a study of taguchi and design of experiments method in injection molding process for polypropylene...

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DOI: 10.1177/07316844070849882008 2008 27: 819 originally published online 31 JanuaryJournal of Reinforced Plastics and Composites

Yung-Kuang Yang, Jie-Ren Shie, Hsin-Te Liao, Jeong-Lian Wen and Rong-Tai Yangfor Polypropylene Components

A Study of Taguchi and Design of Experiments Method in Injection Molding Process

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A Study of Taguchi and Design of ExperimentsMethod in Injection Molding Process for

Polypropylene Components

YUNG-KUANG YANG,* JIE-REN SHIE, HSIN-TE LIAO,JEONG-LIAN WEN AND RONG-TAI YANG

Department of Mechanical EngineeringMing Hsin University of Science and Technology

Hsin Feng, 304, Hsinchu, Taiwan

ABSTRACT: This study analyzes contour distortions, wear mass losses and tensile properties ofpolypropylene (PP) composite components applied to the interior coffer of automobiles. Thespecimens are prepared under different injection molding conditions by changing meltingtemperatures, injection speeds, and injection pressures via three computer-controlled progressivestrokes. The contour distortions, wear and tensile properties are selected as quality targets.The arrangement of sixteen experiments is based on an orthogonal array table. Both the Taguchimethod and the design of experiments (DOE) method are applied to determine an optimal parametersetting. 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, andthe mathematic models can be utilized to predict the contour distortions, wear and tensile propertiesat various injection molding conditions.

KEY WORDS: contour distortions, wear mass losses, tensile strength, injection molding, Taguchi,DOE, optimization.

INTRODUCTION

RECENTLY, BY USING the polypropylene (PP) with a new catalyst, metallocene,the production efficiency and the properties of fibers have been greatly improved.Besides, with the benefit of low production costs, PP becomes popular in variousapplications such as consumer electronic products, automotive components, the chemicalindustry, and raw materials for packing and sealing, etc.The mechanical properties of PP composites have been studied intensively, mostly

through experiments. Chien et al. [1] investigated the effects of molding factors on themechanical properties of injection molded foaming PP parts and coinjection moldingPP parts of foaming core material embedded in non-foaming skin material.The controlling parameters were the injection velocity, the melting temperature, themolding temperature and the back-pressure; the quality targets of the parts were theweights and mechanical properties such as the tensile strength, the flexural strength and

*Author to whom correspondence should be addressed. E-mail: [email protected] 2 and 4 appear in color online: http://jrp.sagepub.com

Journal of REINFORCED PLASTICS AND COMPOSITES, Vol. 27, No. 8/2008 819

0731-6844/08/08 081916 $10.00/0 DOI: 10.1177/0731684407084988 SAGE Publications 2008

Los Angeles, London, New Delhi and Singapore


the stiffness. Ismail and Suryadiansyah [2] examined the degree of degradations on thetensile and morphological properties of the PP/natural rubber (NR) and the PP/recycledrubber (RR) blended at different rubber contents. With similar rubber contents anddegradation conditions, PP/RR blends exhibited a higher percentage of retention of thetensile strength and the Youngs modulus but a lower elongation at break than the PP/NRblends. Sain et al. [3] studied the mechanical properties of the tensile, the flexural andthe un-notched impact strength of the PP composites with a variety of natural fiberssuch as old newsprint, kraft pulp, hemp, and glass fibers. Yao et al. [4] consideredlarge deformation behavior of two commercial biaxially oriented polypropylene (BOPP)resins with different processing properties under high temperatures and high strainrate conditions by means of a Meissner rheometer. Modesti et al. [5] inspected theinfluence of processing conditions on the nano-composites structure, i.e., intercalated orexfoliated, and on the enhancement of mechanical properties of the PP nano-composites.In order to optimize the process parameters, both the screw speed and the barreltemperature profile were varied. In addition, Yang et al. [6] applied the design ofexperiments (DOE) method on the optimization of the injection molding process for thecontour distortions of PP components. The developed regression models can be utilizedto predict the contour distortions at each location under different injection moldingconditions.This study applied Taguchis L16 (2

4) orthogonal table to plan the experiments.Nine controlling factors with two levels for each factor were selected. The contourdistortions, wear mass losses and the tensile strengths are the three selected qualityobjectives. Typically, lower contour distortions, lower wear mass losses, and higher tensilestrengths in the PP components are desirable for products by the injection moldingprocess. For each experiment, the Taguchi method is used to calculate a normalized S/Nratio, which represents the quality characteristic of the considered processes. Choosing thelargest possible S/N ratio then identifies an optimal process parameter level/factorcombination. For side-by-side comparison purposes, regression models that relate thedesired outputs and the significant factors are established through the DOE approach;furthermore, an optimized parameter setting is then determined from those regressionequations.

