 Open Access
 Total Downloads : 898
 Authors : R. A. Kapgate, V. H. Tatwawadi
 Paper ID : IJERTV2IS50446
 Volume & Issue : Volume 02, Issue 05 (May 2013)
 Published (First Online): 01062013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Artificial Neural Network Modelling for WireEDM Processing of Aluminium Silicon Carbide Metal Matrix Composite
R. A. Kapgate, V. H. Tatwawadi
Abstract The complex phenomenon of wire electrical discharge machining (WEDM) is reducing its utilization to cut aluminium silicon carbide with 10% weight metal matrix composite (Al/SiC10% MMC) for industrial applications. This paper presents an experimental investigations and development of mathematical models using ANN tool for selection of WEDM process parameters. 432 classical experiments were used to machine Al/SiC10% MMC by WEDM. The selected eleven process parameters were reduced to five important dimensionless term by using dimensional analysis. The VB based ANN tool with 5,4,1 topology and one hidden layer was developed to train , predict and optimize the data.The univeriate analysis was adapted for observing the most influencing process parameters with its influecing length.The univeriate ANN tool also optimized the values of range bound dimensionless terms for maximizing material removal rate (MRR) , better surface finish (Ra) and minimum electric kerf (Ek) to machine Al/SiC10% MMC. The ANN tool results proved that MRR, Ra and Ek values were significantly influenced by changing important ipi2, ipi4 and ipi5 dimensionless terms.These dimensionaless terms were suggested the effective guidelines to the manufacturer for improving productivity by changing any one or all from the available process parameters.
Index Terms Stir casting, Al/SiC10% MMC, Dimensional analysis, Buckinghams theorem, Feed forward back propagation ANN tool ,1h ANN topology, Sigmoidal function, Univariate analysis.
P
P
1 INTRODUCTION
resently aluminium based composites with SiC and Al2O3 particles are attracted for many engineering industrial appli cations because of their high temperature strength, fatigue strength, damping strength, wear resistance and low friction coef ficient[1].However, machining of Al/SiC10% MMCs using con vention tool materials is very difficult due to presence of abrasive reinforcing phase which causes severe tool wear[2],[3],[4]. Re cently wire electrical discharge machining (WEDM) widely used in industries for precise, complex and irregular shapes of diffi cult to machine electrically conductive materials. In this opera tion, the material removal occurs by the ignition of rapid and repetitive spark discharges between the gaps of workpiece and tool electrode connected in an electric circuit. A small wire of diameter 0.05 0.3 mm is continuously supplied from spool to work piece with a maintained gap of 0.0250.05 mm between wire and workpiece [5],[6],[7]. Because of complicated stochastic process mechanism of machining, the selection of process pa rameters for obtaining higher cutting efficiency and accuracy is still not fully solved, even with the most uptodate CNC WEDM machine [8]. Scot et al.[9] found that discharge current ,pulse duration and pulse frequency were main significant control pa rameters for better MRR and surface finish. Trang et[10] al. uti lized a neural network to model the WEDM process to assess the
optimal cutting parameters.
Literature lacks much to say about the use of WEDM for machin ing Al/SiC10% MMC, so the need has been felt towards the high lighting the process with the goal of achieving mathematical models to select the process parameters for maximum utilization of WEDM with improved process performance.
The present work highlights the development of mathematical models for correlating the inter relationships of various WEDM process parameters to optimize MRR, Ra and Ek of Al/SiC10%
R.A. Kapgate, Research scholer, Department of Mechanical Engg, Priyadarshini Col lege of Engineering, Nagpur, India,
Dr.V.H. Tatwawadi, Principal, Dr. Babasaheb Ambedkar college of engineering and Research, Wanadongari, Nagpur, India,
MMC. This work has been established on the artificial neural network (ANN) approach. Mathematical models developed by ANN fitted to the experimental data were contribute towards the selection of the maximum, minimum and optimum process con ditions.
2 EXPERIMENTAL PROCEDURES
Discontinuous reinforced Al/SiC10% MMC made up by stir cast ing route [11],[12] with SiC average particle size 45 Âµm was used for experimentation. Different sets of 432 machining exper iments were performed on SODICK 350W CNC WEDM with MARK 21 controller (Fig.1). The electrode and other machining conditions were selected as follows

Electrode: Brass with 0.25mm in dia.

