Chapter Eleven 11.1 Fabric Geometry 11.2 Fabric cover and cover factor 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.

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: Fabric cover:

The warp spacing SO gives PO threads per unit length: 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: and the number of weft threads per unit length is determined as

2. The percentage cover The cover can be calculated in percentage:

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.

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.

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

Note: there is a distinction between “cover factor” and “cover” 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: 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.

Warp cover: Weft cover: Fabric cover: = 0.526 + 0.437-0.526 × 0.437 = 0.733 Warp cover factor Weft cover factor

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: 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 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).

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

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 .

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

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:

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 )

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;

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;

1) the warp and weft crimps, CO and Cy 2) 3)

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.