Abstract

Freeform surfaces have become increasingly widespread in the optical systems for enhanced performance and compact lightweight packaging. The geometrical complexity and high precision requirements of optical freeform surfaces for various functional optical applications, has posed great challenges in the design, precision machining, and measurement of these surfaces. This paper presents a model-based self-optimization approach for precision machining and measurement of optical freeform surfaces in the computer controlled bonnet polishing (CCBP) process. To realize the technical feasibility, the process parameters and motion control are accurately performed through modelling and simulation of machining processes, error compensation, and on-machine metrology.

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

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References

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    [Crossref]
  2. Z. C. Cao and C. F. Cheung, “Theoretical modelling and analysis of the material removal characteristics in fluid jet polishing,” Int. J. Mech. Sci. 89, 158–166 (2014).
    [Crossref]
  3. D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
    [Crossref]
  4. R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
    [Crossref]
  5. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
    [Crossref] [PubMed]
  6. H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013).
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    [Crossref]
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    [Crossref]
  18. S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).
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    [Crossref]
  20. Y. T. Su and J.-Y. Sheen, “A process planning strategy for removing arbitrary and axially symmetric profile by a polishing process,” Int. J. Mach. Tools Manuf. 39(2), 187–207 (1999).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  23. Z. Dong, H. Cheng, and H. Y. Tam, “Robust linear equation dwell time model compatible with large scale discrete surface error matrix,” Appl. Opt. 54(10), 2747–2756 (2015).
    [Crossref] [PubMed]
  24. C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
    [Crossref]
  25. M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
    [Crossref]

2016 (3)

Z. C. Cao and C. F. Cheung, “Multi-scale modeling and simulation of material removal characteristics in computer-controlled bonnet polishing,” Int. J. Mech. Sci. 106, 147–156 (2016).
[Crossref]

Z. C. Cao, C. F. Cheung, and X. Zhao, “A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing,” Wear 360–361, 137–146 (2016).
[Crossref]

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

2015 (1)

2014 (3)

2013 (3)

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

H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013).
[Crossref] [PubMed]

J. Chaves-Jacob, J. M. Linares, and J. M. Sprauel, “Improving tool wear and surface covering in polishing via toolpath optimization,” J. Mater. Process. Technol. 213(10), 1661–1668 (2013).
[Crossref]

2012 (1)

2010 (1)

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

2009 (2)

2008 (2)

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref] [PubMed]

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

2006 (1)

2003 (1)

2001 (1)

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

2000 (1)

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

1999 (1)

Y. T. Su and J.-Y. Sheen, “A process planning strategy for removing arbitrary and axially symmetric profile by a polishing process,” Int. J. Mach. Tools Manuf. 39(2), 187–207 (1999).
[Crossref]

1992 (1)

P. J. Besl and N. D. Mckay, “A Method for Registration of 3-D Shapes,” Ieee T Pattern Anal 14(2), 239–256 (1992).
[Crossref]

1982 (2)

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

C. C. Paige and M. A. Saunders, “Algorithm 583: LSQR: Sparse linear equations and least squares problems,” ACM Trans. Math. Softw. 8(2), 195–209 (1982).
[Crossref]

1981 (1)

Beaucamp, A.

Besl, P. J.

P. J. Besl and N. D. Mckay, “A Method for Registration of 3-D Shapes,” Ieee T Pattern Anal 14(2), 239–256 (1992).
[Crossref]

Bingham, R. G.

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Brooks, D.

D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
[Crossref] [PubMed]

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Burge, J. H.

Cao, Z. C.

Z. C. Cao, C. F. Cheung, and X. Zhao, “A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing,” Wear 360–361, 137–146 (2016).
[Crossref]

Z. C. Cao and C. F. Cheung, “Multi-scale modeling and simulation of material removal characteristics in computer-controlled bonnet polishing,” Int. J. Mech. Sci. 106, 147–156 (2016).
[Crossref]

Z. C. Cao and C. F. Cheung, “Theoretical modelling and analysis of the material removal characteristics in fluid jet polishing,” Int. J. Mech. Sci. 89, 158–166 (2014).
[Crossref]

Charlton, P.