Specific resistance of dieelectric fluid, cm : 5*104

Workpiece height: 5and 10mm

Die electric temperature, oC : 2530
Pilot experiments were performed to select test envelope and test points of process parameters for experimental design. These pro cess parameters were listed in Table1 and used in experimental design for the investigation of WEDM process parameters during machining of Al/SiC10% MMC. All eleven selected independent process parameters were manipulated on WEDM control panel and accordingly 2mm, 4mm and 6mm length triangular, circular and rectangular shape (Fig.2) were machined. During machining cutting speed (VC,), gap current (I) and gap voltage (V) were measured from control panel. Surface finish (Ra, Âµm) was meas ured by using Surf Test 300 (Mitituyo make) and the width of cut (b) was measured by using tool makers microscope. The MRR was calculated [13] as:
MRR = Vc *b * h m3/s ———————————– (1)
Where, Vc =cutting speed, m/s, b=width of cut, m
h= height of work piece, m
Fig. 1: Experimental Set Up Table 1: Process Parameters
rem was adapted to develop dimensionless terms for reduction of process parameters.
Fig. 2: Machining of Al/ SiC MMC using WEDM
Sr. Machining .No parameters 
Abbre viation 
Selected values 
Unit 

i. Pulse on time 
ON 
0.5,2,4,6 
Âµs 

ii Pulse off time 
OFF 
12,14, 
Âµs 

16,18 

iii. Main power 
IP 
16,17 
A 

supply peak 

current 

iv Servo reference 
SV 
90,100, 
V 

voltage v Servo speed 
SS 
110, 120 6.66*105, 3.33*105, 
m/s 

0.000125, 

0.00025 

vi Wire tension 
WT 
12,18 
N 

vii Wire speed 
WS 
0.083333, 
m/s 

0.116667 

0.15 

viii Dielectric fluid flow 
DQ 
8.33333* 105 
m3/s 

0.0001166 

ix Al/SiC work 
MT 
0.005, 
M 

piece thickness 
0.01 

x Al/SiC work 
ML 
0.002, 
M 

piece length 
0.004,  
0.006 

xi Al/SiC work 
MS 
Angular, 
M 

piece cross 
circular , 

section 
straight 
Sr. Machining .No parameters 
Abbre viation 
Selected values 
Unit 
i. Pulse on time 
ON 
0.5,2,4,6 
Âµs 
ii Pulse off time 
OFF 
12,14, 
Âµs 
16,18 

iii. Main power 
IP 
16,17 
A 
supply peak 

current 

iv Servo reference 
SV 
90,100, 
V 
voltage v Servo speed 
SS 
110, 120 6.66*105, 3.33*105, 
m/s 
0.000125, 

0.00025 

vi Wire tension 
WT 
12,18 
N 
vii Wire speed 
WS 
0.083333, 
m/s 
0.116667 

0.15 

viii Dielectric fluid flow 
DQ 
8.33333* 105 
m3/s 
0.0001166 

ix Al/SiC work 
MT 
0.005, 
M 
piece thickness 
0.01 

x Al/SiC work 
ML 
0.002, 
M 
piece length 
0.004, 

0.006 

xi Al/SiC work 
MS 
Angular, 
M 
piece cross 
circular , 

section 
straight 
Artificial neural network modeling used to better understand how the change in the levels of any one process parameter of a terms changed MRR, Ra and Ek responses. A combination of the levels of dimensionaless terms, which lead to maximum, minimum and optimum response, can also be located through this approach. ANN models of MRR, Ra and Ek were optimized by minimax principle.

