Ductile irons (DIs) have properties such as high strength, ductility, and toughness, as well as a low degree of melting, good fluidity, and good machining. Having these characteristics make them the most preferred among cast irons. The combination of excellent properties, especially in DI castings with a thin section, make it an alternative for steel casting and forging. But in the manufacture of thin-section parts, fluidity characteristics need to be improved and the liquid metal must fill the mold completely. The fluidity of liquid metal is influenced by many factors depending on the casting processes such as material and mold properties, casting temperature, inoculation, globalization, and grain refinement. In this study, an artificial neural network (ANN) model has been developed that allows for determining the flow distance of the liquid metal in the sand mold casting method under changing casting conditions of DI. Thus, the flow distance was estimated depending on the cross-sectional thickness during the sand casting under changing casting conditions. The experimental parameters were determined as casting temperature, liquid metal metallurgy quality, cross-sectional thickness, and filling time. Filling modeling was performed with FlowCast software. When the results were examined, it was seen that the developed ANN model has high success in predicting the flow distances of the liquid metal under different casting conditions. The calculated coefficient of determination (R 2) value of 0.986 confirms the high prediction performance of the model.
Although there are many alternative materials, more than 90% of the metallic materials used today are iron alloys, which are divided into two groups steel and cast iron according to the carbon (C) content in the alloys . Cast irons are iron-based alloys with a carbon content high enough to exceed their solubility in iron . In comparison with steel, cast irons are known to be economical materials with relatively low melting temperatures, good fluidity, and castability . The material obtained as a result of inoculation and adding small amounts of spheroidizing additives such as Mg and Ce to the molten iron before the casting process is called ductile iron (DI). It consists of sphere-shaped graphite dispersed in a matrix resembling steel. This situation has brought a different dimension to the engineering applications of cast irons . The most commonly used spheroidizing element is Fe–Si–Mg alloys, which are used in an alloyed form with Fe and Si . DI has a very wide range of applications in the automotive industry, such as engines, suspension components, wind turbines, wheel, bearing, gear manufacturing, pistons, and machine tool bearings [5–7]. It has properties of high strength, low melting point, ductility, toughness, and good machinability. These features are the main reason why it is the most preferred among cast irons [8,9]. DI casting, especially due to its high strength-to-density ratio, can be lighter, have better mechanical properties, and be more economical compared to aluminum alloys in the production of thin-section materials [10,11]. In addition, it is a very suitable alloy group as an alternative material for steel casting and forging in thin-section applications [12,13].
The production processes of parts by casting involve two important steps, the first is the filling of the melt into a mold, and the second stage is the process of solidification and cooling . In a study conducted on the mold filling process, it was noted that the liquid metal affects the heat transfer and solidification properties, which in turn affects the fluidity of the liquid metal . In addition, it was explained that the fluidity of the liquid metal during mold filling is affected by the thermal properties of the liquid metal and mold, pouring conditions, reinforcing properties, and solidification mechanisms . Fluidity, in casting terminology, is the distance at which a metal will move through the mold without solidifying when casting at a certain temperature, in other words, the molten metal completely fills the inside of the mold cavity. Metals that are not sufficiently fluid can cause insufficient casting, especially in thinner sections of the casting mold [17,18]. Therefore, it is an important property for obtaining sound castings with thin sections. In addition, it is influenced by many factors, such as viscosity, oxide film, chemical composition, melting point, latent heat, melting surface tension, solidification mode, super heating, the mold surface heat transfer coefficient, specific gravity, mold conductivity, and mold temperature [19,20]. The castability of the metal is a parameter that is determined as the distance for the metal flow in the channel of the sand mold before the flow stops with the progressive solidification process . Fluidity in sand molds depends not only on chemical composition but also on casting temperature, flow rate, section thickness, and metallurgical factors.
In a study on the investigation of DI fluidity, it was determined that the difference in mold material causes different flow distances of the liquid metal at different section thicknesses . In a similar study, casting temperature was found to be important in the casting of thin section parts. It was also observed that the temperature drop and the increased cooling rate affected the mold filling . In another study, it was reported that the flow distance and the range of solidification temperature were inversely proportional . In a study of DI casting with different section thicknesses, it was observed that the flow distance of Fe–C–2Si cast iron was higher than that of Fe–C–2Al cast iron, regardless of the section thickness . In a study investigating the effect of alloy addition on fluidity, casting experiments were carried out at different temperatures by adding various amounts of Cr and Ni to AISI 1040 steel. In the related study, it was determined that the most important factor in fluidity was temperature, and the addition of Cr and Ni increased the fluidity of the steel . In a study examining the effect of Ni and Si contents on the fluidity of Al–Ni–Si alloys, it is understood that the fluidity of Al–Ni–Si alloys can be increased when the Si content is less than 3% by weight and the Ni content varies between 2 and 6% by weight . There are various studies in the literature on the fluidity and flow distance of the liquid metal of DI and different alloys. However, there is no artificial neural network (ANN) model that evaluates the parameters of metallurgical quality, cross-sectional thickness, casting temperature, and filling time in DI together. For this reason, an ANN model has been developed in the study that estimates the flow distance of the liquid metal by considering the four related parameters.
