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The current issue and full text archive of this journal is available at www.emeraldinsight.com/0955-6222.htm

Basic garment pattern generation using geometric modeling method

Basic garment pattern generation

Sungmin Kim Faculty of Applied Chemical Engineering, Chonnam National University, Kwangju, South Korea, and

Chang Kyu Park Department of Textile Engineering, Konkuk University, Seoul, South Korea

7 Received January 2006 Revised July 2006 Accepted July 2006

Abstract Purpose – The generation of individually fit basic garment pattern is one of the most important steps in the garment-manufacturing process. This paper seeks to present a new methodology to generate basic patterns of various sizes and styles using three-dimensional geometric modeling method. Design/methodology/approach – The geometry of a garment is divided into fit zone and fashion zone. The geometry of fit zone is prepared from 3D body scan data and can be resized parametrically. The fashion zone is modeled using various parameters characterizing the aesthetic appearance of garments. Finally, the 3D garment model is projected into corresponding flat panels considering the physical properties of the base material as well as the producibility of the garment. Findings – The main findings were geometric modeling and flat pattern generation method for various garments. Originality/value – Parametrically deformable garment models enable the design of garments with various size and silhouette so that designers can obtain flat patterns of complex garments before actually making them. Also the number and direction of darts can be determined automatically considering the physical property of fabric. Keywords Geometry, Modelling, Garment industry, Fashion design Paper type Research paper

Introduction Three-dimensional computer-aided design has become one of the most indispensable elements in modern industries. It is very difficult to find any design process that is not aided by CAD systems in traditional manufacturing processes of machinery, aircraft, and watercraft and most engineers take it for granted nowadays (Lee, 1999). Of course, such a trend is steadily spreading over garment industries. However, 2D CAD systems are still prevalent and therefore 3D design of garment is difficult. This is partly because of the difficulties in mathematical modeling of the fabric material that. However, a more significant problem is that designers and pattern makers do not think the CAD method to be better than the conventional manual method (Stjepanovic, 1995, Aldrich, 1992). Although such a phenomenon has always been with the initial development period of other purpose CAD systems, it is more serious as well as natural in garment industry because the quality evaluation of the product depends more on human aesthetic sense than on the optimum physical performance. Certainly, there are garments that need functionality more than the aesthetic appearance such as tight-fitting underwear or protective garments, CAD systems will be powerful tools in designing and manufacturing such mass-customized high-functional garments.

International Journal of Clothing Science and Technology Vol. 19 No. 1, 2007 pp. 7-17 q Emerald Group Publishing Limited 0955-6222 DOI 10.1108/09556220710717017

IJCST 19,1

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There are two major basic pattern generation methods in conventional garment design. One is the flat pattern process, where patterns are designed two-dimensionally and the other is the 3D draping method, where a flat fabric is directly formed into a garment on a mannequin. Although it is more difficult to get garment patterns by the latter method, it is more appropriate to make well-fit patterns than the former method and recent studies on automatic pattern generation have focused on the latter method. In that case, some cut lines called as darts are necessary if the garment has undevelopable patches. McCartney et al. tried to develop 3D surfaces using darts and to implement such techniques into pattern generation (McCartney et al., 1999; Collier and Collier, 1990; Heisey et al., 1990a,b). However, full 3D human body data were not easily accessible then that it was difficult to make practical garment patterns. Recently, due to the advancement in non-contact measurement technology, 3D body data became affordable and many studies have been made on this topic (McCartney et al., 2000; Daanen and Water, 1998; Au and Yuen, 1999; Paquette, 1996). Kim et al. tried to generate garment patterns by combining the 3D data of body and garment model. They also developed an interactive pattern design system using a parametrically deformable body model made from the 3D body scan data (Kim and Park, 2004; Kim and Kang, 2002). However, there have been some problems that it is difficult to get the ideal shape of garment by such methods and only the basic patterns can be obtained. In this study, a garment is divided into two zones, one for fit zone and the other for fashion zone. The fit zone is modeled by digitizing the body scan data so that it can provide optimum fit as well as the ideal shape of the garment. The fit zone can be reshaped and resized using basic anthropometric parameters that various sized fit zone can be modeled from a single body scan data. The fashion zone is modeled using parameters that determine the aesthetic appearance of the garment that users can design garments with various silhouette intuitively. Finally, a flat pattern projection algorithm was developed to make flat pattern pieces from three-dimensionally modeled garment considering the physical properties as well as the producibility of fabric. Fit zone modeling Interactive modeling of fit zone from 3D body data A garment can be divided into two zones to facilitate the 3D pattern generation. One is the fit zone, and the other is the fashion zone. The fit zone of a garment is in direct contact with the body surface and is responsible for the comfort of a garment that it must be designed to correctly reflect the shape of underlying body. In our previous research, the fit zone was modeled automatically from the body scan data, however, it was somewhat difficult to get a desirable shape of the fit zone with this method especially for slacks (Kim and Park, 2004; Kim and Kang, 2002). In this study, a fit zone was modeled by capturing and reconstructing the quadrilateral gird structure marked on the surface of a mannequin using a multi-joint coordinate measurement system as shown in Figure 1. The surface model of a fit zone was constructed as a B-Spline surface taking the measured grid points as their control points as shown in Figure 2. The shape of fit zone was then refined to have a smooth shape by adjusting the position of each control point manually. Zebra striping technique was applied to verify the smoothness of the surface visually as shown in Figure 2. Some examples of the fit zones prepared by this method are shown in Figure 3.

Basic garment pattern generation 9

Figure 1. Schematic diagram of fit zone modeling

Figure 2. B-Spline surface based fit-zone modeling

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Figure 3. Examples of fit zones

However, it is certainly meaningless to model the fit zone through the complicated method described above if it should be generated for each body scan data. Therefore, it is necessary to change the shape and size of the fit zone in a parametric way. The shape parameters of the fit zone defined in this study are listed in Table I. The initial values for parameters in Table I are extracted from the originally obtained fit zone model. Then the original fit zone model is deformed according to the user-supplied parameters. The deformation of the fit zone is made by changing the height, the width, and the circumference of each key cross-section of the fit zone as shown in Figure 4. Fashion zone modeling The fashion zone of a garment is usually not in direct contact with the body but is draped freely to make the aesthetic appearance. The aesthetic appearance of a garment

can be evaluated by many factors such as its overall silhouette or the number of folds at its bottom. In our previous research, only the tight fitting basic garments could be designed because the garment patterns were drawn directly on the surface of the body model. So far, costly trial-and-error methods have been used to obtain the desirable aesthetic appearance of a garment because it is very difficult to draw 2D patterns to accommodate to the shapes of imaginary 3D garments. In this study, the fashion zone of a garment is formed parametrically in 3D and projected into 2D pieces that complex patterns can be generated easily from the intuitive 3D previews. Parameters used to design the aesthetic appearance of a garment in this study are listed in Table II. For example, the bottom shape of a skirt can be changed using two parameters including the number and amplitude of bottom fold. A sine curve of specific period and Bodice Parameter Bust girth Front length girth Neck girth Side length Armhole depth Shoulder angle (8)

Skirt Default (in) 33.15 7.42 7.45 4.53 4.89 25

Parameter Waist girth Abdomen girth Hip girth Skirt girth Side length

Default (in) 27.32 33.83 37.25 37.36 13.30


Slacks Parameter Default (in) Waist girth Abdomen Hip girth Thigh girth Side length

27.32 33.83 37.25 22.12 13.30

Table I. Shape parameters for fit zones

Figure 4. Parametric deformation of fit zone

Parameter

Bodice

Default value Skirt

Height Bottom width (percent) Bottom depth (percent) Front insert Side insert Bottom rounding Number of bottom fold Amplitude of bottom fold

6.97 in 80.0 80.0 0 0 0 0 0

11.8 in 90.0 90.0 0 0 0 0 0

Slacks 27.5 in 80.0 80.0 Table II. Shape parameters for fashion zones

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amplitude can be formed using two parameters as shown in Figure 5. Assuming the initial shape of a skirt to be an n-sided cylinder, the shape of its bottom edge can be modified by changing the distance between each edge and the centroid of bottom plane according to the amplitude of sine curve at corresponding angle. As the various 3D shapes of garments can be previewed easily in 3D with this method, it would be possible to obtain appropriate patterns for specific garment more easily. Garments with various shapes can be designed easily by connecting the fit zone and fashion zone together as shown in Figure 6. Flat pattern generation A garment model usually consists of undevelopable surfaces that some cutting lines called the “darts” must be introduced to generate the flat patterns. In this study, darts are defined in either the lateral or the longitudinal direction of a pattern because those directions are approximately parallel to the major UV axes of the B-Spline surface of each pattern. In this method, darts are created along the mesh structure of the surface that it is easy to create as many darts as needed. This method seems acceptable because the darts are usually defined as such in the traditional manual pattern design method. Examples of the defined darts are shown in Figure 7. The strain reduction method was used to flatten the patterns with darts. First, the mesh structure of each pattern was reorganized considering the darts and then projected onto the 2D plane. As each mesh element on a pattern undergoes a certain deformation during the projection, a considerable amount of strain is induced in the flattened pattern. An edge can be defined between every two node on the pattern as shown in Figure 8. By comparing and equalizing the lengths of corresponding edges in

Amplitude of a fold

2p Number of folds

Modulation

Figure 5. Schematic diagram of fashion zone formation


Figure 6. Examples of designed garments

Figure 7. Examples of dart definition

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Figure 8. Schematic diagram of strain reduction

2D and 3D pattern iteratively, residual strain in the projected pattern can be reduced. By this strain reduction method, resulting flat patterns can be obtained. By considering the physical properties of the fabric material such as maximum elastic allowance and maximum shear angle allowance during the strain reduction, even the optimum shapes of patterns for different fabric material can assumed to be obtained. Some examples of flat patterns are shown in Figure 9. Strain reduction is terminated after the rate of change in total strain reached a predefined threshold value. The distribution of residual strain is visualized on the flattened patterns to guide the users for the better placement of darts. However, as the number and positions of darts are determined entirely by the user and therefore the physically optimum number and positions of darts cannot always be obtained by this method. Of course, there are certain algorithms to determine the optimum cutting lines for the flattening of undevelopable surfaces (McCartney et al., 1999, 2000, Wang et al., 2004). But the applicable range of those methods are usually limited and the cutting lines suggested by those methods usually have the arbitrarily curved shapes and it is not desirable to introduce such complicated cutting lines to garment patterns because of the limitations not only in the design but also in the producibility of the garment. In this study, an automatic dart generation algorithm was developed to make approximately linear darts along the mesh structure as described in the manual dart definition method. Assuming the rectangular topology of a pattern, darts can be initiated from one of its four edges and can be drawn inward perpendicular to each edge as shown in Figure 10. The principle of this automatic dart


Figure 9. Examples of flattened patterns with user-defined darts

generation method is described in detail in our previous research (Kim and Kang, 2002). The suitability of the automatically generated darts can be verified by the visualized result of residual strain distribution. Results and discussion As shown in the above examples, garments with various sizes and silhouettes could be designed prior to the actual prototyping process. Therefore, the method developed in this study can be used to reduce the waste of both time and cost in conventional trial-and-error based processes. Once designed, garments are managed by a database system as the templates that users can design a new garment from on a similar one stored in the database to save their time. Conclusion In this study, a basic pattern generation system has been developed which generates flat garment patterns by modeling and flattening the 3D garment models. For this, a garment is divided into two zones including the fit zone and the fashion zone. The fit zone was modeled by digitizing the body scan data so that its size and shape could be modified in a parametric way. The fashion zone was modeled by parameterizing the

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Figure 10. Example of automatic dart formation

aesthetic appearance of garment silhouette so that the users can design various garment intuitively. Also a database management system for garment shape templates has been developed so that the users can design various garments ranging from basic items to fancy ones rapidly. Finally, a flat pattern projection algorithm has been developed to make flat patterns considering the physical properties as well as producibility of garment. Automatic pattern generation system will be a necessary tool to meet the future trend in manufacturing industries such as the mass-customization and the quick-response system. References Aldrich, W. (1992), CAD in Clothing and Textiles, Oxford BSP Professional Books, London. Au, C. and Yuen, M. (1999), “Feature-based reverse engineering of mannequin for garment design”, Computer-Aided Design, Vol. 15 No. 1, pp. 751-9. Collier, B. and Collier, J. (1990), “CAD/CAM in the textile and apparel industry”, Clothing Textile Research Journal, Vol. 8 No. 3, pp. 7-12. Daanen, H. and Water, G. (1998), “Whole body scanners”, Displays, Vol. 19 No. 3, pp. 111-20.

