![Design
factors
Unit Notation
LEVELS
-1 0 1
Electrolyte
concentration
[%] X1 15 20 25
Voltage [V] X2 8 10 12
Feed rate [mm/min] X3 0.1 0.2 0.3
Inter-
electrode gap
[mm] X4 0.2 0.25 0.3
Table 1. Experimental parameters and their levels](https://image.slidesharecdn.com/newmicrosoftpowerpointpresentation2-221226200425-e721f308/85/New-Microsoft-PowerPoint-Presentation-2-pptx-6-320.jpg)
New Microsoft PowerPoint Presentation (2).pptx
- 3. Determination of Plane Temperature Distribution in solid using ANSYS workbench insulated insulated Convective boundary Convective boundary Heat flux 30OC Linear Quadrilateral Element Serendipity Quadratic Quadrilateral Element Given: - All dimensions are in mm Material Selected :- Steel Assume other necessary data. Convection = 40 W/m2 .O C heat flux = 30 W/m2 A B C D E F Domain is A B C D E F A-B Convective boundary B-C incoming Heat flux boundary C-D Convective boundary D-E insulated boundary E-F constant temperature boundary F-A insulated boundary Description Of Problem
- 4. INTRODUCTION
- 5. EXPERIMENTAL SETUP • Experiments are conducted on METATECH (ECMAC) electrochemical machining equipment. • KCl solution is chosen as electrolyte, as it has no passivation effect on the surface of the work piece. • Rectangular block of 20 mm X 20 mm and 25 mm height made of EN 31 tool steel which is a high carbon alloy steel with high degree of hardness, compressive strength and abrasion resistance is chosen as workpiece. • In this study, the collection of experimental data adopts the face center cubic (FCC) design with three levels of each of the four design factors. The process parameters selected for present investigation are electrolyte concentration (X1), voltage (X2), feed rate (X3) and inter-electrode gap (X4). • The design is generated using MINITAB 16.0 statistical package. Table 1 shows the factors and their levels in coded and actual values. • Surface roughness parameter is selected as response variables in the present study. Roughness measurement is done using a stylus-type profilometer, Talysurf (Taylor Hobson, Surtronic 3 + ). Roughness measurements in the transverse direction on the work pieces are repeated five times and average of five measurements of surface roughness parameter values are recorded.
- 6. Design factors Unit Notation LEVELS -1 0 1 Electrolyte concentration [%] X1 15 20 25 Voltage [V] X2 8 10 12 Feed rate [mm/min] X3 0.1 0.2 0.3 Inter- electrode gap [mm] X4 0.2 0.25 0.3 Table 1. Experimental parameters and their levels
- 7. ARTIFICIAL NEURAL NETWORK • Artificial neural networks (ANN) emulating the biological connections between neurons are known as soft computing techniques. ANN can reproduce some functions of human behavior, which are formed by a finite number of layers with different computing elements called neurons. In order to construct a network, the neurons are interconnected. The organization of connections determines the type and objectives of the ANNs. • The processing ability of the network is stored in the inter-unit connection strengths, or weights, which are turned in the learning process. The training algorithm (or learning) is defined as a procedure that consists of adjusting the weights and biases of a network that minimize selected function of error between the actual and desired outputs. • In this study, the back-propagation learning algorithms likely Levenberg Marquardt (LM), gradient descent with variable learning rate and momentum (GDX) and scaled conjugate gradient (SCG) are used to train the networks. • Four process parameters viz. electrolyte concentration, voltage, feed rate and inter-electrode gap are considered. The input layers of the neural network consist of four neurons whereas the output layer has a single neuron that represents the predicted value of Ra . • Some parameters (i.e. the number of training and testing data, learning rate, number of hidden layers and processing function used) affect the accuracy, reliability and effectiveness of the neural network. It is seen that the processing functions, tansig and logsig, produce almost the same performance in different problems. Hence, only the tansig processing function and single hidden layer are used. • A trial and error scheme is used to determine the appropriate number of hidden neurons and numbers of hidden neurons are varied from 3 to 8. The goal of any training algorithm is to minimize the global error such as mean squared error (MSE), mean absolute percentage error (MAPE) and correlation coefficient (R).
- 8. RESULTS AND DISCUSSION • Artificial neural network models for predicting surface roughness have been developed using multi-layer feed forward back propagation algorithm. • To construct, four process parameters viz., electrolyte concentration, voltage, feed rate and inter-electrode gap as the input neurons and corresponding surface roughness as the output neuron. • Considering the FCC design, 31 experiments (datasets) are conducted and Ra values are recorded. For brevity of the paper, the table presenting the experimental results is omitted. The data sets are randomly chosen for training and testing to get rid of any bias. 22 datasets for training and 9 datasets for testing are used. The data points are normalized so that the dataset ranges in -1 to +1. • To construct the models, the hyperbolic tangent sigmoid function in the hidden layer and linear activation function in the output layer is considered. One hidden layer is chosen in the study. The neurons in the hidden layers are varied from 3 to 8 to find out the best neural network model for different training algorithms. To train the network, three different training algorithm viz. Levenberg-Marquardt (L-M) algorithm, gradient descent with variable learning rate and momentum (GDX) algorithm and scaled conjugate gradient (SCG) algorithm are used. • MATLAB 7.8 is used to develop the neural network, train and test the network. In this study, to select the best network, minimum mean squared error (MSE), mean absolute percentage error (MAPE) and maximum correlation coefficient (R) are considered.
