11 Fabric Geometry

8/2/2019 11 Fabric Geometry

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1. Concept: One of the main characteristics of fabric is the

density of yarns or yarn spacing. But in some cases,

such as filter fabrics, for example, this

characteristic is not sufficient, because the space

between the adjacent threads also depends on the

yarn thickness. The yarn diameter should be taken into

consideration.


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It is common to calculate warp cover and weft

cover separately:

o

oo s

de !

y

yy s

de !

yoyof eeeee !Fabric cover:


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The cover reaches the maximum value when the

threads cover the whole fabric area, i.e. d=s,

therefore e=1. It gives the scale from 0 to 1.

The warp spacing SO gives PO threads per unit

length:

o

o

sP

1!

y

y

s

P1

!

and the number of weft threads per unit length is

determined as


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2. The percentage cover

The cover can be calculated in percentage:

100s

dE!


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3. The cover and yarn

linear densityIn practice, we usually deal with yarn count or

linear density. That is why it is advisable to

introduce following terms and use them in

calculations

(only for cotton yarn, the density of yarns in the fabric is 0.91 g/cm3)

Where Tis the yarn linear density in g/km.

6.26/)( Td mm !


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Developing the formula of fractional cover, we

have:

Where S is the yarn spacing in mm; d, the yarn

diameter in mm;P, the density of threads per 10 mm.

266/10// TPPdsde !!!


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4. The cover factorIn the Tex system the product of threads per cm

and the square root of linear density are called

the cover factor

TPK !


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Note: there is a distinction between cover factor and

cover. The former is a conventional measure of the

closeness of setting of the threads running in one direction.The latter signifies the actual efficiency of the yarns in

closing up the cloth. The cover of a cloth may be judged by

the appearance of the cloth when held up against the light,

and it depends not only on the number of threads per cmand their linear density but also on their regularity,

hairiness, fiber composition, twist, and the cloth finishing

processes.


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Any irregularity in construction, as for example in

the uniformity of the spacing of the threads, tendsto reduce the lever of cover. Cover factor is

calculated from only two of these quantities and,

therefore, cant provide a complete indication of

cover.

Cover factor is, however, useful in making

comparisons.


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5. Example:A cotton fabric of plain weave has the following

characteristics: warp 25 tex, 28 ends/cm; weft 15

tex, 30 picks/cm; density of yarn 0.91 g/cm3.

Calculate the warp and weft fractional covers,

fabric cover, warp cover factor and weft cover

factor.


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Warp cover:

Weft cover:

Fabric cover:

= 0.526 + 0.437-0.526 0.437 = 0.733

Warp cover factor

Weft cover factor

526.0

266

2528

266

!!!oo

o

TPe

526.0266

1530

266!!!

yy

y

TPe

yoyof eeeee !

14025/28 !!! ooo TPK

11615/30 !!! yyy TPK


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11.1 Fabric Geometry1. concept:

The spacing relationship of fabric parameters is called fabric

geometry. See Fig. as following.


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2. The purpose of studying

fabric geometry:Knowing the fabric geometry, various problems

can be solved and explained. Such as:

design the fabric with a determined crimp

know warp threads or weft threads will be broken first

the maximum density

fabric thickness the characteristics of the fabric surface

the length of warp and weft needed for a unit lengthfabric


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3. Methods of studying

To build a

geometry model:Assume that the warp

and weft threads haveconstant diameters.

On the diagram in Fig.B ,C on the right, theplain weave fabric isshown.


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4. Analyze the geometry

diagram1) Studying the plan

of the fabric at A Fabric cover can becalculated:

The maximum e is 1. In

this case, the threads are soclosely that they touch oneanother (see the figurebelow).

sde /!


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2) Studying the sectional

diagram below:The axis of the weft thread 1 at B is shown by the

wavy dotted line. The axis wave can be

characterized by the

height or amplitude, hy,

the length, and the

angle of inclination tothe central plane, ty


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3) Studying the sectional

diagram at C The axis of warp thread 2 is shown by the wavy

dotted line.

Comparing the shape of this warp axis with the

shape of axis of the weft thread at B in the figure

we can see the difference in heights of the waves,

i.e. hy is greater than ho. This indicates thedifference in the warp and weft crimps. The weft

crimp, cy, is greater than the warp crimp, cy .


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4) Studying the sectional view

at B and CIt is possible to estimate the maximum theoretical

density of threads. The density of warp threads is

determined by the distance between the axis of theadjacent threads ofO1 and O2 at B. The minimum value

ofOland O

2is :

do + dy

In this case the maximum theoretical density of warp

threads

2

2max min

1 1 1O O

O y O

P Sd d h

! !


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5) Studying the sectional view

at D The axis contains the straight part and two arcs of the circle

of diameterD= do + dy, we can find that there is a certain

relation between ho and hy. The warp displacement, ho,

decreases with a increase of the weft displacement, hy, and

vice versa. The sum of warp and weft displacement is

constant for the given fabric and equals the sum of threads

diameters:

oor ho y o y yh h d d D D h ! ! !


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A mutual position of the warp and weft threads in the fabric

can be characterized by the value of the phase of fabric

construction, which id calculated as a ratio of the warpvertical displacement and the sum of the yarn diameters:

The value of phase varies from 0 to 1. a variety of different

phases can be studied within this range, to simplify thecalculation, it was suggested by ProfessorN.G. Novikov to

consider only nine mutual positions of threads in the square

set fabric.( 1 2 3 4 5 6 7 8 9 )

hor F=1- yo

hF

D D!


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the warp and weft crimps, CO

and Cy;

the distance between the axis of adjacent warp

and weft threads,KO

andKy;

The maximum densities of warp and weft threads,

POmax andPymax;

The warp and weft relative covers, eo and ey;


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the angle of inclination of warp and weft threads to the

central horizontal plane of the fabric, to and ty;

the angle of inclination of the line connected

with the axis of warp and weft threads, to the

central horizontal plane of the fabric, uo and uy;

The thickness of the fabric;

The characteristics of the fabric surface;


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1) the warp and weft crimps, CO

and Cy

o y

O

y

l s

C s

!

y o

yo

l s

C s

!

max(min)

1oo

P s!

2 2minos D h!

max 2 21

oP

D h

!

2 2

O O oK S h!

3)

2)


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Home work A cotton fabric of plain weave has the following

characteristics: warp 15 tex, 50 ends/cm; weft

25 tex, 25 picks/cm, density of yarn 0.91 g/cm3.

Calculate the warp and weft fractional covers,

fabric cover, warp cover factor and weft cover

factor.

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11 Fabric Geometry