Heisey, F., Brown, P. and Johnson, R. (1990a), “Three-dimensional pattern drafting, part 1: projection”, Textile Research Journal, Vol. 60 No. 11, pp. 690-6. Heisey, F., Brown, P. and Johnson, R. (1990b), “Three-dimensional pattern drafting, part 2: garment modeling”, Textile Research Journal, Vol. 60 No. 12, pp. 731-7. Kim, S. and Kang, T. (2002), “Garment pattern generation from body scan data”, Computer-Aided Design, Vol. 35, pp. 611-8. Kim, S. and Park, C. (2004), “Parametric body model generation for garment drape simulation”, Fibers and Polymers, Vol. 5 No. 1, pp. 12-18. Lee, K. (1999), Principles of CAD/CAM/CAE Systems, Addison-Wesley, Reading, MA. McCartney, J., Hinds, B. and Seow, B. (1999), “The flattening of triangulated surfaces incorporating darts and gussets”, Computer-Aided Design, Vol. 31 No. 4, pp. 249-60. McCartney, J., Hinds, B., Seow, B. and Dong, G. (2000), “An energy based model for the flattening of woven fabrics”, Journal of Materials Processing Technology, Vol. 107 No. 1, pp. 312-8. Paquette, S. (1996), “3D scanning in apparel design and human engineering”, IEEE Computer Graphics and Applications, Vol. 16 No. 5, pp. 11-15. Stjepanovic, Z. (1995), “Computer-aided processes in garment production”, International Journal of Clothing Science & Technology, Vol. 7 No. 2, pp. 81-8. Wang, C.C.L., Wang, Y., Tang, K. and Yuen, M.M.F. (2004), “Reduce the stretch in surface flattening by finding cutting paths to the surface boundary”, Computer-Aided Design, Vol. 30, pp. 665-77. Corresponding author Chang Kyu Park can be contacted at: [email protected]

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IJCST 19,1

Prediction of the air permeability of woven fabrics using neural networks

18 Received March 2006 Revised August 2006 Accepted August 2006

Ahmet Çay Ege University, Textile Engineering Department, Izmir, Turkey

Savvas Vassiliadis and Maria Rangoussi Technological Education Institute of Piraeus, Department of Electronics, Athens, Greece, and

Is¸ık Tarakçıog˘lu Ege University, Textile Engineering Department, Izmir, Turkey Abstract Purpose – The target of the current work is the creation of a model for the prediction of the air permeability of the woven fabrics and the water content of the fabrics after the vacuum drying. Design/methodology/approach – There have been produced 30 different woven fabrics under certain weft and warp densities. The values of the air permeability and water content after the vacuum drying have been measured using standard laboratory techniques. The structural parameters of the fabrics and the measured values have been correlated using techniques like multiple linear regression and Artificial Neural Networks (ANN). The ANN and especially the generalized regression ANN permit the prediction of the air permeability of the fabrics and consequently of the water content after vacuum drying. The performance of the related models has been evaluated by comparing the predicted values with the respective experimental ones. Findings – The predicted values from the nonlinear models approach satisfactorily the experimental results. Although air permeability of the textile fabrics is a complex phenomenon, the nonlinear modeling becomes a useful tool for its prediction based on the structural data of the woven fabrics. Originality/value – The air permeability and water content modeling support the prediction of the related physical properties of the fabric based on the design parameters only. The vacuum drying performance estimation supports the optimization of the industrial drying procedure. Keywords Air, Permeability, Neural nets, Porosity, Drying, Modelling Paper type Research paper

Introduction Textile fabrics consist of interlaced yarns or fibers. They are complex materials and their structure is porous. They permit the flow of the air through the constituting materials: yarns and fibers. The discussion about the air permeability of the textile International Journal of Clothing Science and Technology Vol. 19 No. 1, 2007 pp. 18-35 q Emerald Group Publishing Limited 0955-6222 DOI 10.1108/09556220710717026

The authors would like to acknowledge Clothing Textile and Fibre Technological Development SA, in Athens, Greece for the use of the Shirley air permeability tester and Go¨khan Tekstil San. Tic. A.S¸., in Denizli, Turkey, for the kind supply of the woven fabrics. The present work has been partially supported by the “Archimedes 1” EPEAEK Research Project in TEI Piraeus, co-financed by the EU (ESF) and the Greek Ministry of Education.

fabrics deals mainly with the airflow perpendicular to their respective neutral level or the actual level formed by the warp and weft yarns, as it is shown in Figure 1. Air permeability of fabrics is of great significance. Depending on the air flow rate through the fabric under a given pressure drop, textile fabrics get their specific character in terms of thermal properties, or more globally in terms of comfort. Comfort of the textiles is a complex property affecting intensively the acceptance and the performance of the final product. In parallel, the air permeability has a significant influence on the drying behavior of the fabrics and especially in the procedure of vacuum drying. Using vacuum during method, the water content of wet fabrics is removed by suction. Highly porous structures of wet fabrics permit the flow of the air through the mass of the fabrics, resulting into a faster and more effective drying. In the opposite, dense structures block the air flow and subsequently the drying procedure is getting slower, costing in terms of time and energy. The role of the air permeability of the fabrics has an increased importance in the case of the vacuum drying technology. Typically vacuum drying holds the role of a pre-drying stage, positioned before the main drying unit, which operates by heating the wet fabric (stenter). The behavior of fabrics during vacuum drying varies depending on the fabric type and especially on the micro-structural characteristics of the fabric. The comfort of the textile products and the efficiency of specific processing stages of the fabrics, e.g. vacuum drying, are strongly influenced by the air permeability properties. Thus, the prediction of the air permeability fabric becomes of high interest, reflecting on the performance of the end products and the cost of the production procedure. Prediction of the behavior of a fabric during vacuum drying, therefore, becomes equivalent to prediction of its air permeability. Air permeability depends both on the material(s) of the yarn and on the structural parameters of the fabric. In general, the relationship between the air permeability and the structural parameters of the fabric is complex. Theoretically, the calculation of the air permeability is based on the calculation of the porosity of the fabric. As it is explained in the next section, however, there exist known difficulties in determining basic porosity calculation parameters, such as the shape factor, thus restricting its use in practice. Indeed, if the weaving pattern of the fabric is exceptionally loose, the porosity can be estimated from

Air permeability of woven fabrics

19

Air flow Weft

Warp

Figure 1. Airflow through a fabric

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microscopic images of the fabric, by measuring the area of the void space between the yarns. In the case of dense fabrics, however, which represent the most common case in practice, yarns are compressed and jammed. As a result, there does not exist a straightforward and standardized method for the measurement of the porosity. The task becomes even more complex if the fabric porosity has to be calculated rather than measured, in order to serve as a basis for the prediction of air permeability. In practice, the drawback of predicting the vacuum drying performance (water content remaining after pre-drying) of a fabric based on the air permeability values is exactly the need to know these values. If they are to be obtained by measurement, then this presupposes the construction of the fabric. In this case, however, there is no real need to model the efficiency of the vacuum drying; water content can be exactly measured, instead, in a small-scale experiment using fabric samples. Of practical interest is to predict the efficiency of the vacuum drying before the actual production of the fabric takes place, based on technical characteristics of the fabric during the design phase. This information would support a realistic and optimized planning of the production process. This is why prediction of the air permeability of a fabric before its construction becomes essential. In the present work, our aim is to obtain a reliable practical method for the prediction of the air permeability of the fabric during its design phase. Such a prediction will in turn yield an estimate of the behavior of the fabric during vacuum drying (remaining water content) and consequently of the energy consumption expected during the actual production of the fabric. To this end, we investigate both the porosity path and the structural parameters path to the prediction of air permeability of a given fabric type. Following the reasoning given in the next section, we adopt the later path. Furthermore, we investigate a linear and a nonlinear approach to establish a relation between air permeability and micro-structural parameters of the fabric. In the nonlinear context, we propose the use of an artificial neural network (ANN) of the generalized regression type, which is shown to yield satisfactory air permeability prediction values after a fairly modest training period. The network performance is verified on a set of real field measurement data. Air permeability of textile fabrics The fluid flow through textiles depends mainly on the shape arrangement and size distribution of the voids through which the fluid flows. Other critical factors affecting its permeability are the fabric thickness and the applied pressure. Fluid permeability is a complicated physical phenomenon due to the fibrous and non-even structure of the fabric. Thus, the precise definition of the shape characteristics via geometrical calculations is difficult. For that reason the existing research work on the air permeability is limited mainly on fabrics made of monofilament. In a similar sense, the yarns as basic structural elements of the fabrics are approached as wires (Backer, 1951; Rushton and Griffiths, 1971; Perry and Green, 1984; Gooijer et al., 2003a, b). The fact of the fluid flow between the fibers rise questions such as the resistance of entire fiber assemblies to fluid flow (Gooijer et al., 2003a, b; Leisen and Farber, 2004). Darcy’s law fluid describes the flow through a porous structure by a relationship between the pressure gradient along the flow path of a fluid and the average velocity of the fluid on a macroscopic scale. It mainly describes that the flow rate of fluids through porous structure is inversely proportional to the pressure gradient (Zhong et al., 2002):

B¼

mt n DP

ð1Þ

where B is the permeability of the material, m the viscosity of the fluid, t the thickness of the fabric, n is the volumetric velocity of the fluid and DP is the pressure drop across the fabric. The value of B depends on the nature of the porous media and the pore size. Since, the voids in a porous media affect the media permeability, the Kozeny-Carman equation was developed to provide a description of fluid flow based on the filtration properties. One form of this equation is (Zhu and Li, 2003): B¼

13 K 0 S 20 ð1 2 1Þ2 1

ð2Þ

where K0is the Kozeny constant, S0 is shape factor and 1 is the porosity. B is the permeability of the porous media. The shape factor is defined as following: S0 ¼

Surface area of solid phase Volume of solid phase

ð3Þ

Porosity is defined as the ratio of the projected areas of the pores to the total area of the material. It is also defined as the ratio of the void to the total volume (Hsieh, 1995): 1¼12

ra rb

ð4Þ

where ra is the fabric mass density (g/cm3) and rb is the fiber mass density (g/cm3). For the application of the above laws, it is necessary the definition of the shape factor. The non-uniform surface and microstructure as well as the deformability limit essentially the successful approach of the shape factor through geometrical calculations. In addition, the shape factor calculation does not take in account the voids between fibers and it is quite difficult to determine it for these fibrous structures. In the literature has never appeared any detailed study of the Kozeny constant for textile fabrics. In light of the above discussion, we hereafter abandon the porosity path to air permeability prediction and proceed to investigate the relation between the air permeability of the fabrics and its major structural parameters. Given the woven fabric construction process, three parameters are intuitively more attractive for our purposes, namely, the warp yarn density, the weft yarn density and the mass per unit area. Besides, their influence on the woven fabric properties, these parameters are advantageous in that their values either are predefined in the weaving process (warp and weft densities) or can be easily and accurately measured (mass per unit area). Our aim is therefore to establish a general relation between air permeability and these three parameters and then use it to predict air permeability values for given fabric types. As already mentioned in the Introduction section, this would be a result of great practical interest in the industrial fabric production context, because prediction of the air permeability and related fabric properties before mass production of the fabric would facilitate the design of fabrics of optimized performance.


21

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Experimental set of data In order to form an experimental basis for the investigation of the permeability/structural parameters relation, a set of different samples of woven fabric have been produced. All fabric types used are made of 100 percent cotton yarns and they are of plain weave structure. The warp and weft yarn linear densities are Ne 40 and Ne 50, respectively. The warp and weft yarn densities of the samples vary in incremental steps. We have combined six different weft densities and five different warp densities to produce a set of 6 £ 5 ¼ 30 different fabric types in total. Subsequently, the air permeability of the above fabrics was measured under constant pressure drop. Let us note here that, rather than being directly measured, the air permeability is in fact estimated via the measurement of air velocity. Air permeability in (cm3/s/cm2) was measured via the standard BS5636 method, using the Shirley FX 3300-5 air permeability tester. For each one of the 30 fabric types constructed, the air permeability measurement was repeated across five different samples of the given fabric type, thus producing a total of 30 £ 5 ¼ 150 measurements. The five measurements of each fabric type were then averaged to produce an average air permeability value, in order to reduce non-systematic measurement errors in it. The structural fabric parameters, the respective air permeability values (averages across five samples) and the standard deviation of the measurements are given in the Table I. As it can be seen in Table I, air permeability values decreases when warp and weft yarn densities increase. This is a reasonable behavior because the dimensions of the pores through which air flows are getting smaller when moving from looser towards tighter fabric types, where resistance to the airflow is higher. Linear approach: multiple linear regression model Although the relation under investigation is clearly nonlinear, due to the complex dynamics involved in the underlying physical phenomena, a multiple linear regression is still worth as a first attempt, in order to: . arrive to a crude linear approximation of the relation sought; and . obtain a clue as to the relative importance of the three intuitively chosen parameters within this relation. The results of a multiple linear regression analysis of the data in Table I are given in Table II. Data in columns C1, C2, C3 contain weft densities, warp densities and mass per unit area data, respectively, while column C4 contains average air permeability values. In Table II, the p-value in the analysis of variance section is less than 102 3, showing that the regression per se is indeed significant, i.e. there does exist an influential relation between the dependent variable (air permeability) and the three independent variables selected here. The R 2 value is 84 percent (adjusted R 2 is 82.2 percent), showing that 84 percent of the variability in the air permeability data is “explained” by the linear combination of the specific three independent variables. This percentage is high enough to indicate that a linear relation could certainly be used as a crude approximation of the true relation and, at the same time, low enough to justify the investigation of nonlinear alternatives that might explain the remaining variability in the data.

Sample no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Warp yarn density (ends/cm)

Weft yarn density (picks/cm)

Mass per unit area (gr/m2)

Average of air permeability (cm3/s/cm2)

54 54 54 54 54 54 57 57 57 57 57 57 60 60 60 60 60 60 63 63 63 63 63 63 66 66 66 66 66 66

20 25 30 35 40 45 20 25 30 35 40 45 20 25 30 35 40 45 20 25 30 35 40 42 20 25 30 35 40 42

101.0 110.3 119.5 127.3 136.7 144.1 101.2 111.1 120.5 130.7 142.0 146.3 107.9 118.7 129.5 141.4 151.2 153.7 109.0 119.1 129.1 148.5 150.3 154.4 111.2 123.0 134.0 144.4 155.0 160.2

45.74 27.02 15.68 8.76 4.37 2.90 47.94 27.52 14.84 8.99 3.98 2.68 33.98 17.01 9.75 4.56 2.12 1.70 27.68 15.24 7.23 3.22 1.89 1.61 27.28 14.42 6.90 3.19 1.65 1.38

STD of air permeability 1.80 2.44 0.68 0.39 0.15 0.40 1.83 0.78 0.97 0.48 0.24 0.12 1.16 0.79 0.41 0.41 0.07 0.05 0.55 0.64 0.13 0.42 0.08 0.05 1.68 1.39 0.21 0.17 0.06 0.05

Linear approach: modified multiple linear regression model Under a closer examination, sequential sum-of-squares analysis of variance shows that variable C1 (weft density) alone explains a 3825.8/4285.9 or a 89.9 percent of the variability in the air permeability values, while variable C2 (warp density), if incorporated in the linear combination along with C1, contributes a further 430.6/4285.9 or a 9.9 percent. Further, incorporation of the variable C3 (mass per unit area) does not contribute significantly to the linear combination that already contains variables C1 and C2 (99.5/4285.9 or 0.02 percent only). This result prompts the modification of the multiple linear regression in order to exclude warp density from the set of the independent variables. The results of the modified multiple linear regression on the data of Table I are given in Table III. Data in columns C1, C2 contain weft densities and warp densities, respectively, while column C4 contains average air permeability values. In Table III, the p-value in the analysis of variance section remains less than 102 3, showing that this modified regression is still significant, even without warp density in the


23

Table I. Structural parameters and corresponding air permeability measurements for 30 fabric types

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Table II. Results of multiple linear regression analysis on the data of Table I

The regression equation is C4 ¼ 105 2 0.679 C1 2 0.392 C2 2 0.355 C3 Predictor Coef SE coef T P Constant 105.04 16.36 6.42 0.000 C1 20.6793 0.7280 20.93 0.359 C2 20.3920 0.5694 20.69 0.497 C3 20.3551 0.3655 20.97 0.340 S ¼ 5.59416 R 2 ¼ 84.0 percent R 2 (adj) ¼ 82.2 percent Analysis of variance Source DF SS MS F Regression 3 4285.9 1428.6 45.65 Residual error 26 813.7 31.3 Total 29 5099.6 Source DF Seq SS C1 1 3825.8 C2 1 430.6 C3 1 29.5 Unusual observations Obs C1 C4 Fit SE fit 1 20.0 45.74 34.42 2.54 7 20.0 47.94 33.17 2.05

P 0.000

Residual 11.32 14.77

St resid 2.27R 2.84R

Note: R denotes an observation with a large standardized residual

model. The R 2 value is in the same level as before (83.5 or 82.2 percent adjusted), which means that the exclusion of warp densities did not impair the model. Note, however, that the p-values of the three regression coefficients in the Predictor section are now fairly lower than the corresponding p-values in Table II. This means that the modified regression with two independent variables yields a more reliable and robust model.

