Indian Journ al of Fibre & Textile Research Vol. 24, December 1999, pp. 253-257

Calculation of jute yarn diameter and cover factor of commercial jute cloth

B Chatterjee"

Co llege of Textil e Technology, Berhampore 742 10 1, India

Received 13 Jalll/C/l y 1998; revised received alld accepted 3 1 Ma rch 1999

Based on the criti ca l analysi s of the in fo rmati on avai labl e in literature, a reaso nable va lue of constant h~I S heen fou nd out for the calcu lation of yarn diameter in jute cloth fro m the value of gri st. Using Peirce 's geo metry of th e cloth stru cl ure. the boundary of the closest construction of jute cloth has been shown and the zones of typ ica l sack ing and hess i ~1Il clol hs arc identifi ed for engineering simil ar structure.

Keywords: Bulk density, Cover factor, Hessian cloth , Jute sack ing cloth , Yarn di ameter

1 Introduction

The geometrical theory of the cloth structure pioneered by Peirce l has been applied to the cloths produced from cotton, woollen and worsted yarns and a successful guiding principle for engineering as we ll as understanding the behav iour of the cloth structure has been established . Thi s theory can be applied to the cloth produced from other textil e fib res more accurately when a suitabl e va lue of the bulk density of the constitutive yarn is obtained. The present work, having obtained the bulk density, deals with finding out a formula to calcu late the di ameter of jute yarn and subsequentl y app lying it for calculating the cover of commercial jute c loth structure.

2 Calculation of the Diameter of Jute Yarn

There ex ists a good corre lation between the diameter of yarn , when assumed circu lar c ross­section, and its linear density expressed in a suitable system. This re lationship for jute yarn could be expressed I as:

... ( I )

where d is the di ameter (inch) of circu lar cross­section of yarn; C, the linear density (Ib/spyndle); and v, the spec ific vo lume of yarn (c m' /g). The sum of the diameters of warp and weft threads calculated from Eq . ( I) using a suitable va lue of v is taken as the bas is of scale unit in Pe irce's geometrical theor/ . Hence, the choice of a suitable value of specific vo lume of the jute yarn constitutes a fundamental exercise for

a Present address: 2A, Kali charan Dutta Road , Calcutta 700061 , India

the app lication of the theory. A detailed d isc ussion is therefore made based on the ava ilabl e informati on from lite rature to arrive at a cho ice o f a suitab le value of v.

Having understood the necess ity o f a suitable bulk density of jute yarn , W ood house and A lexander" carri ed out an ex periment to ca lculate the de nsity o f jute yarn in diffe rent conditi ons of pac kage and the values are g iven in Table I . He fir st calc ulated the diameter by using the bulk density o r 0.48 (1I v)

obtained from the yarn on weaver's bea m and the following formul a:

d=C tl2 184 ... (2)

A plain and nearly square c lo th was produced from

4/4 Ib jute yarn with II porte rs x 12 shots . Thi s construction was worked out fro m As hcnhurst' s c lo th setting theory" of perfectl y sq uare jammcd c loth . Bul it was observed that the c lo th was not in a sta le o r maximum tex ture and understood that a c loth coul d be made with the same porte rs and shots but from thicker or heavier yarn . Thus , it was co ncluded that eithe r the constant 84 or the bulk de nsity 0.48 should

