Brigita Kolčavová Sirková, Monika Vyšanská Methodology for Evaluation of Fabric Geometry on the Basis of the Fabric Cross-Section Technical University of Liberec, Abstract Faculty of Textile Engineering, A woven fabric structure is defined by mutual threads interlacing in the fabric as well as the Department of Textile Technology, basic parameters of the fabric. The interrelation among fabric parameters can be obtained Liberec, Czech Republic, by considering a geometrical model of the fabric and specific experimental methods. The E-mail: [email protected], geometrical model is mainly concerned with the shape taken up by the yarn in the warp or [email protected] weft cross-section of the fabric. This article provides a possible methodology for evaluation of geometric parameters of threads in the real longitudinal and transverse cross-sections of fabric. From an individual cross-section of the fabric using image analysis it is possible to define the diameter of threads, their deformation, thread spacing, the maximum displace- ment (height of binding wave) of the thread axis, the angle of the thread axis (interlacing angle), the length of the thread axis in the cross-section of the fabric, the crimp of threads in the fabric, and the real shape of the binding wave through wave coordinates. The pa- rameters mentioned are possible to use as input for mathematical modelling of the fabric structure and for prediction of mechanical and end-use properties of fabrics. Key words: fabric geometry, interlacing, cross-section, waviness, height, binding waves. the mechanical and end-use properties The thread density and its cover factor n Introduction of fabrics such as handle, elongation, of the fabrics are limited by the possible crimp, maximal density, and weight [1, mutual positions of the warp and weft All the process of weaving is binding 6]. The fabric structure also determines threads in the space of the binding cell [3, point formation. Their dimensions and the weavability of fabrics and weav- 18]. The mutual positions of the threads tension gradually change from the cloth ing process. To describe the dependen- in the woven fabric create and describe fell in the forming zone to as far as some cies among the fabric structure, weaving the spatial geometry of the interlacing of place of the steady state in the fabric. process and resultant fabric properties, it the woven fabric. Each irregularity in the balance of the is not possible to operate with theoretical variable forces, in the deformation of the models only. In some cases it is neces- binding point (cell), in the accessibility sary to operate with empirical findings Geometry of woven fabric of the sets, in the stability of the weav- which have an acceptable table format – description of basic ing etc. can be deduced from the descrip- or mathematical formulation. The same parameters tion of the mutual relations between the fabric construction (identical density, tension and geometrical changes in the The basic geometrical characteristics of material, yarn count) woven in different binding cell [2 - 5]. For the weave of the the fabric structure of the binding cell are conditions or on different weaving looms fabric, it is characteristic that its pattern possible to summarise as a vector of the can have different variations in the spa- of binding is repeated regularly (periodi- input geometric structural parameters [1]. tial geometry of woven fabric. Empirical cally) across the whole fabric width and This vector consists of the parameters is continuous. In the forming zone it is findings are possible to use not only for mentioned: [dwarp, weft (yarn diameter); possible to evaluate changes in the inter- determination of the fabric structure but hwarp, weft (height of the binding wave), lacing which are given by the different they also establish a basis for calculation ewarp, weft (relative waviness), Dwarp, warp as well as weft tension. In a steady of selected fabric properties, for a de- weft (thread’s sett), A (weft distance), B state it is necessary to respect the regular- scription of various changes in the fabric (warp distance), Lwarp, weft (length of ity of the thread interlacing. This regular- geometry, etc. yarn between yarn intersections), Cwarp, ity defines the final quality of woven fab- weft (crimp of threads), t (thickness of a ric; cross sections in this case have to be The foundation for a study of the ar- fabric). In real woven fabric it generally identical. Each irregularity or difference eal geometry of fabric is the binding cell does not apply that the warp and weft in the cross section determines the fabric (the crossing