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 Manuf. 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 Manuf. 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 Manuf. 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 Manuf. 43, 1579-1593 (2003).
[CrossRef]

R. L. Hecker and S. Y. Liang, "Predictive modeling of surface roughness in grinding," Int. J. Mach. Tools Manuf. 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 Manuf. 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)

Q1. 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 Manuf. 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," Comp. Ind. 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 Manuf. 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 (1)

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]

Agarwal, S.

S. Agarwal and P. V. Rao, "A probabilistic approach to predict surface roughness in ceramic grinding," Int. J. Mach. Tools Manuf. 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 Manuf. (to be published).
[PubMed]

Allanson, D. R.

X. Chen, D. R. Allanson and W. B. Rowe, "Life cycle model of the grinding process," Comp. Ind. 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 Manuf. 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]

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," Comp. Ind. 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 Manuf. 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.

Q1. 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 Manuf. 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 Manuf. 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 Manuf. 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]

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 Manuf. 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 Manuf. 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 Manuf. 43, 755-761 (2003).
[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]

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]

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 Manuf. 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]

Okafor, A. C.

Q1. 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 Manuf. 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]

Rao, P. V.

S. Agarwal and P. V. Rao, "A probabilistic approach to predict surface roughness in ceramic grinding," Int. J. Mach. Tools Manuf. 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 Manuf. (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]

Rowe, W. B.

X. Chen, D. R. Allanson and W. B. Rowe, "Life cycle model of the grinding process," Comp. Ind. 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 Manuf. 36, 883-896 (1996).
[CrossRef]

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]

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]

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, 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 Manuf. 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 Manuf. 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 Manuf. 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]

Comp. Ind. (1)

X. Chen, D. R. Allanson and W. B. Rowe, "Life cycle model of the grinding process," Comp. Ind. 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 Manuf. (1)

Q1. 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 Manuf. 40, 1199-1213 (2000).
[CrossRef]

Int. J. Mach. Tools Manuf. (7)

X. Zhou and F. Xi, "Modeling and predicting surface roughness of the grinding process," Int. J. Mach. Tools Manuf. 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 Manuf. 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 Manuf. 47, 509-520 (2007).
[CrossRef]

R. L. Hecker and S. Y. Liang, "Predictive modeling of surface roughness in grinding," Int. J. Mach. Tools Manuf. 43, 755-761 (2003).
[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 Manuf. 45, 1598-1604 (2005).
[CrossRef]

X. Chen and W. B. Rowe, "Analysis and simulation of the grinding process. Part II. Mechanics of grinding," Int. J. Mach. Tools Manuf. 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 Manuf. 43, 1579-1593 (2003).
[CrossRef]

J. Mach. Tools Manuf. (1)

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

J. Mat. Proc. Tech. (1)

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).

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 (11)

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."

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]

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.

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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

Metrics