Experimental study on an effective method for the friction property of fabrics by the comprehensive handle evaluation system for fabrics and yarns system

Abstract

The main topic investigated in this paper is the effective measurement of the fabric friction property by the comprehensive handle evaluation system for fabrics and yarns (CHES-FY). The optimal system parameters of the CHES-FY were determined using an orthogonal experiment design based on the correlations between four curve parameters from the pulling-out force – the displacement curve of the CHES-FY and the friction coefficient tested by the Kawabata evaluation system for fabric surface tester. The repeatability and stability of the CHES-FY under settings of optimal system parameters were also analyzed. Moreover, the four curve parameters were used to cluster the smoothness/roughness handle of fabrics objectively by the k-means cluster method, and the clustering results of the k-means cluster method were compared with those of the subjective cluster method. Analysis of the results showed that the selected optimal system parameters were a good combination, and the CHES-FY with the optimal system parameters provided an effective and reliable evaluation to the friction coefficient and smoothness/roughness handle of fabrics.

Keywords

friction property orthogonal experiment design smoothness/roughness handle comprehensive handle evaluation system for fabrics and yarns

The friction property is one of the primary mechanical performances of a fabric, which affects the handle, comfort and aesthetics, as well as application of the fabric.^1–3 Many studies on the friction property of fabrics have been conducted, such as that of Izumi et al.,⁴ took up the surface roughness and slipping resistance as tactile parameters to explore the surface properties of fabrics, and three sensory tests were employed to discriminate between surface roughness and slipping resistance of the fabric; Ravandi et al.⁵ studied the dynamic friction property of fabrics and analyzed the relationships between fabric structure and the stick–slip motion; Zurek et al.⁶ investigated the friction behavior of fabrics woven from filament yarns and found that the differences in fabric friction depended on the morphology of the fabrics and the rubbing directions. To study the correlation between friction and smoothness and better meet the requirements of end-use textile products, quantitatively measuring and characterizing the friction properties of fabrics become necessary. Zurek et al.⁷ used a modified Instron tester to measure the frictional resistance of fabrics. Ramgulam et al.⁸ designed a non-contact method of using a laser sensor for the measurement of the surface friction of fabrics. Ramkumar et al.⁹ employed a polymeric artificial finger sensor to measure the frictional characteristics of fabrics by simulating the feeling mechanism of human fingers, and comparisons between instrument measurements and subjective assessments confirmed the accuracy of this method. Taylor and Pollet¹⁰ also developed a tester to evaluate the low-force frictional properties of fabrics against the engineering surface. A well-known friction apparatus is the Kawabata evaluation system for fabric surface tester (KES-F4).¹¹ The KES-F4 uses two testing units, which comprise a series of steel piano wires to simulate the friction ridge in a human’s fingers; during the testing, the two units slide on the surface of a fabric to measure three indices correlated with surface characteristics in order to evaluate a fabric’s friction properties. However, the apparatus mentioned above was designed to test only one pure property during one test; it is not suitable for evaluating the smoothness/roughness handle attribution that is related to multiple mechanical properties of fabrics. Moreover, the comprehensive property of fabrics is not a simple linear combination of different mechanical properties.

An alternative method was presented by extracting a rounded sample through a ring or orifice to evaluate the comprehensive behaviors of fabrics.^12–17As a result, a commercial tester, that is, the PhabrOmeter fabric evaluation system, was developed by Pan.¹⁸ The PhabrOmeter system could use a single instrument to measure the comprehensive response behavior of fabrics in order to evaluate the fabric handle characteristics, where the value of the smoothness handle of a fabric was calculated by featuring the extraction curve parameters that were related to the friction property. However, this method could not measure the pure mechanical and physical properties of fabrics directly.

