Effect of accelerated point distribution on sliver irregularity. Part Ι: characterization of accelerated point distribution

Abstract

This paper introduces a new approach to characterize the accelerated point distribution in roller drafting. The approach uses 2-parameter Weibull distribution and Log-normal distribution to estimate the probability density function of the fiber accelerated point by including the influence of draft ratio and ratch, as well as fiber lengths. The coefficient of variation (CV) of accelerated points is then derived by employing conditional probability. The model was applied to a group of simulated data from literature and newly obtained experimental data of accelerated point distribution. The CV of the fiber accelerated points was compared with the CV from other published accelerated point distributions and the data derived from measurements of sliver irregularity. The model based on Log-normal distribution was proved to adequately characterize the probability density function of the fiber accelerated point. The accelerated point distribution would be a plausible variable to be utilized in the optimization of the draft settings.

Modeling fiber arrangement and distribution during the roller drafting process

“…The distributions for fiber accelerated points are shown in Figure 3. The ideal accelerated points of every fiber elaborated by Lin et al 7 are equal to G/ (1 + D), where G is the gauge length and D is the draft ratio. The Parabolic density function was adopted to estimate the accelerated positions of fibers in the drafting zone.…”

“…The Parabolic density function was adopted to estimate the accelerated positions of fibers in the drafting zone. 6 Weibull distribution and log-normal distribution were proposed by Lin et al 7,8 to describe the accelerated points of fibers during the drafting procedure. The simulated attenuation curves of linear density are illustrated in Figure 4.…”

“…Recently, Yan and Yu 6 described the accelerated-point distribution of floating fibers by a parabolic density. The log-normal distribution was given to fit the accelerated-point distribution of floating fibers during the roller drafting process by Lin et al 7,8 Furthermore, the drafting process has also been simulated by many mathematical and computer models. An assumed random sliver and fiber end distribution were applied in the computer simulation by Johnson.…”

Study on the testing of the accelerated point of the floating fiber in the roller drafting process with an improved method

“…Up to now, the parabolic density function, the triangular distribution, the normal distribution, the exponential function, and the lognormal function have been adopted to fit the accelerated point distribution in the drafting process. 12–16 However, these studies mainly focused on qualitative analysis, and simplified the influence of some factors. Thus, a certain difference between theoretical and practical results was presented.…”

A study on fiber motion in the drafting zone and hook removal

“…Some researchers are concerned about the effect of drawing settings on the reduction in sliver irregularity by means of theoretical derivation and experimental methods. 4,5 Some are focused on reflecting the dynamic movement of fibers in the drafting zone. Huh and Kim 6,7 simulated the velocity distribution and linear density distribution of fiber bundles based on mass balance and momentum balance.…”