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An Application of Queuing Theory to Modeling of Melange Yarns Part I: A Queuing Model of Melange Yarn Structure
Abstract
A queuing model of staple fiber yarn is presented that enables the modeling and a better understanding of fiber migration in a yarn. The model provides a fine yarn structure where the migrational behavior of fibers is associated with the behavior of customers traveling across an open network of queuing systems to get services. Based on this analogy, the underlying mathematical foundation of the queuing theory is used for the modeling of yarn structure and properties. The model uses yarn technical specifications including yarn linear density and twist level, fiber linear density and length distribution, together with specific parameters such as fiber packing density distribution and migration probabilities. The model can be used for modeling a wide range of structurally different yarns; examples include marl, mottle and melange yarns, yarns with different levels of hairiness, and yarns produced by various spinning systems. The model can be used for 3D simulation of yarns in computer-aided design systems for textile design and for the prediction of mechanical properties of yarns.
... This new concept was further advanced in a recent publication (Siewe et al., 2009) where queuing theory is used for a detailed analysis of the behaviour of all fibres in the yarn and fibre distribution over the yarn cross-section. ...
... In the queuing model of a staple yarn structure (Siewe et al., 2009), each virtual location is represented by a queuing system and each fibre is modelled by a customer. The migration of a fibre from one virtual location to a neighbouring virtual location is associated to the movement of a customer from one queuing system to another as discussed in the following section. ...
... The yarn structure formed in this way is considered to be continuous so that there are infinitely many fibres involved. Using these assumptions, the staple fibre yarn structure was modelled as a Jackson open network of queuing systems where each queuing system represents one virtual location (Siewe et al., 2009). Figure 9 shows a simplified model for a yarn with three ring zones. ...
A project aimed at the 3D simulation of textile yarns from technical specifications was begun in 1993 and attracted support from both industry and research councils to enable the formation of a multi-national team of researchers to come together in the UK. Considerable progress has been made particularly in the simulation of knitting yarn and plain knit fabric. In recent times the team has tackled the problem of simulating mixture coloured yarns sometimes called melange. This has necessitated a more complicated model of yarn structure based on queuing theory which is outlined at the end of the paper. References are provided for readers who wish to learn more of the various theories and models that have been used throughout the course of this project.
... The state of disorder of fibers or filaments fragments has always been one of the basic questions when talking about yarn structure. Many researches related to fiber distribution or fiber tracer technique have been carried out; for instance, (Francois, Sergei, Thomas, & Geoffrey, 2009;Morton & Yen, 1952;Zhang, Chen, & Wan, 2003;Zou et al., 2009). In fact, entropy itself presents the disorder of a system all the time. ...
As a function of state, the entropy of yarns characterizes the possible manners in which fiber or filament structure change in different directions. It affects every parameter of the structure and properties of yarns. Defined as the ratio of the volume of inner space to the whole body, the bulk of yarns could be calculated when the factors, such as linear density and diameter of yarns, were measured. Theoretical derivations showed that an exponential relationship exists between entropy and bulk of yarns. Further experiments proved that compared with classical yarns, textured yarns possessed higher bulk and entropy. In case of bundle filaments, the bulk and relative entropy were far lower than that of other linear fiber assemblies, approximately within a narrow scope of around 24% of bulk and 0.27 of relative entropy.
... For the former [13][14][15], although it is simple and straight-forward, the measurement accuracy was largely affected by fibres laying on the yarn surface and greater differences in the helix angle were presented in the inside and outside edges of a flexible yarn. For the latter, the tracer fibre technology [7,[16][17][18] is generally used to capture actual images of fibre configuration in a yarn and then processed with the fast Fourier transform for obtaining the main frequency of yarn twist. This method provides more accurate results of yarn actual twist level [17]. ...
This study presents dynamic measurement and theoretical modelling of flexible yarn dynamics on a moving cylindrical solid. The high speed camera and strain gauge sensor systems were developed and calibrated for the instant measurements of flexible yarn twist and tension on the moving cylindrical solid. The measured values were then used as boundary conditions for a new proposed theoretical model to predict yarn twist and tension distributions on the moving cylindrical solid. Three cases were proposed to evaluate the developed theoretical model and the results indicate that the twist and tension distributions can be theoretically predicted with good accuracy and reliability and the simulated yarn paths generally fit well with observed yarn paths with higher correlation coefficients. Furthermore, with the developed theoretical model, influences of various system parameters were numerically examined and discussed in detail.
