An improved dynamic model and numerical simulation of yarn in the ring spinning system

The nonlinear dynamic behavior of ballooning yarn in the ring spinning system is investigated. An improved dynamic model of ballooning yarn with axial conveying speed is established. Based on Hamilton’s law of variation principle, the three-dimensional dynamic differential equations are derived. Then, the shooting method is employed to solve the two-point boundary value problem of ordinary differential equations. The numerical results of balloon profiles and distribution tension curves of ballooning yarns are discussed. The numerical results imply that with the increase of Ω, the yarn conveying speed increases, the minimum tension at the guide eye increases, and the helical loops of the balloon profile decrease. It is also found that as Ω increases, the spatial area of the guide eye tension [Formula: see text] that forms the dynamic balloon decreases. When the yarn conveying speed is medium or high, under different tensions at the guide eye, the yarn tensions along the height direction of the balloon change in the same trend, and the tensions of the ballooning yarn at the same height are very close. In addition, with the increase of Ω, the distribution tension of the ballooning yarn changes significantly under the same guide eye tension.