Transient Solutions of the Ring-Spinning Balloon Equations

[+] Author and Article Information
D. M. Stump

Department of Civil Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia

W. B. Fraser

School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia

J. Appl. Mech 63(2), 523-528 (Jun 01, 1996) (6 pages) doi:10.1115/1.2788899 History: Received June 06, 1994; Revised January 10, 1995; Online October 26, 2007


In the textile yarn manufacturing process of ring spinning, a loop of yarn rotates rapidly about a fixed axis. The surface generated by the rotating yarn loop is called a balloon . The solutions of the time-independent, nonlinear, yarn-balloon equations have been extensively investigated for a reference frame that rotates with constant angular velocity and are termed quasi-stationary solutions. A linear perturbation stability analysis of these solutions has shown that while single-loop balloons are stable, multiple-loop balloons are typically unstable. In this paper a numerical method for the calculation of transient solutions of the nonlinear time-dependent PDEs is developed, and the stability of representative quasi-stationary balloons subjected to a model velocity impulse is studied. The results of the linearized analysis are confirmed: Single-loop balloons remain stable while multiple-loop balloons typically collapse within only a few spindle revolutions.

Copyright © 1996 by The American Society of Mechanical Engineers
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