ANNs are an artificial intelligence technology developed and inspired by the working mechanism of nerve cells in the human brain. The main purposes of use can be expressed as classification, clustering, curve fitting, forecasting, image processing, and the ability to create solutions to nonlinear problems. In addition, it has many advantages, such as the ability to work with incomplete information, have fault tolerance, process unclear information, and has distributed memory. When the literature is examined, it is seen that ANNs are used in many different fields for purposes such as prediction, diagnosis, classification, clustering, and error detection. Studies related to the field of production show that ANN is used to predict experimental results, analyze the effects of process parameters, and predict mechanical properties in manufacturing, such as casting and welding processes [28–32]. When the studies conducted in the field of production planning are examined, it is seen that the ANN is used to solve the production redistribution problem, the batch sizing problem, and the labor scheduling problem [33–35]. In addition, there are many studies in which ANN is also used in the field of finance and medicine [36–42]. On the other hand, there have been no studies in which fluidity has been examined with ANNs in the process of DI casting into sand molds. With this study, it will be possible to use ANN in new application areas by adding research in a specific casting process to the research studies in the ANN literature. In addition, the examination of fluidity using ANN will make a significant contribution to the casting process literature.
2 Materials and methods
2.1 Filling modeling
In terms of study, filling modeling was performed in the sand mold casting method under changing casting conditions of DI material. Thus, the feed distance of the liquid metal was determined depending on the cross-sectional thickness during the castings made into the sand mold under changing casting conditions. Experiment parameters have been identified as casting temperature range between 1,350 and 1,500°C, the metallurgical quality of liquid metal has a value range of 10–90%, cross-sectional thickness between 1 and 5 mm, and filling time between 3 and 9 s (Table 1).
|Level no.||Cross-sectional thickness (mm)||Casting temperature (°C)||Metallurgical quality (%)||Filling time (s)|
In determining the experimental parameters and in the sand casting method, the parameters have been selected related to the fluidity properties of the alloy which have the most impact on the manufacturing process. Model geometry, a design adapted to the fluidity test model with a width of 20 mm and a length of 500 mm was carried out. In cases where the length of the liquid metal channel has changed, it has been deliberately kept long, so the liquid metal cannot fully progress, thus it is aimed to measure the flow distance of the liquid metal. In addition, it was aimed to determine which thickness castings can be made with the model criterion after the relevant simulation studies by selecting the cross-sectional thickness of 1–5 mm. Figure 1 shows the test bar measurements and the solid model image used in fluidity modeling.
Modeling of casting processes is a necessary mathematical method that the computer can quickly and accurately predict what is happening in the mold in the duration of filling the mold and after filling it. These programs usually calculate using finite difference or finite element techniques. They have the ability to model the given casting geometry with the thermo-physical properties and boundary conditions of the materials that can also be entered by the users and contained in their own databases for different casting and mold materials. The casting geometry of the model was first created as a solid model in the SolidWorks program. Then, it was converted to STL format and transferred to the casting simulation program. In SolidCast casting simulation software, the type and thermo-physical properties of the casting alloy and mold material are defined in Table 2 according to the specified values.
|Material||Thermal conductivity (W/m K)||Specific heat (J/kg K)||Freezing range (°C)||Density (kg/m3)||Latent heat of fusion (J/kg)|
|Casting material||Perlitic DI||25.944||460.24||44.63||7176.06||230115.6|
The material properties of the solid model geometry are transferred to the program by granulating. It is ensured that the specified boundary conditions are solved in the simulation program for each element. The filling modeling studies were carried out with the FlowCast program running depending on the SolidCast casting simulation software. According to FlowCast fluid dynamics criteria, it also calculates factors such as turbulence, incomplete filling, cold joining, and pressure when filling liquid metal into the mold cavity. Figure 2 shows the sample images obtained as a result of FlowCast casting filling modeling.
The approach in a similar study was used to determine the flow distances of the liquid metal from the casting modeling results . In this context, side images were uploaded to the program and the channel length was defined as 500 mm. Subsequently, flow distances were determined.
A total of 108 experiments were carried out depending on the experimental parameters and levels. An example section of the experiment results is given in Table 3.
|Experiment no.||Cross-sectional thickness (mm)||Casting temperature (°C)||Metallurgical quality (%)||Filling time (s)||Experiment results|
2.2 Development of the ANN model
At this stage, an ANN model has been developed to predict flow distances of the liquid metal in sand mold casting processes of DI with high accuracy.
2.2.1 Determination of input and output variables
The parameters of metallurgical quality, cross-sectional thickness, casting temperature, and filling time were determined as input variables. The output variable is the flow distance of the liquid metal. The general structure of the network is shown in Figure 3.
