Optimization of plastic injection molding process parameters for manufacturing a brake booster valve body

Materials and Design 56 (2014) 313–317

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Optimization of plastic injection molding process parameters for manufacturing a brake booster valve body Yi-qi Wang, Jae-gyu Kim, Jung-il Song ⇑ Dept. of Mechanical Engineering, Changwon National University, Changwon 641-773, Republic of Korea

a r t i c l e

i n f o

Article history: Received 2 September 2013 Accepted 18 November 2013 Available online 28 November 2013

a b s t r a c t The plastic injection molding (PIM) process parameters have been investigated for manufacturing a brake booster valve body. The optimal PIM process parameters is determined with the application of computeraided engineering integrating with the Taguchi method to improve the compressive property of the valve body. The parameters considered for optimization are the following: number of gates, gate size, molding temperature, resin temperature, switch over by volume filled, switch over by injection pressure, and curing time. An orthogonal array of L18 is created for the statistical design of experiments based on the Taguchi method. Then, Mold-Flow analyses are performed by using the designed process parameters based on the L18 orthogonal array. The signal-to-noise (S/N) ratio and the analysis of variance (ANOVA) are used to find the optimal PIM process parameters and to figure out the impact of the viscosity of resin, curing percentage, and compressive strength on a brake booster valve body. When compared with the average compression strength out of the 18 design experiments, the compression strength of the valve body produced using the optimal PIM process parameters showed a nearly 12% improvement. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Safety is the prime consideration for automotive manufactures. Undoubtedly, the braking system is the most important part of any vehicle, which should work every time without any failures during life time of the vehicle. A brake booster valve body is a key component of the braking system, which is usually manufactured by plastic injection molding (PIM) technique. PIM is an important manufacturing technique to plastic products due to the advantages of product quality, competitive cost, high productivity, and good mechanical properties [1–8]. The cycle of PIM consists of four stages: plastication, injection, packing, and cooling [4]. The quality of PIM parts is deeply influenced by many factors, such as the material, mold design, and process parameters applied to manufacture them. Due to the high cost and time consuming, the trial-anderror process is not suitable for complex manufacturing process in determining the optimal PIM process parameters [5]. Thus, the Taguchi method, artificial neural networks (ANNs), and genetic algorithm (GA) are applied to optimize the PIM process parameters to achieve the high quality product [6–8]. Subsequently, soft computing has been used for process parameters optimization. To optimize the process parameters, Shie [8] carried out a research which integrates numerical software, back-propagation neural network (BPNN), and GA. When the values of parameters are discrete, the Taguchi method can efficiently find the best specified process ⇑ Corresponding author. Tel.: +82 55 213 3886; fax: +82 55 275 0101. E-mail address: [email protected] (J.-i. Song). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.11.038

parameter level combination with the minimum experiments [9,10]. Therefore, researches are routinely performed in determining the optimal process parameters from different points of view [7–16]. Oktem et al. [11] proposed an approach that employs the Taguchi method to reduce shrinkage for thin-shell plastic components of or-those part through the signal-to-noise(S/N) ratio and the analysis of variance (ANOVA). Ozcelik [12] performed the Taguchi’s L9 (33) orthogonal array design to optimize the effect of injection parameters and weld line on the mechanical properties of polypropylene moldings. Erzurumlu and Ozcelik [13] have minimized the warpage and sink index in the parts made by Polycarbonate/Acrylonitrile Butadiene Styrene, Polyoxymethylene, and Polyamide66 based on the Taguchi optimization method. In this study, the effects of PIM process parameters on the compression strength of a brake booster valve body were investigated by using the Taguchi optimization method. Considering the number of PIM process parameters, an orthogonal array of L18 (21 37) was used for conducting experiments. The effects of resin viscosity and curing percentage having great influence on the quality and shape of products were also discussed. S/N ratio and ANOVA were used to obtain the optimal PIM process parameters. The statistical software MINITAB 14 was used for the robust design methodology based on the Taguchi method. 2. Definition of the Taguchi method The Taguchi method developed by Taguchi has been widely applied in determining the optimal process parameters. It is one

