Design Of Simulation Experiments method for Injection.pdf

8/13/2019 Design Of Simulation Experiments method for Injection.pdf

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Proceedings of the IMProVe 2011

International conference on Innovative Methods in Product Design

June 15th17

th, 2011, Venice, Italy

Design Of Simulation Experiments method for InjectionMolding process optimization

A.O. Andrisano(a)

, F. Gherardini(a)

, F. Leali(a)

, M. Pellicciari(a)

, A. Vergnano(a)

(a)Department of Mechanical and Civil EngineeringUniversity of Modena and Reggio Emilia (Italy)

Article Information

Keywords:Design Of Experiments (DOE),Simulation experiments,Computer Aided Engineering (CAE),

Integrated Design,Injection Molding (IM)

Corresponding author:Francesco GherardiniTel.: +39 059.205.6278Fax.: +39 059.205.6126e-mail: [email protected]

Address: via Vignolese 905/B 41125, Modena (Italy)

Abstract

Purpose:Many studies demonstrate that DOE, CAE and optimization tools can be very effective in

product and process development, however their integration is still under investigation,hampering the applicability of such engineering methods in Industry. This paper presents a

Design Of Simulation Experiments (DOSE) method, developed to determine the optimal setof process parameters (factors) for given product requirements (responses).

Method:The method is developed performing an original selection and integration of engineering

procedures and techniques based on DOE, CAE and multi-objective optimization, chosenaccording to the following criteria: ease of application, time-saving and use of reducedresources.

Result:The developed method consists of two main steps: a first screening of factors based on afractional DOE is followed by a systematic experimental plan based on the Response SurfaceMethodology (RSM), in which only key factors are investigated. A regression model is finallydeveloped to describe the responses as functions of key factors and a multi-objectiveoptimization is proposed to obtain optimal responses by tuning the process factors in theirvariability range. The DOSE method is finally validated on the design of an injection moldedhousing for a biomedical application. This thin shell component has dimension

45mmx37mmx16mm, wall thickness from 2mm to 0,5mm and is made of polyphenylsulfone(PPSU), a high performance thermoplastic.

Discussion & Conclusion:The design method achieves good responses in terms of dimensional and geometricalrequirements (e.g. warpage, shrinkage, sink marks), and improves the shell moldability. TheDOSE method can be easily adopted in industrial product/process development to define theoptimal process parameters for a better final quality of the products.

1 Introduction

Injection Molding (IM) technology allows to producecomplex shaped parts in short cycle time, in largequantities, with good dimensional accuracy and with light

weight. The present industrial trend deals with thedownsizing of products and the integration of aestheticand engineering criteria. Typical examples of plasticmolded parts are complex free-form casing and housings.

The technology trend is to reduce the housing wallthickness [1, 2] and adopt high performance engineeringplastics in order to host a large number of features intosmall volumes and to increase the internal space. Thedrawback is a greater difficulty in filling the mold cavity,due to the high length to thickness ratio [3], and defects,e.g. warpage, sink marks, shrinkage, finally may affect theproduct quality [4].

Many studies have focused on the remarkableinfluence of IM process parameters on final quality,

especially in thin, light and small parts [1, 3-8], but aneffective engineering optimization method has not yetunivocally determined. Even if several mathematicalmodels have been proposed and extensively developed,

some different approaches can be still observed inIndustry:

- technicians experience guides the processparameters setting [9] and the values of the optimalprocess parameters come from empirical and stochasticestimations;

- CAE is concurrently used in product development andprocess simulation, giving graphical and numericalfeedbacks before mold manufacturing. Simulations help toselect suitable materials, however, optimization of theprocess parameters is still based on a trial and errorapproach;

- DOE and optimization methods are used toinvestigate and tune the manufacturing processes,through physical experiments, simulation experiments or asystematic combination of both.

The lack of integration between practical experience,DOE approach and CAE process simulation hampers theknowledge about the influence of the rheological behaviorof polymers along the IM process [1] and inhibits its

effective optimization [10].The present work aims to select and originally integrate

different engineering procedures and techniques todevelop an easy-to-use Design of Simulation Experiments


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A.O. Andrisano et al. Design Of Simulation Experiments method for IM process optimization

June 15th17th, 2011, Venice, Italy Proceedings of the IMProVe 2011

(DOSE) methodology which integrates DOE and CAE toidentify the set of IM process parameters (factors) to betuned for optimizing the product key requirements(responses).

