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

Abstract

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.

Intelligent Winding Machine of Plastic Films for Preventing Both Wrinkles and Slippages

“…Moreover, the nip-load for the taper tensions in Figure 9(b) is N = 70 (N/m) (an empirically determined fixed value). As can be seen from Figure 9(c), when using the non-optimized tension (dashed line), we can see that there is a region in which the tangential stress becomes negative (r/r c = 1.1 to 2.5), a region in which there is a high risk of wrinkle generation [1] [2].…”

Control of Meniscus Formation Using an Electrohydrodynamics Module in Roll-to-Roll Systems for the Stable Coating of Functional Layers

“…In the rewinding section, the web is wound in a tension profile that gradually decreases with time. The tension profile is defined as a taper tension profile, and the wound roll has an internal stress distribution in the circumferential and radial directions [ 32 , 33 , 34 ]. Consequently, the coated functional layer is subjected to a strong nipping pressure, owing to the shape of the wound roll, reducing the thickness.…”

“…In the rewinding section, the web is wound in a tension profile that gradually decreases with time. The tension profile is defined as a taper tension profile, and the wound roll has an internal stress distribution in the circumferential and radial directions [32][33][34].…”