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Structure and Tightness of Woven Fabrics

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Structure and Tightness of Woven Fabrics Indian Journal of Textile Research Vol. 12, June 1987, pp. 71-77 Structure and Tightness of Woven Fabrics S GALUSZYNSKIa School of Textiles, University of Bradford, Bradford BD7 IDP, U'K, Received 1 December 1986; accepted 27 January 1987 Fabric tightness and cover factor are discussed. Cover factor depends on yarn diameter and fabric sett only, whereas the fabric tightness also incorporates the weave. Fabric tightness is defined as the ratio of actual square fa- bric sett over the theoretical maximum square fabric sett for a defined weave and yam. Fabric tightness is recom- mended for use as a coefficient to indicate the fabric structure for comparison of their properties. Some examples are given to show the applicability of the recommendation. Keywords: Cover factor, Fabric tightness, Woven fabric 1 Introduction from Fig. 1, fractional warp cover factor, K I, for The properties of a woven fabric depend on its circular yam cross-sections, is given by: structure, the properties of the fibres and yarn be- ing used, its dimensional changes during the finish- K,=d, ... (2.1) ing process, etc. In published literature on woven PI fabrics, the fabric properties are discussed in and fractional weft cover factor, K , by: terms of fabric geometry or structure without an 2 explicit distinction between these two terms. K =dz 2 ... (2.2) Geometry indicates the values of the relevant pz geometrical parameters, whereas structure indi- cates the manner of construction, i.e. the recipro- Fabric cover factor, K, cal interlacing between the warp and weft K= d2Pl+ d,P2_ d,d2 threads I. .. (2.3) In some publications the fabric structure is indi- P,P2 PIP2 P,P2 cated by fabric cover factor, or cover factor, or fa- bric cover, which are taken to mean the same or from K, and K2• thing. The calculation of the fabric cover factor ... (2.4) does not incorporate weave intersections and K=K,+K2-K,K2 therefore this parameter should not be used to in- dicate the fabric structure (Appendix 1). The par- p ameter which indicates fabric structure is the coef- ficient of fabric tightness, which depends on yam raw material, linear density (count), weave and fa- bric sett. The aim of this paper is to introduce the term 'fabric tightness' in comparison with fabric cover factor. 2 Fabric Cover Factor The fabric cover factor K is defined as the pro- portion of the fabric area covered by actual yarn", In practice, cover factors are calculated for warp KI and weft K2 independently, being given, re- spectively, by the proportion of fabric area covered by the yarn in that particular sheet. Thus, -I 'Present address: SAWTRI, P.O. Box 1124, Port Elizabeth, i--+- RSA Fig. 1- Area covered by yam 71 INDIAN J. TEXT. RES., VOL. 12, JUNE 1987 a b Fig. 2- Kemp's racetrack model of flattened yarn: a- major diameter, b-minor diameter, and d-diameter of circular yarn cross-section where d is the yarn diameter for circular cross- section; suffixes 1 and 2 denoting warp and weft respectively. When dealing with flattened threads the above cover factors are calculated- in terms of the major yarn diameter a (Fig. 2) of flattened thread and thread spacing p; Fig. 3-Hanrilton's fabric geometry = E..! «, ... (2.5) Nr, PI Ial a2 1 =- K2 ... (2.6) K=- ... (2.9) P2 Pr1 Also, in the case of flattened-thread, there is a A similar equation is used for weft cover factor difference in the value of the major yarn diameter, Nr, a, due to the weave and fabric sett. Hamilton" Iii2 proposed a procedure and equations to calculate I the cover factor for a fabric woven in a weave K=- ... (2.10) other than the plain weave in terms of non-limit- Pr2 ing and limiting conditions. With non-limiting conditions, where no distor- and fabric cover factor is calculated by Eq. (2.4). tion of the racetrack" (Fig. 3) occurs, the calcula- 3 Fabric Tightness tion of cover factors is the same as for the plain When assessing the properties of various woven weave given by Eqs (2.4), (2.5) and (2.6). fabrics, there is' a need to define fabric structure With limiting conditions where the effective ma- by a single parameter so the effect of fabric struc- jor diameter, ii, is less than a, and equal: ture on its properties could be seen. This need a=a-O,lb ... (2.7) was recognized-Y and a set of equations have or been put forward for the calculation of