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.