Abstract

We analyze the material removal mechanism of abrasive jet polishing (AJP) technology, based on the fluid impact dynamics theory. Combined with the computational fluid dynamics simulation and process experiments, influence functions at different impingement angles are obtained, which are not of a regular Gaussian shape and are unfit for the corrective figuring of optics. The influence function is then optimized to obtain an ideal Gaussian shape by rotating the oblique nozzle, and its stability is validated through a line scanning experiment. The fluctuation of the influence function can be controlled within ±5%. Based on this, we build a computed numerically controlled experimental system for AJP, and one flat BK7 optical glass with a diameter of 20mm is polished. After two iterations of polishing, the peak-to-valley value decreases from 1.43λ (λ=632.8nm in this paper) to 0.294λ, and the rms value decreases from 0.195λ to 0.029λ. The roughness of this polished surface is within 2nm. The experimental result indicates that the optimized influence function is suitable for precision optics figuring and polishing.

© 2010 Optical Society of America

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References

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  1. S. M. Booij, H. van Brug, and O. W. Fähnle, “A mathematical model for machining spot in fluid jet polishing,” in Optical Fabrication & Testing, OSA Technical Digest Series (Optical Society of America, 2000), pp. 70–72.
  2. A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
    [CrossRef]
  3. O. W. Fähnle, H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surface,” Appl. Opt. 37, 6771–6773 (1998).
    [CrossRef]
  4. M. W. Chastagner and A. J. Shih, “Abrasive jet machining for edge generation,” in Transactions of the North American Manufacturing Research Institution of the Society of Manufacturing Engineers (Society of Manufacturing Engineers, 2007), Vol. 35, pp. 359–366.
  5. X. C. Zhang, “Study on magneto-rheological jet polishing technology,” Ph.D. dissertation (National University of Defense Technology, 2003) (in Chinese).
  6. Z. Y. Dong, Jet Mechanics (Science, 2005) (in Chinese).
  7. L. Yang, Advanced Technology of Optics Manufacturing (Science, 2001) (in Chinese).
  8. L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).
  9. H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
    [CrossRef]
  10. O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
    [CrossRef]
  11. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).
  12. L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
    [CrossRef]
  13. S. M. Booij, “Fluid jet polishing—possibilities and limitations of a new fabrication technique,” Ph.D. dissertation (Delft University of Technology, 2003).

2007 (3)

L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

2006 (1)

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

2005 (1)

A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
[CrossRef]

1998 (1)

1927 (1)

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Booij, S. M.

S. M. Booij, H. van Brug, and O. W. Fähnle, “A mathematical model for machining spot in fluid jet polishing,” in Optical Fabrication & Testing, OSA Technical Digest Series (Optical Society of America, 2000), pp. 70–72.

S. M. Booij, “Fluid jet polishing—possibilities and limitations of a new fabrication technique,” Ph.D. dissertation (Delft University of Technology, 2003).

Chastagner, M. W.

M. W. Chastagner and A. J. Shih, “Abrasive jet machining for edge generation,” in Transactions of the North American Manufacturing Research Institution of the Society of Manufacturing Engineers (Society of Manufacturing Engineers, 2007), Vol. 35, pp. 359–366.

Dai, Y. F.

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).

Dong, Z. Y.

Z. Y. Dong, Jet Mechanics (Science, 2005) (in Chinese).

Fähnle, O. W.

O. W. Fähnle, H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surface,” Appl. Opt. 37, 6771–6773 (1998).
[CrossRef]

S. M. Booij, H. van Brug, and O. W. Fähnle, “A mathematical model for machining spot in fluid jet polishing,” in Optical Fabrication & Testing, OSA Technical Digest Series (Optical Society of America, 2000), pp. 70–72.

Fang, H.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Frankena, H. J.

Guo, P. J.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Horiuchi, O.

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Ikeno, J.

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Jiao, C.

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

Kordonski, W.

A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
[CrossRef]

Li, S.

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

Mizukami, Y.

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Preston, F. W.

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Shibutani, H.

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Shih, A. J.

M. W. Chastagner and A. J. Shih, “Abrasive jet machining for edge generation,” in Transactions of the North American Manufacturing Research Institution of the Society of Manufacturing Engineers (Society of Manufacturing Engineers, 2007), Vol. 35, pp. 359–366.

Shorey, A.

A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
[CrossRef]

Suzuki, H.

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Tricard, M.

A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
[CrossRef]

van Brug, H.

O. W. Fähnle, H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surface,” Appl. Opt. 37, 6771–6773 (1998).
[CrossRef]

S. M. Booij, H. van Brug, and O. W. Fähnle, “A mathematical model for machining spot in fluid jet polishing,” in Optical Fabrication & Testing, OSA Technical Digest Series (Optical Society of America, 2000), pp. 70–72.

Xie, X. H.

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).

