Design of experiments (DOE) is one of the most powerful techniques to improve quality and increase productivity. In this way, through some experiments, conscious changes made to the system to examine their impact on the performance characteristics of system response to them. The design of experiments is the systematic manipulation of a number of variables in which the effects of these manipulations evaluated and from which conclusions are drawn, the results implemented. In the late 1940s, Dr. Taguchi introduced new statistical concepts and later proved to be valuable tools for quality control and improvement. Since then, many Japanese artisans have used this technique to improve products and process quality.
The Taguchi method is quite different from the conventional methods of testing. Taguchi's methodology focuses on designing experiments and performing a limited number of experiments, while in the conventional methods all possible combination should be tested. Orthogonal arrays (OA) used in this method dramatically reduces the number of tests required by identifying a set of robust strategies in designing the experiments and analyzing the results. To consider the three control factors considered in this study, a standard Taguchi-based design, L27, which shown in Table 1 is used. This basic design uses three control elements; each of them has three levels. In addition, this design is capable of examining the interaction between the factors. From the standard design (Table 4), nine experimental runs need to conduct with the combination of levels for each control factor (A–C).
Table 4: The basic Taguchi L9 orthogonal array
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Control factors and levels
|
|
Run
|
C
|
B
|
A
|
|
1
|
1
|
1
|
|
1
|
2
|
2
|
1
|
|
2
|
3
|
3
|
1
|
|
3
|
2
|
1
|
2
|
|
4
|
3
|
2
|
2
|
|
5
|
1
|
3
|
2
|
|
6
|
3
|
1
|
3
|
|
7
|
1
|
2
|
3
|
|
8
|
2
|
3
|
3
|
|
9
|
|
In this study, three major factors that have more effects on the behavior of the plates considered: skin layer layout, impactor shape and core thickness. Three levels for each factor were selected (shown in Table 5) as factor levels.
Table 5: Parameters, codes, and level values used in Taguchi method
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Levels
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Code
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Factors
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3
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2
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1
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Cross-ply
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Quasi-isotropic
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Pure Aluminum
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A
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|
Skin layer
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Spherical
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Parabolic
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Conical
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B
|
|
Impactor shape
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40
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30
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20
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|
C
|
|
Core thickness (mm)
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|
|
|
|
|
|
|
|
|
Table 6 shows the results of experimental tests of response factors based on the Taguchi method selected parameters from Table 4.
Table 6: Modified orthogonal array using basic Taguchi
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Specific Absorbed Energy (J/gr)
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Max. Impact force (KN)
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Max.
Displacement (mm)
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Control factors and levels
|
|
Run
|
C
|
B
|
A
|
|
0.181
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7.51
|
5.67
|
1
|
1
|
1
|
|
1
|
0.178
|
8.84
|
3.83
|
2
|
2
|
1
|
|
2
|
0.258
|
8.54
|
3.98
|
3
|
3
|
1
|
|
3
|
0.153
|
8.67
|
3.54
|
2
|
1
|
2
|
|
4
|
0.221
|
8.41
|
4.78
|
3
|
2
|
2
|
|
5
|
0.146
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8.01
|
5.12
|
1
|
3
|
2
|
|
6
|
0.148
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8.22
|
4.34
|
3
|
1
|
3
|
|
7
|
0.102
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7.78
|
6.32
|
1
|
2
|
3
|
|
8
|
0.103
|
8.99
|
3.62
|
2
|
3
|
3
|
|
9
|
|
5.1. Signal-to-noise ratio analysis
Signal-to-noise ratio (SNR or S/N) is a measure used in engineering that compares the level of a desired signal to the level of background noise. SNR defined as the ratio of signal power to the noise power, often expressed in decibels. The larger-the-better (LB), the smaller- the- better (SB), and the nominal-the-better (NB) are the three types used to analyze the S/N ratio.