A brief literature review, focused on the IM process, isoutlined in the following subsection. Section 2 presents anovel integrated two-steps DOSE method, based on:

identification of process input factors and their variabilityrange (2.1), DOE screening (2.2), Response SurfaceMethodology (RSM) for the identification of the systemresponses (2.3) and final multi-objective optimization(2.4). Section 3 deals with the description of an industrialcase study: in 3.1 and 3.2 product geometry andsimulation model are presented and in 3.3 numericalresults are finally presented. Section 4 proposes someconclusions and future developments. Detailed numericalresults are reported in Appendix.

1.1 Literature review

Scientific literature is rich of theoretic methodologiesdeveloped to set up factors in order to optimize theproduct responses, often based on computer simulation.Many studies demonstrate that DOE, CAE and statisticaltools, such as RSM, can be integrated to solveoptimization problems.

In [11], the authors underline that DOE and Taguchimethods are being effectively applied worldwide to manyindustrial problems. This approach leads to higher qualityon final products and reduces both design costs andtimes.

Many studies are conducted to optimize performancesin the field of IM by the application of experimentaldesign. In [1], the RSM, based on centered CentralComposite Design matrix, is applied to identify the effectsof process parameters on shrinkage and warpage. In [3],

Taguchi method and computer simulations are adopted tostudy warpage in an injection molded thin shell. In [4],several process parameters are analyzed, by Taguchimethod, to investigate their influence on warpage. In [5],the authors investigate the warpage and shrinkage of amolded part with RSM modeled on a Taguchi 3-levelorthogonal array; the process is simulated with Moldflowsoftware. In [6], for a preliminary study, the authorspropose the use of CAE software to identify some crucialsettings for the IM process of a thin-shell plastic part. Apredictive model of warpage, based on RSM andMoldflow analyses, is developed. A 3-levels orthogonalarray is used for sampling the design space. Simulationresults are then validated with physical experiments. In

[7], the minimization of warpage on thin shell plastic isreached by integrating simulations, RSM and geneticalgorithms. In [12], the effect on warpage and shrinkageproduced by process parameters are studied by anexperimental design consisted of a screening phase,based on fractional factorial to identify the main factorsand interactions, and a second phase based on Taguchidesign to optimize the process parameters.

The referenced works present several case studies onthe integration of DOE, CAE and statistical approaches.Many authors, on the other hand, outline that theapplicability of engineering methods in Industry ishowever hampered by different reasons. In [13], theauthors underline that many difficulties exist in DOEapplication, due to the need of planning, use of statistics,

personnels knowledge and training. In [10], the authorsclaim that the wide use of DOE is limited by the lack of aneffective and friendly method for molders and designers

to control defects. On the other hand Industry more andmore demands for thin wall features on plastic parts [7].

Therefore, the goal of this paper is to propose amethod based on an original selection of techniquesavailable in literature, aiming to a reasonable compromisebetween simplicity, applicability, speed and resultsaccuracy through the adoption of an approach based on

computer simulation and statistical analysis.

2 DOSE method

The DOSE method selects and integrates differenttools and techniques used in product and processdevelopment, such as DOE and CAE, with morespecialized ones, like RSM and multi-objectiveoptimization. The core of DOSE is the deep integration ofCAE simulations and DOE and, in first approximation, itdoes not introduce the variability of the molding processparameters, according to [4-7].

The DOSE method is a two-step systematic approachfor the evaluation of the effect of factors on system

responses thanks to numerical simulations.The complete process is described in Fig.1:1. identification of input factors, their variability rangesand system responses;2. first step: DOE screening of factors;3. second step: RSM identification of systemresponses;4. optimization of responses and validation test.

Fig. 1 Workflow diagram.

The first step is a preliminary phase, focused onscreening the process factors by checking their influenceon the responses. It is based on fractional factorial DOEand performed through simulation tools. The selectedfactors are data inputs for the next step.

The second step is based on RSM and exploits anexhaustive DOE plan to sample the space design. Theoutput is a regression model (or metamodel) thatdescribes the system responses as functions of theselected factors.