Pullout theory is very important in improving efficiency, quality, and production costs. Because production efficiency is too low for mechanical drafting equipment, a simple multi-field coupling model of fiber mechanics based on conserving momentum is proposed that considers the distribution of the fiber speed point, slip rate, and friction mechanics. When the roller draft multiple is increased, the position near the rear roller clamp mouth in the draft area will show a sharp decrease of fiber, which is caused by the rapid movement of the front fiber to drive the floating fiber movement, and it is also the existence of the fiber change point. When the roller spacing increases, the draft efficiency decreases, although the pressure applied by the roller to the fibrous strip has a weak effect on the draft efficiency. This research increases our understanding of drawing and provides theoretical support for the design of a new type of drawing.
In order to create realistic loop primitives suitable for the fast computer-aided design (CAD) of the flat knitted fabric, we have a research on the geometric model of the loop as well as the variation of the loop surface. Establish the texture variation model based on the changing process from the normal yarn to loop that provides the realistic texture of the simulative loop. Then optimize the simulative loop based on illumination variation. This paper develops the computer program with the optimization algorithm and achieves the loop simulation of different yarns to verify the feasibility of the proposed algorithm. Our work provides a fast CAD of the flat knitted fabric with loop simulation, and it is not only more realistic but also material adjustable. Meanwhile it also provides theoretical value for the flat knitted fabric computer simulation.
This chapter provides an overview of various methods used for modelling the geometry, structure, and properties of a wide range of textile materials. Methods of experimental design and data analysis leading to regression models are briefly discussed. Models of internal geometry and structural models based on knot theory are described. Models of mechanical and physical properties are considered next, highlighting the link between structure and properties. Examples of continuous and discrete models of textile processes are presented. This chapter concludes with discussion of linear and non-linear optimization methods in application to the performance characteristics of materials and processes.
This chapter presents an overview of mathematical models generated over the past 60 years for the description of the geometry, structure and properties of fibres and fibre assemblies. General fibre functions in various fibre-based products are briefly introduced and linked to the relevant fibre properties. This chapter then proceeds to discuss models that are currently employed in investigations of the structure-property relationship of natural and synthetic fibres at the nano-level including methods of molecular modelling based on quantum mechanics and molecular mechanics. Models of fibre geometry, including the distribution of fibre length and diameter (fineness), fibre cross-section and fibre spatial shape due to crimp are discussed. The linear elastic, linear viscoelastic and non-linear viscoelastic models that characterise the mechanical behaviour of fibres are considered in detail. Factors affecting friction in textiles and models of fibre friction are presented. Structural and micromechanical models of fibre assemblies based on a fibrous unit cell are discussed.
This paper presents a new approach to predict the tensile strength of one-dimensional fibrous materials. The approach combines discrete-event simulation of the fiber flow with agent-based modelling of the fiber slippage. The ability of the elaborated model of the fiber flow to track every fiber separately enables the calculation and analysis of all contacts and forces between the fibers, and the prediction of the material's tensile strength. The model is based on the phenomenon of the strength associated with the fiber slippage effect. Algorithms for modeling the cross-section and the segment tensile strength are developed. Implementation of this algorithm and the study of the behavior of the elaborated model by varying the basic parameters will be described in the Part 2 of the article.
Realistic visualization of cloth has many applications in computer graphics. An ongoing research problem is how to best represent and capture cloth models, specifically when considering computer aided design of cloth. Previous methods produce highly realistic images, however, they are either difficult to edit or require the measurement of large databases to capture all variations of a cloth sample. We propose a pipeline to reverse engineer cloth and estimate a parametrized cloth model from a single image. We introduce a geometric yarn model, integrating state-of-the-art textile research. We present an automatic analysis approach to estimate yarn paths, yarn widths, their variation and a weave pattern. Several examples demonstrate that we are able to model the appearance of the original cloth sample. Properties derived from the input image give a physically plausible basis that is fully editable using a few intuitive parameters.
The first step in the evaluation of physical phenomena in yarns consists of creating a suitable representation of the yarn. Here, we focus on the creation of a realistic grid for the yarn cross-section, which is suitable for mass and heat transfer models. We extend and adapt the virtual location method (VLM) which allows the quick creation of a range of 2D yarn–fiber layouts. We overcome two of its main disadvantages: the presence of too much regularity, and the inability to produce yarn–fiber layouts when blends of fibers with different sizes are present. Our method is based on the standard ring configuration VLM, creating two sets of virtual locations per fiber type, which causes some overlap of the fibers. The overlap is removed with an iteration scheme based on induced movement. The final result is a realistic 2D cross-section of a yarn. A reference implementation is available, and it is shown how the layout can be used to create a grid.