A. Beaucamp, Y. Namba, and P. Charlton, “Corrective finishing of extreme ultraviolet photomask blanks by precessed bonnet polisher,” Appl. Opt. 53(14), 3075–3080 (2014).
[Crossref] [PubMed]

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Chaves-Jacob, J.

J. Chaves-Jacob, J. M. Linares, and J. M. Sprauel, “Improving tool wear and surface covering in polishing via toolpath optimization,” J. Mater. Process. Technol. 213(10), 1661–1668 (2013).
[Crossref]

Cheng, C. H.

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

Cheng, H.

Cheung, B. C. F.

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

Cheung, C. F.

Z. C. Cao, C. F. Cheung, and X. Zhao, “A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing,” Wear 360–361, 137–146 (2016).
[Crossref]

Z. C. Cao and C. F. Cheung, “Multi-scale modeling and simulation of material removal characteristics in computer-controlled bonnet polishing,” Int. J. Mech. Sci. 106, 147–156 (2016).
[Crossref]

Z. C. Cao and C. F. Cheung, “Theoretical modelling and analysis of the material removal characteristics in fluid jet polishing,” Int. J. Mech. Sci. 89, 158–166 (2014).
[Crossref]

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Dong, Z.

Dunn, C. R.

Evans, C.

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

Evans, R.

Fang, F. Z.

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

Freeman, R.

D. D. Walker, R. Freeman, R. Morton, G. McCavana, and A. Beaucamp, “Use of the ‘Precessions’ ™ process for prepolishing and correcting 2D & 2(1/2)D form,” Opt. Express 14(24), 11787–11795 (2006).
[Crossref] [PubMed]

D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
[Crossref] [PubMed]

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Guan, C.

Ho, L. T.

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Kim, D. H.

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Kim, D. W.

Kim, S. W.

Kim, S.-W.

King, A.

D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
[Crossref] [PubMed]

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

Kong, L. B.

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Lee, W. B.

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Li, H.

Li, S.

Linares, J. M.

J. Chaves-Jacob, J. M. Linares, and J. M. Sprauel, “Improving tool wear and surface covering in polishing via toolpath optimization,” J. Mater. Process. Technol. 213(10), 1661–1668 (2013).
[Crossref]

Liu, S. M. Y.

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

Lu, Z. W.

Marks Ii, R. J.

McCavana, G.

Mckay, N. D.

P. J. Besl and N. D. Mckay, “A Method for Registration of 3-D Shapes,” Ieee T Pattern Anal 14(2), 239–256 (1992).
[Crossref]

Messelink, W.

Morton, R.

Namba, Y.

Paige, C. C.

C. C. Paige and M. A. Saunders, “Algorithm 583: LSQR: Sparse linear equations and least squares problems,” ACM Trans. Math. Softw. 8(2), 195–209 (1982).
[Crossref]

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

Park, W. H.

Peng, W.

Pitschke, E.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Rascher, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Riley, D.

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Saunders, M. A.

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

C. C. Paige and M. A. Saunders, “Algorithm 583: LSQR: Sparse linear equations and least squares problems,” ACM Trans. Math. Softw. 8(2), 195–209 (1982).
[Crossref]

Sayle, A.

Schinhaerl, M.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Sheen, J.-Y.

Y. T. Su and J.-Y. Sheen, “A process planning strategy for removing arbitrary and axially symmetric profile by a polishing process,” Int. J. Mach. Tools Manuf. 39(2), 187–207 (1999).
[Crossref]

Simms, J.

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

Smith, G.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Smith, L.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Sperber, P.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Sprauel, J. M.