Table I-Density and packing fraction ofj ul l! yarn in difrcren l packages2

Jute in different condition Conciilion;iI Packing densilY fr~lc tion

g/c ill \

Cloth in press-packed bale o.n O . ..!7

Fibre in press-packed ba le 0.6X 0,-1-1

Cloth in roll for lll 057 (U7

Yarn on weaver's beam OAX 0 . .1 1

Yarn in spool or cheese fo rm 0.55 (U4 \

Yarn in cop form 0.53 OJ4

254 IND IAN J. FIBRE TEXT. RES. , DECEMBER 1999

be increased. Woodhouse and Alexander2 also obtained the diameter of jute ya rn equal to CI12/1 08 and the bulk density of jute yarn was assumed to be 0.80. The constant" was al so found to be 89 in connect ion with li ghtl y wound roll of cloth made from warp and weft ya rn s of approxi mate ly equal count. Warps and wefts per inch were found to be approximately 12 based on the Eq. (2), whereas it is actually poss ible to introduce with difficulty a little more than 18 threads each way . By increas ing the constant value to 126 (d=C '/2/126), it was observed that there was considerable difficu lty in weavin'g 17 porters (= 18.38 threads/in .) cloth and its production wou ld have been imposs ible if ya rn was not excessively good or strong. It was concluded that for best quality with clean and strong 16 Ib/spyndle yarn, the max imum number of warps and wefts per inch with a reasonable production of cloth from the loom appears to be 17 or approximately of 16 porters (= 17.30 threads/in .) cloth . Based on thi s va lue of threads per inch for square jammed cloth, a new value of constant was found to be 120 and the formu la could be written as:

... (3)

The corresponding bulk density calculated from Eq . ( I) was 0.98. To produce 212 twill jammed square cloth from 4/4 Ib jute ya rn , a good agreement2 was also found when Eq. (3) was used for calculating the diameter.

Table 2--Calcu lated densi ty of commerci al jute yarnS

(Tex)'/2t p cm Packing fract ion Ca lcu lated densit y, g/cm'

17 .0 0.52 0.77

25 .5 0.59 0.87

29.5 0.64 0.95

Grosberg3 also described a general formula to calculate the diameter of a ya rn of an y fihre:

d= 1.75x I 0-.1 (tex/fibre density) IIC in . . .. (4)

The constant when cal cul ated using ;1 mClli;ln val ue of pack ing fraction of 0.65 as stated hy Gros berg is fo und to be 11 8 and the corres pondin g theo reti ca l bulk density is 0.95. Us ing the standa rd packing coeffici ent value~ of 0.59, the fo rmula CLlIJ be written as d=C I12/ 11 3 and the corresponding bulk densit y is found to be 0.87. The similar order of packing fraction of jute yarn with (Tex)lI~ t p Clll ranging frolll 20.0 to 32.2 for commercial jute y;trIJ was also obtained by Sur5 (Table 2). The different constants found in d-C relationship are give n in Table J . It is ev ident th at the fo rmul a given in Eq . ( 3) would thus give a most reasonable es timate of jute y;lrll in a cl oth as it was obtained throu gh severa l correct ions to make the cloth setting theoretica l data to fit the experimental observation. Furthermore. th e extent of deviation from the formu la obtained by Grosberg's generalized equati on is found to be the least amo ng all formulae. The density of jute ya rn obtained frolll the Grosberg's approach lies with in the ran ge of va lues" where the yarn is not used in cloth. Co nt ra ry to it , the density obtained from Eq. 0) is hi gher when the jute yarn is used in jammed cloth structure. ju stil"ying the use of thi s va lue for ca lculati on of d i ~lll l e t er more reasonable.

3 Cover Factor of Some Commercial Jute Cloths

One of the most important applicH ti ons of cloth geometry is to calculate the cover rHctor 01" a c loth . In pract ice, this is given by a suitab le factor hased on the proportional area of the fabric COVered by the projection of the threads. In jure system. the cover

Table 3--Constant lor calculation ofjutc yarn diamctcr

Method Constant Packing Spccillc Densit y Commcllt fraction vo lume g/c m"

cm'/g

Peircc 11 6 0.61 1.10 0.91 Based on spccific vo lumc used mostl y for cOltOIl ya rn

Grosberg 11 9 0.65 1.04 0.96 Based 011 gencml formul a from hulk to compl cte filament yarn

Woodhouse 120 0.66 1.02 0.98 Based on pract ical cx pcri c ll cc ;lIld

cxperimcnt ill m~lIl liraC lll rc orj;lIllmcd jutc c101h

Woodhouse 108 0.53 1.26 0.79 Based on pr:lClic:11 ohSC I ' \ ' ~ llioll frolll &Mlinc experimell l

