Original Paper

Prediction of Curling Distance of Dry-Relaxed Cotton Plain Knitted Fabrics Part 1: Theoretical analysis of moments on the loop that force the fabric to curl

Nuray Ucar

Istanbul Technical University, Faculty of Mechanical, Textile Engineering Department, Taksim, Istanbul, TURKEY *Current Address: Georgia Institute of Technology, 801 Ferst Drive, School of Textile&Fiber Engineering, Atlanta, Georgia, 30332-0295, USA

Abstract Prediction of curling distance of dry-relaxed cotton plain knitted fabric has been realized by using multiple regression analysis. One set of the parameters that are used in the multiple regression analysis is the moments on the loop that force the fabric to curl. There have been several studies of the moments on the loop, but the models developed are too complex for practical use. Thus; in the present study, moments on the loop have been determined by means of Castigliano Theorem, which leads to a more usable model. The following results have been obtained: (1) Simple formulas for the moments, M~ and M, , These formulas depend on fabric and yarn parameters, such as

course-wale spacing, yarn diameter and bending rigidity of yarn. MY is the moment that affects the bending and side-curling behavior around the oy axis (Figure 5a). M, is the moment that affects the bending and top/bottom-curling behavior around the ox axis (Figure 5a).

(2) Good agreement between My , M, as presented and those proposed by Postle and Munden was observed[11](My 0.0367 g cm- 0.04 g cm and M, : 0.1896 g cm- 0.175 g cm).

(3) Equations 20, 23, 25 and Table 1 and also previous studies [1,2,4,5,7,8,10,1 11 show that the values of My, and M, increase as the tightness factor and bending rigidity of yarn increase. The values of moment around ox axis, M, , are higher than those around oy axis, M,..

1.Introduction

As mentioned, many of studies about the curling

tendency of knitted fabrics[',2,4°5,710,11,14] have been conducted. The studies about curling tendency of plain-

weft knitted fabric can be classified as experimental or

theoretical. The experimental studies present the relationship between fabric properties and curling

tendency for several different fabrics[2,4,5,'41 In the theoretical studies, the calculations of moments on the

loop, which force the fabric to curl, are performed[7's,'0-'2] PnwPVPr nntna of thPCP Ct11d1PC give anv infnrmatinn

11V ti

about V ~ Vl, l1VlIVling Vl V11V1V uVNMlvv ~a . v w+.J +..~v+++•».. .. .. the cur distance of fabrics. Thus; before

production, it was not possible to predict the curling distance (cm.) of fabric. The aim of this study is to predict the curling distance of plain knitted fabrics, before

production, instead of curling tendency. With this type of model, it will be possible to calculate material loss due to curling during garment preparation and the curling tendency of the knitted fabric structure will be based on this curling distance. Multiple regression analyses have been done using the results of experimental and theoretical study. The experimental study and regression analysis will be presented in Part 2, while the theoretical study is

presented in the present paper. In the theoretical study, moments on the loop that force

fabric to curl have been once again determined by means of Castigliano's Theorem, because of the complexity of

past models[7'8"o,l'] As mentioned in the summary, there are several studies, which present equations for the

moments on the loop, but they are too complex for

practical use. Thus; in the present study, the moments are defined by very simple formula, which are functions of fabric and yarn parameters, such as course-wale spacing [9,12] yarn diameter and yarn bending rigidity . These are

parameters, which are known, before fabric production. The loop length can be determined (for a given number of courses and wales per unit length[121) and yarn diameter, bending rigidity can be measured or calculated, before

production. It was necessary to validate the use of Castigliano's Theorem. Thus, the values of the moments calculated by Castigliano Theorem have been compared with others[7'8'10' "]. It has been seen that the values are very close to those developed by Postle and Munden[ "]. As mentioned, moments on the loop that force fabric to curl will be used in multiple regression analysis presented in Part 2. The following sections will describe the theoretical development of the equations for the force and moments, which cause the fabric to curl.