J. Chaves-Jacob, J. M. Linares, and J. M. Sprauel, “Improving tool wear and surface covering in polishing via toolpath optimization,” J. Mater. Process. Technol. 213(10), 1661–1668 (2013).
[Crossref]

Stamp, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Su, Y. T.

Y. T. Su and J.-Y. Sheen, “A process planning strategy for removing arbitrary and axially symmetric profile by a polishing process,” Int. J. Mach. Tools Manuf. 39(2), 187–207 (1999).
[Crossref]

Tam, H. Y.

To, S.

C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

Walker, D.

Walker, D. D.

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref] [PubMed]

D. D. Walker, R. Freeman, R. Morton, G. McCavana, and A. Beaucamp, “Use of the ‘Precessions’ ™ process for prepolishing and correcting 2D & 2(1/2)D form,” Opt. Express 14(24), 11787–11795 (2006).
[Crossref] [PubMed]

D. D. Walker, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “The first aspheric form and texture results from a production machine embodying the Precession Process,” Optical Manufacturing and Testing Iv 4451, 267–276 (2001).
[Crossref]

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Current Developments in Lens Design and Optical Systems Engineering 4093, 445–450 (2000).
[Crossref]

Wang, T. S.

Weckenmann, A.

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

Whitehouse, D.

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

Wu, J. F.

Yu, G.

Zhang, G. X.

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

Zhang, H. X.

Zhang, X. D.

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

Zhao, X.

Z. C. Cao, C. F. Cheung, and X. Zhao, “A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing,” Wear 360–361, 137–146 (2016).
[Crossref]

ACM Trans. Math. Softw. (2)

C. C. Paige and M. A. Saunders, “Algorithm 583: LSQR: Sparse linear equations and least squares problems,” ACM Trans. Math. Softw. 8(2), 195–209 (1982).
[Crossref]

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

Appl. Opt. (4)

Cirp Ann-Manuf Techn (1)

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

Current Developments in Lens Design and Optical Systems Engineering (1)

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[Crossref]

Int. J. Mech. Sci. (2)

Z. C. Cao and C. F. Cheung, “Multi-scale modeling and simulation of material removal characteristics in computer-controlled bonnet polishing,” Int. J. Mech. Sci. 106, 147–156 (2016).
[Crossref]

Z. C. Cao and C. F. Cheung, “Theoretical modelling and analysis of the material removal characteristics in fluid jet polishing,” Int. J. Mech. Sci. 89, 158–166 (2014).
[Crossref]

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J. Chaves-Jacob, J. M. Linares, and J. M. Sprauel, “Improving tool wear and surface covering in polishing via toolpath optimization,” J. Mater. Process. Technol. 213(10), 1661–1668 (2013).
[Crossref]

Meas. Sci. Technol. (1)

S. M. Y. Liu, B. C. F. Cheung, D. Whitehouse, and C. H. Cheng, “An autonomous multisensor in situ metrology system for enabling high dynamic range measurement of 3D surfaces on precision machine tools,” Meas. Sci. Technol. 27, 115015 (2016).

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D. D. Walker, R. Freeman, R. Morton, G. McCavana, and A. Beaucamp, “Use of the ‘Precessions’ ™ process for prepolishing and correcting 2D & 2(1/2)D form,” Opt. Express 14(24), 11787–11795 (2006).
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D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
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C. F. Cheung, L. T. Ho, P. Charlton, L. B. Kong, S. To, and W. B. Lee, “Analysis of surface generation in the ultraprecision polishing of freeform surfaces,” P I Mech Eng B-J Eng 224, 59– 73 (2010).

