Analysis Of Experimental Results

Published Date: 02 Nov 2017

Chapter 4

Researchers emphasized the Taguchi method in their work because it can help researchers to identify the main factor in injection moulding process from trials of experiment. In this chapter will show the statistical analysis that has been done using application of Taguchi method in replication process for the main effects and the interaction between the process parameters. Then, ANOVA is further elaborated to finalize the optimum level for significant process parameters and measure a confidence level. Lastly, the discussion on the result obtained from the analysed data result.

4.2 Analysis of Experimental Results

In studies of influencing factors that affect the replication capabilities in micro injection moulding, the output of process of demoulding force is used as response variable. As discussed before, the demoulding force of micro injection moulding is important as it affect the quality of the part moulded. The test results were analysed using SN ratio and ANOVA. SN ratio is very useful information for improvement of quality through reduction and improvement of measurement [Ranjit, 2001].

Table.4.1 and Table.4.2 present the result of two different set of experiment. Table.4.1 is set for SN ratio nominal is best and Table.4.2 is set for larger the better.

Table.4.1. Taguchi L16 Orthogonal array for Nominal is Best.

Trial

A

B

C

D

SN ratio

1

1

1

1

1

24.51622

2

1

1

1

2

17.41137

3

1

1

2

1

24.48549

4

1

1

2

2

23.34141

5

1

2

1

1

36.23869

6

1

2

1

2

30.97106

7

1

2

2

1

33.07531

8

1

2

2

2

33.76845

9

2

1

1

1

16.19914

10

2

1

1

2

18.43929

11

2

1

2

1

27.83105

12

2

1

2

2

36.03197

13

2

2

1

1

24.91912

14

2

2

1

2

28.9965

15

2

2

2

1

33.4184

16

2

2

2

2

43.45654

Table.4.2. Taguchi L16 Orthogonal array for Larger the Better

Trial

A

B

C

D

SN ratio

1

1

1

1

1

24.26048

2

1

1

1

2

23.77074

3

1

1

2

1

27.50528

4

1

1

2

2

26.92059

5

1

2

1

1

26.4854

6

1

2

1

2

25.67459

7

1

2

2

1

28.01349

8

1

2

2

2

27.10773

9

2

1

1

1

23.4129

10

2

1

1

2

24.2524

11

2

1

2

1

26.88954

12

2

1

2

2

27.6341

13

2

2

1

1

26.42006

14

2

2

1

2

26.93849

15

2

2

2

1

28.17999

16

2

2

2

2

28.60348

Taguchi Design

Taguchi Orthogonal Array Design

L16(2**4)

Factors: 4

Runs: 16

Columns of L16(2**15) Array

1 2 4 8

Taguchi Analysis: C6, C7, C8, C9, C10, C11, C12, C13, ... versus A, B, C, D

Response Table for Signal to Noise Ratios

Nominal is best (10*Log10(Ybar**2/s**2))

Level A B C D

1 27.98 23.53 24.71 27.59

2 28.66 33.11 31.93 29.05

Delta 0.69 9.57 7.21 1.47

Rank 4 1 2 3

Response Table for Means

Level A B C D

1 20.99 20.07 18.94 21.75

2 21.91 22.84 23.97 21.16

Delta 0.92 2.77 5.03 0.59

Rank 3 2 1 4

Response Table for Standard Deviations

Level A B C D

1 1.2055 1.9781 1.6996 1.4831

2 1.3331 0.5605 0.8390 1.0555

Delta 0.1275 1.4176 0.8606 0.4275

Rank 4 1 2 3

Fig.4.1. Taguchi analysis using data analysis software package, Minitab 16

Taguchi Design

Taguchi Orthogonal Array Design

L16(2**4)

Factors: 4

Runs: 16

Columns of L16(2**15) Array

1 2 4 8

Taguchi Analysis: C6, C7, C8, C9, C10, C11, C12, C13, ... versus A, B, C, D

Response Table for Signal to Noise Ratios

Larger is better

Level A B C D

1 26.22 25.58 25.15 26.40

2 26.54 27.18 27.61 26.36

Delta 0.32 1.60 2.45 0.03

Rank 3 2 1 4

Response Table for Means

Level A B C D

1 20.99 20.07 18.94 21.75

2 21.91 22.84 23.97 21.16

Delta 0.92 2.77 5.03 0.59

Rank 3 2 1 4

Response Table for Standard Deviations

Level A B C D

1 1.2055 1.9781 1.6996 1.4831

2 1.3331 0.5605 0.8390 1.0555

Delta 0.1275 1.4176 0.8606 0.4275

Rank 4 1 2 3

Fig.4.2. Taguchi analysis using data analysis software package, Minitab 16

For the nominal is best show in Table.4.1 is used to determine the optimal level of process parameter such barrel temperature (A), mould temperature (B), holding pressure (C), and injection speed (D) for the result of demoulding force in consistently at optimum condition. Hence, the demoulding force is consistently enough for ejection of moulded parts and achieve a good replication process. The larger the better is used to identify the maximum demoulding force and achieve high SN ratio as explained in Chapter 2. The optimum level for nominal is best for process parameter is A2B2C2D2 while for larger the better is A2B2C2D1 after analysis of SN ratio into consideration (see Fig.4.1 and Fig 4.2). Further analysis on the result is conducted using Minitab 16. Both of the set design of experiment is analysed to define the level process parameters from its main factor in micro injection moulding and the confidence level.

