Abstract

We use a recent experimental technique to measure in situ shear and normal stresses during magnetorheological finishing (MRF) of a borosilicate glass over a range of magnetic fields. At low fields shear stresses increase with magnetic field, but become field-independent at higher magnetic fields. Micromechanical models of formation of magnetic particle chains suggest a complex behavior of magnetorheological (MR) fluids that combines fluid- and solid-like responses. We discuss the hypothesis that, at higher fields, slip occurs between magnetic particle chains and the immersed glass part, while the normal stress is governed by the MRF ribbon elasticity.

© 2010 OSA

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  1. C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48(13), 2585–2594 (2009).
    [CrossRef] [PubMed]
  2. C. Miao, “Frictional forces in material removal for glasses and ceramics using magnetorheological finishing,” Ph.D dissertation (University of Rochester, Rochester, NY, 2010).
  3. C. Miao, J. C. Lambropoulos, and S. D. Jacobs, “Process parameter effects on material removal in magnetorheological finishing of borosilicate glass,” Appl. Opt. 49(10), 1951–1963 (2010).
    [CrossRef] [PubMed]
  4. M. Schinaerl, C. Vogt, A. Geiss, R. Stamp, P. Sperber, L. Smth, G. Smith, and R. Rascher, “Forces acting between polishing tool and workpiece surface in magnetorheological finishing,” Proc. SPIE 7060, 706006 (2008).
    [CrossRef]
  5. Zygo Mark IVxp interferometer, Zygo Corp., CT. This instrument is a four inch HeNe Fizeau interferometer with a wavelength of 632.8 nm. Peak-to-valley (pv) for surface flatness and depth of deepest penetration (ddp) of the spot was measured in microns. The spot is expected to be less than 0.2 μm deep for achieving a good measurement, and spotting time was adjusted to stay below this upper limit.
  6. Zygo New View 5000 noncontacting white light interferometer, Zygo Corp., CT. The surface roughness data were obtained under the following conditions: 20 × Mirau; high FDA Res.; 20 μm bipolar scan length; Min/Mod: 5%, unfiltered.
  7. J. E. De Groote, A. E. Marino, J. P. Wilson, A. L. Bishop, J. C. Lambropoulos, and S. D. Jacobs, “Removal rate model for magnetorheological finishing of glass,” Appl. Opt. 46(32), 7927–7941 (2007).
    [CrossRef]
  8. K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
    [CrossRef]
  9. S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
    [CrossRef]
  10. M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
    [CrossRef]
  11. J. M. Ginder and L. C. Davis, “Shear stresses in magnetorheological fluids: Role of magnetic saturation,” Appl. Phys. Lett. 65(26), 3410–3412 (1994).
    [CrossRef]

2010

2009

C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48(13), 2585–2594 (2009).
[CrossRef] [PubMed]

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
[CrossRef]

2008

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

2007

1996

M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
[CrossRef]

1994

J. M. Ginder and L. C. Davis, “Shear stresses in magnetorheological fluids: Role of magnetic saturation,” Appl. Phys. Lett. 65(26), 3410–3412 (1994).
[CrossRef]

Bishop, A. L.

Carlson, J. D.

M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
[CrossRef]

Davis, L. C.

J. M. Ginder and L. C. Davis, “Shear stresses in magnetorheological fluids: Role of magnetic saturation,” Appl. Phys. Lett. 65(26), 3410–3412 (1994).
[CrossRef]

De Groote, J. E.

Geiss, A.

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

Ginder, J. M.

J. M. Ginder and L. C. Davis, “Shear stresses in magnetorheological fluids: Role of magnetic saturation,” Appl. Phys. Lett. 65(26), 3410–3412 (1994).
[CrossRef]

Gorodkin, S.

S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
[CrossRef]

Jacobs, S. D.

James, R.

S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
[CrossRef]

Jang, K.-I.

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

Jolly, M. J.

M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
[CrossRef]

Kordonski, W.

S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
[CrossRef]

Lambropoulos, J. C.

