Abstract

A concept of material removal based on the principle of conservation of particles momentum in a binary suspension is applied to analyze material removal in magnetorheological finishing and magnetorheological jet processes widely used in precision optics fabrication. According to this concept, a load for surface indentation by abrasive particles is provided at their interaction near the wall with heavier basic (magnetic) particles, which fluctuate (due to collision) in the shear flow of concentrated suspension. The model is in good qualitative and quantitative agreement with experimental results.

© 2011 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]

2010 (2)

2009 (4)

C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and Stephen D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585–2594 (2009).
[Crossref] [PubMed]

C. Miao, S. N. Shafrir, J. C. Lambropoulos, and S. D. Jacobs, “Normal force in magnetorheologial finishing,” Proc. SPIE 7426, 74260C (2009).
[Crossref]

W. Kordonski and S. Gorodkin, “Magnetorheological measurements with consideration for the internal magnetic field in samples,” J. Phys.: Conf. Ser. 149, 012064 (2009).
[Crossref]

S. F. Ang, T. Scholz, A. Klocke, and G. A. Schneider, “Determination of elastic/plastic transition of human enamel by nanoindentation,” Dent. Mater. 15, 1403–1410(2009).
[Crossref]

2008 (2)

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 1T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).
[Crossref]

K. P. Gertzos, P. G. Nikolakopoulos, and C. A. Papadopoulos, “CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant,” Tribol. Int. 41, 1190–1204 (2008).
[Crossref]

2007 (1)

2006 (1)

W. Kordonski, A. Shorey, and M. Tricard, “Magnetorheological jet finishing technology,” J. Fluid Eng. 128, 20–26 (2006).
[Crossref]

2003 (2)

G. B. Basim, I. U. Vakarelski, and B. M. Moudgil, “Role of interaction forces in controlling the stability and polishing performance of CMP slurries,” J. Colloid Interface Sci. 263, 506–515 (2003).
[Crossref] [PubMed]

A. Shorey, S Gorodkin, and W. Kordonski, “Effect of process parameters on surface morphology in MRF,” Technical Digest SPIE TD02, 69–71 (2003).
[Crossref]

2001 (2)

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, 20–33 (2001).
[Crossref]

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

2000 (2)

A. Karion and M. Hunt, “Wall stress in granular Couette flow of mono-sized particles and binary mixtures,” Powder Technol. 109, 145–163 (2000).
[Crossref]

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, “Particle dynamics in sheared granular matter,” Phys. Rev. Lett. 85, 1428–1431 (2000).
[Crossref] [PubMed]

1996 (1)

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[Crossref]

1993 (1)

W. Kordonski, “Elements and devices based on magnetorheological effect,” J. Intell. Mater. Syst. Struct. 4, 65–69(1993).
[Crossref]

1991 (1)

J. A. Tichy, “Hydrodynamic lubrication theory for the Bingham plastic flow model,” J. Rheol. (N.Y.) 35, 477–96 (1991).
[Crossref]

1990 (1)

L. M. Cook, “Chemical processes in glass polishing,” J. Non-Cryst. Solids 120, 152–171 (1990).
[Crossref]

1988 (1)

Y. Mori, K. Yamauchi, and K. Endo, “Mechanism of atomic removal in elastic emission machining,” J. Jpn. Soc. Prec. Eng. 10, 24–28 (1988).
[Crossref]

1986 (1)

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

1966 (1)

P. Perzyna, “Fundamental problems in viscoplasticity,” Adv. Appl. Mech. 9, 243–377 (1966).
[Crossref]

1927 (1)

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

Ang, S. F.

S. F. Ang, T. Scholz, A. Klocke, and G. A. Schneider, “Determination of elastic/plastic transition of human enamel by nanoindentation,” Dent. Mater. 15, 1403–1410(2009).
[Crossref]

Basim, G. B.

G. B. Basim, I. U. Vakarelski, and B. M. Moudgil, “Role of interaction forces in controlling the stability and polishing performance of CMP slurries,” J. Colloid Interface Sci. 263, 506–515 (2003).
[Crossref] [PubMed]

Beaucamp, T. H.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Bishop, A. L.