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strong tool for the design of high quality systems. The Taguchi method was used for statistical design of experiments (DOE) that is simple and effective. The Taguchi method consists of three stages which are system design, parameter design, and tolerance design, respectively [17]. System design involves the application of scientific and engineering knowledge required in manufacturing a product. Parameter design is employed to find optimal process values for improving the quality characteristics. Tolerance design consists of determining and analyzing of the tolerances in optimal settings recommended by parameter design [13]. The Taguchi method is based on the technique of matrix experiments to determine the optimal parameters [9,10]. Taguchi recommends the use of S/N ratio and ANOVA for determining the quality characteristics and indicate the impact of process parameters on optimization purposes.

machine (SPE-350, Hyundai) used in this study is shown in Fig. 1(b). Various specimens manufactured by the PIM machine are shown in Fig. 2(a). The process parameters are designed by the Taguchi method, which will be discussed in the following sub-section. Compression strengths of these specimens are obtained by compression test with a cross head speed of 10 mm/ min as shown in Fig. 2(b). Moreover, the viscosity of resin and curing percentage can efficiently affect the quality of products. Thus, based on the Taguchi analysis, finite element (FE) models of the brake booster valve body with different number of gates were modeled to figure out the impact of the viscosity of resin and curing percentage of the valve body. For this purpose, the commercial software Mold-Flow Plastics Insight (MPI) v5.0 was adopted to simulate the PIM process [18]. 3.2. Design of experiment by the Taguchi method

3. Experimental procedure 3.1. Experimental details Phenolic molding compound (CY3915 30G, Matsushita Electric Works, Ltd., Plastic Materials Division) is shown in Fig. 1(a), which was used to manufacture the brake booster valve body. The PIM

Due to the complex manufacturing process, there are many parameters of the PIM process can affect the quality of a brake booster valve body. Seven PIM process parameters are considered in this study that they are number of gates, gate size, molding temperature, resin temperature, switch over by volume filled, switch over by pressure, and curing time. The gate design drawings are

Fig. 1. (a) Raw material: phenolic molding compound and (b) PIM machine for manufacturing a brake booster valve body.

Fig. 2. (a) Various specimens and (b) set up of compression test.

Fig. 3. Gate design drawings for the cases of (a) 2 gates, (b) 3 gates, and (c) 4 gates.

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Y.-q. Wang et al. / Materials and Design 56 (2014) 313–317 Table 1 The PIM process parameters and their levels. Parameters

Unit

Level 1

Level 2

Level 3

A (Number of gates) B (Gate size) C (Molding temperature) D (Resin temperature) E (Switch over by volume filled) F (Switch over by injection pressure) G (Curing time)

– mm °C °C % MPa s

2 18.68 147.6 85.5 69.57 10.8 108

3 20.78 164.0 95.0 77.30 12.0 120

4 22.86 180.4 104.5 85.03 13.2 132

shown in Fig. 3. These PIM process parameters and levels are shown in Table 1. The values of level 2 are determined based on the conventional value of each parameter. Three levels of number of gates are 2, 3, and 4, respectively. For other parameters, the values of level 1 and level 3 of each parameter are determined by minus and plus 10% of the values of level 2, respectively. According to the Taguchi’s table, the orthogonal array of L18 (21 37) is utilized in this study, which is shown in Table 2. It consists of 18 experiments corresponding to 18 rows. In the matrix, column 1 is arbitrarily designed as an empty column which was denoted by unit column (e) and columns 2–8 are assigned with the PIM process parameters as given in Table 1.

