TRANSIENT SOLUTIONS OF THE RING-SPINNING BALLOON EQUATIONS

In the textile yam manufacturing process of ring spinning, a loop of r am rotates rapidly about a fixed axis. The surface generated by the re lating yam loop is called a balloon. The solutions of the time-indepen dent, nonlinear, yarn-balloon equations have been extensively investig ated for a reference frame that rotates with constant angular velocity and are termed quasi-stationary solutions. A linear perturbation stab ility analysis of these solutions has shown that while single-loop bal loons are stable, multiple-loop balloons are typically unstable. In th is 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 veloc ity impulse is studied The results of the linearized analysis are conf irmed: Single-loop balloons remain stable while multiple-loop balloons typically collapse within only a few spindle revolutions.