Bocquet, L.

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, “Particle dynamics in sheared granular matter,” Phys. Rev. Lett. 85, 1428–1431 (2000).
[Crossref] [PubMed]

Booij, S. M.

S. M. Booij, “Fluid jet polishing,” Doctoral thesis (Technische Universiteit Delft, 2003).

Brooks, D.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Cook, L. M.

L. M. Cook, “Chemical processes in glass polishing,” J. Non-Cryst. Solids 120, 152–171 (1990).
[Crossref]

Dai, Y.

DeGroote, J. E.

Demchuk, S. A.

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

Endo, K.

Y. Mori, K. Yamauchi, and K. Endo, “Mechanism of atomic removal in elastic emission machining,” J. Jpn. Soc. Prec. Eng. 10, 24–28 (1988).
[Crossref]

Freeman, R.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

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 1T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).
[Crossref]

Gans, R. F.

Gertzos, K. P.

K. P. Gertzos, P. G. Nikolakopoulos, and C. A. Papadopoulos, “CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant,” Tribol. Int. 41, 1190–1204 (2008).
[Crossref]

Gleb, L.

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Golini, D.

W. Kordonski, D. Golini, and S. Hogan, “System for abrasive jet shaping and polishing of a surface using magnetorheological fluid,” U.S. patent 5,971,835 (26 October, 1999).

Gollub, J. P.

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, “Particle dynamics in sheared granular matter,” Phys. Rev. Lett. 85, 1428–1431 (2000).
[Crossref] [PubMed]

Gorodkin, G.

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Gorodkin, S

A. Shorey, S Gorodkin, and W. Kordonski, “Effect of process parameters on surface morphology in MRF,” Technical Digest SPIE TD02, 69–71 (2003).
[Crossref]

Gorodkin, S.

W. Kordonski and S. Gorodkin, “Magnetorheological measurements with consideration for the internal magnetic field in samples,” J. Phys.: Conf. Ser. 149, 012064 (2009).
[Crossref]

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Hogan, S.

W. Kordonski, D. Golini, and S. Hogan, “System for abrasive jet shaping and polishing of a surface using magnetorheological fluid,” U.S. patent 5,971,835 (26 October, 1999).

Hunt, M.

A. Karion and M. Hunt, “Wall stress in granular Couette flow of mono-sized particles and binary mixtures,” Powder Technol. 109, 145–163 (2000).
[Crossref]

Jacobs, S.

Jacobs, S. D.

Jacobs, Stephen D.

Karion, A.

A. Karion and M. Hunt, “Wall stress in granular Couette flow of mono-sized particles and binary mixtures,” Powder Technol. 109, 145–163 (2000).
[Crossref]

Kashevsky, B.

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Khusid, B. M.

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

King, A.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Klocke, A.

S. F. Ang, T. Scholz, A. Klocke, and G. A. Schneider, “Determination of elastic/plastic transition of human enamel by nanoindentation,” Dent. Mater. 15, 1403–1410(2009).
[Crossref]

Kordonski, V. I.

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

Kordonski, W.

W. Kordonski and S. Gorodkin, “Magnetorheological measurements with consideration for the internal magnetic field in samples,” J. Phys.: Conf. Ser. 149, 012064 (2009).
[Crossref]

W. Kordonski, A. Shorey, and M. Tricard, “Magnetorheological jet finishing technology,” J. Fluid Eng. 128, 20–26 (2006).
[Crossref]

A. Shorey, S Gorodkin, and W. Kordonski, “Effect of process parameters on surface morphology in MRF,” Technical Digest SPIE TD02, 69–71 (2003).
[Crossref]

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[Crossref]

W. Kordonski, “Elements and devices based on magnetorheological effect,” J. Intell. Mater. Syst. Struct. 4, 65–69(1993).
[Crossref]

W. Kordonski, D. Golini, and S. Hogan, “System for abrasive jet shaping and polishing of a surface using magnetorheological fluid,” U.S. patent 5,971,835 (26 October, 1999).

Kordonski, W. I.

Kordonsky, W.

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Kovacevic, R.