2. Analysis of force that bends the yarn out

of fabric plane

In a dry-relaxed state, scale forces act on the loop in a knitted fabric. These forces arise from tension acting on the structure during knitting, from jamming and also from changing the straight yarn into a loop by bending and twisting. Energy on the loop resulting from these forces causes a many problems such as shrinkage, curling and spirality. Figure l a and Figure l b show a two dimensional

109

schematic of the loop (Oxy plane). The actual loop in the fabric is a three-dimensional structure (Figure 1c). While section BE of the loop is bent downward, section BN is bent upward, by the forces which arise from the interactions with neighboring loops (Figure 1 c, id). This gives a three-dimensional structure. When the fabric is cut,

the interactions between the sets of loops at the edges the fabric are removed and the loops try to move into two-dimensional form and curling begins,14].

of

a

Fig. 1: (a) Schematic illustration of loop in two-dimensional,

(c) Schematic illustration of loop in three-dimensional(b) Schematic illustration of interlocking region in the yox plane , (d)Schematic illustration of interlocking region in the yoz plane

110 J. Text .Eng.,

Several assumptions have been made in the development

of the theory presented here. They are as follows:There is no jamming The yarn has a circular cross-section and is thin, i.e. it has a cylindrical rod shape Frictional forces between loops and between fibers in the yarn weight of the yarn has been neglected

The loop has been taken as a combination of circular arcs and straight lines (Figure 1 a, ZY, AB and DM are circular arcs, YA and BD are straight lines). The loop is assumed to be symmetric, i.e. only a

quarter loop is analyzed (SJ, Figure la). All points shown in Figure 1 are placed in the center of yarn. At point E, the yarn passes from the bottom of the fabric to the top and the yarn at point N forms a neighboring loop (Figure la, lc, id). Points E and N are at the center of intersection region (Figure 1b). There is bending out of fabric plane (oz direction) on sections BE and BN of the loop, because of the yarn

pass each other in this area (Figure ic, id). The bending of sections BE and BN of the loop begins from point B. At point B, two neighbor yarns are side by side (Figure 1 b, id). Hence; there is no bending out of fabric plane at point B (zero displacement) and the force at point B which acts in the oz direction is zero. However, the force increases from point B towards point E and N, and there is distributed load between point B and E, between point B and N

(Figure id). The resultant force of distributed load, Fz , is shown in Figures id, 2a, 2b. The resultant forces of distributed force (FZ ) acts on points E 1 and N 1 points(Figure l d, 2a, 2b). This distributed load can be linear or

parabolic. Because the length of E1B will be similar whether it is linear or parabolic, this distributed load has been assumed to be linear for simplicity (E1B = 2 x EB/3) (Figure id). The same argument can be used for point N1, because of symmetry. In the model (Figure 2a); support has been set at point

B, since there is no any displacement towards z direction (Figure id, 2a). Thus; at point B, there is a force( FB ) resulted from support(Figure 2a.). The same is valid for other part because of symmetry (FD)

Displacement in the oz direction of point E (supported on point B), due to distributed load is equal to d/2 (yam diameter/2)(Figure 1 d, 1 c) (This is

also valid for point N). The distance in the z direction between point S and point E is zero (Figure 1 c).

Hence; displacement in the oz direction of point S

(supported on point B) is equal to d/2 (yam diameter/2)(Figure 1 a, c). FH which is absent in reality

has been applied to point S for displacement of point S as dig , according to Castigliano's Theorem(Figure

2a). As seen in Figure 2.a, the loop can be divided into seven regions:

IMRII: first region, IR1DI: second region, ~DP1: third region, JP1N1J: fourth region, ~N1BI: fifth region, ~BE1J: sixth region, IE1SI: seventh region

Accord

El 5 Z

ing to Castigliano's Theorem (Figure 2a.);

=[ 1 Me , aMe x d ~ x y ] regions a F H

(l)

where: E: elastic modulus of yarn c, w: course and wale spacing, respectively(Figure 2a)(c=1 /C, w=1 /W, C, W: number of course and wale per unit length of fabric, respectively) R: radius of circular section of loop (GOBI, in Figure 2a., see Appendix) d: yarn diameter l: the length of the section where forces is placed(Figure l d, Figure 2a, see Appendix) I : moment of inertia = ir • d4 l 64 bZ : displacement in the z direction (at point S, it equals to d/2) Me X : bending moment around x axis

regn

Fig.2 (a) forces in the z direction between points S and M, (b) distributed load at the interlocking region

Vol. 46, No . 4 (2000) 111

*For First Region, Second and Seventh Region,

Respectively

R-(2.113) J Me x1 '

0

2.113

j Me x2 '

0

aMe xl

aFH

aMe x2

dy = 0

aFH.dy=0

(2)

J Me x7

0

aMe x7

aFH• dy = 0

*For Third Region

FD is calculated by taking a moment about point

B , thus Equation 5 is obtained

(3)

FH . R FD = -

FD+FB=FH

C

(4)

(5)

(6)

Equation 7 is obtained by substituting equation 5 into

equation 6

FB=FHC1+RJ

c

Equation 8 is obtained by a balance of moments.