TAGUCHI EXPERIMENTS AND DESIGN OF EXPERIMENTS METHOD

Taguchi Method

The Taguchi method is a novel approach for improving quality, which applies severalstatistical concepts to quality engineering. The factorial experimental design developedby Taguchi concentrates on reducing variation in the presence of noises. Theseexperiments are established using orthogonal arrays. The Taguchi method combines theeffects of each noise factor and calculates a signal-to-noise ratio (S/N ratio) for eachexperiment. The Taguchi method has been used successfully in several industrialapplications, such as manufacturing processes, mechanical component designs, andprocess optimizations [711].Depending on the objective, there are three different varieties for the Taguchi method as

define the signalnoise (S/N) ratios, which are the nominal-the-better, larger-the-better,and smaller-the-better. The utilization of a mean square deviation can be considered,calculating the average performance characteristic values for each experiment.

820 Y.-K. YANG ET AL.


Three different S/N ratios, corresponding to n experiments, are presented as follows.Nominal-the-better:

S

Nratio 10 log 1

n

Xni1

yi m2" #

10 log ym2 S 2 : 1Larger-the-better:

S

Nratio 10 log 1

n

Xni1

1

y2i

!: 2

Smaller-the-better:

S

Nratio 10 log 1

n

Xni1

y2i

! 10 log y2 3

where S at the right-hand-side of the equation (1), denotes the standard deviation; yi theexperimental data; n the number of performed experiments; m is a targeted value.

Design of Experiments (DOE) Method

The DOE method has been widely applied to various fields: Chao and Hwang [12]proposed an improved Taguchi method for milling CFRP composite; Puertas and Luis[13] optimized the machining parameters for electrical discharge machining of boroncarbide via the DOE method; Lin and Chananda [14] improved the injection moldingquality by four-factor full-factorial design; Yang [15] implemented the DOE to determinethe optimal parameters of photo resist coating process for photolithography in wafermanufacturing; and so on.By the DOE approach, the objective is to identify an optimal setting that minimizes the

measured average distortion and the mass loss under wear conditions as well as maximizesthe tensile strength for the PP produced components. To resolve this type of multi-outputparameter design problem, an objective function, F(x), is defined as follows [16]:

DF Yni1

dwii

!1Pnj1 wi

Fx DF4

where the di is the desirability defined for the ith targeted output; the wi is the weighting ofthe di. For various goals of each targeted output, the desirability, di, is defined in differentforms. If a goal is to reach a specific value of Ti, the desirability di is:

di 0 if YiHighi

: 5

Taguchi and Design of Experiments in Injection Molding 821


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

di 0 if Yi Highi

: 6

For a goal to search for a minimum, the desirability can be defined by the followingformulas:

di 1 if Yi Highi

7

where the Yi is the found value of the ith output during optimization processes; and theLowi and the Highi are the minimum and the maximum values of the experimental data forthe ith output. In the Equation (4), the wi is set to one since the di is equally important in thisstudy. The DF is a combined desirability function [16], and the objective is to choose anoptimal setting that maximizes a combined desirability function DF, i.e., minimize F(x).

Steps for Parameter Optimization

The following steps are the processes for the parameter optimization by both theTaguchi method and the DOE approach:

Step 1. Use the orthogonal array table of Taguchi method to design and conduct theexperiments.

Step 2. Use S/N analysis to obtain an optimal setting that minimizes the contourdistortions and wear mass losses as well maximizes tensile strengths for theTaguchi method.

Step 3. Use DOE analysis to model the relationship between the controlled param-eters and targeted outputs via regression equations. An optimal setting isthen identified by maximizing a combined desirability function that balances thedesirability of each output.

Step 4. Compare and verify the optimal solutions of two different approaches byadditional experiments.

EXPERIMENTAL PROCEDURE AND TEST RESULTS

Material

A commercial high heat and high stiff type of CP-28 PP compounds from STARONE Co. (Taiwan) is the studied material. The basic physical properties are listed asfollows: density of 1.1 g/cm3, tensile strength of 20MPa (under room temperature),flexural strength of 34MPa (under room temperature), hardness of 82 Rockwell, and



heat distortion temperature of 1248C, respectively. To remove excessive moisture,the composite was heated to 808C for 2 hours before the injection molding process.

Schematic of a Specimen

Figure 1 shows the dimensions of a desired final product. It is one of the decorativecomponents used in the automobile interior. Since a smooth transition between thispart and the applied area is crucial for cosmetic purposes, Yang et al. [6] minimizethe product contour distortions at six locations through properly chosen processparameters. For practical usage of products, two additional critical quality targets, suchas the wear mass losses and the tensile strength are included in this study since a longproduct lifetime is desirable. The experiments were carried out on a computerizedreciprocating screw injection molding machine with the capability of a maximuminjection pressure of 170MPa, an injection rate of 130 cm3/sec, and a maximum clampforce of 1334 kN.

