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Modeling of Transverse Compression Behavior of Yarns

DOI:10.13475/j.fzxb.20161004207

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Citation for published version (APA):Guanzhi, L., Qiang, Z., Jun, W., & Gong, R. (2017). Modeling of Transverse Compression Behavior of Yarns.Textile Research Journal, 184-190. https://doi.org/10.13475/j.fzxb.20161004207

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Download date:05. Feb. 2022

Modeling of Transverse Compression Behavior of Yarns

Li Guanzhi 1,2, Zhao Qiang 1,2, Wang Jun 1, 3，Hugh Gong4

（1.School of Textiles, Donghua University，Shanghai; 2.China Textile Academy，Beijing;

3.State Key Laboratory on Fabrics, Donghua University, Shanghai；4.School of Materials,

University of Manchester, M13 9PL, UK

Abstract: On the basis of an ellipse cross-section yarn model, the relationships among the yarn

parameters such as cross-sectional area Sy, yarn cross-sectional perimeter Sp, void ratio Vf, yarn

flattening ratio f, and yarn density ρy during fabric deformation process were evaluated. The

theoretical model indicated that these parameters could be simplified to two factors: Sy and Sp. To

validate the theoretical model, the Finite Element Modeling (FEM) and experimental tests were

conducted to assess the deformation process of a cotton plain fabric. The results showed that the

cross-sectional area varied almost 2 or 3 times more than the cross-sectional perimeter. The rate of

change of the cross-sectional perimeter was about 8~17 %, while which was 17~42 % for

cross-sectional area. The correlation analysis among the ellipse major axis, which has a significant

influence on fabric appearance, the cross-sectional perimeter, and the cross-sectional area was also

conducted. The weak correlation between ellipse major axis and a cross-sectional perimeter was

observed, while ellipse major axis and cross-sectional area was uncorrelated. These findings can

help to overcome the drawbacks of the yarn evenness tester when predicting the fabric appearance

quality.

Keywords: yarn evenness; yarn flattening ratio; finite element analysis; image processing

1 Introduction

Yarn cross-section shape makes a big difference to fabric appearance. As early as

1969, Hearle[1] claimed that yarn cross section was an irregular polygon. The reason

for the irregularity is that the fibers become unevenly distributed in transverse as a

result of stress distribution arising from interactions among fiber property, yarn

property, and spinning parameters among others. Fiber characteristics determine the

cross-sectional shape of yarn in bobbins and spinning process. When considering the

stress yarn suffered during the weaving process, the yarn face to stretching, bending,

rotating and flattening, as a result of the cross-sectional shape of the yarn in fabrics

changed greatly.

In the previous works, to simplify the calculation, most of the researchers

assumed the cross-sectional shape of the yarn in bobbins is circular. In fact, only a

few most compacted yarns for example cords used in automobile tires, the

cross-sectional shape is circular. Ring spinning or rotor yarn was considered to have

an elliptical cross-section. Tsai&Chu[2] pointed out that ring and rotor spun yarns are

more nearly elliptical. The ellipticities f t(f t =a/b, a,b is the major and minor radius of

yarn cross-section) of the best-fit ellipses for ring yarn and rotor spun yarn is 1.09 and

1.07 respectively. The flattening ratio f as f=b/a is 0.917 for ring spun yarns and 0.935

for rotor spun yarns; it shows that rotor yarn was more circular than the ring-spun

yarn which could be attributed to the smaller linear density and yarn twist of

ring-spun yarn. Gunay[3]detected the diameter of the shadow blocked by the yarn core

with CCD sensors and approximated the major and minor radius of the ellipse by the

maximum and minimum length when rotated the yarn, then the flattening ratio f it

could be calculated. He got the values of 30 random locations of a ring-spun yarn with

a yarn count of 17 Ne. The distribution is normal with a mean eccentricity of 0.5

(flattening ratio f =0.866), and the eccentricity is between 0.4 to 0.65(0.76<f <0.99).

