Yarn twist in the ring-spinning balloon

A dynamical theory of twist insertion in ring-spun yarns that brings together the previous work of the authors and their colleagues on the stability of the ring-spinning balloon, and the recent work on yarn twisting dynamics by Miao & Chen (1993), in a single comprehensive theory is derived. It is shown that, to first order in small terms, the equations governing the yarn path and the equations governing the movement of twist along the yarn path are independent of each other. The general solution of the time-dependent twist flow equations is derived. These results are then used to determine formulae for the twist variation in the ring-spinning balloon and in a false twisting system. Some restrictions on the applicability of the theory are also noted.