Double-balloon dynamics model

In this paper a double-balloon dynamic model is presentedfor a whirling yarn of a ring spinning machine with balloon control ring,considering influences of running speed of the yarn, tangential directionair drag and gravitational force on the yarn as well as inertia of the yarn,normal direction air drag and tension of the yarn. Although dynamictreatment of the connecting condition of the yarn at the balloon controlring is very important both for analytical theory and practical applicationto control of ring spinning machine, there have never been derived dynamicanalytical theory considering many practical parameters. In the paper theauthors derived condition equations of the yarn contacting to the controlring, taking account of reaction force of the ring to the yarn andfrictional force between the ring and the yarn. Obtained equations canderive numerically the shape of whirling yarn (balloon shape, inclinationangle of the yarn to bobbin axis) and the yarn tension, if the certainvalues of the system parameter such as diameters of the traveler guide ringand balloon control ring, heights of yarn guide and control ring above thetraveler guide, air drag coefficients of the yarn, coefficient of frictionalforce of control ring to the yarn, revolution speed of the bobbin, etc. aregiven. Numerical calculations results proved validity of the theory. Thetheory derived is applicable to on-line and real time control of the yarntension of ring spinning machine.