Characterization of plantar press-comfort performance of warp-knitted spacer fabrics

Abstract

The main content dealt with in this paper was to present an objective method to evaluate the plantar press-comfort performance of warp-knitted spacer fabrics. It aimed to explain the plantar press-comfort performance of spacer fabric by the compression property and structure parameters of spacer fabric. The compression indexes (compression work, recovery work, hysteresis work and maximum compression force) and structure parameters (diameter and thickness) were utilized to classify the plantar press-comfort performance of warp-knitted spacer fabrics by regression analysis and the K-means cluster method. In order to verify the validity, subjective judgments were also made and compared with the objective K-means cluster method. The experimental results showed that a good correlation existed between the subjective judgment method and objective cluster method. This demonstrates that the compression indexes featured, from spherical compression force–displacement curves and structure parameters, can be utilized to characterize the plantar press-comfort performance of warp-knitted spacer fabrics and is effective in obtaining the fabric evaluation score of plantar press-comfort performance.

Keywords

spacer fabrics plantar press-comfort compression indexes regression analysis cluster analysis spherical compression

Warp-knitted spacer fabrics have been widely used as textile products due to their special sandwich structure, which can provide products with good press-comfort performance. Spacer fabrics are currently produced into ergonomic cushion materials and apparel products by design of a special structure, such as functional bra support,¹ buffer clothing,² insoles and bed mattresses^3,4 and car seats.⁵ In addition, many researchers have made analysis models and effective measurements for physical properties, such as the stab-resistant property,⁶ compression behavior,^7,8 impact behavior,^9–11 structural models,^12–15 sound absorption,^16,17 pressure reduction^18,19 and vibration-absorption and comfort properties.^20,21 In particular, spacer fabrics are utilized as textile-reinforced concrete applications by designing a three-dimensional (3D) structure combining high-performance fibers with a cement-based matrix.^22,23

Spacer fabric is a kind of flexible textile, and is suitable for ergonomic products. Under wearing applications, there exists action and reaction between spacer fabrics and the human body. In order to have a scientific method to explain the contact relationship between the human body and spacer fabrics, an interaction contacting geometry model has been presented. Some parts of the body contacting with spacer fabrics were almost arc-shaped,^20,24 while other contacting parts were almost flat-shaped. The pressure–relief property of spacer fabric is an important characteristic for ergonomic applications, and there are some relations between the pressure–relief property and the pressure–comfort property of spacer fabric. Therefore, it is necessary to consider the objective method and discuss it in accordance with subjective evaluation so as to establish an effective method to characterize the press-comfort property of spacer fabric. Researchers have conducted theoretical modeling of spherical compression, especially on establishing correlation between plane plate compression and spherical compression of spacer fabrics,²⁵ and have discussed the influencing trend of structural parameters of spacer fabric on compression behavior.²⁶ A spherical indenter was generally used to simulate different parts of the body, such as the shoulder region, buttock and human plantar.^27–29 Some researchers have studied the improvement of the performance of insoles to reduce plantar pressure;^30–33 however, there are few reports on the press-comfort level of spacer fabrics under compression based on the compression property, especially for plantar mattress applications.

This paper aims to characterize the plantar press-comfort level of spacer fabric as an insole mattress, and to explore a new objective method to characterize the plantar press-comfort performance of warp-knitted spacer fabrics. It features compression indexes to characterize the compression property and to analyze the influencing trend of structural parameters of spacer fabric on compression behavior. The corresponding pressure indexes, including compression work (CW), recovery work (RW), hysteresis work (HW) and maximum compression force (CF) featured from spherical compression, are used to classify spacer fabrics. Moreover, the subjective method is utilized to group spacer fabrics according to the pressure performance by volunteers. Then, the relationship between the subjective judgment method and the objective cluster method is studied to verify the effectiveness of the objective cluster method.

Theoretical analysis

In this paper, four indexes featured from the spherical compression force–displacement curves obtained by the compression tester JA12002 and two structural parameters were used to objectively evaluate the plantar press-comfort performance of warp-knitted spacer fabrics. In order to verify the feasibility, the number of clusters of plantar press-comfort performance of spacer fabrics was pre-determined by subjective expert panels. The clustering algorithm is effective in automatically making clusters. Thereof, this paper adopts the K-means clustering algorithm^34,35 to classify the plantar press-comfort performance of warp-knitted spacer fabrics.