A. Momber and R. Kovacevic, Principles of Abrasive Water Jet Machining (Springer, 1998).
[Crossref]

Lambropoulos, J.

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 1T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).
[Crossref]

Losert, W.

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, “Particle dynamics in sheared granular matter,” Phys. Rev. Lett. 85, 1428–1431 (2000).
[Crossref] [PubMed]

Lubensky, T. C.

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, “Particle dynamics in sheared granular matter,” Phys. Rev. Lett. 85, 1428–1431 (2000).
[Crossref] [PubMed]

Marino, A. E.

McCavana, G.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Miao, C.

Mici, J.

Momber, A.

A. Momber and R. Kovacevic, Principles of Abrasive Water Jet Machining (Springer, 1998).
[Crossref]

Mori, Y.

Y. Mori, K. Yamauchi, and K. Endo, “Mechanism of atomic removal in elastic emission machining,” J. Jpn. Soc. Prec. Eng. 10, 24–28 (1988).
[Crossref]

Morton, R.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Moudgil, B. M.

G. B. Basim, I. U. Vakarelski, and B. M. Moudgil, “Role of interaction forces in controlling the stability and polishing performance of CMP slurries,” J. Colloid Interface Sci. 263, 506–515 (2003).
[Crossref] [PubMed]

Nikolakopoulos, P. G.

K. P. Gertzos, P. G. Nikolakopoulos, and C. A. Papadopoulos, “CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant,” Tribol. Int. 41, 1190–1204 (2008).
[Crossref]

Papadopoulos, C. A.

K. P. Gertzos, P. G. Nikolakopoulos, and C. A. Papadopoulos, “CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant,” Tribol. Int. 41, 1190–1204 (2008).
[Crossref]

Peng, X.

Perzyna, P.

P. Perzyna, “Fundamental problems in viscoplasticity,” Adv. Appl. Mech. 9, 243–377 (1966).
[Crossref]

Preston, F. W.

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

Prokhorov, I.

W. Kordonsky, I. Prokhorov, S. Gorodkin, G. Gorodkin, L. Gleb, and B. Kashevsky, “Magnetorheological polishing devices and methods,” U.S. patent 5,449,313 (12 September, 1993).

Prokhorov, I. V.

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

Riley, D.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

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 1T,” J. Non-Newtonian Fluid Mech. 148, 47–56 (2008).
[Crossref]

Schneider, G. A.

S. F. Ang, T. Scholz, A. Klocke, and G. A. Schneider, “Determination of elastic/plastic transition of human enamel by nanoindentation,” Dent. Mater. 15, 1403–1410(2009).
[Crossref]

Scholz, T.

S. F. Ang, T. Scholz, A. Klocke, and G. A. Schneider, “Determination of elastic/plastic transition of human enamel by nanoindentation,” Dent. Mater. 15, 1403–1410(2009).
[Crossref]

Shafrir, S. N.

C. Miao, S. N. Shafrir, J. C. Lambropoulos, and S. D. Jacobs, “Normal force in magnetorheologial finishing,” Proc. SPIE 7426, 74260C (2009).
[Crossref]

C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and Stephen D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585–2594 (2009).
[Crossref] [PubMed]

Shen, H. H.

H. H. Shen, “Granular shear flows-constitutive relations and internal structures,” in 15th ASCE Engineering Mechanical Conference (Columbia University, 2002), pp. 1–7.

Shi, F.

Shorey, A.

W. Kordonski, A. Shorey, and M. Tricard, “Magnetorheological jet finishing technology,” J. Fluid Eng. 128, 20–26 (2006).
[Crossref]

A. Shorey, S Gorodkin, and W. Kordonski, “Effect of process parameters on surface morphology in MRF,” Technical Digest SPIE TD02, 69–71 (2003).
[Crossref]

Shorey, A. B.

Shulman, Z. P.

Z. P. Shulman, V. I. Kordonski, E. A. Zaltsgendler, I. V. Prokhorov, B. M. Khusid, and S. A. Demchuk, “Structure, physical properties, and dynamics of magnetorheological suspensions,” Int. J. Multiphase Flow 12, 935–955 (1986).
[Crossref]

Simms, J.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Song, C.

