Mathematical model of multisegment balloons in ring spinning

High-speed ring spinning is limited by issues such as yarn quality and yarn breakage, and the spinning tension significantly affects yarn breakage and winding speed. The shape of the balloon in ring spinning is closely related to the distribution of tension within the yarn. In this study, a force analysis of the balloon yarn was conducted focusing on the balloon section during ring spinning, and a mathematical model of the balloon was established. The model included factors such as the centrifugal force, Coriolis force, and the air resistance of the yarn. Suitable parameters were then selected to extract the balloon trajectory curve and compare it with simulations to validate the model. The model was used to analyze the effects of balloon speed, yarn linear density, balloon bottom radius, balloon height, and yarn tension at the top of the balloon on the yarn tension at the bottom of the balloon, and the overall shape of the balloon. The balloon model established in this study could also be used for the study of balloon yarn tension in other processes. The effects of the main parameters influencing the yarn tension of the multi-balloon can provide a theoretical reference for enhancing the design of high-speed ring spinning.