K-means clustering algorithm

The K-means clustering algorithm is an accurate method with high efficiency in clustering samples with a definite number of clusters. The primary calculation in the K-means clustering algorithm is an iterative process of calculating cluster centers and grouping the sample vector to clusters. The primary steps in the procedure are as follows: (1) select the initial cluster centers; (2) group each sample vector to the nearest cluster; (3) update the cluster centers based on the sample vectors grouped into each cluster; (4) repeat Steps 2 and 3 until there is no change in the cluster centers from the previous iteration in Step 3.

Pretreatment of sample vector

For each spacer fabric sample measured by the compression tester, the number of indexes of the compression property and structure parameters, n, is featured. Each spacer fabric has a corresponding sample vector $Y_{i}'$ formed by these indexes [ $Y_{i 1}'$ , $Y_{i 2}'$ , … , $Y_{in}'$ ], that is, $Y_{i}'$ = [ $Y_{i 1}'$ , $Y_{i 2}'$ , … , $Y_{in}'$ ]. All sample vectors ([ $Y_{1}'$ , $Y_{2}'$ , … , $Y_{m}'$ ]) make up a matrix $Y'$ as follows

[Y'] = [Y_{1}' Y_{2}' : Y_{m}'] = [Y_{11}' Y_{12}' \dots Y_{1 n}' Y_{21}' Y_{22}' \dots Y_{2 n}' : : : : Y_{m 1}' Y_{m 2}' \dots Y_{mn}']

(1)

where m is the number of spacer fabric samples and n is the number of featured indexes.

In order to eliminate the influence of different dimensions of indexes’ values, the matrix in equation (1) is processed by a standardized pretreatment according to equation (2)

Y_{ij} = \frac{Y_{ij}' - {\bar{Y}}_{j}}{σ_{j}}, (i = 1, 2, \dots, m; j = 1, 2, \dots, n)

(2)

where

{\bar{Y}}_{j}

and

σ_{j}

are the mean and standard deviation of all elements in the column j;

Y_{ij}'

and

Y_{ij}

are the element of the matrix before and after standardized pretreatment, respectively. Then, sample vector

Y_{i}'

is transformed into a new sample vector Y_i, and a new matrix

Y = [Y_{1}, Y_{2}, \dots, Y_{m}]

including all samples’ vectors is obtained

[Y] = [Y_{11} Y_{12} \dots Y_{1 n} Y_{21} Y_{22} \dots Y_{2 n} : : : : Y_{m 1} Y_{m 2} \dots Y_{mn}]

(3)

Selecting the initial cluster centers

The initial cluster centers are selected by using a maximin algorithm for the number of clusters, specified as c. The primary steps in selecting the initial cluster centers are as follows: (1) initialize the first cluster center as the values of the input fields for the first sample vector, that is, $v_{1} = [v_{11}, v_{12}, \dots, v_{1 n}]$ ; (2) for each sample vector, the minimum Euler’s distance is calculated between the sample vector and each defined cluster center; (3) select the sample vector with the largest minimum Euler’s distance from the defined cluster centers, and then add a new cluster center with values of the input fields for the selected sample vector, $v_{t} = [v_{t 1}, v_{t 2}, \dots, v_{tn}], t = 1, 2, \dots, c$ ; (4) repeat Steps 2 and 3 until the number of cluster centers, c, has been found, that is, v₁, v₂, … , v_c. When the initial cluster centers have been chosen, the algorithm begins the iterative assign/update process.

Clustering criteria of the sample vector

Generally speaking, the smaller the distance between the two samples vectors, the greater the possibility that they belong to the same cluster. Therefore, Euler’s distance, $D_{it}$ , is used as the clustering criteria for clustering one sample vector Y_i to one cluster center v_t

D_{it} = ‖ Y_{i} - v_{t} ‖ = [\sum_{j = 1}^{n} (Y_{ij} - v_{tj}) 2] 1 / 2 (i = 1, 2, \dots, m; t = 1, 2, \dots, c)

(4)

In order to determine which cluster center the sample vector belongs to, Euler’s distances between sample vector Y_i and all cluster centers are to be calculated. Sample vector Y_i is to be grouped into cluster center v_t for the minimum Euler’s distance between Y_i and v_t. If we have the following equation

D_{it} = min {D_{i 1}, D_{i 2}, \dots, D_{ic}}

(5)

then

Y_{i} \in v_{t}

(6)