Finally, the regression model is integrated within amulti-objective optimization problem for the systemresponses, and an optimal set of values is determined foreach factor by tuning the parameters in their variabilityrange.


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2.1 Input clarification

The optimization goal is the first point to be clarifiedbefore starting the analysis. The formalization of thegoals, and the stressing of the related problems, lead tothe identification of critical factors and the definition ofsystem performances. The identification of factors, i.e.

process parameters, can be performed starting fromdifferent sources, such as literature review, previous dataand studies, technicians experience.

A lot of scientific papers deals with analysis andoptimization of the IM process: many studies [5-7, 9, 10,12, 14] investigate the relevance of several IMparameters on the final quality of molded parts. Lookingat warpage and shrinkage as the main defects to beavoided in IM, a list of related key factors is: filling time,injection pressure, mold temperature, melt temperature,packing pressure and time, cooling time and coolanttemperature. In some cases, other factors areinvestigated, as fill/post fill switchover control and packingprofile in [12], and holding pressure with variable or two-stage profiles [15]. According to the wide scientific

literature, the most influential factors on warpage are:packing pressure [4], melt temperature [2, 12], packingpressure and mold temperature [3], melting temperatureand packing pressure [6].

Once determined which predominant factors affect theprocess, their variability range must be investigated.Upper and lower limits can be calculated from theoreticalor empirical equations, directly found in material datasheets or carried out with trial runs.

System factors must be related to measurableresponses: in IM common significant responses arewarpage, shrinkage, sink marks and dimensional orgeometric features.

2.2 First step: DOE screening of factors

The factors screening is based on experimentaldesign, to evaluate main effects and interactions withoutaffecting the final regression model [16].

The phases of this first step are:- determination of the design space;- realization of simulation experiments;- selection of screened factors.The number of factors and the number of their levels

determine the design space, i.e. a geometricalrepresentation of the number of simulation runs.

Testing all combinations of factors levels, as in a fullfactorial design, requires high computational resourcesbecause the number of runs can be very high when many

factors need to be considered. Many authors [9, 10, 12]suggest the use of fractional factorial design, which usesonly a fraction of the runs required by a full factorialdesign, limiting the experimental runs. In [13] a fractionaltwo-levels factorial is suggest as a good design choice forthe initial stage of the analysis. However, fractionalfactorial design is generally characterized by lowresolution, i.e. the capability to separate only main effectsand low-order interactions, so, at this stage, main effectsand interactions may be aliased with others. In order toget a univocal data interpretation in interaction analysis,the maximum resolution should be used [17].

Anderson and Whitcomb propose [18] the use of aspecific and more efficient design with a minimal number

of runs but high resolution, referred to as Min Res V.Inthis way, no main effects or two factor interactions arealiased with any other main effect or two-factorinteraction, but the number of runs is highly reduced: a

great number of effects can be so easily evaluated by thisscreening design, in order to choose only the significantones. The first step of the proposed method is based onthis minimal factorial design with high resolution.

For conducting the experiments scheduled by DOE,simulations of IM process are set up. All the factorsassume their selected levels according to the DOE matrix.

The results of fractional factorial experiments aregenerally analyzed by evaluating the main effects andmutual interactions for all factors as calculated in [19].

However, the analysis of the screening results can bemore easily and efficiently conducted by graphical toolsdeveloped by statistical software, as in [6, 9, 10, 12, 16].In this way, the magnitude of main effects and interactionscan be plotted: two useful approaches are the Paretocharts and the Normal plots, that are selected for themethod. The Pareto chart plots the effects of the absolutevalue of the standardized effects in decreasing order anddraws a reference line on the chart. Any effect extendingover this reference line is significant. The Normal plotgives the same results of Pareto chart: the line in the plot

indicates where the points would be expected or would fallif there were no effects. Significant effects are larger andfarther from the line than non-significant effects.

This step of the method delivers a list of significantfactors as data input for the second step of DOSEmethod.

2.3 Second step: RSM identification of systemresponses

Response Surface Methodology (RSM) is based onexperimental design to sample the system responses byvarying the parameters in their variability ranges.

