structure and tightness of woven fabrics -...

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

Structure and Tightness of Woven Fabrics

S GALUSZYNSKIaSchool 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 examplesare given to show the applicability of the recommendation.Keywords: Cover factor, Fabric tightness, Woven fabric

1 IntroductionThe properties of a woven fabric depend on its

structure, the properties of the fibres and yarn be-ing used, its dimensional changes during the finish-ing process, etc. In published literature on wovenfabrics, the fabric properties are discussed interms of fabric geometry or structure without anexplicit distinction between these two terms.Geometry indicates the values of the relevantgeometrical parameters, whereas structure indi-cates the manner of construction, i.e. the recipro-cal interlacing between the warp and weftthreads I.

In some publications the fabric structure is indi-cated by fabric cover factor, or cover factor, or fa-bric cover, which are taken to mean the samething. The calculation of the fabric cover factordoes not incorporate weave intersections andtherefore this parameter should not be used to in-dicate the fabric structure (Appendix 1). The par-ameter which indicates fabric structure is the coef-ficient of fabric tightness, which depends on yamraw material, linear density (count), weave and fa-bric sett. The aim of this paper is to introduce theterm 'fabric tightness' in comparison with fabriccover factor.

2 Fabric Cover FactorThe 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 warpKI and weft K2 independently, being given, re-spectively, by the proportion of fabric areacovered by the yarn in that particular sheet. Thus,

'Present address: SAWTRI, P.O. Box 1124, Port Elizabeth,RSA

from Fig. 1, fractional warp cover factor, K I, forcircular yam cross-sections, is given by:

K,=d,PI

... (2.1)

and fractional weft cover factor, K2, by:

K =dz2 pz

Fabric cover factor, K,

K= d2Pl+ d,P2_ d,d2P,P2 PIP2 P,P2

or from K, and K2•

K=K,+K2-K,K2

p

-I

... (2.2)

.. . (2.3)

... (2.4)

i--+-Fig. 1- Area covered by yam

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b

a

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

Fig. 2- Kemp's racetrack model of flattened yarn: a- majordiameter, 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 weftrespectively.

When dealing with flattened threads the abovecover factors are calculated- in terms of the majoryarn diameter a (Fig. 2) of flattened thread andthread spacing p;

«, = E..!PIa2K2=-P2

Also, in the case of flattened-thread, there is adifference in the value of the major yarn diameter,a, due to the weave and fabric sett. Hamilton"proposed a procedure and equations to calculatethe cover factor for a fabric woven in a weaveother than the plain weave in terms of non-limit-ing and limiting conditions.

With non-limiting conditions, where no distor-tion of the racetrack" (Fig. 3) occurs, the calcula-tion of cover factors is the same as for the plainweave given by Eqs (2.4), (2.5) and (2.6).

With limiting conditions where the effective ma-jor diameter, ii, is less than a, and equal:

... (2.5)

... (2.6)

a=a-O,lborii = a- 0,215 b

... (2.7)

... (2.8)

depending on weave, cover factors are calculatedfrom the weave repeat as a whole. Eq. (2.8) shouldbe applied to non-plain woven fabrics in weaveswith floats on both sides (e.g. 2/2 matt weave),whereas Eq. (2.7) for weaves with intersectionsone side and float on the other (e.g. 2/2 twill).Fractional warp cover factor, K 1, is given by thesum of effective major diameters of all threads inthe warp repeat divided by the total space (p r 1)occupied by the warp repeat as a whole, i.e.

72

Fig. 3-Hanrilton's fabric geometry

Nr,

Ial1

K=-Pr1

... (2.9)

A similar equation is used for weft cover factorNr,

Iii2I

K=-Pr2 ... (2.10)

and fabric cover factor is calculated by Eq. (2.4).

3 Fabric TightnessWhen assessing the properties of various woven

fabrics, there is' a need to define fabric structureby a single parameter so the effect of fabric struc-ture on its properties could be seen. This needwas recognized-Y and a set of equations havebeen put forward for the calculation of fabrictightness, or the coefficient of fabric tightness" .

Hamilton" (Fig. 3), applying Kemp's" racetrackmodel, defined fabric tightness, t, as follows:

t = (Kpl + Kpz) actual x 100 (%)(Kpl + Kp2) limit ... (3.1)

where the limit is a theoretical maximum valueread from Fig. 4, and

hiKpl=-SI

.... (3.2)

GALUSZYNSKI: STRUCTURE AND TIGHTNESS OF WOVEN FABRICS

/·9• •K;, + «.

