An Integrated Approach to Dynamic Analysis of the Ring Spinning Process: Part II: With Air Drag

The dynamics of the ring spinning process has been re-analyzed as a coupled set of subproblems; the solutions are obtained numerically. The analyses in Part I and II of this series deal with the case of an uncontrolled balloon. In Part I the effects of air drag as well as gravitational and Coriolis accelerations are ignored. In Part II the effects of air drag are included. These analyses differ from the earlier ones in their choice of the relevant boundary conditions; the ones used here are presumed more realistic. Shapes of the spinning balloons are derived from the conditions of dynamic equilibrium of the yam, from pig-tail to wind-point, as well as that of the traveler. Non-dimen sionalization of the problem, is based on two physical lengths, which allows easy comparison of the balloon shapes for widely different dynamic conditions (including collapsed balloons) on the same plot. Tension distributions along the yarn path can be predicted. Similarly, mass of the traveler required for a specified yam tension at the pig-tail can be calculated. Air drag is found to be particularly useful in controlling the shape and size of the balloon. The numerical solution procedures developed can be used to explore the regions of instability of the balloon.