Determination of clusters

According to equation (4), all sample vectors $[Y_{1}, Y_{2}, \dots, Y_{m}]$ in matrix Y of equation (3) have corresponding minimum Euler’s distances, $D_{it}$ , with one cluster center v_t. So, a matrix A is formed according to Euler’s distances Based on the Euler’s distances in equation (7), each sample vector can be grouped into the nearest cluster according to equations (5) and (6). Then, the matrix M with m dimensions for clusters is yielded

M = [M_{1 α}, M_{2 β}, \dots, M_{it}, \dots, M_{m γ}] T, (α, β, t, γ = 1, 2, \dots, c)

(8)

where T represents transpose of the matrix and

M_{it}

represents that the ith sample vector Y_i is grouped into the rth cluster center v_t. Based on equation (8), all sample vectors have been grouped into the nearest clusters and each cluster v_t is formed by parts of all sample vectors, as shown in equation (9)

v_{t} = {Y_{θ}, \dots, Y_{i}, \dots, Y_{φ}}, (θ, i, φ = 1, 2, \dots, m; t = 1, 2, \dots, c)

(9)

After obtaining equation (9), the first round of K-means clustering completes and all sample vectors have been grouped into clusters.

For the second round of K-means clustering, the cluster centers are to be calculated by the average values of sample vectors in the same cluster of equation (9). Let the number of sample vectors in one cluster center be λ; the jth element, $v_{tj}$ , of the cluster center vector, v_t, is recalculated as follows

v_{tj} = \sum_{k = 1}^{λ} Y_{kj}, (j = 1, 2, \dots, n; t = 1, 2, \dots, c)

(10)

All elements of the cluster center vector, v_t, are shown in equation (11) according to equation (10)

v_{t} = [v_{t 1}, v_{t 2}, \dots, v_{tn}]

(11)

The recalculated cluster center, v_t, is set as the rth cluster center, and all elements in the rth cluster center v_t are renewed. So, all cluster centers are renewed by equation (11). Then, the Euler’s distance, $D_{it}$ , in equation (4) is recalculated between sample vector Y_i and the renewed cluster center v_t. The minimum Euler’s distance between Y_i and the cluster centers can be found by equation (5), and the sample vector Y_i can be grouped into the corresponding cluster center based on equation (6). Thereafter, all sample vectors $[Y_{1}, Y_{2}, \dots, Y_{m}]$ in matrix Y of equation (3) have a renewed minimum Euler’s distance and a renewed matrix as in equation (7) is to be obtained. Each sample vector is regrouped into the nearest cluster according to equation (7), and the matrix M in equation (8) for clusters is reacquired. After obtaining equation (8), all sample vectors are grouped into the nearest clusters, and each cluster has the determined sample vectors listed in equation (9).

When the second round of K-means clustering is completed, each cluster should be checked as to whether its elements have changed or not. If the elements in each cluster are invariable, that is, equations (9)–(11) being invariable, the whole cluster process is completed. If there are variations, the cluster centers of the third round of K-means clustering are to be further recalculated according to equation (10) and are obtained as equation (11). All cluster centers are updated according to vector samples having been grouped based on equation (11); these steps from equations (4)–(11) are repeated until there is no change in the cluster centers in equation (11).

Experimental details

Samples

Twenty-one warp-knitted spacer fabrics by polyester filaments were conditioned in the standard condition, namely (20 ± 2)℃, (65 ± 3)% relative humidity (RH), for 24 h before testing and all experiments were conducted at the above standard condition. The known specifications of the 21warp-knitted spacer fabrics are listed in Table 1.

Table 1.

Specifications of warp-knitted spacer fabrics

	Min.	Max.	Mean	Meanings	Unit
N_f	32.24	480.00	80.84	Number of filaments per square centimeter	Number/cm²
T	3.24	16.74	6.94	Fabric thickness	mm
D_f	59.8	232.3	184.5	Diameter of spacer filament	µm
A_q	18.5	43.1	35.8	Angle of inclination	degree
M_s	333.0	1183.4	590.0	Mass per square meter	g/m²

Subjective judgment method

Twenty-one warp-knitted spacer fabrics with size of 300 mm × 300 mm were selected for subjective judgment. Eight Chinese panelists aged from 20 to 25 formed the subjective judgment panel. Panelists were required to wear the same socks and to stay in the standard condition chamber for 30 min before testing. Five reference samples whose plantar press-comfort performance varied from very uncomfortable, uncomfortable, moderate and comfortable to very comfortable were used to set a five-grade scale of performance (scores 1, 2, 3, 4 and 5) when volunteers performed tread actions using warp-knitted spacer fabrics. Then, the panelists classified the spacer fabrics.

