A study of multi-quality processing parameter optimization for sueded fabric

Abstract

Sueded fabric quality control depends on the processing parameter settings. The quality characteristics considered in this study are surface softness and color difference. The Taguchi method was combined with gray relational analysis (GRA) to optimize the multi-quality sueding processing parameter combinations. First, an orthogonal array is designed by using the design of experiments of the Taguchi method for the major processing parameters of the sueding machine. The signal/noise ratio and analysis of variance are calculated from the measured fabric surface softness and color difference data, significant factors influencing the quality characteristics obtained, and GRA used to remedy the deficiency in the Taguchi method, which is only applicable to single-quality characteristics. The optimum processing parameters of multiple-quality characteristics are obtained from the response table and response diagram of GRA. The quality of suede fabric can be controlled effectively by using the optimum processing parameters to set the processing parameters, and the 95% confidence interval validates the reliability and reproducibility of the experiment.

Keywords

sueding machine Taguchi quality method gray relational analysis processing parameter optimization

Sueding a surface is a technique for developing a surface pile. It has been used for many years to enhance the appearance and hand of fabrics. A sueding machine is composed of many rollers covered with sandpaper, which removes filaments from fabric to give a soft hand.¹ The structure of a sueding machine is shown in Figure 1. The operating principle is that the high-speed roller is covered with sandpaper, contacting the fabric surface. The sharp sand grains adhering to the sandpaper surface destroy the warp yarns or weft yarns on the fabric surface. At the microscopic level, a few warp and weft yarns contacting the sandpaper will break, forming a fluffy surface, similar to the fine touch of suede leather, increasing the added value of product. This is one of the necessary steps of finishing operations in the textile industry. To meet consumer demand for artificial suede as an apparel material, some research has been conducted on improving suede performance, such as the hand, drapability, density, and uniformity of the raised fine fibers, surface abrasion, and pilling resistance. The surface properties are the most important for subjective evaluation. Surface properties such as smoothness, softness, and appearance affect customer preferences.² While suede-like materials made by such methods are satisfactory in many respects, substantial color variations often occur between batch quantities of materials made at different times. It is believed that color variations are caused by changes in coating thickness, pigment to polymer ratio, coating abrasion or buffing depth, etc. Thus, very slight changes in process conditions cause poor color reproducibility and a resultant decrease in customer approval of the suede-like sheet materials.³ Surface softness is the main characteristic of sueded fabric, and surface failure changes the color difference expression. They are the important factors influencing the value of the product. The major processing parameters of a sueding machine include rotational speed of roller, forward/reverse rotation of roller, pressing depth of pressure bar, velocity of worktable, and tensile force of worktable. Only if the processing parameters are set appropriately, can the expected processing quality be obtained. However, the processing parameter combination is variable and complex, the processing conditions are tested and corrected by the operator’s experience and trial-and-error methods, wasting time and materials, and it is difficult to establish a standard work flow.
Figure 1.
Structure of a sueding machine.

According to research available in previous literature, Hasani et al. proposed the Taguchi method with gray relational analysis (GRA) for optimizing the process parameters for open-end spun yarns with multiple performance characteristics.⁴ A gray relational grade obtained from the GRA is used to optimize the process parameters. Optimal process parameters can then be determined by the Taguchi method using the gray relational grade as the performance index. Kuo and Lin developed a testing system for fabric surface softness based on the sled method.⁵ It is proven that the device can effectively and accurately test the surface softness of finished fabrics. Kuo and Tu proposed an advanced method combining GRA with the Taguchi method,⁶ which dealt with the robust parameters in calendering to meet the requirement of multiple characteristics. It adopted the Taguchi method to examine the relationship between different quality characteristics and control factors. Then, this study applied GRA to combine quality characteristics of three samples to obtain optimal parameters controlling calendering quality, to prove reliability and stability of these experiments mentioned above by means of confirmation experiments. Kuo and Su combined GRA with the Taguchi method to optimize multiple-quality injection molding processing parameter combinations.⁷ A L₁₈(2¹× 3⁷) orthogonal array was used to plan out the processing parameters that would affect the injection molding process. Then GRA was applied to resolve the drawback of single-quality characteristics in the Taguchi method, and then the optimized processing parameter combination was obtained for multiple-quality characteristics from the response table and the response graph from GRA. The reliability and reproducibility of the experiment was verified by confirming a confidence interval.

The multiple-quality characteristics of sueded fabric have not been discussed in previously in the literature. This study aims to determine the most important surface softness and color difference values among sueded fabric quality characteristics. It uses the Taguchi method and GRA to work out the correlation coefficient of different quality characteristics to integrate multiple-quality characteristics. The optimized sueding processing parameter combination is determined for quality optimization. The Taguchi method is often used in the case of targeting one single-quality characteristic at a time to find the optimal process parameters. However, the actual production process involves more than one quality characteristic. In addressing such problems, methods like fuzzy theory and artificial neural networks have been proposed, but GRA is a method used to analyze the relationship between sequences, using less data and multiple factors.⁸ GRA can be used to effectively solve the complicated inter-relationships among multiple characteristics. GRA of a gray control system is used as a complex multi-attribute decision-making method.⁹ It allows deduction of the main relationship among factors of the system with a gray method, and identification of the most significant factors that affect the system.

