Abstract
In the production of fabric, the unwinding of thread occurs in the warping and weft insertion processes. In order to achieve low and constant tension of thread or yarn it is necessary to optimize the process of unwinding. Computer simulations are now in use for this purpose, so it is important to obtain a mathematical description of yarn motion. This article is devoted to the derivation of boundary conditions that considerably affect the form of the balloon. In this way, a mathematically well defined model of yarn unwinding will be obtained which could be solved by using the tools of numerical mathematics. The unwinding of yarn from an optimally designed package can be simulated and this knowledge can be used to find an optimal design of packages.
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