Abstract

We investigate the effects of processing parameters on material removal for borosilicate glass. Data are collected on a magnetorheological finishing (MRF) spot taking machine (STM) with a standard aqueous magnetorheological (MR) fluid. Normal and shear forces are measured simultaneously, in situ, with a dynamic dual load cell. Shear stress is found to be independent of nanodiamond concentration, penetration depth, magnetic field strength, and the relative velocity between the part and the rotating MR fluid ribbon. Shear stress, determined primarily by the material mechanical properties, dominates removal in MRF. The addition of nanodiamond abrasives greatly enhances the material removal efficiency, with the removal rate saturating at a high abrasive concentration. The volumetric removal rate (VRR) increases with penetration depth but is insensitive to magnetic field strength. The VRR is strongly correlated with the relative velocity between the ribbon and the part, as expected by the Preston equation. A modified removal rate model for MRF offers a better estimation of MRF removal capability by including nanodiamond concentration and penetration depth.

© 2010 Optical Society of America

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References

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  1. A. B. Shorey, “Mechanisms of material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).
  2. J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D.dissertation (University of Rochester, 2007).
  3. 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).
    [CrossRef]
  4. J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
    [CrossRef]
  5. C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585-2594 (2009).
    [CrossRef] [PubMed]
  6. 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.
  7. Schott North American, Incorporated, 555 Taxter Road, Elmsford, New York 10523, USA.
  8. Zygo Mark IVxp interferometer, Zygo Corporation, Connecticut, USA. This instrument is a four-inch He-Ne Fizeau interferometer with a wavelength of 632.8 nm. Peak-to-valley surface flatness and ddp of the spot were 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.
  9. Zygo New View 5000 noncontacting white light interferometer, Zygo Corporation, Connecticut, USA. The surface roughness data were obtained under the following conditions: 20× Mirau; high frequency domain analysis (FDA) Res.; 20 μm bipolar scan length; Min/Mod: 5%, unfiltered.
  10. J. E. DeGroote, A. E. Marino, J. P. Wilson, A. L. Bishop, and S. D. Jacobs, “Removal rate model for magnetorheological finishing of glass,” Appl. Opt. 46, 7927-7941 (2007).
    [CrossRef] [PubMed]
  11. S. D. Jacobs, “Nanodiamonds enhance removal in magnetorheological finishing,” Finer Points 7, 47-54 (1995).
  12. X. Qu and C. F. J. Wu, “One-factor-at-a-time designs of resolution V,” J. Statist. Plann. Inference 131, 407-416 (2005).
    [CrossRef]
  13. C. Miao, “Frictional forces in material removal for glasses and ceramics using magnetorheological finishing,” Ph.D. dissertation (University of Rochester, 2010).
  14. C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).
  15. Anne Marino, “Magnetic fields in the STM and Q22-Y versus current through electromagnet,” Laboratory for Laser Energetics Magnetorheological Finishing Group internal memo, dated 12 November 2001. The Schinhaerl QED Q22-X MRF machine is similar to the Q22-Y. We use the magnetic field strength values obtained at various magnet currents on the Q22-Y to estimate the magnetic field strength for the Q22-X used in the work of Schinhaerl.
  16. A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
    [CrossRef]
  17. J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.
  18. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214-256 (1927).
  19. U. Mahajan, M. Bielmann, and M. Singh, “Abrasive effects in oxide chemical mechanical polishing,” in Proceedings of the Materials Research Society Symposium (Materials Research Society, 2000), pp. 27-32.
  20. A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finshing,” Appl. Opt. 40, 20-33 (2001).
    [CrossRef]

2009 (2)

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

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

2008 (1)

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).
[CrossRef]

2007 (1)

2005 (1)

X. Qu and C. F. J. Wu, “One-factor-at-a-time designs of resolution V,” J. Statist. Plann. Inference 131, 407-416 (2005).
[CrossRef]

2002 (1)

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

2001 (1)

1995 (1)

S. D. Jacobs, “Nanodiamonds enhance removal in magnetorheological finishing,” Finer Points 7, 47-54 (1995).

1927 (1)

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

Alcantara, M. R.

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

Bielmann, M.

U. Mahajan, M. Bielmann, and M. Singh, “Abrasive effects in oxide chemical mechanical polishing,” in Proceedings of the Materials Research Society Symposium (Materials Research Society, 2000), pp. 27-32.

Bishop, A. L.

Bombard, A. J. F.

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

DeGroote, J. E.

