Abstract

In the field of ultra-precision manufacturing, industrial robotic polishing has the potential to become a more economical and intelligent method than the conventional polishing machines. But the challenge of the robotic polishing lies in the low control accuracy, which seriously affects the polishing quality. In this paper a new region-adaptive path planning method is proposed, where the path is generated adaptively according to the specific form error. Each time only the regions with form error large enough are processed, thereby improving the polishing stability and efficiency. Smooth paths are generated based on the hexagonal meshing of the processing regions to avoid sharp turning, and then the dwell time is calculated by space-variant deconvolution. The PVr metric of the final form error resulting from the robotic polisher converges down to λ/15. In addition this method can reduce the polishing time by 80%, henceforth the stability and efficiency of robotic polishing can be greatly improved.

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

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References

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  1. D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
    [Crossref]
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    [Crossref]
  3. F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  10. X. Tonnellier, P. Comley, X. Q. Peng, and P. Shore, “Robot based sub-aperture polishing for the rapid production of metre-scale optics,” in Proceedings of LAMDAMAP 2013 - Laser Metrology and Performance X (2013).
  11. 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]
  12. H. Y. Tam, H. Cheng, and Z. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
    [Crossref] [PubMed]
  13. T. Wang, H. Cheng, W. Zhang, H. Yang, and W. Wu, “Restraint of path effect on optical surface in magnetorheological jet polishing,” Appl. Opt. 55(4), 935–942 (2016).
    [Crossref] [PubMed]
  14. S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
    [Crossref]
  15. S. Wan, X. Zhang, X. He, and M. Xu, “Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing,” Appl. Opt. 55(36), 10223–10228 (2016).
    [Crossref] [PubMed]
  16. X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
    [Crossref]
  17. Z. Dong and H. Cheng, “Toward the complete practicability for the linear-equation dwell time model in subaperture polishing,” Appl. Opt. 54(30), 8884–8890 (2015).
    [Crossref] [PubMed]
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  19. C. J. Evans, “PVr-a robust amplitude parameter for optical surface specification,” Opt. Eng. 48(4), 043605 (2009).
    [Crossref]

2018 (1)

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

2016 (2)

2015 (1)

2013 (2)

H. Y. Tam, H. Cheng, and Z. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
[Crossref] [PubMed]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

2011 (1)

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

2009 (2)

2008 (2)

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]

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]

2005 (2)

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

2002 (1)

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

1996 (1)

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

1980 (1)

1977 (1)

Beaucamp, A. T. H.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Brecherb, C.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Cheng, H.

Dong, Z.

Doubrovski, V.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Dumas, P.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Dunn, C.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Dunn, C. R.

Evans, C. J.

C. J. Evans, “PVr-a robust amplitude parameter for optical surface specification,” Opt. Eng. 48(4), 043605 (2009).
[Crossref]

Forbes, G.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Freeman, R.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

He, X.

S. Wan, X. Zhang, X. He, and M. Xu, “Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing,” Appl. Opt. 55(36), 10223–10228 (2016).
[Crossref] [PubMed]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Jacobs, S. D.

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

Jiang, X.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Jones, R. A.

Klockea, F.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Kordonski, W. I.

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

Li, H.

McCavana, G.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Morton, R.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Novitskii, N. N.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

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, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

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]

Simms, J.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[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]

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]

Stognij, A. I.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Stukalov, O. M.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Tam, H. Y.

Tricard, M.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Tuecksb, R.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

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, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Wan, S.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

S. Wan, X. Zhang, X. He, and M. Xu, “Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing,” Appl. Opt. 55(36), 10223–10228 (2016).
[Crossref] [PubMed]

Wang, T.

Wei, X.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

Wu, W.

Xu, M.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

S. Wan, X. Zhang, X. He, and M. Xu, “Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing,” Appl. Opt. 55(36), 10223–10228 (2016).
[Crossref] [PubMed]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Yang, H.

Yu, G.

Zhang, H.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Zhang, W.