Research methods

Surface softness

The hand or feel of a fabric surface is known as the fabric surface softness. Based on this, a sliding plate with specially designed surface material and weight imitating the human finger applies a horizontal force to the test fabric surface and slides at a constant speed (like human finger touch), so as to measure the horizontal force between the fabric surface and sliding plate face as the surface softness of the fabric.¹⁰

Color difference

The color difference expression of a fabric surface can be measured by using an optical noncontact surface color difference method. The optical color difference characteristic is formed by scattering from surface bodies of different roughness in white light. In the measurement system, when the white light is projected to a point on the analyte surface, since the white light is light of multiple wavelength, a color difference results A single light spot is not measured at the test point, but fuzzy imaging in an optical system with a diffraction limit. The distribution of light intensity of a point image in space is determined according to the light source spread function. The distribution is described by a Gaussian distribution of the diffusion parameter σ¹¹
$h (x, y) = \frac{1}{2 π σ^{2}} e^{- \frac{x^{2} + y^{2}}{2 σ^{2}}}$
(1)

$σ = kd \approx kD (\frac{1}{u} + \frac{1}{s} - \frac{1}{f})$
(2)
where d is the diameter of the image difference blur circle, D is the diameter of the bore, s is the distance between lens and measurement plane, u is the distance from the lens to the test point, f is the focal length of lens, k is constant and its value is determined by the calibration system. There are color differences, which undergo change, between the fiber surface of unsueded fabric and that of sueded fabric. Therefore, a spectrophotometer was used to measure the color difference. In this study, the spectrophotometer used for measuring the color difference was the eXact Standard (X-Rite Inc., Ltd, USA). It is based on the CIELAB color space, created by the International Commission on Illumination (CIE), and was adopted to calculate the color difference ΔE.

The color difference ΔE, between a sample color $L_{2} a_{2} b_{2}$ and a reference color $L_{1} a_{1} b_{1}$ is, using ${(L}_{1}^{} {, a}_{1}^{} {, b}_{1}^{})$ and ${(L}_{2}^{} {, a}_{2}^{} {, b}_{2}^{})$ as two colors in Lab*
$Δ E_{ab}^{} = \sqrt{(L_{2}^{} - L_{1}^{})^{2} + (a_{2}^{} - a_{1}^{})^{2} + (b_{2}^{} - b_{1}^{})^{2}}$

The L represents lightness, the a is green at one extremity (represented by −a), and red at the other (+a). The b has blue at one end (−b), and yellow (+b) at the other. This study used a spectrophotometer to measure the textile color data so that the absolute value and difference value of the color system could be obtained.¹²

Taguchi quality method

The parameter design method of Taguchi quality engineering is used to convert the quality characteristics of surface softness and color difference into a signal/noise (S/N) ratio, so as to represent the influence of process or product level and error factor.^13,14 The Taguchi method uses a Taguchi orthogonal array for the experiment. The orthogonal array is represented by L_a(b^c), where the subscript a represents the number of experimental combinations, b represents the number of control factor levels, and c represents the number of control factors. The control factors are the parameters which may influence the quality characteristics, and the quality characteristics are the goal of the experiment. The experimental data are calculated by the following equation to obtain the S/N ratio of each experimental combination, and the factor response table is obtained by analysis of variance (ANOVA). The variation value of each control factor at different levels is known, and the factor response graph shows the optimum control factor level value. In order to know whether the control factors have a significant influence on the quality characteristics, the factor importance test uses F-ratio to evaluate the probability of factor variance and error variance being the same sample space. The larger the value, the lower the probability, meaning that the factorial effect changes the sample space.
Orthogonal array

The orthogonal array uses fewer experiments and obtains useful statistical information and reliable factorial effect. It is different from the full factorial experiment which has too many experiments and from fractional factorial experiment which has too complex experimental method. The orthogonal array used in this study is L₁₈(3⁵), i.e. there are 18 experiments, including five factors and three levels, as shown in Table 1.
S/N ratio

Table 1.
Factor condition setting of the sueding machine for five factors, three levels.

No. Factor Level

A Pressing depth (mm) (1) 4.5 × 4; 6.5 × 2

(2) 5.5 × 4; 7.5 × 2

(3) 6.5 × 4; 5.0 × 2

B Tensile force of worktable (kg) (1) 140

(2) 150

(3) 160

C Velocity of worktable (M/min) (1) 12

(2) 13

(3) 15

D Rotational speed of roller (r/min) (1) 40 × 5; 45 × 1

(2) 45 × 5; 50 × 1

(3) 50 × 5; 55 × 1

E Forward/reverse rotation of roller (F/R) (1) F; R; F; R; F; R

(2) F; F; R; F; F; R

(3) F; F; F; R; F; R

Table 2.
The L₁₈(3⁵) orthogonal array.

