Abstract

When grinding an optical surface, the material removal rate depends linearly upon pressure and velocity and upon a proportionality constant which accounts for differences in material properties. A physical description of the grinding process has been postulated which results in the linear pressure and velocity relationships and which also allows the value of the proportionality constant to be determined from a knowledge of material properties alone. Previous attempts at predicting material removal rely strictly upon experimental data to determine the proportionality constant. The postulated description incorporates the combined effects of many individual abrasive particles to statistically determine the proportionality constant in terms of abrasive size and the breaking stress of the glass. A simple example indicates that the result is consistent with experiment.

© 1974 Optical Society of America

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References

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  1. F. W. Preston, J. Glass Technol. 11, 124 (1927).
  2. R. E. Wagner, R. R. Shannon, Appl. Opt. 13, 1683 (1974).
    [CrossRef] [PubMed]
  3. L. H. Meuser, J. Opt. Soc. Am. 61651A (1971).
  4. W. Rupp, Appl. Opt. 11, 2797 (1972).
    [CrossRef] [PubMed]
  5. E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 41.
  6. E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 48.

1974

1972

1971

L. H. Meuser, J. Opt. Soc. Am. 61651A (1971).

1927

F. W. Preston, J. Glass Technol. 11, 124 (1927).

Meuser, L. H.

L. H. Meuser, J. Opt. Soc. Am. 61651A (1971).

Preston, F. W.

F. W. Preston, J. Glass Technol. 11, 124 (1927).

Rupp, W.

Shand, E. B.

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 41.

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 48.

Shannon, R. R.

Wagner, R. E.

Appl. Opt.

J. Glass Technol.

F. W. Preston, J. Glass Technol. 11, 124 (1927).

J. Opt. Soc. Am.

L. H. Meuser, J. Opt. Soc. Am. 61651A (1971).

Other

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 41.

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 48.

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Figures (5)

Fig. 1
Fig. 1

Mechanism for removal of glass during grinding.

Fig. 2
Fig. 2

Division of the area A0 into segments and cells.

Fig. 3
Fig. 3

Functional dependence of E{m} on n.

Fig. 4
Fig. 4

Dependence of particle motion upon tool velocity.

Fig. 5
Fig. 5

Estimation of force sufficient to cause cracking.

Equations (9)

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W ( r , t ) = 0 t K wear R ( t / τ ) p ( r , t ) V ( r , t ) d t ,
H = 0 n ( t ) h d n = 0 n ( t ) υ 0 A · E { m } N d n .
d n = K [ V ( t ) d t / 2 π g ] ,
N = A / a = ( f / κ p 0 ) / a ,
H = 0 t κ K υ 0 2 π g f ξ [ 0 t κ K a 2 π g f p 0 V ( t ) d t ] p 0 V ( t ) d t .
K wear = κ K υ 0 / 2 π g f , R ( t / τ ) = ξ [ 0 t κ K a 2 π g f p 0 V ( t ) d t ] .
K wear 5.0 × 10 6 ( psi ) 1 .
K wear = 0.35 g 3 / 2 π g f = 0.35 / 2 π 2 ( f / π g 2 ) = 0.018 / σ b ,
K wear = 1.5 × 10 6 ( psi ) 1 .

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