The average effects of the factors were calculated and shown in Tables 7. This table include comparing the relative value of the effects based on the delta statistics, which called ranks that is the difference between the lowest and the highest averages for the factor chosen. Core thickness appears as the first effective factor for SAE and impactor shape is as the first one for MD and MIF. The Taguchi analysis of SAE value versus skin layer, impactor shape and core thickness reveals that delta statistics of the core thickness is 2.58, that of impactor shape is 1.16 and skin layer layout is 0.63. This shows that the most significant factor for SAE of AFSP is core thickness, followed by impactor shape and the skin layer layout is the least factor. In case of MD of AFSP, the delta statistics of the impactor shape is 3.81, skin layer layout has a value of 1.31, while that of core thickness is 0.39. This means that the most principle factor for MD of the AFSP is impactor shape, followed by skin layer layout and core thickness. For the MIF, the delta statistics of the impactor shape is 1.12, that of the skin layer layout is 0.4, while that of core thickness is 0.09, this implies that the most important factor here is impactor shape, followed by skin layer layout and the least factor here is core thickness.
Table 7. Taguchi analysis: SEA, MD and MIF versus different factors, Table for S/N ratios
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Response variable
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Specific Absorbed Energy (LB)
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|
Max. Displacement (SB)
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|
Max. Impact Force (SB)
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Factors
|
|
A
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B
|
C
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|
A
|
B
|
C
|
|
A
|
B
|
C
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1
|
|
36.62
|
36.88
|
37.46
|
|
-12.93
|
-15.09
|
-12.92
|
|
-18.19
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-17.80
|
-18.36
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2
|
|
36.29
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35.72
|
36.56
|
|
-13.76
|
-11.28
|
-12.92
|
|
-18.41
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-18.92
|
-18.44
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3
|
|
35.98
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36.28
|
34.88
|
|
-12.45
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-12.78
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-13.31
|
|
-18.59
|
-18.47
|
-18.40
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Delta
|
|
0.63
|
1.16
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2.58
|
|
1.31
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3.81
|
0.39
|
|
0.40
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1.12
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0.09
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Rank
|
|
3
|
2
|
1
|
|
2
|
1
|
3
|
|
2
|
1
|
3
|
|
5.2. Analysis of variance (ANOVA)
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among group means in a sample. ANOVA developed by statistician and evolutionary biologist Ronald Fisher. The ANOVA based on the law of total variance, where the observed variance in a particular variable partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In this study, statistical significance of the impact load parameters affecting the SAE, MD and MIF investigated by ANOVA. The influence of core thickness, skin layer layout and impactor shape on the total variance of the results undertaken for a level of significance of .5%, i.e. for a level of confidence of 99.5%. The ANOVA table also contains the F- values and the percent distribution. By comparing the F-values with the values in the table, one can understand the importance of the factors. If the F-value obtained from a parameter is greater than the calculated value, that particular parameter has a significant effect on the response variable. The main effects of the variables considered for the raw data and the SNR data plotted. Response parameter curves used to investigate the parametric effects on response characteristics. Analysis of variance of raw data and SNR data performed to identify important variables and quantify their effects on response characteristics. The most cost-effective values (optimal settings) of the production variables in terms of mean response characteristics created by analyzing the response curves in Figures 6-8 and Tables 8-10.
Table 8. ANOVA for means for SAE
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Source
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DF
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Seq SS
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Adj SS
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Adj MS
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F
|
P
|
R-Sq
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R-Sq (Adj)
|
Core thickness
|
2
|
561.572
|
561.572
|
280.876
|
620.66
|
0.002
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99.9 %
|
99.5 %
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Skin layout
|
2
|
34.050
|
34.050
|
17.025
|
37.62
|
0.026
|
|
|