When considering the yarn in the fabrics, the yarn was stretched, bent and

flattened; most approaches described the shape of yarn cross-sectional shape as

circular, elliptical, et cetera[4-6] and assumed to have a constant cross-section. In fact,

yarn cross-sectional shape varied depending on the types and structures of the yarns

and fabric. Even in the same yarn, the cross-sectional shape of yarn was different as

result of the compression occurred over the region of contact and released over

low-press contact region. Before, It is hard to study the cross-section deformation due

to the limited of the techniques. Until 2009, Gong[7] abstained continuous yarn

cross-sectional shape scanned by the synchrotron facility of ESRF in France without

destroying the fabric structures. In his detailed study, the yarn cross-sectional shape

can be treated as an ellipse, and ellipse fitting was found to be more suitable for

cotton fabrics. Moreover, also the cross-sectional shape of yarn varied along the yarn

path as a result of deformation. After that, further studies carried out by Ozgen &

Gong[8] investigated the yarn cross-section changes in woven fabrics and the

relationship between the changes in yarn and fabric parameters. A general equation of

change in yarn flattening coefficient was developed with regression analysis method.

These studies could improve the simulations of yarn deformation and fabric

appearance.

However, It is very challenging to predict the fabric appearance with bobbin yarn.

Uster made a great attempt with capacitive yarn evenness testers. The capacitive

evenness tester employs air capacitors as detectors to evaluate yarn evenness from the

principle that the dielectric constant of fiber material is longer than that of air. As the

yarn passes between two metal plates with an electric field, the capacitance changes

the amount of fiber in the yarn section. The changes in capacitance were used to

evaluate yarn evenness and predict fabric appearance qualities. The principle was

based on the assumption that the yarn in bobbins maintained specific numbers during

the process of weaving. In fact, yarn evenness was affected both by fiber numbers and

the air gap between fiber which is known as yarn appearance unevenness, they all

play a major role in fabric appearance. Recently the manufactures of yarn evenness

tester found out the drawback of the capacitive method. So many commercial

equipment providers such as USTER and CHANGLING, they were inclined to add

the photoelectric module in previous capacitive testers to improve the reality of

simulated fabrics[9]. However, the results were still not plausible. While another

reported development in the yarn evenness measurement system, Lawson-Hemphill

EIB, was highly valued which determines the yarn diameter using a line array CCD

sensor to characterize the yarns and simulate yarn board and fabric appearances[10].

Many researchers also made useful attempts towards this work. LIU pointed out

that the evenness tested by EIB was slightly higher than the capacitive testers[11].

Moreover, the CV value is more suitable to represent yarn appearance. Besides, many

researchers devote to the study of yarn appearance test. Carvalho et al [12].presented a

yarn characterization system and yarn diameter measurement using diode laser system.

There have been commendable developments in yarn diameter measurement by image

processing. However, Carvalho[12] et al. acknowledged that the calculated yarn

diameter changes when the image is captured in a different direction. Hamilton[13]

proposed a method to measures both major and minor thread diameters under

conditions of thread tension and compression.

All the above method is from the perspective of yarn quality assurance to

evaluate yarn qualities. They did significant advancements in the study the parameters

changes of yarn cross-sectional shape during the weaving process and which

parameters link the yarn quality and fabric quality. This is the key to consistency

evaluation between yarn qualities and fabric qualities. So this paper further explores

the idea.

2 Theoretical analysis and parameter selection

To evaluate yarn quality and fabric quality with the same criterion, the yarn

cross-sectional shape both the bobbin yarn and yarn in the fabric is assumed to be an

ellipse.

In weaving process, the yarn cross-section is deformed under the forces of

stretching, bending, twisting and flattening. It is evident that the yarn cross-section

parameters, including yarn cross section area Sy, yarn cross section perimeter Sp, fiber

porosity Vf, yarn flattened ratio f, and yarn density ρy, are changing during the weaving

process. Therefore, we will evaluate the changing role of these parameters in the

fabric.

