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29—Migrating-filament theory: Apparent variation of twist with radial position
Abstract
The theory of the migrating-filament yarn developed in the previous paper is applied to the calculation of the form of the projection of the path of a filament onto a plane. In this projection (which is a sinusoidal wave of varying amplitude) the distance between successive turning-points does not correspond exactly to one half-turn of twist, and the amplitude does not correspond exactly to the true helix radius. There is thus an apparent variation of twist with apparent radial position, whose magnitude depends on the rate of migration. This effect has been observed by means of the tracer-filament technique. Its magnitude is in agreement with that calculated from the theory, using observed values of the migration parameter.
... Substituting Equation 11 into Equation 9 for expression G and X from Equation 6 and Equation 9, repectively, we have Equation 12 and Equation 13. ...
In this paper, the strain state of fibres located along the helical line in an extended yarn has been investigated. The slippage and mutual displacement of fibres relative to the yarn for analysis of the strain state of fibres in extended yarn are investigated. It is proposed for expression compressive transverse stress G, in our notation, to use the equation supposed in this work. The stress strain of fibres in extended yarn is examined and a comparison of the stresses between the cross-sectional and longitudinal directions is carried out. It is found that an increase in the twist angle leads to an increase in the compressive transverse stress of fibres in the centre of the yarn. It is also noticed that the axial stress strain depends on the twist angle of the yarn. The results obtained using this relationship are similar to those presented in previous studies. © 2015, Institute of Biopolymers and Chemical Fibres. All rights reserved.
... Riding (1964) observed fibre migration from two perpendicular directions along with the migration pitch of fibres in the yarn. Treloar and Riding (1965) developed the migration theory for filament yarn and showed that observation of pitch variation could be used as a measure of fibre migration. Hearle (1968) adopted the correlogram method to characterize fibre migration and established the theoretical basis for fibre migration behaviour (Hearle and Bose, 1965;Hearle, Gupta and Merchant, 1965). ...
The more the rabbit hairs there are on yarn's outer surface, the better its appearance. In this paper, by analyzing fibre frequency distribution of the microcross-section of five ratios of rabbit hair/cotton blended rotor-spun and ring-spun yarns, we calculate the rabbit hair coefficients of migration in these yarns. From the results, we conclude that more rabbit hairs in rotor-spun yarn are distributed at the outer surface than in ring-spun yarn. Rabbit hair/cotton blended rotor-spun yarn has a better appearance of rabbit hair than ring-spun yarn.
... The structural analysis of yarns, particularly , migration of fibers, has widely reported in the literature and continues to be of interest to many researchers. Merchant (1965), and Treloar and Riding (1965), to name a few, made important contribution on this controversial topic. Various methods have been proposed by researchers to investigate yarn inner structure (Basal, 2003; Morton, 1956; Schwarz, 1951 ). ...
The importance of fiber migration in spun yarns as a means of securing cohesion and strength has been emphasized in the literature. However, analyzing migration behavior of fibers is a time-consuming and tedious task. A three-stage hybrid model was developed to estimate yarn migratory properties based on some physical and mechanical properties of spun yarns. Achieving the objectives of this research, general physical, mechanical, and structural properties of spun yarns together with existing standards were thoroughly studied. At the first stage, using stepwise regression analysis, key variables were selected. At the second stage, data-set was clustered into subpopulations by means of K-means in order to decrease effects of noise, rebate complexity of the patterns, and develop a modular model. At the third stage, using adaptive neuro-fuzzy inference system, the target value was predicted. Finally, evaluation of the proposed model was carried out by applying it on the test set.
A study was conducted on the structure of a single cotton yarn using micro-computer tomography (micro-CT). This article describes two important parameters determining the unevenness of yarn structure, i.e. the migration of staple fibers and packing density of staple fibers in the yarn cross-section. Relationships were found between the variation of staple fiber migration characteristics and the relationship between yarn durability and twist. For the boundary value, the radius and range of migration are the highest, and the variation coefficient of the fiber migration range is the lowest. The number of fibers in the yarn cross-section decreases with twist. Above the boundary twist value, the number of fibers in the yarn cross-section stabilizes at the value corresponding to the number of fibers in the boundary twist.