Recently, the comprehensive handle evaluation system for fabrics and yarns (CHES-FY) has been developed to achieve the goal of measuring mass, bending, friction and tensile/shear properties for both fabrics and yarns in situ and assessing fabric handle by a pulling-out test.^19–21 The friction property can be evaluated based on the principle of capstan equation and the corresponding indices of physical and mechanical properties have been derived by a series of theoretical models.^22–24 The fuzzy mathematics method was used to characterize fabric handle based on the pulling-out force – the displacement curve of the CHES-FY.²⁵ However, the system parameter setting and corresponding effects of the system parameters on the results of the friction characterization of the CHES-FY have not been discussed. Therefore, this paper detailed an experimental study to investigate the optimal system parameters of the CHES-FY for friction testing based on the orthogonal experiment design and correlation analysis; the effective and repeatability of the system for evaluating the friction coefficient and smoothness/roughness handle of fabrics are also discussed under the optimal system parameters.

Experimental details

Samples and primary parameters

A broad selection of 28 wool woven fabrics was collected from a wool mill. The primary parameters of the fabrics are summarized in Table 1, where M is mass per square meter; T is fabric thickness measured under 1 kPa pressure; and

μ_{m}

is the friction coefficient tested by the KES-F4. The fabrics were cut to warp × weft size of 20 cm × 2 cm for the CHES-FY testing. All the samples were conditioned at 20 ± 2℃ and 65 ± 3% relative humanity (RH) for more than 24 hours prior to tests.

Table 1.

Primary parameters of 28 wool woven fabrics

Sample number	M (g/m²)	T (mm)	$μ_{m}$
1	190.7	0.442	0.218
2	188.0	0.214	0.187
3	242.8	0.521	0.201
4	279.5	0.529	0.265
5	165.5	0.452	0.201
6	178.0	0.52	0.206
7	299.3	0.887	0.261
8	271.4	0.449	0.193
9	212.9	0.477	0.225
10	301.6	1.087	0.428
11	177.7	0.712	0.178
12	147.9	0.408	0.165
13	137.1	0.333	0.148
14	159.1	0.379	0.142
15	132.2	0.359	0.156
16	140.3	0.394	0.177
17	169.3	0.481	0.160
18	198.9	0.508	0.163
19	172.5	0.473	0.169
20	141.5	0.352	0.130
21	149.7	0.364	0.123
22	150.2	0.388	0.148
23	145.6	0.381	0.142
24	139.3	0.401	0.168
25	127.8	0.311	0.117
26	149.2	0.433	0.167
27	119.4	0.309	0.117
28	134.8	0.345	0.130

The CHES-FY and the friction test

The schematic structure of the CHES-FY, which comprises a pulling pin, bi-U-shaped pins, a pair of jaws, a force sensor and a digital camera, is illustrated in Figure 1. The horizontal distance between the two jaws (D_JJ), the interval of the bi-U-shaped pins (D_PP), the vertical distance between the jaws and the bi-U-shaped pins (D_JP) and the diameter of bi-U-shaped pins (d) can be adjusted according to experimental conditions (see Figure 1).

Figure 1.

Three-dimensional schematic structure (a), two-dimensional schematic structure with four system parameters (b) and artifact photo (c) of the comprehensive handle evaluation system for fabrics and yarns.

