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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 972941, 6 pages
http://dx.doi.org/10.1155/2013/972941
Research Article

Shock in the Yarn during Unwinding from Packages

Department of Textiles, NTF, University of Ljubljana, Snežniška 5, 1000 Ljubljana, Slovenia

Received 14 December 2012; Revised 18 January 2013; Accepted 4 February 2013

Academic Editor: Lan Xu

Copyright © 2013 Stanislav Praček et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Tension in the yarn and its oscillations during the over-end unwinding of the yarn from stationary packages depend on the unwinding speed, the shape and the winding type of the package, the air drag coefficient, and also the coefficient of friction between the yarn and the package. The yarn does not leave the surface package immediately at the unwinding point. Instead, it first slides on the surface and then lifts off to form the balloon. The problem of simulating the unwinding process can be split into two smaller subproblems: the first task is to describe the motion of the yarn in the balloon; the second one is to solve the sliding motion. In spite of the seemingly complex form of the equations, they can be partially analytically solved as we show in the paper.