Experimental Parameters and Design

The product quality produced by the injection molding is always affected by the processparameters, including the cooling time, the injection pressure, the injection speed, thefilling time, the melting temperature, the ejecting pressure, the molding temperature, thepacking pressure, the geometric shape of the mold, material properties of the meltingmolds, the melting speed, and the heat transfer action of flow field, etc. The influences ofthe injection molding variables (conditions) on the physical and mechanical properties ofthermoplastics have been studied by researchers [1,5,6,9,14,17]. For a preliminary study,the injection molding parameters were simulated by C-MOLD software to identify somecrucial settings.

Tensile specimen

Wear specimen

t = 2mm Unit = mm

Figure 1. Configurations of a specimen.



In Figure 2, enhanced ribs are added to eliminate the distortions of the components,although reducing the thickness of parts is one of the common practices to save productioncosts. Based on the simulation results from C-MOLD, using three progressive strokes canlower the probability of the short injection. Figure 3 illustrates an injection molding setup,with which two components are produced for each injection channel per molding cycle.Table 1 lists the experimental factors and factor levels of the injection molding conditionsbased on the C-MOLD simulation. The melting temperature H1 (i.e., A/8C), the injectionspeed ratio (i.e., B/%), and the injection pressure ratio (i.e., C/%) are the factors forthe first progressive stroke. The melting temperature H2 (i.e., D/8C), the injection speedratio (i.e., E/%), and the injection pressure ratio (i.e., F/%) are the factors of the second

(a) (b)

Injection port

Rib

Figure 2. Photos of a specimen: (a) Exterior; (b) Interior.

Injection stroke

Injection port

Injection port

Ha Hb H1 H2 H3

Ha Hb H1 H2 H3

Figure 3. Schematic shows the injection molding setup.

Table 1. Experimental factors and factor levels.

Experimental factors for three progressive strokes

First stroke Second stroke Third stroke

Levels of experimentalfactors A (8C) B (%) C (%) D (8C) E (%) F (%) G (8C) H (%) I (%)

1 200 20 25 200 20 35 200 20 252 210 30 30 210 30 40 210 30 30



progressive stroke. Similarly, the factors of the third progressive stroke are the meltingtemperature H3 (i.e., G/8C), the injection speed ratio (i.e., H/%), and the injection pressureratio (i.e., I/%).Table 2 lists sixteen runs based on an orthogonal array L16 (2

4), consisting ofnine experimental factors with two levels for each factor. Simultaneously, the cut-awayportions of specimens for wear and tensile tests are also illustrated in Figure 1.Additionally, the melting temperatures of Ha and Hb are set to 40 and 508C,

respectively; the mold temperature is 608C with a packing pressure of 40MPa. All thesefactors are fixed and computer-controlled during the injection molding process.

TEST RESULTS

Contour Distortion Measurement

The amounts of distortion at six critical locations specified by the customersare measured by a precision digimatic caliper (series 500, Mitutoyo Co.) with 10 mmresolution. Figure 1 shows the dimensions of a specimen and six critical locations that havebeen selected to measure the amount of distortions. The average distortion measurementof at six locations is given in Table 2.

Wear Tests

The wear tests were carried out with a Schwingung Reibung and Verschleiss(SRV, manufactured by Optimol Instruments Pruftechnik GmbH; Munchen, Germany)oscillation friction wear tester. The dimensions of the wear test specimens were15mm 15mm 2.45mm and cut directly from the on-line product of the injectionmolding process. The SRV wear tests were performed in ball-on-plane contact witha load of 60N. The ball was a chromium steel ball (AISI E52100) of 10mm in diameter

Table 2. Orthogonal array L16(24) of the experimental runs and results.

First stroke Second stroke Third stroke

Run no. A B C D E F G H I d (mm) r (MPa) "m (mg)