The pulling pin can move up and down to pull a fabric sample through the interval of the bi-U-shaped pins, and the force sensor connecting with the pulling pin can simultaneously record the pulling-out force. By analyzing the deformation of the fabric, the pulling-out process of the CHES-FY is divided into four steps, that is, weighting, bending, friction and stretching steps; the friction step starts at the end of the bending step when the pulling-out force reaches a maximum value and finishes when the fabric start to be stretched by the pins,²⁶ as shown in Figure 2. Thus, the pulling-out force–displacement curve was generally divided into the corresponding four segments referring to the turning points (see Figure 2(b)). Before the maximum value of the pulling-out force, bending deformation is dominant, and the pulling-out force mainly reflects the bending property of the fabric. Thus, the increasing segment of the curve was considered to correspond to the bending step. Thereafter, the pulling-out force suddenly decreases once the fabric begins to slip on the surface of the bi-U-shaped pins by overcoming the static friction, where the dynamical friction coefficient of fabrics is a key factor that affects the slope of the falling segment of the curve. Therefore, the linear fitting slope of the falling segment of the curve (termed as the right-hand slope, S_r) and the maximum pulling-out force (termed as peak value P) were selected as the two curve parameters. The area under the falling segment of the curve (i.e. the right-hand area, A_r) was also extracted to better reflect the features of the falling segment. In the following status of the pulling-out process, the contacting angle between the fabric sample and bi-U-shaped pins is approximately constant, showing a segment of the horizontal curve, which significantly displays the friction behavior of the fabric, so it was selected as another curve parameter and termed as horizontal force (f_m). The fabric keeps sliding along the surface of bi-U-shaped pins until it tends to be stretched with the pulling-out force–displacement curve showing a rapid increase at the last segment (i.e. the stretching step). The four curve parameters for evaluating the friction property of fabrics are illustrated in Figure 2(b).

Figure 2.

The pulling-out process (a) and corresponding pulling-out force–displacement curve with four curve parameters (b) of the comprehensive handle evaluation system for fabrics and yarns.

Design of the orthogonal experiment

The orthogonal experiment was applied to select optimal system parameters in order to better evaluate the friction property of fabrics by the CHSE-FY. The four system parameters, that is, D_JJ, d, D_JP and D_PP, were selected as four factors, and each of the factors was assigned with four levels. Therefore, 16 experiments should be performed for each fabric, and four curve parameters could be featured from each pulling-out–displacement curve of the experiments for each fabric. In order to analyze the effects of the four system parameters on the test results of the fabric friction properties, correlations between the friction coefficient tested by the KES-F4 and curve parameters featured from the CHES-FY were carried out.

Results and discussion

Determination of the optimal system parameters

Orthogonal experiment array with correlation analysis

The four-factor and four-level orthogonal experiment was used to determine the optimal system parameter of the CHES-FY based on the correlations between the friction coefficient and four system parameters. The orthogonal experiment array and results of the correlation analysis are given in Table 2, where L1, L2, L3 and L4 represent the four levels; the indices R_Sr, R_P, R_Ar and R_fm are the correlation coefficients between the right-hand slope, the peak value, the right-hand area and the horizontal force and friction coefficient, respectively. It should be pointed out that the four curve parameters cannot be featured from the curve of experiment no. 4 as there is no typical peak in the pulling-out force–displacement curves at this system parameter setting. Thus, experiment no.4 is considered to be an unexpected selection of the system parameters and can be ignored directly in the experimental analysis.

Table 2.

Orthogonal experiment array and correlation coefficients between the friction coefficient and curve parameters

Experiment no.	Factor				Index
Experiment no.	D_JJ (mm)	D_JP (mm)	d (mm)	D_PP (mm)	R_Sr	R_P	R_Ar	R_fm
1	50 (L1)	45 (L1)	2 (L1)	3 (L1)	−0.820	0.807	0.824	0.688
2	50 (L1)	50 (L2)	4 (L2)	3.5 (L2)	−0.943	0.883	0.820	0.803
3	50 (L1)	55 (L3)	6 (L3)	4 (L3)	−0.867	0.864	0.823	0.851
4	50 (L1)	60 (L4)	10 (L4)	5 (L4)	_	_	_	_
5	55 (L2)	45 (L1)	4 (L2)	4 (L3)	−0.927	0.828	0.873	0.654
6	55 (L2)	50 (L2)	2 (L1)	5 (L4)	−0.939	0.849	0.839	0.771
7	55 (L2)	55 (L3)	10 (L4)	3 (L1)	−0.596	0.754	0.732	0.750
8	55 (L2)	60 (L4)	6 (L3)	3.5 (L2)	−0.917	0.902	0.836	0.903
9	60 (L3)	45 (L1)	6 (L3)	5 (L4)	−0.853	0.802	0.824	0.752
10	60 (L3)	50 (L2)	10 (L4)	4 (L3)	−0.678	0.783	0.710	0.771
11	60 (L3)	55 (L3)	2 (L1)	3.5 (L2)	−0.792	0.766	0.766	0.609
12	60 (L3)	60 (L4)	4 (L2)	3 (L1)	−0.784	0.808	0.754	0.689
13	65 (L4)	45 (L1)	10 (L4)	3.5 (L2)	−0.653	0.860	0.587	0.645
14	65 (L4)	50 (L2)	6 (L3)	3 (L1)	−0.927	0.857	0.880	0.727
15	65 (L4)	55 (L3)	4 (L2)	5 (L4)	−0.838	0.840	0.780	0.841
16	65 (L4)	60 (L4)	2 (L1)	4 (L3)	−0.849	0.878	0.903	0.725