Fig. 4. A meshed FE model of a brake booster valve body with 4 gates.

n 1 X g ¼ 10 log y2 n i¼1 i

g ¼ 10 log

3.3. Finite element (FE) model of a valve body Finite element (FE) analysis of valve body is performed using MPI v5.0 software. Geometry of FE model used in this study corresponds to the real conditions such as, the real dimensions of the product and number of gates for production. The FE model of a brake booster valve body with 4 gates is shown in Fig. 4 that has been meshed with tetrahedron element. Following the L18 orthogonal array, simulations were performed to predict the resin viscosity and curing percentage of the valve body. 4. Results and discussion 4.1. Analysis of the S/N ratio The Taguchi method uses the S/N ratio to qualify the quality characteristic deviating from the desired value. Basically, there are three objective functions for calculating the S/N ratio in the Taguchi method, which are smaller-is-better (Eq. (1)), larger-isbetter (Eq. (2)), and nominal-is-the best (Eq. (3)).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 a

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2

A 2 2 2 3 3 3 4 4 4 2 2 2 3 3 3 4 4 4

B 18.68 20.78 22.86 18.68 20.78 22.86 18.68 20.78 22.86 18.68 20.78 22.86 18.68 20.78 22.86 18.68 20.78 22.86

C 147.6 164.0 180.4 147.6 164.0 180.4 164.0 180.4 147.6 180.4 147.6 164.0 164.0 180.4 147.6 180.4 147.6 164.0

Empty column is denoted by unit column (e).

D 85.5 95.0 104.5 95.0 104.5 85.5 85.5 95.0 104.5 104.5 85.5 95.0 104.5 85.5 95.0 95.0 104.5 85.5

n X

! ð2Þ

! y2i =s2

ð3Þ

i¼1

where g is the S/N ratio, n is the number of experiments, yi is the value of response of ith experiment, and s is mean square error. In this study, resin viscosity, curing percentage, and compression strength were chosen as three responses for the optimization. In case of resin viscosity, the minimum value was preferred, thus, Eq. (1) was applied to calculate the S/N ratio of resin viscosity. In other two cases, the maximum value was preferred, thus, the S/N ratios of curing percentage and compression strength were determined by Eq. (2). The results of S/N responses are listed in Tables 3–5. According to the data presented in Table 3, the parameters combination of the optimal PIM process A3B3C2D1E1F1G2 (number of gates is 4, gate size is 22.86 mm, molding temperature is 164.0 °C, resin temperature is 85.5 °C, switch over by volume filled is set at 69.57%, switch over by injection pressure is set at 10.8 MPa, and curing time is 120 s) was suggested for optimizing

Level

Parametersa e

n 1 X 1=y2i n i¼1

ð1Þ

Table 3 The S/N response table (smaller-is-better) for resin viscosity.

Table 2 An L18 (21 37) orthogonal array of the Taguchi method. Number of experiments

g ¼ 10 log

!

E 69.57 77.30 85.03 77.30 85.03 69.57 85.03 69.57 77.30 77.30 85.03 69.57 69.57 77.30 85.03 85.03 69.57 77.30

F 10.8 12.0 13.2 13.2 10.8 12.0 12.0 13.2 10.8 12.0 13.2 10.8 13.2 10.8 12.0 10.8 12.0 13.2

A

B

C

D

E

F

G

1 2 3

57.21 58.30 58.77

57.85 57.87 58.57

57.96 59.12 57.20

60.65 58.29 55.34

59.18 58.28 56.83

58.17 58.10 58.01

58.10 58.36 57.82

Delta (D) Rank

1.56 4

0.71 5

1.92 3

5.31 1

2.34 2

0.15 7

0.54 6

G 108 120 132 132 108 120 132 108 120 108 120 132 120 132 108 120 132 108

Parameters

Table 4 The S/N response table (larger-is-better) for curing percentage. Level

Parameters A

B

C

D

E

F

G

1 2 3

34.94 34.81 35.13

35.01 35.06 34.80

31.83 35.17 37.87

34.77 35.18 34.93

35.10 34.86 34.92

34.85 35.00 35.02

34.42 34.91 35.54

Delta (D) Rank

0.32 4

0.25 5

6.04 1

0.42 3

0.24 6

0.17 7

1.12 2

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Table 5 The S/N response table (larger-is-better) for compression strength. Level

