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PREDICTION OF FABRIC COMPRESSIVE PROPERTIES USING ARTIFICIAL NEURAL NETWORKS

 

B.R. Gurumurthy

Research scholar Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi 110 016. E-Mail: murthys_iisc@yahoo.co.in

Abstract:

Data analysis relating to a fabric’s compression properties can only be carried out when the limits of compression are known. The study of the compressibility of woven fabrics was initiated with Peirce, Kemp & Hamilton’s approach to circular yarns and flattened yarns of a fabric under pressure. The fit of the pressure-thickness relationship is being improved using the exponential interpolation & extrapolation methods, as well as iterative methods such as the Marquardt algorithm for fitting the curves. Although there is a recent trend towards the automation of studying the structure-property relationship of textile fabrics, an objective and efficient method for predicting properties with a rapid prototype that outputs to sophisticated instruments such as the KES-FB3 is essential. This characterisation of data for fabric materials will help maintain companies’ commercial experience and expertise. This established predicting model can provide guidance to fabric manufacturers, fashion designers and ?[makers-up] in fabric design, fabric selection and the proper use of fabrics. This approach will make online fabric sourcing more realistic. Fabric sourcing experts are now visiting supplier’s websites for tracking fabrics. Overall, this approach provides an opportunity to generate a dynamic database of fabric properties, and hence may result in the development of new fabrics or the updating of existing fabrics to keep pace with fashion.

Key words:

compression energy, flattening factor, bulk density, specific volume

1. Introduction

Compressibility is one of the important properties of fabric, in addition to friction, bending, tension and shear. In garment automation, for instance, compressibility can be a crucial property for successfully separating plies from a stack. With the growing need for better material modelling for simulation purposes, objective measurements of fabric compression will become increasingly important, since static compression gives an indication of the mechanical ‘springiness’ of the material. The lateral compression of a fabric is defined as the intrinsic change in thickness with an appropriate increase in pressure when the fabric is subjected to a barely perceptible pressure, which is generally about 1% of the maximum pressure. Hence a lower volume is registered, which will decrease continually over 5 to 10 successive compression cycles.

In order to compare compression curves from different fabrics, Kawabata introduced four parameters as part of the KES-F (the Kawabata evaluation system for fabrics). The four parameters in the KESFB3 test express the work of compression WC (WC’ is the area under the release curve).

Linearity (LC), resilience of the fabric RC, and relative compressibility EMC, are all calculated as

follows:
Tm To
PdtWC = and PdtWC = ' (1)
To Tm

WC

LC = (2)

(0.5(Pm(To Tm ))

WC'

RC = (3)

WC

Tm

EMC = 1 (4)

T

o

The applied pressure is expressed by ‘P’ and the thickness by ‘T’, with ‘To’ being the thickness at a minimum pressure of 0.5 gf/cm2.

The compressional work per unit area, WC (CN/cm), varies depending on the type of fabric. A more compressible material gives larger values; for example, wool gives a larger value of WC when compared to other fabrics. The difference in the values may be attributed to the surface layer of the fabric, which makes a large contribution to the compressibility (springiness) of the material.

The second distinctive parameter for compression is the linearity of the compression ‘LC’. If the thickness of the fabric decreases linearly with increasing pressure, the LC value would be 1. However all fabrics compress non-linearly, and have an LC value ranging between 0.14 to 0.47. The harder fabrics have a lower value of LC, which would result in a steeper rising compression. The third parameter ‘RC’ represents the hysteresis in the compression graph. Finally, the dimensionless EMC parameter expresses the compressibility of a fabric. The smaller the EMC value, the more incompressible the fabric.

van Wyk’s equations are used to approximate the static low-load compression curves (maximum 10gf/cm2) of both woven and knitted materials generally used in garment automation. The simple two-parameter approach, which excludes the volume in unloaded conditions, is first used as an estimate and gives the starting values for the more refined three-parameter model. All these models give only an approximate fit, considering the complexity of volume and pressure. Some of the constants used in these models are not defined, and there are significant differences between the model values. Therefore, the main problem is to optimise the compression pressure-thickness curve and predict the compression characteristics of woven fabrics by using rapid prototypes such as neural networks which can learn data and analyse the complexity of the relationship between variables,

The study of the compressibility of woven fabrics is initiated coupled with Peirce, Kemp & Hamilton’s approach for circular yarns and flattened yarns of a fabric under pressure. The fit of Pressure-thickness relationship is being improved using exponential interpolation and extrapolation methods, as well as iterative methods like the Marquardt algorithm for fitting the curves to overcome the limitations of existing models. Although there is a recent trend towards the automation of studying the structure/property relationship of textile fabrics, an objective and efficient method for predicting properties with a rapid prototype that outputs to sophisticated instruments like the KES-FB3 is essential.

