Transcript Document

UNIT Ⅲ
Fabric Design
Chapter Eleven
11.1 Fabric Geometry
11.2 Fabric cover and cover factor
1. Concept:
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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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The relative closeness of threads depends on the
density of threads and their diameters.
See Fig. 11.3, the warp spacing is So, the weft
spacing Sy, the diameter of warp thread do and
that of weft dy. The fractional cover e is defined
as the fraction of the fabric area covered by the
threads, i.e. e = d/s
It is common to calculate warp cover and weft
cover separately:
eo 
Fabric cover:
do
so
ey 
dy
sy
e f  eo  e y  eo e y
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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
1
length:
Po 
so
and the number of weft threads per unit length is
determined as P  1
y
sy
2. The percentage cover
The cover can be calculated in percentage:
d
E  100
s
3. The cover and yarn
linear density
In 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
d ( mm )  T / 26.6
(only for cotton yarn, the density of yarns in the fabric is 0.91 g/cm3)
Where T is the yarn linear density in g/km.
Developing the formula of fractional cover, we
have:
e  d / s  Pd / 10  P T / 266
Where S is the yarn spacing in mm; d, the yarn
diameter in mm; P , the density of threads per 10 mm.
4. The cover factor
In the Tex system the product of threads per cm
and the square root of linear density are called
the cover factor
KP T
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 cm
and their linear density but also on their regularity,
hairiness, fiber composition, twist, and the cloth finishing
processes.
Any irregularity in construction, as for example in
the uniformity of the spacing of the threads, tends
to reduce the lever of cover. “Cover factor” is
calculated from only two of these quantities and,
therefore, can’t provide a complete indication of
“cover”.
Cover factor is, however, useful in making
comparisons.
5. Example:
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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:
Po To
28 25
eo 

 0.526
266
266
ey 
Py Ty
266

30 15
 0.526
266
Fabric cover: e f  eo  e y  eo e y
= 0.526 + 0.437-0.526 × 0.437 = 0.733
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Warp cover factor K o  Po To  28 / 25  140
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Weft cover factor K y  Py T y  30 / 15  116
11.1 Fabric Geometry
1. concept:
The spacing relationship of fabric parameters is called fabric
geometry. See Fig. as following.
2. The purpose of studying
fabric geometry:
Knowing the fabric geometry, various problems can
be solved and explained. Such as:
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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 length
fabric
3. Methods of studying
To build a
geometry model:
Assume that the warp
and weft threads have
constant diameters.
On the diagram in Fig.
B ,C on the right, the
plain weave fabric is
shown.
4. Analyze the geometry
diagram
1) Studying the plan
of the fabric at A
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Fabric cover can be
calculated:
e  d/s
The maximum e is 1. In
this case, the threads are so
closely that they touch one
another (see the figure
below).
2) Studying the sectional
diagram below:
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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 to
the central plane, ty
3) Studying the sectional
diagram at C
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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 the
difference in the warp and weft crimps. The weft
crimp, cy, is greater than the warp crimp, cy .
4) Studying the sectional view
at B and C
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It is possible to estimate the maximum theoretical
density of threads. The density of warp threads is
determined by the distance between the axis of the
adjacent threads of O1 and O2 at B. The minimum value
of Ol and O2 is :
do + d y
In this case the maximum theoretical density of warp
threads
1
 1
 1
PO max
SO min
d
2

d

h

O
y
O
2
5) Studying the sectional view
at D
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The axis contains the straight part and two arcs of the circle
of diameter D= 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:
ho  hy  do  d y  D or ho  D  hy
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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 warp
vertical displacement and the sum of the yarn diameters:
hy
ho
F
or F=1D
D
The value of phase varies from 0 to 1. a variety of different
phases can be studied within this range, to simplify the
calculation, it was suggested by Professor N.G. Novikov to
consider only nine mutual positions of threads in the square
set fabric.( 1 2 3 4 5 6 7 8 9 )
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the warp and weft crimps, CO and Cy;
the distance between the axis of adjacent warp
and weft threads, KO and Ky;
The maximum densities of warp and weft threads,
POmax and Pymax;
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;
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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)
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3)
the warp and weft crimps, CO and Cy
l y  so
lo  s y
Cy 
CO 
so
sy
K O  SO 2  ho2
Po max 
 1
Po max   1
so(min)
D2  h2
so min   D 2  h 2
Home work
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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.