FORMULATION OF PI TERMS BY DIMENSIONAL ANALYSIS
As per dimensional analysis [15], material removal rate (MRR) was written in the function form as
f1 = (ON, OFF, IP, SV, SS, WT, WS, DQ, MT, ML, MS. MRR)
= 0 ———————————— (2)
By selecting Mass (M), Length (L), Time () and Current (I) as the basic dimensions, the basic dimensions of the forgoing quan
tities were:
2 3 1 1
ON= , OFF= , IP= I , SV= L M I , SS= L ,
WT= ML 2, WS = L 1, DQ= L3 1, MT= L , ML = L, MS= L, MRR= L3 1, SF=L
According to the Buckinghams – theorem, (n m) number of dimensionless groups [16] are forms. In this case n is 12 and m=4, so we were form dimensionless groups. By choosing ON, IP, WT, and DQ as a repeating variable, eight terms were developed as follows:
3 DESIGN OF EXPERIMENTS
In this study, 432 experiments were designed on the basis of se quential classical experimental design technique [14] that has been generally proposed for engineering applications. The basic classical plan [15] consists of holding all but one of the inde pendent variables constant and changing this one variable over its range
The main objective of the experiments consists of studying the relationship between 11 independent process parameters with the MRR, Ra and Ek dependent responses. Simultaneous changing of all 11 independent parameters was cumbersome and confusing in industrial applications. Hence all 11 independent process parame ters were reduced by dimensional analysis. Buckinghams theo
By substituting the dimensions of each quantity and equating above terms to zero and using dimensional analysis method equation 2 becomes,
——————— (3)
Since 5th, 6th &7 term had same denominator. Hence,
—————————— (4)
———————————– (5)
Where,
=(OFF/ON);
= ((ON2/3 * IP * SV) / (DQ1/3 *WT));
= ((ON2/3 * SS) / (DQ1/3));
=((ON2/3 * WS) / (DQ1/3));
=(( MT* ML * MS) / (ON2/3 *DQ1/3)); ((MRR) / (DQ))
Hence dimensional analysis reduced 12 independent and depend ent variables into only six dimensionless terms.
Similarly, dimensionless terms for surface finish (Ra) and elec tric kerf (Ek) were found by dimensional analysis,
——————————– (6)
And
This is the requirement to make the data flow on neural network. Initialy the values of synaptic weights and thresholds were cho sen randomly between zero and one. The prevailing value (pv) of each percepton was calculated by hyperbolic tan function.
pv (31) = ( 1 es) / ( 1 + es)
The pv values iterated forward and backward to achieve accuracy at sixth place of decimal. The weights and threshold were cor rected in every iteration. The values of weights and thresholds obtained at the end were matured values and indicated the end of learning process of the network.(Table 3 , 4).
Similarly,
((Ra) / (ON2/3 *DQ1/3))
——————————– (7)
And
= ((Ek) / (ON1/3 *DQ1/3))
The relationship between various parameters was unknown. The dependent parameter i.e. and relating to MRR, Ra and Ek were bear an intricate relationship with remaining
terms evaluated on the basis of experimenta tion. The true relationship was difficult to obtain.
This relationship now can be viewed as the hyper plane in five dimensional spaces. To simplify further let us apply ANN meth odollgy for analysis.