Factor No. A B C D E

1 1 1 1 1 1

2 1 2 2 2 2

3 1 3 3 3 3

4 2 1 1 2 2

5 2 2 2 3 3

6 2 3 3 1 1

7 3 1 2 1 3

8 3 2 3 2 1

9 3 3 1 3 2

10 1 1 3 3 2

11 1 2 1 1 3

12 1 3 2 2 1

13 2 1 2 3 1

14 2 2 3 1 2

15 2 3 1 2 3

16 3 1 3 2 3

17 3 2 1 3 1

18 3 3 2 1 2

Table 3.
Experimental data for surface softness.

No. 1 2 3 Average No. 1 2 3 Average

1 25.35 23.77 23.96 24.36 10 25.14 24.97 26.12 25.41

2 24.78 24.25 23.42 24.15 11 21.19 21.53 19.86 20.86

3 23.35 23.06 22.89 23.10 12 24.98 24.99 26.05 25.34

4 21.14 18.04 18.78 19.32 13 25.98 25.93 25.58 25.83

5 22.37 23.06 21.56 22.33 14 18.02 16.31 17.33 17.22

6 19.76 17.36 18.11 18.41 15 17.23 16.69 17.11 17.01

7 21.21 21.61 21.02 21.28 16 18.98 19.32 17.98 18.76

8 19.15 18.29 18.42 18.62 17 21.35 21.11 20.12 20.86

9 20.14 19.24 17.95 19.11 18 19.34 18.49 20.34 19.39

Table 4.
Experimental data for color difference.

No. 1 2 3 Average No. 1 2 3 Average

1 0.52 0.59 0.57 0.56 10 0.56 0.54 0.61 0.57

2 0.48 0.61 0.59 0.56 11 0.52 0.53 0.48 0.51

3 0.53 0.54 0.58 0.55 12 0.61 0.53 0.57 0.57

4 0.50 0.50 0.44 0.48 13 0.59 0.57 0.55 0.57

5 0.55 0.47 0.54 0.52 14 0.43 0.50 0.45 0.46

6 0.48 0.47 0.43 0.46 15 0.42 0.47 0.43 0.44

7 0.46 0.54 0.56 0.52 16 0.47 0.44 0.53 0.48

8 0.48 0.42 0.51 0.47 17 0.55 0.50 0.48 0.51

9 0.51 0.47 0.46 0.48 18 0.53 0.48 0.46 0.49

The Taguchi method uses S/N ratio to define quality characteristics, including nominal-the-best characteristic, small-the-best characteristic, and large-the-best characteristic. The experimental data of surface softness are large-the-best characteristics because the aim is to achieve a much better hand. In contrast, the experimental data of color difference are small-the-best characteristic because the aim is to keep the original color. A large-the-best characteristic is given by
$S / N = - 10 log \frac{\sum_{i = 1}^{n} \frac{1}{y_{i}^{2}}}{n}$
(3)
whereas a small-the-best characteristic is
$S / N = - 10 log \frac{\sum_{i = 1}^{n} y_{i}^{2}}{n} = - 10 log ({\bar{y}}^{2} + S^{2})$
(4)
in which $\bar{y}$ is the average value of the experiment, n is the total number of measurements, S is the standard deviation, and y_i* are the experimental values.
Main effect analysis

The experimental design follows the orthogonal array; the experiment is conducted according to plan, the experimental data of various parameter combinations in the orthogonal array are obtained, and then the response table is established. First, the experimental data value is calculated as quality indicator (i.e. S/N ratio); the calculation method depends on the required quality characteristics. The average response value of various factor levels is obtained, then the main effect value of various factor levels is worked out, and these data are made into response table to analyze the effect of various factors. The larger the main effect value of a factor is, the more significant is the effect of the factor on the system than the other factors. On the contrary, if the main effect value of a factor is much smaller than other factors, the effect on improving quality is not significant (as shown in Table 10 and Figure 4)
${\bar{F}}_{i} = \frac{1}{m} \sum_{j = 1}^{m} y_{i}$
(5)

$Δ F = max {{\bar{F}}_{1}, {\bar{F}}_{2}, \dots, {\bar{F}}_{n}} - min {{\bar{F}}_{1}, {\bar{F}}_{2}, \dots, {\bar{F}}_{n}}$
(6)
where ${\bar{F}}_{i}$ is the mean S/N ratio of the ith level of factor F, $Δ F$ is the value of the main effects of factor F, n is the level of the factor, m is the number of level i in the orthogonal array factor column, and y_i is the S/N ratio produced on each i level row.

Gray relational analysis

GRA implements a comprehensive assessment in total concept for the things and phenomena under the effect of multiple factors.⁴ The gray relation refers to the correlation grade of reference sequence and inspected sequence, the inspected sequence and reference sequence of each grey relational space are compared and sequenced, the gray relational order is defined, representing the correlation grade order of each inspected sequence and reference sequence. GRA judges the correlation grade according to the geometric proximity of inspected sequence curve and reference sequence curve. The more similar the geometry of inspected sequence curve is to that of reference sequence curve, the higher is the correlation grade.

