Polymer-plastics Technology And Engineering 4o1e1r

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Optimization of Injection Molding Process for Tensile and Wear Properties of Polypropylene Components via Taguchi and Design of Experiments Method a

b

c

Yu-Hsin Lin , Wei-Jaw Deng , Cheng-Hung Huang & Yung-Kuang Yang

d

a

Department of Industrial Engineering and Management , Ming Hsin University of Science and Technology , Hsinchu, Taiwan, P.R. China b

Graduate School of Business istration, Chung Hua University , Hsinchu, Taiwan, P.R. China c

Department of Innovative Research , United Ship Design and Development Center, Tamshui , Taipei, Taiwan, P.R. China d

Department of Mechanical Engineering , Ming Hsin University of Science and Technology , Hsinchu, Taiwan, P.R. China Published online: 26 Dec 2007.

To cite this article: Yu-Hsin Lin , Wei-Jaw Deng , Cheng-Hung Huang & Yung-Kuang Yang (2007) Optimization of Injection Molding Process for Tensile and Wear Properties of Polypropylene Components via Taguchi and Design of Experiments Method, Polymer-Plastics Technology and Engineering, 47:1, 96-105, DOI: 10.1080/03602550701581027 To link to this article: http://dx.doi.org/10.1080/03602550701581027

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Polymer-Plastics Technology and Engineering, 47: 96–105, 2008 Copyright # Taylor & Francis Group, LLC ISSN: 0360-2559 print/1525-6111 online DOI: 10.1080/03602550701581027

Optimization of Injection Molding Process for Tensile and Wear Properties of Polypropylene Components via Taguchi and Design of Experiments Method Yu-Hsin Lin1, Wei-Jaw Deng2, Cheng-Hung Huang3, and Yung-Kuang Yang4

ed by [Princeton University] at 22:56 13 November 2014

1

Department of Industrial Engineering and Management, Ming Hsin University of Science and Technology, Hsinchu, Taiwan, P.R. China 2 Graduate School of Business istration, Chung Hua University, Hsinchu, Taiwan, P.R. China 3 Department of Innovative Research, United Ship Design and Development Center, Tamshui, Taipei, Taiwan, P.R. China 4 Department of Mechanical Engineering, Ming Hsin University of Science and Technology, Hsinchu, Taiwan, P.R. China

on the mechanical properties of injection-molded foaming PP parts and coinjection-molding PP parts of foaming core material embedded in nonfoaming skin material. The controlling parameters were the injection velocity, the melting temperature, the molding temperature and the back pressure; the quality targets of the parts were the weights and mechanical properties such as the tensile strength, the flexural strength and the stiffness. Ismail and Suryadiansyah[2] examined the degree of degradations on the tensile and morphological properties of the PP=natural rubber (NR) and the PP=recycled rubber (RR) blended at different rubber contents. With similar rubber contents and degradation conditions, PP=RR blends exhibited a higher percentage of retention of the tensile strength and the Young’s modulus but a lower elongation at break than the PP=NR blends. Sain et al.[3] studied the mechanical properties of the tensile, the flexural and the unnotched impact strength of the PP composites with a variety of natural fibers such as old newsprint, kraft pulp, hemp, and glass fibers. Yao et al.[4] considered the large deformation behavior of two commercial biaxial oriented polypropylene (BOPP) resins with different processing properties under high temperatures and high strain rate conditions by means of a Meissner rheometer. Modesti et al.[5] inspected the influence of processing conditions on the nanocomposites structure, i.e. intercalated or exfoliated, and on the enhancement of mechanical properties of the PP nanocomposites. In order to optimize the process parameters, both the screw speed and the barrel temperature profile were varied. The injection-molding is an important manufacturing process to polymers; it provides products with high dimensional steadiness, low manufacture cycles as well as low