Table III. Results of modified multiple linear regression analysis on the data of Table I

The regression equation is C4 ¼ 111 2 1.38 C1-0.893 C2 Predictor Coef SE coef Constant 111.09 15.11 C1 21.3764 0.1233 C2 20.8933 0.2406 C3 20.3551 0.3655 S ¼ 5.58835 R 2 ¼ 83.5 percent R 2 (adj) ¼ 82.2 percent Analysis of variance Source DF SS Regression 2 4256.4 Residual error 27 843.2 Total 29 5099.6 Source DF Seq C1 1 3825.8 C2 1 430.6 C3 1 29.5 Unusual observations Obs C1 C4 1 20.0 45.74 7 20.0 47.94

T 7.35 211.16 23.71 20.97

P 0.000 0.000 0.001 0.340

MS 2128.2 31.2

F 68.15

P 0.000

SE fit 2.35 1.98

Residual 10.41 15.29

SS

Fit 35.33 32.65

Note: R denotes an observation with a large standardized residual

St resid 2.05R 2.93R

In either case, there still remains a 16 percent of the variability in the air permeability data that are not linearly explicable. Seeking an enhanced model, explicit or implicit, that will capture the nonlinear aspects of the relation under question, we propose here to investigate ANN as one of possible alternatives.


Nonlinear approach: artificial neural networks ANNs are algorithmic structures derived from a simplified concept of the human brain structure. Their various types have already been successfully employed in a wide variety of application fields (Haykin, 1998). Their major functionalities are: . Function approximators. This functionality is exploited in system input-output modeling; and . Classifiers. This functionality is exploited in pattern recognition/classification problems (Lippman, 1987).

25

Under their function approximator form, ANNs have served as a powerful modeling tool, able to capture and represent almost any type of input-output relation, either linear or nonlinear (Majumdar, 2004). The shortcoming of such an ANN-based modeling solution is that the model is implicit. Indeed, rather than formulating an explicit input-output analytic expression, either linear or nonlinear, an ANN processes examples of inputs and outputs, to capture and store knowledge on the system. It can subsequently simulate the system, or predict output values; yet, it cannot offer a closed-form description of the system. Internally an ANN contains a number of nodes, called neurons, organized in layers and interconnected into a net-like structure. Neurons can perform parallel computation for data processing and knowledge representation (Brasquet and Le Cloirec, 2000). Weighted averaging, followed by linear or nonlinear (thresholding) operations, with the possibility of feedback between layers, constitutes the main processing operation in an ANN. The acquired knowledge is stored as the weight values of the nodes. The architecture of a single layer of nodes for a sample ANN is shown in Figure 2 (Matlab, 2005). There exist S nodes in this layer. In the i-th node is computed a linear combination of a vector of R inputs [p1, . . .pR] weighted by weights [wi1, . . . wiR] and a bias term bi is added. The scalar value produced undergoes a transformation by a generally nonlinear function f( · ) to yield the corresponding i-th output, for all i ¼ 1, 2, . . . ,S. Sigmoid, log-sigmoid, hard-limiter or even linear types of functions are employed, resulting in accordingly varying properties of the network. Generally, the ANN architecture is characterized by: . A large number of simple, neuron-like processing elements. . A large number of weighted connections between elements. The weights of these connections store the “knowledge” of the network. The adaptive adjustment of these weight values, while sliding down an error surface constitutes the “learning process” of the network. . Highly parallel and distributed control. . An emphasis on learning internal system representations automatically (Rich and Knight, 1991).

IJCST 19,1

Input

Layer of neurons

W1,1 P1

26 1

P2

n 1

Σ

ƒ

a 1

b 1 n 2

Σ

ƒ

a 2

P3 1 PR WS,R

Figure 2. A sample ANN architecture (a single layer of S nodes)

Σ

b 2 nS

ƒ

aS

bS 1 a = f (Wp+b)

An ANN model is specified by its topology, node characteristics and training rules. These rules specify an initial set of weights and indicate how weights should be adapted to improve the performance of the network by minimizing the error between actual and ideal outputs, when the network is presented with a set of known inputs. A variety of different network models have already been proposed and used in practical applications, such as the Perceptron, the Multilayer Perceptron, the Hopfield Network, the Carpenter/Grossberg classifier, the Back-propagation network, the Self-organizing Map, the Radial Basis Function Network, etc. (Ramesh et al., 1995; Lippman, 1987). In terms of functionality, an ANN undergoes a training phase, where a rich set of examples (pairs of input-output values), called the training set, is presented to the network. The weights in the nodes of the network are iteratively optimized by a gradient-type algorithm, so as to produce correct outputs for all inputs in the training set. Subsequently, the network enters the so-called test phase, where it is asked to produce outputs for unknown inputs presented to it. Decisions are made (i.e. outputs are produced) on the basis of the experience gained by the network over the training set. During the test phase, the network is expected to “generalize” successfully, i.e. to exploit the experience stored in its elements in order to make correct decisions on incoming data that are similar but not identical to the training set data. In the area of the textile and clothing technology often the phenomena are of complex character and nonlinear behavior. Some problems have been solved using ANN already since the decade of the 1990s (Stylios and Sotomi, 1996; Stylios and Parsons-Moore, 1993). Thus, the efficiency of the ANN for the treatment of complex problems in the textile and clothing sector has been already been controlled and found satisfactory.

Generalized regression neural networks Selection of the appropriate type of ANN depends on the peculiarities of the specific problem. Several types of ANNs are promising candidates for the problem under consideration. In fact, any neural network that can take on the form of a universal function approximator will do. These are networks whose output layer nodes operate linearly and can therefore produce practically any real value in the output – as opposed to the limited output values possible when nonlinear/thresholding nodes are employed in the output layer. The major network families in this class are: . Multilayer Perceptrons. . Radial Basis Function Networks (more specifically: GRNN) (Chen et al., 1991). . Elman Networks (Elman, 1990).


27

Among the three competing classes we select GRNNs, because they are known to approximate arbitrarily closely any desired function with finite discontinuities, and although they require an increased number of nodes in their architecture, they can be designed in far less time than necessary for the design and training of, e.g. a multiplayer perceptron. A GRNN contains two layers of neurons, each consisting of N neurons, where N is the cardinality of the training set (number of the input – output pairs available). The first (hidden) layer consists of radial basis function (RBF) neurons while the second (output) layer consists of linear neurons of special structure. Owing to the later, the network can produce any real value in its output. Figure 3(a) shows a RBF neuron sample transfer function. An RBF neuron “fires” or produces an output of 1 when its input lies on or fairly close to its central coordinates. Owing to its symmetry and finite radial support (controlled by a spread parameter), it responds only to local inputs, i.e. those befalling within a neighborhood of controlled radius. Figure 3(b) shows a linear neuron sample transfer function. The linear layer of a GRNN is special in that its weights are set equal to the output values contained in the training set. When a value equal or close to 1 is produced by the first layer and propagated to the second layer, it produces – by means of an inner product operation – a significantly non-zero value at a certain output and practically zero values at the rest of the outputs. During the design phase of the GRNN, the centers of the RBF neurons in the first layer are set equal to the input vectors in the training set. During the test phase, when an unknown input close (similar) to one of the training set inputs appears, the corresponding RBF neuron (or neighboring set of neurons) fires a value equal or close to 1. The second layer performs an inner product between the vector of the first layer outputs and the vector of training set outputs. Training set outputs matched with a

a

+1

1.0

n

0.5 0.0

0 −0.833

+0.833 (a)

n

−1 (b)

Figure 3. A radial basis (a) and a linear; (b) neuron transfer function

IJCST 19,1

28

values close to 1 in this inner product contribute significantly to the output, while the contribution of the rest is negligible. This is how the GRNN generalizes from the training set to unknown inputs. The major shortcoming of a GRNN is that both its layers consist of a number of nodes equal to the vectors in the training set. Given the fact that the training set should be rich enough to be representative of the input space, this number may grow large for a given application. As a counter-balance, however, it has been proved that the GRNN can be designed to produce zero error for any given training set in a very short time. The main fabric construction parameters, warp and weft yarn densities and mass per unit area, are used as the input vector. Therefore, each input – output pair in the training set contains a vector of three inputs (warp density, weft density, mass per unit area) and a single output (air permeability). As mentioned in Experimental set of data section, we have averaged air permeability measurements across sets of five samples for each fabric type. Therefore, our data set consists of 30 independent combinations of values of the three independent variables (warp density, weft density and mass per unit area) along with the respective averaged air permeability per case. We intend to use 24 out of the 30 cases for training and the remaining six cases for testing. This means that the GRNN architecture will have 24 neurons in each of the two layers. Furthermore, in order to reduce the dependency of the results on a specific partition of the data into training and testing sets, we perform a five-ways cross validation test, i.e. we partition the data in five different ways and finally average the results across the five partitions. Figures 4 – 8 show the results from the five different experiments of the five-ways cross-validation. In each figure, the upper plot shows results where the training set is used as test set as well, while the lower plot shows results where the test set was distinct from the training set. Within each plot, stars (*) and circles (o) indicate measured and estimated air permeability values, respectively, while dots ( · ) indicate the ANN performance error (difference between measured and estimated air permeability values). As it can be seen in Figures 4–8, the proposed neural network approximates the air permeability values with a very low output error, regardless of the specific data partition into training and test sets. Error (sum-of-squares) values, tabulated in Table IV, are indeed very low. Moreover, the (appropriately scaled) average error produced by the ANN approach (33.68 *30/6 ¼ 168.4) compares favorably to the respective error produced by the multiple linear regression approach (813.7 or 843.2 for the modified regression). The later is a very encouraging result, as it justifies the extra effort required by the nonlinear approach. Indeed, in terms of the multiple linear regression, it can be claimed that the ANN structure proposed here leaves unexplained only the (168.4/5099.6 ¼ ) 3.3 percent of the total variability in the air permeability data, thus offering a five times better result than the respective 16 percent of the linear regression approach. An error pattern apparent in all lower plots of Figures 4 –8, associates looser fabric types (towards the left side of the horizontal axis) with error values higher than the respective error values for dense fabrics (towards the right side of the horizontal axis). For loose fabrics the pores (between the yarns) are bigger so the yarn mobility is higher, thus the pore dimensions become bigger because of the deformation during the airflow. On the contrary, dense fabrics have very small pores and high resistance to airflow and can preserve their compactness during airflow.


True(*), RB approximation(o), error(.) (Test set = training set) Air permeability

60 40 20

29

0 −20

0

5

10 15 20 Fabric sample index (test set of 24) True(*), RB approximation(o), error(.) (Test set training set)

25

Air permeability

60 40 20 0 0

4 5 2 3 Fabric sample index (test set of 6)

1

6

7

Figure 4. Air permeability estimated (approximated) by the GRNN (partition No. 1)


60 40 20 0 −20

0

5


25

Air permeability

60 40 20 0 0

1


6

7


IJCST 19,1 Air permeability

30

True(*), RB approximation(o), error(.) (Test set = training set) 60 40 20 0 −20

0

5

10 15 Fabric sample index (test set of 24)

20

25

True(*), RB approximation(o), error(.) (Test set training set)


Air permeability

60 40 20 0 0

1


6

7


60 40 20 0 −20

0

5


25


Air permeability

60 40 20 0 0

1


6

7



60 40 20

31

0 −20

0

5


25

Air permeability

60 40 20 0 0

1


6

7


Figure 9 shows the strong correlation between the measured and the predicted by the ANN air permeability values. Air permeability and vacuum-drying performance The next step in the process is to exploit air permeability values in order to predict vacuum drying performance (remaining water content) for a given fabric type. Although there certainly exists a relation between these two quantities, this is again of a complex form. Owing to this relation, however, the air permeability prediction error propagates to the water content prediction value. Since, the relation is not available in an analytic form, experimental vacuum-drying tests, where the remaining water content is measured after drying, are necessary in order to study the error propagation. The tests are performed in a laboratory-scaled vacuum drying unit that was designed and constructed for the purposes of this study. Pre-drying tests using the vacuum drying principle are performed at a constant pump power of 1.5 kW for all fabric samples. Each one of the five different samples of every one of the 30 fabric types presented in Section 3 undergoes the following processing: The fabric is first Data partition no. 1 2 3 4 5 Average error (sum-of-squares)

Error (sum-of-squares) 16.62 22.64 17.10 17.52 94.49 33.27

Table IV. Sum-of-squares error across five partitions and average

IJCST 19,1

Figure 9. Correlation between measured and ANN-predicted air permeability values

Measured air permeability

32

60 50 40 30 20 10 0 0.00

10.00

20.00

30.00

40.00

50.00

60.00

Modelled air permeability

immersed in a water bath and then dried using the vacuum drying procedure. The water content of the fabric type is extracted by averaging across the five sample water content measurements of this type, in order to reduce non-systematic measurement errors in the water content values. These averages for each fabric type are tabulated in Table V (second column). Corresponding averages of air permeability measurements from Table I are repeated in Table V for convenience (fourth column). Figure 10 shows graphically the correlation between the two sets of averaged measurements of the respective quantities, along with a fitted curve based on the least-squares principle. This experimental correlation indicates a structured relation of the two quantities. The fitted curve in Figure 10 shows that the relation is nonlinear, as a result of the complex physical phenomena involved in the process. Could this relation be put into an analytic form, it would offer a viable alternative for the estimation of the water content, thus bypassing the industrious and non-standard porosity calculation. For the purposes of the present study, rather than seeking to formulate an analytic relation, we adopt the experimental relation defined by the graphical fitted curve in Figure 10, as a mapping from air permeability to water content values. For each one of the 30 fabric types, we thus obtain a set of water content prediction values from the air permeability prediction values produced by the GRNN. These are given in Table V (third column). Figure 11 shows the experimental correlation between predicted (via the procedure described above) and measured water content values. The fitted line lies on the diagonal of the plane, showing that the relation between them is identity. Moreover, scatter around the diagonal is limited, showing that the air permeability prediction error is not magnified when propagating to the water content prediction values. These satisfactory experimental results allow us to argue that it is indeed both meaningful and viable to predict fabric performance during vacuum drying (water content) through air permeability prediction, on the basis of an ANN modeling tool trained on a few basic structural parameters of the fabrics, such as the warp and weft density and mass per unit area.