A queuing model of staple yarn structure was presented in Part I of this work, where the migration behaviours of fibres were simulated by the movement of customers in a Markovian network of queuing systems. Part II of the series proposes (i) a multi-dimensional minimization method for estimating the migration probabilities of fibres based on the analysis of the distribution of number of fibres in yarn cross-sections; (ii) a yarn structure simulation algorithm which uses the migration probabilities of fibres, yarn technical specifications (e.g. linear density and twist) and colour composition to produce a realistic three-dimensional image of a melange yarn. The result is a high quality three-dimensional image of a melange yarn showing its fibrous structure as well as the formation of hairiness. Due to the generic nature of the model and the simulation algorithm, this approach can be applied to a wide range of yarns including ring-spun or open-end spun yarns of solid shade or produced from melange blends. Further improvements to the proposed model are discussed including the application of inhomogeneous Poisson process and the analysis of energy relationships which govern the migration behaviour of fibres.
The mechanical and physical properties of spun yarns and fabrics depend not only on mechanical properties of the fibers making up the yarn, but also geometrical arrangement of fibers, known as fiber migration. The main aim of this research is to introduce a new approach to predict migratory behavior 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. A hybrid intelligent model was developed based on a Genetic Fuzzy System (GFS) to model the relationships between migration of fibers in spun yarns and some physical and mechanical properties of spun yarns. Results indicated that the developed fuzzy expert system can be used as an intelligent simulator to predict yarn migratory parameters.
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.
This paper presents a continuous observation and measurement system to acquire spatial distributions of multiple yarn structural parameters and a three-dimensional configuration of fibres in yarns. The system comprises an automatic yarn transmission unit, an optical observation device, image acquisition, analysis and display units. Spatial orientation of fibre, distribution of yarn twist and diameters, fibre radial position and other migration characteristics are, for the first time, determined in a simultaneous fashion. Extensive experiments were carried out to evaluate the system. In addition to the studies on different yarn types, further investigations were made on two types of yarns including the twist in short yarn segments, fibre orientation angle, radial position, migration frequency and amplitude as well the three-dimensional configurations of fibres. The experimental results indicate that the present system has good reliability and repeatability. The measured values are in good agreement with those obtained by other conventional techniques for single-parameter measurements.
Queueing network models have proved to be cost effectwe tools for analyzing modern computer systems. This tutorial paper presents the basic results using the operational approach, a framework which allows the analyst to test whether each assumption is met in a given system. The early sections describe the nature of queueing network models and their apphcations for calculating and predicting performance quantitms The basic performance quantities--such as utilizations, mean queue lengths, and mean response tunes--are defined, and operatmnal relationships among them are derwed Following this, the concept of job flow balance is introduced and used to study asymptotic throughputs and response tunes. The concepts of state transition balance, one-step behavior, and homogeneity are then used to relate the proportions of time that each system state is occupied to the parameters of job demand and to dewce charactenstms Efficmnt methods for computing basic performance quantities are also described. Finally the concept of decomposition is used to stmphfy analyses by replacing subsystems with equivalent devices. All concepts are illustrated liberally with examples
The joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers is derived. The equilibrium state probabilities have the general form P(S) equals Cd(S) f//1(x//1)f//2(x//2). . . f//N(x//N), where S is the state of the system, x//i is the configuration of customers at the ith service center, d(S) is a function of the state of the model, f//i is a function that depends on the type of the ith service center, and C is a normalizing constant. It is assumed that the equilibrium probabilities exist and are unique. Four types of service centers to model central processors, data channels, terminals, and routing delays are considered.
This article reports an attempt to develop a general constitutive theory governing the mechanical behavior of twisted short fiber structures, starting with a high twist case, so that the effect of fiber slippage during yam extension can be ignored. A differential equation describing the stress transfer mechanism in a staple yam is proposed by which both the distributions of fiber tension and lateral pressure along a fiber length during yam extension are derived. Factors such as fiber dimensions and properties and the effect of the discontinuity of fiber length within the structure are all included in the theory. With certain assumptions, the relationship between the mean fiber-volume fraction and the twist level of the yam is also established. A quantity called the cohesion factor is defined based on yarn twist and fiber properties as well as on the form of fiber arrangement in the yam to reflect the effectiveness of fiber gripping by the yam. By considering the yam structure as transversely isotropic with a variable fiber-volume fraction depending on the level of twist, the tensile and shear moduli as well as the Poisson's ratios of the structures are theoretically determined. All these predicted results have been verified according to the constitutive restraints of the continuum mechanics, and the final results are also illustrated schematically.