A new method of modelling fibre migration in a staple-fibre yarn has been developed. The method uses a Markov process and allows all of the main features of yarn structure, such as irregularities of fibre disposition in a cross-section, unevenness, and hairiness, to be modelled. A novel experimental method is reported which allows the paths of individual fibres in yarn cross-sections to be defined in three-dimensional space. It has been shown that the fibre-migration can be considered as a Poisson's flow of events, and that fibre migration characteristics can be expressed in terms of a transition matrix. The method is able to describe a wide range of different yarn structures. The model would be improved by taking account of the fact that fibre migration between zones is not a memory-less process, but the problems associated with making this improvement have yet to be resolved.
This paper, which is a preliminary to a general investigation of the stress-strain and breakage behavior of staple yarns, deals with the stress analysis of a staple yarn under axial strain, based on an ideal yarn geometry that allows for fiber migration, assuming conical helix fiber paths. The position and dimensions of a yarn element based on this conical helix model are defined first, in relation to yarn dimensions, and the radial equilibrium conditions are obtained. The axial stress at any point on the yarn cross section under a given strain is then expressed by using the characteristic stress-strain curve of the fiber for both small and large strains. Thus the stress distribution over the cross section can also be determined.
This study describes a visualization and data analysis method for quantitatively analyzing the migration behavior of staple fiber yarns. The fiber migration of ring spun yarns with different levels of twist is measured and analyzed, and the results confirm the usefulness of the proposed method. The analysis shows reproducibility and generates new information on yarn structure. Furthermore, the data analysis processes are also able to be efficiently automated. The major migration frequency of the fibers along the yarn axis is obtained by frequency analysis. At the same time, the distributions of fiber position and orientation angle of the constituent individual fiber segments, according to the radial position of the yarn cross section, are evaluated. Finally, a parameter, the migration factor, to assess the migration effect as a whole is suggested. The experimental results show that migration reaches a saturation point as yarn twist increases.
An orientation density function of migrating fibers is newly defined to predict the mechanical behavior of yam. Applying the new function to yam with a helical structure produces the same results as the existing theories, and the function is applicable to even more general cases. Ideal migration behavior is mathematically analyzed by introducing two parameters that describe the migration behavior of fibers in the directions of the yarn axis and the yam's radial axis. The relative initial tensile modulus of the migrating yarn is calculated by applying two parameters to the orientation density function. The relative initial modulus depends strongly on both the migration period in the direction of the yarn axis and the degree of migration in the direction of the yam's radial axis.
Lyocell fibers have extraordinary textile properties, but they show a distinct tendency to fibrillate in the wet state. Treatments with crosslinking compounds used for textile finishing could be a practical means of controlling this problem. Some polyfunctional reactive dyestuffs also greatly increase wet abrasion resistance. Fiber tenacity decreases slightly compared to reactive compounds used for easy care finishing.
This paper, which is a preliminary to a general investigation of the stress-strain and breakage behavior of staple yarns, deals with the stress analysis of a staple yarn under axial strain, based on an ideal yarn geometry that allows for fiber migration, assuming conical helix fiber paths. The position and dimensions of a yarn element based on this conical helix model are defined first, in relation to yarn dimensions, and the radial equilibrium conditions are obtained. The axial stress at any point on the yam cross section under a given strain is then expressed by using the characteristic stress-strain curve of the fiber for both small and large strains. Thus the stress distribution over the cross section can also be determined.
Results of measurements of retraction as a function of twist are given for yarns produced by continuous twisting processes, as opposed to the twisting of a fixed length. These are compared with Tattersall's earlier work and also with the predictions of Treloar's theory. When continuous twisting methods are used, the agreement with theory is very good.The tracer filament technique of Morton and Yen is used to examine the path of a filament in the yarn. Measurements of filament angle by this method yield results in close agreement with theory. Visual evidence of filament migration is also provided.This technique also enables possible variations of twist and packing density across the section of the yarn to be examined. Preliminary results indicate that the twist increases towards the centre of the yarn.
The examination of yarns containing one coloured filament enables the behaviour of individual filaments within twisted continuous-filament yarns to be studied. By this means it is possible to correlate the radial position at any one point in a yarn with that at all subsequent points. This has been done for a series of viscose and nylon yams, and the eflfect of variables such as twisting tension, filament size, etc., has been examined. It is shown that the amount of ‘spinning twist’ originally present in the yam has the largest effect.