Sample no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Water content – measured (percentage remaining)

Water content – predicted (percentage remaining)

Air permeability (cm3/s/cm2)

53.65 45.65 40.34 38.21 35.66 32.35 50.53 44.91 40.93 37.49 33.62 32.33 50.19 45.68 39.31 36.00 33.80 32.04 47.89 44.52 40.20 35.72 33.40 32.31 47.77 43.59 37.66 37.09 35.69 29.49

51.83 47.96 42.44 38.36 35.26 34.20 51.93 47.99 42.15 38.53 34.95 34.02 49.97 43.09 38.93 35.39 33.55 33.24 47.89 42.21 37.29 34.45 33.39 33.17 47.83 41.74 37.05 34.41 33.21 32.99

45.74 27.02 15.68 8.76 4.37 2.90 47.94 27.52 14.84 8.99 3.98 2.68 33.98 17.01 9.75 4.56 2.12 1.70 27.68 15.24 7.23 3.22 1.89 1.61 27.28 14.42 6.90 3.19 1.65 1.37

Conclusions For woven textile fabrics of a certain composition, it is known that the efficiency of the vacuum-drying water extraction process is primarily affected by the air permeability of the fabric. In order to estimate the vacuum-extraction efficiency, we propose to predict air permeability of the fabric based on three basic structural parameters of the fabric, namely the warp density, weft density and mass per unit area. An ANN of the generalized regression type (GRNN) is proposed and employed to approximate (predict) air permeability values, when fed in the input with the structural parameter values of a given fabric type. The performance of the proposed neural network is tested on real field data, with very satisfactory results. Specifically, the neural network prediction error is shown to be five times lower than the corresponding error produced by a multiple linear regression applied on the same data. Furthermore, the proposed method has been employed for the prediction of the vacuum-drying process efficiency (water content remaining in the fabric after vacuum drying) with equally satisfactory results. The practical implication of both the above results is that the behavior of a specific fabric type in the vacuum dryer – and therefore the expected energy


33

Table V. Water content measurements (averaged across five samples) and corresponding air permeability of the fabric types in Table I

IJCST 19,1

50 45

34 Figure 10. Experimental correlation between air permeability and water content after vacuum drying (averaged measurement values)

Air permeability

40 35 30 25 20 15 10 5 0 25

30

35

40 45 Water content (%)

50

55

60

Figure 11. Relation between measured and predicted values of water content (percent) after vacuum extraction

modelled data of water content after vacuum extraction

55 50 45 40 35 30 25 20 20

30 40 50 measured data of water content after vacuum extraction

60

consumption during this stage of the fabric production process – can be accurately predicted in the fabric design phase, before actual production takes place, thus allowing for optimized production planning. References Backer, S. (1951), “The relationship between the structural geometry of a textile fabric and its physical properties, part IV: intercise geometry and air permeability”, Textile Research Journal, Vol. 2, pp. 703-14. Brasquet, C. and Le Cloirec, P. (2000), “Pressure drop through textile fabrics-experimental data modeling using classical models and neural networks”, Chemical Engineering Science, Vol. 55, pp. 2767-78. Chen, S., Cowan, C.F.N. and Grant, P.M. (1991), “Orthogonal least-squares learning algorithm for radial basis function networks”, IEEE Transactions on Neural Networks, Vol. 2 No. 2, pp. 302-9. Elman, J.L. (1990), “Finding structure in time”, Cognitive Science, Vol. 14, pp. 179-211.

Gooijer, H., Warmoeskerken, M.M.C.G. and Wassink, J.G. (2003a), “Flow resistance of textile materials, part I: monofilament fabrics”, Textile Research Journal, Vol. 73 No. 5, pp. 437-43. Gooijer, H., Warmoeskerken, M.M.C.G. and Wassink, J.G. (2003b), “Flow resistance of textile materials, part II: multifilament fabrics”, Textile Research Journal, Vol. 73 No. 6, pp. 480-4. Haykin, S. (1998), Neural Networks. A Comprehensive Foundation, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Hsieh, Y.L. (1995), “Liquid transport in fabric structures”, Textile Research Journal, Vol. 65 No. 5, pp. 299-307. Leisen, J. and Farber, P. (2004), “Micro-flow in textiles”, NTC Project F04-GT05, National Textile Center Annual Report, available at: www.ptfe.gatech.edu/faculty/leisen/F04-GT05.html (accessed 14 December 2004). Lippman, R.P. (1987), “An introduction to computing with neural nets”, IEEE ASSP Magazine, pp. 4-22. Majumdar, P.K. (2004), “Predicting the breaking elongation of ring spun cotton yarns using mathematical, statistical and artificial neural network models”, Textile Research Journal, Vol. 74 No. 7, pp. 652-5. Matlab (2005), MATLAB 7 R14, Neural Network Toolbox User’s Guide, The MathWorks Inc., Natick, MA. Perry, R.H. and Green, D.H. (1984), Perry’s Chemical Engineering Handbook, 6th ed., McGraw-Hill, New York, NY, pp. 5-16. Ramesh, M.C., Rjamanickam, R. and Jayaraman, S. (1995), “The prediction of yarn tensile properties by using artificial neural networks”, Journal of Textile Institute, Vol. 86 No. 3, pp. 459-69. Rich, E. and Knight, K. (1991), Artificial Intelligence, McGraw-Hill, New York, NY, pp. 487-524. Rushton, A. and Griffiths, P. (1971), “Fluid flow in monofilament filter media”, Trans. Inst. Chem. Eng., Vol. 49, pp. 49-59. Stylios, G. and Parsons-Moore, R. (1993), “Seam pucker predictions using neural computing”, International Journal of Clothing Science and Technology, Vol. 5 No. 5, pp. 24-7. Stylios, G. and Sotomi, J.O. (1996), “Thinking sewing machines for intelligent garment manufacture”, International Journal of Clothing Science and Technology, Vol. 8 Nos 1/2, pp. 44-55. Zhong, W., Ding, X. and Tang, Z.L. (2002), “Analysis of fluid flow through fibrous structures”, Textile Research Journal, Vol. 72 No. 9, pp. 751-5. Zhu, Q. and Li, Y. (2003), “Effects of pore size distribution and fiber diameter on the coupled heat and moisture transfer in porous textiles”, International Journal of Heat and Mass Transfer, Vol. 46, pp. 5099-111. Further reading Keeler, J. (1992), “Vision of neural networks and fuzzy logic for prediction and optimization of manufacturing processes”, Applications of Artificial Neural Networks III, Vol. 1709, pp. 447-56. Corresponding author Savvas Vassiliadis can be contacted at: [email protected] To purchase reprints of this article please e-mail: [email protected] Or visit our web site for further details: www.emeraldinsight.com/reprints


35


IJCST 19,1

A model for the twist distribution in the slub-yarn

36

Key Laboratory of Science and Technology of Eco-textiles Ministry of Education, Southern Yangtze University, Wuxi, China

Yuzheng Lu, Weidong Gao and Hongbo Wang

Received May 2006 Accepted June 2006

Abstract Purpose – This paper seeks to build a mathematical model to deduct the twists distribution in the slub-yarn. Design/methodology/approach – The model, considering the shearing modulus and polar moment of inertia of the yarn, influenced by the yarn density, is established based on the bar torsion model. The twists distribution in the slub-yarn is concluded based on the analysis of the results. The rules were verified via an indirect method, by testing the breaking strength of the slub-yarn. Findings – The results of the analysis showed that twists in every section of the slub-yarn are in inverse proportion to the square of the line density of the corresponding section. Slub length is a key factor to the twist in the base yarn, and the increase of the slub length will increase the twist; while the multiple is the key factor to the slub twist, and the enhancement of the multiple will decrease the twist significantly. Research limitations/implications – The analysis cannot be verified via a direct method. A new, more conceivable direct method should be utilized to test the result. Originality/value – The paper builds a base for the research of the mechanical properties of slub-yarn and gives directions to the slub-yarn production. Keywords Yarn, Dissipation factor, Shearing, Modelling Paper type Research paper

1. Introduction Slub-yarn is a kind of fancy yarn, whose slub appearance is gained via the variation of the yarn linear density during the spinning process, and because of its special appearance, has been widely used in a variety of garments. The mechanical properties of slub-yarns were analyzed based on mathematical statistics (Grabowska, 2001), but the distribution of the twists in the slub-yarn was not mentioned. In this paper, the twist distribution is deduced based on a mechanical model, which builds a base for the analysis of the mechanical properties of slub-yarns.


2. The mechanism of the uneven distribution of twists Taking slub-yarns produced in ring-spun machine for instance, just like the common yarns, twists are acquired through the rotation of the spindle, equaling to the ratio of the rotation speed of the spindle to the linear velocity of the front roller. Thus, without taking the transfer of twists into account, for the slub-yarn produced by the overfeeding of the back-mid roller method, twists in any part of the slub-yarn would be equal. (Both the rotation speed of the spindle and the linear velocity of the front roller are invariable.) Figure1 (1) shows this kind of uniform distribution of twists.

However, in actual twisting process, the diameter of the base yarn is smaller than that of the slub, thus the polar moment of inertia and torsional rigidity of the two parts have great differences. Suppose the twists of the two parts were equal, the torque in the slub would be stronger than that in the base yarn. While the yarn in a steady state requires that the torque in all cross sections of the slub-yarn must be equal, which yields the decrease of twists in the slub and the increase of twists in the base yarn, and the twists transfer result is well shown in Figure 1(a).

Twist distribution in the slub-yarn 37

3. The mathematical and mechanical model for the twist distribution The torsion of a subject is consistent with the following equation: Ml GI

ð1Þ

a M ¼ GI l

ð2Þ

a¼ For yarn, it can be expressed as: T¼

where a is the torque angle, l is the bar length, G is the shearing modulus, T is the twist of a yarn, M is the leverage of the yarn cross section and I is the polar moment of inertia. It has been proven that the yarn density dy increases linearly with the twist multiple (Barella, 1950), and dy affects the shearing modulus Gy and the polar moment of inertia Iy of the yarn, so before making a model for the twist distribution, it is necessary to analyze the impact of dy on Gy and Iy. Suppose the cross section of the yarn with uniformly distributed fibers is circular, the yarn density on certain cross section is dy, the fiber density is df, and the filling rate of the yarn w is defined as follows:

w¼

dy df

ð3Þ

3.1 The relationship between Gy and dy When there is a shearing load placed on the yarn, both the fibers and pores in the yarn will be deformed. Since, the pores cannot bear any load, all shearing load is acted on the fibers. If the shearing load is relatively small, the shape of the yarn would not change, thus the volume ratio of fibers to pores in the yarn will remain unchanged, and the pores as well as the fibers would have the same strain r. For yarn, the following expression can be acquired:

Figure 1. Twist distribution of slub-yarn

IJCST 19,1

38

Gy ¼

Q Ay r

ð4Þ

where Ay is the area of cross section of yarn, Q is the shearing load. The sum of the shearing load acted on the fibers is equal to Q. Suppose that every fiber has the same shearing modulus Gf, the following expression would be gained: Gf ¼

Q Q ¼ Af g wAy g

ð5Þ

where Af is the sum of the area of all the fibers in certain yarn cross section. From expressions (4) and (5), the following equation can be deduced: Gy ¼ wGf

ð6Þ

3.2 The relationship between Iy and dy The diameter of the yarn dy and f are the key factors to Iy. The area of the pores in yarn cannot be the effective integral area. For the uniform distribution of fibers in the yarn, before calculating the integral, the area differential coefficient dAy should be multiplied by w (Figure 2). Z Z p I y ¼ r 2 dAy w ¼ w r 2 dAy ¼ d4y w ð7Þ 32 Ay

Ay

The relationship between dy and dy can be expressed as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nt 4N t ¼ dy ¼ 2 1; 000pdy 1; 000pwdf

Figure 2. The polar moment of inertia of the yarn cross section

ð8Þ

where Nt is line density of the yarn (tex), and from expressions (7) and (8), the relationship between Iy and dy can be expressed as: Iy ¼

N 2t 2 £ 106 pwd2f

ð9Þ

39

3.3 Rules of the twists distribution From expressions (2), (6) and (9), the following expression can be deduced: N 2t Gf T ¼ M 2 £ 106 pd2f

Twist distribution in the slub-yarn

ð10Þ

For a certain kind of slub-yarn, Gf and df is a constant, and the torque M in any cross section along the yarn axis is equal. So the twist T in any cross section varies inversely as the square of line density of the yarn. TN 2t ¼ CðconstantÞ

ð11Þ

4. Impact of parameters of slub-yarn on twist distribution Slub-yarn is composed of two parts: base yarn and slubs. Its appearance is influenced by the length and linear density of each constitute part (Testore and Minero, 1988; Wang and Huang, 2002). Since, the twist is inversely proportional to the square of linear density, twists should be equal as long as having the same linear density; moreover, the increased linear density leads to the decreased twists. Figure 3 showed the appearance of a regular slub-yarn in a cycle. On the assumption that the slub-yarn is periodic, and according to conservation rule of twists, in a cycle, the twist number would be the product of the cycle length and the design twist, in which the design twist is determined by the spinning machine. For ring-spun machine, the design twist is related to the configuration of the twist gear. Suppose the transition section is not present, the relationship mentioned above can be expressed as follows: T 0l0 þ T 1l1 þ T 2l2 þ · · · þ T nln ¼ T

n X

li

ð12Þ

i¼0

T 0 N 2t0 ¼ T 1 N 2t1 ¼ T 2 N 2t2 ¼ · · · ¼ T n N 2tn

ð13Þ

where T is the design twist, T0 is the twist of the base yarn, l0 is the sum of all base yarn length in a cycle, Nt0 is the linear density of the base yarn, n is the number of slubs with