Panelists were required to perform three kinds of tread actions for each warp-knitted spacer fabric sample, namely standing, walking and jumping, which are designed to simulate three human motions, that is, static standing, walking and jogging for 10 minutes; then, they ranked the scores of the 21 spacer fabrics under three states, and the final score of each spacer fabric in each state was the average score of the eight panelists;³⁶ finally, according to the average grades from the panelists, the samples were separated into three clusters, which was intended to make the difference between clusters obvious and the number of spacer fabrics in each cluster appropriate. After that, samples in the same clusters were further ranked from relatively uncomfortable to relatively comfortable.

Objective compression instrument

A compression tester JA12002 (Figure 1) was chosen to perform the compression test. The indenter could be changed to a spherical one or a plate one. In this paper we chose a spherical indenter to simulate the human plantar as much as possible. In the compression process, the lower surface of spacer fabrics was fixed (with double-sided adhesive) on plane plate to avoid the sliding phenomenon, and the compression speed was set as 12 mm/min. In order to have a broader spread of results, the test was protracted up to a maximum strain of 0.60.

Figure 1.

Schematic diagram of the compression test method.

Typical compression curve and results of spacer fabrics

The typical compression force–displacement curves of the 21 warp-knitted spacer fabric samples conducted by compression tester JA12002 are shown in Figure 2. Four indexes, namely compression work (CW), recovery work (RW), hysteresis work (HW) and maximum compression force (CF), are featured from the spherical compression force–displacement curve at the maximum strain tested (0.60), as shown in Table 2.

Figure 2.

Compression force–displacement curves of the 21 spacer fabrics.

Table 2.

Statistical results of the featured indexes of the 21 spacer fabrics

Sample	CW/mJ	RW/mJ	HW/mJ	CF/N
1	85.02	51.75	33.27	52.25
2	115.25	58.22	57.04	62.45
3	187.71	112.48	75.23	91.32
4	103.62	63.02	40.59	62.90
5	137.44	81.27	56.17	61.93
6	154.23	90.33	63.90	56.87
7	48.26	26.66	21.61	31.55
8	113.23	69.08	44.15	45.31
9	65.12	36.27	28.86	49.65
10	103.19	61.30	41.89	53.91
11	48.50	25.60	22.90	48.18
12	89.64	55.30	34.33	37.63
13	447.60	261.78	185.82	130.08
14	141.55	91.03	50.52	37.42
15	174.56	105.47	69.09	51.23
16	32.87	16.76	16.11	28.24
17	351.55	207.30	144.25	159.38
18	182.99	129.21	53.78	63.65
19	15.75	10.81	4.94	22.53
20	137.13	77.64	59.49	76.33
21	22.23	12.57	9.66	27.15

Results and discussion

Analysis of subjective judgment

According to subjective judgment, ranking values of the 21 warp-knitted spacer fabrics are grouped into three clusters and are listed in Table 3. In order to evaluate the agreement of ranking values of all warp-knitted spacer fabric samples by the eight panelists, the agreement coefficient, W,^36,37 of the ranking values and F-test³⁷ are utilized to test the effectiveness according to statistical analysis of the subjective judgment method

W = \frac{12 S}{p 2 (q 3 - q)}

(12)

where S is the quadratic sum of difference between the ranking value of the ith spacer fabric sample T_i and the average ranking value of all fabric samples’ ranking values, p is the number of panelists and q is the number of spacer fabric samples

S = \sum_{i = 1}^{q} (T_{i} - \bar{T}) 2 = \sum_{i = 1}^{q} T 2 - q \bar{T} 2 (13 a) \bar{T} = \sum_{i = 1}^{q} T_{i} / q (13 b)

F (v_{1}, v_{2}) = \frac{(p - 1) \cdot W}{1 - W}

(14)

Table 3.