- 9. Algorithm Model Training data Testing data MSE MAPE R MSE MAPE R L-M 4-3-1 0.00009157 0.353 0.99956 0.0749445 8.876 0.98458 4-4-1 0.00000205 0.046 0.9999 0.0445753 8.293 0.99038 4-5-1 0.00000043 0.024 1 0.0077101 3.746 0.99831 4-6-1 0.00000420 0.056 0.99998 0.03965559 7.799 0.99107 4-7-1 0.00000382 0.050 0.99997 0.07006014 10.390 0.98382 4-8-1 0.00204939 1.868 0.99996 0.02525059 7.302 0.98012 GDX 4-3-1 0.00048059 0.775 0.99854 0.038141 6.947 0.99106 4-4-1 0.00006021 0.158 0.9997 0.062704 8.209 0.98684 4-5-1 0.00000097 0.032 0.99999 0.011502 4.630 0.99727 4-6-1 0.00000158 0.048 0.99998 0.034425 7.514 0.99265 4-7-1 0.00000125 0.034 0.99991 0.027325 6.925 0.99457 4-8-1 0.00165456 0.990 0.9999 0.052778 7.794 0.99018 SCG 4-3-1 0.00094376 0.893 0.99509 0.09769107 8.527 0.98209 4-4-1 0.00000798 0.107 0.99995 0.051756 7.157 0.98901 4-5-1 0.00000113 0.037 0.99999 0.016579 4.492 0.99662 Comparison of network performances based on different training algorithms
- 10. Comparative study of experimental Ra and ANN predicted Ra data (a) for training set and (b) for testing set
- 11. • Performance of different networks trained and tested with LM, GDX and SCG algorithms are presented in Table 2. From the table, it is seen that architecture 4-5-1 trained using L-M algorithm has the minimum MSE and the architecture is selected as the best performing network. • The architecture also provides the maximum correlation coefficient (R) and minimum MAPE. Again, when networks are trained using GDX algorithm, the architecture 4-5-1 gives the minimum MSE and is selected as the best network. Again, architecture 4-5-1 provides the minimum MSE when the network is trained with SCG algorithm. • It is also seen from the comparative study of the performances among the best networks that the architecture 4-5- 1 trained with L-M algorithm is the best network based on the minimum MSE, minimum MAPE and maximum correlation coefficient (R). • It is also seen that the architecture has the minimum MAPE (0.024%) for training dataset. It implies that the experimental values and ANN predicted values lie very close to each other. • It is observed from the regression analysis that correlation coefficient (R) is 1 for training pattern. Correlation coefficient 1 means the perfect correlation between the experimental and the predicted results. Comparative study of the experimental Ra and ANN predicted Ra is presented in Fig. 1(a) and it is seen that ANN predicted and experimental Ra are close to each other. • Also the network is tested with a separate testing dataset and the comparison of experimental results and predicted results is presented in Fig. 1(b). The correlation coefficient (R) is 0.998381 and it is a good correlation between the predicted and experimental outputs. • From the results, it is obvious that the network gives a good prediction of Ra in ECM of EN 31 tool steel and the network has the generalization capability
- 12. CONCLUSIONS • Neural network model for predicting surface roughness (Ra) in ECM of EN 31 tool steel work-piece is developed using multi-layer feed forward back propagation algorithm. • Electrolyte concentration, voltage, feed rate and inter-electrode gap are considered as the process parameters. The design of experiment is done using FCC with 31 experimental run. • From the experimental results it is seen that the architecture 4-5-1 trained with L-M algorithm gives the best performance as compare to GDX and SCG algorithms for predicting Ra in ECM. • The developed neural network model can predict surface roughness with about 96% accuracy. The network also has a good generalization capability. • Finally, it can be concluded that the developed ANN model is suitable for predicting Ra with high accuracy.
- 13. REFERENCES 1. H. Hocheng, Y.H. Sun, S.C. Lin, P.S. Kao, A material removal analysis of electrochemical machining using flat- end cathode, J. Mater. Process. Technol. 140 (2003) 264-268. 2. P. Asoken, R.R. Kumar, R. Jeypaul, M. Santhi, Development of multi objective optimization models for electrochemical machining process, Int. J. Adv. Manuf. Technol. 39 (2008) 55-63 3. H. H Abuzeid, A.M. Awad, A.H. Senbel, Prediction of electrochemical machining process parameters using artificial neural networks, Int. J. Comp. Sci. Eng. 4 (2012) 125-132. 4. D. Chakradhar, A.G. Venu, Multi-objective optimization of electrochemical machining of EN31 steels by grey relational analysis, Int. Journal of Modeling and Optimization, 1 (2011) 113-117. 5. C. Senthilkumar, G. Ganesan, R. Karthikeyan, Study of electrochemical machining characteristics of Al/SiCp composites, Int. J. Adv. Manuf. Technol. 43 (2009) 256-263. 6. M. Burgera, L. Koll, E.A. Wernera, A. Platz, Electrochemical machining characteristics and resulting surface quality of the nickel-base singlecrystalline material LEK94, J. Manuf. Processes 14 (2012) 62-70. 7. R. Goswami, V. Chaturvedi, R. Chouhan, Optimization of electrochemical machining process parameters using Taguchi approach, Int. J. Eng. Sci. Technol. 5 (2013) 999-1006.