Figure 3. The appearance of a slub-yarn in a cycle

IJCST 19,1

different linear density, Nti (i ¼ 1 to n) is the linear density of the slub, and Ti (i ¼ 1 to n) is the twist of the slub with the linear density Nti, li (i ¼ 1 to n) is the sum of the length of slub with the linear density Nti in a cycle. All parameters mentioned above, except Ti (i ¼ 0 to n), can be controlled in the manufacturing processing, so from expressions (12) and (13), the following expression can be obtained:

40 T

n X

lj

j¼0

Ti ¼ N 2ti

n X

ðl j Þ

N 2tj

ð14Þ

j¼0

Because Nt0 is the smallest in Nti (i ¼ 0 to n), twist of the base yarn T0 is always larger than T, for the thickest slub in yarn with the largest linear density Nti, Ti must be smaller than T. When the slub-yarn is not periodic, a long section of the yarn can be chosen, turning the nonperiodic slub-yarn into periodic one, and then expression (14) can be used to analyze the twist of the chosen section of the slub-yarn. In order to simplify the analyses, the regular slub-yarn only with one slub in its cycle is supposed for analysis. Then expression (14) can be rewritten as following: T0 ¼

Tðl 0 þ l 1 Þ 1 þ l 1 =l 0 ð1 þ RÞ ¼T 2 ¼ T N 1 þ XR2 1 þ ll 10 N t20 N 2t0 Nl 02 þ Nl 12 t0

T1 ¼

t1

t1

Tðl 0 þ l 1 Þ 1 þ l 1 =l 0 1þR ¼T 2 ¼ T 2 1þ R N t X l 2 l0 l1 0 2 1 X 1 þ N t1 N 2 þ N 2 l1 N 2 t0

t1

ð15Þ

ð16Þ

t0

where R ¼ l 1 =l 0 ; X ¼ ðN t1 =N t0 Þ . 1; and X is the multiple. Expression (15) indicates that R is a key factor to T0 while X affects T0 slightly, and T0 increases significantly with the increase of R. Expression (16) reveals that X is a key factor to T1 while R rarely has impact on T1, and the increased X leads to the significant decrease of T1. In practical production, R reflects the length of the slub, thus the control of R can avoid T0 exceeding the critical twist. While the control of X can adjust T1, in case that twists of the slub is too low to make the yarn failure. 5. Experiment verification The model we built up is for analyzing the twist distribution in slub-yarn. To verify its veracity, the most direct method has been used to measure the twists of base yarns and the slub, respectively, however, because the boundary between base yarn and slubs is not easy to identify, the untwist-retwist method cannot obtain the twists of each part correctly. As the twist affects the strength of the yarn directly, an indirect method was employed to verify the twist distribution by, respectively, testing the breaking strength

of the slub-yarn and the corresponding common yarn. The testing results are detailed in Tables I and II. All the tested yarns are spun from the same roving. Results in Tables I and II clearly show that breaking strength of the slub-yarn is stronger than that of the common yarn with the same twist design. It is believed that basic yarns in slub-yarn acquire more twists than the common yarn, and before reaching the critical twists, the increased twists lead to the high breaking strength. The breaking strength of the slub yarn is nearly the same as that of the common yarn with the same calculated twist. It is conceivable that the breaking strength of the slub would be stronger than that of the base yarn in such specific processing conditions, leading to the base yarn becoming the weak point of the yarn. Hence, it is proved that twists of base yarn are approximately in line with the calculated twists. Since, the slub-yarns spun in experiments are regular, just with one slub in a cycle, therefore, according to conservation rules of twist, twists of the slubs should be equal to the calculated twists.

Twist distribution in the slub-yarn 41

6. Conclusion . Twists distribution of the slub-yarn can be deduced through the bar torsion model, and the experimental results showed that the calculated twists is so close to the test result. . Slub length is a key factor to the basic yarn twist, while the multiple mainly affects the twists of the slub. In a slub yarn, the basic yarn twist is always larger than the designing twist, and the twist of the slub with the largest linear density must be smaller than the designing twist. . It is necessary to adjust the slub length to avoid basic yarn twist exceeding critical twist. Increased length of the slub leads to the increased twists of the basic yarn. Multiple of the slub affects twists of the slub significantly, and the increased multiple results in the significant decrease in twists of the slub.

Length of Length of Designing twist the slub basic yarn (/10 cm) Multiple (cm) (cm) No. 1 2 3

No. 1 2 3 4

5 5 10

20 20 15

49.9 49.9 49.9

2 3 2

Calculated basic yarn twist (/10 cm)

Calculated slub twist (/10 cm)

58.7 60.7 71.2

14.7 6.7 17.8

Breaking strength CV (cN) percent 467.7 487.6 537.7

7.5 7.0 6.5

Designing twist (/10 cm)

Breaking strength (cN)

CV percent

49.9 58.5 60.1 71.8

389.1 461.5 486.2 541.2

6.5 3.5 7.3 7.1

Table I. Breaking strength of slub yarns

Table II. Breaking strength of common yarns

IJCST 19,1

42

References Barella, A. (1950), “Law of critical yarn diameter and twist influence on yarn characteristics”, Textile Research Journal, Vol. 20 No. 2, pp. 249-58. Grabowska, K.E. (2001), “Characteristics of slub fancy yarn”, Fibres and Textile in Eastern Europe, No. 1, pp. 28-30. Testore, F. and Minero, G. (1988), “A study of the fundamental parameters of some fancy yarns”, Journal of Textile Institute, Vol. 79 No. 4, pp. 606-19. Wang, J. and Huang, X.B. (2002), “Parameters of rotor spun slub yarn”, Textile Research Journal, Vol. 72 No. 1, pp. 12-16. Corresponding author Weidong Gao can be contacted at: [email protected]



Dimensional characteristics of core spun cotton-spandex 1 3 1 rib knitted fabrics in laundering C.N. Herath and Bok Choon Kang Department of Textile Engineering, Inha University, Incheon, South Korea

Characteristics of core spun cotton-spandex 43 Received May 2006 Accepted August 2006

Abstract Purpose – This paper aims to study the dimensional characteristics such as fabric density variations, dimensional constant parameters, linear and area dimensional changes and spirality angle variations of 1 £ 1 rib knitted structures made from cotton-spandex core spun yarns, under laundering regimes till 10th washing cycle. Design/methodology/approach – Samples of the above fabrics underwent dry, wet and full relaxation treatments and were subjected to standard atmospheric conditions prior to take the measurements. Washing was done in a front loading machine under normal agitation with machine 56 RPM. Each washing regime includes wash, rinse, spin, tumble dry steps. Washing temperature was set at 408C and water intake for washing was 30 l and rinsed with cold water. 0.1 g/l standard wetting agent was used. The mass of the load was maintained constant to 3 kg to keep the material ratio as 1:10. Washing regimes were continued till 10th cycle. Findings – Cotton-spandex rib structures came to a more stable state (minimum energy state) after 10th laundering cycle under the experimental conditions. Cotton did not come to such a state, even after 10th cycle proceeded. ANOVA analysis done under 95 percent confidential level has shown that fabric tightness and relaxation procedures give significant effect on dimensional characteristics of cotton-spandex and cotton rib structures. However, area shrinkage variations of cotton rib fabrics have shown an exception to this. Research limitations/implications – According to the dimensional constant values, evenafter 10th washing cycle, cotton rib structures did not come to a stable position. This should be further investigated to achieve a better stable rib knitted structure. Practical implications – The number of washing cycles can be increased or tumble dry duration can be increased to 120 min. to get a more stable state of cotton rib structures. Originality/value – The results are important for the knitting industry to predict the dimensional behavior of designed knitted fabric under relaxation. These data can be used to set the circular machine parameters to achieve a more stable fabric after laundering. Keywords Cotton, Dimensional measurement, Knitwear, Fabric testing Paper type Research paper

Introduction Geometrical dimensions of knit wear is quite easy to change during laundering and tumble drying (due to its, non balance condition), which results that knit wear will be unfit for use. Dimensional deformation of knit wear is influenced by fabric structure, raw material, structure tightness, etc. (Mikucioniene, 2004, 2001; Quaynor et al., 1999; Wool Science Review, 1971). This work was supported by Inha University Research Grant.


IJCST 19,1

44

During relaxation, internal stresses of knitted structures decrease and gradually moves to an stable balance condition with minimum internal energy (relaxation) and at the same time fabric density values are increased (structure consolidation) (Heap et al., 1983, 1985). In this event, two main forces affect to change their non balance state, as resiliency force of a knitted yarn and frictional forces acting on yarn interlocking points of a stitch (Mikucioniene, 2004; Quaynor et al., 1999). Therefore, to achieve lesser shrinkages during relaxation, researchers and manufacturers have been experimented to add certain amount of raw materials with good resiliency power to the basic raw materials. Thus, during laundering, extra mechanical energy is supplied to yarns in the structure through thorough agitation, in addition to the lubrication effect given by water to the yarn interlocking points of a stitch. Those factors result further shrinkages during laundering. Thus, the occurrence of loop jamming may effect the dimensions of relaxed knitted fabrics. It has been theoretically shown that 1 £ 1 rib structures may have more length jamming and however, in tighter structures both length and width jamming will occur or at least be closely approached than their medium and loose structures (Shanahan and Postle, 1973). During relaxation through laundering, 1 £ 1 rib fabrics show lesser shrinkages than plain fabrics and exhibit higher length shrinkages than their width shrinkages (Mikucioniene, 2004, 2001; Heap et al., 1983, 1985). However, 1 £ 1 rib needs at least 5 washing cycles and certain cases it was reported up to 10 cycles to get more stable shrinkages (Mikucioniene, 2004; Quaynor et al., 1999; Wool Science Review, 1971; Heap et al., 1985). In this experiment, 1 £ 1 rib knitted fabrics of core spun cotton-spandex yarns were subjected to full relaxation and washing regimes up to 10 cycles. Thus, in order to observe any effect with increasing cycle intervals, we increase the cycle interval to three between 5th and 8th washing cycles. Otherwise, cycle interval from 1st to 10th washing cycles were kept as 2. Investigated factors were course and rib density (per cm), stitch length, dimensional changes in length and width directions, area shrinkages and spirality angle variations. The results are compared with those for similar fabrics knitted from 100 percent cotton. Experimental Material About 100 percent Cotton (abbreviation: CO) and core spun cotton/spandex (abbreviation: CO/SP) with 93 percent cotton and 7 percent spandex were used to knit 1 £ 1 rib structures in a circular knitting machine in tight, medium and loose tightness factors. Spandex filaments with 40dtex were used in producing of core spun cotton/spandex yarns. Knitting details for CO and CO/SP rib fabrics are as follows: machine diameter – 30 inch; gauge – 24; RPM – 20; number of positive feeders used – 60; number of needles used-1680. Both material structure fabrics were untreated. Method Full relaxation Cut samples were dry relaxed (laid tension free on a flat surface under 218C ^ 1 at a RH of 65 percent ^ 2 for 48 h) and then, wetted out in a stainless steel water bath containing 0.1 g/l of standard wetting agent, maintaining a constant temperature of 388C for 24 h with minimum agitation. Then, washed thoroughly, briefly hydro

extracted for 1 min and tumble dried for 90 min at 708C. The samples were laid on a flat surface in a conditioning cabinet of 218C ^ 1 at a RH of 65 percent ^ 2 for 24 h with free of tensions. Washing and tumble drying Washing was done in a front loading machine under normal agitation with machine 56 RPM. Each washing regime includes: wash, rinse, spin, and tumble dry steps. Washing temperature set at 408C and water intake for washing was 30 liters and rinsed with cold water. 0.1 g/l standard wetting agent was used. The mass of the load was maintained constant to 3 kg to keep the material ratio as 1:10. Washing regimes was proceeded till 10th cycle. After each selected washing cycle, samples were tumble dried for 90 min. around 708C. Samples were then laid on a flat surface in a conditioning cabinet of 218C ^ 1 at a relative humidity of 65 percent ^ 2 for 24 h, before taking the measurements at the selected washing cycles. At every relaxation stage, measurements were taken as follows: SCSL(structural cell stitch length): length of yarn containing 25 ribs unraveled from the fabric sample was measured with “Zweigle” tester by putting 0.5cN/tex weight on the underside. This weight was good enough to remove crimp in the unraveled yarns. Five yarn lengths were measured from each sample and finally the average loop length for 30 yarn samples was calculated. Based on the SKC(structural knit cell) concept, SCSL values p were calculated; Tightness factor (TF) was calculated as machine tightness factor ( tex/[SCSL/nt]), where nt – number of needles in knitting operation in SKC. Spirality angle was measured according to the IWS 276 standard test method. For each average value of CPC, RPC, stitch length, linear shrinkages and spirality, 30 measurements were taken in each tightness factor. All other measurements were taken according to the ASTM standards. Results and discussions Course and rib density variations Course (CPC) and ribs density (RPC) of 1 £ 1 rib CO and core spun CO/SP fabrics from full relaxation to washing up to 10th cycle behave differently. Figures 1 and 2 show these variations with tight (H), medium (M) and low (L) tightness factors (TF). In 100 percent CO rib fabrics, RPC is gradually, but slowly, increases with full relaxation through wash treatments. However, after 5th cycle, RPC does not change significantly. Low and tight structures show some deviation, after 5th cycle, but, it is hardly to give special reason. In CO/SP rib fabrics, tight and medium structures show steep increase of RPC till 3rd wash cycle. After 8th cycle, RPC is not increase significantly. In low tight structures, steep RPC increasing can be seen till 2nd cycle and after that, gradually, increase its’ RPC. Therefore, it is clear that to become to a more complete relaxation state, at least 5th washing cycle is needed. However, 8th or 10th cycle is better for both 100 percent CO and CO/SP 1 £ 1 rib fabrics. Graphs for both CO and CO/SP between cycle intervals two and three do not show any special fluctuations. Therefore, It is hardly seen any special effect by increasing wash cycle intervals to three with 5th and 8th cycles. CPC of 100 percent CO ribs increase till 5th washing cycle and thereafter it will become almost flat. But, CO/SP rib fabrics show the CPC increasing only till 3rd cycle and after that, curve takes almost flat shape. Thus, tighter structures of CO/SP are showed the flat

Characteristics of core spun cotton-spandex 45

IJCST 19,1

H-TF-CO/SP M-TF-CO/SP L-TF-CO/SP H-TF-CO M-TF-CO L-TF-CO/SP

16

15

46 RPC

14

13

12

Figure 1. RPC changes of CO and CO/SP fabrics

11 Full

W1

W3 W5 Relaxation treatment

W8

W10

34 32 30 H-TF-CO/SP M-TF-CO/SP L-TF-CO/SP H-TF-CO M-TF-CO L-TF-CO

CPC

28 26 24 22 20 18

Figure 2. CPC variations of CO and CO/SP fabrics

16 Full

W1


W8

W10

level of CPC after 1st washing cycle. 100 percent CO rib fabrics take at least 5th cycles to come to a stable state and that for CO/SP rib fabrics is 3rd washing cycles. There is no special fluctuations between 5th and 8th wash cycles compared to other wash cycles with cycle interval two. Therefore, it is possible to say that no effect is given by increasing wash cycle interval from two to three on CPC changes.

