Abstract

A new evolutionary grinding process model has been developed for nanometric control of material removal from an aspheric surface of Zerodur substrate. The model incorporates novel control features such as i) a growing database; ii) an evolving, multi-variable regression equation; and iii) an adaptive correction factor for target surface roughness (Ra) for the next machine run. This process model demonstrated a unique evolutionary controllability of machining performance resulting in the final grinding accuracy (i.e. averaged difference between target and measured surface roughness) of -0.2 ± 2.3(σ) nm Ra over seven trial machine runs for the target surface roughness ranging from 115 nm to 64 nm Ra.

© 2008 Optical Society of America

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    [Crossref]
  35. J.-Y. Han, Major of Astronomy and Space Science, University of Science and Technology, 52 Eoeun-dong, YuseongGu, Daejeon, 305-333, and S.-W. Kim are preparing a manuscript to be called “Evolutionary grinding process simulation for aspheric optical surface of 1 m in diameter.”

2007 (2)

E.-S. Lee and S.-Y. Baek, “A study on optimum grinding factors for aspheric convex surface micro-lens using design of experiments,” Int. J. Mach. Tools & Manufac. 47, 509–520 (2007).
[Crossref]

X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D. D. Walker, “Subsurface damage in precision ground ULE and Zerodur surfaces,” Opt. Express 15, 12197–12205 (2007).
[Crossref] [PubMed]

2006 (2)

L. Wang, Y. Zhu, and Q. Zhang, “Mechanical design of the stressed-lap polishing tool,” Proc. SPIE 6024, 60241Y (2006).
[Crossref]

W. Yao, Y. Zhang, and J. Han, “Machining characteristics and removal mechanisms of reaction bonded silicon carbide,” Proc. SPIE 6149, 61490W (2006).
[Crossref]

2005 (2)

S. Agarwal and P. V. Rao, “A probabilistic approach to predict surface roughness in ceramic grinding,” Int. J. Mach. Tools & Manufac. 45, 609–616 (2005).
[Crossref]

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

2003 (3)

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Z. B. Hou and R. Komanduri, “On the mechanics of the grinding process - Part I. Stochastic nature of the grinding process,” Int. J. Mach. Tools & Manufac. 43, 1579–1593 (2003).
[Crossref]

R. L. Hecker and S. Y. Liang, “Predictive modeling of surface roughness in grinding,” Int. J. Mach. Tools & Manufac. 43, 755–761 (2003).
[Crossref]

2002 (2)

G. Kim, “Evaluation of Pre-estimation Model to the Inprocess Surface Roughness for Grinding Operations,” Int. J. Korean Soc. of Precision Eng. 3, 24–30 (2002).

X. Zhou and F. Xi, “Modeling and predicting surface roughness of the grinding process,” Int. J. Mach. Tools & Manufac. 42, 969–977 (2002).
[Crossref]

2001 (3)

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[Crossref]

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

2000 (1)

A. C. Okafor and Y. M. Ertekin, “Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics,” Int. J. Mach. Tools & Manufac. 40, 1199–1213 (2000).
[Crossref]

1998 (2)

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

X. Chen, D. R. Allanson, and W. B. Rowe, “Life cycle model of the grinding process,” Computers in Industry 36, 5–11 (1998).
[Crossref]

1996 (2)

Y. Namba, “Ultraprecision grinding of chemical vapor deposited silicon carbide mirrors for synchrotron radiation,” Proc. SPIE 2856, 323–330 (1996).
[Crossref]

X. Chen and W. B. Rowe, “Analysis and simulation of the grinding process. Part II. Mechanics of grinding,” Int. J. Mach. Tools & Manufac. 36, 883–896 (1996).
[Crossref]

1995 (1)

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

1994 (1)

W. K. Kahl, “Ductile grinding of silicon carbide as a production method for reflective optics,” Proc. SPIE 1994, 31–38 (1994).
[Crossref]

1992 (2)

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Agarwal, S.

S. Agarwal and P. V. Rao, “A probabilistic approach to predict surface roughness in ceramic grinding,” Int. J. Mach. Tools & Manufac. 45, 609–616 (2005).
[Crossref]

S. Agarwal and P. V. Rao, “Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding,” J. Mach. Tools & Manufac. (to be published).
[PubMed]

Allanson, D. R.