Subjective evaluation of the plantar press-comfort performance of the 21 spacer fabrics

Comfortable cluster	Fabric no.	19#	12#	21#	7#	3#	16#	4#	9#
	Stand average	4.50	4.75	4.50	4.25	4.63	4.25	4.50	3.75
	Walk average	4.50	4.63	4.50	4.25	4.50	4.13	4.13	3.63
	Jump average	4.50	4.38	4.50	4.13	4.25	4.13	4.00	3.38
	Total rank value	14	21	23	37	40	49	51	58
Moderate cluster	Fabric no.	1#	18#	20#	11#	2#	10#
	Stand average	3.38	3.13	3.63	3.25	2.88	3.63
	Walk average	3.25	3.00	3.38	3.13	2.50	3.38
	Jump average	3.25	3.13	3.25	3.13	2.50	3.25
	Total rank value	74	76	91	98	101	107
Uncomfortable cluster	Fabric no.	14#	13#	6#	8#	15#	17#	5#
	Stand average	1.25	1.00	1.38	1.25	1.75	1.13	1.00
	Walk average	1.25	1.00	1.38	1.25	1.50	1.13	1.00
	Jump average	1.13	1.00	1.25	1.25	1.25	1.13	1.00
	Total rank value	139	140	143	143	143	148	152

The two degrees of freedom are

v_{1} = (p - 1) - 2 / q and v_{2} = (q - 1) \cdot v_{1}

(15)

According to Table 3, the agreement coefficient, W, is equal to 0.932. When the confidence level is selected as 0.01, $F = \frac{(8 - 1) \times 0.932}{1 - 0.932} = 95.94 > F_{0.99} (20, 140) \approx 2.00$ . This indicates that the subjective judgments of plantar press-comfort performance by eight panelists are effective and their rank values of the 21 spacer fabric samples are at the 0.01 confidence level.

According to the average score and total rank value shown in Table 3, the 21 warp-knitted spacer fabrics were separated into three grades. Figure 3 shows the total rank according to the plantar press-comfort level of the spacer fabrics. There existed obvious difference for the three grades. Eight spacer fabrics were allocated into the comfortable cluster, six spacer fabrics in the moderate cluster and seven spacer fabrics in the uncomfortable cluster.

Figure 3.

Rank graph of the plantar press-comfort performance of the 21 spacer fabrics.

Regression analysis

Correlation of structural parameters and fabric evaluation score

In the analysis of double relevant variables in SPSS software, correlation analysis is conducted amongst the four compression indexes in Table 2, the structural parameters in Table 1 and the subjective evaluation score in Table 3. As shown in Table 3, there are three grades whose results are basically consistent, so static stand grades are chosen to explore correlation of the featured indexes and fabric evaluation score (E_s). Their correlation coefficients are listed in Table 4. CW, RW, HW, CF, T, D_f, M_s, A_q, N_f and Es are the compression work, recovery work, hysteresis work, maximum compression force, fabric thickness, diameter of the spacer filament, mass per square meter, angle of inclination, number of filaments per square centimeter and fabric evaluation score, respectively.

Table 4.

Statistical correlations between the featured indexes and properties of spacer fabrics

	CW	RW	HW	CF	T	D_f	M_s	A _q	N _f	E_s
CW	1
RW	.996**	1
HW	.991**	.974**	1
CF	.900**	.883**	.913**	1
T	.542*	.589**	.466*	.272	1
D_f	.585**	.591**	.568**	.612**	.543*	1
M_s	.821**	.852**	.763**	.727**	.551**	.464*	1
A_q	−.290	−.283	−.295	−.080	−.231	−.055	−.132	1
N_f	−.313	−.311	−.310	−.279	−.508*	−.812**	−.201	−.202	1
E_s	−.625**	−.622**	−.620**	−.453*	−.625**	−.599**	−.286	.411	.464*	1

Correlation is significant at the 0.01 level (two-tailed). *Correlation is significant at the 0.05 level (two-tailed).

According to the results in Table 4, fabric thickness (T ) has a certain relation with compression work (CW ), recovery work (RW ) and hysteresis work (HW ), and correlation is significant at the 0.01 level (two-tailed) and 0.05 level (two-tailed); fabric thickness (T ) has a certain correlation with the fabric evaluation score (E_s); the correlation coefficients is 0.625, which illustrates that there is a definite relationship between fabric thickness (T) and the fabric evaluation score (E_s). There is a correlation between the diameter of the spacer filament (D_f) and compression work (CW), recovery work (RW), hysteresis work (HW) and the maximum compression force (CF), where all correlation coefficients were greater than 0.550; the diameter of the spacer filament (D_f) has some relation with the fabric evaluation score (E_s); the correlation coefficients is 0.599. So, when characterizing the plantar press-comfort performance, it is necessary to consider the influence of fabric thickness (T) and the diameter of the spacer filament (D_f).

