Scientia Iranica B (2019) 26(6), 3304{3312

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringhttp://scientiairanica.sharif.edu

Prediction of critical fraction of solid in low-pressuredie casting of aluminum alloys using arti�cial neuralnetwork

C� . Tekea,1;�, M. C�olakb, A. Kirazc, and M. _Ipekc

a. Institute of Natural Sciences, Sakarya University, 54187, Sakarya, Turkey.b. Department of Mechanical Engineering, Bayburt University, 69000, Bayburt, Turkey.c. Department of Industrial Engineering, Sakarya University, 54187, Sakarya, Turkey.

Received 17 April 2018; received in revised form 22 May 2018; accepted 7 January 2019

KEYWORDSCritical fraction ofsolid;Arti�cial neuralnetwork;Low pressure diecasting;Casting simulation.

Abstract. Casting simulation programs are computer programs that digitally modelthe casting of an alloy in the sand, shell, or permanent mold and, then, the cooling andsolidi�cation processes. However, obtaining consistent results out of casting modelingdepends on the incorporation of many accurate parameters and boundary conditions.Critical Fraction of Solid (CFS), which is one of the most important of these parameters, isde�ned as the point where solid dendrites do not allow any ow of the liquid metal in themushy zone. Since the CFS value varies based on many factors, inconsistent results canbe experienced in the modeling applications. In this study, the CFS value obtained duringthe solidi�cation of various commercial aluminum alloys' casting process, carried out usinglow-pressure die casting method, is predicted by using Arti�cial Neural Network (ANN)method based on alloy type, grain re�ner and modi�er additions, initial mold temperature,and pressure level parameters. In the scope of the study, 162 experiments are conducted.The results obtained from the low-pressure die casting experiments using a special modeldesigned for the study are validated by using SOLIDCast casting simulation. The CFSvalues are obtained in this validation range of 33% to 61%. These CFS values are used inthe development of ANN models. Mean Absolute Error (MAE), Mean Absolute PercentageError (MAPE), and Mean Square Error (MSE) are used to assess the prediction accuracyof the ANN models. Calculated values of MAE, MAPE, and MSE are 0.0188, 7.06%, and0.0006, respectively. The results show that the proposed ANN model predicts a CFS valuewith high accuracy.© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

One of the most important issues in the casting processis that liquid metal and its alloys �ll the mold cavity

1. Present address: Department of Industrial Engineering,Bayburt University, 69000, Bayburt, Turkey.

*. Corresponding author.E-mail address: cagatayteke@bayburt.edu.tr (C� . Teke)

doi: 10.24200/sci.2019.50819.1881

properly, and casting without any void is obtainedduring solidi�cation. The success in this issue is di-rectly related to the runner and the riser in the castingprocess. The design of the casting parts integrated withthe runners and the risers is de�ned as the moldingdesign. The production of quality casting parts byusing the minimum metal is aimed at the moldingdesign, especially in today's market competitive condi-tions [1,2]. The advancement in computer technologyhas enabled the use of casting simulation software formolding design in the casting industry. It is possible

C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312 3305

to produce strong casting in one attempt by designingand modeling using casting simulation programs in thecomputer environment. However, the actual boundaryconditions of casting in the foundry environment needto be provided accurately in the computer programto obtain a successful result. The computer programcarries out calculations based on boundary conditions,and the material properties are de�ned by the user.Therefore, it is not possible to obtain correct resultsby providing wrong data [1-5]. Some of the boundaryconditions that are e�ective in the casting simulationprogram and need to be added correctly include thesolidi�cation rate, the temperature gradient, the in-terfacial heat transfer coe�cient for the casting-moldinterface, the thermal properties of the mold material,the casting temperature, the alloy shrinkage rate, themold �lling time of the liquid metal, and the CriticalFraction of Solid (CFS) value for continuing feedingin the mushy zone. The CFS value is one of theimportant factors for feeding during the solidi�cationof the castings [3-6].