The system responses are described by regressionmodels as function of the input variables to obtain 3D

graphical representations, i.e. Response Surfaces (RSs).The general purpose of a DOE study is to determine

which level of a selected factor can lead to bestperformance: by a Taguchi approach, as in [2-4, 10, 12,14], it is possible to determine which of the testedcombinations of factors levels produces the best results.In other studies [1, 5, 6, 8], an approach based on RSMallows to develop a regression model, i.e. predictivemodel of the system behavior.

The purpose of this second step is to determine theoptimal values in all the factors domains and not onlyamong the tested combinations in experimental plan: inthis way, RSM is selected for the method to generate apredictive model that can be queried by an optimization

tool in the next phase.The second step of the proposed methodology consists

of the following phases:- determination of the design space,- realization of simulation experiments,- creation of regression model.The design space is determined on the number of

significant factors and their levels. The significant factorsare varied within their variability ranges, while the non-significant are set at the levels that reduce variations ofresponses according to the results of the previous DOEphase.

An experimental plan explores the space of theindependent variables, i.e. the significant factors. Aregression model can be developed through differentexperimental matrix: in [4] and in [7] a Taguchi design anda full factorial are respectively used, but these do notrepresent the most efficient choices. One of the mostfitted and relevant experimental design for a RSM


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application is Central Composite Design (CCD) that isvery efficient in reducing the number of runs, as claimedin [17], with respect to a full factorial 3-levels design. Thesimulation experiments are so conducted according to theCCD experimental matrix in order to sample the designspace.

Based on numerical simulation results, the responses

are expressed as functions of input factors andpolynomial models for the available data set:

(1)

where0, i, ijare tuning coefficients, nis the number ofmodel factors and is an error term.

The number of runs is strictly related to the order of theregression model and to the number of unknowncoefficients. From this point of view, CCD is a veryefficient tool in RSM to calculate the empirical relationshipfor the RS without loss of accuracy [20].

2.4 Optimization of responses and validation

test

Optimization of IM involves multiple factors andmultiple responses. The goal is to determine acombination of levels for every factor through a multi-objective optimization. Each level has to satisfy therequirements (i.e. optimization criteria) for the responses[20].

A constrained non-linear approach is selected andused to solve a numerical multi-objective optimization. Atypical non-linear constrained optimization problem isfinding a vector x that is a local minimum to a scalarfunction f(x)subject to constraints on the allowablex[21]:

(2)subject to:

where f(x):RnR is the objective function, ci(x) areconstraint functions, E is the set of equality constraintsand I the set of inequality constraints. To solve theproblem, an algorithm based on Sequential QuadraticProgramming (SQP) is used.

After obtaining a combination of optimal values forevery process factors, a validation test can be conductedusing optimized values for the factors to check the validityof the predictive model.

3 Case study

The developed method is applied to the IM processsimulation of the cover of a thin shell housing for abiomedical electronic device, aimed to the radiolocationand tracking of patients in a hospital.

The goal of the study is to determine the set ofparameters which leads to the best part moldability withthe lowest global warpage. Two particular geometricfeatures are investigated on the blue upper cover shownin Fig. 2: the lower edge, where the cover is coupled withthe transparent base, and the top hole, where the blackcylindrical antenna is fitted to the cover.

The interference fitting for the antenna assembly

demands for a circularity of the top hole conform to classH of the standard ISO 2768. The same limit is given forthe planarity of the lower edge surface required for matingwith the corresponding surface in the lower shell part of

the housing. The cover is made of polyphenylsulfone(PPSU), a high performance amorphous thermoplastic.The commercial name is Radel R5000, by Solvay, and itis used in applications for surgical tools and instruments,hospital goods and dental applications because of itsresistance to autoclave sterilization. A second market forPPSU is electronics and automotive applications because

of its resistance at high temperature and for its gooddielectric properties.

Fig. 2 Radiolocation and tracking device.

3.1 Product and mold geometry

The dimensions of the housing, shown in Fig. 3, are45mmx37mmx16mm and the wall thickness range from2mm to 0,5mm.

The mold is provided with a cold runner system,consisting of a runner and a submarine gate. The runneris conic, with maximum diameter of 7,1mm, minimumdiameter of 4,5mm, and length of 50mm. The tunnel of the

submarine gate is pointed tapered, with a circular gate of1,2mm diameter. The mold has one cavity and heatingrods.