1 1 1 1 1 1 1 1 1 1 0.078 22.35 2.32 1 1 1 1 1 1 1 2 2 0.085 28.11 2.33 1 1 1 2 2 2 2 1 1 0.057 26.38 2.34 1 1 1 2 2 2 2 2 2 0.233 28.49 2.15 1 2 2 1 1 2 2 1 1 0.160 23.00 2.06 1 2 2 1 1 2 2 2 2 0.150 23.20 2.17 1 2 2 2 2 1 1 1 2 0.115 26.75 2.58 1 2 2 2 2 1 1 2 1 0.073 26.28 2.49 2 1 2 1 2 1 2 1 2 0.195 26.32 2.610 2 1 2 1 2 1 2 2 1 0.060 25.95 2.811 2 1 2 2 1 2 1 1 2 0.178 26.88 1.312 2 1 2 2 1 2 1 2 1 0.145 29.12 1.313 2 2 1 1 2 2 1 1 2 0.255 25.31 2.314 2 2 1 1 2 2 1 2 1 0.293 28.37 1.915 2 2 1 2 1 1 2 1 2 0.215 28.42 2.516 2 2 1 2 1 1 2 2 1 0.115 28.13 1.9



with an average hardness of 62 2 HRC. The applied stroke was 2mm with a testfrequency of 20Hz and test duration of 15min, respectively. It yielded a total slidingdistance of 72m under the selected testing parameters. The mass loss (i.e., m) wasmeasured after each wear test. The experimental results are listed in Table 2.

Tensile Tests

The tensile stress has a definite correlation with the tensile test. Figure 1 showsthe location of the cut tensile test specimen. Using the ASTM D63891 specification, thetest was performed with a 25 kN computerized MTS model 810 closed-loop servo-hydraulic system (manufactured by MTS Systems Co.; MN, USA) at a speed of 1mm/minunder the room temperature. The specimens were monotonically loaded in tension untilfracture. Software was employed to control the procedure and continuously recordthe load and the compliance displacement. The calculated tensile stresses (i.e., ) are listedin Table 2.

RESULTS AND DISCUSSION

Taguchi Results

The Taguchi method can be employed to obtain an optimal process parameterlevel/factor combination. It applies the signal-to-noise (S/N) ratio to represent the qualitycharacteristic and an optimal setting will have the largest possible S/N ratio.In this study, typically, PP products with small contour distortions and wear mass losses

as well as large tensile strengths are desirable. Therefore, the smaller-the-better S/N ratioformula (i.e., Equation (3)) is chosen for both the contour distortion and the wear massloss. In addition, the larger-the-better S/N ratio formula (i.e., Equation (2)) is applied forthe tensile strength.Table 3 presents the calculated S/N ratios by the Taguchi method, while Table 4 lists the

S/N ratio for different levels of controlled factors. In Table 4, A2, B1, C2, D2, E1, F2, G1,H2 and I1 represent the largest S/N ratios for factors A, B, C, D, E, F, G, H and I,respectively. Consequently, A2B1C2D2E1F2G1H2J1 is an optimal parameter combinationof the injection molding process. Namely, this setting yields a combination of the meltingtemperature of 2108C (i.e., A), the injection speed ratio of 20% (i.e., B), and the injectionpressure ratio of 30% (i.e., C) for the first progressive stroke; the melting temperature2108C (i.e., D), the injection speed ratio of 20% (i.e., E), and the injection pressure ratio of40% (i.e., F) for the second progressive stroke; the factors of the third progressive strokeare the melting temperature of 2008C (i.e., G), the injection speed ratio of 30% (i.e., H),and the injection pressure ratio of 25% (i.e., I).

DOE Results

DEFINITION OF AN OBJECTIVE FUNCTIONThe experimental results of contour distortions ( in mm), wear mass losses (m in mg)

and tensile stresses ( in MPa) are listed in Table 2. The objective of this study is to identifyan optimal setting that gives a minimized average contour distortion at six criticallocations and a minimized mass loss as well as a maximized tensile stress. The foundoptimal solution would have to strike the balance between these three-targeted outputs.



Hence, Equation (7) will be selected as a desirability function form for minimizing theaverage contour distortion and the mass loss. On the other hand, Equation (6) is suitablefor maximizing the tensile stress. Furthermore, these individual desirability functions arerolled into Equation (4) as a combined desirability function. More details can be found inthe Myerss book [16].

ANOVA RESULTSThe analysis of variance (ANOVA) is conducted and the results are shown in Table 5(a),

(b) and (c). A Model F Value is calculated from a model mean square divided bya residual mean square. It is a test comparing a model 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 thatany 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 terms in the model havea significant effect on the response [16]. Similarly, an F Value on any individual factorterms is calculated from a term mean square divided by a residual mean square. It is a testthat compares a term variance with a residual variance. If the variances are close to thesame, the ratio will be close to one and it is less likely that the term has a significant effecton the response. Furthermore, if a P Value of any model terms is very small (less than0.05), the individual terms in the model have a significant effect on the response.Table 5(a) shows the ANOVA result of the . A Model F Value of 8.33 with a Model

P Value of 0.0089 implies that the selected model is significant and there is only a 0.89%

Table 3. S/N ratios of Taguchi experimental results.