Zhang, X.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

S. Wan, X. Zhang, X. He, and M. Xu, “Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing,” Appl. Opt. 55(36), 10223–10228 (2016).
[Crossref] [PubMed]

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Zunkea, R.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Appl. Opt. (6)

Chin. Opt. Lett. (1)

Int. J. Mod. Phys. B (1)

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

Measurement (1)

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, “Chebyshev fitting of complex surfaces for precision metrology,” Measurement 46(9), 3720–3724 (2013).
[Crossref]

Opt. Eng. (1)

C. J. Evans, “PVr-a robust amplitude parameter for optical surface specification,” Opt. Eng. 48(4), 043605 (2009).
[Crossref]

Opt. Express (1)

Precis. Eng. (3)

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

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]

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Proc. SPIE (2)

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 79–87 (2005).
[Crossref]

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Tech. Phys. Lett. (1)

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Other (2)

X. Tonnellier, P. Comley, X. Q. Peng, and P. Shore, “Robot based sub-aperture polishing for the rapid production of metre-scale optics,” in Proceedings of LAMDAMAP 2013 - Laser Metrology and Performance X (2013).

M. De Berg, M. Van Kreveld, M. Overmars, and O. C. Schwarzkopf, Computational Geometry (Springer, Berlin, Heidelberg, 2000), Chap. 7.

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Figures (11)

Fig. 1
Fig. 1 Schematic of region-adaptive method.
Fig. 2
Fig. 2 Processing regions of different surface shapes.
Fig. 3
Fig. 3 Schematic of hexagonal grids numbering system.
Fig. 4
Fig. 4 The adjustment of processing regions after hexagonal meshing.
Fig. 5
Fig. 5 Primary traversal paths diagram.
Fig. 6
Fig. 6 The results calculated by proposed deconvolution algorithm (parameter setting: Niter = 20; γ = 0.1; Tmin = 0.05 s; Tmax = 5 s;).
Fig. 7
Fig. 7 ABB robotic polisher and the polishing pad.
Fig. 8
Fig. 8 The schematic diagram of the experiment plan.
Fig. 9
Fig. 9 The measured profile of polishing pad and the corresponding tool influence function.
Fig. 10
Fig. 10 Form error maps and polishing paths.
Fig. 11
Fig. 11 PVr of form error map and polishing time.

Tables (3)

Tables Icon

Table 2 Specifications of the robotic polisher

Tables Icon

Table 3 Detailed working conditions

Equations (10)

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

R e g = { ( x , y ) | e r r m ( x , y ) > t + } with e r r R = { e r r ( x , y ) | 0 < x 2 + y 2 < m 2 R 2 } e r r m = e r r R + 3 r m s ( e r r R ) t ,
{ x = 3 4 p d h e x y = 3 2 ( q + 1 2 p ) d h e x ,
D ( A , B ) = max ( | Δ p | , | Δ q | , | Δ p + Δ q | ) with Δ p = p A p B ,
X ' ( n ) ( t ) = X ( n ) ( t ) G ( t ; σ ) Y ' ( n ) ( t ) = Y ( n ) ( t ) G ( t ; σ ) with G ( t ; σ ) = 1 2 π σ exp ( t 2 2 σ 2 ) 3 σ < t < 3 σ ,
z ( x , y ) = T I F ( x , y ) T ( x , y ) ,
z ^ = H ^ T ^ ,
min E ( T ^ ) = min max i { | δ i | | 0 < x i 2 + y i 2 < k 2 R 2 } s .t δ = e ^ p H ^ T ^ e p = e r r + 3 r m s ( e r r R ) t T min < T ^ < T max ,
min E p ( T ^ ) = 1 p log i exp ( p d i ) with d i = δ ^ i 2.
E p = E p T ^ = { i ζ ^ i d i | 0 < x i 2 + y i 2 < k 2 R 2 } with d = 2 H ^ T d i a g ( ζ ^ ) ( e ^ p H ^ T ^ ) d i a g ( ζ ^ ) = ( ζ ^ 1 0 0 ζ ^ M N ) ζ ^ i = exp ( p d i ) / i exp ( p d i ) .
convolution: B ^ ( M N × 1 ) = H ^ ( M N × J ) A ^ ( J × 1 ) B ( x , y ) = j = 1 J T I F ( μ j , η j ) ( x μ j , y η j ) A ^ ( j ) correlation: A ^ ( J × 1 ) = H ^ T ( J × M N ) B ^ ( M N × 1 ) A ^ ( j ) = x y T I F ( μ j , η j ) ( x μ j , y η j ) B ( x , y ) ,

Metrics