3.2 Simulation model

The part is modeled with a three-dimensional solidelements representation. A Finite Elements model of thehousing is created by meshing the geometry into 264.000tetrahedron elements [8]. The choice of solid tetrahedronmesh helps in precision and reliability of the analysis. Thecommercial CAE simulation software Moldex3D, byCoreTech System, is used to simulate the IM process.


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Fig. 3 Geometry of shell housing and runner system.

3.3 DOSE method results

The following section presents the results of theapplication of the DOSE method on the optimization ofthe blue housing cover.

3.3.1 Input clarification

The preliminary phase is the identification of inputcontrol factors, variability ranges and responses of thesystem.

According to the scientific literature (see subsection2.1), several factors affect the geometric shape of moldedparts. The present work investigates the following controlfactors: melt temperature, mold temperature, injectiontime, injection pressure, packing time and pressure andfilling to packing (F/P) switchover point.

For each factor, a variability range is determined onthe basis of technological data and of previousexperiences in the same field: melt and mold temperatureare set by commercial data sheet of PPSU, injection time,packing time and F/P switchover point by techniciansexperience, injection and packing pressure by trial runs,as in Tab. 1.

Factor Variability range Units

Melt Temperature 340-400 C

Mold Temperature 138-163 C

Injection time 0,3-0,9 s

Max. injection pressure 90-150 MPa

Packing time 2-9 sPacking pressure 90-150 MPa

F/P switch point 92-98 %

Tab. 1 Factors and their variability range.

The system responses are the global warpage of the

part and two geometrical features: the planarity of thelower edge surface of the shell housing and the circularityof the antenna hole. The values of those responses aremeasured as the displacements of measurement nodesfrom nominal positions. As in Fig. 4, 27 measurementnodes are set on the lower edge surface and 24measurement nodes are set on the antenna hole edge.

Fig. 4 Measurement nodes on the housing mesh model

The global warpage is evaluated by the average totaldisplacement of all mesh nodes from their nominalpositions; the planarity of the lower edge surface isdetermined by the average z-displacement of themeasurement nodes; the circularity of the upper hole isdetermined by a circularity index based on radiusvariation, i.e. the absolute difference between the nominalradius value and the average radius of measurementnodes of each run.

3.3.2 First step: DOE screening of factors

The first-step is the screening of process factors basedon DOE. 7 factors with 2 levels are chosen. The factorsand their relative levels are shown in Tab. 2.

FactorLower

level (-1)

Upper

level (+1)Units

Melt Temperature 360 380 C

Mold Temperature 140 160 C

Injection time 0,5 0,7 s

Max. injection pressure 105 135 MPaPacking time 4 7 s

Packing pressure 105 135 MPa

F/P switch point 94 97 %

Tab. 2 Levels for experimental design.

The selection of levels values is determined inside thevariability range for each factor.

To plan and conduct experimental design, acommercial software for DOE (Design Expert, by Stat-

Ease) is used. For screening design, a minimal fractionalfactorial design with resolution V is selected, with 2-levelsfor each factor: it represents a good alternative to thestandard two-level factorial designs [22]. In this way only30 runs are needed instead of 128 runs as in a fullfactorial design.

For carrying out the runs, a standard PC (Intel Core2Duo CPU E8400 @ 3.00GHz, 2.0GB RAM, NVIDIAGeForce 8800 GT) is used to demonstrate theapplicability of the method: the run time is around twohours, so the screening phase takes two and a half days.

The simulation experiments are executed as describedin Appendix 1 and their responses are reported in Tab. 3.

Run Globalwarpage(mm)

Zdisplacement(mm)

Deltaradius(mm)

1 0,057 0,031 0,067


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2 0,065 0,037 0,072

3 0,066 0,036 0,076

4 0,059 0,033 0,067

5 0,043 0,024 0,048

6 0,034 0,019 0,039

7 0,040 0,021 0,049

8 0,040 0,023 0,0469 0,060 0,035 0,066

10 0,040 0,021 0,049

11 0,033 0,017 0,040

12 0,034 0,019 0,039

13 0,060 0,034 0,065

14 0,059 0,034 0,066

15 0,065 0,036 0,076

16 0,066 0,037 0,075

17 0,041 0,023 0,047

18 0,042 0,022 0,050

19 0,042 0,024 0,047

20 0,068 0,039 0,075

21 0,059 0,034 0,066

22 0,034 0,018 0,041

23 0,036 0,021 0,041

24 0,035 0,019 0,041

25 0,060 0,033 0,069

26 0,067 0,039 0,074

27 0,065 0,036 0,076

28 0,035 0,019 0,041

29 0,060 0,035 0,066

30 0,039 0,020 0,048

Tab. 3 Results of fractional factorial design for DOEscreening on system factors.