Analysis of the significances of the factors and levels

The range analysis was used to determine the sequence of significant factors and levels based on the average value (K_ij) of each factor at four levels and the corresponding range value (R_j), which are listed in Table 3.

Table 3.

Average value and range value of orthogonal experiments

		Average value and range value
		Factor D_JJ	Factor D_JP	Factor d	Factor D_PP
Based on index R_Sr	K ₁ _j	−0.877	−0.813	−0.850	−0.782
	K ₂ _j	−0.845	−0.872	−0.873	−0.826
	K ₃ _j	−0.777	−0.773	−0.891	−0.830
	K ₄ _j	−0.817	−0.850	−0.642	−0.877
	R_j	−0.100	−0.099	−0.249	−0.095
Based on index R_P	K ₁ _j	0.851	0.824	0.825	0.807
	K ₂ _j	0.833	0.843	0.840	0.853
	K ₃ _j	0.790	0.806	0.856	0.838
	K ₄ _j	0.859	0.863	0.799	0.830
	R_j	0.069	0.057	0.057	0.046
Based on index R_Ar	K ₁ _j	0.822	0.777	0.833	0.798
	K ₂ _j	0.820	0.812	0.807	0.752
	K ₃ _j	0.764	0.775	0.841	0.827
	K ₄ _j	0.788	0.831	0.676	0.814
	R_j	0.059	0.056	0.164	0.075
Based on index R_fm	K ₁ _j	0.781	0.685	0.833	0.714
	K ₂ _j	0.770	0.768	0.747	0.740
	K ₃ _j	0.705	0.763	0.808	0.750
	K ₄ _j	0.735	0.772	0.722	0.788
	R_j	0.076	0.088	0.111	0.074

According to the range value (R_j), the significances of the factors, on the basis of index R_Sr, are in the order d > D_JJ > D_JP > D_PP. Similarly, another three significant sequences of the factors can be obtained based on the corresponding index and range value. In order to synthesize the four sequences of the factors, a quantitative method was used to set numerical values as 1, 2, 3 and 4 by the sequence of the factors, and thus the sequences of the factors were transformed into numerical values, where the smaller the values are, the more significant the factor is. The results of the numerical values are summarized in Table 4.

Table 4.

Numerical values of factors by significant sequence

	Numerical value of significant sequence of factors
	D_JJ	D_JP	d	D_PP
Based on index R_Sr	2	3	1	4
Based on index R_P	1	2	2	4
Based on index R_Ar	3	4	1	2
Based on index R_fm	3	2	1	4
Sum of numerical values of each factor	9	11	5	14

From Table 4, the effects of the diameter of bi-U-shaped pins (d) are the most significant, as indicated by the smallest sum of its numerical values. The following are D_JJ and D_JP, and the weakest significant factor is D_PP with the largest sum of numerical value. Therefore, the integrated significances of the factors are in the order d > D_JJ > D_JP > D_PP.

