huang, Q. Bi, Y. Wang, and C. Sun, “5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement,” Int. J. Mach. Tools Manuf. 84, 1–8 (2014).
[Crossref]

S. Ibaraki, T. Iritani, and T. Matsushita, “Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe,” Int. J. Mach. Tools Manuf. 58, 44–53 (2012).
[Crossref]

G. Zhang, S. To, and G. Xiao, “A novel spindle inclination error identification and compensation method in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 78, 8–17 (2014).
[Crossref]

S. Zhang and S. To, “The effects of spindle vibration on surface generation in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 71, 52–56 (2013).
[Crossref]

G. Zhang, S. To, and G. Xiao, “The relation between chip morphology and tool wear in ultra-precision raster milling,” Int. J. Mach. Tools Manuf. 80, 11–17 (2014).
[Crossref]

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

J. Mater. Process. Technol. (1)

W. B. Lee, C. F. Cheung, W. M. Chiu, and T. P. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Meas. Sci. Technol. (2)

L. Kong, C. Cheung, S. To, W. Lee, and K. Cheng, “Measuring optical freeform surfaces using a coupled reference data method,” Meas. Sci. Technol. 18(7), 2252–2260 (2007).
[Crossref]

C. Cheung, L. Kong, and M. Ren, “Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method,” Meas. Sci. Technol. 21(11), 115109 (2010).
[Crossref]

Micromachines (Basel) (1)

S. Wang, C. F. Cheung, M. Ren, and M. Liu, “Fiducial-Aided Robust Positioning of Optical Freeform Surfaces,” Micromachines (Basel) 9(2), 52 (2018).
[Crossref]

Opt. Express (2)

Precis. Eng. (3)

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

S. D. Phillips, B. Borchardt, W. T. Estler, and J. Buttress, “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines,” Precis. Eng. 22(2), 87–97 (1998).
[Crossref]

Other (9)

K. Medicus, J. D. Nelson, and M. Brunelle, “The need for fiducials on freeform optical surfaces,” in Optical System Alignment, Tolerancing, and Verification Ix, J. Sasian and R. N. Youngworth, eds. (Spie-Int Soc Optical Engineering, Bellingham, 2015).

M. Brunelle, J. Yuan, K. Medicus, and J. D. Nelson, “Importance of Fiducials on Freeform Optics,” in Optifab 2015, J. L. Bentley and S. Stoebenau, eds. (Spie-Int Soc Optical Engineering, Bellingham, 2015).

E. Olesch, C. Faber, R. Krobot, R. Zuber, and G. Häusler, “Quantitative Deflectometry Challenges Interferometry,” in Fringe2013:7th International Workshop on Advanced Optical Imaging and Metrology, W. Osten, ed. (Springer Berlin Heidelberg, Berlin, Heidelberg, 2014), pp. 907–910.

S. Moriyasu, Y. Yamagata, H. Ohmori, and S. Morita, “Probe type shape measuring sensor, and NC processing equipment and shape measuring method using the sensor,” (Google Patents, 2003).

H. Ohmori, Y. Watanabe, W. M. Lin, K. Katahira, and T. Suzuki, “An ultraprecision on-machine measurement system,” in Key Engineering Materials, (Trans Tech Publ, 2005), 375–380.

F. Niehaus, S. Huttenhuis, and A. Pisarski, “Fabrication and measurement of freeform surfaces using an integrated machining platform,” in Freeform Optics, (Optical Society of America, 2013), FW1B. 4.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” in SPIE Astronomical Telescopes + Instrumentation, (International Society for Optics and Photonics, 2010), 773908–773908–773910.

W. Lee, S. To, and C. Cheung, Design and advanced manufacturing technology for freeform optics, (The Hong Kong Polytechnic University).

X. Zhang, L. Jiang, and G. Zhang, “Novel method of positioning optical freeform surfaces based on fringe deflectometry,” CIRP Ann.- Manuf. Tech. (2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1 Flow-process of the proposed FAOMP.
Fig. 2
Fig. 2 Positioning remounted workpiece by using on-machine laser probe measuring fiducials (references).
Fig. 3
Fig. 3 The process of the machining freeform surfaces in FAOPM.
Fig. 4
Fig. 4 Positioning machined surface in measurement instrument and evaluation using fiducial aided CAD (reference model).
Fig. 5
Fig. 5 The flow chart of the measurement of freeform surface in FAOPM.
Fig. 6
Fig. 6 Development on-machine measurement system on the ultra-precision raster milling and the machined surfaces for calibration.
Fig. 7
Fig. 7 Matching the measured points to the designed surface.
Fig. 8
Fig. 8 Errors of (a) the rotational parameters and (b) translational parameters under different geometric error of the on-machine measurement system.
Fig. 9
Fig. 9 Standard deviation of (a) rotational parameters and (b) translational parameters under different geometric error of the on-machine measurement system.
Fig. 10
Fig. 10 Quadrate fixture and the fiducials with the pre-processed workpiece.
Fig. 11
Fig. 11 Configuration for machining the freeform surface.
Fig. 12
Fig. 12 Measuring the workpiece by multi sensor CMM.
Fig. 13
Fig. 13 (a) Machined surface and (b) the 3D error map of the surface.
Fig. 14
Fig. 14 (a) The source path and the revised compensation path (b) 3D topography of the surface after compensation.

Tables (6)

Tables Icon

Table 1 Six parameters for obtaining measured surface

Tables Icon

Table 2 Simulated deviations of the parameters and the surface profile

Tables Icon

Table 3 Uncertainty error contributors in the on-machine process

Tables Icon

Table 4 Calibrated positions of the ball center in the designed surface

Tables Icon

Table 5 PSD values of the repeat measurement

Tables Icon

Table 6 Machining parameters of raster milling

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

T( m )=[ c(γ)c(φ) s(γ)c( r y )+c(γ)s(φ)s(ϕ) s(γ)s(ϕ)c(γ)s(φ)c(ϕ) δ x s(γ)c(φ) c(γ)c(ϕ)s(γ)s(φ)s(ϕ) c(γ)s(ϕ)+s(γ)s(φ)c(ϕ) δ y s(φ) c(φ)s(ϕ) c(φ)c(ϕ) δ z 0 0 0 1 ]
F( m )=min i=1 N | PTP' | 2
|F(i)-F(j)|<= ς F *max(1,|F(j)|) |m(i)m(j)|<= ς m *max(1,|m(j)|)
E f eva,i =( S( u i , v i )T Q i ) n ( u i , v i )
min i=1 N | P i T Q i | 2
z=50 (x/50) 3 +50 (x/50) 3 x[5,5],y[5,5]
z=0.025cos(x)+0.025cos(y) x[5,5],y[5,5]
z=(-1/250) x 2 +(1/92000) x 4 (1/25) y 2 x[15,15],y[5,5]
q ¯ i,j,k = 1 N j j=1 N j q i,j,k ; Δ q i,j,k = q i,j,k q ¯ i,j,k ; d i,j,k =||Δ q i,j,k ||
S D i,j,k = j=1 N j d 2 i,j,k ( N j 1) PS D i,j,k = i=1 N i ( N j 1)S D 2 i,j,k i=1 N i ( N j 1)