Stanislav Praček

Shock in the Yarn during Unwinding from Packages

Tension in the yarn and its oscillations during the over-end unwinding of the yarn from stationary packages depend on the unwinding speed, the shape and the winding type of the package, the air drag coefficient, and also the coefficient of friction between the yarn and the package. The yarn does not leave the surface package immediately at the unwinding point. Instead, it first slides on the surface and then lifts off to form the balloon. The problem of simulating the unwinding process can be split into two smaller subproblems: the first task is to describe the motion of the yarn in the balloon; the second one is to solve the sliding motion. In spite of the seemingly complex form of the equations, they can be partially analytically solved as we show in the paper.

Fictitious forces in yarn during unwinding from packages

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.

The Effect of Winding Angle on Unwinding Yarn

In the production of fabric, the unwinding of thread occurs in the warping and weft insertion processes. In order to achieve low and constant tension of thread or yarn it is necessary to optimize the process of unwinding. Computer simulations are now in use for this purpose, so it is important to obtain a mathematical description of yarn motion. This article is devoted to the derivation of boundary conditions that considerably affect the form of the balloon. In this way, a mathematically well defined model of yarn unwinding will be obtained which could be solved by using the tools of numerical mathematics. The unwinding of yarn from an optimally designed package can be simulated and this knowledge can be used to find an optimal design of packages.

Balloon theory of yarn during unwinding from packages

Yarn unwinding from a package is a key problem in many textile processes, such as weft insertion and warping. Stability of the unwinding has a direct influence on the efficiency of the entire textile process and the quality of the final product. The quality of the yarn is numerically expressed mainly in terms of mechanical quantities. In the unwinding process, viscoelastic properties are the most important. They depend on how the yarn is stressed. The quality of the yarn that is being unwound should not be reduced, unless this reduction does not significantly lower the quality of the fabric. We strive to achieve as large warping and weaving speeds as possible; therefore, our aim is to improve the theory of cross-wound package unwinding and to find the necessary modifications of the yarn unwinding process. The goal of our contribution is to state the equations of motion that describe the unwinding yarn.

Yarn motion during unwinding from packages

We study the motion of yarn modelled as a one-dimensional inelastic string. In textile production, the yarn is being withdrawn from cross-wound packages in warping and weft insertion. During unwinding, there appear forces in the yarn that are approximately proportional to the square of the unwinding velocity. The yarn tension is not constant, but it oscillates within some interval. This is especially noticeable in over-end unwinding from a static cross-wound package. Even when the yarn is not strongly stressed, so that the tension never exceeds a few percent of the breaking strength, the yarn can still break sometimes. The production process requires as large warping and weaving speeds as possible; therefore, it is necessary to improve our understanding of the cross-wound package unwinding and to find the necessary modifications of the yarn unwinding process. In addition to empirical tests, it has proved useful to study yarn unwinding by mathematical modelling and computer simulations. We state the equations of motion that describe the yarn unwinding and develop a mathematical model that permits to simulate the process of unwinding.

Theory of Yarn Dynamics during Unwinding from Packages

We derive the system of coupled nonlinear differential equations that govern the motion of yarn in general. The equations are written in a (non-uniformly) rotating observation frame and are thus appropriate for description of over-end unwinding of yarn from stationary packages. We comment on physical significance of virtual forces that appear in a non-inertial frame and we devote particular attention to a lesser known 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.

Model for Yarn Transport Systems

In textile production the yarn is being withdrawn from cross-wound packages in warping and weft insertion. During unwinding there appear forces in the yarn that are approximately proportional to the square of the unwinding velocity. During unwind the yarn tension is not constant, but it oscillates within some interval. This is especially noticeable in over-end unwinding from a static cross wound packages, where the yarn is being withdrawn with a high velocity in the direction of the package axis. Even when the yarn is not strongly stressed, so that the tension does not exceed a few percent of the breaking strength, the yarn still can break sometimes. This is why we think that a cross-wound package is not an ideal form of a package and that such packages are not always made without flaws.

Mathematical Model for Yarn Unwinding Part Ι: Cylindrical Packages

Stability of the yarn unwinding directly affects the efficiency of the textile production process and the quality of the final product. A package with an optimal shape will result in an optimal shape of the balloon. In addition, the yarn tension will be small and steady even at high unwinding velocity. Computer modeling is a valuable tool in the search for the optimal package shape. We demonstrate a mathematical model for simulating the unwinding from cylindrical and conic packages. We show how the winding angle and the apex angle influence the angular velocity of the yarn during the unwinding. Since the centrifugal forces on the yarn in the balloon depend on the angular velocity, this velocity has a large influence on the tension that we wish to reduce.

Mathematical Model for Yarn Unwinding Part ΙΙ: Conic Packages

Mathematical modeling can be used to simulate the unwinding of yarn from packages of different shapes. This method can be applied to design packages that can sustain high unwinding velocities at low and steady tension in the yarn. In the case of conic packages the angular velocity of unwinding depends not only on the winding angle as is the case for cylindric packages, but also on the apex angle. We will show that the dimensionless angular velocity depends very little on the apex angle. The apex angle, however, also determines the effective radius of the package at the lift-off point, therefore the angular velocity can be proportionally higher. We will compare unwinding from a cylindrical and a conic package with equal smallest radius and show that unwinding from the conic package is faster due to higher average radius of the package at the lift-off point.