Study on Numerical Simulations of Yarn Unwinding from Packages

The system of coupled nonlinear differential equations that governs yarn motion in general is derived. Because the equations are expressed in a (non-uniformly) rotating observation frame, they can be used to describe yarn unwinding from stationary packages. We discuss the physical implications of virtual forces that occur in non-inertial frames, with a focus on a lesser-known force that only arises in non-uniformly rotating frames. When the unwinding point is near the package's edges, the quasi-stationary approximation is invalid since the angular velocity is changing with time, we show that this force should be considered. In this transient regime, when yarn movement becomes complex, the additional force has an effect on yarn dynamics, which can lead to yarn slippage and even breakage.