Optimization of wind-up tension of webs preventing wrinkles and slippage with experimental verification

Abstract

This paper describes the optimization method of wind-up tension to prevent wound roll defects, mainly star defect (wrinkling) and telescope (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. 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 tangential stresses under the constraint of nonnegative tangential stresses. At the same time, we consider the friction conditions to prevent the slippage between web layers due to a decrease of radial stresses and friction force. 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 linear 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 condition, and we confirmed theoretically and experimentally that the in-roll stress distributions were very much improved for preventing wrinkle and slippage by optimization method proposed.