On the dynamic model of yarn with time-dependent tension.

In order to control yarn vibration and improve carpet quality, it is essential to research the fluctuation of yarn tension and its influences during tufting process. Assuming the polypropylene yarn has linear elasticity with a circular cross-section, we take the dynamic tension as the output and the friction acted on yarn by Jacquard roller as the input. At the moment of clutch operation and release, the tension fluctuation of polypropylene yarn during transmission from pulling roller to Jacquard roller was theoretically analyzed. A mathematical model describing yarn tension fluctuation was derived based on the moment of momentum theorem and mass conservation. The dynamic tension was obtained by applying Laplace’s transformation, providing the input-breaking moment as a step response. The result shows that tension fluctuation has an important influence on the carpet quality; therefore, it is necessary to carefully design the Jacquard roller and the control friction plate of clutch. Moreover, the effects of the yarn length between Jacquard rollers and pulling rollers on natural frequency and damping coefficient of yarn tension fluctuation were analyzed. [ABSTRACT FROM PUBLISHER]