The solidi�cation of the aluminum alloys occurs ina solidi�cation temperature range between the liquidustemperature and the solidus temperature, in which theliquid and solid phases coexist [7]. The viscosity ofthe liquid alloy increases due to the dendritic branchesgrowing along with the progress of the solidi�cation,and the liquid ow becomes di�cult in this semi-solidregion; however, the feeding still goes on. With theprogress of the solidi�cation, dendritic networks areestablished and dendrites become stronger by holdingtogether [8]. The resistance to uid ow from theinterfaces between the dendrites begins to form. Withfurther solidi�cation, the feed stops and no more liquid ow is allowed when the solid ratio of the semi-solidregion reaches the level that will resist the liquid ow.The point at which no more uid ow is allowedby the growing dendrites along with the progress ofsolidi�cation is de�ned as CFS. Figure 1 shows theCFS on the cooling curve of an exemplary alloy. The

shrinkage of the piece can be provided by the riseruntil it reaches the CFS value. In this case, there willbe no shrinkage on the part as the feed path will beopen. However, the feed path is clogged below the CFSvalue, and since the ow of liquid is interrupted, unfedregions are seen in the casting part, even though thereis enough liquid metal to feed the part in the riser.Thus, the product has to be discarded. Therefore, thedetermination of the CFS value in the critical sectionsfor each piece is very important for the e�ective use ofcasting simulation programs and for the production offaultless parts [6,9].

The CFS value is not a constant value, whichvaries only based on the alloy. The change in theCFS value is a�ected by the cooling and solidi�cationconditions of the alloy. Since the size of the dendrites tobe formed during solidi�cation will be shorter, the CFSvalues are expected to increase for the alloys with anarrower solidi�cation temperature range. This meansthat it is possible to feed the part without being subjectto a longer dendritic blockage. Similarly, since there isenough time for the formation and growth of dendritesin the alloys in a wider solidi�cation temperature range,the liquid ow will be di�cult at the lower soliditylevels and the feed will stop [9].

There are a limited number of studies on theCFS, which is important for the casting process. Theresults of a study on determining the CFS values by athermocouple method for A319 and A356 alloys havebeen found to be consistent with the values determinedby other thermal methods [10]. However, some studiesreport that the thermal analysis method has beena�ected by the solubility rate of the elements in thealloy, thus showing inconsistent results [11]. In anotherstudy, the issue of modeling the CFS in the die castingof the aluminum alloys has been studied using modelingtechniques experimentally by a specially developedpermanent mold. Initial mold temperature and grainre�ner addition have been taken into account in model-ing the CFS [12]. In a similar study, the e�ect of grain

Figure 1. (a) CFS point on the cooling curve of a given alloy. (b) Stopping the feed of the metal reaching the CFSvalue [9].

3306 C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312

re�ner addition on CFS value has been experimentallyinvestigated in sand casting [8].

The Arti�cial Neural Network (ANN) is an arti-�cial intelligence technology developed by the inspira-tion of the ways neurons operate in the human brain. Itis generally used for prediction, classi�cation, and pat-tern recognition. The main characteristics of ANN aremodeling of non-linear problems, fast data processing,and the ability to manage the unreliable or imprecisedata [13]. These characteristics make it possible to useANN in many �elds such as manufacturing, produc-tion planning, �nance, and medicine. Studies aboutmanufacturing �eld show that ANN has been used forpredicting experimental results, analyzing the e�ects ofprocess parameters, and predicting mechanical prop-erties in manufacturing such as casting and weldingprocesses [14-18]. Considering the studies carried outin the �eld of production planning, it is seen that ANNhas been used to solve the production back allocationproblem, lot-sizing problem, and workforce schedulingproblem [19-21]. Considering the studies done in the�eld of medicine, it is seen that ANN has been usedfor the purposes such as disease diagnosis, predictionof bone loss rate, and sti�ness estimation [22-26]. Someexamples of the objectives of using the ANN in the �eldof �nance are bankruptcy prediction, credit scoring,resource allocation, portfolio selection, in ation fore-casting, and revenue management [27-30].

The aim of this study is to predict the CFS valuein low-pressure die casting of aluminum alloys. Forthis purpose, ANN is used because e�ects of di�erentvalues of the experiment parameters can be analyzede�ciently. Moreover, this study is the �rst researchattempt to predict the CFS value in low-pressure diecasting of aluminum alloys by the ANN method.