4.3 Analysis of Main Effects on Nominal is Best.

The ANOVA analysis is conducted to measure the level of confidence. The ANOVA helps to determine the most significant factor that influences the output of experimental. B is the most significant factor with 0.003 which lower compared to α-value which generally 0.05 in Fig.4.3. From the information above, the main effects of the process parameter was investigated using Minitab 16. In Fig.4.4 illustrate the main effect in SN ratio for the process parameter. For main effects plotted shown that B is most significant followed by C. However, A and D is not very significant in main effects plotted. Then, in Fig.4.5 indicate the interaction between the process parameter for SN ratio. The interaction between the process parameter shown that significant result between A and C, and A and D. To sum up, the mould temperature and holding pressure are the significant in contribution for demoulding force. The setting level of A2B2C2D2 is confirmed to be better settings for process parameter after the main effects is considered. The interaction improved the quality surface of moulded parts to achieve good level of quality. The interaction of A and C proven that the barrel temperature and holding pressure affect the solidification of moulded parts. The interaction of A and D specify of the melt fills in the micro cavity is significant.

ANOVA: PSNRA1 versus A, B, C, D

Factor Type Levels Values

A fixed 2 1, 2

B fixed 2 1, 2

C fixed 2 1, 2

D fixed 2 1, 2

Analysis of Variance for PSNRA1

Source DF SS MS F P

A 1 1.88 1.88 0.07 0.791

B 1 366.61 366.61 14.35 0.003

C 1 208.20 208.20 8.15 0.016

D 1 8.60 8.60 0.34 0.573

Error 11 281.08 25.55

Total 15 866.38

S = 5.05498 R-Sq = 67.56% R-Sq(adj) = 55.76%

Fig.4.3. ANOVA from data analysis software package, Minitab 16

Fig.4.4.The main effects of process parameters in SN ratio of nominal is best

Fig.4.5. The interaction of main effects in SN ratio of nominal is best

4.4 Analysis of Main Effects on Larger the Better

The same procedure like above for the main effects of larger the better is determined using Minitab 16. The information in Table.4.2 gives the information for the main effects of SN ratio illustrated in Fig.4.6. Apparently, the main effects for the larger the better shown C is the most significant and B is the second most significant. The same result from normal is better, A and D shows no significant result. The interaction of process parameter shown in Fig.4.7 defines a significant result between A and D. Then, ANOVA analysis for SN ratio for larger the better conducted gives that factor C is the most significant with 0.000 followed by B with 0.001 lower than α-value of 0.005 (see Fig.4.8).

Hence, the most important factors that affect were mould temperature and holding pressure for the maximum demoulding force in micro injection moulding. The mould temperature is generally most important influence in micro injection moulding. The holding pressure is for larger the better defines that the increased time for holding pressure for solidification of polymer to achieve enough mechanical properties to be ejected from the mould. Interaction between barrel temperature and injection speed play the important role due the increased time in holding pressure. The injection speed must be fast enough and and the barrel temperature is essential in melt fills into the cavity. Therefore, the setting level of A2B2C2D1 is the best for maximum demoulding force can be achieved.

Fig.4.6. the main effects of process parameters in SN ratio of larger the better

Fig.4.7. The interaction of main effects in SN ratio of larger the better

ANOVA: PSNRA1 versus A, B, C, D

Factor Type Levels Values

A fixed 2 1, 2

B fixed 2 1, 2

C fixed 2 1, 2

D fixed 2 1, 2

Analysis of Variance for PSNRA1

Source DF SS MS F P

A 1 0.4201 0.4201 0.84 0.379

B 1 10.2035 10.2035 20.44 0.001

C 1 24.1060 24.1060 48.28 0.000

D 1 0.0044 0.0044 0.01 0.927

Error 11 5.4917 0.4992

Total 15 40.2258

S = 0.706575 R-Sq = 86.35% R-Sq(adj) = 81.38%

Fig.4.3. ANOVA from data analysis software package, Minitab 16

4.5 Analysis of Interaction of Main Effects in Taguchi Application

4.6 Summary