Yang, L.

L. Yang, Advanced Technology of Optics Manufacturing (Science, 2001) (in Chinese).

Yu, J. C.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Zhang, X. C.

X. C. Zhang, “Study on magneto-rheological jet polishing technology,” Ph.D. dissertation (National University of Defense Technology, 2003) (in Chinese).

Zhou, L.

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).

Appl. Opt. (1)

J. Soc. Glass Technol. (1)

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Opt. Eng. (1)

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Opt. Precision Eng. (1)

L. Zhou, Y. F. Dai, X. H. Xie, “Machining reachability in ion beam figuring,” Opt. Precision Eng. 15, 160–166 (2007).

Precision Eng. (1)

O. Horiuchi, J. Ikeno, H. Shibutani, H. Suzuki, and Y. Mizukami, “Nano-abrasion machining of brittle materials and its application to corrective figuring,” Precision Eng. 31, 47–54(2007).
[CrossRef]

Proc. SPIE (2)

A. Shorey, W. Kordonski, and M. Tricard, “Deterministic, precision finishing of domes and conformal optics,” Proc. SPIE 5786, 310–318 (2005).
[CrossRef]

L. Zhou, X. H. Xie, Y. F. DaiC. Jiao, and S. Li, “Ion beam figuring system in NUDT,” Proc. SPIE 6722, 67224A (2007).
[CrossRef]

Other (6)

S. M. Booij, “Fluid jet polishing—possibilities and limitations of a new fabrication technique,” Ph.D. dissertation (Delft University of Technology, 2003).

S. M. Booij, H. van Brug, and O. W. Fähnle, “A mathematical model for machining spot in fluid jet polishing,” in Optical Fabrication & Testing, OSA Technical Digest Series (Optical Society of America, 2000), pp. 70–72.

M. W. Chastagner and A. J. Shih, “Abrasive jet machining for edge generation,” in Transactions of the North American Manufacturing Research Institution of the Society of Manufacturing Engineers (Society of Manufacturing Engineers, 2007), Vol. 35, pp. 359–366.

X. C. Zhang, “Study on magneto-rheological jet polishing technology,” Ph.D. dissertation (National University of Defense Technology, 2003) (in Chinese).

Z. Y. Dong, Jet Mechanics (Science, 2005) (in Chinese).

L. Yang, Advanced Technology of Optics Manufacturing (Science, 2001) (in Chinese).

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Figures (12)

Fig. 1
Fig. 1

Schematic drawing of the parameters in the AJP system.

Fig. 2
Fig. 2

Wall shear stress distribution of the normal impact jet.

Fig. 3
Fig. 3

Distribution of normal impact fluid field: (a) velocity field and (b) pressure field.

Fig. 4
Fig. 4

Distribution of 45 ° oblique impact fluid field: (a) velocity field, and (b) pressure field.

Fig. 5
Fig. 5

Influence functions shape at different impingement angles: (a) 90 ° and (b) 60 ° .

Fig. 6
Fig. 6

Sketch of rotating polishing system.

Fig. 7
Fig. 7

Optimized influence function profile: (a) 3D figure, (b) 2D view, and (c) transverse profile.

Fig. 8
Fig. 8

Typical Gaussian shape influence function in AJP.

Fig. 9
Fig. 9

Profile of line scanning experiment: (a) profile of line scanning, (b) transverse profile, and (c) longitudinal profile.

Fig. 10
Fig. 10

Polishing system during processing (shield is not included).

Fig. 11
Fig. 11

Experimental result of corrective figuring: (a) initial surface, (b) surface after one iteration, and (c) surface after two iterations.

Fig. 12
Fig. 12

Roughness of the polished surface.

Equations (9)

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T 0 T 0 max = 0.18 H r ( 0.18 H r + 9.43 r H ) exp [ 114 ( r H ) 2 ] .
d R ( r , θ ) = k P ( r , θ , α ) V ( r , θ , α ) d t ,
P = F S = f μ f S = τ s μ f ,
d R ( r , θ ) = k μ f τ s ( r , θ , α ) V ( r , θ , α ) d t .
R ˙ ( r , θ ) = d R ( r , θ ) d t = k μ f τ s ( r , θ , α ) V ( r , θ , α ) .
V ( r , θ , α ) = V n ( r , θ , α ) + V t ( r , θ , α ) .
R ˙ ( r , θ ) = d R ( r , θ ) d t = k μ f τ s ( r , θ , α ) V t ( r , θ , α ) = k μ f W ˙ ( r , θ , α ) ,
R ˙ ω ( r , θ ) = T 2 π 0 2 π 0 L R ˙ ( r , θ ) d r d θ = k T 2 π μ f 0 2 π 0 L W ˙ ( r , θ , α ) d r d θ ,
G ( x , y ) = Re x 2 + y 2 2 σ 2 ,

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