ANN MODEL DEVELOPMENT
The ANN is capable of performing nonlinear mapping between the input and output space parameters due to its large parallel interconnection between different layers and the nonlinear pro cessing characteristics. An artificial neuron basically consists of a computing element that performs the weighted sum of the input signal and the connecting weight. The sum is added with the bias or threshold. And the resultant signal is then passed through a nonlinear function of sigmoid or hyperbolic tangent type. Each neuron is associated with three parameters whose learning can be adjusted; these are the connecting weights, the bias and the slope of the nonlinear function. For the structural point of view a neural network may be single layer or it may be multilayer. In multilayer structure, there is one or many artificial neurons in each layer and for a practical case there may be a number of layers. Each neuron of the one layer is connected to each and every neuron of the next layer. The basic ANN model is as shown in figure 3.
3.2.1 Feed forward back propogation Neural Network model
The mathematical models for MRR, Ra and Ek were dedeveloped by feed forword back propogation ANN model. The neural network used in this case was predictive in nature with supervised learning. It was range bound for all input factors. In neural network terminology total input and output cells were 10. As per the dimensional analysis total input parameters were five and network with one hidden layers was reasonable to simulate
i.e.1 h ANN topology (Fig.3). All five dimensionaless terms were scaled down between zero and one using their maximum and minimum values as given.
Scaled values =
(Current value Min. valu) / (max. value min. value)
Figure 3: Basic ANN Model
Thus it was very easy to answer what would be the output parameter if input factors were known. A separate VB base program was written for this prediction. This program simulated the structure (Fig. 3) of entire network using final values of weights and thresholds. It carried out the single iteration using scaled values of input factors to generate the scaled values of output parameter. This scaled value was further translated to its physical value by reverse scaling calculations. In this way once the network went through the learning process, it was capable of predicting output parameters viz. matrial removal rate , surface finish and electric kerf immediately. The complex relationship in manipulation of the output was not truly known but the numerical results were obtainable. Moreover these results were least affected by discrepant error.

Training to ANN model for MRR
The output MRR (opi1) was developed by computing the weights and threshold values from node of first layer to the connected other nodes of hidden and output layers. The de tails of training the ANN model as givenin table 2.
Table 2: ANN parameters used to train the ANN network
Sr. No.
Parameters
ANN training values
1
Number of hidden layer
01
2
Learning factor
0.01
3
Transfer function used
Sigmoidal
4
Number of hidden neurons
4
5
Number of epochs
10000
6
Momentum factor
0.5
101.05
9.732891
18.9216
2.686327
0.9887
93.88503
24.72
2.36443
0.656152
4.06412
21.70783
29.57289
14.5999
2.89046
8.997999
4.803129
2.56823
25.01509
35.76814
3.16876
5.9203
4.28675
2.174713
23.6796
101.05
9.732891
18.9216
2.686327
0.9887
93.88503
24.72
2.36443
0.656152
4.06412
21.70783
29.57289
14.5999
2.89046
8.997999
4.803129
2.56823
25.01509
35.76814
3.16876
5.9203
4.28675
2.174713
23.6796
S1,1
S1,2
S1,3
S1,4
S1,1
S1,2
S1,3
S1,4
Table3: Weights and thresholds of all nodes from layer 1 to layer 2
1
2
3
4
5
Threshold
1
X0,1
transform by
= (1 e 1* S1,i ) /
(1 e 1* S1,i )
=
X1,1
2
*
X0,2
X1,2
3
X0,3
X1,3
4
X0,4
X1,4
X0,5
1
0.435345
0.492075
1.208969
0.64691
0
0.435345
0.492075
1.208969
0.64691
0
Table4: Weights and thresholds of all nodes from layer 2to layer 3
1
1
2
3
4
Threshold
*
X1,1
=
S2,1
transform by (1 e 1* S2,i ) /
(1 e 1* S2,i ) =
X2,1
X1,2
X1,3
X1,4
1
Figure 4: ANN Topology for MRR
Figure 4: 5,4,1 ANN topology for MRR with weights and thresholds
Figure 4: ANN Topology for MRR
Figure 4: 5,4,1 ANN topology for MRR with weights and thresholds
Figure 4: ANN Topology of MRR
Figure5: Comparision between actual and ANN outputs for MRR
The weights and threshold values were given in Table 3 and 4. Hence after training to the ANN model an ANN equation was developed as
opi1= (1 e 1*sum (layer 2 cell 0) )/ (1 e 1*sum (layer 2 cell 0) )
Where, sum (layer 2 cell 0) =
0.435344673*X1,1 +0.49207543*X1,2 +1.208969181*X1,3 –
0.646909037*X1,4 – 0.0000000
And X1,1 , X1,2, X1,3, X1,4 were computed from Table 2 as follows :
X1,1= (1 e 1*sum (layer 1cell 0) )/ (1 e 1*sum (layer 1cell 0) )
Where, sum (layer1 cell 0) =
101.0500693*X0,1 +9.732891283*X0,2 +18.92160414*X0,3
+2.68632748*X0,4 0.988699129*X0,5 – 93.88502863
X1,2= (1 e 1*sum (layer 1cell 1) )/ (1 e 1*sum (layer 1cell 1) )
Where, sum (layer1 cell 1) =
24.71998941*X0,1 2.364433503*X0,2 +0.656152358*X0,3
4.064121616*X0,4 +21.70782525*X0,5 29.57289105
X1,3= (1 e 1*sum (layer 1cell 2) )/ (1 e 1*sum (layer 1cell 2) )
Where, sum (layer1 cell 2) =
14.59988996*X0,1 2.890455464*X0,2 +8.997999049*X0,3
+4.803129141*X0,4 +2.568229507*X0,5 25.01508634
X1,4= (1 e 1*sum (layer 1cell 3) )/ (1 e 1*sum (layer 1cell 3) )
Where, sum (layer1 cell 3) =
35.76814034*X0,1 +3.168759738*X0,2 5.920299799*X0,3
+4.286749827*X0,4 +2.17471322*X0,5 +23.67960855
The corelaion and root mean square error of the model was 0.815868 and 0.0000000624 respectively.
By using similar approach ANN models for Ra nalues were developed.
FF
FF