Fabric de- 11 3 0.59 1.1 5 0.87 Based 0 11 slambrd p~ l c kill i-' c{)c li"icl clll sign table valuc

CHATf ERJEE: JUTE YAR N DIAMETER & COVER FACTOR OF JUTE CLOTH ') - ~

-))

factor K c o u ld be calcu lated by mU ltip ly ing th reads one face of the c lo th to the o the r. The c lo th cove r K, per inch by the square root o f yarn linear d e n s ity is g iven by :

(lb/spynd le). If p is the spacing be tween the th reads, Kc= KI+K2-KIX K1/120 ... (6)

the n by us ing Eq . (3) . 1/7

... (5) w he re KI and K1 are the wa rp and weft cove r factors K=nC -= 120d/p respecti ve ly g ive n b y th e Eq. (5). The cover facto rs o f

It appears from Eq. (5) th a t w he n the cover fac to r som e commercia l jute c lo th s !> were c alcu late d and a re

IS 120, t he thread mus t to uc h where they cross fro m g ive n in Table 4. It is unde rs tood fro m Tab le 4 that. ill

Table 4-Cover factor of jute cloth

Sampl e Fabri c quality" Porters Linear density Cover fac tor Cloth cove r factor /3 No. xShots (warpxweft ) (K 1x K2) (K,.)

Ib/spyndle

Cuban sugar SxS S.50x 24.6 S2.l x37.7 9 1 0.)5

2 D.W. Nitrate plain 5x8 IOx29 34.2x43. 1 65 : 0.)5

3 English corn sacks Sx8 IOx30 54.7x43.S 79 o.:n -4 E. twill s 5xS IOx22 51 .3xS7.5 7.1 .043 ' 5 G.S . heavy twill Sx9 IOx46 S2.0x61.0 101 "1)22

6 G.S. light twi ll 7xS IOx23 71 .Sx3S.4 '807 11.4)

7 L. twill SxS IOx30 S2.0x61 .0 96 o:n S B. twill 6xS IOx3 2.7 61.5x45.5 X4 (n l

9 A. twill 8x9 IOx2S .9 S2.0x54.& 100 Ins 10 Hycees plain Sx9 IOx3 2.5 54.7x54.5 X2 - 0) I

II Hycees li ght 8x9 IOx30 54.7x43.8 7<) o.:n 12 Sugar twill s 6xS IOx30.7 6l.5x44.3 ~n o. :n 13 G.S.60 6xS IOx29.6 6l.5x61 .0 ~n 0.)4 14 Hess ian bag ' ll x l2 8.25x I2 . 1 34.2x4 1.7 64 0.68 15 Hessian bag II x l2 S.25x I2.8 34.2x42 .9 65 .') 0.65 16 Cotton packs 9x lO 8.25x I0.9 280x33.0 5:1 - 0.76 17 Cotton packs 9x<) 8.25x8.4 28 .0x23.2 46 0.9H 18 Hessian 8xS S.25xS.9 24.Sx23.9 4X.X 0.9:1 19 Hessian <)x8 S.25xS.7 27.9x23.6 46.0 0'<)5

20 Hessian 9x9 8.25x24.<) 27.9x24.9 47.0 oln 21 Hessian II x l2 8.25x9.6 34.2x37.3 flO.<) 0.85 22 Hessian II x l4 8.25 x I0.0 34.2x44.& 65.<) 0. li2 23 Hessian II x l4 8.25x I4.5 34.2x53.4 72.4 0.57 24 Cloth obtained from ISx lS IOx lO 6 1.5x56.9 8<) .2 1.0

