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TECHNICAL PAPERS

Stress Field in Finite Width Axisymmetric Wound Rolls

[+] Author and Article Information
Y. M. Lee, J. A. Wickert

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890

J. Appl. Mech 69(2), 130-138 (Jun 05, 2001) (9 pages) doi:10.1115/1.1429934 History: Received October 02, 2000; Revised June 05, 2001
Copyright © 2002 by ASME
Topics: Stress , Tension
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References

Altmann,  H. C., 1968, “Formulas for Computing the Stresses in Center-Wound Rolls,” J Tech. Assoc. Paper Pulp Indust., 51, pp. 176–179.
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Tramposch,  H., 1967, “Anisotropic Relaxation of Internal Forces in a Wound Reel of Magnetic Tape,” ASME J. Appl. Mech., 34, pp. 888–894.
Yagoda,  H. P., 1980, “Resolution of a Core Problem in Wound Rolls,” ASME J. Appl. Mech., 47, pp. 847–854.
Connolly, D., and Winarski, D. J., 1984, “Stress Analysis of Wound Magnetic Tape,” ASLE Tribology and Mechanics of Magnetic Storage Media, Special Publication 16, ASLE, pp. 172–182.
Pfeiffer,  J. D., 1979, “Prediction of Roll Defects from Roll Structure Formula,” J. Tech. Assoc. Paper Pulp Indust., 62, pp. 83–88.
Hakiel,  Z., 1987, “Nonlinear Model for Wound Roll Stresses,” J. Tech. Assoc. Paper Pulp Indust., 70, pp. 113–117.
Willett,  M. S., and Poesch,  W. L., 1988, “Determining the Stress Distributions in Wound Reels of Magnetic Tape Using a Nonlinear Finite-Difference Approach,” ASME J. Appl. Mech., 55, pp. 365–371.
Bourgin,  P., and Bouquerel,  F., 1993, “Winding Flexible Media: A Global Approach,” Adv. Inf. Storage Syst., 5, pp. 493–512.
Keshavan,  M. B., and Wickert,  J. A., 1997, “Air Entrainment During Steady State Web Winding,” ASME J. Appl. Mech., 64, pp. 916–922.
Good, J. K., Pfeiffer, J. D., and Giachetto, R. M., 1992, “Losses in Wound-on Tension in the Centerwinding of Wound Rolls,” Web Handling, ASME AMD-149, ASME, New York, pp. 1–12.
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Cole, A., and Hakiel, Z., 1992, “A Nonlinear Wound Roll Stress Model Accounting for Widthwise Web Thickness Nonuniformities,” Web Handling, ASME AMD-149, ASME, New York, pp. 13–24.
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Figures

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Schematic of a finite width wound roll comprising the inner core and wound web regions
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Collocated point radial compliance of (a) hollow cylindrical and (b) cup-shaped cores. The parameter values are as specified in Table 1 (plastic).
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Axisymmetric finite element model used to determine wound roll stresses σrθz, and σrz, shown illustratively for a hollow cylindrical core
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Comparison of the radial and circumferential stresses along centerline z=0 as determined through the present (–) and one-dimensional (-----; Hakiel 7) models. The parameter values are as specified in Table 1 (plastic, hollow core).
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Convergence of σr at points P1 and P2 in Fig. 3 for (a) plastic and (b) aluminum cores. The radial stress converges well along the roll’s centerline in each case, and at the edge of the core-web interface for the plastic material.
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Cross-web variation of σr along the core-web interface for hollow (a) plastic and (b) aluminum cores; NZ=80 (○○○○ ), and NZ=160 (–). The shaded zones in (b) denote regions where the stresses have not converged to three significant digits.
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Surface and contour representations of the radial and cross-web variation of σr;NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, hollow core).
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Surface and contour representations of the radial and cross-web variation of σθ;NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, hollow core).
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Radial and cross-web variations of (a) σz and (b) σrz;NZ=80 (surface) and NZ=160 (○○○○ ; first layer only). The parameter values are as specified in Table 1 (plastic, hollow core).
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Surface and contour representations of the radial and cross-web variation of σr;NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, cup-shaped core).
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Surface and contour representations of the radial and cross-web variation of σθ;NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, cup-shaped core).
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Variations of σr and σθ along the roll’s centerline with increasing numbers of web layers: 25 percent, 50 percent, and 100 percent of a full roll; NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, cup-shaped core).
Grahic Jump Location
Radial and cross-web variations of σr and σθ with increasing numbers of web layers: 25 percent, 50 percent, and 100 percent of a full roll; NR=100,NZ=80. The parameter values are as specified in Table 1 (plastic, cup-shaped core).

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