Abstract

Although magnetorheological finishing (MRF) is a deterministic finishing technology, the machining results always fall short of simulation precision in the actual process, and it cannot meet the precision requirements just through a single treatment but after several iterations. We investigate the reasons for this problem through simulations and experiments. Through controlling and compensating the chief errors in the manufacturing procedure, such as removal function calculation error, positioning error of the removal function, and dynamic performance limitation of the CNC machine, the residual error convergence ratio (ratio of figure error before and after processing) in a single process is obviously increased, and higher figure precision is achieved. Finally, an improved technical process is presented based on these researches, and the verification experiment is accomplished on the experimental device we developed. The part is a circular plane mirror of fused silica material, and the surface figure error is improved from the initial λ/5 [peak-to-valley (PV) λ=632.8nm], λ/30 [root-mean-square (rms)] to the final λ/40 (PV), λ/330 (rms) just through one iteration in 4.4min. Results show that a higher convergence ratio and processing precision can be obtained by adopting error control and compensation techniques in MRF.

© 2011 Optical Society of America

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  1. S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).
  2. D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
    [CrossRef]
  3. M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
    [CrossRef]
  4. C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).
  5. S. Li and Y. Dai, Accuracy Modeling Technology of Precision and Ultra-precision Machine Tool (National University of Defense Technology, 2007).
  6. H. Fang, P. Guo, and J. Yu, “Dwell function algorithm in fluid jet polishing,” Appl. Opt. 45, 4291–4296 (2006).
    [CrossRef] [PubMed]
  7. J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
    [CrossRef] [PubMed]
  8. Y. Dai, C. Song, X. Peng, and F. Shi, “Calibration and prediction of removal function in magnetorheological finishing,” Appl. Opt. 49, 298–305 (2010).
    [CrossRef] [PubMed]
  9. M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
    [CrossRef]
  10. Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).
  11. J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).
  12. L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
    [CrossRef]
  13. H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).
  14. H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18, 22973–22981(2010).
    [CrossRef] [PubMed]

2010 (2)

2009 (4)

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
[CrossRef] [PubMed]

2008 (1)

C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).

2007 (1)

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

2006 (2)

H. Fang, P. Guo, and J. Yu, “Dwell function algorithm in fluid jet polishing,” Appl. Opt. 45, 4291–4296 (2006).
[CrossRef] [PubMed]

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

2005 (1)

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

1999 (1)

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Cao, J.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Dai, Y.

Y. Dai, C. Song, X. Peng, and F. Shi, “Calibration and prediction of removal function in magnetorheological finishing,” Appl. Opt. 49, 298–305 (2010).
[CrossRef] [PubMed]

H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18, 22973–22981(2010).
[CrossRef] [PubMed]

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).

S. Li and Y. Dai, Accuracy Modeling Technology of Precision and Ultra-precision Machine Tool (National University of Defense Technology, 2007).

DeMarco, M.

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

Dumas, P.

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

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

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Fang, H.

Forbes, G.

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

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

Fu, T.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Golini, D.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Gorodkin, G. R.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Gu, X.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Guo, P.

Hogan, S.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Hu, H.

H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18, 22973–22981(2010).
[CrossRef] [PubMed]

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

Jacobs, S. D.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Jiao, C.

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

Kordonski, W. I.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Li, S.

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

S. Li and Y. Dai, Accuracy Modeling Technology of Precision and Ultra-precision Machine Tool (National University of Defense Technology, 2007).

Liu, Y.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Lu, Z.

Miao, J.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Peng, X.

H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18, 22973–22981(2010).
[CrossRef] [PubMed]

Y. Dai, C. Song, X. Peng, and F. Shi, “Calibration and prediction of removal function in magnetorheological finishing,” Appl. Opt. 49, 298–305 (2010).
[CrossRef] [PubMed]

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).

Prokhorov, I. V.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Shi, F.

Y. Dai, C. Song, X. Peng, and F. Shi, “Calibration and prediction of removal function in magnetorheological finishing,” Appl. Opt. 49, 298–305 (2010).
[CrossRef] [PubMed]

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

Song, C.

Y. Dai, C. Song, X. Peng, and F. Shi, “Calibration and prediction of removal function in magnetorheological finishing,” Appl. Opt. 49, 298–305 (2010).
[CrossRef] [PubMed]

C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).

Strafford, T. D.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Sun, S.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Tian, Y.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Tricard, M.

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

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

Wang, F.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Wang, T.

Wu, J.

Xie, X.

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

Xu, Z.

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

Yang, Y.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Yang, Z.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Yu, J.

Zhang, H.

Zhang, Z.

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

Zhou, L.

