Matematical Model for Yarn Unwinding from Packages

Yarn unwinding from a package is important in many textile processes. The stability of the unwinding process has a direct influence on the efficiency of the process and on the quality of the end product. During the unwinding, the tension is oscillating. This is especially noticeable in over-end unwinding from a static package, where the yarn is being withdrawn with a high velocity in the direction of the package axis. The optimal form of the package allows an optimal shape of the yarn balloon and low and steady tension even at very high unwinding velocities.The purpose of this work is to write down the equations that describe the motion of yarn during unwinding and to construct a mathematical model whichwould permit to simulate the process of unwinding.