This study analyzes the wear and the tensile properties of polypropylene (PP) components, which are applied to the interior coffer of automobiles. The specimens are prepared under different injection molding conditions by changing the melting temperature, the injection speed, and the injection pressure via three computercontrolled progressive strokes. The wear and tensile properties are adopted as the quality targets. Experiments of 16 experimental runs are based on an orthogonal array table, and apply the Taguchi method and the design of experiments (DOE) approach to determine an optimal parameter setting. In addition, a side-by-side comparison of two different approaches is provided. In this study, regression models that link the controlled parameters and the targeted outputs are developed, and the identified models can be used to predict the tensile and wear properties at various injection molding conditions. Keywords DOE; Injection molding; Optimization; Taguchi; Tensile stress; Wear

1. INTRODUCTION Recently, the polypropylene (PP) with a new catalyst, metallocene, the production efficiency and the properties of fibers are greatly improved. Besides, because of the low production cost, PP has become popular in various applications such as the consumer electronic products, the automotive components, chemical industry, and raw materials for packing and sealing, etc. The mechanical properties of polypropylene composites have been studied intensively, mostly through experiments. Chien et al.[1] investigated the effects of the molding factors Address correspondence to Yung-Kuang Yang, Department of Mechanical Engineering, Ming Hsin University of Science and Technology, 1 Hsin Hsing Road, Hsin Feng, 304 Hsinchu, Taiwan, P. R. China. E-mail: [email protected]

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WEAR AND TENSILE PROPERTIES OF POLYPROPYLENE

costs. However, many studies[1,5–8] found that the injection molding processing parameters have crucial effects on the quality of products. A correct setting of injection molding conditions is, therefore, a major concern in the plastics industry. The parameters that govern the injection-molding process are the filling time, the melting temperature, the molding temperature and the packing pressure. The Taguchi method has been used successfully in several industrial applications, such as manufacturing processes, mechanical component design, and process optimization[9–13]. These experiments are established using orthogonal arrays. The Taguchi method combines the effects of each noise factor and calculates a signal-to-noise ratio (S=N ratio) for each experiment. In addition, the design of experiments (DOE) method was implemented[14]. The DOE method has been widely applied to various fields. Zalba et al.[15] conducted 23 factorial experiments to design a thermal energy storage system. Puertas and Luis[16] applied the DOE method to optimize the machining parameters for electrical discharge machining of boron carbide; Lin and Chananda[17] improved the injection-molding quality by four-factor full-factorial design, and so on. This study applied Taguchi’s L16 orthogonal table to plan the experiments. Nine controlling factors with two levels for each factor were selected. The wear mass loss and the tensile stress are two selected quality objectives. Typically, high tensile stresses and low wear mass losses in the PP components are desirable for the injection-molding process. First, the Taguchi method calculates an S=N ratio, which represents the quality characteristic. An optimal process parameter level=factor combination is then chosen by selecting the largest possible S=N ratio. Furthermore, the DOE method is applied to obtain an optimal parameter setting from regression models that relate the desired outputs with the significant factors. Finally, a side-by-side comparison of two different approaches is provided.

Larger-the-better n 1X 1 S=N ¼ 10 log n i¼1 y2i

Smaller-the-better n 1X y2 S=N ¼ 10 log n i¼1 i

ð2Þ

! ¼ 10 logð y2 Þ

ð3Þ

where S denotes the standard deviation; yi the data obtained from experiments; n represents the number of experiments. 2.2. Design of Experiments (DOE) Method The objective of this study was to identify an optimal setting that minimizes the measured mass loss under wear conditions and maximizes the tensile strength for the PP produced components. To resolve this type of multioutput parameter design problems, an objective function, F(x), is defined as follows[18], !Pn1 n Y w j¼1 i wi DF ¼ di ð4Þ i¼1 F ðxÞ ¼ DF where the di is the desirability defined for the ith targeted output and the wi is the weighting of the di. For various goals of each targeted output, the desirability, di, is defined in different forms. If a goal is to reach a specific value of Ti, the desirability di is: if Yi 3 Lowi di ¼ 0 Yi Lowi di ¼ if Lowi < Yi < Ti Ti Lowi Yi Highi di ¼ if Ti < Yi < Highi Ti Highi di ¼ 0

2. TAGUCHI APPROACH AND DESIGN OF EXPERIMENTS METHOD

!