Training to ANN model for Ra
Figure 6 : ANN topology for Ra
The output Ra (opi2) was developed by computing the weights and threshold values from node of first layer to the connected other nodes of hidden and output layers(Fig.6). The training to the ANN model was given the equation for opi2 as follows
opi2= (1 e 1*sum (layer 2 cell 0) )/ (1 e 1*sum (layer 2 cell 0) )
Where, sum (layer 2 cell 0) =
1.67157 *X1,1 +2.067592*X1,2+1.615761*X1,3
+2.627413*X1,4+0.00000
And X1,1, X1,2, X1,3, X1,4 were computed as follows :
X1,1= (1 e 1*sum (layer 1cell 0) )/ (1 e 1*sum (layer 1cell 0) )
Where, sum (layer1 cell 0) =
+0.703816*X0,5 – 0.796271
X1,3= (1 e 1*sum (layer 1cell 2) )/ (1 e 1*sum (layer 1cell 2) )
Where, sum (layer1 cell 2) =
0.18306*0,10.55774*X0,2 +2.265147*X0,30.81074*X0,4
0.78555*X0,5 – 0.092133
X1,4= (1 e 1*sum (layer 1cell 3) )/ (1 e 1*sum (layer 1cell 3) )
Where, sum (layer1 cell 3) =
0.731863*X0,1+0.547867*X0,21.47733*X0,3 – 1.42728*X0,4
+0.019396*X0,5 + 0.29746
The comparision between experimental and computed error of the ANN model for Ra is given in figure7. While the corelaion and root mean square error of the model was 0.844417 and 0.0011 respectively.
Figure 7: Comparision between experimental and Computed ANN values for Ra

