On the theory of ring spinning

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Abstract
The mathematical model for balloon formation in the ring spinning process has been well established since the mid-1950s. The availability of present day computational power has made it possible to carry out a comprehensive analysis of the equations which it is hoped will give fresh insight into the physics of ring spinning. This paper is mainly concerned with free balloon spinning (without control rings). The relation between guide eye tension and traveller mass is explored in detail and an important transition region in this dependence is identified. The dependence of this transition region on bobbin radius, balloon height and air drag is also examined in detail. The practical application of the theory is discussed and theoretical minimum traveller mass against balloon height curves are produced. The results of a simulation of one traverse of the ring rail up and down the conical chase of a cop-structured bobbin is presented. Finally, the theory is modified to allow for the presence of a control ring and results that show the effect of the control ring on the guide eye tension against traveller mass dependence are presented.

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