An Integrated Approach to Dynamic Analysis of the Ring Spinning Process: Part I: Without Air Drag and Coriolis Acceleration

We have re-analyzed the dynamics of the ring spinning process as a coupled set of subproblems and have obtained the solutions numerically. The analyses in Parts I and II of this series deal with the case of an uncontrolled balloon. In Part I we ignore the effects of air drag as well as gravitational and Coriolis accelerations. In Part II we include the effects of air drag. These analyses differ from the earlier ones in their choice of the relevant boundary conditions; those used here we presume are more realistic. The shapes of the spinning balloons are derived from the conditions of dynamic equi librium of the yam, from pigtail to wind-point, as well as that of the traveler. Non dimensionalization of the problem is based on two physical lengths, allowing 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, the mass of the traveler required for a specified yarn tension at the pigtail can be calculated. Air drag is particularly useful in controlling the shape and size of the balloon. The numerical solution procedures we have developed can be used to explore the regions of instability of the balloon.