Abstract

Belt magnetorheological finishing (Belt-MRF) is a promising tool for large-optics processing. However, before using a spot, its shape should be designed and controlled by the polishing gap. Previous research revealed a remarkably nonlinear relationship between the removal function and normal pressure distribution. The pressure is nonlinearly related to the gap geometry, precluding prediction of the removal function given the polishing gap. Here, we used the concepts of gap slope and virtual ribbon to develop a model of removal profiles in Belt-MRF. Between the belt and the workpiece in the main polishing area, a gap which changes linearly along the flow direction was created using a flat-bottom magnet box. The pressure distribution and removal function were calculated. Simulations were consistent with experiments. Different removal functions, consistent with theoretical calculations, were obtained by adjusting the gap slope. This approach allows to predict removal functions in Belt-MRF.

© 2017 Optical Society of America

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References

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    [PubMed]
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  4. C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).
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    [PubMed]
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2017 (1)

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

2016 (2)

C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).

Y. Bai, L. Li, D. Xue, and X. Zhang, “Rapid fabrication of a silicon modification layer on silicon carbide substrate,” Appl. Opt. 55(22), 5814–5820 (2016).
[PubMed]

2014 (2)

K. Ren, X. Luo, L. Zheng, Y. Bai, L. Li, H. Hu, and X. Zhang, “Belt-MRF for large aperture mirrors,” Opt. Express 22(16), 19262–19276 (2014).
[PubMed]

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

2011 (1)

2010 (3)

2008 (3)

H. M. Laun, C. Gabriel, and G. Schmidt, “Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

M. Das, V. K. Jain, and P. S. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tools Manuf. 48, 415–426 (2008).

2007 (1)

2005 (1)

J. Engmann, C. Servais, and A. S. Burbidge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newt. Fluid Mech. 132, 1–27 (2005).

2001 (2)

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40(1), 20–33 (2001).
[PubMed]

1999 (1)

F. Zhang, J. Yu, and X. Zhang, “Magnetorheological finishing technology,” Opt. Precis. Eng. 7(5), 1–8 (1999).

1998 (1)

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

1927 (1)

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

Bai, Y.

Bishop, A. L.

Burbidge, A. S.

J. Engmann, C. Servais, and A. S. Burbidge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newt. Fluid Mech. 132, 1–27 (2005).

Dai, Y.

Das, M.

M. Das, V. K. Jain, and P. S. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tools Manuf. 48, 415–426 (2008).

Degroote, J. E.

Demarco, M.

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

Dumas, P.

C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

Engmann, J.

J. Engmann, C. Servais, and A. S. Burbidge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newt. Fluid Mech. 132, 1–27 (2005).

Flug, P.

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

Gabriel, C.

H. M. Laun, C. Gabriel, and G. Schmidt, “Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).

Gans, R. F.

Geiss, A.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Ghoshdastidar, P. S.

M. Das, V. K. Jain, and P. S. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tools Manuf. 48, 415–426 (2008).

Golini, D.

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

Gorodkin, S.

He, J.

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

Hel, J.

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Hogan, S.

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

Hou, J.

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Hu, H.

Huang, W.

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Jacobs, S. D.

Jain, V. K.

M. Das, V. K. Jain, and P. S. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tools Manuf. 48, 415–426 (2008).

Kordonski, W.

Kordonski, W. I.

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40(1), 20–33 (2001).
[PubMed]

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

Lambropoulos, J. C.

Laun, H. M.

H. M. Laun, C. Gabriel, and G. Schmidt, “Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).

Li, L.

Lormeau, J. P.

C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).

Luo, Q.

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Luo, X.

Maloney, C.

C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).

Marino, A. E.

Miao, C.

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).

Rascher, R.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Ren, K.

Schinhaerl, M.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Schmidt, G.

H. M. Laun, C. Gabriel, and G. Schmidt, “Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).

Schneider, G.

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

Servais, C.

J. Engmann, C. Servais, and A. S. Burbidge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newt. Fluid Mech. 132, 1–27 (2005).

Shi, F.

Shorey, A. B.

Smith, G.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Smith, L.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Song, C.

Sperber, P.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Stamp, R.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Vogt, C.

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

Wilson, J. P.

Xue, D.

Yang, F.

J. C. Lambropoulos, F. Yang, and S. D. Jacobs, “Toward a mechanical mechanism for material removal in magnetorheological finishing,” in Optical Fabrication and Testing Workshop (Optical Society of America, 1996), pp. 150–153.

Yang, H.

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

Yu, J.

F. Zhang, J. Yu, and X. Zhang, “Magnetorheological finishing technology,” Opt. Precis. Eng. 7(5), 1–8 (1999).

Yuan, Z.

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Zhang, F.

F. Zhang, J. Yu, and X. Zhang, “Magnetorheological finishing technology,” Opt. Precis. Eng. 7(5), 1–8 (1999).

Zhang, X.

Zhang, Y.

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Zheng, L.

Zheng, Y.

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

Appl. Opt. (6)

Int. J. Mach. Tools Manuf. (1)

M. Das, V. K. Jain, and P. S. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tools Manuf. 48, 415–426 (2008).

J. Non-Newt. Fluid Mech. (1)

J. Engmann, C. Servais, and A. S. Burbidge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newt. Fluid Mech. 132, 1–27 (2005).

J. Non-Newtonian Fluid Mech. (1)

H. M. Laun, C. Gabriel, and G. Schmidt, “Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).

J. Soc. Glass Technol. (1)

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

Opt. Eng. (1)

H. Yang, J. He, W. Huang, and Y. Zhang, “Spot breeding method to evaluate the determinism of magnetorheological finishing,” Opt. Eng. 56(3), 035101 (2017).