Correlation of featured indexes by objective spherical compression and fabric evaluation score

A multiple linear regression analysis is done with SPSS statistical software to feature four indexes (independent variables) by objective spherical compression curve and the fabric evaluation score (E_s) (dependent variable). The multiple linear regression analysis for the featured indexes and fabric evaluation score (E_s) was conducted and the result is shown in Figure 4. This shows that there is a good linear relationship between the four independent variables and the fabric evaluation score (E_s) (dependent variable). So, it is viable to adopt the multivariate linear regression method to analyze the experimental results. As shown in Table 3, there are three grades whose results are basically consistent, so we choose the static stand grade to explore the correlation of the featured indexes and the fabric evaluation score (E_s).

Figure 4.

Regression of compression work, recovery work, hysteresis work and maximum compression force and fabric evaluation score.

Regression between the featured indexes by objective spherical compression and fabric evaluation score

By using “Enter” method, the multiple linear regression analysis is conducted by considering the compression indexes (CW, RW, HW and CF) and structure parameters (T and D_f) as independent variables and the fabric evaluation score (E_s) as a dependent variable. The multiple linear regression equation is obtained

E_{s} = 5.851 + 0.020 RW - 0.055 HW + 0.025 CF - 0.137 T - 0.011 D_{f}

(16)

As shown in equation (16), the variable compression work (CW) is removed and it keeps five independent variables, which is due to compression work (CW) equal to the sum of recovery work (RW) and hysteresis work (HW). The multiple linear regression coefficients R² is 0.637, which shows that the regression equation established is relatively better. When putting the data of RW, HW, CF, T and D_f of sample 1 into equation (16), E_s = 3.45, the subjective evaluation score is 3.38. So, there is only a small difference.

Discussion between subjective and objective clusters

According to the K-means clustering method, the sample vector is composed of compression work (CW), recovery work (RW), hysteresis work (HW), maximum compression force (CF), the diameter of the spacer filament (D_f) and fabric thickness (T), that is, [CW, RW, HW, D_f, T]. Then, matrix Y′ in equation (1) is formed by the 21 spacer fabric sample vectors, and the standardized matrix Y in equation (3) is derived by equation (2). Then, the three initial cluster centers are chosen using a maximin algorithm by selecting the principle of the initial cluster centers. The three cluster centers from 1 to 3 are accordant with sample vectors, as sample no. 19, 18 and 13, respectively.

After grouping each sample vector to the corresponding cluster based on the minimum Euler’s distance in equation (5) and updating the cluster centers based on the sample vectors in equation (9), the invariable cluster centers are acquired by two iterative processes. All sample vectors are grouped into clusters and are listed in Table 5.

Table 5.

Clustering members’ results of the 21 warp-knitted spacer fabrics

Cluster no.1	Fabric no.	7#	9#	11#	12#	16#	19#	21#
	Euler’s distance	9.622	51.932	61.962	56.728	18.028	74.023	71.122
Cluster no.2	Fabric no.	1#	2#	3#	4#	5#	6#	8#
	Euler’s distance	64.689	42.272	71.396	40.646	23.569	33.226	46.320
	Fabric no.	10#	14#	15#	18#	20#
	Euler’s distance	41.627	29.083	48.662	66.249	18.710
Cluster no.3	Fabric no.	13#	17#
Cluster no.3	Euler’s distance	63.394	63.394

It can be seen from Table 5 that three clusters are objectively formed by the K-means clustering algorithm. In order to have comparisons with the subjective clusters in Table 3, cluster 1 has seven samples (7#, 9#, 11#, 12#, 16#, 19#, 21#), cluster 2 has 12 samples (1#, 2#, 3#, 4#, 5#, 6#, 8#, 10#, 14#, 15#, 18#, 20#) and cluster 3 has two samples (13#, 17#). In fact, spacer fabrics 13# and 17# are super uncomfortable, which can be verified from subjective judgments of the two fabrics reaching the top three highest. According to Table 3, the 21 fabrics are grouped into three clusters by subjective judgments. The comfortable cluster includes 19#, 12#, 21#, 7#, 3#, 16#, 4# and 9#, the moderate cluster includes 1#, 18#, 20#, 11#, 2# and 10# and the uncomfortable cluster includes 14#, 13#, 6#, 8#, 15#, 17# and 5#.

