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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

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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