unit Ⅲ fabric design chapter eleven 11.1 fabric geometry 11.2 fabric cover and cover factor

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UNIT Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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Page 1: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

UNIT Ⅲ Fabric Design

Chapter Eleven 11.1 Fabric Geometry11.2 Fabric cover and cover factor

Page 2: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.

Page 3: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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

Page 4: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor
Page 5: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

It is common to calculate warp cover and weft cover separately:

o

oo s

de y

yy s

de

yoyof eeeee Fabric cover:

Page 6: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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:

oo s

P1

yy s

P1

and the number of weft threads per unit length is determined as

Page 7: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

2. The percentage cover

The cover can be calculated in percentage:

100s

dE

Page 8: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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

(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.

6.26/)( Td mm

Page 9: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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

Page 10: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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

TPK

Page 11: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.

Page 12: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.

Page 13: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.

Page 14: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

Warp cover:

Weft cover:

Fabric cover:

= 0.526 + 0.437-0.526 × 0.437 = 0.733

Warp cover factor

Weft cover factor

526.0266

2528

266 oo

o

TPe

526.0266

1530

266 yy

y

TPe

yoyof eeeee

14025/28 ooo TPK

11615/30 yyy TPK

Page 15: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

11.1 Fabric Geometry

1. concept:The spacing relationship of fabric parameters is called fabric geometry.

See Fig. as following.

Page 16: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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 length

fabric

Page 17: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.

Page 18: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

4. Analyze the geometry diagram

1) Studying the plan of the fabric at A

Fabric cover can be calculated:

The maximum e is 1. In this case, the threads are so closely that they touch one another (see the figure below).

sde /

Page 19: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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 to the central plane, ty

Page 20: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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 the difference in the warp and weft crimps. The weft crimp, cy, is greater than the warp crimp, cy .

Page 21: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

4) Studying the sectional view at B and C

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 + 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

Page 22: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

5) Studying the sectional view at D

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:

o or ho y o y yh h d d D D h

Page 23: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor
Page 24: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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:

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 )

h or F=1- yohF D D

Page 25: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor
Page 26: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor
Page 27: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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;

Page 28: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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;

Page 29: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

1) the warp and weft crimps, CO and Cy

o yO

y

l sC

s

y oy

o

l sC

s

max(min)

1o

oP s

2 2minos D h

max 2 21

oPD h

2 2O O oK S h

3)

2)

Page 30: UNIT Ⅲ Fabric Design Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor

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.