2.1 Theoretical analysis and parameter selecting

0

01

0

0

1

2b

2a 2a’

2b’

Fig. 1. yarn cross section model, (a) under natural conditions, and (b) in fabric.

Fig. 1(a) shows the cross-section model of individual yarn, with the major axis of

2a and minor axis of 2b. Other parameters are fiber porosity Vf, the yarn cross-section

area , yarn cross-section perimeter , yarn density ρy and yarn flattening

coefficient f. Fig. 1(b) presents the yarn cross section of a yarn in a fabric. The yarn

cross-section major axis and minor axis are 2a’ and 2b’ respectively, with the fiber

porosity factor Vf’, yarn cross-section area ‘, yarn cross section perimeter ’, yarn

density ρy’ and yarn flattening coefficient f ’.

The following study is based on the assumption that the fiber number n, fiber

cross-section area Sf and fiber density ρf are constant in yarn and fiber axial slip does

not exist during the weaving process.

Fiber porosity: = ×, ′ = ×

. Since the total fiber area × is the

same before and after weaving, the fiber porosity in the yarn is inversely proportional

to yarn cross-section area, i.e. ∝ .

Yarn density: ρy=× × ×× = × × = × ρ . Similar to fiber porosity, yarn

density is also inversely proportional to yarn cross-section area, i.e. ρ ∝ .

Yarn cross-section perimeter , yarn cross-section area , and yarn flattening

coefficient f:

yarn cross-section perimeter can be obtained through the following formula.

=4a 1 − sin( ) = 4 1 − (1 − ) sin( ) （1）

From the above formula, the relationship between the yarn cross-section

perimeter, is a co-determination of and , also ∝ .

From the above analysis, it can be obtained that fiber porosity Vf and yarn

density ρy are both proportional to yarn cross-section area . While the relationship

between the yarn cross-section perimeter and yarn cross-section area is

complex, which needs a further verification. Hence and are two major yarn

cross-section parameters considered in this paper.

yarn cross-section perimeter and yarn cross-section area are determined

by the surface fiber of the yarn. The following study is based on the assumption that

the outer fiber of the yarn was closed packed. Then the changes of yarn parameters

was decided by the air gap surrounded by outer fiber of the yarn. Here is 3 tpyes of

packing deformation under compressions:

When the fiber porosity Vf is minimum as shown in Fig2(a)，all the fibers tightly

packed together. So during the process of yarn facing the compression of stress, the

cross-section perimeter increase while almost maintaine the same Fig2(b),

form 1; When he fiber porosity Vf is maximum as shown in Fig2(c), inside of the

yarn is empty. If the outer fibers tied together during the compression process rather

than slip into the yarn core, the cross-section perimeter almost maintaine the same

while decrease, in Fig2(d), form 2; If the yarn slip into the yarn core as shown in

Fig2(f), the cross-section perimeter decrease and decrease, form 3. The

reality yarn must be one of the form 1-3, which need further studies.

form1

(a) (b)

form2

(c) (d)

form3

(e) (f)

Fig. 2 Analysis of yarn compression.

Yarn cross-section area Sy and yarn cross-section perimeter Sp in the fabric is

caused by the forces acting on the contact area of yarns. Those forces are influenced

by many complex factors, such as yarn property, weaving process, and fabric structure

and so on. To investigate the variation of the yarn during the weaving process, the

finite element analysis (FEA) is adopted.

2.2 Model construction and simulation

In the current study, the plain woven fabric composed of 20 tex cotton yarn is

taken as the control group. Warp cover factor and weft cover factor of the fabric are

16 and 12 respectively. The yarn was designed as a cotton yarn packed by 60 fibers.

Assuming that the major axis of the oval yarn cross-section is 2a=0.2mm, and the

minor axis is 2b=0.16mm. The yarn parameters set in Abaqus[14] (software) are

presented in Table 1. The generated fabric model is shown in Fig.3(a). The file was

imported into Abaqus software, and assuming that three weft yarns alternatingly

moved according to the interlacing, the relative displacement is set as 0.42mm.