X. Chen, D. R. Allanson, and W. B. Rowe, “Life cycle model of the grinding process,” Computers in Industry 36, 5–11 (1998).
[Crossref]

Andersen, T.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Anderson, D. S.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Angel, J. R. P.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Ardeberg, A. L.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Baek, S.-Y.

E.-S. Lee and S.-Y. Baek, “A study on optimum grinding factors for aspheric convex surface micro-lens using design of experiments,” Int. J. Mach. Tools & Manufac. 47, 509–520 (2007).
[Crossref]

Baldwin, A.

Basile, G.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Beckers, J.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 2003), Chap. 7.

Bifano, T. G.

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

Burge, J. H.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Caso, A.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Cattaneo, G.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Cebrian, J. A.

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

Chen, M.

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

Chen, X.

X. Chen, D. R. Allanson, and W. B. Rowe, “Life cycle model of the grinding process,” Computers in Industry 36, 5–11 (1998).
[Crossref]

X. Chen and W. B. Rowe, “Analysis and simulation of the grinding process. Part II. Mechanics of grinding,” Int. J. Mach. Tools & Manufac. 36, 883–896 (1996).
[Crossref]

Citterio, O.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Davison, W. B.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

DeRigne, S. T.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Dong, S.

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

Drueding, T. W.

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

Ertekin, Y. M.

A. C. Okafor and Y. M. Ertekin, “Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics,” Int. J. Mach. Tools & Manufac. 40, 1199–1213 (2000).
[Crossref]

Evans, R.

Fawcett, S. C.

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

Ghigo, M.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Goncharov, A.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Han, J.

W. Yao, Y. Zhang, and J. Han, “Machining characteristics and removal mechanisms of reaction bonded silicon carbide,” Proc. SPIE 6149, 61490W (2006).
[Crossref]

Han, J.-Y.

J.-Y. Han, Major of Astronomy and Space Science, University of Science and Technology, 52 Eoeun-dong, YuseongGu, Daejeon, 305-333, and S.-W. Kim are preparing a manuscript to be called “Evolutionary grinding process simulation for aspheric optical surface of 1 m in diameter.”

Hecker, R. L.

R. L. Hecker and S. Y. Liang, “Predictive modeling of surface roughness in grinding,” Int. J. Mach. Tools & Manufac. 43, 755–761 (2003).
[Crossref]

Hille, B. B.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Hou, Z. B.

Z. B. Hou and R. Komanduri, “On the mechanics of the grinding process - Part I. Stochastic nature of the grinding process,” Int. J. Mach. Tools & Manufac. 43, 1579–1593 (2003).
[Crossref]

Inasaki, I.

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Iwamuro, F.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Kahl, W. K.

W. K. Kahl, “Ductile grinding of silicon carbide as a production method for reflective optics,” Proc. SPIE 1994, 31–38 (1994).
[Crossref]

Ketelsen, D. A.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Kim, G.

G. Kim, “Evaluation of Pre-estimation Model to the Inprocess Surface Roughness for Grinding Operations,” Int. J. Korean Soc. of Precision Eng. 3, 24–30 (2002).

Kittrell, W. C.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Komanduri, R.

Z. B. Hou and R. Komanduri, “On the mechanics of the grinding process - Part I. Stochastic nature of the grinding process,” Int. J. Mach. Tools & Manufac. 43, 1579–1593 (2003).
[Crossref]

Laguarta, F.

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

Lee, E.-S.

E.-S. Lee and S.-Y. Baek, “A study on optimum grinding factors for aspheric convex surface micro-lens using design of experiments,” Int. J. Mach. Tools & Manufac. 47, 509–520 (2007).
[Crossref]

Lee, H.

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[Crossref]

Li, S.

S. Li, Z. Wang, and Y. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mat. Proc. Tech. (to be published).

Liang, S. Y.

R. L. Hecker and S. Y. Liang, “Predictive modeling of surface roughness in grinding,” Int. J. Mach. Tools & Manufac. 43, 755–761 (2003).
[Crossref]

Lin, W.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Liu, Q.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Lupon, N.

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

Maihara, T.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Martin, H. M.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Mochida, D.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Morantz, P.

