Abstract

To obtain removal functions (RFs) with high removal rate and stability in the polishing of silicon carbide mirror, an optical fabrication technology based on fixed abrasive diamond pellets (FADPs) is adopted. In this paper, we focus on the removal characteristics of FADPs, including removal profile, removal rate, stability of RFs, and surface roughness. Diamond pellets polishing is analyzed theoretically with respect to removal rate and stability. A universal algorithm is proposed for computing theoretical removal profile of different distribution models. By evaluating the cutoff frequency of RFs, optimized parameters including speed ratio and eccentricity are confirmed. A series of experiments are conducted to verify the effectiveness of the algorithm; within 300 min (even more), the pellets could provide highly stable RFs with about 5 times removal rate than loose abrasives; the surface roughness 4.86 nm is obtained.

© 2012 Optical Society of America

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References

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  1. L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).
  2. M. Johns and A. Carnegie, “Giant Magellan telescope,” Proc. SPIE 5382, 85–92 (2004).
    [CrossRef]
  3. M. A. Ealey and G. Q. Weaver, “Developmental history and trends for reaction bonded silicon carbide mirrors,” Proc. SPIE 2857, 66–72 (1996).
    [CrossRef]
  4. H. Y. Tam and H. B. Cheng, “Removal rate and surface roughness in the lapping and polishing of RB-SiC optical components,” J. Mater. Process. Technol. 192–193, 276–280 (2007).
    [CrossRef]
  5. X. Wang and X. J. Zhang, “Theoretical study on removal rate and surface roughness in grinding a RB-SiC mirror with a fixed abrasive,” Appl. Opt. 48, 904–910 (2009).
    [CrossRef]
  6. X. Wang and X. J. Zhang, “Study on experiment of grinding SiC mirror with fixed abrasive,” Proc. SPIE 7282, 72820K (2009).
  7. R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra34–39 (1963).
  8. R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt. 13, 1683–1689 (1974).
    [CrossRef]
  9. H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
    [CrossRef]
  10. D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
    [CrossRef]
  11. 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, 958–964 (2003).
    [CrossRef]
  12. H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
    [CrossRef]
  13. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16, 18942–18949 (2008).
    [CrossRef]
  14. W. J. Fen, Z. W. Lu, and H. X. Zhang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
    [CrossRef]
  15. L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).
  16. D. W. Kim, S. W. Kim, and J. H. Burge, “Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions,” Opt. Express 17, 21850–21866 (2009).
    [CrossRef]

2010 (2)

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

2009 (4)

2008 (1)

2007 (1)

H. Y. Tam and H. B. Cheng, “Removal rate and surface roughness in the lapping and polishing of RB-SiC optical components,” J. Mater. Process. Technol. 192–193, 276–280 (2007).
[CrossRef]

2005 (1)

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

2004 (1)

M. Johns and A. Carnegie, “Giant Magellan telescope,” Proc. SPIE 5382, 85–92 (2004).
[CrossRef]

2003 (1)

1999 (1)

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

1996 (1)

M. A. Ealey and G. Q. Weaver, “Developmental history and trends for reaction bonded silicon carbide mirrors,” Proc. SPIE 2857, 66–72 (1996).
[CrossRef]

1992 (1)

L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

1974 (1)

Boyer, C.

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

Brooks, D.

Burge, J. H.

Carnegie, A.

M. Johns and A. Carnegie, “Giant Magellan telescope,” Proc. SPIE 5382, 85–92 (2004).
[CrossRef]

Charles, L. C.

L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Cheng, H. B.

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

H. Y. Tam and H. B. Cheng, “Removal rate and surface roughness in the lapping and polishing of RB-SiC optical components,” J. Mater. Process. Technol. 192–193, 276–280 (2007).
[CrossRef]

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Cheng, K.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Crampton, D.

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

Dumas, P.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

Dunn, C. R.

Ealey, M. A.

