Abstract

Mixed-mode grinding occurs when a bound abrasive works in both brittle and ductile regimes simultaneously. Substrates ground in a mixed-mode behavior show reduced curvature induced by compressive surface forces than loose abrasives as demonstrated by observing the Twyman effect. This reduction in bending corresponds to reduced subsurface damage. This is verified by controlled acid etching, which shows the exponential decay of the compressive force per unit length. Loose abrasive particles, added to maintain pad wear due to low pressures, have no effect on the measured stresses. If loose abrasive wear ceases, the pads glaze. Glazing creates near-specular surfaces while reducing measurable stress. These effects for borosilicate glass and Trizact grinding pads are explored and quantified.

© 2012 Optical Society of America

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References

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  1. F. Twyman, “Polishing of glass surfaces,” Proceedings of the Optical Convention (Northgate & Williams, 1905), p. 78.
  2. F. W. Preston, “The structure of abraded glass surfaces,” Trans. Opt. Soc. 23, 141–164 (1922).
    [CrossRef]
  3. A. J. Dalladay and F. Twyman, “The stress conditions in diamond cut glass,” Trans. Opt. Soc. 23, 165–169 (1922).
    [CrossRef]
  4. A. J. Dalladay, “Some measurements of the stresses produced at the surfaces of glass by grinding with loose abrasives,” Trans. Opt. Soc. 23, 170–174 (1922).
    [CrossRef]
  5. C. V. Muffoletto, “Reflective and refractive scattering of ultraviolet radiation caused by state of the art optical grinding and polishing techniques,” Proc. SPIE 315, 85–89 (1981).
  6. E. G. Nikolova, “On the Twyman effect and some of its applications,” J. Mater. Sci. 20, 1–8 (1985).
    [CrossRef]
  7. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. A 82, 172–175 (1909).
    [CrossRef]
  8. O. Podzimek, “Residual stress and deformation energy underground surfaces of brittle solids,” CIRP Ann. 35, 397–400 (1986).
    [CrossRef]
  9. W. J. Rupp, “Twyman effect for ULE,” in Optical Fabrication and Testing Workshop (Optical Society of America, 1987), pp. 25–30.
  10. D. Golini and S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt. 30, 2761–2777 (1991).
    [CrossRef]
  11. J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).
  12. J. C. Lambropoulos, S. Xu, T. Fang, and D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Opt. 35, 5704–5713 (1996).
    [CrossRef]
  13. Z. Zhong and V. C. Venkatesh, “Semi-ductile grinding and polishing of ophthalmic aspherics and spherics,” CIRP Ann. 44, 339–342 (1995).
    [CrossRef]
  14. N. S. Ong and V. C. Venkatesh, “Semi-ductile grinding and polishing of Pyrex glass,” J. Mater. Process. Technol. 83, 261–266 (1998).
    [CrossRef]
  15. J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
    [CrossRef]
  16. D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
    [CrossRef]
  17. N. J. Brown and B. A. Fuchs, “Shear mode grinding,” in Proceedings of the 43rd Annual Symposium on Frequency Control (IEEE, 1989), pp. 606–610.

2011 (1)

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

2005 (1)

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

1998 (1)

N. S. Ong and V. C. Venkatesh, “Semi-ductile grinding and polishing of Pyrex glass,” J. Mater. Process. Technol. 83, 261–266 (1998).
[CrossRef]

1996 (2)

J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).

J. C. Lambropoulos, S. Xu, T. Fang, and D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Opt. 35, 5704–5713 (1996).
[CrossRef]

1995 (1)

Z. Zhong and V. C. Venkatesh, “Semi-ductile grinding and polishing of ophthalmic aspherics and spherics,” CIRP Ann. 44, 339–342 (1995).
[CrossRef]

1991 (1)

1986 (1)

O. Podzimek, “Residual stress and deformation energy underground surfaces of brittle solids,” CIRP Ann. 35, 397–400 (1986).
[CrossRef]

1985 (1)

E. G. Nikolova, “On the Twyman effect and some of its applications,” J. Mater. Sci. 20, 1–8 (1985).
[CrossRef]

1981 (1)

C. V. Muffoletto, “Reflective and refractive scattering of ultraviolet radiation caused by state of the art optical grinding and polishing techniques,” Proc. SPIE 315, 85–89 (1981).