,.,"1

f·Z

/.,

••••_- 'lor;' NJ c{;.'-_ •.• 1'0

Fig. 4-Hamilton's limiting fabric geometry

... (3.3)

Here, s is the thread spacing at intersection withinthe partial geometry (Fig. 3), and b, the minor di-ameter of flattened thread.

ln Hamilton's:' notation, s is identified as P j,

KPi as Kl, and Kp2 as KI·ln the ~ase of plain weave, the weave repeat in

both warp and weft directions consists of twoequal intersection units, so the intersection spacingis equal to the average thread spacing for the yamsheet as a whole. Thread spacing for the partialgeometry is thus given by:

s = PI -(a- b),

and the corresponding cover factors by:

b, b2Kpi = - and Kp2=-

51 h

Fabric balance a jpo the ratio between warp andweft threads cover factor, is given by:

... (3.4)

orfrom Eqs (3.2), (3.3) and (3.4)

... (3.4a)

and yam balance p, the ratio between minor di-ameters of flattened weft and warp threads:

... (3.5)

Using the appropriate values of a ip or 1/ a ip

and p, K PI + K P2 limit is read from Fig. 4 and tis calculated from Eq. (3.1).

When dealing with non-plain weave fabrics thefirst step is to calculate values of pi I and P i2 givenby:

pi= ~ (Pr- f Pi)n, 1

... (3.6)

where n i is the number of intersection units perweave repeat; nf' the number of float units perweave repeat; P,., the space occupied by the weaverepeat as a whole; P f' the thread spacing for floatunit; and suffixes 1 and 2 denote warp and weftrespectively.

Thread spacings for the partial geometry 5 arethen calculated as s= pi-(a- b); and for partialwarp and weft cover factors KPI = h/s!,Kp2 = bZ/s2, fabric balance, a ipo is obtained fromFig. 4 and fabric tightness t is calculated from Eq.(3.1 ).

Russells put forward a definition of a 'construc-tion factor', t, which indicates the fabric tightnessin Hamilton's meaning to describe the fabric struc-ture:

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

Some of the values of K4 (giving a number ofthreads per 10 em), m, g are as follows for yarn

... (3.13) count in tex;

Values of K4 = 1354.4 for wool= 1283.9 for polyester-wool (55/45)= 1528.6 for cotton.

... (3.7)

where

... (3.8)

... (3.9)

Here, N is the actual number of threads per unitlength in the fabric; N, .the theoretical maximumnumber of threads per unit length in the fabric;Nr,the number of threads in the weave repeat; d,the yarn diameter; and I, the number of intersec-tions per thread in the weave repeat.

The value of the yarn diameter (mm) varieswith raw material, yarn twist and yam tension, butis taken here as

... (3.10)

where K3 is the constant which varies with the rawmaterial (Table 1).Some of the values of K 3 are given in Table 1.

Both formulae, especially the latter, do notmake a precise distinction between weaves withthe same average number of intersections orcorresponding limiting value. Hence, a new set ofequations was proposed", where Brierley's? settingformula is incorporated into the calculation. Brier-ley's formula for the theoretical maximum squarefabric sett, N, states that:

... (3.12)

and warp sett:

NI = Nw»

Yam

Table 1- Values of K 3 for various yarnsValue of K3

0.0392-0.03980.03890.03980.04020.04170.04300.03260.tJ3790.0474

CottonViscose, cotton likeWorsted, wool-polyesterWorsted, fine woolWorsted, coarse woolWoollenFilament viscose (crepe)Filament viscose (warp)Filament polyamide

74

where

... (3.14)

u=H1-g) ... (3.15)

nTex1 x Tex,Tex = ------'----"--nl Tex, + nz Tex.

... (3.16)

Here, K 4, is a coefficient depending upon the rawmaterial and count system; Tex, the average yamcount; NI, the unknown value of the warp sett; N2,

the unknown value of the weft sett; n, the totalnumber of threads in the weave repeat; nl,2' thenumbers of threads of a defined count within theweave repeat; TexI,2' the defined counts of threadswithin the weave repeat; F, the average weft orwarp float of the weave; m, a first coefficient de-pendent on the weave; and g, a second coefficientdependent on the weave.