This paper uses GRA to find out the correlation between the suede fabric quality characteristics resulting from various experiments of orthogonal array and the target values. The GRA is implemented for the surface softness and color difference of suede fabric, defined as follows.

Target values of surface softness and color difference of suede fabric:

Reference sequence
$< label / > X_{0} = (x_{0} (1), x_{0} (2))$

Surface softness and color difference of suede fabric resulted from various experiments of orthogonal array
$< label / > X_{i} = (x_{1} (1), x_{1} (2)), i = 1, 2, \dots, 18$

The correlation between target values and experimental observations is the correlation coefficient
$γ (x_{0} (k), x_{i} (k)) = \frac{ζ {max}_{1 \leq m \leq 18} {max}_{k} Δ_{0, m} (k)}{Δ_{0, i} (k) + ζ {max}_{1 \leq m \leq 18} {max}_{k} Δ_{0, m} (k)}, k = 1, 2; i = 1, 2, \dots, 18$
(7)

Point relation of X_i about X₀ at point k: $γ (x_{0} (k), x_{i} (k))$ describes the degree of relationship of $X_{0}, X_{i}$ at point k, representing local characteristic of the $X_{0}, X_{i}$ relationship. The mean of $γ (x_{0} (k), x_{i} (k))$ is known as the correlation grade of X_i to X₀
$γ (X_{0}, X_{i}) = \frac{1}{n} \sum_{k = 1}^{n} γ (x_{0} (k), x_{i} (k))$
(8)

When the target values of surface softness and color difference of a suede fabric are imported as reference sequence, the correlation grade to the observed values resulting from various experiments with an L₁₈ orthogonal array can be calculated. The main effect analysis is implemented and the optimum suede fabric processing parameter combination can be obtained from the response diagram and response table.

Analysis of variance

After the experiment designed by Taguchi, the experimental data must be processed by ANOVA to obtain a complete experimental result. The ANOVA has two purposes: one is to evaluate the experimental errors; the other is to test the factor importance. The ANOVA of experimental data, free from subjective evaluation, can separate the relevance of various control factors to experimental errors. The importance of various factors is displayed in quantized values, not omitting important factors, increasing the accuracy of prediction.

The computing equations and method of ANOVA are as follows.
Degrees of Freedom (DOF)

The DOF of various factors equals to the level number minus one; the total number of DOFs is total number of experiments minus one, the error DOF is total DOF minus the sum of DOFs of various factors (as shown in Tables 5 and 6).
Correction factor

$CF = \frac{1}{n} (\sum_{j = 1}^{n} y_{i})^{2}$
(9)
where y is the S/N ratio of experimental observations and n is the total number of observations.
Total sum of squares

$TSS = \sum_{j = 1}^{n} y_{j}^{2} - CF$
(10)

Main effect square sum

$SS = \frac{\sum_{i = 1}^{n / m} (\sum_{j = 1}^{m} y_{ij})^{2}}{m} - CF$
(11)
where $y_{ij}$ is the number of j observed values for the ith level and m is the number of observed values of each level (as shown in Tables 5 and 6).
Sum squared error

$SSE = TSS - \sum_{k = 1}^{p} {SS}_{p}$
(12)
where p is the number of factors.
Mean square and mean square of error

$MS = \frac{SS}{DF}$
(13)

$MSE = \frac{SSE}{DFE}$
(14)

Table 5.
S/N ratio for surface softness

No. S/N ratio No. S/N ratio No. S/N ratio

1 27.72 7 26.56 13 28.24

2 27.65 8 25.39 14 24.70

3 27.27 9 25.60 15 24.61

4 25.66 10 28.10 16 25.45

5 26.97 11 26.37 17 26.38

6 25.26 12 28.07 18 25.73

Table 6.
S/N ratio for color difference.

No. S/N ratio No. S/N ratio No. S/N ratio

1 5.02 7 5.65 13 4.88

2 4.99 8 6.53 14 6.73

3 5.19 9 6.37 15 7.12

4 6.36 10 4.87 16 6.35

5 5.66 11 5.84 17 5.83

6 6.74 12 4.87 18 6.18

as shown in Tables 5 and 6.
F ratio

The F ratio represents the relationship between factorial effect and error variance. Larger F ratio represents more significant effect of the factor on the system, so the F ratio can be used to arrange the importance sequence of factors. If the F ratio is smaller than 1, the factorial effect is slight. If the F ratio is larger than 4, the factorial effect is strong. The F ratio is defined as mean square of factor divided by mean square of pooled error (as shown in Tables 5 and 6)
$F = \frac{MS}{MSE}$
(15)

Net square sum

$SS' = SS - DF \times MSE$
(16)

Contribution percentage

$ρ = \frac{SS'}{TSS} \times 100 %$
(17)

Confidence interval

The ANOVA has certain evaluation criteria for the selected control factors of suede fabric processing parameters, so the response table and response diagram can be used to predict the factor combination for improving the experimental result, and then the confirmation experiment is conducted to observe whether the experimental result and the prediction result are in a certain confidence interval. It is proved that the mathematical model built by using the experimental data obtained from orthogonal array experiment is rational. According to the obtained optimum factor level setting value, the additive model is used to predict the S/N ratio in optimum condition, as shown in Tables 5 and 6. The computing equation is
$\overset{\land}{S} N = \bar{T} + \sum_{i = 1}^{n} (F_{i} - \bar{T})$
(18)
where $\bar{T}$ is the general average of S/N ratios and F_i is the S/N ratio of significant factor level value.