Mex3+Fp•y-FJ •C 31+y~=0

Mex32

= FZ • -3

y l+yl-Fo.

By substituting Equation 5 into Equation 9

R

C21 1 FHR y Mex3 =FZ 3 +y)+ C

Me 3

aFH

R =-y

C

C 2.l 1 FH =O~Mex3 =FZ 3 +yJ

(7)

(8)

(9)

(10)

(11)

(12)

By substituting Equation 11 and Equation 12 into the

general equation, Equation 13 obtained,

112

2.1/3

f Me x 3 '

0

Me 3

aFHdy=F_ 5

6

R

C

2•l

3 J3I*For Forth Region

Equation 14 is obtained by a balance of moments

(13)

Mex4+Fz y+FD. 2 l +y-Fz4 l +y= 0 3 3

(14) The same method used to derive the equation for the third region is applied for forth region and Integral equation

(equation 15) is obtained.

1

0

Mex4 'aMex4

aFHdy = FZ .

41

3

41

3

R

C

R

C

21

3

1C

2

( 4l c- 3 +

41 l 2 C--

3 3

*For Fifth Region

Equation 16 is obtained by a balance of moments

Me5 +F y+F c- 4' + + x Z Z ~ y

FD C-?l +y-F(C+y)=0 Z

3

Applying same method

gets Equation 17,

21/3

f Mex5 '

0

aMex5' dy F

Z

as before

aFH

to the fifth

R 4l 2l 1

c 3 3 2

1 2l 2

2. 3 )

region

(is)

(16)

one

R 41(21 C 3 3

1 2l 3

63)

*For Sixth Region

Equation 18 is obtained by a balance of moments

Mex6 +FB •y+FZ •C 3 +y I+FZ •C +Fp •(c+y)-FZ •Cc+ 3 +yJ=O

21 c- 3 Y

X211

JJ

(17)

(18)

J. Text . Eng.,

The same method used before yields Equation 19. FB is

obtained from equation 7.

21/3

j Me z 6

0

o Me z 6

3FHdz = F z

1

2

•R.( 1 C

6

2112

3

2l

3 J3

Equation 20 is obtained by substituting of Equations 2,3,4,13,15,17,19 into Equation 1

. E I S_ =F..

+ F_

+F:•

+F

(19)

\3

6 R (2i 4l R 21 41ll 41 R 1 411 2 C3•c•3Cc-3JI+3•c'2•Cc-3l CR 31c 311-~R 3`C3112

~•R•Cl2 31J J - [ •C3 6~D3 JI (20) The length of R and l have been calculated in the Appendix (see Appendix.). I is calculated using Equation 21. bZ is equal to d/2 (yarn diameter/2) at point S. Thus; FZ is calculated by using Equation 20. The relation between Fz and fabric tightness factor has been shown in Figure 3. In this study; the diameter (d) of the yarn has been

calculated by using the specific gravity of cotton fiber (p = 1.52 gc _m__3 for rcotton~6l) and linear density of the yarn

(Tex), i.e.; (d=(4 ' Tex 1314000 • p) 0.5), instead of the equation shown by Shinn~131. Calculating diameter in this way yields a smaller value than that given by Shinn's equation (for example 0.013 cm.- 0.019 cm.~131 for 30 Ne, cotton). In this analysis the calculated diameter is

preferred, since it is closest to the diameter of a pure fiber assembly (without bulky or air). It is thought that the

points between the loop, where the forces and moments are acting, in the knitted fabrics behave as fiber assemblies, with little or no bulk. In this analysis, it was necessary to measure the bending

rigidity of cotton yarn. But, because a pure bending tester is not available for measuring of yarn bending rigidity, Equation 22~3~ has been used to find the approximate value of B (bending rigidity of cotton yarn) (Figure 4a). Thus; the measurement structure shown in Figure 4b has been proposed. One end of yarn is clamped on a support (A).