A critical problem in the study by Komori and Makishima about the microstructural characterization of general fiber assemblies is analyzed, and a modified approach is presented in this paper. The modified theory is able to predict satisfactorily such parameters as the mean values of the number of fiber contacts and fiber segments between contacts in an unbonded fiber system. For a bonded fibrous structure like a nonwoven material, the relative proportions, the distributions of the bond lengths, and the free fiber lengths are also provided based on the modified theory. The theory has been applied to three typical fibrous systems to calculate the microstructural parameters that are believed useful for further studies of these systems.
Principles of yarn manufacture from staple fibres are presented in a book intended to provide a comprehensive review of principles for newcomers to the industry and a comprehensive reference source for the practising textile technologist. The 22 chapters cover: introduction; opening and cleaning; blending and mixing; carding; roller drafting, doubling and fibre control; autolevelling; combing; package formation and drawing prior to spinning; the spinning process; fibre migration and displacement; intermittent spinning machines; conventional frame spinning machines; open-end spinning; Repco self-twist spinning; spinning developments; yarn folding; yarn preparation; static electrification and atmospheric control; yarn properties; yarn faults; speciality yarns; and tow-to-sliver conversion and bulked acrylic yarn production. References for further reading are provided at the end of each chapter (168 references in all) and the book is completed by an appendix, consisting of flow charts for the different processing sequences, and a subject index.
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.
A model is presented for the structure of staple fibre yarns, which includes some random characteristics. A number of properties of the yarn are then evaluated for these structures. The results are compared with experimental values for yarns made from Tencel fibres.
Treloar’s vision [J. Textile Inst. 56, T359-T380 (1965)] of an ideal fiber intersecting the cylindrical yarn at all radii with the same (mean) frequency is not accurate and consequently the derived model does not correspondent to reality. This paper introduces a modified model of radial fiber migration in yarns and it is shown that the length of a fiber increases equidistantly with the steps of radius and each fiber in the yarn approximately follows a conical path. The derived theoretical relations were found to be in acceptable agreement with the experimental observations.
An earlier idealized theory of fiber contact by Komori and Makishima is modified on the same geometric-probabilistic basis by taking account of steric hindrances be tween fibers. A new characteristic fiber length called the persistent length is introduced to define the basic fiber segments that can be treated as independent statistical elements. The theory predicts that steric hindrance between fibers brings about two opposite effects on fiber contact: on the one hand, it diminishes the chance of contact by restricting the free fiber length on which a new contact may be formed, and on the other hand, it enhances contact by narrowing the free volume in the mass where a fiber can be located without touching the contact parts formed earlier. The total of these two determines the probability of contact, which depends strongly on the per sistent fiber length. The exclusion effect is formulated by a self-consistent mean-field analysis and evaluated explicitly for two idealized fibrous systems (2D and 3D random assemblies).
A mathematical model of a helix with variable radius is developed to analyze geo metric and mechanical properties of a migrating fiber. The factors concerned include the frequency and amplitude of fiber migration as well as the equivalent radial position and equivalent helix height of the fiber. This treatment permits the application of experimentally determined migration patterns defined by those factors. The derived properties are the curvature and torsion components of the migrating fibers, bending moments, torque, strain energy distribution, and total strain energy. The terminal force and couple are calculated as functions of the length of the helix axis. A critical migration amplitude is identified where the axial component of the couple and trans verse component of the force change their direction. The implication of these behaviors for yam properties such as total yam torque and local pressure distribution is also revealed. Cylindrical and sinuous helices are compared, with the effects of the amplitude and frequency of fiber migration quantitatively determined.
A detailed study is made of the effects of yarn size and twist on fiber migration in staple yarns. A simple theoretical model is developed to calculate migration force in a surface fiber as a function of yarn size, twist and processing tension. The theoretical model proved useful, not only in explaining the experimental results, but also in providing some unex pected additional information. In particular, it demonstrates that some scatter of data in experimental results can be expected theoretically. Among all the variables considered thus far in this series of papers [1, 2], yarn size and twist appear to be the most influential variables controlling fiber migration in staple yarns.