2. Materials and methods

2.1. MaterialThe determination of aluminum alloys for the ex-periments is based on chemical composition. Thedi�erences in chemical composition directly a�ect so-lidi�cation. For this reason, attempts have been

made to make su�cient and proper alloy selection inorder to gather information about all aluminum castingalloys commonly used in the casting industry. Thus,this study aims to obtain results that will representnot only alloys used in the experiments but also allaluminum casting alloys. Alloys selected for use in theexperiments are given in Table 1.

2.2. Experimental studyThe low-pressure die casting experiments was carriedout using a model with a specially designed geome-try. The model was designed to have a measurableshrinkage void in the casting part of the inner sectionduring solidi�cation. Therefore, there should be across-section to form a bottleneck on the model. Withthe early solidi�cation of this section, the feed pathof the casting part was clogged and shrinkage voidsformed at the internal parts due to inadequate feed.The CFS value can be quantitatively examined con-sidering the proportion of these shrinkage voids. Thedesigned geometry was used to have a geometry to formdistinctive porosity under di�erent casting conditions(pressure, initial mold temperature, etc.), di�erentalloys, and the di�erent CFS values. The suitabilityof the design was veri�ed using SOLIDCast castingsimulation software during the stage of model design.For this purpose, modeling studies were carried outunder di�erent casting conditions and with di�erentCFS values by using the cast alloys planned to beused in the experiments. The formation of porosityin various sizes was expected to be in accordance withthe results, and the conformity of the design was testedaccordingly. Figure 2 shows the model geometry usedin the experiments, measurements, and the module val-ues obtained from the SOLIDCast casting simulationprogram.

Considering the current market conditions, theparameters with the greatest e�ect on the CFS andthe formation of the porosity were taken into accountfor determining the parameters of the low-pressuredie casting experiment. Three di�erent temperatureand pressure values were determined based on the sizeof the part to examine the e�ect of the initial moldtemperature and pressure. Al5Ti1B master alloy was

Table 1. Chemical composition of the alloys used in the experiments (Al balance), wt.% [31].

Alloy Fe Si Cu Mn Mg Zn Ti Sn

A319 0.70 4.00-6.00 2.00-4.00 0.20- 0.60 0.15 0.20 0.20 0.05

A413 0.60 11.50-13.50 0.10 0.40 0.10 0.10 0.15 0.05

A380 1.00 7.50-9.00 3.00-4.00 0.50 0.30 1.00 0.20 0.10

A360 0.50 9.00-10.00 0.10 0.40-0.60 0.30-0.45 0.10 0.15 0.05

A356 0.20 6.60-7.40 0.02 0.03 0.30-0.45 0.04 0.08-0.14 0.05

AlCu4Si 0.30 0.35 4.00-5.00 0.10 0.10 0.10 0.05 0.05

C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312 3307

Figure 2. The �nal model design and geometry used in the casting experiments.

Table 2. The experiment parameters.

ParametersLevels

I II III IV V VI

Alloy type A319 A413 A380 A360 A356 AlCu4Si

Grain re�ner addition No addition TiB | | | |

Modi�er addition No addition Sr | | | |

Initial mold temperature (�C) 200 300 400 | | |

Pressure level (mbar) 250 500 1000 | | |

used as a grain re�ner to have an e�ect of 0.2% Ti.Al10Sr master alloy was used as a modi�er to have ane�ect of 0.1% Sr. The experimental parameters aregiven in Table 2.

The produced mold was connected to a hydraulicopening-closing press. This system was used to �ll themold with the liquid metal under the speci�ed pressureand to open the molds after solidi�cation. The surfacesof the molds were cleaned with dry ice before castingand painted with the wash. The ceramic runner wasadded to the low-pressure die casting mold runner box,and the liquid metal was heated to prevent solidi�ca-tion in the runner before casting. After slagging anddegassing by nitrogen, the liquid metal prepared inaccordance with the experiment parameters were takenfrom the furnace and poured into the sprue by means ofa hand casting ladle using primary ingot for each alloy.With the applied pressure, the liquid metal in the sprue�lled the mold and, thus, the casting was carried out.Upon the solidi�cation after applying pressure for 5minutes, the mold opened and the samples were takenusing ejector pins. The low-pressure die casting methodis schematically shown in Figure 3.