To find the behavior of CPC and RPC with their stitch lengths, we plotted the following graphs to establish mathematical models. Figures 3 and 4 show these behavior. Reference state were taken as full relaxation and after 10th washing cycle. After full relaxation and 10th washing cycle, both RPC and CPC show a linear geometrical correlation with an intercepts to loop length 2 1. Therefore, we established following mathematical model to describe the behavior of them in full relaxation and after 10th washing cycle. R ¼ a0 þ a1/L and C ¼ a2 þ a3/L; where R-RPC; C-CPC; L-loop length; a0, a1, a2, a3-constants Following Tables I and II gives the values for a0, a1, a2 and a3 constants. Based on these loop geometrical data, we calculated the dimensional constants, which can be used to design a dimensionally stable fabric.


Dimensional constants (K-values) To calculate dimensional constant values for 1 £ 1 rib structures, accepted following mathematical models associated with structural knitted cell (SKC) concept given in scheme 1 was used. Scheme 1. Dimensional constant calculation formulae CU ¼

KC ; lU

WU ¼

KW ; lU

KP ¼

KC KW

K S ¼ C U xW U xl 2U ¼ K C xK W where CU - course units per fabric length (considered 1 cm),WU - Ribs per fabric width (considered 1 cm), lU - average total length of yarn in the SKC (SCSL). Kc, Kw, Ks and Kp (poisson’s function or loop shape factor) are non dimensional parameters. 16 Full-CO/SP Wash10-CO/SP Full-CO Wash10-CO

14 12

RPC

10 8 6 4 2 0 0

1

3 2 1/Loop length

4

5

Figure 3. RPC changes with loop length2 1 (cm2 1)

IJCST 19,1

40 Full-CO/SP Wash10-CO/SP Full-CO Wash10-CO

35 30

48 CPC

25 20 15 10 5

Figure 4. CPC changes with loop length2 1 (cm2 1)

Table I. Constant values for CPC and RPC models for CO/SP and CO rib fabrics

0 0

Material

Relaxation stage

CO/SP

Full relaxation After 10th wash cycle Full relaxation After 10th wash cycle

CO

2 3 1/Loop length

1

4

5

a0

a1

R 2*

a2

a3

R 2*

4.22 1.87 6.27 2.14

2.31 2.83 1.55 2.56

0.934 0.988 0.999 0.972

1.61 1.55 24.89 21.95

6.89 7.22 5.96 5.36

0.985 0.969 0.979 0.977

Note: R 2 * – regression correlation coefficient

Tables II and III give the calculated K-values for CO/SP and CO 1 £ 1 rib fabrics. Thus, according to the calculation of CV percent of Kp, in CO/SP rib structures, at full relaxation, Kp values has CV percent of 2.73 and but, after 3rd cycle, at 5th and 8th cycles, CV percent are around 0.6-0.75. Then, at 10th cycle, CV percent of Kp reduces up to 0.50. At full relaxation of 100 percent CO shows a CV percent of 5.43 and it varies within the range of 5-5.42 values till 5th cycle. Then, it increases and at 10th cycle, it reaches up to 6.29 percent. Thus, there is no significant effect by increasing cycle interval by 3 between 5th and 8th cycles. Therefore, we assume that CO/SP rib structures became more stable (relaxed) state than CO rib fabrics. Then, relaxation (changing loop shape factor) and consolidation (by increasing CPC and RPC during laundering) of the rib structure occurred at the same time as given in some other literature (Heap et al., 1983, 1985). Thus, CO and CO/SP rib fabrics give different values during full relaxation as well as in further relaxation during washing. It is clear that after full relaxation, both material structures are undergone to further relaxation states – complete relaxation (Quaynor et al., 1999). Almost all the K-values of CO and CO/SP rib structures are increased at 10th washing cycle. Thus, CO/SP rib fabrics show

TF

Ks

Kc

Kw

Kp

L M H L M H L M H L M H L M H L M H

100.53 94.17 88.72 106.15 98.67 93.65 107.63 100.93 93.36 106.68 99.76 93.05 107.03 99.64 90.40 106.86 99.43 90.45

14.68 14.41 14.19 15.50 14.89 14.79 15.7 15.17 14.69 15.61 15.10 14.66 15.67 15.08 14.46 15.64 15.06 14.45

6.84 6.53 6.25 6.84 6.62 6.33 6.87 6.65 6.35 6.83 6.61 6.34 6.82 6.61 6.25 6.83 6.60 6.26

2.14 2.21 2.26 2.26 2.24 2.33 2.28 2.28 2.31 2.28 2.28 2.31 2.29 2.28 2.31 2.28 2.28 2.30

Full relax Wash cycle 1

49 Wash cycle 3 Wash cycle 5 Wash cycle 8 Wash cycle 10

Notes: TF- tightness factor (tex1/2 cm2 1); L - low TF; M - medium TF and H - high TF

TF

Ks

Kc

Kw

Kp

L M H L M H L M H L M H L M H L M H

59.76 60.21 57.86 60.64 59.60 58.38 60.52 61.00 58.79 60.70 61.81 58.80 60.96 61.93 58.79 61.02 61.97 58.83

9.23 9.59 9.57 9.45 9.56 9.75 9.47 9.79 9.84 9.50 9.90 9.78 9.53 9.90 9.96 9.53 9.92 9.98

6.47 6.27 6.04 6.41 6.24 5.99 6.38 6.23 5.97 6.38 6.24 5.93 6.39 6.25 5.90 6.40 6.24 5.89

1.42 1.53 1.58 1.47 1.53 1.63 1.48 1.57 1.65 1.49 1.58 1.65 1.49 1.58 1.68 1.49 1.59 1.69

Characteristics of core spun cotton-spandex

Table II. K-values for CO/SP rib fabrics

Full relax Wash cycle 1 Wash cycle 3 Wash cycle 5 Wash cycle 8 Wash cycle 10

Notes: TF- tightness factor (tex1/2 cm2 1); L - low TF; M - medium TF and H - high TF

higher K-values than that of 100 percent CO rib fabrics, due to its higher CPC, WPC values and higher resiliency power of spandex component in the yarn core. Therefore, material with good resiliency power can give a positive effect on relaxation and consolidation of knitted structures (Mikucioniene, 2004; Quaynor et al., 1999).

Table III. K-values for 100 percent CO rib fabrics

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50

Liner dimensional changes Linear dimensional changes in length and width wise in cotton/spandex and 100 percent cotton 1 £ 1 rib fabrics were measured under full relaxation and laundering treatments. These linear shrinkage percentages for each sample were calculated by following formula. Shrinkage percentage ¼ [(L0 2 L1)/L0] £ 100; where L0 – the distance between data lines, before relaxation treatment and L1- same distance, after relaxation. Figures 5-8 show results of CO and CO/SP fabrics during full relaxation laundering. Both rib material structures show higher length shrinkages than their width shrinkages (Quaynor et al., 1999; Heap et al., 1983, 1985; Anand et al., 2002). After 10th wash cycle, CO/SP rib fabrics give higher length shrinkages (around 30-38 percent) compared to their width shrinkages (around 6-13 percent), whereas CO rib fabrics also show higher length shrinkages (around 15-21 percent) with compared to their width shrinkages (around 9-15 percent). Therefore, we can summarize than CO/SP rib fabrics show higher length and lower width shrinkages than CO rib fabrics. Reason for high length shrinkages of CO/SP rib fabrics may be due to good power of resiliency of spandex core (Mikucioniene, 2004; Quaynor et al., 1999). Then, length wise loop jamming also increased and resulted higher length shrinkages (Shanahan and Postle, 1973). The above mentioned length and width shrinkage behavior of CO/SP and CO rib fabrics can be justified by course and wale spacing values given in Table IV. In CO and CO/SP rib fabrics, length shrinkages reduce and width shrinkages increase, while increasing their structure tightness, at each relaxation stage (an anisotropic behavior with tightness factor). Thus, CO and CO/SP rib fabrics with medium and loose 40 TF-H

TF-M

TF-L

Length shrinkages (%)

35

30

25

20

Figure 5. Length shrinkages of CO/SP rib fabrics

15

Full

W1


W8

W10

Note: TF- tightness factor (tex1/2 cm–1); L-low TF; M-medium TF and H-high TF


16 TF-H

TF-M

TF-L

Width shrinkage (%)

12

51 8

4

0

Full

W1


W8

W10


Figure 6. Width shrinkages of CO/SP rib fabrics

25 TF-H

TF-M

TF-L

Length shrinkages (%)

20

15

10

5

0

Full

W1


W8

W10


Figure 7. Length shrinkages of CO rib fabrics

IJCST 19,1

16 TF-H

TF-M

TF-L

14 12 Width srinkage (%)

52

10 8 6 4 2 0

Figure 8. Width shrinkages of CO rib fabrics

Table IV. Density and spacing changes of ribs and courses of CO/SP and CO rib fabrics from full relaxation to 10th washing cycle

Full

W1


W8

W10


Rib CO/SP CO

Spacing reduction (percent) Density increase (percent) Spacing reduction (percent) Density increase (percent)

3.29 3.39 1.18 1.16

H-TF Course 5.50 5.27 4.59 4.81

Rib 3.22 3.33 1.11 1.12

M-TF Course 6.47 6.92 4.80 5.04

Rib 3.04 3.14 0.99 0.93

L-TF Course 9.2 10.14 5.29 5.58

Notes: TF – tightness factor (tex1/2 cm2 1); L - low TF; M - medium TF and H - high TF

structure tightness do not show much difference in their length shrinkages (for CO, 4 percent average and for CO/SP, 2.8 percent average) compared to their tight fabrics (difference between tight and medium, for CO ,21.56 percent average and for CO/SP ,16.9 percent). When considering width shrinkages, CO/SP rib fabrics with loose and medium structure tightness have a difference of 27 percent average (higher than in the case of length shrinkages as mentioned above), but tight fabrics show more significant difference than this (the difference between tight-loose fabrics is ,80 percent average and between tight and medium is ,40 percent average). In the case of width shrinkages of CO rib fabrics, loose and medium fabrics show ,32 percent average difference and tight fabrics give more difference than this (between loose and tight fabrics ,56 percent average difference, and between medium and tight fabrics 18 percent average difference). Therefore, structure tightness gives significant influence on dimensional changes.

However, after full relaxation, laundering treatments give further dimensional changes due to attain to a more stable condition of rib stitches. At a glance, comparing of full relaxation and 10th cycle, for CO/SP rib fabrics, length shrinkages by 4.68, 5.4 and 7.2 percent and width shrinkages by 4.22, 21, 15.9 percent increases and for CO rib fabrics, length shrinkages by 14, 13, 7.6 percent and width shrinkages by 13, 12, 10 percent increases reported for loose, medium and tight fabrics, respectively. Table IV gives the course and wale density and their spacing changes of CO/SP and CO rib structures from full relaxation to 10th washing cycle. According to the data given in Table IV, following justifications for linear shrinkages can be made: . For CO/SP and CO rib fabrics, course spacing reduction percentages is higher than rib spacing reduction percentages. Therefore, length shrinkages are higher than width shrinkages and CO/SP show higher course spacing reduction, leading to higher length shrinkages than CO. . In CO and CO/SP material structures, fabrics with low tightness(L-TF) show higher course spacing reduction percentages, leading to higher length shrinkages in lengthwise compared to tight fabrics (H-TF). . For CO and CO/SP material structures, tight fabrics (H-TF) show higher rib spacing reduction percentages. This leads to higher width shrinkages in tight fabrics than loose fabrics (L-TF). However, most of literature suggest maximum allowable linear shrinkage for 1 £ 1 rib structure is length £ width: ^ 5 £ ^ 5 percent (most safer limits) (Knopten and Fong, 1970). However, our samples showed higher values than this. Area shrinkage variations To calculate area shrinkage (S), following formula was used: S ¼ {½LL0 £ LW 0 2 LL1 £ LW 1 =½LL0 £ LW 0 } £ 100 percent where LL0 and LW0 are the length and widthwise distance between data lines before relax treatment and LL1 and LW1 are the same distances, but after laundering treatments. Figures 9 and 10 give the variations of area shrinkages of CO and CO/SP rib fabrics during laundering treatments up to 10th cycle. CO/SP rib fabrics reported 38-43 percent average area shrinkages and CO rib fabrics showed 25-31 percent average area shrinkages (comparatively lesser). Thus, CO/SP rib tight fabrics show lower area shrinkages compared to medium and loose structures, because, its’ higher fabric density give restriction to change the area. Thus, comparatively lower length shrinkage of CO/SP H-TF fabrics may also affect to this result. CO/SP fabrics show 4.5 percent average reduction of area shrinkages, while structure tightness increases from loose to tight. However, CO rib fabrics show no significant difference in area shrinkages between structure tightness at each relaxation stage (from full relaxation to 10th cycle). Reason may be that their CPC and RPC are not much difference as CO/SP to give a significant area shrinkage difference. Average standard deviation of area shrinkage values of CO rib fabrics between three tightness factors is 0.72.