1922 (3)

F. W. Preston, “The structure of abraded glass surfaces,” Trans. Opt. Soc. 23, 141–164 (1922).
[CrossRef]

A. J. Dalladay and F. Twyman, “The stress conditions in diamond cut glass,” Trans. Opt. Soc. 23, 165–169 (1922).
[CrossRef]

A. J. Dalladay, “Some measurements of the stresses produced at the surfaces of glass by grinding with loose abrasives,” Trans. Opt. Soc. 23, 170–174 (1922).
[CrossRef]

1909 (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. A 82, 172–175 (1909).
[CrossRef]

Beaucamp, A.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Brown, N. J.

N. J. Brown and B. A. Fuchs, “Shear mode grinding,” in Proceedings of the 43rd Annual Symposium on Frequency Control (IEEE, 1989), pp. 606–610.

Burge, J. H.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Dalladay, A. J.

A. J. Dalladay and F. Twyman, “The stress conditions in diamond cut glass,” Trans. Opt. Soc. 23, 165–169 (1922).
[CrossRef]

A. J. Dalladay, “Some measurements of the stresses produced at the surfaces of glass by grinding with loose abrasives,” Trans. Opt. Soc. 23, 170–174 (1922).
[CrossRef]

Doubrovski, V.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Dunn, C.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Fang, T.

J. C. Lambropoulos, S. Xu, T. Fang, and D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Opt. 35, 5704–5713 (1996).
[CrossRef]

J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).

Freeman, R.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Fuchs, B. A.

N. J. Brown and B. A. Fuchs, “Shear mode grinding,” in Proceedings of the 43rd Annual Symposium on Frequency Control (IEEE, 1989), pp. 606–610.

Golini, D.

Hobbs, G.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Jacobs, S. D.

Johnson, J. B.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Kim, D. W.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Lambropoulos, J. C.

J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).

J. C. Lambropoulos, S. Xu, T. Fang, and D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Opt. 35, 5704–5713 (1996).
[CrossRef]

Lindquist, A.

J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).

McCavana, G.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Morton, R.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Muffoletto, C. V.

C. V. Muffoletto, “Reflective and refractive scattering of ultraviolet radiation caused by state of the art optical grinding and polishing techniques,” Proc. SPIE 315, 85–89 (1981).

Nikolova, E. G.

E. G. Nikolova, “On the Twyman effect and some of its applications,” J. Mater. Sci. 20, 1–8 (1985).
[CrossRef]

Ong, N. S.

N. S. Ong and V. C. Venkatesh, “Semi-ductile grinding and polishing of Pyrex glass,” J. Mater. Process. Technol. 83, 261–266 (1998).
[CrossRef]

Parks, R. E.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Podzimek, O.

O. Podzimek, “Residual stress and deformation energy underground surfaces of brittle solids,” CIRP Ann. 35, 397–400 (1986).
[CrossRef]

Preston, F. W.

F. W. Preston, “The structure of abraded glass surfaces,” Trans. Opt. Soc. 23, 141–164 (1922).
[CrossRef]

Riley, D.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Rupp, W. J.

W. J. Rupp, “Twyman effect for ULE,” in Optical Fabrication and Testing Workshop (Optical Society of America, 1987), pp. 25–30.

Simms, J.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Stoney, G. G.

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. A 82, 172–175 (1909).
[CrossRef]

Twyman, F.

A. J. Dalladay and F. Twyman, “The stress conditions in diamond cut glass,” Trans. Opt. Soc. 23, 165–169 (1922).
[CrossRef]

F. Twyman, “Polishing of glass surfaces,” Proceedings of the Optical Convention (Northgate & Williams, 1905), p. 78.

Venkatesh, V. C.

N. S. Ong and V. C. Venkatesh, “Semi-ductile grinding and polishing of Pyrex glass,” J. Mater. Process. Technol. 83, 261–266 (1998).
[CrossRef]

Z. Zhong and V. C. Venkatesh, “Semi-ductile grinding and polishing of ophthalmic aspherics and spherics,” CIRP Ann. 44, 339–342 (1995).
[CrossRef]

Walker, D. D.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Wei, X.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Xu, S.

Zhong, Z.

