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.
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June 1996
Technical Papers
Transient Solutions of the Ring-Spinning Balloon Equations
D. M. Stump,
D. M. Stump
Department of Civil Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia
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W. B. Fraser
W. B. Fraser
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia
Search for other works by this author on:
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. Jun 1996, 63(2): 523-528 (6 pages)
Published Online: June 1, 1996
Article history
Received:
June 6, 1994
Revised:
January 10, 1995
Online:
October 26, 2007
Citation
Stump, D. M., and Fraser, W. B. (June 1, 1996). "Transient Solutions of the Ring-Spinning Balloon Equations." ASME. J. Appl. Mech. June 1996; 63(2): 523–528. https://doi.org/10.1115/1.2788899
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