S/N Ratio(dB) Normalized

Run no. d r "m d r "m Total

1 22.1211 26.9848 52.7654 0.8031 0.0000 0.2564 1.05942 21.4116 28.9765 52.7654 0.7534 0.8664 0.2564 1.87623 24.9334 28.4240 52.7654 1.0000 0.6261 0.2564 1.88244 12.6405 29.0939 53.5556 0.1392 0.9175 0.3749 1.43165 15.9176 27.2330 53.9794 0.3687 0.1080 0.4385 0.91526 16.4782 27.3097 53.5556 0.4079 0.1413 0.3749 0.92427 18.7860 28.5468 52.0412 0.5695 0.6795 0.1477 1.39678 22.6940 28.3914 52.3958 0.8432 0.6119 0.2009 1.65609 14.1993 28.4044 51.7005 0.2483 0.6175 0.0966 0.962510 24.4370 28.2812 51.0568 0.9652 0.5639 0.0000 1.529211 14.9753 28.5887 57.7211 0.3027 0.6977 1.0000 2.000412 16.7726 29.2836 57.7211 0.4285 1.0000 1.0000 2.428513 11.8692 28.0645 52.7654 0.0852 0.4697 0.2564 0.811214 10.6528 29.0575 54.4249 0.0000 0.9017 0.5054 1.407115 13.3512 29.0721 52.0412 0.1890 0.9080 0.1477 1.244716 18.7860 28.9849 54.4249 0.5695 0.8701 0.5054 1.9450

Table 4. A response table for S/N ratios.

Factor A B C D E F G H I

Level 1 1.3927 1.6463 1.4572 1.1856 1.5492 1.4587 1.5795 1.2841 1.6029Level 2 1.5411 1.2875 1.4766 1.7482 1.3846 1.4751 1.3543 1.6497 1.3309



chance that the Model F Value could occur due to noise. A P Value for the modelterm A (the melting temperature at the first progressive stroke) is 0.0070, which is lessthan 0.05, indicating that the model term A is significant. Similarly, the model term B(the speed ratio at the first progressive stroke) and F (the pressure ratio at the secondprogressive stroke) are also significant. There are two interaction interactions of factors,CH and GJ, which have impact on the . According to the hierarchy principle [18],the terms C (the pressure ratio at the first progressive stroke), G, H, and I (themelting temperature, the speed ratio, and the pressure ratio at the third progressive stroke,respectively) have to be selected. Even the Model P Value for these terms is more than0.05. C, G, H, and I are also significant terms for the .Table 5(b) lists the ANOVA result of the . A Model F Value of 700.54 with a

Model P Value of 0.0014 implies that the selected model is significant and there is onlya 0.14% chance that the Model F Value could occur due to noise. The P Values for

Table 5(b). ANOVA results of the r.

Source Sum of squares Degree of freedom Mean square F Value P Value

Model 65.57 13 5.04 700.54 0.0014A: temperature (8C) 12.15 1 12.15 1686.84 0.0006B: speed ratio (%) 1.07 1 1.07 148.78 0.0067C: pressure ratio (%) 4.06 1 4.06 563.92 0.0018D: temperature (8C) 19.89 1 19.89 2762.72 0.0004E: speed ratio (%) 1.35 1 1.35 186.89 0.0053F: pressure ratio (%) 0.15 1 0.15 21.13 0.0442G: temperature (8C) 0.67 1 0.67 93.39 0.0105H: speed ratio (%) 10.46 1 10.46 1452.33 0.0007I: pressure ratio (%) 1.74 1 1.74 241.17 0.0041BH 0.71 1 0.71 98.20 0.0100BJ 1.42 1 1.42 197.42 0.0050DH 0.15 1 0.15 20.57 0.0453FJ 6.60 1 6.60 916.31 0.0011Residual 0.01 2 0.01 Total 65.58 15

Table 5(a). ANOVA results of the d.


Model 0.074 9 0.008 8.33 0.0089A: temperature (8C) 0.016 1 0.016 16.12 0.0070B: speed ratio (%) 0.007 1 0.007 7.52 0.0336C: pressure ratio (%) 0.004 1 0.004 4.11 0.0890F: pressure ratio (%) 0.018 1 0.018 18.09 0.0054G: temperature (8C) 0.000 1 0.000 0.09 0.7785H: speed ratio (%) 0.001 1 0.001 1.11 0.3331I: pressure ratio (%) 0.005 1 0.005 5.31 0.0608CH 0.008 1 0.008 8.03 0.0298GJ 0.013 1 0.013 12.95 0.0114Residual 0.006 6 0.001 Total 0.080 15



all model terms are significant. Additionally, BH, BJ, DH and FJ havesignificant influences on the .Table 5(c) gives the ANOVA result of the m. A Model F Value of 12.32 with

a Model P Value of 0.0005, implying that the selected model is significant and there isonly a 0.05% chance that the Model F Value could occur due to noise. A P Value forthe 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, themodel terms E and F (the speed ratio and the pressure ratio at the second progressivestroke, respectively) are significant. In addition, the model term G (the temperatureat the third progressive stroke) is significant. There are no interactions of factors thathave impact on the m.