In order to evaluate the observed values effectively, the confidence interval must be calculated. The computing equation is:
confidence interval of theoretical prediction values

${CI}_{1} = \sqrt{F_{α; 1, v_{2}} \times MSE \times \frac{1}{n_{eff}}}$
(19)
where $F_{α; 1, v_{2}}$ is the F ratio with significance level α, α is the significance level, the confidence level is 1 − α, v₂ is the DOF of the pooled error mean square, MSE is the pooled error mean square, and n_eff is effective observed value, i.e.
$n_{eff} = \frac{Totalnumberofexperiments}{1 + [TotalDOFoffactorsforestimatingmean]}$
(20)

confidence interval of confirmation experiment calculated values

${CI}_{2} = \sqrt{F_{α; 1, v_{2}} \times MSE \times (\frac{1}{n_{eff}} + \frac{1}{r})}$
(21)
where r is the number of confirmation experiments, r ≠ 0.

Finally, the 95% confidence interval is used to validate whether the predicted mean is effective, the verification expression is
$\overset{\land}{S} N - CI \leq μ \leq \overset{\land}{S} N + CI$
(22)

Experimental descriptions

The equipment and materials for this experiment are now described.

The sueding machine used for the experiment is the YB-099, made by Yubung Co., Ltd, Taiwan. The fabric surface softness testing system was based on the sled method developed by Kuo and Lin.⁵ The spectrophotometer used for measuring the color difference is the eXact Standard (X-Rite Inc., Ltd, USA). The material used for the experiment is polyethylene terephthalate (PET), T75D/72F SDWT150D/144F SDW 142T90T, Plain weave.

The orthogonal array was designed by using the Taguchi design of experiment method. There are five design factors after experimental design analysis; each design factor has three levels, as shown in Table 1. Therefore, an L₁₈(3⁵) orthogonal array is used to allocate the processing parameters of the sueding machine, as shown in Table 2. According to the orthogonal array designed processing parameters, the material is processed by the sueding machine. There are 18 experiments conducted for surface softness and color difference, respectively, and each experiment is repeated three times and the mean values taken. As the suede fabric surface softness is expected to be high, it is a large-the-best characteristic and the S/N ratio is calculated using equation (3). The color difference is expected to be small, so it is a small-the-best characteristic and the S/N ratio is calculated using equation (4). Finally, calculations provide the S/N ratio, GRA, and ANOVA.

Results and discussion

Once the experiments were completed, the data in Tables 3 and 4 were obtained. The S/N ratios of each group of experimental quality characteristics were calculated and the data in Tables 5 and 6 were obtained. The response surface diagrams of surface softness and color difference are shown in Figures 2 and 3.
Figure 2.
The response diagram of surface softness.

Figure 3.
The response diagram of color difference.

Figure 4.
The response graph for the GRA.

According to the response surface diagram, the influence of significant factors, i.e. pressing depth and velocity of worktable, on the surface softness and color difference can be seen. When pressing depth is in level 2 (5.5 × 4; 7.5 × 2 mm) and velocity of worktable is in level 2 (13 M/min), there is a good surface softness, while when pressing depth is in level 2 (5.5 × 4; 7.5 × 2 mm) and velocity of worktable is in level 3 (15 M/min), there is a good color difference.

The surface softness and color difference were set as quality characteristics in this experiment. The target values are 28.2419 and 7.1205, respectively, according to the S/N ratios in Tables 5 and 6. The ANOVA is calculated from the S/N ratios, as shown in Tables 7 and 8. The importance of F-ratio observation factor effect shows that pressing depth has the most influence on surface softness and color difference, followed by velocity of worktable and rotational speed of roller. In case of great pressure and rapid speed of sueding machine, the sandpaper on the roller has the most friction with the fiber surface, so as to change the surface morphology most significantly and generate the largest effect.
Table 7.
Analysis of variance table for surface softness

Source DOF SS MS F-ratio Confidence Significance

A 2 10.91 5.45 1536.92 0.9999 Yes

B 2 2.55 1.28 359.91 0.9999 Yes

C 2 5.39 2.70 759.48 0.9999 Yes

D 2 3.96 1.98 558.20 0.9999 Yes

E 2 1.56 0.78 219.26 0.9999 Yes

Error 7 – –

Total 17 24.40

Table 8.
Analysis of variance table for color difference.