ð5Þ

if Yi = Highi

for a goal is to find a maximum, the desirability is shown as follows:

2.1. Taguchi Method The Taguchi method, depending on the objective, proposed three different mean square deviations for the signal–noise (S=N) ratios, which are nominal-the-better, larger-the-better and smaller-the-better. The mean square deviation can be considered the average performance characteristic values for each experiment. The three different signal–noise ratios, corresponding to n experiments, are presented below: Nominal-the-better: " # n 1X 2 S=N ¼ 10 log ðyi mÞ ¼ 10 log½ð y mÞ2 þ S 2 n i¼1 ð1Þ

di ¼ 0 if Yi 3 Lowi Yi Lowi di ¼ if Lowi < Yi < Highi Highi Lowi di ¼ 1

ð6Þ

if Yi = Highi

For a goal to search for a minimum, the desirability can be defined by the following formulas: if Yi 3 Lowi di ¼ 1 Highi Yi di ¼ if Lowi < Yi < Highi Highi Lowi di ¼ 0

ð7Þ

if Yi = Highi

where the Yi is the found value of the ith output during optimization processes; the Lowi and the Highi are the

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minimum and the maximum values of the experimental data for the ith output. In the Eq. (4), the wi is set to one since the di is equally important in this study. The DF is a combined desirability function[18], and the objective is to choose an optimal setting that maximizes a combined desirability function DF, i.e., minimizes F(x).

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2.3. Steps of Process Parameter Optimization The following steps are the processes for the parameter optimization by both the Taguchi method and the DOE approach: Step 1. Use an orthogonal array table of Taguchi method to design and conduct the experiments. Step 2. Conduct S=N analysis to obtain an optimal setting that minimizes the wear mass losses and maximizes tensile strengths for the Taguchi method. Step 3. Use DOE analysis to model the relationship between the controlled parameters and targeted outputs via regression equations. An optimal setting is then identified by maximizing a combined desirability function, DF. Step 4. Compare and the optimal solutions of two different approaches by additional experiments. 3. EXPERIMENTAL 3.1. Material A commercial high heat and high stiff type of -28 PP compounds from STAR ONE Co. (Taiwan) is the chosen

FIG. 1.

material. The basic physical properties are listed as follows: density of 1.1 g cm3, tensile strength of 20 MPa (under room temperature), flexural strength of 34 MPa (under room temperature), hardness of 82 Rockwell, and heat distortion temperature of 124C, respectively. To remove excessive moisture, the compound was heated to 80C for 2 h before the injection molding process. 3.2. Schematic of a Specimen The dimensions of a desired final product is shown in Fig. 1. It is one of decorative components used in the automobile interior. Two critical quality targets including the tensile strength and the wear mass loss are included in this study. The experiments were carried out on a computerized reciprocating screw injection-molding machine with capability of a maximum injection pressure of 170 MPa, an injection rate of 130 cm3 sec1, and a maximum clamp force of 1334 kN. 3.3. Experimental Parameters and Design The product quality produced by the injection molding is always affected by the process parameters like the cooling time, the injection pressure, the injection speed, the filling time, the melting temperature, the ejecting pressure, the molding temperature, the packing pressure, etc. The effects of the molding variables on the physical and mechanical properties of thermoplastics have been studied by researchers[1,5–8]. For a preliminary study, C-MOLD1 software was used to identify some crucial settings for the injection molding process.

Configurations of a specimen.

WEAR AND TENSILE PROPERTIES OF POLYPROPYLENE

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FIG. 2.

Photos of a specimen.

In Fig. 2, enhanced ribs are added to eliminate the distortions of the components. Based on the simulation results from C-MOLD1, using three progressive strokes can significantly lower the probability of the short injection. An injection molding setup, with which two components are produced for each injection channel per molding cycle, is illustrated in Fig. 3. The experimental factors and factor levels of the injection molding conditions based on the C-MOLD1 simulation are listed in Table 1. The melting temperature H1 (i.e., A=C), the injection speed ratio (i.e., B=%), and the injection pressure ratio (i.e., C=%) are the factors for the first progressive stroke. The melting temperature H2 (i.e., D=C), the injection speed ratio (i.e., E=%), and the injection pressure ratio (i.e., F=%) are the factors of the second progressive stroke. The factors of the third progressive stroke are the melting temperature H3 (i.e., G=C), the injection speed ratio (i.e., H=%), and the injection pressure ratio (i.e., J=%). In Table 2 are listed 16 runs based on an orthogonal array L16(24), consisting of nine experimental factors with two levels for each factor. The specimens for tensile and wear tests are also shown in Fig. 1. The melting temperatures of Ha and Hb are set to 40 and 50C, respectively; the mold temperature is 60C

FIG. 3. Schematic shows the injection molding setup.