Vol.46, No . 4 (2000)

The other end of the yarn has been placed on support (B) whose surface has been polished to minimize friction, allowing the yarn to easily slide by means of its own weight. A scaled mirror has been placed behind the supports to enable the reading of the deflection (b). A scale has been placed at the mid point of AB (Figure 4b). The distance between mirror and supports is 2 mm. It has been avoided from being too long length of yarn on the support B (less than 2 cm, Figure 4b.). Otherwise; it will cause frictional force against to sliding although the surface of supports has been polished. The distance between supports has also been set to neither too long also nor too short (10 cm., Figure 4b). Otherwise, too long distance between supports can cause to fall down of yarn from the support (B), due to yarn's weight. Too short distance between supports can cause considerable amount of unravel of twist of the short yarn and also, deflection

(b) can be very small for sensitive reading. To see the amounts of unravel of twist from the yarn; a yarn of length 25-cm, was removed from the bobbin and placed into the clamp of the device that is used to measure the twist amount in the yarn. Another sample of yarn from the same bobbin (about 27 cm) was hung for 1 minute, with only one end of yarn clamped (Figure 4c). After 1 minute; the amount of twist remaining in the yarn has been measured at the same device. 10 measurements have confirmed that the difference in twist amount between yarn that is not hung and yarn that is hung is negligible. Thus; when all these conditions have been taken into consideration, the length of yarn on the support B was set to 2 cm. and the distance between supports (A and B) was set to 10 cm.

In this way; the bending rigidity (B) for the 20 Ne (29.5 Tex) cotton yarn has been determined to be 0.8x102 gcm2. This is the average of ten measurements. It is necessary to validate this value by comparing it with the other B values from the literature. However, there are some difficulties with comparing this value with other B values at the literature, because the properties of the used in this study do not match those of the yarns used in the literature (they vary in linear density, twist and also fiber type). Consequently, to see the degree of approximation; this value has been compared with the value presented by Postle and Munden1"~ (B=1.2x10"2 gcm2 for 88.6 Tex worsted knitting yarn). When these two values (0.8x10"2

gcm2 for 29.5 Tex cotton knitting yarn and 1.2x10"2 gcm2. for 88.6 Tex worsted knitting yarn ) are compared with each other, it is hypothesized that the worsted knitting yarn will have less twist than cotton knitting yam, since the yarn linear density of worsted yarn is higher than that of the cotton knitting yarn. And also; the elastic modulus of the wool fiber is some lower than that of cotton fiber~6l. Thus, the bending rigidity of worsted knitting yarn can be expected to be somewhat lower than that of the cotton knitting yarn. But, at the same time, the bending rigidity of worsted knitting yarn can be expected to be somewhat higher than that of the cotton knitting

113

yarn, since its linear density is higher than that of the cotton knitting yarn. When these situations are considered, it has been determined that the calculation of Equation 22

gives a reasonable approximation to the value of bending rigidity. As seen from Equation 20, FZ depends on the yarn diameter, course-wales spacing and bending rigidity of

yarn (d,c,w,B(E I), respectively). As pointed out by previous studies and seen from Equation 20 and Figure 3, FZ will increase as the elastic modulus of the yarn(E) and tightness factor(K) are increased. In Figure 4 and Equation 22; where, b: displacement, q: weight of yarn per unit length, BE I(bending rigidity of yarn)

I : moment of inertia = f' d4 / 64 (21)

_ 9 ,1x4

S

-2•L S .x3 +LS •x (22.

3. Moments causing the curling of dry-relaxed plain knitted fabrics

Loop head and loop legs are bent out of fabric plane by FZ force (Figure 5a). This bending causes an accumulation of energy on the loop. Thus, when the fabric is cut, curling at the edges begins with the discharging of this energy. At the top and bottom edges of fabric, curling occurs from the back to the front, however, at the sides of the fabric, curling happens from the front to the back (Figure 5a, 5b)"141. ~As known, this is due to bending rigidity for negative curvature being lower than the corresponding value for positive curvature, when the bending moment is applied around the axis parallel to the courses. For negative curvature, the face of the fabric is on the concave side of the bent fabric. The opposite is true for positive curvature. The bending rigidity for positive curvature is lower than the corresponding value for negative curvature, when the bending moment is applied around the axis parallel to wales~2,4,51As pointed out by Hamilton and Postle~51, when the axis of the bending moment is applied parallel to the courses , two of the yarns belonging to the loop leg in each loop are deformed. For the alternative case, only one yarn in each loop is deformed. Thus, it can be said that the value of the moment about the x axis(parallel to courses) can be higher than the value of the moment about y axis. When the loop leg moves out of the fabric plane, both torsion and bending are applied on the loop~''8"0""~. As seen from Figures 6a and 6b, the force FZ will move the point Na from the E level to the N level. Thus, FZ will cause torsion about the oy axis along a circle with radius d, at point E. The magnitude of this torsional moment is approximately FZ • d. There is also a bending moment about oy axis. The magnitude of this bending moment is FZ GW (Figure lb and 6c) (GW=2 GU, see appendix). Thus, the effective moment about oy axis is My and it is

