Integrating Taguchi principle with neural network to minimize ingate velocity for aluminium alloys.1. INTRODUCTION
Computers are beginning to have some capability of optimizing a filling system design. In most cases, it helps in decision making, where industrial expertise is not sufficient. However, simulation software Simulation software is based on the process of imitating a real phenomenon with a set of mathematical formulas. It is, essentially, a program that allows the user to observe an operation through simulation without actually running the program. is often inefficient, especially in case where a large number of parameters needs to be examined. The resulting large number of simulation runs coupled with lengthy execution times per run (on the order of hours or even days) may render such investigations totally impractical.
The runner system design, named a vortex-gate, has been explored for aluminium gravity casting to control flow of the liquid metal below the critical velocity. In a study of a vortex gate concept to find important dimension of the vortex runner system and minimize the outlet velocity, the integrating Taguchi principle with neural networks system has been developed.
2. BACKGROUND AND CURRENT STATUS
Recent work by Campbell (2003, 2004) has demonstrated the effect of liquid metal flow and the surface turbulence on the reliability of aluminium castings. It has been found to be important to minimize the surface turbulence during filling a mould to attain reliable mechanical properties of the castings. Extremely high velocities at which the liquid metal enters the mould is damaging to metal. The theoretical background of critical velocity concept by Campbell has been confirmed experimentally for liquid aluminium by Runyoro at al. For nearly all liquid metals this critical velocity is close to 0.5[ms.sub.-1], involving aluminium alloys (Campbell, 2003).
The idea to use a novel runner system, named a "vortex gate", for uphill gravity pouring was introduced by Campbell (2003). The vortex gate was investigated by Hsu at al. A computational fluid dynamics Computational fluid dynamics
The numerical approximation to the solution of mathematical models of fluid flow and heat transfer. Computational fluid dynamics is one of the tools (in addition to experimental and theoretical methods) available to solve and real-time X radiography radiography: see X ray. were used for these studies. The main role of the real-time radiography was to verify the results of computational modelling. In this work, simulations show flow to dampen the circular motion In physics, circular motion is rotation along a circle: a circular path or a circular orbit. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. quickly, implying that the internal losses in the flow as a result of turbulence are an overestimation o·ver·es·ti·mate
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.
2. To esteem too greatly. in contrast with the video radiography. The results presented that the vortex gate has the potential to reduce the velocities to get quiet filling of melt into moulds. There are no rules to calculate and optimize the vortex gate dimensions in references.
Recently, research on runner and gating systems has included a growing number of papers on optimization algorithms, the focus being to generate routines to assist the designer in the work of mould and part design. Prasad Prasāda (Sanskrit: प्रसाद), prasād/prashad (Hindi), Prasāda in (Kannada), prasādam (Tamil), or prasadam at al. developed the artificial neural network (artificial intelligence) artificial neural network - (ANN, commonly just "neural network" or "neural net") A network of many very simple processors ("units" or "neurons"), each possibly having a (small amount of) local memory. system to generate the process parameters for the pressure die casting die casting
Forming metal objects by injecting molten metal under pressure into dies or molds. An early and important use of the technique was in the Linotype machine (1884), but the mass-production automobile assembly line gave die casting its real impetus. process. With this network, the selection of the process parameters can be carried out by any inexperienced user without prior knowledge of the die casting process.
In the work by Karunakar & Datta, an attempt was made to predict major casting defects like cracks, misruns, scabs, blowholes and air-locks by using back-propagation neural networks from the data collected from a foundry. The neural network neural network or neural computing, computer architecture modeled upon the human brain's interconnected system of neurons. Neural networks imitate the brain's ability to sort out patterns and learn from trial and error, discerning and extracting was trained with parameters like green compression strength, green shear strength For the shear strength of soil, see .
Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear. , permeability, moisture percent and melting conditions as inputs and the presence/absence of defects as outputs. After the training was over, the set of inputs of the casting that is going to be made was fed to the network and the network could predict whether the casting would be sound or defective. Thus the neural network makes a forecast about the nature of the casting just before the pouring stage.
The abductive neural network analysis method is used by Lee & Lin for simulation and optimization of runner system parameters for multi-cavity moulds. It has been shown that prediction accuracy in an abductive network is much higher than that in a traditional network. Abductive neural analysis based on the abductive modelling technique is able to represent complex and uncertain relationships between injection analysis results and runner and gating systems design.