Tichy, J. A.

J. A. Tichy, “Hydrodynamic lubrication theory for the Bingham plastic flow model,” J. Rheol. (N.Y.) 35, 477–96 (1991).
[Crossref]

Tricard, M.

W. Kordonski, A. Shorey, and M. Tricard, “Magnetorheological jet finishing technology,” J. Fluid Eng. 128, 20–26 (2006).
[Crossref]

Vakarelski, I. U.

G. B. Basim, I. U. Vakarelski, and B. M. Moudgil, “Role of interaction forces in controlling the stability and polishing performance of CMP slurries,” J. Colloid Interface Sci. 263, 506–515 (2003).
[Crossref] [PubMed]

Walker, D. D.

D. D. Walker, A.T. H. Beaucamp, D. Brooks, R. Freeman, A. King, G. McCavana, R. Morton, D. Riley, and J. Simms, “Novel CNC polishing process for control of form and texture on aspheric surfaces,” Proc. SPIE 4451, 267–276 (2001).
[Crossref]

Wilson, J. P.

Yamauchi, K.

Y. Mori, K. Yamauchi, and K. Endo, “Mechanism of atomic removal in elastic emission machining,” J. Jpn. Soc. Prec. Eng. 10, 24–28 (1988).
[Crossref]

Zaltsgendler, E. A.

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Figures (15)

Fig. 1
Fig. 1

Schematic of MRF. (a) MRF interface, (b) contact zone, (c) polishing spot interferogram.

Fig. 2
Fig. 2

Induced by magnetic field mechanical properties of MR polishing fluid. (a) storage modulus, (b) normal stress.

Fig. 3
Fig. 3

Induced by magnetic field rheological properties of MR fluid.

Fig. 4
Fig. 4

Calculated shear stress and fluid velocity distribution across the gap formed by the moving wall and the surface of lens.

Fig. 5
Fig. 5

Comparison of calculated material removal rate profile with both experimental removal rate profile and pressure distribution.

Fig. 6
Fig. 6

Dependence of particle force (removal rate) on MR fluid yield stress.

Fig. 7
Fig. 7

Effect of magnetic field on the calculated particle force and the experimental removal rate.

Fig. 8
Fig. 8

Effect of gap geometry on the particle force and the removal rate. (a) Calculated removal rate profiles, (b) experimental polishing spot on a convex surface, (c) experimental polishing spot on a flat surface.

Fig. 9
Fig. 9

Effect of particle size on the removal rate. (a) Polishing spot taken with particles size of 1 μ m , (b) polishing spot taken with particles size of 4 μ m , (c) rheological measurements allow equalization of the yield stress.

Fig. 10
Fig. 10

Results of calculations of surface indentation by abrasive particles.

Fig. 11
Fig. 11

MR jet polishing spots and removal rate profiles. (a) MR jet spot, (b) water jet spot, (c) experimental MR jet removal rate profiles for two different jet velocities.

Fig. 12
Fig. 12

Experimental MR jet removal rates profiles for different fluids.

Fig. 13
Fig. 13

Calculated velocity profiles in the MR jet impingement zone.

Fig. 14
Fig. 14

Experimental and calculated MR jet removal rate profiles.

Fig. 15
Fig. 15

Results of calculations of surface indentation with MR jet. (a) contact tensile stress radial distribution, (b) penetration depth radial distribution.

Equations (8)

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τ 22 = K · ρ p · d p 2 · γ ˙ 2 ,
G p = K · π 4 · ρ p · d p 4 · γ ˙ 2 ,
μ = Min { A · μ μ + τ 0 γ ˙ .
σ p = ( 1 2 · ϑ M ) · G p 2 · π · r c 2 .
r c = [ ( 3 4 · G p · r a ) · k E ] 1 3 ,
k E = ( 1 ϑ M 2 E M + 1 ϑ a 2 E a ) ,
h t = ( 9 16 ) 1 3 · ( G p E r ) 2 3 · ( 1 r a ) 1 3 ,
M = μ 0 · κ a · H 2 η 0 · γ ˙

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