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TECHNICAL PAPERS

Width-Wise Variation of Magnetic Tape Pack Stresses

[+] 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(3), 358-369 (May 03, 2002) (12 pages) doi:10.1115/1.1460911 History: Received March 01, 2001; Revised November 22, 2001; Online May 03, 2002
Copyright © 2002 by ASME
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References

Altmann,  H. C., 1968, “Formulas for Computing the Stresses in Center-Wound Rolls,” Journal of the Technical Association of the Paper and Pulp Industry, 51, pp. 176–179.
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.
Tramposch,  H., 1965, “Relaxation of Internal Forces in a Wound Reel of Magnetic Tape,” ASME J. Appl. Mech., 32, pp. 865–873.
Tramposch,  H., 1967, “Anisotropic Relaxation of Internal Forces in a Wound Reel of Magnetic Tape,” ASME J. Appl. Mech., 34, pp. 888–894.
Heinrich,  J. C., Connolly,  D., and Bhushan,  B., 1986, “Axisymmetric, Finite Element Analysis of Stress Relaxation in Wound Magnetic Tapes,” ASLE Trans., 29, pp. 75–84.
Hakiel,  Z., 1987, “Nonlinear Model for Wound Roll Stresses,” Journal 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.
Zabaras,  N., Liu,  S., Koppuzha,  J., and Donaldson,  E., 1994, “A Hypoelastic Model for Computing the Stresses in Center-Wound Rolls of Magnetic Tape,” ASME J. Appl. Mech., 61, pp. 290–295.
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.
Benson,  R. C., 1995, “A Nonlinear Wound Roll Model Allowing for Large Deformation,” ASME J. Appl. Mech., 62, pp. 853–859.
Qualls,  W. R., and Good,  J. K., 1997, “An Orthotropic Viscoelastic Winding Model Including a Nonlinear Radial Stiffness,” ASME J. Appl. Mech., 64, pp. 201–208.
Lee, Y. M., and Wickert, J. A., 2002, “Stress Field in Finite Width Axisymmetric Wound Rolls,” ASME J. Appl. Mech., submitted for publication.
Bhushan, B., 1992, Mechanics and Reliability of Flexible Magnetic Media, Springer-Verlag, New York.
Hakiel, Z., 1992, “On the Effect of Width Direction Thickness Variations in Wound Rolls,” Second International Conference on Web Handling, Oklahoma State University, pp. 79–98.
Kedl, D. M., 1992, “Using a Two Dimensional Winding Model to Predict Wound Roll Stresses that Occur due to Circumferential Steps in Core Diameter or to Cross-Web Caliper Variation,” Second International Conference on Web Handling, Oklahoma State University, pp. 99–112.
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.
Greenwood,  J. A., and Williamson,  J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, A295, pp. 300–319.
Bogy,  D. B., 1970, “On the Problem of Edge-Bonded Elastic Quarter-Planes Loaded at the Boundary,” Int. J. Solids Struct., 6, pp. 1287–1313.

Figures

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Magnified view of a region in a magnetic tape pack exhibiting interlayer buckling
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(a) An axisymmetric hub that is also symmetric with respect to the pack’s midplane, and (b) model of the hub and tape layer substructures
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(a) An axisymmetric hub having no particular midplane symmetry, and (b) model of the hub and tape layer substructures
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Collocated point radial compliance of (a) the symmetric hub of Fig. 2, and (b) the asymmetric hub of Fig. 3
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Measured stress-strain response in compression of a magnetic tape stack over five loading cycles; sample dimensions: 102 mm×12.7 mm×12.7 mm
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Typical measured stress-strain response of a magnetic tape stack over a single load–unload cycle; sample dimensions: 102 mm×12.7 mm×12.7 mm
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(a) Variability of the measured bulk radial modulus for nine nominally identical media samples. (b) Measurements averaged over all samples (• • • •), and the least-squares fit to the modulus model (–); c=1.61×107 N/mm4.26 and m=3.26.
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Radial stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σr over the r−z plane; constant tension, NR=100,NZ=80.
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Circumferential stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σθ in the r−z plane; constant tension, NR=100,NZ=80
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Predicted change in tape width. The maximum value at the hub-tape interface is about 14 μm, or 1100 ppm.
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Radial stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σr in the r−z plane; linear cross-tape tension gradient, NR=100,NZ=80.
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Circumferential stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σθ in the r−z plane; linear cross-tape tension gradient, NR=100,NZ=80.
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Radial stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σr in the r−z plane; parabolic cross-tape tension gradient, NR=100,NZ=80.
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Circumferential stress field in the symmetric hub case study. The insets depict the hub’s cross section and a contour representation of σθ in the r−z plane; parabolic cross-tape tension gradient, NR=100,NZ=80.
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Radial stress distribution (a) in the down-tape direction at three positions across the width, and (b) across the tape’s width at the hub-tape interface; NZ=40 (○ ○ ○ ○) and NZ=80 (–). Shaded zones indicate where the solution did not converge to three significant figures.
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Radial stress field in the asymmetric hub case study. The insets depict the hub’s cross-section and a contour representation of σr in the r−z plane; constant tension, NR=100,NZ=80.
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Circumferential stress field in the asymmetric hub case study. The insets depict the hub’s cross section and a contour representation of σθ in the r−z plane; constant tension, NR=100,NZ=80.

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