Training to ANN model for Ek
Figure 8 : ANN topology for Ek
The output Ek (opi3) was developed by computing the weights and threshold values from node of first layer to the connected other nodes of hidden and output layers(Fig.8). The training to the ANN model was given the equation for opi3 as follows
Opi3= (1 e 1*sum (layer 2 cell 0) )/ (1 e 1*sum (layer 2 cell 0) )
Where, sum (layer 2 cell 0) =
1.38395*X1,1+2.512747*X1,2+1.632333*X1,3
+ 0.414591*X1,4+0.00000
And X1,1 , X1,2, X1,3, X1,4 were computed as follows :
1.058274*X
0,1
0.25715*X
0,2
+0.75411*X
0,3
+2.966452*X
0,4
X1,1= (1 e 1*sum (layer 1cell 0) )/ (1 e 1*sum (layer 1cell 0) )
0.10655*X0,5 +0.80149
X1,2= (1 e 1*sum (layer 1cell 1) )/ (1 e 1*sum (layer 1cell 1) )
Where, sum (layer1 cell 1) =
Where, sum (layer1 cell 0) =
3.03121*X0,1 +1.8908*X0,2 1.00558*X0,3 0.84576*X0,4
0.04437*X0,5 – 0.60978
X = (1 e 1*sum (layer 1cell 1) )
0.189792*X
0,1
0.42598*X
0,2
+0.389551*X
0,3
0.06788*X
0,4
1,2
(layer 1cell 1) )/ (1 e 1*sum
Where, sum (layer1 cell 1) =
2.154639*X0,1 +0.565142*X0,2 0.63369*X0,3 –
0.79475*X0,4 +0.027828*X0,5 1.39463
X1,3= (1 e 1*sum (layer 1cell 2) )/ (1 e 1*sum (layer 1cell 2) )
Where, sum (layer1 cell 2) =
1.536739*X0,1 0.58743*X0,2+2.198514*X0,3
0.13694* X0,4 + 0.44775*X0,5 + 0.801512
X1,4= (1 e 1*sum (layer 1cell 3) )/ (1 e 1*sum (layer 1cell 3) )
Where, sum (layer1 cell 3) =
3.800913*X0,1 +1.21408*X0,2 +0.863574*X0,3 +5.377673*X0,4
3.41478*X0,50.25185
The comparision between experimental and computed error of the ANN model for Ek is given in figure9. While the corelaion and root mean square error of the model was 0.844417 and 0.0011 respective ly.
Figure 9: Comparision between experimental and Computed ANN values for Ek

PREDICTION OF OUTPUTS BY ANN PREDICTION TOOL
The relationship was developed through ANN modeling was not sufficient because it was mere a training to the model. Hence prediction was necessary to predict the output from the trained data.
The predictive tool was developed on supervised learning process with feed forward back propogation ANN model. After the training of the ANN model, prediction of any experiment was carried out to find the output at the same experiment. The predictive tool was given the output(opi2) for experiment number 376 as 0.00060654 with error 0.00031.(Fig.10)
Figure 10: prediction tool of ANN model

OPTIMAL SOLUTION FOR ANN MODELS
Optimization in case of ANN models was carried out using univariate analysis approach. This was the method for deciding highly influential input parameters . It primarily computed diffential dy/dx values for all inputs. Here the
value of one of the x variable was increased by 0.01 and change in output was recorded. After computing in this manner for all variables the order sequence of influence was obtained. It was provided the better insight to intraction process and variables. In order to decrease the output most dominating factor was incremented. Sensitivity was checked after every increment . This process ended when output did not decreased or the range to which any input variable can be incremented was exausted.
In ANN model the input values were scaled between 1 to 1 . By using univariate analysis most infuenting variable and its length of influence was determined. Initialy randomly selected first parameter was shown maximum influence but after certain length of maximum influence of input variable some other input variable may turn out to be maximum influential. This way when either all imput varibales were reached to maximum value i.e.1 or value of output did not improved then optimal solution was obtained.
For the MRR most influential input parameter was ipi3 and optimal solution was computed as table 5.
Table 5 : optimized value of MRR
Sr No. Input variable Opt. values Max. Values 1 ipi1 6 6
2 ipi2 0.290739295 0.290739295
3 ipi3 1.30376E07 1.21141E07
4 ipi4 0.000302853 0.000302853
5 ipi5 0.00002 0.00002
Optimum soln 9.94886E08 5.7528E07
For the Ra most influential input parameter were ipi2, ipi 4 and ipi5 with influental length 168, 45, and 44 consequetively. The optimal solution was computed as table 6.
Table6: Optimized value of Ra
Sr. No.
Input variable
Opt.values
Min. Values
1
ipi1
6
6
2
ipi2
1.283603261
0.290739295
3
ipi3
1.21141E07
1.21141E07
4
ipi4
0.000533814
0.000302853
5 ipi5 0.000042946 0.00002
Optimum soln 0.004044575 0.014710946
For the Ek most influential input parameter were ipi4 and ipi5 with influental length 61 and 59(Table7) consequetively. The optimal solution was computed as table 8.

