Balloon theory of yarn during unwinding from packages

Yarn unwinding from a package is a key problem in many textile processes, such as weft insertion and warping. Stability of the unwinding has a direct influence on the efficiency of the entire textile process and the quality of the final product. The quality of the yarn is numerically expressed mainly in terms of mechanical quantities. In the unwinding process, viscoelastic properties are the most important. They depend on how the yarn is stressed. The quality of the yarn that is being unwound should not be reduced, unless this reduction does not significantly lower the quality of the fabric. We strive to achieve as large warping and weaving speeds as possible; therefore, our aim is to improve the theory of cross-wound package unwinding and to find the necessary modifications of the yarn unwinding process. The goal of our contribution is to state the equations of motion that describe the unwinding yarn.