By comparing the four average values of each factor, the significant sequence of the four levels for each factor based on each index can be determined, as shown in Table 5. It is clear that the excellent level of factor d can be selected as L3, as level L3 is regarded as the first significant level by three indices and the second significant level by an index. Similarly, the excellent levels of factors D_JJ and D_JP are selected as L1 and L4, respectively. For factor D_PP, levels L4 and L3 have similar effects, and thus both of them are initially selected for excellent levels. Therefore, two superior combinations of the levels of the four system parameters (d, D_JJ, D_JP and D_PP) are as follows: L3, L1, L4 and L3, and L3, L1, L4 and L4. The two combinations are not in the 16 experiments of orthogonal design; they are named as experiments no. 17 and no. 18, respectively. Thus, annex experiments should be adopted to compare these two experiments in order to determine better system parameters for the friction test of fabrics.

Table 5.

Significant sequences of four levels for each factor based on each index

	Sequence of level
	D_JJ	D_JP	d	D_PP
Based on index R_Sr	L1 > L2 > L4 > L3	L2 > L4 > L2 > L3	L3 > L2 > L2 > L4	L4 > L3 > L2 > L1
Based on index R_P	L4 > L1 > L2 > L3	L4 > L2 > L1 > L3	L3 > L2 > L1 > L4	L2 > L3 > L4 > L1
Based on index R_Ar	L1 > L2 > L4 > L3	L4 > L2 > L1 > L3	L3 > L1 > L2 > L4	L3 > L4 > L1 > L2
Based on index R_fm	L1 > L2 > L4 > L3	L4 > L2 > L3 > L1	L1 > L3 > L2 > L4	L4 > L3 > L2 > L1

Comparisons between experiments no.17 and no.18

Based on the selected system parameters, the pulling-out tests were carried out for experiments no.17 and no.18. The correlation coefficients between curve parameters and friction coefficients and the coefficients of variation (C.V.) of curve parameters were calculated and are given in Table 6.

Table 6.

Result comparisons between experiments no.17 and no.18

	Correlation with friction coefficient				C.V. of curve parameters (%)
Experiment	Right-hand slope (S_r)	Peak value (P)	Right-hand area (A_r)	Horizontal force (f_m)	Right-hand slope (S_r)	Peak value (P)	Right-hand area (A_r)	Horizontal force (f_m)
No.17	−0.895	0.912	0.851	0.900	0.973	1.201	1.015	0.910
No.18	−0.901	0.907	0.854	0.887	0.816	0.937	0.921	0.895

C.V.: coefficient of variation.

As observed, the correlation coefficients of the peak value (P) and horizontal force (f_m) of experiment no.17 are larger than those of experiment no.18, while the correlation coefficients of the right-hand slope (S_r) and right-hand area (A_r) of experiment no.17 are slightly smaller than those of experiment no.18. Thus, regarding the correlation with friction coefficient, there is no significant difference between experiments no.17 and no.18. However, the C.V.s of the four curve parameters of experiment no.17 are all larger than those of experiment no.18. This can be explained because the larger C.V. means higher sensitivity of the experiment to discriminate fabrics with a close friction property. Hence, experiment no.17 with the higher absolute C.V. being 0.973, 1.201, 1.015 and 0.910 compared with those (0.816, 0.937, 0.921 and 0.895) of experiment no.18 can better evaluate the friction property and improve the sensitivity of the CHES-FY. Therefore, the optimal system parameters are from experiment no.17 and are concluded as follows: the diameter of bi-U-shaped pins is 6 mm; the horizontal distance between the jaws is 50 mm; the vertical distance between the jaw and bi-U-shaped pins is 60 mm; and the interval of the bi-U-shaped pins is 4 mm.

By relating the curve parameters of the CHES-FY with the optimal system parameters to the friction coefficient by the KES-F4, a multiple regression model for the prediction of the friction coefficient of fabrics was developed. The entry method was adopted to conduct the modeling based on an analysis of variance (ANOVA) at the 95% confidential level. The regression model is shown in Equation (1)

Frictioncoefficient = 0.120 - 0.088 S_{r} - 0.013 P + 0.001 A_{r} + 0.011 f_{m} (R^{2} = 0.848)

(1)

The regression model fits well, as indicated by the high determination coefficient (R²) and the p-value (<0.001).

