AN INTEGRATED APPROACH TO DYNAMIC ANALYSIS OF THE RING SPINNING PROCESS .4. INHERENT INSTABILITY OF THE FREE BALLOON

This paper will show that the theory of ring spinning developed by Batra et al. and subsequently by Fraser can be used to explain recent experimental results obtained at the SRRC. In particular, Fraser showed that the quasi-stationary, nonlinear equations of motion relevant to ring spinning, including the effect of centripetal acceleration and air drag force, developed earlier by several investigators exhibit a bifurcation phenomenon typical of many other nonlinear systems in mathematical physics. This investigation shows that the bifurcation analysis applied in a way that simulates formation of the bobbin, even a chase of the bobbin, reveals meta-stability in parametric space, which can be used to explain the instabilities in free (no control rings) balloon profiles observed experimentally.