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Calendering Pseudoplastic and Viscoplastic Fluids With Slip at the Roll Surface

[+] Author and Article Information
E. Mitsoulis1

School of Mining Engineering and Metallurgy, National Technical University of Athens, Zografou 15780, Athens, Greecemitsouli@metal.ntua.gr

S. Sofou

School of Mining Engineering and Metallurgy, National Technical University of Athens, Zografou 15780, Athens, Greece

1

To whom correspondence should be addressed.

J. Appl. Mech 73(2), 291-299 (Jul 25, 2005) (9 pages) doi:10.1115/1.2083847 History: Received September 10, 2004; Revised July 25, 2005

The lubrication approximation theory (LAT) is used to provide numerical results for calendering a sheet from an infinite reservoir. The Herschel–Bulkley model of viscoplasticity is employed, which reduces with appropriate modifications to the Bingham, power-law, and Newtonian models. A dimensionless slip coefficient is introduced to account for the case of slip at the roll surfaces. The results give the final sheet thickness as a function of the dimensionless power-law index (in the case of pseudoplasticity), the Bingham number or the dimensionless yield stress calculated at the nip (in the case of viscoplasticity), and the dimensionless slip coefficient in both cases. Integrated quantities of engineering interest are also calculated. These include the maximum pressure, the roll-separating force, and the power input to the rolls. Decreasing the power-law index or increasing the dimensionless yield stress lead to excess sheet thickness over the thickness at the nip. All engineering quantities calculated in dimensionless form increase substantially with the departure from the Newtonian values. The presence of slip decreases pressure and the engineering quantities and increases the domain in all cases.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of the calendering process and definition of variables: (a) Feed from an infinite reservoir and (b) feed with a finite sheet

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Figure 2

Pressure distribution for power-law fluids with n=0.5, for various values of the slip coefficient, B

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Figure 3

Pressure distribution for power-law fluids with a slip coefficient B=0.01, for various values of the power-law index, n

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Figure 4

Pressure distribution for Bingham plastics with Bn=0.1, for various values of the slip coefficient, B

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Figure 5

Pressure distribution for Bingham plastics with a slip coefficient B=0.01, for various values of the Bingham number, Bn

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Figure 6

Dimensionless leave-off distance, λ∞, for pseudoplastic fluids as a function of the power-law index, n, for various values of the slip coefficient, B

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Figure 7

Dimensionless leave-off distance, λ∞, for viscoplastic fluids as a function of the dimensionless yield stress calculated at the nip,  ∣τy*∣x=0, for various values of the slip coefficient, B

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Figure 8

Operating variables for pseudoplastic fluids as a function of the power-law index, n, for various values of the slip coefficient, B: (a) maximum pressure, P, (b) force factor, F, and (c) power factor, E

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Figure 9

Operating variables for Bingham plastics as a function of the dimensionless yield stress calculated at the nip,  ∣τy*∣x=0, for various values of the slip coefficient B: (a) maximum pressure, P, (b) force factor, F, and (c) power factor, E

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Figure 10

Operating variables for Herschel–Bulkley fluids with n=0.5 as a function of the dimensionless yield stress calculated at the nip,  ∣τy*∣x=0, for various values of the slip coefficient, B: (a) maximum pressure, P, (b) force factor, F, and (c) power factor, E

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Figure 11

Yielded and unyielded regions in calendering according to LAT: (a) qualitatively predicted by Gaskell (1), (b) calculated for a Bingham plastic without slip (Bn=1 and B=0), (c) calculated for a Bingham plastic with slip (Bn=1 and B=0.1)

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Figure 12

Axial shear stress distributions at the roll surface for a Bingham plastic without slip (Bn=1 and B=0) and with slip (Bn=1 and B=0.1)

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Figure 13

Axial velocity distribution along the centerline for a Bingham plastic without slip (Bn=1 and B=0) and with slip (Bn=1 and B=0.1) in the region −λ<x′<+λ

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