Analysis of system repeatability and stability

To validate the repeatability and stability of the CHES-FY under the setting of the optimal system parameters and to test the effectivity of this system for evaluating the friction property of different kinds of fabrics, the fabrics of five types of materials (cotton, viscose, ultra-high molecular weight polyethylene (UHMWPE), aramid and polyester) were used to wrap the bi-U-shaped pins, as shown in Figure 3, and three repeat tests were carried out by using each type of the wrapped bi-U-shaped pins for each of the 28 fabric samples. Four curve parameters were featured from the pulling-out force–displacement curves, and Equation (1) was employed to integrate the four curve parameters of each test into a value in order to make the analysis more convenient. The C.V. of the predicted friction coefficient of every three repeat tests was calculated and is statistically given in Table 7. It should be pointed out that fabrics no.7, no.8 and no.18 cannot be tested by the bi-U-shaped pins wrapped by the cotton fabric as the corresponding pulling-out force–displacement curves of these fabrics are monotonically increasing, not showing the typical peak value. This may be due to the specific structure of the fabric surface with suede accents. Thus, it also implies that the bi-U-shaped pins wrapped by cotton may not be suitable for measuring fuzzy suede fabrics.

Figure 3.

The bi-U-shaped pins wrapped by five types of materials: (a) cotton; (b) viscose; (c) ultra-high molecular weight polyethylene; (d) aramid; (e) polyester.

Table 7.

The statistic results of the coefficient of variation (C.V.) of the predicted friction coefficients for 28 fabrics under five types of wrapped bi-U-shaped pins

C.V.	Cotton	UHMWPE	Viscos	Aramid	Polyester
Min	0.002	0.005	0.003	0.002	0.001
Max	0.073	0.049	0.042	0.047	0.067
Mean	0.017	0.013	0.011	0.014	0.006

UHMWPE: ultra-high molecular weight polyethylene.

Except for these three experiments of fabrics no.7, no.8 and no.18, the predicted friction coefficients of the three repeat tests of each fabric are very close for every type of wrapped bi-U-shaped pins, as indicated by the maximum value of C.V. below 0.1. Therefore, the repeatability of the tests is good. It also indicates that the CHES-FY with the selected optimal system parameters can obtain stable pulling-out force–displacement curves, and curve parameters and the corresponding friction coefficient calculated from the curve parameters are very stable.

Table 8 gives the correlation coefficients between the four curve parameters measured by the CHES-FY with five types of wrapped bi-U-shaped pins and friction coefficients tested by the KES-F4. The settings of the four system parameters of the CHES-FY are also the same as the selected optimal system parameters in experiment no. 17. It can be seen from Table 8 that all the four curve parameters from the CHES-FY with five types of wrapped bi-U-shaped pins are significantly correlated with the friction coefficients tested by the KES-F4, with the absolute correlation coefficients ranging from 0.762 to 0.931. This result further explains that it is proper to use the four curve parameters to evaluate the friction property. Moreover, the good correlations between the curve parameters and friction coefficient also sustain the stability and repeatability of the CHES-FY for evaluating a fabric’s friction coefficient.

Table 8.

Correlation coefficients between the four curve parameters and friction coefficients tested by the Kawabata evaluation system for fabric surface tester

	Peak value (P)	Right slope (S_r)	Right area (A_r)	Horizontal force (f_m)
Cotton	0.931	−0.808	0.909	0.908
UHMWPE	0.878	−0.925	0.762	0.850
Viscos	0.898	−0.881	0.883	0.852
Aramid	0.881	−0.844	0.859	0.869
Polyester	0.905	−0.914	0.866	0.888

Correlation is significant at the 0.01 level (two-tailed).

UHMWPE: ultra-high molecular weight polyethylene.

