The Effect of a Slub on the Stability of the Ring-spinning Balloon

In a recent paper, the authors have described a computational model for investigating the effect of a heavy slub passing through a ring-spinning balloon. In that paper, the additional mass in the slub was modeled by a gaussian-distribution function which allowed the total mass and length of the slub to be represented by two independent variables, Q and σ, respectively. Some limited results for a freely ballooning yarn were given. In this paper, the model of the previous paper is extended to allow for the effect of a control ring at the mid-balloon height, and a more extensive investigation of the solution space of the model is presented. It is shown that the effect of the control ring is greatly to extend the range of traveler-mass-parameter values over which the balloons are stable and, furthermore, the lower limit of these values is remarkably insensitive for a range of slubs with a total additional mass of up to 400%.