REGRESSION MODELSConsidering the most significant terms from Table 5(a), (b) and (c), regression models

can be developed. Mathematic predicted models for the average distortion, the tensilestress and the mass loss are shown as follows:

10:8069 0:0063 A 0:0043 B 0:0418 C 0:0134 F 0:0677 G 0:0512H 0:493 J 0:0019 CH 0:0024 GJ 8

224:9925 0:1743 A 0:9833 B 0:2015 C 0:338D 0:058 E 3:338 F 0:041 G 1:3875H 5:475 J 0:01 BH 0:0285 BJ 0:0046DH 0:1228 FJ 9

m 4:9125 0:025D 0:04 E 0:1 F 0:025 G: 10

Furthermore, by investigating the correlation coefficients, R2, which measures thestrength of a linear relationship between the experimental data and the predicted valuesfrom the regression models, the proportion of total variability in the deviation thatcan be explained by Equation (8) is:

R2 SSModelSSTotal

0:0740:080

92:50% 11

where SS is the abbreviation of sum of squares.

Table 5(c). ANOVA results of the Dm.


Model 2.14 4 0.54 12.32 0.0005D: temperature (8C) 0.25 1 0.25 5.76 0.0352E: speed ratio (%) 0.64 1 0.64 14.74 0.0027F: pressure ratio (%) 1.00 1 1.00 23.04 0.0006G: temperature (8C) 0.25 1 0.25 5.76 0.0352Residual 0.48 11 0.04 Total 2.62 15



Similarly, the proportion of total variability in the deviation that can be explained byEquation (9) is:

R2 SSModelSSTotal

65:5765:58

99:98% 12

and the proportion of total variability in the m deviation that can be explained byEquation (10) is:

R2 SSModelSSTotal

2:142:62

81:67%: 13

MODEL ADEQUACY CHECKThe adequacy of the regression models will be inspected to confirm that the models have

extracted all relevant information from the experimental data. The primary diagnostic toolis residual analysis [18]. The residuals are defined as the differences between the actual andpredicted values for each point in the design. The residual results for the , the and them are shown in Table 6. If a model is adequate, the distribution of residuals shouldbe normally distributed. The Minitab [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 distribution2. Alternative hypothesis: the residual data does not follow a normal distribution.

The vertical axis of Figures 4(a)4(c) has a probability scale and the horizontal axishas a data scale. A least-square line is then fitted to the plotted points. The line formsan estimate of the cumulative distribution function for the population from which dataare drawn.

Table 6. Residual results of the d, r and Dm.

d (mm) r (MPa) "m (mg)

Run no. Actual Pred. Residual Actual Pred. Residual Actual Pred. Residual

1 0.078 0.078 0.0000 22.35 22.38 0.03 2.3 2.21 0.092 0.085 0.086 0.0013 28.11 28.08 0.03 2.3 2.21 0.093 0.057 0.079 0.0221 26.38 26.35 0.03 2.3 2.11 0.194 0.233 0.210 0.0234 28.49 28.52 0.03 2.1 2.11 0.015 0.160 0.139 0.0215 23.00 23.00 0.00 2.0 1.96 0.046 0.150 0.173 0.0228 23.20 23.20 0.00 2.1 1.96 0.147 0.115 0.115 0.0004 26.75 26.72 0.03 2.5 2.36 0.148 0.073 0.071 0.0016 26.28 26.31 0.03 2.4 2.36 0.049 0.195 0.192 0.0031 26.32 26.32 0.00 2.6 2.86 0.2610 0.060 0.026 0.0344 25.95 25.95 0.00 2.8 2.86 0.0611 0.178 0.202 0.0243 26.88 26.88 0.00 1.3 1.46 0.1612 0.145 0.158 0.0133 29.12 29.12 0.00 1.3 1.46 0.1613 0.255 0.229 0.0259 25.31 25.28 0.03 2.3 2.11 0.1914 0.293 0.281 0.0116 28.37 28.40 0.03 1.9 2.11 0.2115 0.215 0.219 0.0038 28.42 28.48 0.06 2.5 2.21 0.2916 0.115 0.149 0.0338 28.13 28.07 0.06 1.9 2.21 0.31



0.999(a)

(b)

(c)