To evaluate main and interactions effects a Paretochart and a Normal plot are created. They both representmain effects and interactions.

Pareto charts are shown in Fig. 5-a, 5-b and 5-c. Themain effects and interactions are plotted in decreasingorder of the absolute value of the effects. Any effect thatextends over the orange reference line on the chart isconsidered as significant.

Normal plots give the same result of the Pareto chart,as in Fig. 6-a, b and c. The significant effects deviate fromthe reference line more than the non significant effects.

The significance of factors is determined as follow: themost significant factors determine important variation inthe system responses. The screening output is the

following selected number of significant parameters: melttemperature (B), mold temperature (C), packing time (E)and packing pressure (F).

The other factors, as described in subsection 2.1,which have lower influence on the system responses, areset to the level that reduces the variation of responsesaccording to the results of the previous DOE and aremaintained constant in the following experiments.


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Fig. 5 Pareto charts of main effects and interactions on a)

global warpage, b) planarity, c) circularity (only the first ten

significant main effects or interactions are represented).

Fig. 6 Normal plots of main effects and interactions on a)

global warpage, b) planarity, c) circularity.

3.3.3 Second step: RSM identification of systemresponses

The second step is the determination of systemresponses by RSM. Design experiments are thenimplemented considering only the significant factors foundby the screening DOE, i.e. melt temperature, moldtemperature, packing time and packing pressure.

A CCD design is used for the development of aregression model. The factorial portion of CCD is a fullfactorial design with all combinations of the factors at twolevels (coded levels +1 and -1): those levels are fixed atthe same values of the previous screening design. Anumber of 8 star points and a central point (coded level 0)

are added. The star points correspond to an -value equalto 2. The simulation experiments are executed accordingto Appendix 2 and their responses are shown in Tab. 4.

RunGlobal

warpage(mm)

Zdisplacement

(mm)

Deltaradius(mm)

1 0,057 0,031 0,067

2 0,064 0,035 0,074

3 0,059 0,033 0,067

4 0,066 0,036 0,076

5 0,058 0,033 0,065

6 0,065 0,037 0,072

7 0,060 0,034 0,065

8 0,067 0,039 0,074

9 0,033 0,017 0,040

10 0,039 0,020 0,048

11 0,035 0,019 0,041

12 0,041 0,022 0,049

13 0,034 0,022 0,049

14 0,040 0,023 0,046

15 0,036 0,020 0,040

16 0,042 0,024 0,047

17 0,043 0,024 0,049

18 0,056 0,031 0,064

19 0,047 0,026 0,055

20 0,051 0,029 0,058

21 0,052 0,027 0,059

22 0,050 0,029 0,055

23 0,076 0,043 0,08524 0,027 0,014 0,032

25 0,049 0,028 0,057

Tab. 4 Result according to CCD with =2.

A regression model is formulated on the CCD outputdata. A second order polynomial regression model forboth warpage and geometrical features is developed. Asecond order polynomial is suitable for detecting thepresence of important interactions between factors.

By Design Expert, the regression models aregenerated. The analysis of the correlation coefficients R

2

and R2

adj, defined as in [17], shows excellent fitting of thedeveloped regression models, due to their values that are

all above 0,97. After determining the coefficients of Eq. 1by least square error fitting, the final statistical model toestimate the responses are given, in terms of actualvalues:


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Global warpage:

(3)

Z displacement for planarity:

(4)

Delta radius for hole circularity:

(5)

3.3.4 Optimization of responses and validationtest

The optimization of responses and validation test arethen performed. The regression model is interfaced withan effective multi-objective optimization to find theoptimum process parameter values. The optimization

problem is solved by a constrained non-linear approachas in Eq. 2 with Matlab:

(6)

subject to constraints:

where qis the optimization variable and its lower (lb) andupper (ub) boundaries are respectively lb=[340, 138, 2,90] and ub=[400, 163, 9, 150]. The constraints Creflectthe geometric tolerance values for the planarity and thecircularity.

