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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

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

Grahic Jump Location
Figure 2

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

Grahic Jump Location
Figure 3

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

Grahic Jump Location
Figure 4

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Figure 10

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

Grahic Jump Location
Figure 12

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Figure 15

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

Grahic Jump Location
Figure 14

Measured compressive stress-strain response over three successive trials

Grahic Jump Location
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.

Grahic Jump Location
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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In