Theory of String Motion in the Textile Process of Yarn Unwinding

Abstract

Unwinding of yarn from stationary helically wound cylindrical packages is of fundamental importance in many textile processes. From the mathematical point of view, the unwinding yarn is a complex non-linear system with multiple solutions and bifurcation phenomena. The yarn is described as a flexible yet non-extensible uniform string moving through space under the action of the air drag and takes the shape of a "balloon". In this paper we derive a very general system of partial differential equations that describe the motion of this string during unwinding. We provide a physical interpretation of individual terms in the equations of motion with a particular emphasis on virtual forces which appear in the rotating coordinate system. We show that, in addition to the centrifugal and Coriolis forces, a third virtual force needs to be taken into account in rotating coordinate systems with time-varying angular velocity.

Non‐ionic surfactants for enhancing electrospinability and for the preparation of electrospun nanofibers

“…Electrospinning is a simple, versatile and powerful approach to producing nanofibers from various synthetic and natural polymers 1–5. Nanofibers sometimes behave extremely well in many respects due to nano‐effects,6–8 for example remarkable strength, high surface energy and surface reactivity, and excellent thermal and electric conductivity, and serve as promising materials in nanotechnology and a highly versatile platform for a broad range of applications in widely different areas such as photonic structures, microfluid channels (nanofluidics), catalysis, sensors, medicine, environmental engineering, defense and security, energy storage, invisibility devices (e.g.…”

Shock in the Yarn during Unwinding from Packages

“…Angle is the winding angle of the yarn on the package. The general equation of motion for the yarn was derived and justified in one of the previous works [10]:…”

Oscillations in the Yarn Tension During the Yarn Unwinding from Packages

“…In packages of general shape (cylindrical or conical) the relation between the angular velocity of the yarn during unwinding , the unwinding speed V and the package radius c at the lift-off point, where the yarn lifts off from the package surface, is (Praček, 2007):…”

“…This demonstrates that theoretical modelling of yarn unwinding process can be used to simulate and then optimize the parameters of the package construction and the unwinding process. In our previous work (Praček, 2007) we showed how such a mathematical model can be devised and we described some general characteristics of the unwinding process. In this work we review the results of our extensive simulations and show how the unwinding properties of a package can be improved by using alternating layers of parallely wound and cross wound layers.…”