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[Crossref]

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Z. C. Cao, C. F. Cheung, and X. Zhao, “A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing,” Wear 360–361, 137–146 (2016).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Architecture of the model-based self-optimization system for form error compensation in computer controlled bonnet polishing.
Fig. 2
Fig. 2 Experimental setup of the on-machine measurement system.
Fig. 3
Fig. 3 Scanning path and sampling positions for the on-machine measurement.
Fig. 4
Fig. 4 Schematic diagram of tool path generator for freeform polishing.
Fig. 5
Fig. 5 Trajectory generation for corrective polishing of freeform surfaces.
Fig. 6
Fig. 6 (a) mean and (b) S/N ratio factor response graphs for the average removal depth.
Fig. 7
Fig. 7 The form correction process of freeform polishing of sinusoidal surface.
Fig. 8
Fig. 8 The form correction process of freeform polishing of progressive lens surface.

Tables (4)

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Table 1 The fixed process parameters in Taguchi design of simulation experiments

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Table 2 The control factors and levels in Taguchi design of simulation experiments

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Table 3 The peak-to-valley ( Rt) value and root-mean-square ( Rq) value of the form error for corrective polishing of sinusoidal surface

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Table 4 The peak-to-valley ( Rt) value and root-mean-square ( Rq) value of the form error for corrective polishing of progressive lens surface

Equations (14)

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R(x,y)= 2η K ac V c t H w tanα ( R a σ z ) 1/2 P(x,y, R b ,d,ω,Y,ν,φ, η 1 , η 2 )V(x,y,S,φ, R b ,d)
V(x,y,S,φ, R b ,d)= πS 30 ( xcotφ( R b d) ) 2 (sinφ) 2 + y 2 (cosφ) 2
P(x,y, R b ,d,ω,Y,ν,φ, η 1 , η 2 )= p 0 ( 1 x 2 a 2 y 2 a 2 ) 1/2 + (12v)(1+v) Y ωcosφ(2 η 2 + η 1 /3) p 0 y( R b d) a 2 ( 1 x 2 a 2 y 2 a 2 ) 1/2 + (1v) 2 Y ωcosφ(2 η 2 + η 1 /3)π p 0 y 2a
F N = 2 3 Y (1 v 2 ) R b 1/2 d 3/2
Z a ( x k , y k )= i=1 N t R( x k ξ i , y k η i )D( ξ i , η i )
D( ξ i , η i )= T f ( ξ i , η i )+ T a ( ξ i , η i )
T f ( ξ i , η i )= Δd( ξ i , η i ) V f ( ξ i , η i )
Z p ( x k , y k )= Z m ( x k , y k ) Z a ( x k , y k )
Z d ( x k , y k ) =Z m ( x k , y k ) Z f ( x k , y k )
Z a ( x k , y k )= Z ak , Z d ( x k , y k )= Z dk , R( x k ξ i , y k η i )= R ki D( ξ i , η i )= D i , T f ( ξ i , η i )= T fi , T a ( ξ i , η i )= T ai ,
[ Z a1 Z a2 Z a N r ]=[ R 11 R 12 R 1 N t R 21 R 22 R 2 N t R N r 1 R N r 1 R N r N t ][ T f1 T f2 T f N t ]+[ R 11 R 12 R 1 N t R 21 R 22 R 2 N t R N r 1 R N r 1 R N r N t ][ T a1 T a2 T a N t ]
[ Z a1 Z a2 Z a N r 0 0 0 ]=[ R 11 R 12 R 1 N t R 21 R 22 R 2 N t R N r 1 R N r 1 R N r N t λ 0 0 0 λ 0 0 0 λ ][ D 1 D 2 D N t ]
Z=sin( 2πx 60 )+cos( 2πy 60 )
Z=0.462× 3 ×( 2 x 2 +2 y 2 1 )0.015×2 2 ×( 3 x 2 y y 3 ) 0.046×2 2 ×( 3 x 2 y+3 y 3 2y ) +0.007×2 2 ×( 3 x 3 +3x y 2 2x )+0.007×2 2 ×( x 3 3x y 2 ) +0.0064×2 3 ×( 10 x 4 y+20 x 2 y 3 12 x 2 y+10 y 5 12 y 3 +3y )

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