**1.3.1 Weave factor**

It is a number that accounts for the number of interlacements of warp and weft in a given repeat. It is also equal to average float and is expressed as:

Modeling of Woven Fabrics Geometry and Properties 5

The properties of the fabric depend on the fabric structure. The formal structure of a woven fabric is defined by weave, thread density, crimp and yarn count. The interrelation between fabric parameters can be obtained by considering a geometrical model of the fabric. The model is not merely an exercise in mathematics. It is not only useful in determining the entire structure of a fabric from a few values given in technological terms but it also establishes a base for calculating various changes in fabric geometry when the fabric is subjected to known extensions in a given direction or known compressions or complete swelling in aqueous medium. It has been found useful for weaving of maximum sett structures and also in the analysis and interpretation of structure-property relationship of woven fabrics. Mathematical deductions obtained from simple geometrical form and physical characteristics of yarn combined together help in understanding various

The geometrical model is mainly concerned with the shape taken up by the yarn in the warp or weft cross-section of the fabric. It helps to quantitatively describe the geometrical parameters. The basic model (Pierce, 1937) is shown in figure 5. It represents a unit cell interlacement in which the yarns are considered inextensible and flexible. The yarns have circular cross-section and consist of straight and curved segments. The main advantages in

Fig. 4. Ten-end Huck-a-back weave

phenomena in fabrics.

considering this simple geometry are:

Fig. 5. Peirce's model of plain weave

**2. Geometrical model of woven structures** 

**2.1 Basic relationship between geometrical parameters** 

$$M = \frac{E}{I} \tag{1}$$

Where *E* is number of threads per repeat, *I* is number of intersections per repeat of the crossthread.

The weave interlacing patterns of warp and weft yarns may be different. In such cases, weave factors are calculated separately with suffix1 and 2 for warp and weft respectively.

Therefore, <sup>1</sup> 1 2 *<sup>E</sup> <sup>M</sup> <sup>I</sup>* ; *E*1 and *I*2 can be found by observing individual pick in a repeat

and <sup>2</sup> 2 1 *<sup>E</sup> <sup>M</sup> <sup>I</sup>* ; *E*2 and *I*1 can be found by observing individual warp end in a repeat.

#### **1.3.2 Calculation of weave factor**

#### **1.3.2.1 Regular weaves**

Plain weave is represented as <sup>1</sup> <sup>1</sup> ; for this weave, *E*1 the number of ends per repeat is equal to 1+1=2 and *I*2 the number of intersections per repeat of weft yarn =1+ number of changes from up to down (vice versa) =1+1=2.

Table 1 gives the value of warp and weft weave factors for some typical weaves.


Table 1. Weave factor for standard weaves

E1 and E2 are the threads in warp and weft direction I2 and I1 are intersections for weft and warp threads

#### **1.3.2.2 Irregular weaves**

In some weaves the number of intersections of each thread in the weave repeat is not equal. In such cases the weave factor is obtained as under:

$$M = \frac{\sum E}{\sum I} \tag{2}$$

Using equation 2 the weave factors of a ten-end irregular huckaback weave shown in figure 4 is calculated below.

$$\text{Weave factor, } M\_- = \frac{10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10}{10 + 6 + 10 + 6 + 10 + 6 + 10 + 6 + 10 + 6} = \frac{100}{84} = 1.19$$

Fig. 4. Ten-end Huck-a-back weave

4 Woven Fabrics

*<sup>E</sup> <sup>M</sup>*

Where *E* is number of threads per repeat, *I* is number of intersections per repeat of the cross-

The weave interlacing patterns of warp and weft yarns may be different. In such cases, weave factors are calculated separately with suffix1 and 2 for warp and weft respectively.

*<sup>I</sup>* ; *E*2 and *I*1 can be found by observing individual warp end in a repeat.

equal to 1+1=2 and *I*2 the number of intersections per repeat of weft yarn =1+ number of

Weave E1 I2 E2 I1 M1 M2 1/1 Plain 2 2 2 2 1 1 2/1 Twill 3 2 3 2 1.5 1.5 2/2 Warp Rib 2 2 4 2 1 2 2/2 Weft Rib 4 2 2 2 2 1

In some weaves the number of intersections of each thread in the weave repeat is not equal.

*<sup>E</sup> <sup>M</sup> I*

Using equation 2 the weave factors of a ten-end irregular huckaback weave shown in figure

10 6 10 6 10 6 10 6 10 6 84 

Weave factor, *<sup>M</sup>* 10 10 10 10 10 10 10 10 10 10 100 1.19

Table 1 gives the value of warp and weft weave factors for some typical weaves.

*<sup>I</sup>* ; *E*1 and *I*2 can be found by observing individual pick in a repeat

thread.

Therefore, <sup>1</sup> 1

1

**1.3.2.1 Regular weaves** 

**1.3.2.2 Irregular weaves** 

4 is calculated below.

and <sup>2</sup> 2

*<sup>E</sup> <sup>M</sup>*

2 *<sup>E</sup> <sup>M</sup>*

**1.3.2 Calculation of weave factor** 

Plain weave is represented as <sup>1</sup>

changes from up to down (vice versa) =1+1=2.

Table 1. Weave factor for standard weaves

E1 and E2 are the threads in warp and weft direction I2 and I1 are intersections for weft and warp threads

In such cases the weave factor is obtained as under:

*<sup>I</sup>* (1)

<sup>1</sup> ; for this weave, *E*1 the number of ends per repeat is

(2)