Tab. 1 Yarn parameters in Abaqus

yarn density

fabric

thickness

Young

modulus X

Young

modulus Y

Young

modulus Z

20tex 0.3 3820Mpa 3820Mpa 3820Mpa

cotton fiber

density

friction

coefficient

Poisson's

ratio X

Poisson's

ratio Y

Poisson's ratio

Z

1.54g/cm3 0.2 0.3 0.4 0.4

Fig. 3 Contours of the fabric weaving modeling.

For simplicity, the middle yarn in Fig. 3 was chosen to compare the variation of

the yarn cross-section perimeter and yarn cross-section area before and after weaving.

Fig. 4 shows the change of yarn cross-section as a function of time during fabric

weaving. It can be observed that the rate of the change of the yarn cross-section

perimeter is smaller than that of the yarn cross-section area. The range coefficient is

used to present the deviation ratio after weaving. The yarn cross-section perimeter is

decreased by 9.02%, while the reduction of the yarn cross-section area is 27.67%. J% = × 100% （2）

Where: J is range coefficient, is the maximum or during weaving,

and is the minimum or during weaving.

Fig. 4 Yarn cross-section parameter variations with time during fabric weaving process.

Different section views of one yarn are also evaluated as shown in Fig 5. Half of

the unit cell was chosen as shown in the red frame in Fig 3(b), 10 yarn cross sections

views are selected evenly. The yarn cross-section perimeter and area are calculated,

and the similar changing rule is obtained, as shown in Fig. 6, the yarn cross-section

perimeter is decreased by 7.54% and the decline of the area is 17.33%.

Fig. 5 Different section views of the same yarn in the fabric.

Fig.6 Yarn cross-section parameter variations at different section views of the simulated yarn.

3 Experimental test

3.1 Obtaining yarn cross section within a fabric

It is hard to get the continual variation of yarn cross-section during the whole

weaving process. Considering that the yarn cross section variation is concerned with

the forces acting on the yarn, which is verified by the FEA analysis, the different

forces acting on the yarn contact positions and non-contact positions lead to different

variations of the yarn cross-sections. Therefore, in the following section, the yarn

cross sections in various positions of yarn are selected to study the yarn cross section

changing the rule.

Experimental Material: Cotton plain fabric woven in Bonas-Varitex machine.

The fabric parameters are as follows:wrap cover factor 16, weft cover factor 12,

yarn density 18tex, yarn twist 890 turns/10cm, and the yarn is spun using the cotton

fibers with the Micronaire value of 4.2.

To guarantee non-destructive image data collecting, the French Synchrotron

Radiation Facility ESRF is adopted. Beamline ID19 was used for x-ray scanning of

the fabric samples and using the 2048*2048 resolution ratio FReLoN camera to take

pictures of the fabric. The image resolution is 1.4um/pixel; every single image

corresponds to fabric with the size of 2.8*2.8mm. 1/2 weave repeat unit image is

randomly selected, shown in Fig. 7.

Fig. 7 Yarn cross-section parameter variations at different section views of the same yarn in a real

fabric.

3.2 Extraction of yarn cross-section perimeter and area from the images

In this part, the first step is to denoise the yarn cross-section image with median

filter method. After binarization processing, the close operation was used to eliminate

noise and adhesion further. Then watershed algorithm was carried out to segment the

image. Small dots in the picture were removed by imimposemi function and

bwareaopen function. Candy algorithm was used to detect the edges of the yarn

cross-section. At last fit_ellipse function was used to fit the yarn and calculate the

length of major and minor radius of the ellipse, as flow shown in Fig 8.

Fig. 8 Extraction of yarn cross-section parameters.