This paper presents a discussion on the effective operation of the geometric cause of fiber migration in staple yarns. The experimental investigation is extended to some of the roving and drafting operation variables which had not been studied earlier. It is shown that the roving twist and drafting ratio have a significant effect on the rate of fiber migration. The influence of drafting tenacity was found to be negligible. Statis tical analysis shows that over 90% of the resolved effects are controlled by the mean fiber position.
In this paper the theories of fiber migration have been reviewed. Modification of an analysis of migration in a 7-ply structure has been carried out. The frequency of migration is predicted for two models, and it suggests that slack forma tion is the mechanism for outward migration in an open structure, while forced buckling of the central fiber is the corre sponding mechanism for a packed structure, such as occurs in practical spinning.
The slack needed to initiate outward migration was analyzed and found to be dependent on the geometry and fiber arrangement in the zone hetween the roller nip and the point of yarn formation. On the other hand, the buckling strain in practical spinning theoretically depends on the surrounding fiber matrix, the twisting tension, and the mechanical properties of the fiber.
A stochastic analysis of fiber migration is presented. The possibility of coupling the results from such a treatment with those available from a mechanical analysis is discussed by means of an example.
Measurement of the fibre-packing density in the cross-section of a range of wool worsted yarns indicates that these are slightly hollow at the core, with the maximum packing density occurring about one-quarter of the yarn radius from the yarn axis. A comparison of these results with those obtained on cotton-viscose rayon yarns by other workers is also made.
A method is described whereby any preferential radial distribution of a particular fibre component in a blended yarn, relative to the yarn axis, may be measured and represented by a single numerical parameter, termed the Migration Index. The migration index is based on zoned fibre counts taken on a suitable number of yarn cross-sections (fifty has been found to be adequate for normal purposes) and expresses the actual migration of the component in terms of the maximum possible which could have occurred in the given yarn. Thus, a migration index of ± 100% represents complete separation of the component in question from the other fibres, the positive and negative signs denoting outward and inward migration, respectively, whilst a migration index of zero may be taken to represent uniform distribution of the component throughout the yarn cross-section. The migration index of the second component in a binary blend is equal in value, but opposite in sign, to that of the component under consideration.
A study of the migration of fibres in open-end-spun yarns is reported. Samples of viscose rayon yarns were produced by the drum and air-vortex methods, and the results obtained on them were compared with those for a ring-spun yarn made from the same fibre. Migration was studied by determining three parameters: the helix profile, the mean fibre position, and the r.m.s. deviation, i.e., the root-mean-square value of the radial deviation of the helix profile from the mean fibre position. The geometry of fibre-packing in the yarn cross-section and the fibre extent were also studied.It is shown that open-end-spun yarns are somewhat different in character from ring-spun yarns and that the most basic structural differences are found in the fibre extent, fibre migration, and fibre-packing density. The fibre migration in an open-end-spun yarn is shown to be as little as one-sixth of that in a typical ring-spun yam, and the difference in structure is important in that it can affect the yarn properties. It is concluded that the observed low strength of most open-end-spun yarns can be attributed to the poor fibre extent and inferior fibre migration within the yarn body and that their relatively high elongation can be explained in terms of the folded and entangled nature of the fibres.An examination of the fibre geometry in the yarn shows that the design features of drum spinners are important with regard to the determination of the fibre extent, a tangential feed being preferable to an axial one.The yarn cross-sections demonstrate that open-end spun yarns generally have a lower fibre-packing density than ring-spun yarns, which tends to give the yarn a more bulky nature; this is consistent with what might be expected from an assembly of tangled fibres.
The theory is based on the assumption that the paths of all the filaments in a continuous-filament yarn are identical, except for a displacement along, and rotation about, the yarn axis. The path of the single filament is characterized by a regular periodic migration between the axis and the periphery; the form of this path is derived on the basis of the assumption of a uniform packing density. The equations by which the path is defined involve two dimensionless parameters, one related to the twist and the other to the period of migration.Formulae are derived for the retraction on twisting, and for the stress-strain curve, for yarns in which migration occurs. These are shown to reduce to the corresponding formulae derived from the coaxial-helix theory in the limiting case when the rate of migration is small. Numerical examples are worked out to show the effect of the rate of migration on the retraction and the stress. From these results it is concluded that for rates of migration in the range likely to be encountered in actual yarns, the difference between the migrating-filament and coaxial-helix theories is in the most extreme case barely significant.This conclusion provides a justification for the general application of the simpler coaxial-helix theory in dealing with the mechanical properties of yarns.