Morita, S.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Nagel, R. H.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Namba, Y.

Y. Namba, “Ultraprecision grinding of chemical vapor deposited silicon carbide mirrors for synchrotron radiation,” Proc. SPIE 2856, 323–330 (1996).
[Crossref]

Novi, A.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Ohmori, H.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Okafor, A. C.

A. C. Okafor and Y. M. Ertekin, “Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics,” Int. J. Mach. Tools & Manufac. 40, 1199–1213 (2000).
[Crossref]

Owner-Petersen, M.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Paul, T.

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Peters, J.

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Pierre, Y. B.

Y. B. Pierre, The Design and Construction of Large Optical Telescopes (Springer-Verlag, New York, 2003), Chap. 4.

Rao, P. V.

S. Agarwal and P. V. Rao, “A probabilistic approach to predict surface roughness in ceramic grinding,” Int. J. Mach. Tools & Manufac. 45, 609–616 (2005).
[Crossref]

S. Agarwal and P. V. Rao, “Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding,” J. Mach. Tools & Manufac. (to be published).
[PubMed]

Riewaldt, H.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 2003), Chap. 7.

Rowe, W. B.

X. Chen, D. R. Allanson, and W. B. Rowe, “Life cycle model of the grinding process,” Computers in Industry 36, 5–11 (1998).
[Crossref]

X. Chen and W. B. Rowe, “Analysis and simulation of the grinding process. Part II. Mechanics of grinding,” Int. J. Mach. Tools & Manufac. 36, 883–896 (1996).
[Crossref]

Samhouri, M. S.

M. S. Samhouri and B. W. Surgenor, “Surface roughness in grinding: on-line prediction with adaptive neuro-fuzzy inference system,” Automatic controls laboratory, Department of Mechanical and Materials Engineering, Queen’s university, http://me.queensu.ca/people/surgenor/research/controls/NAMRI2005onlineprediction.pdf.
[PubMed]

Shore, P.

Snel, R.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Surgenor, B. W.

M. S. Samhouri and B. W. Surgenor, “Surface roughness in grinding: on-line prediction with adaptive neuro-fuzzy inference system,” Automatic controls laboratory, Department of Mechanical and Materials Engineering, Queen’s university, http://me.queensu.ca/people/surgenor/research/controls/NAMRI2005onlineprediction.pdf.
[PubMed]

Svelto, G. F.

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

Tonnellier, X.

Tonshoff, H. K.

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Trebisky, T. J.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Uehara, Y.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Vega, F.

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

Walker, D. D.

X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D. D. Walker, “Subsurface damage in precision ground ULE and Zerodur surfaces,” Opt. Express 15, 12197–12205 (2007).
[Crossref] [PubMed]

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Wang, L.

L. Wang, Y. Zhu, and Q. Zhang, “Mechanical design of the stressed-lap polishing tool,” Proc. SPIE 6024, 60241Y (2006).
[Crossref]

Wang, Z.

S. Li, Z. Wang, and Y. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mat. Proc. Tech. (to be published).

West, S. C.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Wilson, R. N.

R. N. Wilson, Reflecting Telescope Optics II (Springer-Verlag, Berlin Heidelberg, 1999), Chap. 1.

Wilson, S. R.

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

Wu, Y.

S. Li, Z. Wang, and Y. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mat. Proc. Tech. (to be published).

Xi, F.

X. Zhou and F. Xi, “Modeling and predicting surface roughness of the grinding process,” Int. J. Mach. Tools & Manufac. 42, 969–977 (2002).
[Crossref]

Yang, M.

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[Crossref]

Yao, W.

W. Yao, Y. Zhang, and J. Han, “Machining characteristics and removal mechanisms of reaction bonded silicon carbide,” Proc. SPIE 6149, 61490W (2006).
[Crossref]

Yin, S.

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

Young, R. S.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

Zhang, F.

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

Zhang, Q.

L. Wang, Y. Zhu, and Q. Zhang, “Mechanical design of the stressed-lap polishing tool,” Proc. SPIE 6024, 60241Y (2006).
[Crossref]

Zhang, Y.