4. Results

Using the methods discussed in section 3.2, the yarn cross-section parameters of

Section 1 to Section 10 in Fig. 7 were obtained and presented in Table 2. It is

observed that the minimum yarn flattened ratio f occurs at the intersection point,

which means the yarn is heavily flattened. However, in the middle of two intersection

point, f is the maximum. These results agree with the previous study conducted by

Gong [7]and the simulation results in section 2. Additionally, f is continually reduced

from the middle to the intersection point. Similar changing rules of the oral yarn

cross-section area and perimeter are seen in Fig9.However, from Fig 9, it is apparent

that the decrease rate of the yarn cross-section perimeter is slower than that of yarn

cross-section area. The reduction of yarn cross-section perimeter is 17.33%, while it is

41.60% for the yarn cross-section area. This tendency of results is consistent with the

simulation work, but the experimental value is larger than the simulation results,

which could be explained that the simulation work did not include some assumptions

such as; a circular fiber cross-sectional shape, and uniform distribution fibers.

Tab. 2 Yarn cross-section parameters of different yarn cross sections in fabric.

Section No. Sp Sy a b f=b/a

1 0.601 0.0262 0.1046 0.0798 0.763

2 0.548 0.0217 0.0960 0.0720 0.750

3 0.545 0.0214 0.0957 0.0711 0.743

4 0.530 0.0194 0.0957 0.0645 0.673

5 0.549 0.0207 0.0992 0.0664 0.670

6 0.510 0.0166 0.0960 0.0552 0.575

7 0.551 0.0187 0.1055 0.0564 0.535

8 0.497 0.0153 0.0931 0.0517 0.555

9 0.523 0.0160 0.1023 0.0498 0.487

10 0.524 0.0156 0.1037 0.048 0.463

Fig. 9 Yarn cross-section perimeter and area variations of Section 1-10.

In Hirai’s study[15-16], the yarns were compressed under three different forces,

T5g, T50g and T1000g. The yarn cross-section images of the yarns before and after

compress were collected. To further verify the theoretical and simulation results, we

used the same method to obtain the yarn cross-section parameter variation of the yarn

images provided by Hirai. The results showed that the yarn cross-section perimeter

decreased by 12.24% after stress, and the yarn cross-section area decreased by

35.81%. The changing rule that the decreasing rate of yarn cross-section perimeter is

slower than that of yarn cross-section area is the same. Both are consistent with the

simulation results.

Also, fabrics, especially some high cover factor woven fabric such as poplins,

intersection point was highly flattened. The appearance of these fabrics is influenced

by the major radius of the ellipse. Basing on correlation analysis between the

perimeter and area of the yarn cross-section in Fig 10, we can draw a conclusion that

there is no- correlation between the major radius and cross-section area. However, the

yarn cross-section perimeter exist weak correlation with the major radius. Which

means, when predicting fabric appearance by yarn, the cross-section perimeter is

more reliable than area.

5. Conclusion

Based on the assumption that yarn cross-section is an ellipse, we used the FEA

method and experimental verify method. The following conclusions are obtained:

(1) During the weaving process, yarn is more inclined to slip into the yarn core,

form 3, both the cross-section perimeter Sp decrease and cross-section perimeter Sy

decrease.

(2) The variation of the yarn cross-section parameters, yarn cross-section area Sy,

yarn cross-section perimeter Sp, fiber porosity factor Vf, yarn flattening coefficient f

and yarn density ρy during the yarn deformation in weaving process can be simplified

to yarn cross-section area Sy and yarn cross-section perimeter Sp.

(3) During the yarn deformation process, the change rate of the yarn

cross-section perimeter is far less than that of the yarn cross-section area. The change

rate of the yarn cross-section perimeter is between 8% to 17%. For the yarn

cross-section area, the change rate is 14% to 42%, which is 2 to 3 times the yarn

cross-section perimeter.

(4) Fabric appearance was mainly affected by the major radius of yarn

cross-sectional elliptical shape. Moreover, major radius and cross-section area Sy exist

no- correlation; however, the yarn cross-section perimeter Sp exist weak correlation.

When predicting fabric appearance from the yarn properties, the parameter

cross-section perimeter is more reliable than area.

The current study is beneficial to improve existed the drawback of yarn evenness

testers in predicting fabric appearance. The work is helpful to evaluate yarn quality

and fabric quality with the same criterion and provide a new view of designing a new

evenness testers.

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