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

Abstract

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.

The energy consumption prediction of the direct cabling machine based on balloon theory

“…The above derivation formula refers to the derivation formula of the balloon section of yarn in the literature. 31 According to the parameters of the spindle which belongs to the direct cabling machine, the initial value of the mathematical model equation for the balloon motion is determined.…”

“…Ao et al 14 studied the twist and distribution of the wrapped yarn after optimizing the wrapped spinning of hollow ingot based on the balloon theory. Many scholars have improved the mathematical model of the balloon of ring spinning frame by improving the control algorithm 15,16 and considering the special factors. 17–20 It can be seen that the balloon theory is mature in the field of textile machinery, especially in the ring spinning frame, but there is a lack of balloon research on the direct cabling machine.(2) Research on energy consumption of direct cabling machine…”