Source DOF SS MS F-ratio Confidence Significance

A 2 4.60 – 187.70 0.9999 Yes

B 2 0.99 40.39 0.9999 Yes

C 2 2.00 – 81.75 0.9999 Yes

D 2 1.28 – 52.21 0.9999 Yes

E 2 0.36 – 14.69 0.9999 Yes

Error 10 – – – –

Total 17 9.32

The optimum processing parameter combination was analyzed by GRA. The target values of surface softness and color difference are used as reference sequence, i.e. $X_{0} = (28.2419, 7.1205)$ . The difference sequence, gray correlation coefficient, and correlation grade results of reference sequence and orthogonal array sequences are shown in Table 9. The response table and response diagram of GRA can be obtained by main effect analysis, as shown in Table 10 and Figure 4. According to the response table and response diagram, the optimum parameter combination for sueding process is A2B3C3D2E1, i.e. pressing depth 4.5 × 4; 6.5 × 2 (mm), tensile force of worktable 160 (kg), velocity of worktable 15 (M/min.), rotational speed of roller 45 × 5; 50 × 1 (r/min), forward/reverse rotation of roller (F/R) FRFRFR. This provides optimal parameter combinations of multiple-quality characteristics, which revealed that they had greatest correlation with the quality characteristics set in the reference sequence, and the quality characteristics obtained most met the demand.
Table 9.
The deviation sequences, gray relational coefficients, and grades.

No. $Δ_{0, i} (1)$ $Δ_{0, i} (2)$ $γ_{0, i} (1)$ $γ_{0, i} (2)$ $γ_{0, i}$ Rank

1 0.0184 0.2944 0.8747 0.2838 1.1584 0.5792

2 0.0209 0.2990 0.8595 0.2805 1.1400 0.5700

3 0.0344 0.2717 0.7862 0.3010 1.0871 0.5436

4 0.0914 0.1068 0.5720 0.5319 1.1039 0.5519

5 0.0451 0.2052 0.7353 0.3655 1.1008 0.5504

6 0.1055 0.0541 0.5351 0.6972 1.2323 0.6161

7 0.0596 0.2065 0.6754 0.3639 1.0394 0.5197

8 0.1008 0.0828 0.5467 0.5967 1.1434 0.5717

9 0.0937 0.1059 0.5656 0.5340 1.0996 0.5498

10 0.0052 0.3159 0.9616 0.2692 1.2308 0.6154

11 0.0663 0.1797 0.6510 0.3979 1.0490 0.5245

12 0.0060 0.3163 0.9556 0.2689 1.2245 0.6123

13 0.0000 0.3148 1.0000 0.2699 1.2699 0.6350

14 0.1255 0.0552 0.4900 0.6925 1.1825 0.5913

15 0.1285 0.0000 0.4837 1.0000 1.4837 0.7418

16 0.0988 0.1084 0.5520 0.5280 1.0801 0.5400

17 0.0660 0.1807 0.6519 0.3966 1.0486 0.5243

18 0.0889 0.1320 0.5790 0.4767 1.0557 0.5278

Table 10.
The response table for the GRA.

A B C D E

Level 1 0.5741 0.5735 0.5786 0.5598 0.5898

Level 2 0.6144 0.5553 0.5692 0.5980 0.5677

Level 3 0.5389 0.5986 0.5797 0.5697 0.5700

Difference 0.0755 0.0432 0.0105 0.0382 0.0221

Rank 1 2 5 3 4

When the optimal sueding processing parameter combination is obtained by GRA, the confirmation experiment is conducted. The theoretical prediction values can be calculated from the significant factors in the ANOVA table. According to equation (18), the prediction values of surface softness and color difference are 29.9067 dB and 7.0465 dB, respectively; according to equation (19), the 95% confidence intervals of surface softness and color difference are 27.8974–31.9160 dB and 5.0372–9.0557 dB, respectively. After three confirmation experiments, the experimental average values of surface softness and color difference are 27.5036 and 6.8167, respectively. The confirmation experiment values of surface softness and color difference are in the confidence interval, proving that the results of this experiment are reliable. Table 11 shows the percentage error of verification experiment values and target values. The mean errors of surface softness and color difference are 2.6141% and 4.2667%, respectively.
Table 11.
The percentage errors for the verification experiment values and the target values.

Confirmation Experiment No. Verification experiment values
Target values
Error (%)

surface softness color difference surface softness color difference surface softness color difference

1 27.6100 6.8365 28.2419 4.8683 2.2374 3.9878

2 27.3898 6.8295 28.2419 4.8683 3.0171 4.0867

3 27.5110 6.7840 28.2419 4.8683 2.5879 4.7256

Conclusions

In this study, which combines the Taguchi method with GRA, the optimal level of sueding machine processing parameters was found with the least number of experiments. According to the response table and response diagram obtained by GRA, the optimum processing parameter combination for sueding quality are pressing depth 4.5 × 4; 6.5 × 2 (mm), tensile force of worktable 160 (kg), velocity of worktable 15 (M/min), rotational speed of roller 45 × 5; 50 × 1 (r/min), forward/reverse rotation of roller (F/R) FRFRFR the optimum combination is A2B3C3D2E1. Table 7 shows that the significant factors influencing the surface softness are the pressing depth, velocity of worktable, and rotational speed of roller. Table 8 shows the significant factors influencing the color difference are also the pressing depth, velocity of worktable, and rotational speed of roller. After three confirmation experiments, the confirmation experiment values and theoretical prediction values of surface softness and color difference are in the confidence interval, proving that the experimental results are reproducible, the selection of significant factors is appropriate, and that this experiment is reliable. In addition, Table 11 shows the percentage error of verification experiment values and target values; the mean errors of surface softness and color difference are 2.6141% and 4.2667%, respectively. The optimum combination of sueding machine processing parameters is thus obtained by using the Taguchi method and GRA in this study.