IJCST 19,1

44 TF -H TF-H

TF -M TF-M

TF -L TF-L

54

Area shrinkage (%)

42

40

38

36

Figure 9. Area shrinkages of CO/SP rib fabrics

34 Full

W1


W8

W10


35 TF-H

TF-M

TF-L

30

Area shrinkage (%)

25

20

15

10

5

Figure 10. Area shrinkages of CO rib fabrics

0 Full

W1


W8

W10


At a glance, CO and CO/SP rib fabrics show further area shrinkages, after full relaxation towards 10th laundering cycle. Comparing full relaxation and 10th cycle, CO rib fabrics show 10.92, 16.57, 8 percent and CO/SP rib fabrics show 9.9, 7.55, 8.3 percent area shrinkage increases for loose, medium and tight fabrics, respectively. According to the literature, area shrinkages of most ensure machine washability of rib structures lie with in ^ 8 percent (Knopten and Fong, 1970). Similar to linear shrinkages, area shrinkages of our samples are also out of this limit.


Spirality angle variations In theory, Spirality angle changes is restricted by higher structure tightness and the angle is increased during relaxation progress in laundering due to vigorous action of heat and tumbler action – wale distortion increased (Anand et al., 2002; De Araujo and Smith, 1989). Thus, spirality angle of rib structures show significantly lesser values and lesser changes than plain fabrics, due to balance structure of rib fabrics (Anand et al., 2002). Figures 11 and 12 show spirality angle variations up to 10th cycle for CO and CO/SP rib fabrics. It is clear that due to lesser tightness factor/lesser density of L-TF, wale distortion is higher than M-TF and H-TF. During wetting and vigorous tumbling action, these wale distortions further increase within washing regimes. Therefore, spirality angle increase during progressing of laundering and higher angles are shown with L-TF than M-TF and H-TF. Owing to higher CPC and RPC values of CO/SP rib structures (higher spacing reductions as in Table IV) results lesser spirality angles even after 10th washing cycle, compared to CO rib structures. Reason is that higher structure tightness impose higher opposition with providing less space to distort the wales during relaxation. 4 TF-H

TF-M

TF-L

Spirality angle (degrees)

3.5

3

2.5

2

1.5

1 Full

W1

W3 W5 W8 Relaxation treatment

W10

Figure 11. Spirality changes in CO rib fabrics

IJCST 19,1

3 TF-H

TF-M

TF-L

56

Spirality angle (degrees)

2.5

2

1.5

1

0.5

Figure 12. Spirality changes in CO/SP rib fabrics

0 Full

W1


W8

W10

However, All spirality angle values of CO/SP and CO rib fabrics lie within the acceptable range (, 58). But, spirality angles of CO/SP lesser than that of CO rib fabrics. Reason for this characteristics of CO/SP rib fabric is the higher structure tightness, due to the resiliency power of spandex core. ANOVA analysis First, we have done a two factor ANOVA analysis for relaxation treatments from full relaxation to 10th cycle. By this, we observed the significance of effectiveness of tightness factor and relaxation progress. Table I and II gives the results for CO/SP and CO rib fabrics, respectively.. It has considered the significant level of 95 percent (a ¼ 0.025) for CO and CO/SP fabrics (Tables V and VI). From these two tables, for linear, area shrinkages (except for CO rib fabrics) and spirality angle changes, tightness factor and relaxation treatments effect significantly under 95 percent significant level. But, area shrinkage of CO has insignificantly effected by relaxation and structure tightness. Then, we did two factor ANOVA analysis for 3rd, 5th and 8th cycles to observe any effect by increasing washing cycle interval from two to three. But, there is no significant effect was noticed under 95 percent confidential level (a ¼ 0.025) for CO and CO/SP rib fabrics (Table VII). Conclusions Both CO and CO/SP rib fabrics show further shrinkage possibilities (consolidation), after their full relaxation. Same time, relaxation of knitted loops also take place. Higher

course and wale density values reported by CO/SP fabrics. CO and CO/SP structures have shown linear correlation to loop length 2 1 with an intercept. After 10th washing cycle, CO/SP fabrics show most stable state (by Kp values) than CO rib fabrics. Thus, K-values of CO/SP are significantly higher than CO rib fabrics. Higher length shrinkages and lower width shrinkages reported with CO/SP rib fabrics than CO rib fabrics. Tight fabrics show lower length shrinkage and higher width shrinkage for both CO and CO/SP rib fabrics. CO/SP fabrics show higher area shrinkages than CO fabrics. Their tight fabrics show lesser area shrinkages. But, CO/SP rib fabrics do not show significant area shrinkage differences with their structure tightness. CO/SP rib fabrics give lesser spiality angles (, 2.58) than CO fabrics (, 48). Tight fabrics show lesser spirality angle changes than loose and medium fabrics. Tightness factor and relaxation treatment affect on length-, width-, area- and spirality- changes of CO/SP and CO rib fabrics significantly, except area shrinkages of CO/SP rib fabrics. Thus, increasing washing cycle from two to three do not give any significant effect.

Dimensional characteristic changes

Effect of tightness factor

Effect of relaxation treatment

Length width Area Spirality

S S S S

S S S S

( p , 0.0001) ( p , 0.0001) ( p ¼ 0.002) ( p , 0.0001)

( p ¼ 0.004) ( p , 0.0001) ( p ¼ 0.0001) ( p ¼ 0.0001)

Dimensional characteristic changes

Effect of tightness factor

Effect of relaxation treatment

Length width Area Spirality

S ( p , 0.0001) S ( p , 0.0001) NS ( p ¼ 0.45) S ( p , 0.0001)

S ( p , 0.0001) S ( p , 0.0001) NS ( p ¼ 0.46) S ( p ¼ 0.0004)

Table VI. ANOVA for CO rib fabrics

Notes: S: significant (95 percent); NS: not significant (95 percent)

CO/SP NS p ¼ 0.50 CO NS p ¼ 0.25

Kc

Kw

Kp

NS p ¼ 0.56 NS p ¼ 0.33

NS p ¼ 0.36 NS P ¼ 0.99

NS p ¼ 0.42 NS p ¼ 0.42

Tested parameter Length Width Area shrinkage shrinkage shrinkage

Stitch density

Spirality

NS p ¼ 0.12 NS p ¼ 0.24

NS p ¼ 0.16 NS p ¼ 0.12

NS p ¼ 0.17 NS p ¼ 0.10

NS p ¼ 0.13 NS p ¼ 0.16

NS p ¼ 0.06 NS p ¼ 0.05

Notes: NS: not significant at 95 percent level; p: probability of existing

57

Table V. ANOVA for CO/SP rib fabrics

Notes: S: significant (95 percent); NS: not significant (95 percent)

Ks


Table VII. ANOVA analysis for CO and CO/SP rib fabrics for 3rd, 5th and 8th

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References Anand, S.C., Brown, K.S.M., Higgins, L.G., Holmes, D.A., Hall, M.E. and Conrad, D. (2002), “Effect of laundering on the dimensional stability and distortion of knitted fabrics”, AUTEX Res. J., Vol. 2 No. 2, p. 85. De Araujo, M.D. and Smith, G.W. (1989), “Spirality of knitted fabrics, part 1: the nature of spirality”, Text. Res. J., Vol. 59 No. 5, p. 247. Heap, S.A., Greenwood, P.F., Leah, R.D., Eaton, J.T., Stevens, J.C. and Keher, P. (1983), “Prediction of finished weight and shrinkages of cotton knits- starfish project, part I: an introduction and general over view”, Text. Res. J., Vol. 53, p. 109. Heap, S.A., Greenwood, P.F., Leah, R.D., Eaton, J.T., Stevens, J.C. and Keher, P. (1985), “Prediction of finished weight and shrinkages of cotton knits- starfish project, part II: shrinkage and the reference state”, Text. Res. J., Vol. 55, p. 211. Knopten, J.J.F. and Fong, W. (1970), “Dimensional properties of knitted wool fabrics; part IV: 1 £ 1 rib and half-cardigen structures in machine-washing and tumbler drying”, Text. Res. J., Vol. 40 No. 12, p. 1095. Mikucioniene, D. (2001), “The reasons of shrinkage of cotton weft knitted fabrics”, Material Science, Vol. 7 No. 4, p. 304. Mikucioniene, D. (2004), “The dimensional change of used pure and compound cotton knit wear”, Material Science, Vol. 10 No. 1, p. 93. Quaynor, L., Nakajima, M. and Takashi, M. (1999), “Dimensional changes in knitted silk and cotton fabrics with laundering”, Text. Res. J., Vol. 69, p. 285. Shanahan, W.J. and Postle, R. (1973), “Jamming of knitted structures”, Text. Res. J., Vol. 43 No. 7, p. 532. Wool Science Review (1971), Vol. 41, p. 14. Corresponding author Bok Choon Kang can be contacted at: [email protected]



Experimental analysis and modelling of textile transmission line for wearable applications Michel Chedid Saab Training Systems AB, Jo¨nko¨ping, Sweden, and

Ilja Belov and Peter Leisner School of Engineering, Jo¨nko¨ping, University, Jo¨nko¨ping, Sweden

Experimental analysis and modelling 59 Received July 2006 Revised August 2006 Accepted August 2006

Abstract Purpose – The paper seeks, by means of measurement and modelling, to evaluate frequency dependent per-unit-length parameters of conductive textile transmission line (CTTL) for wearable applications and to study deterioration of these parameters when CTTL is subjected to washing. Design/methodology/approach – The studied transmission line is made of Nickel/Copper (Ni/Cu) plated polyester ripstop fabric and is subjected to standard 608C cycle in a commercial off-the-shelf washing machine. The per-unit-length parameters (resistance and inductance) and characteristic impedance of the line are extracted from measurements before and after washing. Using the measurement data an equivalent circuit is created to model the degradation of the line. The circuit is then integrated in a three-dimensional transmission line matrix (TLM) model of the transmission line. Findings – Both an electrical equivalent circuit and a TLM model are developed describing the degradation of the conductive textile when washed. A severe deterioration of the electrical parameters of the line is noticed. Experimental and modelling results are in good agreement in the addressed frequency band. Research limitations/implications – Analysis is performed for frequencies up to 10 MHz. The developed TLM model can be used to conduct parametric studies of the CTTL. To counteract the degradation of the line, protective coating is to be considered in further studies. Originality/value – This paper extends knowledge of the subject by experimental and simulation-based characterization of the CTTL when subjected to washing cycles. Keywords Textiles, Electronics industry, Modelling, Impedance voltage Paper type Research paper

Introduction Both civilian and military markets of wearable applications are growing rapidly. Wearable electronics is designed to be body-worn while in use. It has to satisfy several design requirements: portability during operation, operation constancy, controllability, robustness and ergonomics (Chedid and Leisner, 2005). These requirements are crucial to guarantee good fitness of electronics to the human body. A wearable system has normally a modular architecture where different types of modules, e.g. sensors, radio and computer modules, are distributed on the body communicating to each other. A body area network based on conductive textile transmission lines (CTTL) that carries both direct current (DC) power and alternating current (AC) data signals, eliminates the The work was partly funded by the Swedish Knowledge Foundation through the Industrial Research School for Electronics Design, and Vinnova through the Summit Programme.


IJCST 19,1

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need for traditional cables between the modules within the wearable system. This requires a low DC resistance to deliver power and known characteristic impedance in order to build matched transceivers. In order to get a wearable system to comply with the requirements on robustness and ergonomics, the conductive textile should exhibit the following characteristics: durability, washability and flexibility. Therefore, the CTTL for networking requires an analysis of the mechanical and electrical characteristics of such material and how it reacts to environmental stresses. Several studies have been done about conductive textile characteristics. In Cottet et al. (2003) conductive textile characteristics were studied and modelled for high frequency signal transmission. In Gorlick (1999) a separate power and data bus was developed where different modules could be connected to the bus through stingers. In Wade and Asada (2006) DC behaviour of conductive fabric networks was studied. In Jayoung et al. (2005) the effects of mechanical stresses on conductive textile were addressed at low frequencies. Robustness to washing induced stresses in combination with complex frequency dependent behaviour of the studied transmission line (TL) has not been investigated earlier. In this research the deterioration of the electrical properties of the CTTL is investigated by means of measurement of the per-unit-length parameters when CTTL is subjected to environmental stresses in form of washing cycles. Based on experiment, an equivalent circuit model is derived to predict the deterioration of the electrical properties. The circuit is then integrated in a three-dimensional transmission line matrix (TLM) model and the results are compared to experiment. Experimental setup In Figure 1, the flowchart of experimental and modelling steps is presented. The studied CTTL has a length of 1 m. It consists of two stripes of conductive textile with a low surface resistivity, sewed onto a non-conductive textile. Hardware modules are connected to the CTTL through conventional snap fasteners, see Figure 2. The conductive textile is a Nickel/Copper (Ni/Cu) polyester ripstop from Laird Technologies. Ripstop is made of very fine polyester filaments plainly woven with coarse fibres ribbed at intervals to stop tears, see Figure 3. To make it conductive, every filament is plated first with a thin layer of Copper followed by another layer of Nickel. The conductive layer has an approximate thickness of 1 mm. Electrical characteristics of the textile, taken from manufacturer’s datasheet, are shown in Table I. The snap fasteners are normally used in grounding products, e.g. electrostatic discharge (ESD) wrist straps. Before attaching the snaps to the textile, a highly conductive silicone based paste (volume resistivity: 0.01 V cm) is used to establish a reliable electrical connection between the snaps and the conductive textile. Silicone paste is chosen for its elastic properties compared to conductive silver epoxy adhesives, which were shown to be unreliable when exposed to washing. The width of the conductive stripes is 6 cm. They are folded to 2 cm before sewing onto the non-conductive textile which acts as a substrate, see Figure 3. The width of 6 cm is taken in order to achieve adequate DC resistance for power transmission. Taking the value of surface resistivity supplied by the manufacturer, the estimated value of the CTTL’s DC resistance is 2.3 V.