2. Theory

2.1. Assumptions for studying the compressive behaviour of woven fabrics using a mathematical model
  1. The yarns in the fabric are assumed to be elastic and isotropic, although there are some anisotropy and in-elastic properties.
  2. The yarn is assumed to be a solid cylinder.
  3. The geometry of the yarn surface is assumed to be smooth and uniform (which is in fact not smooth, because of the yarn twist and the protruded fibres present on yarn surface); the resistance of the fine hairs on the yarn surface is therefore ignored.
  4. The difference caused by different fibres and fibre arrangements arising from different spinning technologies is assumed to have been captured in the material constant, and is not considered for modelling.
  5. The fabric is assumed to be completely relaxed; this means that the fabric does not have any residual force within itself.
  6. The response of the fabric to different machine settings (yarn tension, yarns per dent, beat up-force, etc., and post-weaving treatments (desizing, bleaching, softening, dyeing, reducing weight, etc.,) will not be taken into consideration.
  7. Change in crimp crowns is assumed to occur in a transverse direction and is not taken into account when calculating geometric thickness; the longitudinal deformation due to lateral pressure is negligible.
  8. Yarn rigidity, slippage between the fibres or filaments, crimp balance and crimp interchange effects in longitudinal directions is negligible under low pressure, and its effect is not considered.
  9. The compressive force applied on the fabrics is at low pressure, ranging from 0.5 to 50 gf/cm2.
  10. On compression threads moving closer to attain equilibrium conditions following different cross section models and its phenomenon is not taken into consideration.

2.2 Peirce model for change in thickness

Figure 1 . Peirce unit cell model

From Pierce’s geometry, the fabric thickness ‘t’ is calculated, which is the sum of the crimp height and the diameter. Let the crimp height be ‘h’ and the yarn diameter be ‘d’.

Fabric thickness ‘t’ is given by

t = h1 +d1 or h2 + d2 (5)

Since the yarn diameters are assumed to be circular, we have

t= max (t1, t2) (6)

where:

N1 and N2 are warp and weft counts,

e is the flattening factor, and

t is the thickness of fabric.

In reality, cross sections are far from circular, and later models modified the cross section; the racetrack (the rectangle with circular arcs at the sides) was widely adopted for mathematical tractability. The compressed thread may be considered to have the form of a flattened elliptical cross section, where the area of the ellipse is given by

abπ

(7)

4

where ‘a’ and ‘b’ are major and minor diameters. But this is not true; when pressure is applied, the threads spread unevenly, and can attain a configuration which can be assumed to lie somewhere between the ellipse and the rectangular with circular arcs. For ?structural reasons, the limit of compression where the crowns are flattened must be considered, and hence a flattening factor ‘e’ must be introduced.

By introducing the flattening factor ‘e’, which is a function of crimp of yarn, cloth setting, and count, the flattening factor ‘e’ is obtained by [12].

C% C%

1 + 2 1 1

= 0.28 e

+

nn

21 N1 N2 (8)

2.3. Change in thickness for non-circular yarns

Figure 2. Kemp’s race-track geometry cross-section

In the case of industrial fabrics like canvas and tarpaulins subjected to large deformation by compressive force, would result in jamming of either warp or weft. In large deformations, one has to consider different assumptions for the analysis, introduce change into the structural elements and then infer the thickness. It would be appropriate to fix the limits of compression using Kemp’s racetrack model for flattened yarns [3] with changes in pick spacing, diameter of yarns, crimp height etc.

This new shape, which is termed the race-track section, is rectangular with semi-circular ends, and is used as the basis for an extension of Peirce’s theory to the more general case of non-circular threads.

