Mathematical Model for Yarn Unwinding Part Ι: Cylindrical Packages

Stability of the yarn unwinding directly affects the efficiency of the textile production process and the quality of the final product. A package with an optimal shape will result in an optimal shape of the balloon. In addition, the yarn tension will be small and steady even at high unwinding velocity. Computer modeling is a valuable tool in the search for the optimal package shape. We demonstrate a mathematical model for simulating the unwinding from cylindrical and conic packages. We show how the winding angle and the apex angle influence the angular velocity of the yarn during the unwinding. Since the centrifugal forces on the yarn in the balloon depend on the angular velocity, this velocity has a large influence on the tension that we wish to reduce.