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Technical Briefs

Optimization of Wind-Up Tension of Webs Preventing Wrinkles and Slippage

[+] Author and Article Information
Hiromu Hashimoto

 Tokai University, 1117 Kitakaname, Hiratsuka-shi, Kanagawa-ken 259-1292, Japanhiromu@keyaki.cc.u-tokai.ac.jp

J. Manuf. Sci. Eng 131(5), 054501 (Sep 23, 2009) (4 pages) doi:10.1115/1.4000096 History: Received April 09, 2008; Revised August 17, 2009; Published September 23, 2009

This paper describes the optimization method of wind-up tension to prevent wound roll defects, mainly star defects and slippage, based on the optimum design technique. Hakiel’s nonlinear model with air entrainment effects is applied to analyze in-roll stress distributions in the radial and tangential directions (1987, “Nonlinear Model for Wound Roll Stresses  ,” Tappi J., 70(5), pp. 113–117). It is well known experimentally that a decrease in the wind-up tension prevents star defects due to negative tangential stress under winding. Thus, in the present optimization method, wind-up tension is gradually decreased in the radial direction to minimize the averaged value of tangential stresses under the constraint of non-negative tangential stresses. Furthermore, the relation of the slippage between wound film layers and in-roll stress of a roll is considered. Successive quadratic programming, which is the typical mathematical programming method, is used as the optimization technique. Wind-up tension is expressed by the third-order spline curve of a radial coordinate. The liner function with respect to the radial coordinate is used as the original wind-up tension. The optimized wind-up tensions are obtained for various winding conditions, and we confirmed that the in-roll stress distributions were very much improved for preventing wrinkles and slippage by the optimization method proposed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Typical defect in wound roll: (a) star defect and (b) telescoping

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Figure 2

In-roll stresses

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Figure 3

Center winding with a nip

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Figure 4

Method of changing wind-up tension

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Figure 5

In-roll stress distribution for center winding with a nip

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Figure 6

Friction characteristics in wound roll for center winding with a nip

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