2.2.2 Determining the type of network
Although there are many types of ANNs, it can be said that multilayer perceptron, LVQ network, ART networks, SOM networks, and Elman network are widely used. Multilayer perceptrons are also known as feed-forward back propagation network structures. This network structure has a fairly wide range of uses due to its ability to generate solutions to nonlinear problems and make generalizations . For this reason, multilayer perceptrons have been preferred as the network type.
2.2.3 Determination of the training and test set
While developing ANN models, a data set related to the problem area is needed. This data set is divided into training and test set. A large number of samples in the training and test set will allow training and testing of the network with different samples, thus this will have a positive effect on the performance of the network. As for the problem area, examples may contain a number of non-numeric data. In this case, these data must be digitized. So ANNs work with numeric data . Another aspect in determining the training and test set concerns the size of the training and test set. Usually, 70–80% of the total data is used in training and 20–30% is used in the testing process. This issue was also taken into account while determining the training and test set, and 86 of the total 108 experimental data were used to train the network, also 22 were used to measure the performance of the network. The data in the training and test set are subjected to normalization before being delivered to the network. The applied normalization formula is as follows:
|Data no.||Cross-sectional thickness (mm)||Casting temperature (°C)||Metallurgical quality (%)||Filling time (s)||Experiment results|
|Data no.||Cross-sectional thickness (mm)||Casting temperature (°C)||Metallurgical quality (%)||Filling time (s)||Experiment results|
2.2.4 Selection of the training algorithm and the transfer function
Although there are many different training algorithms used in the ANN, the Levenberg–Marquardt training algorithm was used because it is faster and more reliable than other training algorithms . As a transfer function, the Log-Sigmoid function formula is used as given below:
2.2.5 Determination of the number of neurons in the hidden layer
Regarding the ANN, there is no clear approach that expresses what kind of network topology should be created in which situations. In multilayer perceptrons, the number of neurons in the input and output layers can be determined according to the type of problem, but the number of neurons in the hidden layer cannot be determined clearly. For this reason, the performances of multilayer perceptron models with different neuron numbers in the hidden layer have been studied. As a result of these studies, the number of neurons in the hidden layer of the model with the least error value is determined as the most appropriate neuron number of the hidden layer .
2.2.6 Measuring the performance of the network
The performance of a developed ANN model is measured by the correct estimation rate of the samples in the test set. In some cases, the network can predict the data in the training set with a very high accuracy rate, but this prediction rate may remain very low in the test set. In this case, it is concluded that the network memorizes instead of learning. In order to avoid such situations and to achieve high prediction accuracy, the network is tested with a test set consisting of samples that are not included in the training set. The high performance of the network depends on the minimum difference between the estimated values produced for the samples in the test set and the output values in the test set. At this stage, the performance measurement of the ANN models will be performed with Mean Absolute Percentage Error (MAPE) and R 2:
3 Results and discussion
The Matlab software was used in the development of ANN models. In order to determine the ANN model with the best prediction performance, ANN models with different hidden layer neuron numbers were created. Each ANN model was subjected to a training and testing process. The prediction performances of these models are shown in Figure 4.
As Figure 4 is examined, it is seen that the prediction performance of these models changes as the number of neurons in the hidden layer of ANN models changes. Prediction performances vary approximately between 81 and 95%, and the highest prediction performance was achieved when the number of neurons in the hidden layer was six. Thus, the ANN model that gives the best prediction performance was determined, and the prediction performance of this model was determined as 95.12%. Then, regression analysis was performed for this model. The result of the analysis is included in Figure 5.
As a result of the analysis, the regression equation and the coefficient of determination (R 2) were obtained. The coefficient of determination calculated expresses the harmony of the actual flow distance of the liquid metal and the estimated flow distance of the liquid metal produced by the ANN model. The closer the obtained value is to one, the better the fit. Here, the R 2 value is calculated as 0.986. This obtained value emphasizes that the developed ANN model makes quite successful predictions as it was shown in some other previous works [46–54].
In this study, it is aimed to estimate the flow distance of the liquid metal in the sand casting process of DI depending on the parameters of cross-sectional thickness, casting temperature, metallurgical quality, and filling time. In this context, ANN models with different numbers of neurons in the hidden layer have been developed. The data obtained from 108 experiments were used in the training and testing processes of these models. Then, the prediction performances of the models were examined in terms of the MAPE error measure and it was determined that the ANN model with six neurons in its hidden layer had the best prediction performance. In addition, regression analysis was performed for this model. Thus, the regression equation and R 2 were obtained. The R 2 value calculated for this ANN model also confirms the high prediction consistency of the relevant model (R 2 = 0.986).
Funding information: This research received no external funding.
Conflict of interest: The author declares no conflict of interest.
Data availability statement: Not applicable.
Ethical approval: The conducted research is not related to either human or animal use.
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