M. A. Ealey and G. Q. Weaver, “Developmental history and trends for reaction bonded silicon carbide mirrors,” Proc. SPIE 2857, 66–72 (1996).
[CrossRef]

Egert, C. M.

L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Ellerbroeka, B.

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

Fen, W. J.

Feng, Z. J.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Freeman, R.

Golini, D.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

Hogan, S.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

Johns, M.

M. Johns and A. Carnegie, “Giant Magellan telescope,” Proc. SPIE 5382, 85–92 (2004).
[CrossRef]

Jones, R. A.

R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra34–39 (1963).

Kathy, W. H.

L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Kim, D. W.

Kim, S. W.

King, A.

Kordonski, W. I.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

Lu, Z. W.

McCavana, G.

Morton, R.

Shannon, R. R.

Simard, L.

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

Tam, H. Y.

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

H. Y. Tam and H. B. Cheng, “Removal rate and surface roughness in the lapping and polishing of RB-SiC optical components,” J. Mater. Process. Technol. 192–193, 276–280 (2007).
[CrossRef]

Wagner, R. E.

Walker, D. D.

Wang, X.

X. Wang and X. J. Zhang, “Theoretical study on removal rate and surface roughness in grinding a RB-SiC mirror with a fixed abrasive,” Appl. Opt. 48, 904–910 (2009).
[CrossRef]

X. Wang and X. J. Zhang, “Study on experiment of grinding SiC mirror with fixed abrasive,” Proc. SPIE 7282, 72820K (2009).

Wang, Y. W.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Weaver, G. Q.

M. A. Ealey and G. Q. Weaver, “Developmental history and trends for reaction bonded silicon carbide mirrors,” Proc. SPIE 2857, 66–72 (1996).
[CrossRef]

Zhang, H. X.

Zhang, X. J.

X. Wang and X. J. Zhang, “Study on experiment of grinding SiC mirror with fixed abrasive,” Proc. SPIE 7282, 72820K (2009).

X. Wang and X. J. Zhang, “Theoretical study on removal rate and surface roughness in grinding a RB-SiC mirror with a fixed abrasive,” Appl. Opt. 48, 904–910 (2009).
[CrossRef]

Appl. Opt. (3)

Int. J. Mach. Tools Manuf. (1)

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

J. Mater. Process. Technol. (2)

H. Y. Tam and H. B. Cheng, “Removal rate and surface roughness in the lapping and polishing of RB-SiC optical components,” J. Mater. Process. Technol. 192–193, 276–280 (2007).
[CrossRef]

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

Opt. Express (3)

Proc. SPIE (6)

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing in commercial precision optics manufacturing,” Proc. SPIE 3782, 378280 (1999).
[CrossRef]

X. Wang and X. J. Zhang, “Study on experiment of grinding SiC mirror with fixed abrasive,” Proc. SPIE 7282, 72820K (2009).

L. Simard, D. Crampton, B. Ellerbroeka, and C. Boyer, “The TMT instrumentation program,” Proc. SPIE 7735, 773523 (2010).

M. Johns and A. Carnegie, “Giant Magellan telescope,” Proc. SPIE 5382, 85–92 (2004).
[CrossRef]

M. A. Ealey and G. Q. Weaver, “Developmental history and trends for reaction bonded silicon carbide mirrors,” Proc. SPIE 2857, 66–72 (1996).
[CrossRef]

L. C. Charles, C. M. Egert, and W. H. Kathy, “Advanced matrix based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Other (1)

R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra34–39 (1963).

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Figures (9)

Fig. 1.
Fig. 1.

Different practical polishing pads with diamond pellets.

Fig. 2.
Fig. 2.

Planetary motion model sketch of model 1. (a) Lateral view, (b) top view, and (c) combined speed of point M .

Fig. 3.
Fig. 3.

Ideal RFs of model 1 under condition of (a) different speed ratios and (b) different eccentricity.

Fig. 4.
Fig. 4.

(a) 3D shape normalized RF. (b) Normalized amplitude frequency spectrum curve of (a).

Fig. 5.
Fig. 5.

