Simulations of Yarn Unwinding from Packages

Yarn unwinding from stationary packages has an important role in many textile processes. In order to achieve high unwinding velocity that can lead to increased production rate, it is necessary to develop packages with a suitable geometry, dimensions, and winding type. The optimal design of the package leads to an optimal form of the balloon and low and uniform tension at high unwinding speed. In this work I will show a simple mathematical model which can be used for simulating the unwinding process. Using experimental values I will find a relation between the angular velocity of the yarn around the axis and the tension. This will allow me to calculate the oscillations of the tension in the yarn during the unwinding from packages of different geometries and with different winding angles. I will find an optimal design for a package of a new generation