In the experimental study, 162 experiments wereconducted. Results obtained from these experimentsare used in the development of the ANN models. Asmall experimental set is given in Table 3.

2.3. Arti�cial neural network modelsIn this study, ANN models were constructed to predictCFS value in low-pressure die casting of aluminum

Figure 3. Schematic of low pressure die castingmethod [32].

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Table 3. A small experimental set.

Datano.

Alloytype

Grainre�ner

addition

Modi�eraddition

Initial moldtemperature

(�C)

Pressurelevel

(mbar)

CFS(%)

1 A319 0 0 200 250 392 A319 0 0 200 500 3928 A413 0 0 200 250 3429 A413 0 0 200 500 3666 A380 0 0 300 1000 4067 A380 1 0 300 250 5387 A360 1 0 200 1000 5495 A360 1 0 300 500 54117 A356 1 1 200 1000 57118 A356 0 0 300 250 35� � � � � � � � � � � � � � � � � � � � �161 AlCu4Si 1 1 400 500 57162 AlCu4Si 1 1 400 1000 59

Figure 4. The basic architecture of the developed ANN models.

alloys. The feed forward back propagation algorithmis preferred because it is often used as an approxima-tor [33]. The developed ANN models consist of threelayers. These are input layer, hidden layer, and outputlayer. The alloy type, grain re�ner addition, modi�eraddition, initial mold temperature, and pressure levelparameters a�ecting CFS value in low-pressure diecasting were de�ned as input variables in the ANNmodels. The CFS value was de�ned as the outputvariable in the ANN models. There is no precise andspeci�c rule in determining the number of neurons inhidden layer. It is usually determined by applying atrial-and-error method. The small number of neuronsin hidden layer may cause the ANN to be too inade-quate to solve the problem. On the other hand, thehigh number of neurons in hidden layer may causeover�tting and a decrease in network generalizationcapacity. Thus, the optimal number of neurons in

hidden layer is determined by comparing the predictiveperformance of ANN models with di�erent neuronnumbers in hidden layer [34]. The basic architectureof the developed ANN models is shown in Figure 4.

In ANN models, all data processed in the networkmust be numerical [22]. Therefore, alloy type, grainre�ner addition, and modi�er addition parameters areconverted to numerical values. For example, if thegrain re�ner addition is available, value 1 is assigned;otherwise, value 0 is assigned. The data used in theANN model are either normalized or used with real val-ues. It is known that normalizing the data a�ects thelearning performance of ANN models positively [33].The following equation is used for data normalization:

X =(Xi �Xmin)

(Xmax �Xmin); (1)

where X is the normalized data, Xi is the actual data,

C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312 3309

Table 4. A small normalized experimental set.

Datano.

Alloytype

Grainre�ner

addition

Modi�eraddition

Initial moldtemperature

(�C)

Pressurelevel

(mbar)

CFS(%)

1 0 0 0 0 0 0.2142862 0 0 0 0 0.333333 0.21428628 0.2 0 0 0 0 0.03571429 0.2 0 0 0 0.333333 0.10714366 0.4 0 0 0.5 1 0.2500067 0.4 1 0 0.5 0 0.71428687 0.6 1 0 0 1 0.7500095 0.6 1 0 0.5 0.333333 0.75000117 0.8 1 1 0 1 0.857143118 0.8 0 0 0.5 0 0.071429� � � � � � � � � � � � � � � � � � � � �161 1 1 1 1 0.333333 0.857143162 1 1 1 1 1 0.928571

Xmin is the minimum value of actual data, and Xmaxis the maximum value of actual data. The data arenormalized between 0 and 1. Some of the normalizeddata are given in Table 4.