W. Yao, Y. Zhang, and J. Han, “Machining characteristics and removal mechanisms of reaction bonded silicon carbide,” Proc. SPIE 6149, 61490W (2006).
[Crossref]

Zhao, Q.

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

Zhou, X.

X. Zhou and F. Xi, “Modeling and predicting surface roughness of the grinding process,” Int. J. Mach. Tools & Manufac. 42, 969–977 (2002).
[Crossref]

Zhu, Y.

L. Wang, Y. Zhu, and Q. Zhang, “Mechanical design of the stressed-lap polishing tool,” Proc. SPIE 6024, 60241Y (2006).
[Crossref]

CIRP Annals - Manufacturing Technology (1)

H. K. Tonshoff, J. Peters, I. Inasaki, and T. Paul, “Modeling and simulation of grinding processes,” CIRP Annals - Manufacturing Technology 41, 677–688 (1992).
[Crossref]

Computers in Industry (1)

X. Chen, D. R. Allanson, and W. B. Rowe, “Life cycle model of the grinding process,” Computers in Industry 36, 5–11 (1998).
[Crossref]

Int. J. Korean Soc. of Precision Eng. (1)

G. Kim, “Evaluation of Pre-estimation Model to the Inprocess Surface Roughness for Grinding Operations,” Int. J. Korean Soc. of Precision Eng. 3, 24–30 (2002).

Int. J. Mach. Tools & Manufac. (8)

X. Zhou and F. Xi, “Modeling and predicting surface roughness of the grinding process,” Int. J. Mach. Tools & Manufac. 42, 969–977 (2002).
[Crossref]

S. Agarwal and P. V. Rao, “A probabilistic approach to predict surface roughness in ceramic grinding,” Int. J. Mach. Tools & Manufac. 45, 609–616 (2005).
[Crossref]

E.-S. Lee and S.-Y. Baek, “A study on optimum grinding factors for aspheric convex surface micro-lens using design of experiments,” Int. J. Mach. Tools & Manufac. 47, 509–520 (2007).
[Crossref]

S. Yin, S. Morita, H. Ohmori, Y. Uehara, W. Lin, Q. Liu, T. Maihara, F. Iwamuro, and D. Mochida, “ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2m Subaru telescope,” Int. J. Mach. Tools & Manufac. 45, 1598–1604 (2005).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics,” Int. J. Mach. Tools & Manufac. 40, 1199–1213 (2000).
[Crossref]

R. L. Hecker and S. Y. Liang, “Predictive modeling of surface roughness in grinding,” Int. J. Mach. Tools & Manufac. 43, 755–761 (2003).
[Crossref]

X. Chen and W. B. Rowe, “Analysis and simulation of the grinding process. Part II. Mechanics of grinding,” Int. J. Mach. Tools & Manufac. 36, 883–896 (1996).
[Crossref]

Z. B. Hou and R. Komanduri, “On the mechanics of the grinding process - Part I. Stochastic nature of the grinding process,” Int. J. Mach. Tools & Manufac. 43, 1579–1593 (2003).
[Crossref]

Opt. Eng. (3)

T. W. Drueding, S. C. Fawcett, S. R. Wilson, and T. G. Bifano, “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[Crossref]

F. Vega, N. Lupon, J. A. Cebrian, and F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[Crossref]

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[Crossref]

Opt. Express (1)

Proc. SPIE (8)

M. Chen, F. Zhang, Q. Zhao, and S. Dong, “Ultraprecision grinding machining of optical aspheric surface in ductile mode,” Proc. SPIE 4451, 191–199 (2001).
[Crossref]

A. Novi, G. Basile, O. Citterio, M. Ghigo, A. Caso, G. Cattaneo, and G. F. Svelto, “Lightweight SiC foamed mirrors for space applications,” Proc. SPIE 4444, 59–65 (2001).
[Crossref]

L. Wang, Y. Zhu, and Q. Zhang, “Mechanical design of the stressed-lap polishing tool,” Proc. SPIE 6024, 60241Y (2006).
[Crossref]

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[Crossref]

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. D. Walker, “The Euro50 Extremely Large Telescope,” Proc. SPIE 4840, 214–225 (2003).
[Crossref]