Impactor shape
|
2
|
115.092
|
115.092
|
57.546
|
127.16
|
0.008
|
|
|
Residual error
|
2
|
0.905
|
0.905
|
0.453
|
|
|
|
|
Total
|
8
|
711.799
|
|
|
|
|
|
|
|
Table 9. ANOVA for means for MD
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Source
|
DF
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Seq SS
|
Adj SS
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Adj MS
|
F
|
P
|
R-Sq
|
R-Sq (Adj)
|
Core thickness
|
2
|
0.1480
|
0.1480
|
0.07401
|
0.142
|
0.413
|
98.6 %
|
94.5 %
|
Skin layout
|
2
|
0.8388
|
0.8388
|
0.41941
|
0.805
|
0.110
|
|
|
Impactor shape
|
2
|
6.4247
|
6.4247
|
3.21234
|
61.68
|
0.016
|
|
|
Residual error
|
2
|
0.1042
|
0.1042
|
0.05208
|
|
|
|
|
Total
|
8
|
7.5157
|
|
|
|
|
|
|
|
Table 10. ANOVA for means for MIF
|
Source
|
DF
|
Seq SS
|
Adj SS
|
Adj MS
|
F
|
P
|
R-Sq
|
R-Sq (Adj)
|
Core thickness
|
2
|
0.00667
|
0.00667
|
0.003333
|
1.56
|
0.390
|
99.8 %
|
99.1 %
|
Skin layout
|
2
|
0.21740
|
0.21740
|
0.108700
|
50.95
|
0.019
|
|
|
Impactor shape
|
2
|
1.72287
|
1.72287
|
0.861433
|
403.80
|
0.002
|
|
|
Residual error
|
2
|
0.00427
|
0.00427
|
0.002133
|
|
|
|
|
Total
|
8
|
1.95120
|
|
|
|
|
|
|
|
5.3. Estimation of optimum response characteristics
Specific absorbed energy
The larger-the-better characteristic used to determine the largest SAE that would be the ideal situation for this study. Meanwhile, the larger SNR projected as the best response given in plate manufacturing which would be the ideal situation. Fig. 6 shows the graphs used to determinate the optimal values of parameters from this experimental test. In this Figure, the factor of skin layer layout of the plate (A) at level 1 (cross-ply) shows the best result. In addition, the best results for impactor shape (B) observed at the level 1 (conical). Meanwhile, the core thickness of the plate (C) gives the best results at the level 1 (40 mm). There are no conflicts to determine the optimal skin layer layout, impactor shape and the core thickness of the plate and the criteria of the largest response and highest SNR followed. Therefore, the optimal combination of levels for all three factors of production provides the best SAE found to be A1-B1-C1.
Maximum displacement
In this response factor, the-smaller-the-better characteristic used and the smallest MD value would be the ideal situation The SB characteristic used to determine the smallest MD that would be the ideal situation for this study. Fig. 7 shows the graphs used to determinate the optimal values of parameters from this experimental test. In this Figure, the factor of skin layer layout of the plate (A) at level 3 (pure Aluminum) shows the best result. In addition, the best results for impactor shape (B) observed at the level 2 (spherical). Meanwhile, the core thickness of the plate (C) gives the best results at the level 1 (40 mm). Therefore, the optimal combination of levels for all three factors of production provides the best MD found to be A3-B2-C1.
Maximum impact force
In the last response factor, the-smaller-the-better characteristic used and the smallest MIF value would be the ideal situation The SB characteristic used to determine the smallest MIF that would be the ideal situation for this study. Fig. 8 shows the graphs used to determinate the optimal values of parameters from this experimental test. In this Figure, all the control factors (A, B and C) at the level 1 provides the best results (cross-ply, conical and 40 mm respectively). Therefore, the optimal combination of levels for all three factors of production provides the best MIF found to be A1-B1-C1.
In order to validate the results obtained from the Taguchi method, three validation tests performed for each response characteristics (SAE, MD and MIF) at optimal levels of the production variables. The results given in Table 11. Results show good agreement between actual data from experimental tests and those predicted by current model. So optimal values of production parameters predicted in Table 11 are valid.
Table 11. Predicted response values and results of actual values
|
Performance responses
|
Optimal combination of parameters
|
Predicted response values
|
Actual values from experimental tests
|
Specific Absorbed Energy (J/gr)
|
A1 B1 C1
|
81.99
|
82.40
|
Max. Displacement (mm)
|
A3 B2 C1
|
3.24
|
3.62
|
Max. Impact Force (KN)
|
A1 B1 C1
|
7.53
|
7.51
|
|
Figure 9 illustrates sandwich samples with different procedures tested using spherical impactor. Since the analysis of specimen damage and its mechanism of destruction is not the subject of this article, it is merely a case report. As can be seen, the spherical impactor have entered the plate with aluminum and quasi-isotropic surfaces from the top but stopped in the foam core of the plate while for cross-ply skin layer, impactor passes through the bottom plate. In addition, the surface damage of the sample with a quasi-isotropic skin layer is greater than the surface damage of the sample with cross-ply skin. This phenomenon is due to the higher impact force in this case. The separation of skin layer saw in the cross-ply sample, which not observed in the quasi-isotropic case. Also in the evaluation of impact depth, in this case, the maximum penetration belongs to the plate with cross-ply skin layer and the lowest one is to the plate with pure aluminum surface.