By comparing the subjective and objective results, it is found that objective clusters shows a similar trend to those in subjective clusters according to the sequences of spacer fabrics. Although there is little variation in the moderate samples, 5#, 6#, 8#, 14# and 15# are objectively grouped into Cluster 2 as the moderate cluster, while these samples are subjectively judged be in the uncomfortable cluster; 3# and 4# are subjectively judged to be in the comfortable cluster, while they are objectively grouped into cluster 2 as the moderate cluster; 11# is objectively grouped into cluster 1 as the comfortable cluster, while it is subjectively grouped into cluster 2 as the moderate cluster,; the sequences of objectively clustered samples in clusters basically follow the sequences of subjectively clustered samples in clusters with the decline of plantar press-comfort performance. There is a good accordance of clustering plantar press-comfort performance of warp-knitted spacer fabrics between the subjective judgment method and objective K-means clustering method, which demonstrates that it is feasible and effective to characterize the plantar press-comfort performance of warp-knitted spacer fabrics based on the featured indexes of the compression force–displacement curve.

Conclusion

This paper has analyzed the feasibility of evaluating the plantar press-comfort performance of warp-knitted spacer fabric by the objective compression curve. Four indexes, namely compression work, recovery work, hysteresis work and maximum compression force, are featured from spherical compression force–displacement curves. The four indexes have high correlation coefficients larger than 0.88 and also have significant relations with the diameter of the spacer filament, fabric thickness, mass and the fabric evaluation score. It is found that the four compression indexes plus the two structure parameters have significant relations with the plantar press-comfort performance and can be used to evaluate the plantar press-comfort performance of warp-knitted spacer fabrics. The compression indexes and structure parameters are formed into a sample vector representing the plantar press-comfort performance of warp-knitted spacer fabric according to the K-means clustering algorithm, and are efficient in objectively grouping the number of clusters. Subjective judgments have also been made to group spacer fabrics into three clusters, namely comfortable, moderate and uncomfortable. Comparisons of experimental and clustering results of warp-knitted spacer fabrics indicate that good accordance exists between the subjective judgment method and objective clustering method. It may be possible to show that the compression indexes featured from spherical compression force–displacement curves and structure parameters can be utilized to characterize the plantar press-comfort performance of warp-knitted spacer fabrics and are effective to obtain the fabric evaluation score.

Footnotes

Declaration of conflicting interests

The author(s) 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 is supported by Project (Grant11272086, 51203022) supported by National Natural Science Foundation of China, and supported by Fok Ying Tung (huoyingdong) Education Foundation(151071), and supported by the Fundamental Research Funds for the Central Universities (2232014A3-02, EG2016001) and supported by “DHU Distinguished Young Professor Program (B201307)”.

References

Yip

. Study of three-dimensional spacer fabrics: molding properties for intimate apparel application. J Mater Process Technol 2009; 209: 58–62.

Liu

Long

et al.

Impact compressive behavior of warp-knitted spacer fabrics for protective applications. Text Res J 2012; 82: 773–788.

Doyen

Mues

Molenberghs

et al.

Spacer fabric supported flat-sheet membranes: a new era of flat-sheet membrane technology. Desalination 2010; 250: 1078–1082.

Feng

. Development of the warp knitted spacer fabrics for cushion applications. J Ind Text 2008; 37: 213–223.

Fangueiro

et al.

Application of warp-knitted spacer fabrics in carseats. J Text Inst 2007; 98: 337–344.

Miao

Kong

Jiang

. The experimental research on the stab resistance of warp-knitted spacer fabric. J Ind Text 2013; 43: 281–301.

Liu

Zhao

et al.

Compression behavior of warp-knitted spacer fabrics for cushioning applications. Text Res J 2012; 82: 11–20.

Liu

et al.

Experimental analysis of spherical compression of warp-knitted mesh spacer fabrics. JFBI 2014; 7: 141–152.

Liu

. Protective properties of warp-knitted spacer fabrics under impact in hemispherical form. Part I: impact behavior analysis of a typical spacer fabric. Text Res J 2014; 84: 422–434.

10.

Liu

. Protective properties of warp-knitted spacer fabrics under impacting hemispherical form. Part II: effects of structural parameters and lamination. Text Res J 2014; 84: 312–322.

11.

Guo

Long

Zhao

. Investigation on the impact and compression-after-impact properties of warp-knitted spacer fabrics. Text Res J 2013; 83: 904–916.

12.

Guo

Long

Sun

et al.

Theoretical modeling of spacer-yarn arrangement for warp-knitted spacer fabrics and experimental verification. Text Res J 2013; 83: 1467–1476.

13.

