Optimum Winding Tension and Nip-Load into Wound Webs for Protecting Wrinkles and Slippage

Abstract

This paper describes the novel optimization method of wind-up tension to prevent wound roll defects, mainly star defect (wrinkling) and telescoping (slippage), based on the optimum design technique. Modified Hakiel model with air entrainment effects is applied to analyze in-roll stress distributions in the radial and tangential directions. In the present optimization method, the wind-up tension is gradually changed 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 a typical mathematical programming method, is used as the optimization technique. The optimized wind-up tensions are obtained for various winding conditions, and we confirmed theoretically and experimentally that the in-roll stress distributions are very much improved for preventing both wrinkling and slippage simultaneously by the optimization method being proposed.