Experimental analysis and modelling

Conductive Textile TL 1-port Reflection Measurement Per Unit Length Parameter Extraction Equivalent Circuit Model

Conductive Textile Specification TLM Model Washing Cycle

61 Figure 1. Flowchart of the experimental and modelling steps

Figure 2. Experimental sample of the textile TL

Conductive textile

2cm

Nonconductive textile

Mag= 322x

100µm

EHT = 10.00 kv WD = 4mm

Signal A = SE2 Date : 26 Sep 2005 Photo No. = 37 Time : 12:09

Figure 3. Architecture of the CTTL (left) and a scanning electron microscope picture of the conductive textile (right)

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62

Using a network analyzer (NA) HP8714ET, measurements are performed on the CTTL stretched in the air 10 cm above a lab table. The experimental testing atmospheric conditions were measured to be 50 ^ 5 per cent for the relative humidity and 22 ^ 18C for the temperature. As a part of experimental study, the constructed CTTL is subjected to washing. A washing cycle consisted of a standard 150 min cycle in a commercial off-the-shelf washing machine (Elektro Helios TF 1002). The washing cycle included pre-washing at 408C, main washing at 608C, three rinsing sub-cycles and centrifuging. Washing was conducted without laundry detergent. After washing, the CTTL is dried at room temperature. Measurement procedure When designing a given communication system based on TL, the frequency dependent characteristic impedance of the TL determines the quality of communication. To ensure maximum power transfer between the transceivers, their input impedance must be matched to the TL characteristic impedance. The signal power at the receiver reaches a maximum when the transmitter, TL and receiver impedances are matched. A complete knowledge of the complex characteristic impedance of the TL is required in order to design an impedance matching network in the transceivers. Another reason for the measurement of the TL’s characteristics is to study the degradation of the conductive textile when it is washed. The parameters of main interest are R (resistance per-unit-length in V/m), L (inductance per-unit-length in H/m), G (conductance per-unit-length of the dielectric medium between conducting surfaces in S/m) and C (capacitance per-unit-length between conducting surfaces in F/m). Together, they form an RLGC model of the TL, see Figure 4. These parameters define propagation constant g and characteristic impedance ZC as equations 1 and 2, (Eisenstadt and Eo, 1992):

g¼

Table I. Ni/Cu polyester ripstop characteristics

Figure 4. RLGC model of a transmission line

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðR þ jvLÞðG þ jvCÞ

ð1Þ

Textile thickness (mm)

Filament thickness (mm)

Ni-Cu layer thickness (mm)

Surface resistivity of textile (Ohms/square)

Density of yarns (yarn/m)

Density of filaments (filament/yarn)

178

25

1

0.07

3,600

35

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R þ jvL ZC ¼ G þ jvC

ð2Þ

where v ¼ 2pf, and f is the frequency. In order to estimate unknown per-unit-length parameters of the CTTL, two reflection measurements are done for two different test setups: one end of the TL is always connected to the output port of the NA while the other end of the TL is short-circuit for the first measurement and open-circuit for the second measurement, see Figure 5. When a balanced TL is measured (as it is the case for the studied CTTL), it is necessary to connect a balance-to-unbalance balun (transformer) between the instrument and the TL. A balun is required for measuring balanced TL because the NA’s output terminal is unbalanced. Open/short/load calibration is done when the balun is connected to ensure accurate measurements. The measurements are done for the frequency range from 300 kHz to 10 MHz. The measured parameters, Gs and Go, are the voltage reflection coefficients for the short- and open-circuit measurement setup, respectively. Letting Z0 denote the NA’s impedance and l the length of the TL, ZC and g can be obtained from equations (3)-(6) (Agilent Technologies, 2002): 1 þ Go Z open ¼ Z 0 ð3Þ 1 2 Go Z short ¼ Z 0

1 þ Gs 1 2 Gs

Experimental analysis and modelling 63

ð4Þ

Z0 Textile Transmission Line

AC

Network Analyzer

Shortcircuit

Unbalancedto-balanced balun

Z0 Textile Transmission Line

AC

Network Analyzer

Unbalancedto-balanced balun

Opencircuit

Figure 5. Short- and open-circuit measurement setup for the textile TL

IJCST 19,1

ZC ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z open Z short

1 g ¼ tanh21 l

ð5Þ

sffiffiffiffiffiffiffiffiffiffiffi Z short Z open

ð6Þ

64 Combining equations (1), (2), (5) and (6), the four per-unit-length parameters can then be extracted as shown in equations (7)-(10) (Eisenstadt and Eo, 1992): R ¼ ReðZ C gÞ

ð7Þ

ImðZ C gÞ v

ð8Þ

L¼

g ZC

G ¼ Re

ð9Þ

g ZC

Im C¼

ð10Þ

v

where Re( ) and Im( ) denote the real part and imaginary part, respectively. The characteristic impedance can be approximated theoretically from the geometric configuration of the TL (Figure 6), (Gevorgian and Berg, 2001). Data provided in Table II gives a theoretical value of the characteristics impedance 194.7 V. Considering the fact that the CTTL is designed for installation on a human body, the TL will be bended in different directions and therefore the impedance will vary with time. However, studying the characteristics for the TL with a rigid geometry still gives a pointer on how conductive textile degrades when subjected to washing cycles. s w

Figure 6. Schematic of the CTTL cross-section

Table II. Dimensions of the CTTL

t h

Thickness of substrate (h) Width of conductive stripe (w) Actual thickness of conductive stripe (t) Separation between stripes (s) Relative permittivity of substrate (1r)

εr

0.5 mm 20 mm 0.45 mm 10 mm 3.6

Equivalent circuit of the CTTL Having performed the reflection measurements the resistance and inductance per-unit-length are extracted, see Figure 7. Rwc0( f ) and Lwc0( f ) are the extracted parameters from measurement before washing while effective parameters Rwc1( f ) and Lwc1( f ) are extracted from measurement made after washing. The large variation in the extracted inductance per-unit-length at low frequencies is due to variation from NA measurements. The capacitance per unit length (C) is found to be constant with a value of 22 pF/m. In addition, the conductance per unit length (G) at the frequencies considered approaches zero and is therefore neglected. The extracted data for Rwc0( f ) and Lwc0( f ) in Figure 7, is used to derive the RLGC model (Figure 4) of the CTTL before washing. By examining the measurement data for frequencies up to 10 MHz, Rwc0( f ) is fitted with pffiffiffi a linear function of frequency f and Lwc0( f ) is fitted with a nonlinear function of f . Since, the length of the studied TL is 1 m, the extracted parameters are considered as the per-unit-length parameters. The analytical expressions for per-unit-length parameters Rwc0( f ) and Lwc0( f ) are given in equations (11) and (12), respectively: Rwc0 ð f Þ ¼ 2:7 þ 3:3 · 1027 f ½V=m Lwc0 ð f Þ ¼ 656 þ

2:1 · 106 7:3 · 103 þ 2:5


ð11Þ

pffiffiffi ½nH=m f

ð12Þ

The CTTL changes characteristic behaviour due to washing. The new behaviour can be simulated by loading the RLGC model with an electrical equivalent circuit shown in Figure 8. This circuit consists of a resistor and two RC sub-circuits placed in series. 1200

200 Rwc1

L(nH/m)

R(Ohm/m)

180

0 washing cycle 1 washing cycle

1000

160 40 0 washing cycle 1 washing cycle

20

Lwc0

800

Lwc1

600 400 200

Rwc0 0

0 0

2

4

6

Frequency(MHz)

8

10

0

2

4

6

Frequency(MHz)

8

10

Figure 7. Extracted per-unit-length parameters Rwc0, Rwc1 (left) and Lwc0, Lwc1 (right) before and after washing

Figure 8. CTTL model after washing cycle (left) and a representative simplified circuit (right)

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The resistor R1 represents the fact that part of the conductive layer is washed out resulting in a reduction of effective conductivity and therefore higher resistance. The capacitances C2 and C3 represent the cracks that have built up within the conductive layer. These cracks force the current to take alternative paths and thus further increasing the resistance of the line (R2 þ R3). As the frequency increases the decreasing impedance of the capacitors C2 and C3 causes the current through R2 and R3 to decrease, respectively. At sufficiently high frequencies these RC sub-circuits are more or less shortcut and the only resistance seen is R þ R1. This explains the negative slope of the curve for parameter Rwc1 and the positive slope of the curve for parameter Lwc1 in Figure 7. The per-unit-length parameters corresponding to the original RLGC model are kept as they are to make it possible to load the line with the equivalent circuit in the subsequently created TLM model. The introduction of two RC sub-circuits proved to be sufficient to capture the CTTL’s behaviour when fitting the model to the measurement data. Furthermore, these two sub-circuits represent the fact that the displacement current through the various cracks is not attributed to a specific frequency. It rather increases within a frequency band. The loaded line can be represented as impedance X in series and admittance Y in parallel with the line conductors, see Figure 8. Admittance Y is not altered after washing due to the fact that the geometrical configuration of the CTTL and the material between the lines remain unchanged. Impedance X can be calculated from equation (13): 1 1 þ R3 = ð13Þ Xð f Þ ¼ Rð f Þ þ j2pfLð f Þ þ R1 þ R2 = j2pfC 2 j2pfC 3 The values of components R1, R2, R3, C2 and C3 can be extracted from the measurement by solving a system of nonlinear equation (14): 8 ReðXð f 1 ÞÞ ¼ Rwc1 ð f 1 Þ > > > > > > ReðXð f 2 ÞÞ ¼ Rwc1 ð f 2 Þ > > < ReðXð f 3 ÞÞ ¼ Rwc1 ð f 3 Þ ð14Þ > > > ImðXð f 1 ÞÞ ¼ Lwc1 ð f 1 Þ > > > > > : ImðXð f 3 ÞÞ ¼ Lwc1 ð f 3 Þ It is worth noting that parameters Rwc1 and Lwc1 do not stand for fundamental resistance and inductance, rather being the real part and the imaginary part of impedance X, respectively, with the imaginary part normalized to 2pf. Therefore, they are attributed as effective parameters. Taking f1 ¼ 1 MHz, f2 ¼ 5 MHz, f3 ¼ 10 MHz, the equation system is solved. The frequencies are chosen to capture boundary conditions and the dynamics in between. Using the values obtained from measurement results in the following values for the equivalent circuit in Figure 8: R1 ¼ 174.5 V R2 ¼ 5.8 V R3 ¼ 13.9 V C2 ¼ 17.1nF, C3 ¼ 1.1nF. TLM model of CTTL Constructing a TLM model requires beside the geometrical data, the electrical properties of materials used, i.e. conductivity, permittivity and permeability. Using the

method proposed in (Henn, 1998) to approximate surface resistivity of conductive textiles, the effective conductivity of the textile can be calculated as follows. Let df denote the diameter of the conductive filament and d the thickness of the Ni/Cu layer, then the area of the metal layer, Am, can be calculated according to equation (15): p 2 d f 2 ðdf 2 2dÞ2 Am ¼ ð15Þ 4 Every yarn is composed of n filaments. Let reff denote the effective resistivity of the Ni/Cu layer, then the resistance per-unit-length, r, of one yarn can be calculated according to equations (16) and (17): n 1 X 1 ¼ r reff =Am 1

r¼

reff nAm

ð16Þ

ð17Þ

Having the yarn density, N, which describes the number of yarn per-unit-length of textile, the surface resistivity of the textile, rs, can be approximated as in equation (18): " #21 N X 1 r reff rs ¼ ¼ ¼ ð18Þ r N nNA m 1 The effective conductivity, seff, can then be calculated according to equation (19): 1 1 seff ¼ ¼ ð19Þ reff nNAm r s Taking into account the values given in Table I, results in the effective conductivity of the studied conductive textile, 1.50 £ 106 S/m. A commercially available electromagnetic simulation tool, Flo/EMC from Flomerics is used in TLM simulations. The TLM tool solves Maxwell’s equations in time domain. The frequency domain data is then computed. The computational mesh is composed of cuboids of different size. Absorbing boundary conditions represent open faces of the computational domain. Convergence tests have been performed to determine the effect of the open boundary location on the simulation results. Convergence criterion is satisfied when initial system energy decays by at least 60 dB. The conductive textile in the CTTL is modelled as thin plates of isotropic dielectric material with fixed frequency independent relative permittivity and permeability and a fixed conductivity. These thin plates are penetrable to electromagnetic fields and the skin effect is simulated with acceptable accuracy. Wires are used to establish electrical connection between the two conducting plates. The NA is simulated by a wire port, including a voltage source and a 50 V impedance. For the wire port the TLM tool includes the wire current in the output, and associates with it the load impedance. A post-processing tool determines the signals entering and leaving the model through the port, resulting in the voltage reflection coefficient. In order to properly define thin plates in TLM simulation, their equivalent thickness teq has to be specified. It is calculated from the surface resistivity of the conductive


IJCST 19,1

textile provided by the manufacturer and from its effective conductivity seff. Every stripe in CTTL is made of three layers of conductive textile and therefore teq is calculated according to equation (20): teq ¼

68

Number of layers 3 ¼ 28:5 mm ¼ 1:5 £ 106 £ 0:07 seff r s

ð20Þ

Equation (21) (Chen and Fang, 2000) approximates the resistance of a rectangular cross-sectional conductor at a given frequency: s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 1 pf meff ð21Þ þ Rð f Þ ¼ 2 seff wt eq 4seff ðw þ t eq Þ2 where meff and w are the effective permeability and the width of the stripe, respectively. Although this formula takes only into account the skin effect of the TL conductors, it still gives an initial approximation of the permeability of the Ni/Cu layer. Using the measured value of resistance at 10 MHz, the effective relative permeability mr is predicted to be 350. In TLM simulations where other physical effects are included such as the proximity effect (Figure 9), mr is adjusted to 325 to get better agreement with measurement data. The input parameters used in the TLM simulations are summarized in Table III. As can be seen in Figure 9 the distribution of the surface current is frequency-dependent. Higher frequencies cause the surface current to flow on the innermost edges of the CTTL. This represents the proximity effect and together with the skin effect tends to cause the TL’s resistance to rise with increasing frequency. Modelling versus measurement Voltage reflection coefficients are obtained from measurements and from TLM simulations performed for the open- and short-circuit setups (Figure 5). Effective Surface Current (Amps/m) > 0.7 0.622 0.544 0.467 0.389 0.311

Figure 9. Surface current distribution in the CTTL TLM model at 300 kHz (left) and at 10 MHz (right)

0.233 0.156 0.0778

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