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with a packing pressure of 40 MPa. All these factors are fixed and computer-controlled during the injection molding process. 3.4. Testing Apparatus 3.4.1. Tensile Tests The configuration of the tensile test specimens is shown in Fig. 1. The ASTM D638–91 specification is followed for tensile tests by using a 25 kN computerized MTS model 810 closed-loop servo-hydraulic system (manufactured by MTS Systems Co.; MN, USA) at a speed of 1 mm min1 under the room temperature. The specimens were monotonically loaded in tension until fracture. The load and the displacement were continuously recorded by software. The calculated stress is listed in Table 2. Figure 4 shows a typical stress-strain curve for the tensile test specimens under the condition A1B2C2D2E2F1 G1H1J2 (Run no. 7 of Table 2) of the injection-molding process. Figure 4 also indicates that the ultimate stress value is 26.75 MPa; the specimen reaches a strain value of 0.155 when the breakage occurs. 3.4.2. Wear Tests The wear tests were carried out with a Schwingung Reibung and Verschleiss (SRV, manufactured by Optimol Instruments Pru¨ftechnik GmbH; Mu¨nchen, ) oscillation friction wear tester. 15 15 2.45 mm was the dimensions of the wear test specimen cut from the online product of the injection-molding process. The SRV wear tests were performed in ‘‘ball-on-plane’’ with a load of 60 N. The ball was a chromium steel ball (AISI E52100) that was 10 mm in diameter with an average hardness of 62 2 HRC. The stroke was 2 mm, and the frequency and test duration were 20 Hz and 15 min, respectively. The above stroke, frequency, and test

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TABLE 1 Experimental factors and factor levels Experimental factors for three progressive stroke First stroke

Levels of experimental factors

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1 2

Second stroke

Third stroke

A (C)

B (%)

C (%)

D (C)

E (%)

F (%)

G (C)

H (%)

J (%)

200 210

20 30

25 30

200 210

20 30

35 40

200 210

20 30

25 30

duration resulted in a total sliding distance of 72 m. The mass loss was measured after each wear test. A typical plot for the variation of friction coefficient versus sliding distances when performing a wear test, with a specimen produced from the A1B2C2D2E2F1G1H1J2 (Run no. 7 of Table 2) setting is given in Fig. 5. The experimental results of tensile stresses (r in MPa) and wear mass losses (Dm in mg) are listed in Table 2. 4. RESULTS AND DISCUSSION 4.1. Taguchi Results The Taguchi method can be used to obtain an optimal process parameter level=factor combination. It applies the signal-to-noise (S=N) ratio to represent the quality characteristic and an optimal setting shall have the largest possible S=N ratio. In this study, typically, PP products with large tensile strengths and small wear mass losses are desirable.

Therefore, the larger-the-better S=N ratio formula i.e., Eq. (2) was chosen for the tensile strength, simultaneously, the smaller-the-better S=N ratio formula, i.e. Eq. (3) was applied for the wear mass loss. The calculated S=N ratios by the Taguchi method for each experiment are given in Table 3, while Table 4 lists the response tables for S=N ratios of each factor and level. In Table 4, A2, B1, C1, D2, E1, F2, G1, H2 and J2 represent the largest S=N ratios for factors A, B, C, D, E, F, G, H and J, respectively. Consequently, A2B1C1D2E1F2G1H2J2 is an optimal parameter combination of the injection-molding process. Namely, this setting yields a combination of the melting temperature of 210C (i.e., A), the injection speed ratio of 20% (i.e., B), and the injection pressure ratio of 25% (i.e., C) for the first progressive stroke; the melting temperature 210C (i.e., D), the injection speed ratio of 20% (i.e., E), and the injection pressure ratio of 40% (i.e., F) for the second progressive stroke; the factors of the third progressive stroke are the melting temperature

TABLE 2 Orthogonal array L16 of the experimental runs and results First stroke

Second stroke

Third stroke

Run no.