0.999

0.99

0.99

0.95

0.95

0.80

0.80

0.50

0.50

0.20

0.20

0.05

0.05

0.01

0.01

0.001

0.001

Prob

abilit

yPr

obab

ility

0.9990.990.950.800.500.200.050.01

0.001

Prob

abilit

y

Average:-0.0000391 Anderson-darling normality test

Anderson-Darling normality test

Anderson-Darling normality test

P Value: 0.580

P Value: 0.087

P Value: 0.505

A-squared: 0.285

A-squared: 0.622

A-squared: 0.319

Residual_

Residual_

N:16

0.03 0.02 0.01 0.00

0.000.05

0.3 0.20.1 0.0

Residual_m0.1 0.2 0.3

0.05

0.01 0.02 0.03

St.Dev: 0.0198127

Average:-0

N:16St.Dev: 0.0309839

Average: 0.0016875

N:16St.Dev: 0.178315

Figure 4. (a) 4 Normal probability plot for the residual of , (b) 4 Normal probability plot for the residual of ,(c) 4 Normal probability plot for the residual of Dm.



As a P Value that is smaller than 0.05, it will be classified as significant, and thenull hypothesis has to be rejected. All of the P Values shown on the lower right-handside of Figures 4(a)(c) are larger than 0.05; thus, the residuals for the , the and the mfollow a normal distribution and the predictive regression models have extracted allavailable information from the experimental data. The rest of the information definedas residuals can be considered as errors from performing the experiments.

Comparisons of Confirmation Tests

The first confirmation run (No. 1 in Table 7) is an optimal parameter combinationidentified by the Taguchi method with temperature settings of 2108C, 2108C and 2008C,speed ratios of 20%, 20% and 30%, and injection pressure ratios of 30%, 40% and 25%for the first, the second and the third progressive strokes, respectively. With this setting,it predicts the , the , and the m to be 0.16mm, 29.19MPa and 1.46mg, respectively.On the other hand, the second confirmation run (No. 2 in Table 7) is an optimal setting

by the DOE method with a desirability value of 0.83, conducted with temperaturesettings of 2008C, 2108C and 2008C, speed ratios of 20%, 20% and 29.8%, injectionpressure ratios of 30%, 40% and 25.2% for the first, the second and the third progressivestrokes, respectively. This setting is identified from the regression models and byminimizing F(x) in Equation (4). The predicted values for the , the and the m are0.10mm, 27.33MPa, and 1.46mg, respectively.In Table 7, the predicted results from the optimal conditions are compatible in the wear

mass loss and around 6% difference for the tensile strengths. Nevertheless, the DOEapproach has an average contour distortion of 0.10mm vs. 0.16mm from the Taguchimethod.

CONCLUSION

Both the DOE method and the Taguchi method were applied to find an optimal settingfor the injection molding process. The identified optimal setting for the DOE approachstrikes the balance between the contour distortions, the tensile strength and the wear massloss of PP composite components. On the other hand, the result from the Taguchi methodsearched for an optimal solution within all possible combinations of factors and levels;eventually, an optimal combination is selected if it gives a maximized normalizedcombined 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 2108C(i.e., A), the injection speed ratio of 20% (i.e., B), and the injection pressure ratioof 30% (i.e., C) for the first progressive stroke; the melting temperature 2108C (i.e., D),

Table 7. Confirmation runs and an optimal setting showing results for the d, r and Dm.

First stroke Second stroke Third stroke Pre./Exp. Pre./Exp. Pre./Exp.

Runno.

A(8C)

B(%)

C(%)

D(8C)

E(%)

F(%)

G(8C)

H(%)

I(%)

d

(mm)r

(MPa)"m(mg)

1 210.0 20.0 30.0 210.0 20.0 40.0 200.0 30.0 25.0 0.16/0.17 29.12/28.40 1.46/1.522 200.0 20.0 30.00 210.0 20.0 40.0 200.0 29.8 25.2 0.10/0.12 27.33/27.90 1.46/1.48



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 arethe melting temperature of 2008C (i.e., G), the injection speed ratio of 30% (i.e., H),and the injection pressure ratio of 25% (i.e., I).

2. The optimal parameter setting via the DOE approach with desirability value of 0.83 canbe shown as follows: the setting for the first progressive stroke is with the meltingtemperature of 2008C (i.e., A), the injection speed ratio of 20% (i.e., B), and theinjection pressure ratio of 30% (i.e., C); the melting temperature 2108C (i.e., D), theinjection 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 themelting temperature of 2008C (i.e., G), the injection speed ratio of 29.8% (i.e., H), andthe injection pressure ratio of 25.2% (i.e., I).

3. For these two different methods, the optimal parameters are almost identical, with onlyminor difference in the parameter A (the melting temperature of the first stroke).However, the DOE approach has an average contour distortion of 0.10mm vs. 0.16mmfrom the Taguchi method.