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

Appl. Opt. (3)

J. Appl. Opt. (1)

Y. Liu, J. Cao, Z. Xu, Y. Tian, T. Fu, and F. Wang, “Improvement of image matching algorithm based on gray correlation,” J. Appl. Opt. 28, 536–540 (2007) (in Chinese).

J. Changchun Univ. Sci. Technol. (1)

J. Miao, Y. Yang, X. Gu, S. Sun, Z. Yang, and Z. Zhang, “The moment invariants and its appliance of image retrieval based on shape features,” J. Changchun Univ. Sci. Technol. 32, 126–129 (2009) (in Chinese).

J. Mech. Eng. (1)

L. Zhou, X. Xie, Y. Dai, C. Jiao, and S. Li, “Realization of velocity mode in flat optics machining using ion beam,” J. Mech. Eng. 45, 152–156 (2009) (in Chinese).
[CrossRef]

J. Natl. Univ. Defense Technol (1)

H. Hu, X. Peng, Y. Dai, and F. Shi, “Algorithm and implementation of magnetorheological finishing with spiral scan path,” J. Natl. Univ. Defense Technol 31, 5–9 (2009) (in Chinese).

Nanotechnol. Precis. Eng. (1)

C. Song, Y. Dai, and X. Peng, “Polishing parameters of magnetorheological finishing for high-precision optical surfaces,” Nanotechnol. Precis. Eng. 6, 424–429 (2008) (in Chinese).

Opt. Express (1)

Proc. SPIE (3)

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

M. Tricard, P. Dumas, G. Forbes, and M. DeMarco, “Recent advanced in sub-aperture approaches to finishing and metrology,” Proc. SPIE 6149, 614903 (2006).
[CrossRef]

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

Other (2)

S. Li and Y. Dai, Accuracy Modeling Technology of Precision and Ultra-precision Machine Tool (National University of Defense Technology, 2007).

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

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Figures (12)

Fig. 1
Fig. 1

Stability of MRF removal function: (a) removal function data measured using interferometer and (b) relative change ratio following the running time.

Fig. 2
Fig. 2

Time linear behavior of MRF removal function: (a) relation between maximum removal depth and dwell time and (b) relation between volume material removal and dwell time.

Fig. 3
Fig. 3

Simulation with considering the machine locating error: (a) initial figure error, (b) removal function, (c) ideal residual figure error and (d) residual figure error introduced in locating error.

Fig. 4
Fig. 4

Removal function added into the calculation error.

Fig. 5
Fig. 5

Removal function tangential and rotary positioning error.

Fig. 6
Fig. 6

Mismachining tolerance due to dwell time implementation error in the spiral scan mode: (a) hole in the center of the part and (b) bulge in the center of the part.

Fig. 7
Fig. 7

Calculated removal function with image matching method.

Fig. 8
Fig. 8

Removal function positioning error control: (a) ideal situation, (b) general four-spot positioning method, and (c) improved four-spot positioning method.

Fig. 9
Fig. 9

Manufacturing results with and without the spot positioning error compensation: (a) initial figure error without compensation, (b) figure error after MRF without compensation, (c) initial figure error with compensation, and (d) figure error after MRF with compensation.

Fig. 10
Fig. 10

Schematic drawing of the acceleration implementation course.

Fig. 11
Fig. 11

Improved process flow of the MRF.

Fig. 12
Fig. 12

Experimental results adopting the improved process flow: (a) initial figure error and (b) figure error after MRF with error control and compensation.

Equations (12)

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

h ( x , y ) = r ( x , y ) * * d ( x , y ) .
e ( x , y ) = h ( x , y ) r ( x , y ) * * d ( x , y ) .
e ( x , y ) = h ( x , y ) r ( x , y ) * * d ( x , y ) ,
δ e ( x , y ) = | e ( x , y ) e ( x , y ) | / e ( x , y ) .
A = R A + T ,
R = R x * R y * R z .
R x = [ 1 0 0 0 0 cos α sin α 0 0 sin α cos α 0 0 0 0 1 ] R y = [ cos β sin β 0 0 0 1 0 0 sin β cos β 0 0 0 0 0 1 ] R z = [ cos θ sin θ 0 0 sin θ cos θ 0 0 0 0 1 0 0 0 0 1 ] .
T = [ 1 0 0 l 0 1 0 m 0 0 1 m 0 0 0 1 ] .
P m = T · P w ,
T = [ 1 0 δ x 0 1 δ y 0 0 1 ] · [ cos δ θ sin δ θ 0 sin δ θ cos δ θ 0 0 0 1 ] .
{ x m = δ x + x w · cos δ θ y w · sin δ θ y m = δ y + x w · sin δ θ + y w · cos δ θ .
{ ( v k + 1 / 2 2 v k 1 / 2 2 ) / 2 a + v k + 1 / 2 = s v k + 1 / 2 v k 1 / 2 = a t 1 t 1 + t 2 = t k .

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