Matematical Model for Yarn Unwinding from Packages

Stanislav Praček,Sluga Franci

doi:10.3390/mca15050853

Abstract

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 This is especially noticeable in over-end unwinding from a static package, where the yarn is being withdrawn with a high velocity in the direction of the package axis.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.

Highlights

Yarn unwinding is an essential step in many textile processes [1]
She modified Mack’s equations[3] and included terms that describe the Corolis force. She found solution for a balloon that forms during unwinding from stationary cylindrical package when quasistationary conditions apply
Cross-wound packages made using circumferential driving of the tube do not permit to achieve the unwinding speeds necessary on fast weaving loom, where the cross-wound package is used as a wefting package

Summary

INTRODUCTION

Yarn unwinding is an essential step in many textile processes [1]. The quality of the fabric that is produced directly depends on the regularity of the unwinding: the tension in the yarn should be low and constant. She modified Mack’s equations[3] and included terms that describe the Corolis force She found solution for a balloon that forms during unwinding from stationary cylindrical package when quasistationary conditions apply. Fraser et al have applied mathematical theory of perturbations to correctly eliminate the time dependance from equations of motion in stationary conditions[6]. They have show that the entire time dependance can be shifted to moving boundary conditions. In this manner the innitial-value problem of partial differential equations can be reduced to a boundary problem which is much easier to solve. We will show how a simple model function that describes the package can be used to estimate the unwinding properties of packages of different geometries and different winding types

THEORETICAL PART

SIMULATION MODEL

CONCLUSION