Abstract
This paper describes how balloon profiles and thread tensions may be calculated, given the requisite properties of the yarn and the spinning frame, by solving the equations of motion of the ballooning thread and by considering the forces acting at the cap edge or on the traveller. It is possible to include the effects of air drag and Coriolis forces by carrying out the calculations on a differential analyzer. The influence of top tension on the balloon profile is investigated in air and in vacuum, and, in particular, the characteristic licking of the cap is seen to be a consequence of air drag and low tension. It is associated with the tendency to form a double balloon at low tensions in vacuum.
Calculated profiles agree reasonably well with those observed for corresponding tensions at the top guide on a practical cap-spinning system. The balloon is shown to be determined by two parameters involving the various technical features such as yarn tension and denier and the dimensions of the spinning frame.
The forces at the cap edge and on the traveller are considered. As an example, the equation at the cap edge is combined with those of the ballooning thread to show how bobbin tension is de creased by increasing the bobbin radius and by decreasing the friction between the cap edge and the yarn. The calculations confirm that licking may arise when the bobbin is full even though it does not occur when it is empty. The bobbin tension calculated for a given bobbin radius, on the assumption of a perfectly smooth cap, agrees well with the observed tension in a practical system.
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