Abstract

Wheel polishing, a new optical fabrication technique, is proposed for super-smooth surface fabrication of optical components in high-precision optical instruments. The machining mechanism and the removal function contours are investigated in detail. The elastohydrodynamic lubrication theory is adopted to analyze the deformation of the wheel head, the pressure distribution, and the fluid film thickness distribution in the narrow machining zone. The pressure and the shear stress distributions at the interface between the slurry and the sample are numerically simulated. Practical polishing experiments are arranged to analyze the relationship between the wheel–sample distance and the machining rate. It is demonstrated in this paper that the wheel–sample distance will directly influence the removal function contours. Moreover, ripples on the wheel surface will eventually induce the transverse prints on the removal function contours. The surface roughness of fused silicon is reduced to less than 0.5 nm (rms) from initial 1.267 nm (rms). The wheel polishing technique is feasible for super-smooth surface fabrication.

© 2012 Optical Society of America

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References

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  1. T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
    [CrossRef]
  2. M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
    [CrossRef]
  3. M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
    [CrossRef]
  4. H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
    [CrossRef]
  5. J. R. Arthur and R. O. Tatchyn, “Radiation properties of the Linac coherent light source: Challenges for x-ray optics,” Proc. SPIE 4143, 1–8 (2001).
    [CrossRef]
  6. M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
    [CrossRef]
  7. Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
    [CrossRef]
  8. B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamental of Fluid Film Lubrication (Taylor & Francis, 2004), pp. 91–97.
  9. P. Yang and S. Z. Wen, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication,” J. Tribol. 112, 631–636 (1990).
    [CrossRef]
  10. D. Zhu and S. Z. Wen, “A full numerical solution for the thermal elastohydrodynmaic problem in elliptical contacts,” J. Tribol. 106, 246–254 (1984).
    [CrossRef]
  11. S. F. Soares, D. R. Baselt, J. P. Black, K. C. Jungling, and W. K. Stowell, “Float-polishing process and analysis of float-polished quartz,” Appl. Opt. 33, 89–95 (1994).
    [CrossRef]
  12. Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
    [CrossRef]
  13. Y.-T. Su and Y.-C. Kao, “An experimental study on machining rate distribution of hydrodynamic polishing process,” Wear 224, 95–105 (1999).
    [CrossRef]
  14. M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
    [CrossRef]

2007 (2)

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

2005 (1)

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

2001 (1)

J. R. Arthur and R. O. Tatchyn, “Radiation properties of the Linac coherent light source: Challenges for x-ray optics,” Proc. SPIE 4143, 1–8 (2001).
[CrossRef]

2000 (1)

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

1999 (1)

Y.-T. Su and Y.-C. Kao, “An experimental study on machining rate distribution of hydrodynamic polishing process,” Wear 224, 95–105 (1999).
[CrossRef]

1995 (2)

Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

1994 (1)

1992 (2)

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

1990 (1)

P. Yang and S. Z. Wen, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication,” J. Tribol. 112, 631–636 (1990).
[CrossRef]

1984 (1)

D. Zhu and S. Z. Wen, “A full numerical solution for the thermal elastohydrodynmaic problem in elliptical contacts,” J. Tribol. 106, 246–254 (1984).
[CrossRef]

Ando, M.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Arthur, J. R.

J. R. Arthur and R. O. Tatchyn, “Radiation properties of the Linac coherent light source: Challenges for x-ray optics,” Proc. SPIE 4143, 1–8 (2001).
[CrossRef]

Baselt, D. R.

Black, J. P.

Cao, J.

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

Chen, C.

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

Deguchi, A.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Endo, K.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Gao, H.

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

Goto, H.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Hada, K.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Hamrock, B. J.

B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamental of Fluid Film Lubrication (Taylor & Francis, 2004), pp. 91–97.

Higomura, M.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Hsiau, J.-S.

Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
[CrossRef]

Jacobson, B. O.

B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamental of Fluid Film Lubrication (Taylor & Francis, 2004), pp. 91–97.

Jungling, K. C.

Kakiuchi, H.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Kameishi, K.

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

Kanaoka, M.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Kaneta, M.

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

Kao, Y.-C.

Y.-T. Su and Y.-C. Kao, “An experimental study on machining rate distribution of hydrodynamic polishing process,” Wear 224, 95–105 (1999).
[CrossRef]

Kohama, Y.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Mimura, H.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Miura, T.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Mori, Y.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Morita, K.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Murakami, K.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Nakamura, N.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Negishi, M.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Nishikawa, H.

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

Nomura, K.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Ohkubo, Y.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Ohno, N.

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

Sakai, T.

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

Sano, Y.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Schmid, S. R.

B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamental of Fluid Film Lubrication (Taylor & Francis, 2004), pp. 91–97.

Soares, S. F.

Stowell, W. K.

Su, Y.-T.

Y.-T. Su and Y.-C. Kao, “An experimental study on machining rate distribution of hydrodynamic polishing process,” Wear 224, 95–105 (1999).
[CrossRef]

Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
[CrossRef]

Suzuki, K.

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Takimoto, M.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Takino, H.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Tatchyn, R. O.

