Numerical Analysis of Fiber Fleece Behavior in Roller Drafting in a Transient State

Abstract

Drafting is an important process to achieve parallel fibers along the bundle axis and to reduce the linear density of the bundle appropriate for the next process. However, it is very difficult to control the motion of each fiber or fiber groups completely with rollers. 1 Roller drafting causes a linear density irregularity in the fiber bundle, which provides many problems not only for the quality of the textile product, but also for the efficiency of the manufacturing process. After the first suggestion of regular variability of bundle thickness due to roller drafting [1], there have been Abstract Fiber bundle thickness irregularity from a roll draft mechanism was analyzed in the time domain on the basis of a theoretical model (Partial Differential Equation, PDE, system) for bundle flow. As the governing equations that consisted of continuity and motion equations turned out to be nonlinear, being coupled between variables, etc., a numerical method was established to solve the problem. In particular, the Forward-Time Central-Space (FTCS) difference formula with an explicit Euler scheme as the Finite Difference Method (FDM) was applied. Then the system of equations, which were in algebraic form, was solved according to given initial and boundary conditions in an iterative fashion. Results from this research confirmed that the theoretical response of the output linear density to the disturbance of drafting condition agreed very well with experiment. The transient state of the velocity profile faded out more quickly than that of the linear density profile. The response of the output bundle thickness to the step change perturbation depended on process conditions or material properties. With certain model parameters, the disturbed linear density of the output sliver converged to a fixed value or had an increasing variation magnitude. This indicated that the characteristics of the output bundle thickness could change according to the bundle properties or to the process conditions, which could induce unstable changes in thickness.

Analyzing roller drafting dynamics with stochastic perturbations: Simulation approach

“…15 The bundle flow model, described by the governing equations of equations 1-4, was discretized by the FTCS (Forward-Time Central-Space) method to achieve the numerical stability, while decreasing the calculation time. 16 For perturbations of the operating conditions, the boundary conditions were given as a function of time as follows: Figure 3 shows examples of the linear density behavior of the fiber bundle inside the drafting zone. In this case, the input linear density variation had an exponentially damped cosinusoidal autocorrelation.…”

“…The bundle flow model, described by the governing equations of equations 1–4, was discretized by the FTCS (Forward-Time Central-Space) method to achieve the numerical stability, while decreasing the calculation time. 16 For perturbations of the operating conditions, the boundary conditions were given as a function of time as follows: …”

Simulation of drawing process based on fiber arrangement in the sliver with straightness and separation degree

“…The dynamic behavior of the fiber bundle and sliver thickness variation in the drafting zone were also simulated by using some mathematical models. 2,9–14 Recently, the discrete-event model was applied into simulating the variation tendency of fiber number qualitatively and fiber distribution in the drafting zone. 15–17 A simple multi-field coupling model of fiber mechanics based on conserving momentum has been proposed that considers the distribution of the fiber speed point, slip rate and friction mechanics.…”

Modeling fiber arrangement and distribution during the roller drafting process

“…9 Huh and Kim [10][11][12] tried to formulate and simulate the dynamic behavior of a fiber bundle in the roller drafting and derive the attenuation curves of linear density. Kim et al [13][14][15][16] also analyzed the sliver thickness variation and fiber behavior theoretically. Later, a discrete-event simulation model of onedimensional fibrous material was applied in the simulation of the roll-drafting process elaborated by Cherkassky.…”