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

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.