Sulaiman & Gethin used a network for metal flow analysis in the pressure die casting process to predict the metal flow characteristics in the filling system by simplifying the complex Navier-Stokes equation Navier-Stokes equation
A partial differential equation which describes the conservation of linear momentum for a linearly viscous (newtonian), incompressible fluid flow. In vector form, this relation is written as Eq. .
All abovementioned a·bove·men·tioned
The one or ones mentioned previously. works have indicated that the methodology of artificial neural networks can be used to replace the trial-and-error technique.
3. DESIGN OF EXPERIMENTS FOR GRAVITY CASTING SIMULATION RUNS
Design of experiments (DoE) procedure was used to systematically organize experiment runs to improve processes.
It involves a fraction of the possible parameter combinations for a given experiment, which results in conducting a minimum number of experiments without losing significant information. This combination fraction is chosen according to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. rules and statistic matrices called Taguchi's orthogonal arrays. The DoE procedure is divided into three stages: experiment design, experiment running and statistical analysis.
DoE methodology was applied to the vortex gate optimization. Experiment design involves the choice of design parameters and parameter levels, as well as the choice of the appropriate orthogonal array according to desired resolution. The parameter ranges of the design variables are given in Table 1. The chosen orthogonal array defines the number of casting simulation runs to conduct and the parameter level values, which are carried out in the second stage of DoE. Simulations for the present work were conducted using Flow3D software. For the experiment, [L.sub.9] orthogonal array with four columns and nine rows was used. The experimental layout for four gating system factors using [L.sub.9] orthogonal array is shown in Table 2. During the third stage, analysis of variance (ANOVA anova
see analysis of variance.
ANOVA Analysis of variance, see there ) determines which parameters are statistically important along with their influence in the process. Preliminary simulation runs proved that the most significant factor that affecting the value of velocity in the outlet of the vortex runner are:
* outlet diameter
* inlet velocity
4. PREDICTIVE NEURAL NETWORK MODEL
An artificial neural network's (ANN) main characteristics are architecture, which defines the way that neurons are connected to each other, and training algorithm, which determines the way that weight factors are corrected.
In the proposed ANN architecture, neurons are arranged in layers. The first layer is the input layer and its neurons are the same in number as the input parameters (ingate diameter, outlet diameter, outlet length, inlet velocity), while the last layer has as many neurons as the output parameters (outlet velocity). In the ANN model the training algorithm of back-propagation was used. Table 2 illustrates the runner and gating system parameters used for flow simulations. The outlet velocities from the simulations were used as the output parameters to train proposed back-propagation neural network in Figure 2.
Pre-processing of input signals prior to input to the neural network is carried out as follows to improve convergence. All input and output data are scaled so that they are confined to a subinterval of (0.1 ... 0.9). Each input or output parameter X is normalized as [X.sub.n] before being applied to the neural network, according to the following equation
[X.sub.n] = [0.8 ((X - [X.sub.min])/([X.sub.max] - [X.sub.mn]))]+ 0.1 (1)
where [X.sub.max] and [X.sub.min] are the maximum and minimum values of the data parameter X.
[FIGURE 2 OMITTED]
Other network architectures were also tried with different training algorithms and different numbers of hidden layers and hidden neurons.
From realized experimental tests on the proposed vortex runner system and back-propagation neural network the following conclusions can by drawn:
* based on the modelling of the neural network, the relationships between the vortex gate parameters and outlet velocity of the melt can be obtained
* neural network models can replace casting simulation software to design the vortex gate dimensions
* the predictions by the network within the input range agree closely with the values obtained from the simulations
* the accuracy of the tested networks can be different but within the acceptable limit.
The authors wish to acknowledge the support of the grant agency of the Ministry of Education of the Slovak Republic under the contract DAAD 0300/2008
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FEM Finite Element Method
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Tab. 1. Gating system parameters and their levels Ingate Outlet diameter diameter Level/Factor [mm] [mm] 1 90 20 2 105 27.5 3 120 35 Outlet Inlet length velocity Level/Factor [mm] [[ms.sup.-1]] 1 90 1.5 2 110 2 3 125 3 Tab. 2. Experiment plan using [L.sub.9] orthogonal array Experiment number/ Parameter Ingate Outlet level diameter diameter 1 1 1 2 1 2 3 1 3 4 2 1 5 2 2 6 2 3 7 3 1 8 3 2 9 3 3 Experiment number/ Parameter Outlet Inlet level length velocity 1 1 1 2 2 2 3 3 3 4 2 3 5 3 1 6 1 2 7 3 2 8 1 3 9 2 1