A

B

C

D

E

F

G

H

J

r MPa

Dm mg

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

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

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

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

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

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

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

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

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

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

22.35 28.11 26.38 28.49 23.00 23.20 26.75 26.28 26.32 25.95 26.88 29.12 25.31 28.37 28.42 28.13

2.3 2.3 2.3 2.1 2.0 2.1 2.5 2.4 2.6 2.8 1.3 1.3 2.3 1.9 2.5 1.9

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WEAR AND TENSILE PROPERTIES OF POLYPROPYLENE

TABLE 3 S=N Ratios of Taguchi experimental results S=N Ratio (dB) Run no.

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FIG. 4. A typical plot of stress-strain curve under the condition A1B2C2D2E2F1G1H1J2 (Run no. 7 of Table 2).

of 200C (i.e., G), the injection speed ratio of 30% (i.e., H), and the injection pressure ratio of 30% (i.e., J). 4.2. DOE Results 4.2.1. Definition of an Objective Function The objective of this study is to identify an optimal setting maximizing tensile stresses as well as minimizing wear mass losses. Hence, Eq. (6) was selected as a desirability function form for maximizing the tensile stress. On the other hand, the Eq. (7) is suitable for minimizing the wear mass loss. A combined desirability function can be calculated from Eq. (4)[18]. 4.2.2. ANOVA Results The analysis of variance (ANOVA) was conducted and the results are shown in Table 5a and 5b. A ‘‘Model F Value’’ is calculated from a model mean square divided by a residual mean square. It is a test of comparing a model

FIG. 5. A typical variations of friction coefficient under the condition A1B2C2D2E2F1G1H1J2 (Run no. 7 of Table 2).

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

Normalized

r

Dm

r

Dm

Total

26.9848 28.9765 28.4240 29.0939 27.2330 27.3097 28.5468 28.3914 28.4044 28.2812 28.5887 29.2836 28.0645 29.0575 29.0721 28.9849

52.7654 52.7654 52.7654 53.5556 53.9794 53.5556 52.0412 52.3958 51.7005 51.0568 57.7211 57.7211 52.7654 54.4249 52.0412 54.4249

0.0000 0.8664 0.6261 0.9175 0.1080 0.1413 0.6795 0.6119 0.6175 0.5639 0.6977 1.0000 0.4697 0.9017 0.9080 0.8701

0.2564 0.2564 0.2564 0.3749 0.4385 0.3749 0.1477 0.2009 0.0966 0.0000 1.0000 1.0000 0.2564 0.5054 0.1477 0.5054

0.2564 1.1228 0.8824 1.2924 0.5465 0.5163 0.8272 0.8128 0.7141 0.5639 1.6977 2.0000 0.7261 1.4071 1.0557 1.3755

variance with a residual variance. If the variances are close to the same, the ratio will be close to one and it is less likely that any of the factors have a significant effect on the response. As for a ‘‘Model P Value’’ , if the ‘‘Model P Value’’ is very small (less than 0.05) then the in the model have a significant effect on the response[18]. Similarly, an ‘‘F Value’’ on any individual factor is calculated from a term mean square divided by a residual mean square. It is a test that compares a term variance with a residual variance. If the variances are close to the same, the ratio will be close to one and it is less likely that the term has a significant effect on the response. Furthermore, if a ‘‘P Value’’ of any model is very small (less than 0.05), the individual in the model have a significant effect on the response. Table 5a lists the ANOVA result of the r. A ‘‘Model F value’’ of 700.54 with a ‘‘Model P value’’ of 0.0014 suggested that the selected model is significant. The ‘‘P values’’ for all model term are significant (i.e., less than 0.05). Additionally, ‘‘BH’’ , ‘‘BJ’’ , ‘‘DH’’ and ‘‘FJ’’ have significant influences to the r. Table 5b gives the ANOVA result of the Dm. A ‘‘Model F value’’ of 12.32 with a ‘‘Model P value’’ of 0.0005 implies that the selected model is significant. A ‘‘P value’’ for the model term ‘‘D’’ (the melting temperature at the second progressive stroke) is 0.0352, which is less than 0.05, indicating that the model term ‘‘D’’ is significant. Similarly, the model term ‘‘E’’ and ‘‘F’’ (the speed ratio and the pressure ratio at the second progressive stroke, respectively) are significant. The model term ‘‘G’’ (the