J. R. Arthur and R. O. Tatchyn, “Radiation properties of the Linac coherent light source: Challenges for x-ray optics,” Proc. SPIE 4143, 1–8 (2001).
[CrossRef]

Wang, S.-Y.

Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
[CrossRef]

Wen, S. Z.

P. Yang and S. Z. Wen, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication,” J. Tribol. 112, 631–636 (1990).
[CrossRef]

D. Zhu and S. Z. Wen, “A full numerical solution for the thermal elastohydrodynmaic problem in elliptical contacts,” J. Tribol. 106, 246–254 (1984).
[CrossRef]

Wu, M.

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

Yamamoto, H.

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

Yamamura, K.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Yamauchi, K.

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Yang, P.

P. Yang and S. Z. Wen, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication,” J. Tribol. 112, 631–636 (1990).
[CrossRef]

Yasutake, K.

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

Zhu, D.

D. Zhu and S. Z. Wen, “A full numerical solution for the thermal elastohydrodynmaic problem in elliptical contacts,” J. Tribol. 106, 246–254 (1984).
[CrossRef]

Zhu, Y.

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

Appl. Opt. (1)

J. Cryst. Growth. (1)

Y. Mori, K. Yamamura, K. Endo, K. Yamauchi, K. Yasutake, H. Goto, H. Kakiuchi, Y. Sano, and H. Mimura, “Creation of perfect surfaces,” J. Cryst. Growth. 275, 39–50 (2005).
[CrossRef]

J. Tribol. (3)

M. Kaneta, H. Nishikawa, K. Kameishi, T. Sakai, and N. Ohno, “Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication,” J. Tribol. 114, 75–80 (1992).
[CrossRef]

P. Yang and S. Z. Wen, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication,” J. Tribol. 112, 631–636 (1990).
[CrossRef]

D. Zhu and S. Z. Wen, “A full numerical solution for the thermal elastohydrodynmaic problem in elliptical contacts,” J. Tribol. 106, 246–254 (1984).
[CrossRef]

Nanotechnology. (1)

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, and N. Nakamura, “Super-smooth polishing on aspherical surfaces,” Nanotechnology. 6, 111–120 (1995).
[CrossRef]

Proc. SPIE (4)

M. Ando, M. Negishi, M. Takimoto, A. Deguchi, N. Nakamura, M. Higomura, and H. Yamamoto, “Super-smooth surface polishing on aspherical optics,” Proc. SPIE 1720, 22–23 (1992).
[CrossRef]

H. Gao, J. Cao, M. Wu, Y. Zhu, and C. Chen, “Process technology for supersmooth surface machining,” Proc. SPIE 4231, 208–213 (2000).
[CrossRef]

J. R. Arthur and R. O. Tatchyn, “Radiation properties of the Linac coherent light source: Challenges for x-ray optics,” Proc. SPIE 4143, 1–8 (2001).
[CrossRef]

T. Miura, K. Murakami, K. Suzuki, Y. Kohama, K. Morita, K. Hada, and Y. Ohkubo, “Nikon EUVL development progress update,” Proc. SPIE 6517, 651707 (2007).
[CrossRef]

Sci. Technol. Adv. Mater. (1)

M. Kanaoka, H. Takino, K. Nomura, Y. Mori, H. Mimura, and K. Yamauchi, “Removal properties of low-thermal-expansion materials with rotating-sphere elastic emission machining,” Sci. Technol. Adv. Mater. 8, 170–172 (2007).
[CrossRef]

Wear (2)

Y.-T. Su, S.-Y. Wang, and J.-S. Hsiau, “On machining rate of hydrodynamic polishing process,” Wear 188, 77–87 (1995).
[CrossRef]

Y.-T. Su and Y.-C. Kao, “An experimental study on machining rate distribution of hydrodynamic polishing process,” Wear 224, 95–105 (1999).
[CrossRef]

Other (1)

B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamental of Fluid Film Lubrication (Taylor & Francis, 2004), pp. 91–97.

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Figures (7)

Fig. 1.
Fig. 1.

Machining mechanism schematic diagram of the wheel polishing.

Fig. 2.
Fig. 2.

Deformation of the wheel: h1 is the total deformation amount and h2 is the wheel deformation amount. The fluid film thickness is h1h2.

Fig. 3.
Fig. 3.

Pressure distribution for different rotating parameters. (The x axis represents the normalized position in the direction of slurry motion.)

Fig. 4.
Fig. 4.

Fluid film thickness (unit: micrometers) distribution in the parallel surface of the sample surface [10].

Fig. 5.
Fig. 5.

(a) Dynamic pressure and (b) the shear stress distributions in the direction of slurry motion.

Fig. 6.
Fig. 6.

Removal function contours of different wheel–sample distances (a) 0 μm, (b) 5 μm, and (c) 10 μm. (d) Vertical profile of the removal function contours of the 10 μm mode.

Fig. 7.
Fig. 7.

Surface roughness before and after being processed for different wheel–sample distances: (a) 0 μm, (b) 5 μm, and (c) 10 μm.

Equations (3)

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

h(x,y)=h0+s(x,y)+d(x,y)s(x,y)=x22R+y22R,
3h2hxpx+h32px2+3h2hypy+h32py2=6μUhx,
d(x,y)=2πEAp(x,y)dxdy(xx)2+(yy)2,

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