In the developed ANN models, the Levenberg-Marquardt training algorithm is used. Furthermore,Gradient Descent with Momentum (GDM) was used asa learning algorithm. The logsig (log-sigmoid) functionwas used as a transfer function. Logsig function is givenby:

a = logsig(n) =1

1 + e�n : (2)

3. Results and discussion

Simulations based on the developed ANN modelswere conducted through the MATLABr 7.10 (R2010a)mathematical software. Then, 162 experimental datawere used as dataset to feed the ANN model. Thenumber of neurons in hidden layer of the network wasdetermined as 10 for the test and analysis. The test andanalysis were carried out in two stages to determinethe optimal topology of the network. In the �rststage, 3 di�erent training and test sets were randomlygenerated using the existing data set (70% training set�30% test set, 80% training set �20% test set, 90%training set �10% test set). The network was trainedseparately with these 3 datasets. While the networkwas being trained, learning of the network reachedthe desired level after 300 iterations. Therefore, thenumber of iterations in network training is set to300. After completing the training, the ANN outputswere compared to the actual values obtained from

the experiments. Mean Absolute Error (MAE), MeanAbsolute Percentage Error (MAPE), and Mean SquareError (MSE) as error types were selected to measurethe predictive performance of the ANN. MAE, MAPE,and MSE are de�ned as follows:

MAE =1n

nXt=1

jAt � Ftj ; (3)

MAPE =100%n

nXt=1

����At � FtAt

���� ; (4)

MSE =1n

nXt=1

(At � Ft)2 ; (5)

where At is the actual data, Ft is the forecast at timet, and n is the number of samples.

According to the results in Table 5, it is seen thatwhen the size of the training data set increases, theerror rate of the ANN model decreases. When 90% ofcurrent dataset is used for training, the ANN modelgives the best performance for prediction.

In the second stage, the number of neurons inthe hidden layer that will provide the best prediction

Table 5. MAE, MAPE, and MSE values of the developedANN models.

Ratio of the training set70% 80% 90%

MAE 0.061124 0.044159 0.029762MAPE (%) 14.599454 13.996248 8.545339MSE 0.009970 0.003136 0.001212

3310 C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312

performance is determined when 90% of the currentdataset is used for training. For this reason, ANNmodels with di�erent neurons (3-4-5-6-7-8-9-10-15-20)in the hidden layer were formed. These ANN modelswere trained with a current training set. After com-pleting the training, the outputs of the networks werecompared to test set including the actual values ob-tained from the experiments. MAE, MAPE, and MSEwere selected to measure the predictive performance ofthe networks. Results of the ANN models are shownin Figures 5 to 7.

Results show that the number of neurons in thehidden layer to maximize the prediction performanceis 7. Therefore, the optimal topology of the networkis 5 neurons in the input layer, 7 neurons in the

Figure 5. MAE values of the developed ANN modelsconsisting of di�erent number of neurons in the hiddenlayer.

Figure 6. MAPE values of the developed ANN modelsconsisting of di�erent number of neurons in the hiddenlayer.

Figure 7. MSE values of the developed ANN modelsconsisting of di�erent number of neurons in the hiddenlayer.

Figure 8. Correlation between experimental andpredicted values for the CFS.

hidden layer, and 1 neuron in the output layer. Whenconsidering MAE, MAPE, and MSE, the proposedANN model predicts CFS values with 98.12%, 92.94%,and 99.94% performances, respectively.

Figure 8 shows regression analysis of the ANNmodel consisting of 7 neurons in the hidden layer.Regression equation and correlation coe�cient values(R2) of the proposed ANN model are given in therelated �gure.

Regression analysis clearly shows that the ANNmodel including 7 neurons in the hidden layer andusing training set consisting of 90% of current datasetproduces the most realistic results (R2 = 0:9963).