Zhang

Jiang

Miao

et al.

Three-dimensional computer simulation of warp knitted spacer fabric. Fibers Text East Eur 2012; 92: 56–60.

14.

Du ZQ, Li M, Wu YX, et al. Analysis of spherical compression performance of warp-knitted spacer fabrics. J Ind Text 2017; 46: 1362–1378.

15.

Brisa

VJD

Helbig

Kroll

. Numerical characterization of the mechanical behaviour of a vertical spacer yarn in thick warp knitted spacer fabrics. J Ind Text 2015; 45: 101–117.

16.

Dias

Monaragala

Needham

et al.

Analysis of sound absorption of tuck spacer fabrics to reduce automotive noise. Meas Sci Technol 2007; 18: 2657–2657.

17.

Liu

. Sound absorption behavior of knitted spacer fabrics. Text Res J 2010; 80: 1949–1949.

18.

Feng

. Pressure reduction of spacer fabrics. J Donghua Univ (English Edition) 2007; 24: 1672–1676.

19.

Du ZQ, Wu YX, Li M and He LG. Analysis of structure of warp-knitted spacer fabric on pressure indices. Fiber Polym 2015; 16: 2491–2496.

20.

. A study of spherical compression properties of knitted spacer fabrics Part I: theoretical analysis. Text Res J 2012; 82: 1569–1578.

21.

Mozhgan

Mohammad

. Thermal insulation property of spacer fabrics integrated by ceramic powder impregnated fabrics. J Ind Text 2012; 43: 20–33.

22.

Roye

Gries

. 3-D textiles for advanced cement based matrix reinforcement. J Ind Text 2007; 2: 163–173.

23.

Koeckritz

Cherif

Weiland

et al.

In situ polymer coating of open grid warp-knitted fabrics for textile reinforced concrete application. J Ind Text 2010; 40: 157–169.

24.

. A study of spherical compression properties of knitted spacer fabrics, Part II: comparison with experiments. Text Res J 2013; 83: 794–799.

25.

Hou

Silberschmidt

. A study of computational mechanics of 3D spacer fabric: factors affecting its compression deformation. J Mater Sci 2012; 47: 3989–3999.

26.

Yang

Liu

et al.

Effect of structural parameters on compression performance of warp-knitted spacer fabric. J F B I 2015; 8: 267–276.

27.

Liu

et al.

Experimental analysis of spherical compression of warp- knitted mesh spacer fabrics. J F B I 2014; 7: 141–152.

28.

Liu

. Study on structure and mechanical properties of spacer fabric. Adv Mater Res 2011. 332–334: 1093–1096.

29.

Liu

. Analysis on plane and ball compression behavior of spacer fabric. Adv Mater Res 2011. 332–334: 1045–1048.

30.

Hayakawa Y. Study on a High Performance Insole with Human Compatibility. In: Jobbágy Á (ed.) 5th European IFMBE Conference, Budapest, Hungary, 14–18 September 2011, pp. 810–813. Berlin: Springer.

31.

Zequera M, Stephan S and Paul J. Effectiveness of insole in reducing plantar pressure and improving gait on diabetic patient. In: Karger CM, Wong S, Cruz AL (eds) 4th Latin American Congress on Biomedical Engineering, Margarita Island,Venezuela, 24–28 September 2007, pp. 718–722. Berlin: Springer.

32.

Zequera ML, and Solomonidis S. Performance of insole in reducing plantar pressure on diabetic patients in the early stages of the disease. In: 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, Argentina, 31 August–4 September 2010, pp. 2982–2985. New Jersey: IEEE Computer Society.

33.

Actis

Ventura

et al.

Multi-plug insole design to reduce peak plantar pressure on the diabetic foot during walking. Med Biol Eng Comput 2008; 46: 363–371.

34.

Dhanachandra

Manglem

Chanu

. Image segmentation using K-means clustering algorithm subtractive clustering algorithm. Proc Comp Sci 2015; 54: 764–771.

35.

Gao

Zhou

et al.

Determination of featured parameters to cluster stiffness handle of fabrics by the CHES-FY system. Fiber Polym 2013; 14: 1768–1775.

36.

Kendall

Smith

. The problem of m rankings. Ann Math Statist 1939; 10: 275–287.

37.

Legendre

Coefficient of concordance. In: Salkind

(ed). Encyclopedia of research design, 1st ed. Los Angeles, CA: SAGE Publications, Inc, 2010, pp. 164–169.