of an end and pick) in a binding points lie in the same plane [2], fault. The structure of the woven fabric is plan view [11]. The initial idea of the see balanced and unbalanced fabric in usually defined by the weave, the mate- areal structure is a model of woven fab- Figures 1 & 2 (see page 42). rial of the yarn, thread density, and yarn ric which has crossing points formed in count [4]. These specifications determine one plane. This geometry operates with The interlacing of one end and pick creates the areal geometry of woven fabric. Ar- hundred-per-cent cover of the fabric and the binding cell of the woven fabric. The eal geometry defines only some selected with the possibility of mutual recalcula- size of the binding cell is defined by the properties of the fabric. A significant role tion of thread densities and yarn count for actual spacing of the weft and warp yarn. in describing woven fabric behaviour is the same cover factor of the fabric and The spacing of the weft yarn presents played by the three-dimensional geom- weaving resistance. This creates a false the depth of the binding cells along the etry. The spatial geometry is affected by impression that it is possible to weave longitudinal axis and the spacing of the the type and adjustment of the weaving however dense woven fabric in any com- warp yarn presents the binding cell in loom. The fabric geometry influences bination of the warp and weft density. the direction of the transverse axis. The Kolčavová Sirková B, Vyšanská M. Methodology for Evaluation of Fabric Geometry on the Basis of the Fabric Cross-Section. 41 FIBRES & TEXTILES in Eastern Europe 2012; 20, 5(94): 41-47. the limits of possible fabric densities, about the stability of the weaving etc. can be deduced from the description of mutual relations between tension and geometrical changes in the binding cell. The condition of the mathematical for- mulation of the binding wave and yarn cross-section for individual interlacing is given in [2]. Many attempts have been made to find a suitable model describ- ing the binding cell, i.e. to express math- Figure 1. Geometry of the unit cell for non- Figure 2. Geometry of the unit cell for bal- balanced woven fabric in plain weave [2]. anced woven fabric in plain weave [2]. ematically the shape of the binding wave in a given thread crossing in a fabric in a steady state. The Peirce model [12, 27], hyperbolic model, and sine shape are the models most used, which are related to plain weave, as is known. The model must be equally operative, and must de- scribe the binding repeat of the threads of both sections (longitudinal and transverse sections) as well as the influence of the bending rigidity and material profile on the shape of the threads interlacing in the Figure 3. Definition of the binding wave for the longitudinal and transverse fabric cross- passage from the right side on the reverse section [2]. side of the fabric and by contraries [1]. general formulation of thread spacing is The height of the binding wave hwarp and Previous geometric models result from given by Equations 1 and 2. hweft is given by Equations 5 - 6. initial geometric assumptions about yarn axes and cross-sections [2]. The central 1 weft distance = = axes of the binding wave are formed only (1) hwarp ewarp .d s (5) Dweft [piks/100mm mm]] h = (1− e ). d from abscissas or from ring arches and weft warp s (6) abscissas, from other curves. The yarn d + d 1 d = warp weft (7) cross-section at the binding points of the warp distance = (2) s D [ends / 100100mm mm]] 2 fabric is possible to substitute by circular warp The thickness of the woven fabric t is or other shapes [14]. For calculation of thread spacing for oth- the double value of the maximum from er than plain kinds of interlacing [1], i.e. values h +d /2 and h +d /2 [3]. We can The problems with the application of bindings where many combinations of 0 0 u u express the thickness of the fabric by the Peirce’s model [12] or other models are non-interlacing (floating) threads exist in following Equation 8. in the description of some real parameters an interlacing of warp or weft, it is pos- of the woven fabric (values dwarp, dweft, sible to use Equations 3 and 4. 100 2 2 hwarp, hweft, etc.) which usually we do ( ) − ( ) 2hwarp d warp 2hweft d weft .n 2 . 4. d s d s not know. Estimation of these geometric D t = (d wrp + d weft ).max + , + 2 + + + + weft distance = d warp d weft d warpparametersd weft d warpcan bed weftrealised d bywarp usingd weft im - 2 − 2 + − pp 1 . 4. (d s ) (d s ) d 2 .(n2 pp 1 ). age analysis through fabric cross-section (3)2h d 2h d 100 2 2 warp warp weft weft t.n=2 (d. 4.