Abstract

We present a simulation technique to predict tool influence functions (TIFs) based on the Precessions polishing process, which is driven by addressing mass fabrication of the European Extremely Large Telescope mirror segments. Precessions polishing requires accurate and predictable TIFs to optimize the multiple process parameters, particularly when sequential polishing runs are performed by different polishing tools. In this paper, the static and dynamic TIFs are simulated based on the Preston equation. The velocity distribution is calculated according to the geometry of the precession motion. The pressure distribution at the polishing spot is calculated by means of finite element analysis (FEA). The FEA result is validated by direct force measurement with a simulation error of 4.3%. The simulation results of TIFs are verified by an experiment that shows the residual errors are less than 5% for both static and dynamic TIFs.

© 2013 Optical Society of America

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References

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2012

2010

C. Miao, J. C. Lambropoulos, and S. D. Jacob, “Process parameter effects on material removal in magnetorheological finishing of borosilicate glass,” Appl. Opt. 49, 1951–1963 (2010).
[CrossRef]

Z. Li, S. Li, Y. Dai, and X. Peng, “Optimization and application of influence function in abrasive jet polishing,” Appl. Opt. 49, 2947–2953 (2010).
[CrossRef]

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

2008

G. H. Sanders, “Managing a big ground-based astronomy project: the Thirty Meter Telescope (TMT) project,” Proc. SPIE 7017, 70170H1 (2008).
[CrossRef]

W. Yang, Y. Guo, Y. Li, and Q. Xu, “Pressure and velocity dependence of the material removal rate in the fast polishing process,” Appl. Opt. 47, 6236–6242 (2008).
[CrossRef]

2006

2005

2004

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE 5489, 1–10 (2004).
[CrossRef]

2003

1979

1927

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

Beaucamp, A.

Brooks, D.

Casali, M.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

D’Odorico, S.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Dai, Y.

Evans, R.

Freeman, R.

Gilmozzi, R.

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE 5489, 1–10 (2004).
[CrossRef]

González, J. C.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Guo, Y.

Hubin, N.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Jacob, S. D.

Jones, R. A.

Kasper, M.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Käufl, H. U.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Kim, D. W.

Kim, S.

Kim, S. W.

King, A.

Kissler-Patig, M.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Lambropoulos, J. C.

Li, H.

Li, S.

Li, Y.

Li, Z.

Marchetti, E.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

McCavana, G.

Messelink, W.

Miao, C.

Morton, R.

Pasquini, L.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Paufique, J.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Peng, X.

Preston, F. W.

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

Ramsay, S.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Richichi, A.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Ruch, E.

E. Ruch, “The challenge of the optics in future extremely large telescopes” in Astronomy at the Frontiers of Science (Springer, 2011), p. 229.

Sanders, G. H.

G. H. Sanders, “Managing a big ground-based astronomy project: the Thirty Meter Telescope (TMT) project,” Proc. SPIE 7017, 70170H1 (2008).
[CrossRef]

Siebenmorgen, R.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Vernet, J.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Walker, D. D.

Xu, Q.

Yang, W.

Yu, G.

Zerbi, F. M.

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Appl. Opt.

J. Soc. Glass Technol.

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

Opt. Express

Proc. SPIE

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE 5489, 1–10 (2004).
[CrossRef]

G. H. Sanders, “Managing a big ground-based astronomy project: the Thirty Meter Telescope (TMT) project,” Proc. SPIE 7017, 70170H1 (2008).
[CrossRef]

S. Ramsay, S. D’Odorico, M. Casali, J. C. González, N. Hubin, M. Kasper, H. U. Käufl, M. Kissler-Patig, E. Marchetti, J. Paufique, L. Pasquini, R. Siebenmorgen, A. Richichi, J. Vernet, and F. M. Zerbi, “An overview of the E-ELT instrumentation programme,” Proc. SPIE 7735, 773524 (2010).
[CrossRef]

Other

E. Ruch, “The challenge of the optics in future extremely large telescopes” in Astronomy at the Frontiers of Science (Springer, 2011), p. 229.

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Figures (12)

Fig. 1.
Fig. 1.

Detailed geometry of bonnet tool for Precession polishing.

Fig. 2.
Fig. 2.

Sketch of space movement of the tool of the precess.

Fig. 3.
Fig. 3.

Velocity distribution simulation results: R80 tool, 0.7 mm offset.

Fig. 4.
Fig. 4.

FEA model of Precessions polishing.

Fig. 5.
Fig. 5.

The absolute pressure distribution FEA result.

Fig. 6.
Fig. 6.

Experimental setup of the force measurement on the machine.

Fig. 7.
Fig. 7.

Force measurement result with different z offset.

Fig. 8.
Fig. 8.

Normalized TIFs simulation results.

Fig. 9.
Fig. 9.

Static and dynamic TIFs on the Zerodur part.

Fig. 10.
Fig. 10.

Comparison of normalized 2D static TIF simulation and measurement results in the x and y directions.

Fig. 11.
Fig. 11.

Comparison of normalized 2D dynamic TIFs simulation and measurement results in the x and y directions.

Fig. 12.
Fig. 12.

Residuals between normalized 2D simulated and experimental TIFs.

Tables (1)

Tables Icon

Table 1. Material Properties for the Modeling

Equations (4)

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Δh(x,y)=k·ν(x,y)·p(x,y),
R(r)=1T0Tk·v(x,y)·p(x,y)·dt=k2πθ0θ0v(x,y)·p(x,y)·dθ,
v1(x,y)=2·cosρ·(Rd)1s·(sα)·(sβ)·(sγ)·ω0,
f=Ap(x,y)dxdy.

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