RESULTS AND DISCUSSION
3.5.1 Development of terms
The Buckinghams theorem formulated six dimensionless terms and each term was given the importance of each dimen sionless group. The first term implied the effect of spark fre quency of wire EDM process on MRR, Ra and Ek values. The second term showed the importance of spark energy supplied
to the wire so as to minimize the breakage of wire which has taken a major nonproductive time during WEDM. Third, fourth and fifth terms were relate with the role of servo speed, wire speed and product variability during machining. Finally the last term reflected the outputs MRR, Ra and Ek resposes.
Table 7:Most influential input parameter for Ek
Output Influence
opi4 opi4 
1 2 
52 59 
4 5 
1.305338 1.260094 
mathematical model suggested by this ANN programme was – sum(layer2cell 0) =1.67157*X1,1+2.067592*X1,2+1.615761*X1,3+ 
opi4 
3 
40 
4 
1.190099 
2.627413*X1,4+0.00000.This equation calculated the computed 
opi4 
4 
61 
5 
1.142835 
Ra values and also helpful for prediction programme of the ANN. 
opi4 
5 
40 
4 
1.075545 
The predicted values of any experiment were calculated very easily just by inserting the experiment number into prediction 
opi4 
6 
61 
5 
1.031752 
ANN programe. The univariate programme of the ANN was con 
opi4 
7 
29 
4 
0.98016 
cluded about the sensitivity of the model and optimized values of 
opi4 opi4 
1 2 
52 59 
4 5 
1.305338 1.260094 
mathematical model suggested by this ANN programme was – sum(layer2cell 0) =1.67157*X1,1+2.067592*X1,2+1.615761*X1,3+ 
opi4 
3 
40 
4 
1.190099 
2.627413*X1,4+0.00000.This equation calculated the computed 
opi4 
4 
61 
5 
1.142835 
Ra values and also helpful for prediction programme of the ANN. 
opi4 
5 
40 
4 
1.075545 
The predicted values of any experiment were calculated very easily just by inserting the experiment number into prediction 
opi4 
6 
61 
5 
1.031752 
ANN programe. The univariate programme of the ANN was con 
opi4 
7 
29 
4 
0.98016 
cluded about the sensitivity of the model and optimized values of 
var Revolution length pi_var op. value
the same mathematical model of ANN.
3.5.3 ANN modelling for Ra
The 432 experimental data was trained in 5, 4, 1 topology of ANN programme. In this prograame one hidden layer was used and developed topology was calculating the weights and thresolds of every perceptron. The prevailing values (pv) of each perceptron were used to caluculate the computed Ra values. The
opi2= (1 e
1*sum (layer 2 cell 0) )/ (1 e 1*sum (layer 2 cell 0) ) Where,
opi4 8 10 5 0.971729
Table 8: Optimal solution for Ek
Sr. No. 
Input variable 
Opt. values 
Min. Values 
1 
ipi1 
6 
6 
2 
ipi2 
0.290739295 
0.290739295 
3 
ipi3 
1.21141E07 
1.21141E07 
4 
ipi4 
0.00112918 
0.000302853 
5 ipi5 0.000119607 0.00002
Optimum soln. 0.971729385 2.826809158
3.5.2 ANN modelling for MRR
Mathematical model was developed by using sigmoidal function in the the ANN Programme. This ANN program provid ed 5,4,1 ANN topology for the MRR and also suggested the val ues of weights and threshold in the topology for calculating the prevailing values of each node and for calculating the computed response of the MRR. The wights and threshold values were giv en the table 3 from input layer to hidden and in table 4 was showed the above values from hidden layer to final computed layer. From the table 3 , threshold values for node 1 of hidden layer was 93.88503 while the weights accumulated to the above said node were 101.05 ,9.732891, 18.9216, 2.686327and – 0.9887 hence the pv values were very easily calculated. The pre diction tool was greatly used for predicting any values of the ex periments and also provided the error within experimental and predicted values of the ANN model. Finally univeriate analysis of the ANN model suggested the sensitivity of the mathematical model with 0.01 differetial and gave most influential process pa rameter for better effect on MRR. The univeriate process sug gested that ipi3 (servo speed) parameter was more influenting on