Opt. Express (2)

Opt. Photonics News (1)

D. Golini, G. Schneider, P. Flug, and M. Demarco, “The Ultimate Flexible optics manufacturing technology: Magnetorheological Finishing,” Opt. Photonics News 12(10), 20–24 (2001).

Opt. Precis. Eng. (1)

F. Zhang, J. Yu, and X. Zhang, “Magnetorheological finishing technology,” Opt. Precis. Eng. 7(5), 1–8 (1999).

Proc. SPIE (4)

M. Schinhaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smith, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).

W. Huang, Y. Zhang, J. Hel, Y. Zheng, Q. Luo, J. Hou, and Z. Yuan, “Research on the magnetorheological finishing (MRF) technology with dual polishing heads,” Proc. SPIE 9281, 92811U (2014).

C. Maloney, J. P. Lormeau, and P. Dumas, “Improving low, mid and high-special frequency errors on advanced aspherical and freeform optics with MRF,” Proc. SPIE 10009, 100090R (2016).

W. I. Kordonski, D. Golini, P. Dumas, and S. Hogan, “Magnetorheological suspension-based finishing technology,” Proc. SPIE 3326, 527–535 (1998).

Other (3)

A. B. Shorey, “Mechanisms of material removal in magnetorheological finishing of glass,” Ph.D. dissertation (University of Rochester, 2000).

J. C. Lambropoulos, F. Yang, and S. D. Jacobs, “Toward a mechanical mechanism for material removal in magnetorheological finishing,” in Optical Fabrication and Testing Workshop (Optical Society of America, 1996), pp. 150–153.

http://www.tekscan.com .

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Figures (17)

Fig. 1
Fig. 1 Schematic of the Belt-MRF method.
Fig. 2
Fig. 2 The simulation polishing results on spot distribution differences of MRF and Belt-MRF (a) Initial surface error map of ⌀600mm flat [2]. (b) Aimed MRF spot, used to calculate dwell time. (c) Actual MRF spot, with distribution changed linearly. (d) Simulative polishing residual map, using aimed MRF spot. (e) Simulative polishing residual map, using actual MRF spot. (f) Aimed Belt-MRF spot [2], used to calculate dwell time. (g) Actual Belt-MRF spot, with distribution changed linearly. (h) Simulative polishing residual map, using aimed Belt-MRF spot. (i) Simulative polishing residual map, using actual Belt-MRF spot.
Fig. 3
Fig. 3 The gap between the belt and the workpiece in Belt-MRF. (a) The geometrical relationship. (b) The gap slope distribution as θ varies.
Fig. 4
Fig. 4 Distribution of the virtual ribbon in Belt-MRF.
Fig. 5
Fig. 5 Simulated normalized removal functions vs. the x distance, for different k. Parameters: h0 = 3.0 mm and θ = −0.4°.
Fig. 6
Fig. 6 Simulated normalized removal functions vs. the x distance, for different h0. Parameters: k = −0.01 and θ = −0.4°.
Fig. 7
Fig. 7 Simulated normalized removal functions, vs. the x distance, for different θ. Other parameters: k = −0.01 and h0 = 3.0 mm.
Fig. 8
Fig. 8 Belt-MRF prototype.
Fig. 9
Fig. 9 Calibration of the gap thickness and gap slope.
Fig. 10
Fig. 10 Configuration of the normal pressure test.
Fig. 11
Fig. 11 Calculated and measured pressure distributions, for the slope angles of −0.4° and −0.6°.
Fig. 12
Fig. 12 Experimental results. (a) Removal spots, for −0.6° (left), and −0.4° (right). (b) Schematic of the spot centerline profile.
Fig. 13
Fig. 13 Experimental and simulated removal function centerline profiles, for the slope angles of −0.4° and −0.6°.
Fig. 14
Fig. 14 Removal spots and model simulation results, for different slope angles. (a) Removal spots, for slope angles ranging from 0.4° (top) to −0.6° (bottom). (b) Comparison of experimental and simulated profiles.
Fig. 15
Fig. 15 Minimal gap gm for positive slope angles θ.
Fig. 16
Fig. 16 Removal spots and model simulation results, for different initial gap thicknesses. (a) Removal spots, for gap thicknesses ranging from 3.5 mm (top) to 2.0 mm (bottom). (b) Comparison of experimental and simulated profiles.
Fig. 17
Fig. 17 Intensity of the magnetic field B along the vertical direction from the belt bottom.

Tables (4)

Tables Icon

Table 1 Experimental conditions.

Tables Icon

Table 2 VRR and PRR of the removal function, for different slope angles.

Tables Icon

Table 3 VRR and PRR of the removal function, for different gap thicknesses.

Tables Icon

Table 4 Parameters of the removal function model.

Equations (9)

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

Δz( x )=κp( x )v( x )Δt.
g( x )= g 0 +x k g = g 0 +xtanθ.
dh( x ) dx = k h ( x )p( x ),0x60.
p( x )= k p ( x )( h( x )g( x ) ).
dh( x ) dx = k h ( x )p( x )= k h ( x ) k p ( x )( h( x )g( x ) )=k( x )( h( x )g( x ) ).
h( x )= 1 k ( k g k g e kx + g 0 k+( h 0 g 0 )k e kx + k g kx ).
p( x )= k p ( ( h 0 g 0 k g k ) e kx + k g k ).
k p B 2.4 .
Δz( x ) Δt =κp( x )v( x )=κv( x ) k p ( ( h 0 g 0 k g k ) e kx + k g k ).

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