Lee, S. J.

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

Marino, A. E.

Miao, C.

Mici, J.

Min, B.-K.

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

Munoz, B. C.

M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
[CrossRef]

Rascher, R.

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

Schinaerl, M.

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

Seok, J.

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

Shafrir, S. N.

Smith, G.

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

Smth, L.

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

Sperber, P.

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

Stamp, R.

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

Vogt, C.

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

Wilson, J. P.

Appl. Opt.

Appl. Phys. Lett.

J. M. Ginder and L. C. Davis, “Shear stresses in magnetorheological fluids: Role of magnetic saturation,” Appl. Phys. Lett. 65(26), 3410–3412 (1994).
[CrossRef]

J. Magn. Magn. Mater.

K.-I. Jang, J. Seok, B.-K. Min, and S. J. Lee, “Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method,” J. Magn. Magn. Mater. 321(9), 1167–1176 (2009).
[CrossRef]

Journal of Physics: Conference Series

S. Gorodkin, R. James, and W. Kordonski, “Magnetic properties of carbonyl iron particles in magnetorheological fluids, 11th International Conference on Electrorheological and magnetorheological Suspensions (ERMR08, Dresden, Germany),” Journal of Physics: Conference Series 149, 012051 (2009).
[CrossRef]

Proc. SPIE

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

Smart Mater. Struct.

M. J. Jolly, J. D. Carlson, and B. C. Munoz, “A model of the behaviour of magnetorheological materials,” Smart Mater. Struct. 5(5), 607–614 (1996).
[CrossRef]

Other

Zygo Mark IVxp interferometer, Zygo Corp., CT. This instrument is a four inch HeNe Fizeau interferometer with a wavelength of 632.8 nm. Peak-to-valley (pv) for surface flatness and depth of deepest penetration (ddp) of the spot was measured in microns. The spot is expected to be less than 0.2 μm deep for achieving a good measurement, and spotting time was adjusted to stay below this upper limit.

Zygo New View 5000 noncontacting white light interferometer, Zygo Corp., CT. The surface roughness data were obtained under the following conditions: 20 × Mirau; high FDA Res.; 20 μm bipolar scan length; Min/Mod: 5%, unfiltered.

C. Miao, “Frictional forces in material removal for glasses and ceramics using magnetorheological finishing,” Ph.D dissertation (University of Rochester, Rochester, NY, 2010).

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Figures (5)

Fig. 1
Fig. 1

Shear stress as a function of magnet current.

Fig. 2
Fig. 2

Pressure as a function of magnet current.

Fig. 3
Fig. 3

Peak removal rate (a) and volumetric removal rate (b) as a function of magnet current.

Fig. 4
Fig. 4

Calculated magnetic susceptibility χ = M/H for CI particles, based on the data by Jang et al. [8]

Fig. 5
Fig. 5

The correlation of (a) the fluid yield stress τY, (b) the normal stress σn, and (c) their ratio with applied magnetic field H for a CI volume fraction of ϕ = 0.45. The solid line denotes the predictions of the Jolly et al. model [10], the dashed lines those of Ginder and Davis [11], and the filled circles our measurements.

Tables (1)

Tables Icon

Table 1 Overview of experimental data. The magnet currents of 5-22.5 A correspond to magnetic induction of 0.98-3.08 kG, respectively, or magnetic fields in the range 78-245 kA/m in SI units

Equations (6)

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τ Y =   0. 1143 ϕ J p 2 /   [ μ 1 µ 0  h 3 ]
=   π   /   ( 6 ϕ )
J p =   [ ( 3 / 2 ) ( α α 3 ) +   ( 1 α 3 ) Js ]   /   [ +   ( 3 / 2 ) ϕ ( α α 3 ) ]
=  3 ϕ J p 2 /   [ µ 1 µ 0 h 3 ]
normal stress  σ n =  E  ( strain )   =   ( 0. 3 / 1 . 7 ) ϕ J p 2 /   [ µ 1 µ 0 h 3 ]
B ave = ϕ B

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