Parameters A

B

C

D

E

F

G

1 2 3

32.23 32.63 32.65

32.17 32.70 32.63

30.19 32.61 34.70

32.13 32.75 32.62

32.34 32.54 32.63

32.06 32.72 32.72

31.91 32.59 33.00

Delta (D) Rank

0.42 6

0.53 5

4.51 1

0.62 4

0.29 7

0.67 3

1.08 2

resin viscosity. For the cases of optimizing curing percentage and compression strength, the optimal combination was A3B2C3D2E1F3G3 and A3B2C3D2E3F23G3, respectively. Moreover, the ranks of all the parameters were sorted by delta, D, (the range of three levels). The parameter having higher rank corresponding to higher delta value means that this factor contributes to the PIM process more effective than other lower rank parameters.

contribution (P%) of variance, and p-value. For the calculations, two reference books are recommended, which are dealing with the design and analysis of experiments [19,20]. The Seq SS of design factor k is the same as the Adj SS of design factor k which is given by

Seq SSk ¼ Adj SSk ¼

ð4Þ

l¼1

The Adj MS and F of design factor k are given by

Adj MSk ¼

F¼

Adj SSk DF k

ð5Þ

Adj SSk Seq SSE  DF k DF E

ð6Þ

where E⁄ is error. And SST is the total sum of squares which is given by

SST ¼

4.2. Analysis of variance (ANOVA)

N X  2 3 ðmk Þl  m l

n X ðgi  mÞ2

ð7Þ

i¼1

Analysis of variance (ANOVA) was also applied to find the influence of process parameters shown in Tables 6–8. ANOVA can also provide the degrees of freedom (DF), sequential sums of squares(Seq SS), adjusted sums of squares (Adj SS), adjusted mean square( Adj MS), the F-statistic (F) from the Adj MS, the percentage

The percentage contribution of the design factors to the response is obtained by using the following equation [9]:

P¼

SSk  100 SST

ð8Þ

Table 6 Summary of ANOVA results for resin viscosity. DF

Seq SS

Adj SS

Adj MS

F

P (%)

p-Value

A B C D E F G

2 2 2 2 2 2 2

53,383 56,637 94,924 73,1142 12,5172 1064 3793

53,383 56,637 94,924 73,1142 12,5172 1064 3793

26,691 28,318 47,462 36,5571 62,586 532 1896

8.95 9.50 15.92 122.61 20.99 0.18 0.64

4.97 5.27 8.83 68.01 11.64 0.10 0.35

0.054 0.050 0.025 0.001 0.017 0.845 0.588

Error Total

3 17

8944 10,75059

8944

2981

(significant) (significant) (significant) (significant)

0.83 100

Table 7 Summary of ANOVA results for curing percentage. DF

Seq SS

Adj SS

Adj MS

F

P (%)

p-Value

A B C D E F G

2 2 2 2 2 2 2

14.90 6.84 4613.83 23.98 13.32 2.46 132.18

14.90 6.84 4613.83 23.98 13.32 2.46 132.18

7.45 3.42 2306.91 11.99 6.66 1.23 66.09

0.51 0.23 157.80 0.82 0.46 0.08 4.52

0.31 0.14 95.10 0.49 0.27 0.05 2.72

0.645 0.805 0.001 (significant) 0.520 0.672 0.921 0.124

Error Total

3 17

43.86 4851.37

43.86

14.62

0.90 100

Table 8 Summary of ANOVA results for compression strength. DF

Seq SS

Adj SS

Adj MS

F

P (%)