The optimal values for the minimization of the globalwarpage (Y1), lower edge surface planarity (Y2) and holecircularity (Y3) are represented by the combination offactors values shown in Tab. 5:

MeltT.

(C)

MoldT.

(C)

Packt.

(s)

Packp.

(MPa)

Y1(mm)

Y2(mm)

Y3(mm)

values 350 138 3,17 150 0,019 0,010 0,028

Tab. 5 Optimized values of factors and relative responses.

Graphical representations of optimized data areplotted. Only few of the RSs show significant effects offactors interactions on systems responses. Two samples

are shown in Fig. 7-a and Fig. 7-b. The interactionsbetween B and C for the optimized values of A and D aresignificant. The relative 2D contour plots are visible in thex-y plane of the 3D graphs.


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Fig. 7-a Surface plot of interaction between factors B and C,

for fixed values of A and D, in global warpage analysis.

Fig. 7-b Surface plot of interaction between factors B and C,

for fixed values of A and D, in delta radius analysis.

The graphical analysis of all 3D RSs leads to thefollowing considerations:

- there are no stationary points in the domains of thefactors;

- the optimal values that minimize the responses lie onthe boundary of factors domains for factors A, B and D;

- there are not significant second order interactionsbetween factors A, B and D: all the RSs have noimportant curvatures but have quite planar trends;

- C is the only factor that shows interactions with theother factors, especially with B.

In order to validate the developed regression model,an additional simulation is performed by setting thefactors to the predicted optimal values of Tab. 5, as avalidation test. If the results of this validation test presenta low relative error with the predictive values (Tab. 5), thedeveloped regression model is suitable for describing theprocess behavior. Tab. 6 reports the results of thisadditional simulation based on the optimized combinationof factors values.

MeltT.

(C)

MoldT.

(C)

Packt.

(s)

Packp.

(MPa)

Y1(mm)

Y2(mm)

Y3(mm)

values 350 138 3,17 150 0,022 0,010 0,027

Tab. 6 Optimized values of factors and relative responses.

The results in Tab. 6 show good agreement with thosepresented in Tab. 5 and then an acceptable relative error.

4 Conclusion and discussion

The optimization of factors values in the field of IM isnon univocally solved by researchers and industrialengineers, because many approaches have beendeveloped, but some lacks are still identified.

Starting from the analysis of the wide state-of-the-art

and scientific literature, methods and tools are selected,integrated and proposed in the present paper as asuitable trade-off between ease of use, speed and resultsaccuracy.

A two-step experimental method is so developed toquickly determine the optimal process parameters toimprove the quality of molded parts by integrating CAEsimulation and experimental design methods.

In the first step, significant factors are identified by aneffective factorial design. In the second step, the factorsare used to implement a CCD experimental plan in theRSM. Predictive models for system responses aredeveloped as regression models and an optimal set ofprocess parameters is identified by multi-objectiveoptimization. A final simulation is run to confirm theresults.

The proposed method leads to an easy-to-useapproach, because of the procedural approach thatguides the user and helps him by the use of well-knowntechniques and graphical tools analysis. As aconsequence, there is a reduction of uncertainties infactors selection and in experimental plan iteration, alsodue to the screening phase of this two-step method. Theevaluation of the results leads to the followingconsiderations:

- CAE simulations of IM process cannot substitutephysical experiments but, especially in first stages ofproduct development design, they can help in predictingthe product performances and the process requirements

with a less expensive and more efficient approach;- the use of simulation experiments enhances the

analysis of the molding process by showing the influenceof factors on the responses; for example the analysis ofthe packing phase leads to understand in which momentthe introduction of further molten polymer is unnecessary,due to the frozen gate, saving energy and reducing thecycle time;

- the test of the all factors that affect IM process is veryexpensive and time consuming, so in many studies theyare chosen arbitrarily as data input for experimentaldesign. Conversely, in the proposed method, a greatnumber of effects can be easily evaluated by efficient wellstructured screening design, in order to choose only the

significant ones;- the application of DOE method is supported bystatistical software. However, the fractional factorial andthe CCD matrices are easy-to-use and widely available;

- the use of RSM and multi-objective optimizationallows to determine the optimal values in all the factorsdomains and not only among the tested combinations inexperimental plan;

- warpage and geometrical features cannot be directlycontrolled because they are typically driven by physicalphenomena difficult to model. The difficulty in predictingthe system responses as function of input factors isovercome by the use of a quadratic regression model.

