Structure and Tightness of Woven Fabrics

Indian Journal of Textile Research Vol. 12, June 1987, pp. 71-77

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 fabric 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 being 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 indicates 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 fabric 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 indicate the fabric structure (Appendix 1). The par- p ameter which indicates fabric structure is the coefficient of fabric tightness, which depends on yam raw material, linear density (count), weave and fabric 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 proportion of the fabric area covered by actual yarn", In practice, cover factors are calculated for warp KI and weft K2 independently, being given, respectively, 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

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 ,.,

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 diameter 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 'construction factor', t, which indicates the fabric tightness ... (3.4a) in Hamilton's meaning to describe the fabric structure:

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. Brier- Having the theoretical maximum and actual va- ley's formula for the theoretical maximum square lues of the square fabric sett, the fabric tightness, fabric sett, N, states that: 1, is determined by

· .. (3.19) ... (3.12)

Some of the values of K4 (giving a number of and warp sett: threads per 10 em), m, g are as follows for yarn NI = Nw» ... (3.13) count in tex;

Values of K4 = 1354.4 for wool = 1283.9 for polyester-wool (55/45) Table 1- Values of K 3 for various yarns = 1528.6 for cotton. Yam Value of K3 Cotton 0.0392-0.0398 Values of g(suffix 1 denotes warp and 2 weft}: Viscose, cotton like 0.0389 Worsted, wool-polyester 0.0398 if FI = F2 g= - 21.3 Worsted, fine wool 0.0402 Worsted, coarse wool 0.0417 or if FI > F2 g= - 21.3 Woollen 0.0430 or if FI < F2 g= - 312 Filament viscose (crepe) 0.0326 Filament viscose (warp) 0.tJ379 or for weft cords g= - 2 Filament polyamide 0.0474 Values of m (1-warp, 2-weft)

74 GALUSZYNSKI: STRUCTURE AND TIGHTNESS OF WOVEN FABRICS

(1) F\=F2 and between two different fabrics: plain weave and hop sacks 0.45 0.39 ~= twill (~)4 ... (3.21) satins and sateens 0.42 Wry tv• (2) broken twills where subscripts x and y denote fabrics x and y N\=fiJ2);N2=fiFJ) 0.39 respectively, and K 5 constant. (3) long and short floats 0.42, add 7-8% to calcu- Applying Eq. (3.21) to the weaves used in the lated values experiment (Fig. 5) and taking the value of Wr for the plain weave as 100%, it is apparent that, for (4) diagonals: FJ = F2 0.51 the same fabric sett: FJ #- F2 0.42 take greater value of F into calculation - Wr for a 2/2 weft-faced rib is about 72% of the value for plain weave, (5) combined warp weaves 0.365, take FJ into calculation - Wr for a 2/1 warp-faced rib is about 50% of the value for plain weave, (6) combined weft weaves 0.31 " " " - Wr for a 2/2 warp-faced rib is about 37% of the (7) warp cords 0.42 value for plain weave, (8) weft cords 0.35 " "" " - Wr for a 2/2 matt weave is about 28% of the (9) crepe weaves 0.42 " value for plain weave, and (10) ribs: - Wr for a 2/2 twill is about 31% of the value for weft ribs; plain weave. 2/1, 2/2 and 2/3; 0.35 F-average for weave, Comparison of the above with the experimental g= -2/3 values in Fig. 4 shows a close agreement. warp ribs; The other published set of values of the weav- 211,2/2 and 2/3; 0.35; F\; g= - 2/3 ing resistance for different weaves is that of Ch'en other ribs; as cords. Jui-Lung", who dealt with plain weave, twills and If the coefficient of fabric tightness, or fabric diagonals. A distinction between the last two kinds tightness, is taken to indicate the fabric structure, of weaves was made by Brierley, who showed fabrics with the same values of the coefficient them to have different values of the relevant coef- should have the same, or closely similar, values of ficients. When the appropriate values of Brierley's some of their properties. coefficients are used together with Eq. (3.21) the calculated values of W,., in terms of the plain 4 Fabric Tightness and Fabric Properties weave, give close agreement with Ch'en Jui-Lung's results (graph): Considering some of the fabric mechanical properties, e.g. elastic modulus, weaving resistance 2/2 twill: from the equation 31.0%, from the (the force which acts against the reed during beat- graph 31.0%; up), in terms of published data, the following facts 0 - emerge: Wr , (N) 0 - 2 - 3 A'" - 4 4.1 Weaving Resistance r- 0 - 5 • - 6 Values of the weaving resistance, W,. for cotton- 0·8 •

Vincel fabrics (in different weaves and ~oven on a 0·6 MAV loom), shown in Fig. 58, support the propo- sition that the values of the coefficient of fabric 0·4 tightness can be used to assess fabric properties. o 2 The results also verify the prediction that fabrics with the same value of the coefficient should have I• the same value of relevant properties. In this case, fabrics with the same value of t have the same va- Fig. 5-Effect of fabric tightness (t) on weaving resistance (w,) lue of W,.,and the relation between tand Wris: for various weaves: (1) plain weave, (2) 212 weft faced rib, (3) 2/1 warp-faced rib, (4) 212 warp-faced rib, (5) 212 matt, and ... (3.20) (6) 212 twill