MRR. This ipi3 meant the = ((ON2/3 * SS) / (DQ1/3)) and it was directly influenting the maximum values of MRR. Since this was the ratio hence by increasing spark on (ON) value or servo speed (SS) MRR was increased. The optimization of ANN model was also suggested by the univariate process. The input process pa
rameters with optimized MRR of 9.94886E08 m3/s were given in table 5 which was better than computed maximum MRR for
the computed Ra. The Ra was greatly influential by input parameter ipi2, ipi 4 and ipi5 with influental length 168, 45, and
44 consequetively . The ipi2 means spark energy supplied duringWEDM process and the parameters included into this terms were = ((ON2/3 * IP * SV) / (DQ1/3 *WT)). This was sugeested that just by increasing ON or IP or SV values machin ing process can improve the Ra values. Similarly ipi4 and ipi5 means wire speed factor and product variablility. It was conclud ed that if the wire speed increased then Ra improves. And product variability sugeessted that if shape changed then also Ra changed. The optimized values of Ra were calculated by ANN optimize programme as 0.004044575 Âµm.
3.5.4 ANN modelling for Ek
The ANN training to the experimental data was given the mathemaical equation for opi3 = (1 e 1*sum (layer 2 cell 0) )/ (1 e
1*sum (layer 2 cell 0) ) Where , sum (layer 2 cell 0) = 1.38395 *X1,1 +
2.512747*X1,2+1.632333*X1,3 + 0.414591*X1,4+0.00000. This train
ing also used 5,4,1 ANN topology with one hidden layer. The output data of ANN training tool was used for prediction of Ek values. Fi nally the univariate analysis suggested that ipi4 and ipi5 were most influenting factors with influential length adjustment from 52 to 29 and 61 to 10. The optimized value of Ek was 0.971729385 m which was better than minimized values of equation.

CONCLUSION
The true power and advantage of neural networks lies in their ability to represent both linear and nonlinear relationships and in their ability to learn these relationships directly from the data being modelled. Hence use of ANN tool concluded that

WEDM process has proved its adequacy to machine Al/SiC10% MMC under acceptable volumetric mate rial removal rate (MRR) which was reached upto 9.94886E08 m3/s, surface finish (Ra) 0.004044575
Âµm and electric kerf (Ek) 0.971729385 m.

The dimensionless terms have provided the idea about combined effect of process parameters in that terms. A simple change in one process parameter in the group helped the manufacturer to maintain the required MRR and Ra values so that the productivity improved.

The mathematical models developed after training to 5,4,1 ANN topology with one hidden layer were useful for predicting the characteristics of Wire elec tric discharge machining and this models could be effectively utilized for prediction of machining pa rametes of Al/ Sic10% MMCs in wide spread engi neering applications.

The univeriate analysis and optimized tool of ANN pro gramme for WEDM process parameters were provideed guidelines for effective process parametes of WEDM process. This parameters selection helped the manufacturing engineers to maximize Al/SiC10% MMC utilization for industrial applications for high er machining performances.

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