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TABLE 4 The response tables for S=N Factor

A

B

C

D

E

F

G

H

J

Level 1 Level 2

0.7821 1.1925

1.0662 0.9084

1.0148 0.9598

0.7316 1.2430

1.0714 0.9033

0.8411 1.1336

1.1063 0.8684

0.8383 1.1363

0.9806 0.9940

TABLE 5A ANOVA results of r

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Source Model A: temperature (C) B: speed ratio (%) C: pressure ratio (%) D: temperature (C) E: speed ratio (%) F: pressure ratio (%) G: temperature (C) H: speed ratio (%) J: pressure ratio (%) BH BJ DH FJ Residual Total

Sum of squares

Degree of freedom

Mean square

F value

P value

65.57 12.15 1.07 4.06 19.89 1.35 0.15 0.67 10.46 1.74 0.71 1.42 0.15 6.60 0.01 65.58

13 1 1 1 1 1 1 1 1 1 1 1 1 1 2 15

5.04 12.15 1.07 4.06 19.89 1.35 0.15 0.67 10.46 1.74 0.71 1.42 0.15 6.60 0.01 –

700.54 1686.84 148.78 563.92 2762.72 186.89 21.13 93.39 1452.33 241.17 98.20 197.42 20.57 916.31 – –

0.0014 0.0006 0.0067 0.0018 0.0004 0.0053 0.0442 0.0105 0.0007 0.0041 0.0100 0.0050 0.0453 0.0011 – –

TABLE 5B ANOVA results of Dm Source Model D: temperature (C) E: speed ratio (%) F: pressure ratio (%) G: temperature (C) Residual Total

Sum of squares

Degree of freedom

Mean square

F value

P value

2.14 0.25 0.64 1.00 0.25 0.48 2.62

4 1 1 1 1 11 15

0.54 0.25 0.64 1.00 0.25 0.04 –

12.32 5.76 14.74 23.04 5.76 – –

0.0005 0.0352 0.0027 0.0006 0.0352 – –

temperature at the third progressive stroke) is significant. There are no interactions of factors that have impacts on the Dm. 4.2.3. Regression Models Considering the most significant from Table 5a and 5b, regression models can be developed. Mathematic predicted models for the tensile stresses and the wear mass

losses are shown as follows: r ¼ 224:9925 þ 0:1743 A þ 0:9833 B 0:2015 C þ 0:338 D þ 0:058 E þ 3:338 F 0:041 G þ 1:3875 H þ 5:475 J 0:01 BH 0:0285 BJ 0:0046 DH 0:1228 FJ

ð8Þ

Dm¼4:91250:025Dþ0:04E 0:1F þ0:025G ð9Þ

WEAR AND TENSILE PROPERTIES OF POLYPROPYLENE

Furthermore, by investigating the correlation coefficients, R2, which measures the strength of a linear relationship between the experimental data and the predicted values from the regression models, the proportion of total variability in the r deviation that can be explained by Eq. (8) is R2 ¼

SSModel 65:57 ¼ 99:98% ¼ 65:58 SSTotal

ð10Þ

where SS is the abbreviation of ‘‘Sum of Squares’’. Similarly, the proportion of total variability in the Dm deviation that can be explained by Eq. (9) is