The horizontal and vertical diameters of the threads are denoted by ‘a’ and ‘b’ respectively. The scale unit ‘D’ is equal to the sum of the vertical diameters:

D =b + b = h + h (9)

12 12

Peirce’s formulae and tables of functions may be used for part of this section, the variables being

' ''' ''

p , p ,l ,l ,c ,c

1 21212

The relationships between these variables and the structural particulars p , p ,l ,l ,c ,c are as

1 21212

follows:

p ' =p (a b )

22 22

(10)

l' = l (a b )

11 22

' ''

and c =(l' p )/ p = cp /[ p (a b )] (11)

1 12 2122 22

'' '

similarly, for p1,l and c2 .

2

Thus, if the term (a b ) is known,

22 '''

p,l ,c can be easily calculated from the structural particulars, p,l1, and c1 . Similarly, a knowledge

211 2 '' '

of (a1 b1) is required for the calculation of p1,l2 and c2

''

From the circular thread theory, assuming ‘θ’, the angle of crimp, to be small, and p2 and l1 large, the following relation holds as a useful approximation:

a

h1 = 3 4 p ' 2 c ' 1 * (12)
Hence, from equations (11) &, (12), the following relation is obtained:
b1 +b2 = 3 4 c p [ p1 2 2 (a2 b2 )] + 3 4 c p [ p2 1 1 (a1 b1)] (13)
If the thread flattening coefficient ‘e’ is defined by
e = b (14)

and ‘d’ is the diameter of the circular thread of equal area, then it can be easily shown that

1

b =d

(15)

41e

1+ ()

⎢⎥

πe

[(1e)/ e]

and (ab) =d 4 = df (e), say (16) [e/(1e) + ]

π

hence

4

b1 +b2 =

p ()] +4

cp [ d fe

cp [ p df ()e ] (17)

122 22

211 11

3

3

4

1

1

(18)

p ()] +4

cp [ dfe

p ()]1 = d1

cp [ dfe

+d2

122 22

211 11

3

3

4 1e

4 1e

[1+1 ]

[1+2 ]

⎜⎟

⎜⎟

π e

π e

1

2

This equation contains the unknowns d ,d,e and e2 . Assuming that d1 and d2 can be accurately

1 21

estimated from the count of the warp and weft yarns, then if a further relation is evolved between e1

and e2 (for example, in special cases it may be valid to assume e =e =1, the two variables e1 and

12

e2 can be reduced to one ‘e’.

In such cases, a graphical method of solving the equation may be conveniently be adopted, that is, by plotting both sides of the final equation against ‘e’, the intersection of two curves giving the required value ‘e’.

2.4. Change in the cover factor of the fabric

Hamilton[13] defines the fabric tightness which could be used for comparison of fabrics at different configurations as the ratio of the sum of the fabric cover factors to the sum of the cover factors of the maximum-set fabric with the same ratio of cover factors. This is simply expressed as:

(K +K )

12 actual

T = (19)

(K +K )

1 2 lim it

d1

Here, the warp cover factor K = where d is the warp yarn diameter and p1 the thread spacing,

11

p

1

d2

and the weft cover factor K = where d and p2 are the weft yarn diameters and thread

22

p

2

spacing respectively. The term '(K1 +K ) refers to the actual values of a specific fabric, the

2 actual

value (K +K ) is determined graphically from graphs from Hamilton’s paper.

1 2 lim it

Hamilton and others were concerned that yarns in fabrics are not circular in the cross-section, and they therefore used modified equations to allow for yarn flattening. This procedure is no doubt essential for calculating a wide range of properties and dimensions. The Peirce equations assume a circular cross-section, rather than an elliptical or race-track shape, such as may occur in a more open fabric. Hence we need to use yarn diameter rather than arbitrary or measured major & minor diameters.

2.5. Specific volume of fabric

Bulk density is defined as the density of bulk materials. Bulk density is a material property, and is given by the following equation:

3 fabricweight(gm / cm2)

Fabricbulkdensity(gms / cm ) = (20)

Thickness(cm)

Then

3 Thickness(cm)

Fabricspecificvolume(cm / gm) = (21)

Fabricareaweight(gms / cm2)

3. Experimental

3.1 Materials

Table 1. Characteristics of woven fabric

Sl no Fabric no Variety Warp count(Ne) Weft count(Ne) EPI PPI C1% C2% Geometric thickness(mm)
1 3 Cotton 48 37 92 80 5 5 0.2431
2 4 Cotton 42 40 100 92 5 3 0.2159
3 5 Cotton 40 36 92 80 7 7 0.2616
4 6 Cotton 40 12 100 48 10 7 0.4496
5 7 Cotton 40 40 112 84 7 7 0.2489