75 INDIAN J. TEXT. RES., VOL. 12,JUNE 1987

4/4 twill: from the equation 9.7%, from the graph tion has to be given, i.e. weave. But, if the fabric 11.0%; structures for various weaves have to be defined, the only parameter is fabric tightness. In graphical 1/3 diagonal: from the equation 24.3%, from the form the fabric tightness would give one curve, graph 24.0%; whereas cover factor would 'give a family of curves 3/5 diagonal: from the equation 6.0%, from the where each weave would be represented by a dif- graph 8.3%; ferent curve. A simple relation between fabric structure, de- 2/6 diagonal: from the equation 6.0%, from the scribed by fabric tightness, and its properties al- graph 6.3%; lows the prediction on the fabric properties in Thus, his findings support the calculations and terms of structure, or to defme the structure for conclusion that fabrics with the same value of t prescribed properties. should have the same value of weaving resistance, Calculation of fabric tightness does not require which is not applicable when the fabric cover fac- any additional measurements apart from fabric tor is used instead of tightness. There can be a sett, weave, yarn count and raw material. Cover case where the cover factor would be equal to 1.0, factor, if yarn flattenings are included, requires or greater than one, and W, zero (no intersections) measuring of minimum and maximum yarn diame- because t would equal zero. ters. The examples given show the superiority of the 4.2 Fabric Elastic Modulus fabric tightness over the cover factor as the par- The next parameter to be considered for assess- ameter to describe the fabric structure, especially ing the application of the coefficient of fabric when fabric properties are referred to its structure. tightness is fabric elastic modulus, E, and for this purpose the results obtained" for cotton-Vincel fa- References brics are used. The results (Fig. 6) show that fa- 1 The Oxford English Dictionary, Vols IV and X (Clarendon bric elastic modulus in warp direction depends on Press, Oxford, England) 1961_ the coefficient of fabric tightness, and the relation 2 Peirce F T, J Text lnst, 28 (1937) T45. between the parameters can be described by the 3 Hamilton J B, J Text Inst, 55 ( 1964) T66. linear equation: 4 Kemp A, J Text Inst, 49 (1958)T44. 5 RussellHW, TextInd,129(1965)51. E=K6t+K7 ... (3.22) 6 GaIuszynski S, J Text lnst, 72 (1981) 44. 7 Brierley S, Text Mfr, 57 (1931) 3; 78 (1952) 349. where K 6 and K 7 are constants. 8 GaIuszynski S, The effects of fabric structure on beat-up resistance in weaving, Ph 0 thesis, University of Leeds, In a similar way the fabric tightness can be used 1978. to assess the effect of fabric structnre on some 9 Ch'en Jui-Lung, Technol Text Ind USSR, 2 (1960) 79. other fabric properties such as seam slippage, sew- ability, dimensional change, etc. Appendix 1- Examples of Calculation of Fabric Tightness and Cover Factor 5 Summary Both the cover factor and fabric tightness can Cotton fabric, warp and weft 22 tex x 2, N, = 200 ends per be applied to identify the fabric structure; how- 10 em, Nz = 190 picks per 10 cm; Assumption: the yam has a circular cross-section. ever, when the former is used, additional informa- Plain Weave 0_ 1 A- 2 Fabric Cover Factor: 0- 3 Weft cover factor from Eq. (2.2) •• - 4 • - 5

Yam diameter (dz) from Eq. (3.10) and Table I

dz = K /C= 0.0395 144 = 0.262 mm I I__~I ~I ~I +-__-+I -+. II 0-5 0-6 0-7 0-8 0-9 P-IC kspacing, snaci pz =- 100 = 0.524 mm 190 Fig. 6 - Effect of fabric tightness (t)on fabric elastic modulus (in 0.262 warp direction); (I) plain weave, (2) 212 weft-faced rib, (3) 2/1 K2 =--= 0.500 warp-faced rib, (4) 212 warp-faced rib, and (5) 212 matt 0.524

76 GALUSZYNSKI: STRUCTURE AND TIGHTNESS OF WOVEN FABRICS

Warp cover factor from Eq. (2.1) Fabric tightness t,

t= 193.9/230.4 = 0.841 K=~I PI

Yarn diameter d I is equal to d, since the same yarn is used 212 Twill for warp and weft. The fabric cover factor remains unchanged, being equal to 0.702 but the fabric tightness obtains a new value. . 100 Actual fabric square sett from Eq. (3.18) and value of g for Warp spacing, P I = - = 0.500 mm 200 Ft= F2;

0.262 04 06 K =--=0.524 Nu=200 x 190 = 19304threads/lO cm I 0.500 Theoretical maximum fabric square sett from Eq. (3.12) Fabric cover factor from Eq. (2.4) 39 N = 1528.6 x 2° / j44 = 302.0 threads/lO cm

K= KI + K2 -KI K2= 0.524+0.500-0.500xO.524=0.702 Fabric tightness from Eq. (3.19)

Fabric Tightness t= 193.4/302.0=0.640 which is different than that for the plain weave. Na t=- N 3/1 Diagonal Actual fabric square sett is calculated from Eq. (3.18) Fabric cover still unchanged, and equal to 0.702, and the ac- Na = NI~~g-I)N2 HI- 8) tual fabric square sett from Eq. (3.18)

Nu= 193.4 threads/lO em Warp float FI is equal to weft float F2, so Theoretical maximum fabric square sett from Eq. (3.12) and g= -21.3 m=0042.

N, = 200( - 2/3}/( - 213-I) X 1901/(1 + 213) = 20004 X 1900.6 N= 1528.63°42 j44 = 365.5 threads/lO cm

= 193.9 threads/l0 em. Fabric tightness from Eq. (3.19) Theoretical maximum fabric square sett from Eq. (3.12) t= 193.4/365.5 = 0.530 The above examples show how delusive the fabric cover K F'" factor is in comparison with the fabric tightness. All three fa- N- 4 - !fu brics have the same sett so they have the same value of fabric cover factor, but they have different structures due to the 0 45 1528.6 X 1 . weaves, and this is shown through the variation of the fabric N= 23004 threads/l0 em j44 tightness.