Fictitious forces in yarn during unwinding from packages

Abstract

In this paper we discuss the general equation of motion for yarn in a rotating coordinate system. This equation is often used to describe the motion of yarn that is unwinding from packages. The rotating coordinate system is non-inertial and the equation of motion therefore contains fictitious forces. We comment on the physical significance of fictitious forces that appear in a non-inertial frame and we devote particular attention to a less known Euler force that only appears in non-uniformly rotating frames. We show that this force should be taken into account when the unwinding point is near the edges of the package, when the quasi-stationary approximation is not valid because the angular velocity is changing with time. The additional force has an influence on the yarn dynamics in this transient regime, where the movement of yarn becomes complex and can lead to yarn slipping and even breaking.

An analytical approach of filament bundle swinging dynamics, Part I: Modeling filament bundle by ANCF

“…In the process of textile production, a large range of yarn movement is a common phenomenon, for example, in the drafting, winding, unwinding, or warping processes. The quality of yarn is affected by many factors, such as high-frequency vibration, 5 friction forces, 6 and air resistance. 7 The dynamics simulation is an important means to understand yarn dynamic behavior.…”

“…In recent years, the dynamic behavior of yarn has been studied more and more deeply. Pracˇek and Pusˇnik 6 and Pracˇek et al 7 set up a yarn motion equation to analyze the stress of the yarn during the unwinding process of stress, taking into account the Coriolis force, the centripetal force, and the Euler force, but the influence of yarn cross-section diameter, gravity, and tangential air resistance were not considered. Hossain et al 10 analyzed the kinematic characteristics of the yarn in the spinning process.…”