given as follows:

M y = ~(F_ .d)2 +(F _ • IGW I)z (23)

My is the moment that affects the bending and side-curling behavior about the oy axis(Figure 5a-5b). The

Fig. 4 Measurement bending rigidity of yarn

(a) general prencible, (b) measuring system (c) unravel of twist from yarn

Fig. 3 Relation between FZ and tigthness factor (K= fEiex / L, L: loop length , Tex cm')

114 J. Text . Eng.,

moment that tends to bend the loop out of fabric plane around the oy axis has been calculated by Postle and Munden, to be 0.04 g' cm. for worsted knitted fabric(l/d=17.1, 2x44.3 tex yarn, l:loop length, d:yarn diameter)"1. Using Equation 23; the moment has been calculated to be 0.0367-g cm. These values are very close to each other. Bending moment at the point E will bend point E, about the ox axis at point N, (Figure 1 c, id, 6c). The magnitude of this bending moment is FZ EZ (Figure 6c and 1 b)(EZ= 2' EG, see appendix). The bending moment about the ox axis has been shown by Mx1 and it is as follows:

Mx1= FZ EZ (24)

MX =2 • MX 1= 2 • FZ EZ (25)

There is similar bending moment (Mx1) at point T

(Figure la, 5a). Hence, MX (Equation 25), is the moment that affects the bending and top/bottom-curling behavior about the ox axis(Figure 5a-5b). The moment that tends to bend the loop out of fabric plane about ox axis has been calculated by Postle and Munden, to be 0.175 g cm. for a worsted knitted fabric (l/d=17.1, 2x44.3 tex yarn, l:loop length, d:yarn diameter)'. Using Equation 25, this moment has been calculated to be 0.1896-g cm. Again, these values are very close to each other. Since it has been found that the value of the moment

determined by Equations 23 and 25 (0.0367-g cm. , 0.1896-g cm) are very close to values (0.04-g' cm., 0.175-

8 cm.) developed by Postle and Munden', Equations 23, 25 will be used during the multiple regression analysis in Part 2. Also, it should be noted that it is enough to know the yarn count to determine yarn diameter, loop length that is determined before fabric production (for number of courses and wales per unit length~121) and bending rigidity of the yarn(B=E.I) to be able to calculate FZ , MX , My by Equations 20,23 and 25. Thus, values of the force and moments can be easily calculated before knitted fabric

production, by simply knowing some yarn properties that are easily obtained before fabric production.

As seen from Equations 20, 23 and 25 and previous studies1''2'4'5'''8"°" 11, the values for the moments will increase as tightness factor (Table 1) and bending rigidity of yarn are increased. As seen from Table 1 and from

previous studies"2,4,5,7,8,10,11], the values of the moments about the x is are higher than the values of the moments about the y axis(MX is bigger than Mr).

Fig. 5: Curling behavior,

(a) the effects of moments, (b) curling of fabric

Vol. 46, No . 4 (2000) 115

4. Discussion and Results

In this part of the study, the moments on the loop that affect the curling distance have been once again determined by means of Castigliano Theorem. Thus, the moments could be defined by very simple formula (Equation 20,23,25), by using known fabric and yarn parameters before fabric production. To validate the values for these moments; they have been compared with values developed by Postle and Munden~11~. The calculated moment values are very close to those developed by Postle and Munden~' 1]( 0.0367 g cm- 0.04 g cm and 0.1896 g' cm- 0.175 g cm.). As seen from Equations 23, 25, 20 and from previous studies~124578 ,,10,111 the values of the moment will increase as tightness factor (Table 1) and bending rigidity of yarn are increased. As seen from Table 1 and from previous studies"2°4,5,7'8°'0"11, the value of the moment about the ox axis are higher than the values of the moment about the oy-axis(MX is bigger than My. My is the moment that affects the bending and side-curling behavior around the oy axis. MX is the moment that affects the bending and top/bottom-curling behavior about the ox axis).