4. The developed regression models can be utilized to predict the average contourdistortions, wear mass losses and tensile properties of PP components under differentinjection molding conditions. Namely, the implementation of the DOE method withmaximizing the desirability function is a systematic approach to identify an optimalparameter setting of the injection molding process; thus, the trial-and-error process canbe avoided so that the efficiency of designing an optimal solution is greatly improved.

5. Normality analysis on the residual data of the regression models ensures that themodels are adequate and extract all applicable information from the experimental data.

ACKNOWLEDGMENTS

The authors would like to thank the National Science Council of the Republic of China,for financially supporting this research (Contract No. NSC95-2622-E-159-001-CC3) andMing Hsin University of Science and Technology (Contract No. MUST-95-ME-005).

REFERENCES

1. Chien, R. D., Chen, S. C., Lee, P. H. and Huang, J. S. (2004). Study on the Molding Characteristics andMechanical Properties of Injection-Molded Foaming Polypropylene Parts, Journal of Reinforced Plastics andComposites, 23(4): 429444.

2. Ismail, H. and Suryadiansyah. (2004). A Comparative Study of the Effect of Degradation on the Properties ofPP/NR and PP/RR Blends, Polymer-Plastics Technology and Engineering, 43(2): 319340.

3. Sain, M., Suhara, P., Law, S. and Bouilloux, A. (2005). Interface Modification and MechanicalProperties of Natural Fiber-Polyolefin Composite Products, Journal of Reinforced Plastics and Composites,24(2): 121130.

4. Yao, W., Jia, Y., An, L. and Li, B. (2005). Elongational Properties of Biaxially Oriented Polypropylene withDifferent Processing Properties, Polymer-Plastics Technology and Engineering, 44(3): 447462.

5. Modesti, M., Lorenzetti, A., Bon, D. and Besco, S. (2005). Effect of processing conditions on morphology andmechanical properties of compatibilized polypropylene nanocomposites, Polymer, 46(23): 1023710245.

6. Yang, Y. K., Shie, J. R., Yang, R. T. and Chang, H. A. (2006). Optimization of Injection Molding Process forContour Distortions of Polypropylene Composite Components via Design of Experiments Method, Journal ofReinforced Plastics and Composites, 25(15): 15851599.

7. Tarng, Y. S. and Yang, W. H. (1998). Application of Taguchi Method to the Optimization of the SubmergedArc Welding Process, Materials and Manufacturing Processes, 13(3): 455467.



8. Connor, A. M. (1999). Parameter Sizing for Fluid Power Circuits Using Taguchi Method, EngineeringDesign, 10(4): 377390.

9. Liu, S. J. and Chang, C. Y. (2003). The Influence of Processing Parameters on Thin-Wall Gas AssistedInjection Molding of Thermoplastic Materials, Journal of Reinforced Plastics and Composites, 22(8): 711731.

10. Lin, C. L. (2004). Use of the Taguchi Method and Grey Relational Analysis to Optimize Turning Operationswith Multiple Performance Characteristics, Materials and Manufacturing Processes, 19(2): 209220.

11. Yang, Y. K. and Tzeng, C. J. (2006). Die Casting Parameter Sizing for AZ91D in Notebook Computer BaseShell, Materials and Manufacturing Processes, 21(5): 484489.

12. Chao, P. Y. and Hwang, Y. D. (1997). An Improved Taguchis Method in Design of Experiments for MillingCFRP Composite, International Journal of Production Research, 35(1): 5166.

13. Puertas, I. and Luis, C. J. (2004). A study of Optimization of Machining Parameters for Electrical DischargeMachining of Boron Carbide, Materials and Manufacturing Processes, 19(6): 10411070.

14. Lin, T. and Chananda, B. (2004). Quality Improvement of an Injection-Molded Product Using Design ofExperiments: a Case Study, Quality Engineering, 16(1): 99104.

15. Yang, Y. K. (2006). Optimization of a Photo Resists Coating Process for Photolithography in WaferManufacturing via Design of Experiments Method, Microelectronics International, 23(3): 2632.

16. Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology, 2nd edn, John Wiley and SonsInc., New York.

17. Yang, Y. K. (2006). Optimization of Injection Molding Process for Mechanical and Tribological Propertiesof Short Glass Fiber and Polytetrafluoroethylene Reinforced Polycarbonate Composites with GreyRelational Analysis: A Case Study, Polymer-Plastics Technology and Engineering, 45(7): 769777.

18. Douglas, C. M. (1997). Design and Analysis of Experiments, 4th edn, John Wiley & Sons, Inc., pp. 101245.

19. Minitab Inc. (2000). Quality Plaza, 1829 Pine Hall Road, State College, PA 16801-3008, USA.



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