p-Value

A B C D E F G

2 2 2 2 2 2 2

0.6683 0.9981 61.0467 1.3060 0.2657 1.7610 3.5908

0.6683 0.9981 61.0467 1.3060 0.2657 1.7610 3.5908

0.3342 0.4990 30.5233 0.6530 0.1328 0.8805 1.7954

0.43 0.64 38.92 0.83 0.17 1.12 2.29

0.9. 1.39 84.80 1.81 0.37 2.45 4.99

0.687 0.588 0.007 (significant) 0.516 0.852 0.433 0.249

Error Total

3 17

2.3530 71.9896

2.3530

0.7843

3.27 100

Y.-q. Wang et al. / Materials and Design 56 (2014) 313–317

From the results of ANOVA as presented in Table 6, it is found that parameters B, C, D, and E are significant parameters due to the p-values of them are less or equal than 0.05. Moreover, the resin temperature (D) has a great effect on the resin viscosity due to the highest percentage contribution of 68.01%. However, the molding temperature (C) has a very remarkable effect on increasing curing percentage and improving compression strength of the brake booster valve body. To obtain the maximum compression strength, level 3 of parameter C is determined due to its significance on compression strength. Although parameters (B, D, and E) are not showing significance in Tables 7 and 8, they are significant on resin viscosity as shown in Table 6. Thus, B3D1E1 are determined. For the rest parameters, the previous suggestion (A3F3G3) based on Table 8 are used. From the above discussion, the optimal PIM process parameters are A3B3C3D1E1F3G3. 4.3. Verification test A verification test is very important in engineering analysis to validate the optimized results. Integrate the studies of resin viscosity, curing percentage, and compression strength, the parameters showing significance should be considered in advance for finding the optimal PIM process parameters. The others can be decided based on the result of S/N ratio. The verification test was only conducted by using the levels of optimal PIM process parameters, A3B3C3D1E1F3G3 for obtaining the maximum compression strength, resulted from optimization process. The brake booster valve body produced using the optimal PIM process parameters has a compression strength of 36.36 MPa. When compared with the average compression strength out of the 18 design experiments, the compression strength of the valve body produced using the optimal PIM process parameter showed a nearly 12% improvement. It is clearly indicated that the Taguchi method optimizes efficiently the PIM process parameters and the efficient improvement can improve the safety performance of a vehicle. 5. Conclusions The Taguchi optimization method is presented to determine the optimal PIM process parameters for improving compression strength of a brake booster valve body. MPI v5.0 was integrated with the Taguchi method to simulate and determine the optimal PIM process parameters for resin viscosity and curing percentage. Seven design parameters were selected as variable parameters with three levels of each. An L18 (21 37) orthogonal array was used for the design of experiment. The software MINITAB 14 was applied to calculate S/N ratio and ANOVA. Finally, a verification test was carried out to validate the optimal parameters for improving compression strength. From these analyses, the following points are noted: (1) The S/N ratio of the resin viscosity case was calculated by the objective function of smaller-is-better. The optimal combination of the PIM process parameters was suggested as A3B3C2D1E1F1G2. It means that number of gates is 4, gate size is 22.86 mm, molding temperature is 164.0 °C, resin temperature is 85.5 °C, switch over by volume filled is set at 69.57%, switch over by injection pressure is set at 10.8 MPa, and curing time is 120 s. From the ANOVA results, that the resin temperature has a great effect on the resin viscosity due to the highest percentage contribution of 68.01%. (2) The S/N ratios of both cases of curing percentage and compression strength were calculated by the objective function of larger-is-better. The optimal combination for the case of

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curing percentage and compression strength was A3B2C3D2E1F3G3 and A3B2C3D2E3F23G3, respectively. The molding temperature has a very remarkable effect on increasing curing percentage and improving compression strength of the brake booster valve body. Considering the significant parameters, the optimal PIM process parameters are A3B3C3D1E1F3G3 for obtaining the maximum compression strength. (3) The results of the verification test at the optimal PIM process parameters show that the valve body has a 12% improvement compared with the average compression strength out of 18 design experiments. The efficient improvement can improve the safety performance of a vehicle.

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