Woodhouse' s experiment

25 -do- Il x l l 16x l6 47.6x44 74.2 1.0 26 -do- t2x l2 16x l6 5 1.9x48 7') . 1 1.0 27 -do- 13x l3 16x l6 56.2x52 H 9 1.0 2S -do- 14x l4 16x l6 60.5x56 gX.3 1.0 29 -do- 15x l5 16x l6 64.9x60 92.5 1.0 30 -do- 16x l6 16x l6 69.3 x64 ')6 .:1 III 3 1 -do- 17x l7 16x l6 73.5x68 ')')') III 32 -do- 18x lS 16x l6 77.Sx72 103. 1 1.0 33 Same as No. 24. 2/2 twill 12x l9 4/4x4/4 104x76 11 4. 1 1.0

d oth

34 -do- 19x20 4/4x4/4 95xSO 11 1.7 1.0 35 -do- IOx22 4/4x4/4 86.5xS8 111.1 1.0

"Trouble experienced during weaving sample Nos. 31 & 32

256 INDI AN J. FIBRE TEXT. RES. , DECEMBER ISl9'J

general, the cover factor of the sacking cloth is higher than that of the hess ian quality cloth and the warp cover factor of sacking cloth is always higher than the weft cover fac tor. Thus, the sacking cloth is warp faced type justifying the necess ity of using a relati ve ly better quality thread in warp directi on than in weft direction . In hess ian quality, the difference in warp and weft cover factors is low even though in some cases the weft cover factor crosses the warp cover factor. So, the better qu ality of both warp and weft is always required to be used in the production of hessian fabrics which is already found in practice . The data also show that the carpet backing quality is almost of square one, ~~dicating the importance of using good quality yam- 111 both warp and weft directions.

4 Closest Construction of Jute Cloth It is known from Peirce ' s cloth geometrical theory'

that the closest constructi on for both directi ons can be given by:

{i -( p, I D)2}"2 +{I -( p21 D)2}"2 = I .. . (7)

For plai n woven jute cloth , the relationship can be written as: [1 - {1 20,81 KJ I + ,8 ) }2]"2

... (8) + [I-{120IK

2(1+,8 ) }2]'12 = I

where ,8 = (C, I C2),,2 and C1 & C2 are the linear

densities (lb/spyndle) of warp and weft threads

1201..--·-,.....---..,.",---,---,--,.--------,

1'90 n: o f­u « U-

n: lJ.J > 6 0 o U

f-u-LJJ

~

3 0

Hess ion

OL------~~----~~------~90n---~120 o 3 0 6 0 WARP COVER FACTOR(K l )

Fig. I~over fac tor of j ute cloth with l imiting cu rves fro m clos­est constructi on

respectivel y. For a given va lue of ,8, the Eq. (8) when plotted in Fig. I gives ri se to a bounded region of feasible structures generated by the curv' obtai ned from Eq. (8) and of K1= 120, K2=1 20 includi ng the point of ori gin . For ,8=1, i.e . Iblspynd lc is same along warp and weft directi ons , Eq. (8) heco ll1 e.~ :

(1 - 36001 K,2)"2 + (I - 36001 K~ ) '12 = I ... (9)

For square j ammed jute cloth. the co ver I'actor would then be KI=K2=69 .3. In an ex periment made hy Woodhouse2

, it was fo und tha t in 16 porters nearl y square cl oth , as also given in Tabl e 4. the cover factor in warp direction is equal to the theo retical lim iti ng value, while along weft it is very c lose to the theoretica l li miting va lues. So, it represent s a state or c losest constructi on of the c loth . In 17 and 18 porters square cloth s, the cover fac tors vvhi ch exceed the theoretical limit ing va lue ( 120) result ed in ex treme di ffi culty during weav ing2 when attempts were made to insert the more number of threads per inch beyond the limit of closest construc ti on. Thi s type or phenomenon is obvious as it is evieicl lt I'rom Fig. I that the tightness, as defined by the nearness of fab ric to the maximum sett 7

, reaches a hi gh order. For twill wea ve (3 harness, 2/ 1), the equation or closest construction4 would be: [I - {(3601 K", - 1)( ,8 /2( 1 + ,B))}2]"2

+ [I-{ (360IK,,2 - 1)(1/2( 1+ ,8 )) }2],, 2 = I ... ( 10)

where Kal and Ka2 are the co ver factors or \ovarp and weft when the average spacin gs or threads in ~ I wea ve repeat are used in calcul ati on. II' /3= I. for squ are closest constructi on, K,,/ = K,,]=80.7. sho win g 16.YI'c increase in limiting cover compared to th at of plai n closest constructi on and indicating the effect of fl oat by the degree of ease with whi ch more number of threads per inch could be in serted th an woul d he possible in case of plain weave.

