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TECHNICAL PAPERS

Analysis of Core Buckling Defects in Sheet Metal Coil Processing

[+] Author and Article Information
P. M. Lin, J. A. Wickert

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

J. Manuf. Sci. Eng 125(4), 771-777 (Nov 11, 2003) (7 pages) doi:10.1115/1.1619177 History: Received March 01, 2003; Revised August 01, 2003; Online November 11, 2003
Copyright © 2003 by ASME
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References

Yagoda,  H. P., 1980, “Resolution of a Core Problem in Wound Rolls,” ASME J. Appl. Mech., 47, pp. 847–854.
Hakiel,  Z., 1987, “Nonlinear Model for Wound Roll Stresses,” Journal of the Technical Association of Paper and Pulp Industry,70, pp. 113–117.
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.
Lee,  Y. M., and Wickert,  J. A., 2002, “Stress Field in Finite Width Axisymmetric Wound Rolls,” ASME J. Appl. Mech., 69, pp. 130–138.
Gerhardt,  T. D., 1990, “External Pressure Loading of Spiral Paper Tubes: Theory and Experiment,” ASME J. Eng. Mater. Technol., 112, pp. 144–150.
Seide,  P., 1962, “The Stability Under Axial Compression and Lateral Pressure of Circular-Cylindrical Shells With a Soft Elastic Core,” J. Aerosp. Sci., 29, pp. 851–862.
Kyriakides,  S., and Youn,  S. K., 1984, “On the Collapse of Circular Confined Rings Under External Pressure,” Int. J. Solids Struct., 20, pp. 699–713.
Bottega,  W. J., 1988, “On the Constrained Elastic Ring,” J. Eng. Math., 22, pp. 43–51.
Bottega,  W. J., 1989, “The Effect of Wall Compliance on the Behavior of a Confined Elastic Ring,” ASME J. Appl. Mech., 56, pp. 712–714.
Bucciarelli,  L. L., and Pian,  T. H. H., 1967, “Effect of Initial Imperfection on the Stability of a Ring Confined to an Imperfect Rigid Boundary,” ASME J. Appl. Mech., 34, pp. 979–984.
Chicurel,  R., 1968, “Shrink Buckling of Thin Circular Ring,” ASME J. Appl. Mech., 35, pp. 608–610.
Sun,  C., Shaw,  W. J. D., and Vinogradov,  A. M., 1995, “One-Way Buckling of Circular Rings Confined Within a Rigid Boundary,” ASME J. Pressure Vessel Technol., 117, pp. 162–169.
Lu,  H., Feng,  M., Lark,  R. J., and Williams,  F. W., 1999, “The Calculation of Critical Buckling Loads for Externally Constrained Structures,” Communications in Numerical Methods in Engineering,15, pp. 193–201.
Herrmann,  G., and Zagustin,  E. A., 1967, “Stability of an Elastic Ring in a Rigid Cavity,” ASME J. Appl. Mech., 34, pp. 263–270.
McGhie,  R. D., and Brush,  D. O., 1971, “Deformation of an Inertia-Loaded Thin Ring in a Rigid Cavity With Initial Clearance,” Int. J. Solids Struct., 7, pp. 1539–1553.
Brush, D. O., and Almroth, B. O., 1975, Buckling of Bars, Plates, and Shells, McGraw-Hill, New York.

Figures

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Photograph of a v-buckling defect in a sheet metal coil. A ring has been placed inside the core to prevent it from further buckling damage. Courtesy of Alcoa Corporation.
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Schematic of the coil model which includes the inner core and coil region
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Axisymmetric finite element model for analyzing stresses in a wound coil of sheet metal
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(a) Radial and (b) circumferential stresses as predicted by the two-dimensional coil stress model
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(a) Radial and (b) circumferential stress profiles taken along a centerline section of the sheet metal coil
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Buckling model in which the core is subjected to the uniform external pressure arising from the coil’s internal stresses, and an elastic foundation representing core-coil contact
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(a) Radial displacement profile at iteration i=3, and (b) foundation stiffness function which captures regions of positive displacement. Parameter values are as listed in Table 1.
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Convergence characteristics of numerical algorithm. (—) Solutions with relaxation (α=0.1, 0.2, and 0.3), and ([[dashed_line]]) solution without relaxation. Parameter values are listed in Table 1.
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Convergence of buckling pressure pcr at imax=15 for α=0.1
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Deformed (–) and undeformed ([[dashed_line]]) shapes of the core at each iteration i toward the converged v-buckled shape
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Load-deflection diagram for cores with various level of imperfection. (–) Solutions for a core with geometric imperfection amplitudes ε (0.5, 1, 1.5, and 2% of ri), and ([[dashed_line]]) critical pressure for the perfect core.
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Load-deflection profile of cores with varying imperfection wavenumber n for ε=1% of ri
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Maximum radial displacement δwmax for varying wavenumber n at p=80, 90, and 95% of pcr
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(a) Buckling pressure pcr and maximum radial stress σr,max for various process tensions Tw, and (b) factor of safety f against core buckling. ([[dashed_line]]) denotes pcr and f for ε=1, 2, and 5% of ri at n=ncr.
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(a) Buckling pressure pcr and maximum radial stress σr,max for various core inner radius ri, and (b) factor of safety f against core buckling. ([[dashed_line]]) denotes pcr and f for ε=1, 2, and 5% of ri at n=ncr.
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(a) Buckling pressure pcr and maximum radial stress σr,max for various core thickness tc, and (b) factor of safety f against core buckling. ([[dashed_line]]) denotes pcr and f for ε=1, 2, 5% of ri at n=ncr.

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