APPENDIX

The real loop shape can be described by elliptical and helical lines, instead of the circular arc and straight line model shown in Figure l a~710 ° 11] However, the mathematical calculations based on the model of Figure 1 a are easier to use than a elliptical and helical line model. Also, at section 3, it has been shown that this kind of assumption does not greatly affect values of the moments

(0.0367 g• cm and 0.04 g cm --- 0.1896 g cm and 0.175 g cm.). Hence, geometrical calculations have been made using the model shown in Figure 1 a and l b.

Table 1 Moments value

Fig. 6 Yarn motion from E level to N level

116 J. Text . Eng.,

As seen in Figure 1.b,

EG 1 OB and line EF is parallel to the loop leg F is at the center of the yarn

B is at the center of the yarn

(OBI HOEI = R - w/4 +d/2 (26)

tan a= d I c (27)

+IFGI IOGI=C4 - ~) (28)

IEGI _ ~I0EI2 _ IOG2 I11 (29)

Equation 30 is obtained by substituting Equation 26 and Equation 28 into Equation 29,

IEGI- ~C~+~\z-C~_~+IFG\2(30)

vl tan a

(31)

By Substituting Equation 27 into Equation 31,

~FGI JEG=- ~ (32) d/c

Equation 33 is obtained by combining Equation 30 and Equation 32,

J ~ (33)

IFGI is calculated from Equation 33 and it is substituted into Equation 32. Thus, Equation 34 is obtained.

(EG)=1=

d

w2 +4d2 w 1 d-2+2

4wd + 8wc2d

(d2 2 +c

c

(34)

The difference between the length of EG and the length of EB is very small (BEG-EBB=0.005 cm. for d:0.039 cm., c:0.13 cm., w:0.176 cm.). Also, the difference between the length of EG and the length of BN is very small (JEG-BNI=0.002 cm. for d:0.039 cm., c:0.13 cm., w:0.176 cm.). To reduce the number of parameters that must be

calculated, it has been assumed that they are equal to each other and are given by 1, i.e.;

(EGG=IEBI=IBNh/

As seen from Figure 1 b;

GU= FU -FG (35)

FU = d/2 (36)

FGA calculated from Equation 33 and IFUI are substituted into Equation 35. Thus, Equation 37 is obtained.

GU =-2

2 2 1w2+4d2 d3-d w+d 2

2 2+4wd+8wcd

2d2 +2C2(37)

References [1] I. Davis, J.D. Owen, Journal of the Textile Institute, 62,p.181(1971)

[2] H.M. Elder, T.H. Somashekar, Journal of the Textile Institute ,66, p. 49(1975)

[3] J.M. Gere, S.P. Timoshenko, Mechanics of Materials, Third Edition, PWS-Kent Publishing Company- Boston (1990)

[4] V.L. Gibson, R. Postle, Textile Research Journal , 48, p.14(1978)

[5] R.J. Hamilton, R. Postle, Textile Research Journal, 44, p. 336(1974)

[6] Harris Handbook of Textile Fibers, published by Harris Research Laboratories, Washington DC, (1954)

[7] B. Hepworth, G.A.V. Leaf,The Shape of the Loops in an Undeformed Plain Weft-Knitted Fabric, in "Studies in Modern Fabrics"(edited by P.W. Harrison), the

Textile Institute, Manchester,(1970) [8] B. Hepworth, G.A.V. Leaf,Journal of the Textile

Institute ,67, p.241(1976) [9] DL. Munden, Journal of the Textile Institute, 50,

p.T448(1959) [10] R. Postle, D.L Munden, Journal of the Textile

Institute , 58, p. 329(1967)

[1 1 ] R. Postle, DL. Munden, Journal of the Textile Institute, 58, p.352(1967)

[12] R. Postle, Journal of the Textile Institute , 59, p.65, (1968)

[13] WE. Shinn, Textile Research Journal , 25, p.270, (1955)

[14] F. Weisse, J.H. Dittrich, 0. Wiedmaier, G. Buhler, Melliand Textilberichte, 76(3), p.136 (1995)

Vol. 46, No . 4 (2000) 117