Evaluating smoothness/roughness handle by the CHES-FY

k-means cluster analysis of smoothness/roughness handle

To study the feasibility of the CHES-FY for evaluating the comprehensive friction property, that is, smoothness/roughness handle, of wear fabrics, the k-means cluster method was adopted to discriminate the smoothness/roughness handle of fabrics based on the measurements of the CHES-FY with selected optimal system parameters. As well as the original 28 wool woven fabrics, another 11 woven fabrics (numbered from #29 to #39), which include cotton, polyester and cotton/polyester blended fabrics with the thickness ranging from 0.245 to 0.599 mm and mass ranging from 145.2 to 227.8 g/m², are also included to extend the range of smoothness/roughness handle. The process of the k-means cluster method has been described in previous studies.²⁵ Briefly, the four curve parameters of each pulling-out curve–displacement curve were featured, forming a sample vector. The smoothness/roughness handle of fabrics was considered to be classified as five clusters; thus, five initial cluster centers were assigned, as shown in Table 9. Each sample vector was then assigned to the corresponding cluster based on the minimum Euler’s distance and, thereafter, the cluster centers were updated based on the mean of the sample vectors. This process was iterated until the invariable cluster centers were acquired. The cluster process was carried out using the SPSS 19 statistics software, and five clusters were objectively formed. The cluster results are summarized in Table 10, where cluster no.1, cluster no.2, cluster no.3, cluster no.4 and cluster no.5 represent a very smooth cluster, a smooth cluster, a moderate cluster, a rough cluster and a very rough cluster, respectively.

Table 9.

Initial clustering center

	Cluster center
	1	2	3	4	5
Right-hand slope (S_r)	−0.22	−1.30	−1.94	−1.72	−5.61
Peak value (P)	3.37	13.71	21.14	24.96	55.64
Right-hand area (A_r)	13.0	62.0	112.0	152.0	237.0
Horizontal force (f_m)	2.35	6.94	8.49	13.35	29.46

Table 10.

Objective clustering results of 39 fabrics

Cluster no.1

Sample no.

#12

#13

#14

#15

#16

#20

#21

#22

#23

#24

#25

Euler’s distance

8.9

0.8

13.0

3.9

2.0

1.6

3.9

1.9

2.0

2.3

2.0

Sample no.

#27

#28

#29

#30

#33

#34

#36

#37

Euler’s distance

11.5

2.2

13.3

13.9

5.2

14.6

11.3

12.5

Cluster no.2

Sample no.

#11

#17

#19

#26

#31

#32

#35

#38

#39

Euler’s distance

9.6

8.5

6.9

7.5

10.6

11.1

8.7

11.0

2.4

5.9

19.3

Cluster no.3

Sample no.

#18

Euler’s distance

17.8

6.6

7.0

Cluster no.4

Sample no.

Euler’s distance

7.3

15.8

14.0

25.4

Cluster no.5

Sample no.

#10

Euler’s distance

0.0

Comparisons with subjective assessments

Subjective assessments were also employed to classify the 39 samples into five clusters in order to compare them with the objective evaluation results. Eight judges aged from 20 to 28 formed the subjective judgment panel and made judgments according to the AATCC (American Association of Textile Chemists and Colorists) evaluation method.²⁷ Five reference samples with very smooth, smooth, moderate, rough and very rough handle were used to train the judges. Ranking value, ranging from 1 to 39, was adopted to synthesize the assessment results from the eight judges. The results are given in Table 11.

Table 11.

Subjective cluster results of 39 fabrics

Very smooth cluster

Sample no.

#12

#13

#15

#20

#21

#24

#27

#28

#29

#33

#37

Ranking value

113

111

110

Smooth cluster

Sample no.

#14

#16

#19

#22

#23

#25

#26

#30

#31

#34

Ranking value

126

118

114

179

127

116

117

120

145

157

169

Sample no.

#35

#36

#38

Ranking value

170

123

180

Moderate cluster

Sample no.

#11

#17

#18

#32

#39

Ranking value

196

187

214

192

191

216

223

233

Rough cluster

Sample no.

