Woven Fabric Calculation(1)

Woven Fabric Calculation Cover Factor Definition: Cover factor indicates the extent to which the area of a fabric is covered by one set of threads. For any fabric there are two cover factors: the warp cover factor and the weft cover factor. The cloth cover factor is obtained by adding the weft cover factor to the warp cover. Calculation: The cover factor in SI units is calculated as: Cover Factor (SI)

threads / cm X tex 10

Example : Tex=20; threads/cm=28 Cover factor (SI) =(28 x √20)/10 =12.5 Cover Factor (Pierce) Cover Factor (Pierce) =

n N

where n= threads/inch and N is cotton count

Example Tex=20 count, threads/cm=28 Cotton Count=590.5/20 =29.5’s Threads/inch =28 x 2.54 =71 Cover Factor (Pierce) =71/√29.5 =12.9 The resultant cover factor between SI units and Pierce is less than 5%. For any given thread spacing, plain weave has the largest number intersections per unit area. All other weaves have fewer intersections than plain weave. The likely weavability of all fabrics woven with the same weave and from similar yarns can be forecast from their cover factor. Plain weave fabrics with warp and weft cover factors of 12 in each direction are easy to weave. Thereafter weaving becomes more difficult and for cover factors of 14+14 fairly strong weaving machines are required. At a cover factor of 16+16, the plain structure jams and a very strong loom with heavy beat-up is needed to deform the yarns sufficiently to obtain a satisfactory beating-up of the weft.

Three cloths with the same cover factor (K=12) woven with yarns of different linear densities are shown in Table 1. It can be seen that how thread spacing and linear density have to be adjusted to maintain the required cover factor and how cloth area density and thickness are affected. Table 1 Comparison of fabrics with identical warp and weft cover factors woven with yarns of different linear densities (SI units) Cloth A B C

Threads per cm n1 n2 24 24 12 12 6 6

Linear density N1 N2 25 25 100 100 400 400

Cover factor K1 K2 12 12 12 12 12 12

Weight (g/m2) 130 260 520

thickness mm 0.28 0.56 1.12

Fractional Cover In fabrics constructed from yarns, cover may be considered as the fraction of the total fabric area that “covered” by the component yarns. An over-simplification of the idea for woven fabric is shown in Figure 1.

Figure 1: Fractional Cover The yarn has a circular cross-section of diameter, d, and adjacent yarns are displaced by a distance s. The fractional cover is then d/s. In the ideal model, s will be equal to 1/n, where n is the number of threads per unit length. The fractional cover could be expressed in terms of d and n Fractional cover = d X n Grosberg showed that yarn diameter d=4.44 √(tex/fiber density x 10-3 . Fractional cover, Cf=4.44 √(tex/fiber density) x threads/cm x 10-3

Example: What is the fractional cover for the warp in a fabric with 35 ends/cm, woven from yarn of 30 tex? The fibre density is 1.5 g/cm3. Cf=4.44 √30/1.5 x 35 x 10-3 Cf=0.695 Ie. 69% is covered by warp yarn.

Total Cover The total area covered by the fabric (Plain weave) is ABCD. The shaded area is the part of the total area covered by both yarns, and, because of this, it would not be strictly accurate merely to add the warp and weft cover values together and quote them as the total cover.

Figure 1: Unit cell of Plain Fabric The shaded areas are each d1 x d2 and the total area of the cell is s1 x s2. By definition, fractional cover, C, =d/s. Hence d1 = C1s1 d2 =C2s2 d1 d2 = C1s1 C2s2 Expressed as a fraction of total area s1 x s2, the shaded area becomes: d1 d2 = C1s1 C2s2 / s1 x s2 = C1 C2 The term C1 C2 must be deducted from the sum of C1 and C2, hence Total fractional cover = C1 + C2 - C1 C2 Example: A plain cotton fabric is woven to the following details: warp: 20 tex, 28 ends/cm; Weft: 35 tex, 25 picks/cm (density of cotton 1.52 g/cm3) What is the total cover factor? Warp cover: C1=4.44x √20/1.52 x 28 x 10-3 =0.451; Weft cover : C2=4.44x √35/1.52 x 25 x 10-3=0.533 Total fractional cover is C1 + C2 - C1 C2 =0.451 + 0.533 – 0.451x0.533 =0.744 Theoretically, about 74% of the total area of this cotton sheeting is therefore covered by yarn.