A similar exercise is ca rriecl out to obtain the equation for closest 212 twill con s t rllc t i o n ~ and it can be written as:

[I - {( 2401 K", - 1)( ,8 1( 1 + ,8 )) }' r +[I-{ (240IK"2 - 1)( I/( I + ,8)) }2],,, = I

.. . ( I I )

where Kal , Ka2 and ,8 have th e sallle meanings as described earlier. For ,8= I and for ~ I square closest construction, Ka,=Ka2=87.8. Thi s value is hi gher th an that for 211 weave due to the increase in hi gher fl oat length . This value is very c lose to a nearl y square cloth (212 twill) produced from 414 I b/s pynd Ie wa rp and weft threads in the ex periment carri ed out by

CHATIERJEE : JUTE YARN DIAMETER & COVER FACTOR OF JUTE CLOTH 257

Woodhouse2. Having pl otted a ll these cover factors in

Fig. I, it is found that there are distinct zones which can be identified for the c lass of hess ian and sacking cloth and fabric produced in Woodhouse's experiment2

. In general, :t is seen that the sack ing cloth has higher value of warp cover factor (64-82) and varied va lues of weft cover factor (37-60). Thi s variation is required for the purpose of packing different sizes of grains. But for hess ian, the warp cover factor (30-37) is much lower while the weft cover factor lies between 22 and 60. This results in an

moderately open to c lose structure . The {3 values of these commercial cloths range from 0.22 to 0 .95. For hessian, {3 is higher (0.67-0.98) than that for sacking cloth (0.22-0.45). It is clearly seen from Fig. I that the commercial jute cloths of these two varieties are far from the limiting curves of jammed cloth structure for

the corresponding values of {3.

T he data obtained by Woodhouse2 (for (3 =1 ) show the attempts systematica ll y made to produce the jammed square cloths, the last two (Nos 31 & 32) of which exceed the cover factor va lues obtained from the theoretical boundary of closes t construction. This corroborates the condition of weaving when the maximum trouble was experienced2

, indicating the difficulty in achieving such value of cover in practice. Some values of the cover factor of 2/2 twill weave

cloth ({3=I) produced in the Woodhouse's experimene are also ploted in Fig. I and show the structure crossing the boundary of limiting curve of plain weave to a large extent but nearer to the boundary of similar curve of 2/2 twill weave with (3= I of square jammed structure.

5 Conclusion

Based on the practi cal observati on and theoretica l formula made by Grosberg fo r a general case. a suitable formul a [d( inc h)=(C( lb/spy ndk ) 11121120 j to calcul ate the di ameter of jute ya rn has been obtained. It is then used to calcul ate the cover factor of some commercial jute cloth s. T he theore ti cal cover of j ammed cloth has a lso been obtained and its application in understanding the ti ghtness of ju te cl oth is explained . For plain square jammed c loth . the cove r factor is found to be 69.3, for 211 twill it is 80 .7 and for 2/2 twill it is 87 .8. The zones for two mai n c lasses of jute fabric , viz. Sacking and hess ian . are also ident i fi ed.

Acknowledgement

The author is grate ful to Late Dr. P.c. Dasgupta , Ex-principal, In stitute of Jute Techn ology. Calcutta, for allowing to use the library for the work .

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3 Hearle J W S. Gro~crg P & B:lckc r S. Slnf('llImllll<'c'lio llics

ojjibres, yam s alld ./idJrics. Vo l I (Wil ey- lllt erscicIl L'e. Ne w York ). 1969.

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5 Sur D. Some .I'll/dies all [li e S[melll l' O/jll[(' r{lm ill r('lar inl1 10

irs physical charac[eris[ics. Ph D thesi s. Universit y ()f Cal­culla, 1978.

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