Cutoff frequency curves of model 1 about (a) speed ratio and (b) eccentricity.

Fig. 6.
Fig. 6.

Contrast of experimental and theoretical RFs: (a) 3D experimental RF of model 1; (b) 2D experimental RF of model 1; (c) 2D normalized theoretical RF of model 1; (d) 3D experimental RF of model 5; (e) 2D experimental RF of model 5; (f) 2D normalized theoretical RF of model 5.

Fig. 7.
Fig. 7.

Removal shape of different usage time of the polishing pad. (a) 3D shape and (b) 2D shape.

Fig. 8.
Fig. 8.

Removal magnitude curves of fixed and loose abrasive both in 10 min.

Fig. 9.
Fig. 9.

Roughness results after polishing process with the pellets of diamond granularity: (a) 1.5 μm, R a = 4.86 nm ; (b) 3 μm, R a = 6.97 nm ; (c) 5 μm, R a = 7.75 nm ; and (d) 17 μm, R a = 21.28 nm .

Tables (5)

Tables Icon

Table 1. Parameters of Pellets We Used

Tables Icon

Table 2. Different Kinds Distribution Models, Optimized Parameters, and Removal Functions of Fixed Diamond Pellets

Tables Icon

Table 3. Parameters for Profile Experiments

Tables Icon

Table 4. Parameters for Stability Experiments

Tables Icon

Table 5. Parameters for Removal Rate Experiments

Equations (8)

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

f = w 1 / w 2 ,
g = e / r 0 .
{ { X A = e e · ( 1 cos ( w 2 · t ) ) Y A = e · sin ( w 2 · t ) { X B = e 2 · r e · ( 1 cos ( w 2 · t ) ) + 2 · r · ( 1 cos ( w 1 · t ) ) Y B = 0 + e · sin ( w 2 · t ) 2 · r · ( sin ( w 1 · t ) ) { X C = e r e · ( 1 cos ( w 2 · t ) ) + r 2 r · sin ( π / 6 w 1 · t ) Y C = 3 1 / 2 · r + e · sin ( w 2 · t ) ( 2 r · cos ( π / 6 w 1 · t ) 3 1 / 2 · r ) { X D = e + r e · ( 1 cos ( w 2 · t ) ) + 2 r · cos ( π / 3 w 1 · t ) r Y D = 3 1 / 2 · r + e · sin ( w 2 · t ) + ( 3 1 / 2 · r 2 r · sin ( π / 3 w 1 · t ) ) { X E = e + 2 · r e · ( 1 cos ( w 2 · t ) ) 2 · r · ( 1 cos ( w 1 · t ) ) Y E = 0 + e · sin ( w 2 · t ) + 2 · r · ( sin ( w 1 · t ) ) { X F = e + r e · ( 1 cos ( w 2 · t ) ) + 2 r · sin ( π / 6 w 1 · t ) r Y F = 3 1 / 2 · r + e · sin ( w 2 · t ) + ( 2 r · cos ( π / 6 w 1 · t ) 3 1 / 2 · r ) { X G = e r e · ( 1 cos ( w 2 · t ) ) + r 2 r · cos ( π / 3 w 1 · t ) Y G = 3 1 / 2 · r + e · sin ( w 2 · t ) ( 3 1 / 2 · r 2 r · sin ( π / 3 w 1 · t ) ) .
M A ¯ < r | M B ¯ < r | M C ¯ < r | M D ¯ < r | M E ¯ < r | M F ¯ < r | M G ¯ < r ,
| v | = | v 1 + v 2 | = ( v 1 2 + v 2 2 2 v 1 v 2 cos β ) 1 / 2 = ( ( R 1 w 1 ) 2 + ( R 2 w 2 ) 2 2 R 1 w 1 R 2 w 2 cos β ) 1 / 2 ,
d t = d α / w 2 .
R ( r ) = d z = α α K · P · v / w 2 · d α ,
R F ( w ) = FFT ( R n ( r ) ) ,

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