When comparing this study with similar studiesabout CFS in the literature, a number of di�erencescan be detected among them. Akar et al. con-ducted a study for determining the CFS value ofAl-4.3% Cu alloy in the die-casting process. Theinitial mold temperature and grain re�ner additionparameters were used while determining the CFS value.When initial mold temperature was 155�C and grainre�ner addition was available, CFS value was foundas 52% [12]. Kay�kc� and C�olak carried out a studyfor determining the CFS value of A380 alloy in thesand-casting process. Grain re�ner addition parameterwas taken into account in modeling CFS. CFS valuewas determined as 50% when grain re�ner additionwas available [8]. In this study, the ANN model basedon alloy type, grain re�ner addition, modi�er addition,initial mold temperature, and pressure level parameterswas developed for predicting the CFS value in thelow-pressure die casting process. The CFS value wasobtained as 54% when the alloy type was A380, grainre�ner was used, initial mold temperature was 400�C,and the pressure was 250 mbar. In addition, the CFSvalue was obtained as 57% when the alloy type wasA356, grain re�ner was used, modi�er was used, initialmold temperature was 200�C, and the pressure was500 mbar.

4. Conclusions

In this study, the di�culty of determining the CFS

C� . Teke et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 3304{3312 3311

in low-pressure die casting of aluminum alloys wasdiscussed. The ANN model with the best performancewas investigated by developing multiple predictionmodels to calculate this factor. The data obtainedfrom the experimental study were veri�ed by usingSOLIDCast casting simulation, and the results of thisveri�cation were used in the ANN models. VariousANN models were developed by changing both thetraining set ratio (70%-80%-90%) and the neuronnumbers in the hidden layer (3-4-5-6-7-8-9-10-15-20),and the changes in the performances of these modelswere analyzed. The aim here is to determine theoptimum ANN architecture that provides the bestprediction performance. MAE, MAPE, and MSEde�ned as standard statistical error measures were usedto calculate the performance of ANN. All of the errormeasures calculated showed that the best predictionperformance was obtained from the ANN model witha 90% training set ratio and 7 neurons in the hiddenlayer. Moreover, the correlation coe�cient value (R2 =0:9963) also veri�es this performance.

It will be possible to analyze how the variationof di�erent input parameters a�ects the CFS by usingthe developed ANN model. Therefore, the researchersare able to obtain a CFS value very close to thereal one. The study is expected to be a guide formodeling the parameters required to be predicted inthe experimental studies of various casting methods byusing ANN model.

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Biographies

C�a�gatay Teke was born in Sakarya, Turkey in 1987.He received his BS degree in 2009, his MS degreein 2012, and his PhD degree in 2018 in IndustrialEngineering at Sakarya University. He is currentlyan Assistant Professor at the Industrial EngineeringDepartment at Bayburt University. His research in-terests include arti�cial neural networks, maintenancemanagement, fuzzy logic, and simulation.

Murat C�olak was born in 1981 in Adapazar�. Hecompleted his primary, secondary, and high schooleducations in Sakarya. In 2004, he received his BSdegree from Zonguldak Karaelmas University, KarabukTechnical Education Faculty, Metal Education Depart-ment. In 2006, he started to work as a ResearchAssistant at Sakarya University. In 2009, he re-ceived his MS Degree and PhD degree in 2015 fromSakarya University, Department of Metal Education.His research interests include casting, solidi�cation,modeling, microstructure, material science, and castingsimulation. Since 2015, he has been working as an aca-demician at Bayburt University Faculty of Engineering.

Alper Kiraz was born in 1985. He graduated in2007 from the Department of Industrial Engineering atSakarya University, where he started his undergraduatestudies in 2003. He started his master's degree inIndustrial Engineering at Sakarya University in 2007and started his career as a Research Assistant atSakarya University, Faculty of Engineering, Depart-ment of Industrial Engineering, at the beginning of theyear. His research interests are fuzzy logic, arti�cialneural networks, multi-criteria decision-making meth-ods, quality management, optimization, and virtuallaboratories. He is currently an Assistant Professorat the Industrial Engineering Department at SakaryaUniversity.

M�umtaz _Ipek was born in Sakarya, Turkey in 1969.He obtained his BS degree in 1991 and his MS degreein 1995 in Industrial Engineering at Istanbul TechnicalUniversity. He �nished PhD courses and completedPhD thesis at Sakarya, Turkey in 2007 and receivedthe degree in Industrial Engineering. He started hisacademic position at Sakarya University and now worksas an Assistant Professor at this university.