In the past, when sueded cloth was processed by machine, it needed to be tested circularly by a trial-and-error method and sueding machine processing parameters adjusted many times till the finished product reached the target values. The optimum combination of processing parameters for various fabric types can be obtained by using this new method. Once the database is built, the personnel can adjust the processing parameters of a sueding machine immediately according to the fabric type and quality target value, so as to economize the materials, manpower, and time for sueding, closing, measurement, and calibration cycle operations. The efficiency of the process is obviously increased and stable quality is obtained, enhancing the competitiveness of fabric enterprises.

No.	Factor	Level
A	Pressing depth (mm)	(1) 4.5 × 4; 6.5 × 2
(2) 5.5 × 4; 7.5 × 2
(3) 6.5 × 4; 5.0 × 2
B	Tensile force of worktable (kg)	(1) 140
(2) 150
(3) 160
C	Velocity of worktable (M/min)	(1) 12
(2) 13
(3) 15
D	Rotational speed of roller (r/min)	(1) 40 × 5; 45 × 1
(2) 45 × 5; 50 × 1
(3) 50 × 5; 55 × 1
E	Forward/reverse rotation of roller (F/R)	(1) F; R; F; R; F; R
(2) F; F; R; F; F; R
(3) F; F; F; R; F; R

Factor No.	A	B	C	D	E
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	2	1	1	2	2
5	2	2	2	3	3
6	2	3	3	1	1
7	3	1	2	1	3
8	3	2	3	2	1
9	3	3	1	3	2
10	1	1	3	3	2
11	1	2	1	1	3
12	1	3	2	2	1
13	2	1	2	3	1
14	2	2	3	1	2
15	2	3	1	2	3
16	3	1	3	2	3
17	3	2	1	3	1
18	3	3	2	1	2

No.	1	2	3	Average	No.	1	2	3	Average
1	25.35	23.77	23.96	24.36	10	25.14	24.97	26.12	25.41
2	24.78	24.25	23.42	24.15	11	21.19	21.53	19.86	20.86
3	23.35	23.06	22.89	23.10	12	24.98	24.99	26.05	25.34
4	21.14	18.04	18.78	19.32	13	25.98	25.93	25.58	25.83
5	22.37	23.06	21.56	22.33	14	18.02	16.31	17.33	17.22
6	19.76	17.36	18.11	18.41	15	17.23	16.69	17.11	17.01
7	21.21	21.61	21.02	21.28	16	18.98	19.32	17.98	18.76
8	19.15	18.29	18.42	18.62	17	21.35	21.11	20.12	20.86
9	20.14	19.24	17.95	19.11	18	19.34	18.49	20.34	19.39

No.	1	2	3	Average	No.	1	2	3	Average
1	0.52	0.59	0.57	0.56	10	0.56	0.54	0.61	0.57
2	0.48	0.61	0.59	0.56	11	0.52	0.53	0.48	0.51
3	0.53	0.54	0.58	0.55	12	0.61	0.53	0.57	0.57
4	0.50	0.50	0.44	0.48	13	0.59	0.57	0.55	0.57
5	0.55	0.47	0.54	0.52	14	0.43	0.50	0.45	0.46
6	0.48	0.47	0.43	0.46	15	0.42	0.47	0.43	0.44
7	0.46	0.54	0.56	0.52	16	0.47	0.44	0.53	0.48
8	0.48	0.42	0.51	0.47	17	0.55	0.50	0.48	0.51
9	0.51	0.47	0.46	0.48	18	0.53	0.48	0.46	0.49

No.	S/N ratio	No.	S/N ratio	No.	S/N ratio
1	27.72	7	26.56	13	28.24
2	27.65	8	25.39	14	24.70
3	27.27	9	25.60	15	24.61
4	25.66	10	28.10	16	25.45
5	26.97	11	26.37	17	26.38
6	25.26	12	28.07	18	25.73

No.	S/N ratio	No.	S/N ratio	No.	S/N ratio
1	5.02	7	5.65	13	4.88
2	4.99	8	6.53	14	6.73
3	5.19	9	6.37	15	7.12
4	6.36	10	4.87	16	6.35
5	5.66	11	5.84	17	5.83
6	6.74	12	4.87	18	6.18