The evaluation of the DOSE results leads to thefollowing observations:

- the regression model developed by least square errorfitting shows a good behavior in predicting the systemresponses, as checked by the correlation coefficients andshown by the validation test. Moreover a further


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regression model was developed by Gaussian method tocheck the adequacy of the first model, and it shows highconvergence in results;

- the developed RSs present global minima outside theinvestigated design space. This behavior is not related tothe model adopted for RSs, as confirmed by thecomparison with Gaussian regression model;

- the housing cover has been produced in a limitedpre-series using different values of process factors: theuse of the DOSE optimized factors leads to betterperformances in terms of warpage reduction, fittingdimensional and geometrical requirements and goodrespect of functional requirements.

The most important factor involved in geometrydeformation of the thin shell housing is packing pressure,whose higher values reduce warpage and distortions. Theoptimization method leads to individuate an optimal valuefor packing time, that is internal to the factor variabilityrange.

Future work deals with the validation of the developedmethodology through a wide physical experimental

campaign, currently ongoing. The limits introduced by thedeterministic nature of numerical simulations will be finallyevaluated by the comparison between simulation andphysical IM process behavior.

Appendix

Appendix 1. Fractional factorial design for screening 7factors, with 2 levels each, based on Min Res V [22]:

Run A B C D E F G

1 -1 -1 -1 1 -1 -1 1

2 -1 1 -1 -1 1 -1 -1

3 -1 1 1 1 -1 -1 1

4 -1 -1 1 -1 -1 -1 15 1 1 1 1 1 1 1

6 -1 -1 -1 -1 1 1 -1

7 1 1 -1 -1 -1 1 -1

8 -1 1 -1 1 1 1 -1

9 1 -1 1 -1 1 -1 -1

10 1 1 -1 1 -1 1 1

11 -1 -1 -1 1 -1 1 -1

12 -1 -1 -1 1 1 1 1

13 -1 -1 1 1 1 -1 -1

14 1 -1 -1 1 1 -1 -1

15 1 1 -1 1 -1 -1 -1

16 -1 1 1 -1 -1 -1 -1

17 1 1 -1 -1 1 1 1

18 1 1 1 -1 -1 1 1

19 -1 1 1 -1 1 1 -1

20 1 1 1 1 1 -1 -1

21 1 -1 -1 -1 1 -1 1

22 1 -1 -1 -1 -1 1 1

23 1 -1 1 1 1 1 -1

24 -1 -1 1 -1 -1 1 -1

25 1 -1 1 1 -1 -1 -1

26 -1 1 1 -1 1 -1 1

27 1 1 -1 -1 -1 -1 1

28 -1 -1 1 1 -1 1 1

29 1 -1 1 1 1 -1 130 -1 1 -1 -1 -1 1 1

Appendix 2. Central Composite Design with =2 for 4factors:

Run A B C D

1 -1 -1 -1 -1

2 1 -1 -1 -1

3 -1 1 -1 -14 1 1 -1 -1

5 -1 -1 1 -1

6 1 -1 1 -1

7 -1 1 1 -1

8 1 1 1 -1

9 -1 -1 -1 1

10 1 -1 -1 1

11 -1 1 -1 1

12 1 1 -1 1

13 -1 -1 1 1

14 1 -1 1 1

15 -1 1 1 1

16 1 1 1 117 -2 0 0 0

18 2 0 0 0

19 0 -2 0 0

20 0 2 0 0

21 0 0 -2 0

22 0 0 2 0

23 0 0 0 -2

24 0 0 0 2

25 0 0 0 0

Acknowledgement

The authors acknowledge GRAF SpA (Modena, Italy)for the economical sustain, Cattini SRL, Dr. A. Vaccariand Dr. M. Ansaloni for their technical contribution. Animportant thanks go to the Interdepartmental Centre forApplied Research and Services in the Field of AdvancedMechanics and Engine Design - INTERMECH-MO.RE.,supported by the European funds POR FESR 2007-2013for the Emilia-Romagna region.

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