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R2 ¼

SSModel 2:14 ¼ 81:67% ¼ 2:62 SSTotal

ð11Þ

4.2.4. Regression Model Adequacy Check The adequacy of the regression models were inspected to confirm that the models have extracted all relevant information from the experimental data. The primary diagnostic tool is residual analysis[14]. The residuals are defined as the differences between the actual and predicted values for each point in the design. The residual results for the r and the Dm are shown in Table 6. If a model is adequate, the distribution of residuals should be normally distributed. Minitab1[19] program is used to perform a normality test. For the normality test, the hypotheses are listed as follows: 1. Null hypothesis: the residual data follows a normal distribution. 2. Alternative hypothesis: the residual data does not follow a normal distribution. TABLE 6 Residual results of the r and the Dm r (MPa) Dm (mg) Run no. Actual Pred. Residual Actual Pred. Residual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

22.35 28.11 26.38 28.49 23.00 23.20 26.75 26.28 26.32 25.95 26.88 29.12 25.31 28.37 28.42 28.13

22.38 28.08 26.35 28.52 23.00 23.20 26.72 26.31 26.32 25.95 26.88 29.12 25.28 28.40 28.48 28.07

0.03 0.03 0.03 0.03 0.00 0.00 0.03 0.03 0.00 0.00 0.00 0.00 0.03 0.03 0.06 0.06

2.3 2.3 2.3 2.1 2.0 2.1 2.5 2.4 2.6 2.8 1.3 1.3 2.3 1.9 2.5 1.9

2.21 2.21 2.11 2.11 1.96 1.96 2.36 2.36 2.86 2.86 1.46 1.46 2.11 2.11 2.21 2.21

0.09 0.09 0.19 0.01 0.04 0.14 0.14 0.04 0.26 0.06 0.16 0.16 0.19 0.21 0.29 0.31

103

The vertical axis of Fig. 6a and 6b has a probability scale and the horizontal axis with a data scale. A leastsquare line is then fitted to the plotted points. The line forms an estimate of the cumulative distribution function for the population from which data are drawn. As a ‘‘P-Value’’ that is smaller than 0.05, it will be classified as ‘‘significant’’ , and the null hypothesis has to be rejected. All of the ‘‘P-values’’ shown on the lower right-hand side of Fig. 6a and 6b are larger than 0.05; thus, the residuals for the r and the Dm follow a normal distribution and the predictive regression models have extracted all available information from the experimental data. The rest of the information defined as residuals can be considered as errors from performing the experiments. 4.2.5. Optimal Setting for Desirability An optimal setting is selected among the candidates listed in Table 7. These candidates are obtained by choosing appropriate combinations of factors that maximize the desirability function in Eq. (4) from random starting points. The first run in Table 7 can be chosen as an optimal setting since it gives a maximized value of desirability by the DOE method. 4.3. Comparisons of Confirmation Tests The first confirmation run (No. 1 in Table 8) is an optimal parameter combination identified by the Taguchi method with temperature settings of 210 , 210 and 200C, speed ratios of 20, 20 and 30%, injection pressure ratios of 25, 40 and 30% for the first, second and third progressive strokes, respectively.With this setting, it predicts the r, and the Dm to be 30.09 MPa and 1.46 mg, respectively. Further, the second confirmation run (No. 2 in Table 8) is an optimal setting by the DOE method with a desirability value of 0.94 conducted with temperature settings of 209.8, 210.0 and 200.01C, speed ratios of 20.41, 20.0 and 28.59%, injection pressures ratios of 28.07, 39.97 and 26.95% for the first, second and third progressive stroke, respectively. This setting is identified from the regression models and by minimizing F(x) in Eq. (4). The predicted values for the r and the Dm are 29.12 MPa, and 1.47 mg, respectively. In Table 8, the predicted results from the optimal conditions are compatible for two different methods in the wear mass loss and about 3% difference in the tensile stress. 5. CONCLUSIONS Both the DOE method and the Taguchi method were applied to find an optimal setting of the injection molding process. The DOE approach finds solution that balances desirability from targeted outputs. On the other hand, the result from the Taguchi method chooses an optimal solution from combinations of factors if it gives a maximized

ed by [Princeton University] at 22:56 13 November 2014

104

YU-HSIN LIN ET AL.

FIG. 6.