Z. Zhong and V. C. Venkatesh, “Semi-ductile grinding and polishing of ophthalmic aspherics and spherics,” CIRP Ann. 44, 339–342 (1995).
[CrossRef]

Appl. Opt. (2)

Ceram. Trans. (1)

J. C. Lambropoulos, T. Fang, A. Lindquist, and D. Golini, “The Twyman Effect under loose abrasive lapping and deterministic microgrinding,” Ceram. Trans. 70, 59–70 (1996).

CIRP Ann. (2)

Z. Zhong and V. C. Venkatesh, “Semi-ductile grinding and polishing of ophthalmic aspherics and spherics,” CIRP Ann. 44, 339–342 (1995).
[CrossRef]

O. Podzimek, “Residual stress and deformation energy underground surfaces of brittle solids,” CIRP Ann. 35, 397–400 (1986).
[CrossRef]

J. Mater. Process. Technol. (1)

N. S. Ong and V. C. Venkatesh, “Semi-ductile grinding and polishing of Pyrex glass,” J. Mater. Process. Technol. 83, 261–266 (1998).
[CrossRef]

J. Mater. Sci. (1)

E. G. Nikolova, “On the Twyman effect and some of its applications,” J. Mater. Sci. 20, 1–8 (1985).
[CrossRef]

Proc. R. Soc. A (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. A 82, 172–175 (1909).
[CrossRef]

Proc. SPIE (3)

C. V. Muffoletto, “Reflective and refractive scattering of ultraviolet radiation caused by state of the art optical grinding and polishing techniques,” Proc. SPIE 315, 85–89 (1981).

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. Hobbs, 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, 58690E (2005).
[CrossRef]

Trans. Opt. Soc. (3)

F. W. Preston, “The structure of abraded glass surfaces,” Trans. Opt. Soc. 23, 141–164 (1922).
[CrossRef]

A. J. Dalladay and F. Twyman, “The stress conditions in diamond cut glass,” Trans. Opt. Soc. 23, 165–169 (1922).
[CrossRef]

A. J. Dalladay, “Some measurements of the stresses produced at the surfaces of glass by grinding with loose abrasives,” Trans. Opt. Soc. 23, 170–174 (1922).
[CrossRef]

Other (3)

F. Twyman, “Polishing of glass surfaces,” Proceedings of the Optical Convention (Northgate & Williams, 1905), p. 78.

W. J. Rupp, “Twyman effect for ULE,” in Optical Fabrication and Testing Workshop (Optical Society of America, 1987), pp. 25–30.

N. J. Brown and B. A. Fuchs, “Shear mode grinding,” in Proceedings of the 43rd Annual Symposium on Frequency Control (IEEE, 1989), pp. 606–610.

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Figures (8)

Fig. 1.
Fig. 1.

Semiductile material behavior while grinding. Diamonds that do not protrude far from the surface do not work on the material in a brittle fashion due to the compressibleness of the binder. Peak removal depth is based on the brittle fracture.

Fig. 2.
Fig. 2.

Compressive force change with etch time. Variations in slope correlate with the depletion of F ions in the acid solution.

Fig. 3.
Fig. 3.

Typical thickness change of the substrate due to time in the etchant. Glass removal rate is linear with time.

Fig. 4.
Fig. 4.

Total compressive grinding force for various sized loose and bound abrasives.

Fig. 5.
Fig. 5.

Interferometric fringes of a 2.5 mm thick ground window before and after etching. Several waves of power are added to the measured surface based on the compressive grinding stress alone.

Fig. 6.
Fig. 6.

Change in surface compression with run time under glazing conditions. The 5mL/min and 1mL/min case reach a nonzero equilibrium. The 0.06mL/min case does not reach a stable value.

Fig. 7.
Fig. 7.

Surface roughness image of a surface run with a glazed pad before and after etching. The plateaus in (a) completely disappear after 2 s in the etchant, yet the surface roughness only sees a slight, 20 nm RMS increase.

Fig. 8.
Fig. 8.

Change in compressive grinding force with etching. An exponential distribution still exists showing the plateau layer has little to no effect on the overall surface forces.

Tables (1)

Tables Icon

Table 1. Grinding Parameters for Twyman Effect Tests

Equations (8)

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

R=at2,
P0=Es6a(1ν),
σ=P0td.
σ=Est26tf(1ν)R,
P(ξ)=P0eξ/td,
Δsag=C(dt)2,
P0=4Es3(1ν)C.
SiO2+4(NH4)HF2(NH4)2SiF6+2NH4F+2H2O.

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