On the Transversal Vibration of Pile-Yarn with Time-Dependent Tension in Tufting Process
In this paper, the non-linear tranverse vibration of an axially moving pile-yarn with time-dependent tension are investigated. The pile-yarn material is modeled as Kelvin-Voigt element. A partial-differential equation governing the transverse vibration is derived from the Newton’s second law. The Galerkin method and the fourth order Runge-Kutta method are used to solve the governing non-linear differential equation. The effects of the transport speed, the tension perturbation amplitude and the damping coefficient on the dynamic behaviour of the system are numerically investigated.
X. P. Gao et al., "On the Transversal Vibration of Pile-Yarn with Time-Dependent Tension in Tufting Process", Applied Mechanics and Materials, Vols. 29-32, pp. 1517-1523, 2010