(a) Normal probability plot for the residual of r; (b) Normal probability plot for the residual of Dm.

temperature 210C (i.e., D), the injection speed ratio of 20% (i.e., E), and the injection pressure ratio of 40% (i.e., F) for the second progressive stroke; the factors of the third progressive stroke are the melting temperature of 200C (i.e., G), the injection speed ratio of 30% (i.e., H), and the injection pressure ratio of 30% (i.e., J).

normalized combined S=N ratio of targeted outputs. The results are summarized as follows: 1. The optimal setting by the Taguchi method is with the melting temperature of 210C (i.e., A), the injection speed ratio of 20% (i.e., B), and the injection pressure ratio of 25% (i.e., C) for the first progressive stroke; the melting

TABLE 7 Optimal setting for injection molding processes First stroke

Second stroke

Third stroke

Run no.

A ( C)

B (%)

C (%)

D ( C)

E (%)

F (%)

G ( C)

H (%)

J (%)

Predicted r

Predicted Dm

Desirability

1 2 3 4 5

209.80 207.66 206.08 209.85 210.00

20.41 20.54 20.00 21.06 30.00

28.07 26.20 25.00 26.07 25.02

210.00 208.82 210.00 210.00 209.61

20.00 20.00 20.85 21.07 21.62

39.97 40.00 39.99 40.00 40.00

200.01 200.00 200.00 200.96 200.23

28.59 29.83 29.61 27.26 22.90

26.95 28.01 25.65 30.00 25.00

29.12 29.12 29.40 29.11 28.96

1.47 1.49 1.50 1.53 1.54

0.94 0.93 0.93 0.92 0.90







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WEAR AND TENSILE PROPERTIES OF POLYPROPYLENE

TABLE 8 Confirmation runs and an optimal setting showing results for the r and Dm

ed by [Princeton University] at 22:56 13 November 2014

First stroke

Second stroke

Third stroke

Run no.

A (C)

B (%)

C (%)

D (C)

E (%)

F (%)

G (C)

H (%)

J (%)

Pre.=Exp. r

Pre.=Exp. Dm

1 2

210 209.80

20 20.41

25 28.07

210 210.0

20 20.0

40 39.97

200 200.01

30 28.59

30 26.95

30.09=29.65 29.12=28.70

1.46=1.53 1.47=1.51

2. The optimal parameter setting via the DOE approach with desirability value of 0.94 can be shown as follows: the setting for the first progressive stroke is with the melting temperature of 209.8C (i.e., A), the injection speed ratio of 20.41% (i.e., B), and the injection pressure ratio of 28.07% (i.e., C); the melting temperature 210.0C (i.e., D), the injection speed ratio of 20.0% (i.e., E), and the injection pressure ratio of 39.97% (i.e., F) for the second progressive stroke; the factors of the third progressive stroke are the melting temperature of 200.01C (i.e., G), the injection speed ratio of 28.59% (i.e., H), and the injection pressure ratio of 26.95% (i.e., J). 3. For these two different methods, the optimal parameters are almost identical with some minor differences in the parameter ‘‘C’’ (the injection pressure ratio of the first stroke), ‘‘H’’ and ‘‘J’’ (the injection speed ratio and injection pressure ratio of the third stroke). Nevertheless, the predicted results from the optimal conditions are compatible for the Taguchi method and the DOE approach in the wear mass loss and about 3% difference in the tensile stress. 4. The developed regression models can be used to predict both the tensile properties and wear mass losses of PP components. Hence, a trial-and-error process can be eliminated so that the efficiency of deg an optimal solution is greatly improved. ACKNOWLEDGMENT The authors would like to thank the National Science Council of the Republic of China, for financially ing this research (Contract No. NSC95–2622-E159-01-CC3) and Ming Hsin University of Science and Technology (Contract No. MUST-96-ME-001). REFERENCES 1. Chien, R.D.; Chen, S.C.; Lee, P.H.; Huang, J.S. Study on the molding characteristics and mechanical properties of injection-molded foaming polypropylene parts. J. Reinf. Plast. Comp. 2004, 23 (4), 429–444. 2. Ismail, H.; Suryadiansyah. A comparative study of the effect of degradation on the properties of PP=NR and PP=RR blends. Polym. Plast. Technol. Eng. 2004, 43 (2), 319–340.

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