J. E. DeGroote, A. E. Marino, J. P. Wilson, A. L. Bishop, and S. D. Jacobs, “Removal rate model for magnetorheological finishing of glass,” Appl. Opt. 46, 7927-7941 (2007).
[CrossRef] [PubMed]

J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D.dissertation (University of Rochester, 2007).

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).
[CrossRef]

Jacobs, S. D.

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

J. E. DeGroote, A. E. Marino, J. P. Wilson, A. L. Bishop, and S. D. Jacobs, “Removal rate model for magnetorheological finishing of glass,” Appl. Opt. 46, 7927-7941 (2007).
[CrossRef] [PubMed]

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

S. D. Jacobs, “Nanodiamonds enhance removal in magnetorheological finishing,” Finer Points 7, 47-54 (1995).

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.

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Jang, K. I.

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Joekes, I.

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

Knobel, M.

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

Kordonski, W. I.

Lambropoulos, J. C.

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

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.

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Lee, S. J.

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Lee, S. O.

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Mahajan, U.

U. Mahajan, M. Bielmann, and M. Singh, “Abrasive effects in oxide chemical mechanical polishing,” in Proceedings of the Materials Research Society Symposium (Materials Research Society, 2000), pp. 27-32.

Marino, A. E.

Marino, Anne

Anne Marino, “Magnetic fields in the STM and Q22-Y versus current through electromagnet,” Laboratory for Laser Energetics Magnetorheological Finishing Group internal memo, dated 12 November 2001. The Schinhaerl QED Q22-X MRF machine is similar to the Q22-Y. We use the magnetic field strength values obtained at various magnet currents on the Q22-Y to estimate the magnetic field strength for the Q22-X used in the work of Schinhaerl.

Miao, C.

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

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

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Mici, J.

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

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Min, B. K.

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Preston, F. W.

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

Qu, X.

X. Qu and C. F. J. Wu, “One-factor-at-a-time designs of resolution V,” J. Statist. Plann. Inference 131, 407-416 (2005).
[CrossRef]

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).
[CrossRef]

Romanofsky, H.

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Rorrer, G.

J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.

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).
[CrossRef]

Seok, J.

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Shafrir, S. N.

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

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Shorey, A. B.

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

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

Singh, M.

U. Mahajan, M. Bielmann, and M. Singh, “Abrasive effects in oxide chemical mechanical polishing,” in Proceedings of the Materials Research Society Symposium (Materials Research Society, 2000), pp. 27-32.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Welty, J. R.

J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.

Wicks, C. E.

J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.

Wilson, J. P.

Wilson, R. E.

J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.

Wu, C. F. J.

X. Qu and C. F. J. Wu, “One-factor-at-a-time designs of resolution V,” J. Statist. Plann. Inference 131, 407-416 (2005).
[CrossRef]

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.

Appl. Opt. (3)

Finer Points (1)

S. D. Jacobs, “Nanodiamonds enhance removal in magnetorheological finishing,” Finer Points 7, 47-54 (1995).

J. Intell. Mater. Syst. Struct. (1)

A. J. F. Bombard, M. Knobel, M. R. Alcantara, and I. Joekes, “Evaluation of magnetorheological suspensions based on carbonyl iron powders,” J. Intell. Mater. Syst. Struct. 13, 471-478 (2002).
[CrossRef]

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).

J. Statist. Plann. Inference (1)

X. Qu and C. F. J. Wu, “One-factor-at-a-time designs of resolution V,” J. Statist. Plann. Inference 131, 407-416 (2005).
[CrossRef]

Proc. SPIE (1)

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).
[CrossRef]

Tribol. Trans. (1)

J. Seok, S. O. Lee, K. I. Jang, B. K. Min, and S. J. Lee, “Tribological properties of a magnetorheological (MR) fluid in a finishing process,” Tribol. Trans. 52, 460-469 (2009).
[CrossRef]

Other (11)

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

J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D.dissertation (University of Rochester, 2007).

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.

Schott North American, Incorporated, 555 Taxter Road, Elmsford, New York 10523, USA.

Zygo Mark IVxp interferometer, Zygo Corporation, Connecticut, USA. This instrument is a four-inch He-Ne Fizeau interferometer with a wavelength of 632.8 nm. Peak-to-valley surface flatness and ddp of the spot were 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 Corporation, Connecticut, USA. The surface roughness data were obtained under the following conditions: 20× Mirau; high frequency domain analysis (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, 2010).

C. Miao, S. N. Shafrir, H. Romanofsky, J. Mici, J. C. Lambropoulos, and S. D. Jacobs, “Frictional investigation for magnetorheological finishing (MRF) of optical ceramics and hard metals,” in Optical Fabrication and Testing (Optical Society of America, 2008).

