Abstract
This paper describes the optimization method of winding tension for preventing the wound roll defects, mainly the star defects and slippage, based on the optimum design technique. In the analysis of in-roll stress distributions in the radial and circumferential directions, Hakiel's nonlinear model with and without air entrainment effects is basically applied. It is well known experimentally that a decrease in the winding tension has the effects of preventing the star defects due to negative circumferential stress under winding. So, in the present optimization method the winding tension is gradually decreased in the radial direction to minimize the averaged value of circumferential stresses, under the constraint of non-negative circumferential stresses. The successive quadratic programming (SQP), which is the typical mathematical programming method, is used as the optimization technique and the winding tension is expressed by the 3rd order spline curve of radial coordinate. The liner function with respect to radial coordinate is used as an original winding tension. The optimized winding tensions are obtained for various winding conditions, and it is confirmed that the in-roll stress distributions are very much improved by the present method.