fabric ii = a- 0,215 b ... (2.8) tightness, or the coefficient of fabric tightness" . Hamilton" (Fig. 3), applying Kemp's" racetrack depending on weave, cover factors are calculated model, defined fabric tightness, t, as follows: from the weave repeat as a whole. Eq. (2.8) should be applied to non-plain woven fabrics in weaves t = (Kpl + Kpz) actual x 100 (%) ... (3.1) with floats on both sides (e.g. 2/2 matt weave), (Kpl + Kp2) limit whereas Eq. (2.7) for weaves with intersections one side and float on the other (e.g. 2/2 twill). where the limit is a theoretical maximum value Fractional warp cover factor, K 1, is given by the read from Fig. 4, and sum of effective major diameters of all threads in the warp repeat divided by the total space (p r1) hi Kpl=- .... (3.2) occupied by the warp repeat as a whole, i.e. SI 72 GALUSZYNSKI: STRUCTURE AND TIGHTNESS OF WOVEN FABRICS • • K;, + «. /·9 ,., "1 f·Z /., ••••_- 'lor;' NJ c{;.'-_ •.• 1'0 Fig. 4-Hamilton's limiting fabric geometry and yam balance the ratio between minor di- ... (3.3) p, ameters of flattened weft and warp threads: Here, s is the thread spacing at intersection within ... (3.5) the partial geometry (Fig. 3), and b, the minor di- ameter of flattened thread. Using the appropriate values of a ip or 1/ a ip ln Hamilton's:' notation, s is identified as P j, KPi as Kl, and Kp2 as KI· and p, K PI + K P2 limit is read from Fig. 4 and t ln the ~ase of plain weave, the weave repeat in is calculated from Eq. (3.1). both warp and weft directions consists of two When dealing with non-plain weave fabrics the equal intersection units, so the intersection spacing first step is to calculate values of pi I and P i2 given is equal to the average thread spacing for the yam by: sheet as a whole. Thread spacing for the partial geometry is thus given by: pi= ~ (Pr- f Pi) ... (3.6) n, 1 s = PI -(a- b), and the corresponding cover factors by: where n i is the number of intersection units per weave repeat; nf' the number of float units per b, b2 weave repeat; P,., the space occupied by the weave Kpi = - and Kp2=- repeat as a whole; P f' the thread spacing for float 51 h unit; and suffixes 1 and 2 denote warp and weft Fabric balance a jpo the ratio between warp and respectively. weft threads cover factor, is given by: Thread spacings for the partial geometry 5 are then calculated as s= pi-(a- b); and for partial KPI ... (3.4) warp and weft cover factors = h/s!, Kp2 = bZ/s2, fabric balance, a ipo is obtained from Fig. 4 and fabric tightness t is calculated from Eq. or (3.1 ). from Eqs (3.2), (3.3) and (3.4) Russells put forward a definition of a 'construc- tion factor', t, which indicates the fabric tightness ... (3.4a) in Hamilton's meaning to describe the fabric struc- ture: 73 INDIAN J. TEXT. RES., VOL. 12, JUNE 1987 where ... (3.7) ... (3.14) where u=H1-g) ... (3.15) ... (3.8) nTex1 x Tex, Tex = ------'----"-- ... (3.16) nl Tex, + nz Tex. ... (3.9) Here, K 4, is a coefficient depending upon the raw Here, N is the actual number of threads per unit material and count system; Tex, the average yam length in the fabric; N, .the theoretical maximum count; NI, the unknown value of the warp sett; N2, number of threads per unit length in the fabric; the unknown value of the weft sett; n, the total Nr,the number of threads in the weave repeat; d, number of threads in the weave repeat; nl,2' the the yarn diameter; and I, the number of intersec- numbers of threads of a defined count within the tions per thread in the weave repeat. weave repeat; TexI,2' the defined counts of threads The value of the yarn diameter (mm) varies within the weave repeat; F, the average weft or with raw material, yarn twist and yam tension, but warp float of the weave; m, a first coefficient de- is taken here as pendent on the weave; and g, a second coefficient dependent on the weave. From the above equations a new set is put for- ... (3.10) ward, so the actual square fabric sett, N a' of a particular fabric can be calculated: where K3 is the constant which varies with the raw material (Table 1). NJ Some of the values of K 3 are given in Table 1. N=-a U · .. (3.17) W Both formulae, especially the latter, do not make a precise distinction between weaves with or from Eqs (3.14) and (3.15) the same average number of intersections or corresponding limiting value. Hence, a new set of · .. (3.18) equations was proposed", where Brierley's? setting formula is incorporated into the calculation.
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