Y. Namba, “Ultraprecision grinding of chemical vapor deposited silicon carbide mirrors for synchrotron radiation,” Proc. SPIE 2856, 323–330 (1996).
[Crossref]

W. K. Kahl, “Ductile grinding of silicon carbide as a production method for reflective optics,” Proc. SPIE 1994, 31–38 (1994).
[Crossref]

W. Yao, Y. Zhang, and J. Han, “Machining characteristics and removal mechanisms of reaction bonded silicon carbide,” Proc. SPIE 6149, 61490W (2006).
[Crossref]

Other (12)

M. S. Samhouri and B. W. Surgenor, “Surface roughness in grinding: on-line prediction with adaptive neuro-fuzzy inference system,” Automatic controls laboratory, Department of Mechanical and Materials Engineering, Queen’s university, http://me.queensu.ca/people/surgenor/research/controls/NAMRI2005onlineprediction.pdf.
[PubMed]

Lund observatory, Euro50 optical design, http://www.astro.lu.se/~torben/euro50/optics.html.

OWL, 100 m OWL design, http://www.eso.org/projects/owl/OWL_design.html.

TMT, Thirty Meter Telescope Construction Proposal, http://www.tmt.org/news/TMT-Construction Proposal-Public.pdf.

GMT, Giant Magellan Telescope Conceptual Design Report, http://www.gmto.org/CoDRpublic.

R. N. Wilson, Reflecting Telescope Optics II (Springer-Verlag, Berlin Heidelberg, 1999), Chap. 1.

Y. B. Pierre, The Design and Construction of Large Optical Telescopes (Springer-Verlag, New York, 2003), Chap. 4.

J.-Y. Han, Major of Astronomy and Space Science, University of Science and Technology, 52 Eoeun-dong, YuseongGu, Daejeon, 305-333, and S.-W. Kim are preparing a manuscript to be called “Evolutionary grinding process simulation for aspheric optical surface of 1 m in diameter.”

P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 2003), Chap. 7.

ISO, “Geometrical Product Specifications (GPS) - Surface texture: Profile method - Nominal characteristics of contact (stylus) instruments, 4.4”, (3274-ENGL 1996), p.8.

S. Li, Z. Wang, and Y. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mat. Proc. Tech. (to be published).

S. Agarwal and P. V. Rao, “Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding,” J. Mach. Tools & Manufac. (to be published).
[PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic illustration of the grinding configuration

Fig. 2.
Fig. 2.

Surface roughness (Ra) and (a) Feed rate (crosses, triangles, and dots are corresponded to 16.5, 9.3, and 6.9 µm in grain size) and (b) linear speed of work-piece rotation; Note that the three fitted trend lines come from Eq. 6 and 7 in Table A1 in Appendix.

Fig. 3.
Fig. 3.

Comparison between (a) grinding errors; and (b) standard deviation of residuals with (solid circles and bars) and without (open squares and bars) target correction factor of evolutionary process control

Fig. 4.
Fig. 4.

Feed rates to achieve the experimented sequence of true target surface roughness with (solid triangles representing the actual experiment data) and without (open rhombuses indicating the computed data using Eq. (6)) evolutionary process control

Fig. 5.
Fig. 5.

Measured surface roughness vs. (a) linear speed of work-piece rotation and (b) distance from the work-piece center for seven trial grinding runs

Tables (3)

Tables Icon

Table 1. Resulting input values for the grinding variables collected after seven machine runs were completed

Tables Icon

Table 2. Exponents and coefficient of regression (β, γ and δ), nominal (RaT) and true (RaTR) target surface roughness, measured surface roughness (RaM) and target correction factor (Δ)

Tables Icon

Table A1. Characteristics of initial grinding data

Equations (7)

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

G i , F i , V PLij , Ra Mij ( i = 1 , . . . , N )
i = i + 1
Ra TRij = Ra Tij Δ i 1
Ra Tij = δ i G i α i F i β i V PLij γ i
T i = 2.5 ( L F i )
c F 1 , c F 2 , c F 3 and c F 4 are from Ra = c F 1 + c F 2 F + c F 3 F 2 + c F 4 F 3
c V 1 , c V 2 , c V 3 and c V 4 are from Ra = c V 1 + c V 2 V PL + c V 3 V PL 2 + c V 4 V PL 3

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