From the above equations a new set is put for-ward, so the actual square fabric sett, N a' of aparticular fabric can be calculated:

NJN=-a UW

· .. (3.17)

or from Eqs (3.14) and (3.15)

· .. (3.18)

Having the theoretical maximum and actual va-lues of the square fabric sett, the fabric tightness,1, is determined by

· .. (3.19)

Values of g(suffix 1 denotes warp and 2 weft}:

if FI = F2 g= - 21.3

or if FI > F2 g= - 21.3

or if FI < F2 g= - 312

or for weft cords g= - 2

Values of m(1-warp, 2-weft)


(1) F\=F2plain weave and hop sackstwillsatins and sateens

0.450.390.42

(2) broken twillsN\=fiJ2);N2=fiFJ) 0.39

(3) long and short floats 0.42, add 7-8% to calcu-lated values

(4) diagonals: FJ = F2FJ #- F2

0.510.42 take greater value of F

into calculation

(5) combined warp weaves 0.365, take FJ intocalculation

(6) combined weft weaves 0.31 " " "

(7) warp cords 0.42

(8) weft cords 0.35

(9) crepe weaves 0.42

(10) ribs:weft ribs;2/1, 2/2 and 2/3; 0.35 F-average for weave,g= -2/3warp ribs;211,2/2 and 2/3; 0.35; F\; g= - 2/3other ribs; as cords.

If the coefficient of fabric tightness, or fabrictightness, is taken to indicate the fabric structure,fabrics with the same values of the coefficientshould have the same, or closely similar, values ofsome of their properties.

" " ""

4 Fabric Tightness and Fabric Properties

Considering some of the fabric mechanical pro-perties, e.g. elastic modulus, weaving resistance(the force which acts against the reed during beat-up), in terms of published data, the following factsemerge:

4.1 Weaving Resistance

Values of the weaving resistance, W,. for cotton-Vincel fabrics (in different weaves and ~oven on aMAV loom), shown in Fig. 58, support the propo-sition that the values of the coefficient of fabrictightness can be used to assess fabric properties.The results also verify the prediction that fabricswith the same value of the coefficient should havethe same value of relevant properties. In this case,fabrics with the same value of t have the same va-lue of W,.,and the relation between tand Wris:

... (3.20)

and between two different fabrics:

~= (~)4Wr tvy •

... (3.21)

where subscripts x and y denote fabrics x and yrespectively, and K 5 constant.

Applying Eq. (3.21) to the weaves used in theexperiment (Fig. 5) and taking the value of Wr forthe plain weave as 100%, it is apparent that, forthe same fabric sett:

"

- Wr for a 2/2 weft-faced rib is about 72% of thevalue for plain weave,

- Wr for a 2/1 warp-faced rib is about 50% of thevalue for plain weave,

- Wr for a 2/2 warp-faced rib is about 37% of thevalue for plain weave,

- Wr for a 2/2 matt weave is about 28% of thevalue for plain weave, and

- Wr for a 2/2 twill is about 31% of the value forplain weave.

Comparison of the above with the experimentalvalues in Fig. 4 shows a close agreement.

The other published set of values of the weav-ing resistance for different weaves is that of Ch'enJui-Lung", who dealt with plain weave, twills anddiagonals. A distinction between the last two kindsof weaves was made by Brierley, who showedthem to have different values of the relevant coef-ficients. When the appropriate values of Brierley'scoefficients are used together with Eq. (3.21) thecalculated values of W,., in terms of the plainweave, give close agreement with Ch'en Jui-Lung'sresults (graph):

2/2 twill: from the equation 31.0%, from thegraph 31.0%;

Wr 0 - ,(N) 0 - 2

'" - 3

r- 0 A - 4

• - 5

0·8 • - 6

0·6

0·4

o 2

I •

Fig. 5-Effect of fabric tightness (t) on weaving resistance (w,)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

(6) 212 twill

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

4/4 twill: from the equation 9.7%, from the graph11.0%;

1/3 diagonal: from the equation 24.3%, from thegraph 24.0%;



Thus, his findings support the calculations andconclusion that fabrics with the same value of tshould have the same value of weaving resistance,which is not applicable when the fabric cover fac-tor is used instead of tightness. There can be acase where the cover factor would be equal to 1.0,or greater than one, and W, zero (no intersections)because t would equal zero.

4.2 Fabric Elastic Modulus

The next parameter to be considered for assess-ing the application of the coefficient of fabrictightness is fabric elastic modulus, E, and for thispurpose the results obtained" for cotton-Vincel fa-brics are used. The results (Fig. 6) show that fa-bric elastic modulus in warp direction depends onthe coefficient of fabric tightness, and the relationbetween the parameters can be described by thelinear equation:

... (3.22)E=K6t+K7

where K 6 and K 7 are constants.

In a similar way the fabric tightness can be usedto assess the effect of fabric structnre on someother fabric properties such as seam slippage, sew-ability, dimensional change, etc.

