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TECHNICAL PAPERS

Corrugation and Buckling Defects in Wound Rolls

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

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

J. Manuf. Sci. Eng 128(1), 56-64 (Jul 13, 2005) (9 pages) doi:10.1115/1.2113068 History: Received June 12, 2004; Revised July 13, 2005

Sheet metal, paper, and polymer webs are often stored and processed as large rolls comprising thousands of layers. Depending on the elastic properties of the web material, the roll’s dimensions, the type of core, and the winding tension, the stresses that develop within the roll can be sufficiently high to cause local or gross buckling defects to form. For instance, the cylindrical core onto which the web is wound can collapse, a failure mode that is termed “v-buckling.” In other cases, while the core might remain intact, a group of layers interior to the roll can wrinkle into a near-sinusoidal corrugated pattern around the circumference. This paper examines such “starring” defects analytically and experimentally. Measurements on a laboratory-scale web transport system are used to validate the model, and to identify conditions where no defects occur and the roll has acceptable quality, where starring patterns develop, and where v-buckling occurs. For particular core and web materials, the tension and diameter are the primary variables that influence the roll’s stability, and demarcations between stable and buckled configurations are identified in the tension-diameter design space. A model for the elastic stability of the roll-core system is developed, in which the corrugated layers are treated as multiple rings subjected to the resultant pressure generated by the roll’s internal stresses, and to the elastic support provided by the core and neighboring web layers. At the onset of corrugation, adjacent web layers couple through surface contact which is incorporated in the model as an elastic shear layer.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A sheet metal coil that exhibits starring defects (courtesy of Alcoa Corporation)

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Figure 2

A schematic of the wound roll’s geometry as incorporated in the axisymmetric stress model

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Figure 3

Parameter values used in case studies for sheet metal coils, and for model validation with the laboratory-scale test stand

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Figure 4

(a) Radial and (b) circumferential stresses within an aluminum coil. Dimensions and properties are as listed in Fig. 3.

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Figure 5

(a) Schematic of a wound roll where a group of corrugated layers develops between the core and the roll’s outermost layers. (b) The corrugated layers are supported elastically by the core and by the outermost layers.

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Figure 6

(a) Model for determining the core’s stiffness kc, and (b) an orthotropic finite element model of the roll’s remaining layers O for calculating the bulk web stiffness ko

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Figure 7

Kinematics of adjacent elements in their compressed S(1) and buckled S(2) states. The elastic shear layer is represented by a circumferential spring of stiffness ks,i.

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Figure 8

(a) Resultant radial stress Δσr, and (b) circumferential stress σθ within an aluminum coil. In (b), σθ is shown approximated (solid line) and predicted (dashed line) on the basis of the full stress model 1,2,3,4,5.

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Figure 9

(a) Transport system used in experiments on wound roll formation. (b) The take-up roll comprises a central aluminum hub, a foam base layer, a fiber core, and the web layers. (c) A typical three-ply spirally wound paper core used in the experiments.

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Figure 10

Wound roll with no visible defects for tc=0.5mm, T=0.8N, and NL=1200

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Figure 11

Wound roll with starring defects for tc=0.5mm, T=1.4N, and NL=1200. The wavelength of the corrugation pattern is approximately 1mm.

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Figure 12

Wound roll with a v-buckling defect for tc=0.5mm, T=1.5N, and NL=1200

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Figure 13

Presence of wound roll defects with respect to tension and number of layers for tc=0.3mm. The data points denote experimental values. The predicted boundaries for no defects, starring (dashed line), and v-buckling (solid line) are shown for comparison.

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Figure 14

Measured compressive stress-strain response over three successive trials

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Figure 15

Buckling pressure as a function of corrugation wavenumber for n=60. Parameters are listed in Fig. 3.

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Figure 16

Shear stress ks,iδi∕L between adjacent web layers (solid line) and threshold μσr for slippage (dashed line). Parameters are as listed in the final column of Fig. 3.

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Figure 17

Demarcations between no defects, starring (dashed line), and v-buckling (solid line) for aluminum sheet metal coils wound using (a) negative-gradient, (b) constant, and (c) positive-gradient tension profiles

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