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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Volume were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(5), 846-852; doi:10.3390/mca15050846

Numerical Simulations of Yarn Unwinding from Packages

Department of textile, NTF, University of Ljubljana, Snežniška 5, SI-1000 Ljubljana, Slovenija
Author to whom correspondence should be addressed.
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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We derive a system of coupled nonlinear differential equations that govern the motion of yarn in general. The equations are written in a (non-uniformly) rotating observation frame and are thus appropriate for description of over-end unwinding of yarn from stationary packages. We comment on physical significance of virtual forces that appear in a non-inertial frame and we devote particular attention to a lesser known force, that only appears in non-uniformly rotating frames. We show that this force should be taken into account when the unwinding point is near the edges of the package, and the quasi-stationary approximation is not valid because the angular velocity is changing with time. The additional force has an influence on the yarn dynamics in this transient regime where the movement of yarn becomes complex and can lead to yarn slipping and even breaking.
Keywords: yarn dynamics; eqations of motion; virtual forces; nunerical simulations yarn dynamics; eqations of motion; virtual forces; nunerical simulations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Praček, S.; Franci, S. Numerical Simulations of Yarn Unwinding from Packages. Math. Comput. Appl. 2010, 15, 846-852.

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