Double-balloon dynamics model
双气圈动力学模型的建立与求解

In this paper a double-balloon dynamic model is presented for a whirling yarn of a ring spinning machine with balloon control ring,considering influences of running speed of the yarn,tangential direction air drag and gravitational force on the yarn as well as inertia of the yarn,normal direction air drag and tension of the yarn.Although dynamic treatment of the connecting condition of the yarn at the balloon control ring is very important both for analytical theory and practical application to control of ring spuming machine,there have never been derived dynamic analytical theory considering many practical parameters.In the paper the authors derived condition equations of the yarn contacting to the control ring,taking account of reaction force of the ring to the yarn and frictional force between the ring and the yarn.Obtained equations can derive numerically the shape of whirling yarn (balloon shape,inclination angle of the yarn to bobbin axis) and the yarn tension,if the certain values of the system parameter such as diameters of the traveler guide ring and balloon control ring,heights of yarn guide and control ring above the traveler guide,air drag coefficients of the yarn,coefficient of frictional force of control ring to the yarn,revolution speed of the bobbin,etc.are given.Numerical calculations results proved validity of the theory.The theory derived is applicable to on-line and real time control of the yarn tension of ring spinning machine.