Source	DOF	SS	MS	F-ratio	Confidence	Significance
A	2	10.91	5.45	1536.92	0.9999	Yes
B	2	2.55	1.28	359.91	0.9999	Yes
C	2	5.39	2.70	759.48	0.9999	Yes
D	2	3.96	1.98	558.20	0.9999	Yes
E	2	1.56	0.78	219.26	0.9999	Yes
Error	7				–	–
Total	17	24.40

Source	DOF	SS	MS	F-ratio	Confidence	Significance
A	2	4.60	–	187.70	0.9999	Yes
B	2	0.99		40.39	0.9999	Yes
C	2	2.00	–	81.75	0.9999	Yes
D	2	1.28	–	52.21	0.9999	Yes
E	2	0.36	–	14.69	0.9999	Yes
Error	10		–	–	–	–
Total	17	9.32

No.	$Δ_{0, i} (1)$	$Δ_{0, i} (2)$	$γ_{0, i} (1)$	$γ_{0, i} (2)$	$γ_{0, i}$	Rank
1	0.0184	0.2944	0.8747	0.2838	1.1584	0.5792
2	0.0209	0.2990	0.8595	0.2805	1.1400	0.5700
3	0.0344	0.2717	0.7862	0.3010	1.0871	0.5436
4	0.0914	0.1068	0.5720	0.5319	1.1039	0.5519
5	0.0451	0.2052	0.7353	0.3655	1.1008	0.5504
6	0.1055	0.0541	0.5351	0.6972	1.2323	0.6161
7	0.0596	0.2065	0.6754	0.3639	1.0394	0.5197
8	0.1008	0.0828	0.5467	0.5967	1.1434	0.5717
9	0.0937	0.1059	0.5656	0.5340	1.0996	0.5498
10	0.0052	0.3159	0.9616	0.2692	1.2308	0.6154
11	0.0663	0.1797	0.6510	0.3979	1.0490	0.5245
12	0.0060	0.3163	0.9556	0.2689	1.2245	0.6123
13	0.0000	0.3148	1.0000	0.2699	1.2699	0.6350
14	0.1255	0.0552	0.4900	0.6925	1.1825	0.5913
15	0.1285	0.0000	0.4837	1.0000	1.4837	0.7418
16	0.0988	0.1084	0.5520	0.5280	1.0801	0.5400
17	0.0660	0.1807	0.6519	0.3966	1.0486	0.5243
18	0.0889	0.1320	0.5790	0.4767	1.0557	0.5278

	A	B	C	D	E
Level 1	0.5741	0.5735	0.5786	0.5598	0.5898
Level 2	0.6144	0.5553	0.5692	0.5980	0.5677
Level 3	0.5389	0.5986	0.5797	0.5697	0.5700
Difference	0.0755	0.0432	0.0105	0.0382	0.0221
Rank	1	2	5	3	4

Confirmation Experiment No.	Verification experiment values	Target values	Error (%)
1	27.6100	6.8365	28.2419	4.8683	2.2374	3.9878
2	27.3898	6.8295	28.2419	4.8683	3.0171	4.0867
3	27.5110	6.7840	28.2419	4.8683	2.5879	4.7256

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: The work was supported by the Ministry of Science and Technology of the Republic of China (grant number: MOST 104-2221-E-011-156-).

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Factor No.	A	B	C	D	E
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	2	1	1	2	2
5	2	2	2	3	3
6	2	3	3	1	1
7	3	1	2	1	3
8	3	2	3	2	1
9	3	3	1	3	2
10	1	1	3	3	2
11	1	2	1	1	3
12	1	3	2	2	1
13	2	1	2	3	1
14	2	2	3	1	2
15	2	3	1	2	3
16	3	1	3	2	3
17	3	2	1	3	1
18	3	3	2	1	2

Confirmation Experiment No.	Verification experiment values		Target values		Error (%)
	surface softness	color difference	surface softness	color difference	surface softness	color difference
1	27.6100	6.8365	28.2419	4.8683	2.2374	3.9878
2	27.3898	6.8295	28.2419	4.8683	3.0171	4.0867
3	27.5110	6.7840	28.2419	4.8683	2.5879	4.7256

Factor No.	A	B	C	D	E
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	2	1	1	2	2
5	2	2	2	3	3
6	2	3	3	1	1
7	3	1	2	1	3
8	3	2	3	2	1
9	3	3	1	3	2
10	1	1	3	3	2
11	1	2	1	1	3
12	1	3	2	2	1
13	2	1	2	3	1
14	2	2	3	1	2
15	2	3	1	2	3
16	3	1	3	2	3
17	3	2	1	3	1
18	3	3	2	1	2

Factor No.	A	B	C	D	E
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	2	1	1	2	2
5	2	2	2	3	3
6	2	3	3	1	1
7	3	1	2	1	3
8	3	2	3	2	1
9	3	3	1	3	2
10	1	1	3	3	2
11	1	2	1	1	3
12	1	3	2	2	1
13	2	1	2	3	1
14	2	2	3	1	2
15	2	3	1	2	3
16	3	1	3	2	3
17	3	2	1	3	1
18	3	3	2	1	2