5 SummaryBoth the cover factor and fabric tightness can

be applied to identify the fabric structure; how-ever, when the former is used, additional informa-

0_ 1A - 20- 3•• - 4• - 5

I I__~I ~I ~I +-__-+I -+.I I 0-5 0-6 0-7 0-8 0-9

Fig. 6 - Effect of fabric tightness (t)on fabric elastic modulus (inwarp direction); (I) plain weave, (2) 212 weft-faced rib, (3) 2/1

warp-faced rib, (4) 212 warp-faced rib, and (5) 212 matt

76

tion has to be given, i.e. weave. But, if the fabricstructures for various weaves have to be defined,the only parameter is fabric tightness. In graphicalform the fabric tightness would give one curve,whereas cover factor would 'give a family of curveswhere each weave would be represented by a dif-ferent curve.

A simple relation between fabric structure, de-scribed by fabric tightness, and its properties al-lows the prediction on the fabric properties interms of structure, or to defme the structure forprescribed properties.

Calculation of fabric tightness does not requireany additional measurements apart from fabricsett, weave, yarn count and raw material. Coverfactor, if yarn flattenings are included, requiresmeasuring of minimum and maximum yarn diame-ters.

The examples given show the superiority of thefabric tightness over the cover factor as the par-ameter to describe the fabric structure, especiallywhen fabric properties are referred to its structure.

References1 The Oxford English Dictionary, Vols IV and X (Clarendon

Press, Oxford, England) 1961_2 Peirce F T, J Text lnst, 28 (1937) T45.3 Hamilton J B, J Text Inst, 55 ( 1964) T66.4 Kemp A, J Text Inst, 49 (1958)T44.5 RussellHW, TextInd,129(1965)51.6 GaIuszynski S, J Text lnst, 72 (1981) 44.7 Brierley S, Text Mfr, 57 (1931) 3; 78 (1952) 349.8 GaIuszynski S, The effects of fabric structure on beat-up re-

sistance in weaving, Ph 0 thesis, University of Leeds,1978.

9 Ch'en Jui-Lung, Technol Text Ind USSR, 2 (1960) 79.

Appendix 1- Examples of Calculation of FabricTightness and Cover Factor

Cotton fabric, warp and weft 22 tex x 2, N, = 200 ends per10 em, Nz = 190 picks per 10 cm; Assumption: the yam has acircular cross-section.

Plain WeaveFabric Cover Factor:Weft cover factor from Eq. (2.2)

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

dz = K /C= 0.0395 144 = 0.262 mm

P- k snaci 100IC spacing, pz = - = 0.524 mm190

0.262K2 =--= 0.5000.524


Warp cover factor from Eq. (2.1)

K=~I

PI

Yarn diameter d I is equal to d, since the same yarn is usedfor warp and weft.

. 100Warp spacing, P I = - = 0.500 mm

200

0.262K =--=0.524

I 0.500

Fabric cover factor from Eq. (2.4)

K= KI + K2 -KI K2= 0.524+0.500-0.500xO.524=0.702

Fabric Tightness

Nat=-

N

Actual fabric square sett is calculated from Eq. (3.18)

Na = NI~~g-I)N2 HI- 8)

Warp float FI is equal to weft float F2, so

g= -21.3

N, = 200( - 2/3}/( - 213-I) X 1901/(1 + 213) = 20004 X 1900.6

= 193.9 threads/l0 em.

Theoretical maximum fabric square sett from Eq. (3.12)

K F'"N- 4- !fu1528.6 X 10.45

N= j44 23004 threads/l0 em

Fabric tightness t,

t=193.9/230.4 =0.841

212 Twill

The fabric cover factor remains unchanged, being equal to0.702 but the fabric tightness obtains a new value.

Actual fabric square sett from Eq. (3.18) and value of g forFt= F2;

Nu=20004x 19006= 19304threads/lO cm

Theoretical maximum fabric square sett from Eq. (3.12)

N = 1528.6 x 2°39/ j44 = 302.0 threads/lO cm

Fabric tightness from Eq. (3.19)

t= 193.4/302.0=0.640

which is different than that for the plain weave.

3/1 DiagonalFabric cover still unchanged, and equal to 0.702, and the ac-tual fabric square sett from Eq. (3.18)

Nu= 193.4 threads/lO em

Theoretical maximum fabric square sett from Eq. (3.12) andm=0042.

N= 1528.63°42 j44 = 365.5 threads/lO cm

Fabric tightness from Eq. (3.19)

t= 193.4/365.5 = 0.530

The above examples show how delusive the fabric coverfactor is in comparison with the fabric tightness. All three fa-brics have the same sett so they have the same value of fabriccover factor, but they have different structures due to theweaves, and this is shown through the variation of the fabrictightness.

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structure and tightness of woven fabrics -...

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