Ranking value

253

257

261

Very rough cluster

Sample no.

#10

Ranking value

272

288

312

The effectiveness coefficient of ranking value (W) and F hypothesis test were also utilized to evaluate the effectiveness of ranking values, which can be expressed as

W = \frac{12 \sum_{i = 1}^{n} (T_{i} - \sum_{i = 1}^{n} T_{i} / n) 2}{m^{2} (n^{3} - n)}

(2)

F (ν_{1}, ν_{2}) = \frac{(m - 1) W}{1 - W}, ν_{1} = (n - 1) - \frac{2}{m}, ν_{2} = (m - 1) ν_{1}

(3)

where T_i is the ranking value of the ith sample; m is the number of judges; and n is the number of samples. According to Table 11, the effectiveness coefficient (W) is 0.84. The subjective assessments of the smoothness/roughness handle are effective and the ranking values of the 39 samples are confident at the 0.01 level, as indicated by F(38, 264) = 36.7 > F_0.99(38, 264) = 1.59.

By comparing Table 11 with Table 10, it can be seen that results of objective clusters by the k-means cluster method are similar to those of subjective assessments. Although there exist variations for some samples between adjacent clusters, such that samples #14, #16, #22, # 23, #25, #30, #34 and #36 are assigned to the very soft cluster by the k-means cluster method based on measurements of the CHES-FY, but are assigned to the soft cluster by judges in subjective assessments. However, it can be found that the ranking values of these samples are very close to the samples in the very soft cluster, and there are no large gaps between the clustering results of the objective and subjective evaluations. Therefore, the CHES-FY with the selected system parameters can be used to effectively characterize the smoothness/roughness handle of fabrics based on the four curve parameters.

Conclusions

Experimental investigations of measuring friction properties of fabrics using the CHES-FY were reported. Orthogonal experiment design was employed to analyze the optimal system parameters of the CHES-FY based on the selected four curve parameters and their correlations with friction coefficients tested by the KES-F4. Results showed that the four system parameters were listed in the order of significance for the friction testing as diameter of bi-U-shaped pins (d), horizontal distance between the jaws (D_JJ), vertical distance between the jaws and bi-U-shaped pins (D_JP) and interval of the bi-U-shaped pins (D_PP); also, the optimal system parameters were determined based on the orthogonal experiment and comparison analysis as follows: the diameter of bi-U-shaped pins is 6 mm; the horizontal distance between the jaws is 50 mm; the vertical distance between the jaw and bi-U-shaped pins is 60 mm; and the interval of the bi-U-shaped pins is 4 mm. Using the optimal system parameters, a regression model was also developed to predict a fabric’s friction coefficient. Moreover, five types of fabrics were used to wrap the bi-U-shaped pins, and three repeatable tests for each kind of wrapped bi-U-shaped pins were conducted. Low C.V.s of the repeatable tests showed good repeatability and stability of the CHES-FY for measuring friction coefficients of fabrics that comprised different materials. In addition, comparisons between objective clusters and subjective clusters of fabric smoothness/roughness handle were carried out. Results showed that the CHES-FY with k-means cluster method provided a feasible method for characterizing the smoothness/roughness handle of fabrics. It can be deduced that the four curve parameters featured from a pulling-out–displacement curve contain the main information of a fabric’s friction property, and the CHES-FY with the selected optimal system parameters can be used to characterize the friction coefficient and smoothness/roughness handle of fabrics effectively and stably.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Natural Science Foundation of China projects (grant numbers 11272086 and 51203022), the Fundamental Research Funds for the Central Universities (2232014A3-02, CUSF-DH-D-2016006 and CUSF-DH-D-2016020), the “DHU Distinguished Young Professor Program (B201307)” and the Fok Ying Tung (huoyingdong) Education Foundation (151071). The authors are grateful to the China scholarship council (CSC) for the scholarship (number 201506630046) provided to one of the authors (Sun), and supported by the National Key Research and Development Program of China (Grant No.2016YFC0802802).

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