Anne Marino, “Magnetic fields in the STM and Q22-Y versus current through electromagnet,” Laboratory for Laser Energetics Magnetorheological Finishing Group internal memo, dated 12 November 2001. The Schinhaerl QED Q22-X MRF machine is similar to the Q22-Y. We use the magnetic field strength values obtained at various magnet currents on the Q22-Y to estimate the magnetic field strength for the Q22-X used in the work of Schinhaerl.

U. Mahajan, M. Bielmann, and M. Singh, “Abrasive effects in oxide chemical mechanical polishing,” in Proceedings of the Materials Research Society Symposium (Materials Research Society, 2000), pp. 27-32.

J. R. Welty, C. E. Wicks, R. E. Wilson, and G. Rorrer, “Dynamic pressure of a viscous flow moving at the surface of a solid object increases with the fluid velocity,” in Fundamentals of Momentum, Heat, and Mass Transfer (Wiley, 2001), p. 150.

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Figures (11)

Fig. 1
Fig. 1

Views of the dual load cell setup for in situ measurement of both drag force and normal force (details are given in Refs. [5, 13]).

Fig. 2
Fig. 2

Drag force ( F d ) and normal force ( F n ) as a function of nanodiamond concentration for BK7 glass. STM process parameters are given in Table 1. Also plotted are drag force data (star) for BK7 from the work of DeGroote (Table C.12 in Ref. [2]).

Fig. 3
Fig. 3

Drag force ( F d ) and normal force ( F n ) as a function of penetration depth for BK7 glass. STM process parameters are given in Table 1. Also plotted are normal force data on BK7 glass from the Schinhaerl work (star) [3], where wheel speed was 425 rpm and magnet current was 10 A .

Fig. 4
Fig. 4

Drag force ( F d ) and normal force ( F n ) as a function of magnetic field strength (current in A) for BK7 glass. STM process parameters are given in Table 1. Also plotted are normal force data on BK7 glass from the Schinhaerl work (star) [3].

Fig. 5
Fig. 5

Drag force ( F d ) and normal force ( F n ) on BK7 glass as a function of the relative velocity between the part and the MR fluid ribbon. STM process parameters are given in Table 1.

Fig. 6
Fig. 6

Shear stress as a function of process parameters for BK7 glass: (a) nanodiamond concentration, (b) penetration depth, (c) magnetic field strength, and (d)  relative velocity. STM process parameters are given in Table 1.

Fig. 7
Fig. 7

VRR and PRR for BK7 glass as a function of nanodiamond concentration ( C nd ): (a)  VRR - C nd , (c)  PRR - C nd , (e)  VRR - C nd 1 / 3 , and (f)  PRR - C nd 1 / 3 . STM process parameters are given in Table 1. (b) and (d) also include the removal data for BK7 from the work of DeGroote [10]. [Note: The horizontal axes in (c) and (d) are scaled to the 1 / 3 power of those for (a) and (b).]

Fig. 8
Fig. 8

VRR and PRR for BK7 glass as a function of penetration depth: (a) VRR and (b) PRR. STM process parameters are given in Table 1.

Fig. 9
Fig. 9

VRR and PRR for BK7 glass as a function of magnetic field strength: (a) VRR and (b) PRR. STM process parameters are given in Table 1.

Fig. 10
Fig. 10

VRR and PRR for BK7 glass as a function of the relative velocity between the part and the wheel: (a) VRR and (b) PRR. STM process parameters are given in Table 1.

Fig. 11
Fig. 11

Experimental MRR data versus MRR model for BK7. The fitted curves are forced through the origin.

Tables (3)

Tables Icon

Table 1 Magnetorheological Fluid Condition and Spot Taking Machine Settings for All Experiments a

Tables Icon

Table 2 Experimental Data for Various Nanodiamond Concentrations and Spot Taking Machine Operating Settings

Tables Icon

Table 3 Magnetorheological Fluid Ribbon Width at Various Magnetic Field Strengths a

Equations (3)

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

MRR = C p , MRF ( τ , FOM ) · E K c H V 2 · τ · v .
VRR [ B nd · ϕ nd 1 / 3 C nd 1 / 3 + B CI · ϕ CI 4 / 3 C CI ] · E K c H v 2 · τ · D · v .
PRR [ B nd · ϕ nd 1 / 3 C nd 1 / 3 + B CI · ϕ CI 4 / 3 C CI ] · E K c H v 2 · τ · v .

Metrics