Dynamic tension analysis of yarn strand in tufting jacquard carpets

It is essential to research the forming of yarn tension and its effects during tufting process for controlling its vibration due to the control of jacquard roller and improving the carpet quality.Assuming that the yarn strand is linearly elastic with a circular cross section,taking the dynamic tension as an output and the braking moment applied on the jacquard roller as an input,at a moment of clutch operating and releasing,the dynamic tension fluctuations of yarn strand during transmitting between the jacquard roller and drag roller are theoretically analyzed.A mathematical model describing the yarn strand tension fluctuation is derived from the law of moment of momentum and yarn strand mass conservation law.The dynamic tension is obtained by applying Laplace′s transformation and provided that the input braking moment is a step response.The amplitude,frequency and damping coefficient of yarn tension fluctuation are obtained.The results show that the braking moment has an important influence on the yarn strand tension fluctuations,suggesting a necessity of precise design and control of jacquard roller and friction plate of clutch.At the same time,the effect of the length of yarn strand from jacquard rollers to drag rollers on natural frequency and damping coefficient of fluctuation of yarn strand tension are analyzed.