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TECHNICAL PAPERS

Contribution of Support Means to Stresses Developed in Sheet Metal Coils

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

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

J. Manuf. Sci. Eng 126(3), 591-598 (Sep 07, 2004) (8 pages) doi:10.1115/1.1763185 History: Received January 01, 2003; Revised December 01, 2003; Online September 07, 2004
Copyright © 2004 by ASME
Topics: Sheet metal , Stress
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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,” Tribology and Mechanics of Magnetic Storage Media, ASLE Special Publication SP-16 , pp. 172–182.
Hakiel,  Z., 1987, “Nonlinear Model for Wound Roll Stresses,” Journal of the Technical Association of Paper and Pulp Industry,70, pp. 113–117.
Pfeiffer,  J. D., 1966, “Internal Pressures in a Wound Roll of Paper,” Journal of the Technical Association of the Paper and Pulp Industry,49, pp. 342–347.
Bourgin,  P., and Bouquerel,  F., 1993, “Winding Flexible Media: A Global Approach,” Adv. Inf. Storage Syst., 5, pp. 493–512.
Hakiel, Z., 1992, “On the Effect of Width Direction Thickness Variations in Wound Rolls,” Proceedings of the 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,” Proceedings of the 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 Publication AMD-149 , pp. 13–24.
Gerhardt,  T. D., 1990, “External Pressure Loading of Spiral Paper Tubes: Theory and Experiment,” ASME J. Eng. Mater. Technol., 112, pp. 144–150.
Lee,  Y. M., and Wickert,  J. A., 2002, “Stress Field in Finite Width Axisymmetric Wound Rolls,” ASME J. Appl. Mech., 69, pp. 130–138.
Zienkiewicz, O. C., and Taylor, R. L., 1989, The Finite Element Method, McGraw-Hill, New York.

Figures

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Schematic model for a coil comprising the central core and the wound sheet metal regions
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(a) Cross-sectional view of a sheet metal coil that is supported by a solid drive shaft during winding or unwinding (b) cross-web variation of the support’s collocated radial compliance along the core-web interface
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(a) Cross-sectional view of a sheet metal coil that is supported by drive chucks during winding or unwinding (b) cross-web variation of the support’s collocated radial compliance along the core-web interface
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(a) Cross-sectional view of a sheet metal coil that is supported only by its hollow core (b) cross-web variation of the support’s collocated radial compliance along the core-web interface
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Schematic cross-sectional view of the finite element model for analyzing stresses in a wound coil of sheet metal, illustratively having a hollow core and no drive shaft or chucks
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Radial stress field when the sheet metal coil and core are supported by a solid drive shaft. The inset depicts a contour representation of σr over the r−z plane.
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Circumferential stress field when the sheet metal coil and core are supported by a solid drive shaft. The inset depicts a contour representation of σθ over the r−z plane.
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Convergence characteristics of the coil’s centerline stress profiles with NZ=10, 20, 30, and 40 (light line type). The arrow denotes solutions with increasing NZ. For comparison, the solutions obtained using the approximate support stiffness in Eqs. (2122) are also shown (heavy line type).
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Comparison of the centerline (a) radial and (b) circumferential stresses predicted by the two-dimensional (–) and one-dimensional ([[dashed_line]]) models
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Radial stress field when the sheet metal coil and core are supported by drive chucks. The inset depicts a contour representation of σr over the r−z plane.
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Circumferential stress field when the sheet metal coil and core are supported by drive chucks. The inset depicts a contour representation of σθ over the r−z plane.
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Radial stress field when the sheet metal coil is supported only by the hollow core. The inset depicts a contour representation of σr over the r−z plane.
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Circumferential stress field when the sheet metal coil is supported only by the hollow core. The inset depicts a contour representation of σθ over the r−z plane.

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