INTRODUCTION
Due to increased competition, the industries are facing the challenging issue
of meeting the performance of components/systems which is getting more and more
demanding as the days roll out. The composites materials in general and Metal
Matrix Composites (MMCs) in particular have emerged as the promising alternatives
to the conventional materials for the industries such as automotive, aerospace,
electronics, military etc. (Lin et al., 2003).
This is because of the potentially attractive properties the MMCs offer high
specific strength and stiffness, increased wear resistance, etc. Despite of
these merits, the applications of MMCs is not fully realized in commercial sense
for the common man use which can be attributed to some of the following reasons
(Cramer et al., 2002; Golzar
and Poorzeinolabedin, 2010):
• 
High cost of manufacture of MMCs 
• 
Higher manufacturing cost involved in producing a component from a MMC 
• 
Lack of experience and knowledge in how to design with advanced composites 
• 
Lack of affordable process for producing advanced composites parts in
high volume suitable to industry standards (ex. automotive production standards) 
It is observed that the high cost involved in producing a component is one
of the main reasons hindering the widespread use of MMCs. Though it is possible
to produce the MMCs components to near net shape, the final conversion of these
parts into applicable engineering components is always associated with machining
either by turning or milling to the desired shape, size, dimensions and surface
finish (Ramanujam et al., 2010). The main reason
for higher cost in producing a part from MMCs can be attributed to their poor
machinability. This is due to hard and abrasive nature of the reinforcement
used in MMCs.
Surface roughness is an important attribute of job quality. A good surface
finish is essential for improving the tribological properties, aesthetic appeal
of the product, etc. The production of excessively better surface finish involves
higher cost of manufacturing. Therefore researchers have attempted to develop
prediction model and identify suitable cutting parameters using different methodologies
viz., the multiple regression technique, Response Surface Methodology (RSM),
Neural Network (NN) and fuzzy set based modelling. Artificial Neural Network
(ANN) modeling has been found very effective for surface roughness prediction
(Abburi and Dixit, 2006). Kohli
and Dixit (2005) have presented an artificial neural network based methodology
which requires a small sized data set for the network training.
Neural networks and fuzzy set theory are two popular soft computing techniques
apart from many other techniques available. Artificial neural networks are a
humble attempt to model biological neural networks. An artificial neuron determines
its output by calculating the weighted sum of the inputs to represent the total
strength of the input signals and applying a suitable activation (threshold)
function to the sum.
Number of researchers has used these tools to develop prediction models in
various machining process. Chandrasekaran et al.
(2010) have reviewed research work spanning over two decades on the application
of these methods in modeling and optimization of various machining processes.
In the area of machining, neural network modeling techniques have been commonly
used for the prediction of surface roughness, cutting forces, tool wear, tool
life and dimensional deviation. Risbood et al. (2003)
developed a Multi Layer Perception (MLP) neural network for the prediction of
surface roughness and dimensional deviation in wet turning of steel with a High
Speed Steel (HSS) tool. The input layer has four neurons correspond to feed
(f), cutting speed (v), depth of cut (d) and acceleration of radial vibrations
(a) of the tool. They obtained the error in prediction of surface roughness
less than 20%. The Radial Basis Function (RBF) neural network used by Sonar
et al. (2006) predicts almost same accuracy in a shorter computational
time. Akkus and Asilturk (2011) have used the ANN, fuzzy
logic and regression model to predict the surface roughness in hard turning
of AISI 4140 steel and compared the result. With least mean squared error (MSE)
they found the fuzzy logic model to be the best prediction model followed by
the regression model and the ANN model. Pradhan and Biswas
(2010) also used neural network and fuzzy logic to predict various responses
(material removal rate, tool rate wear and radial over cut) in electrical discharge
machining of AISI D2 steel.
Rajasekaran et al. (2011) have applied the fuzzy
logic for prediction of surface roughness in turning of Carbon Fiber Reinforced
Polymer (CFRP) composite using the Cubic Boron Nitride (CBN) cutting tool. Barman
and Sahoo (2009) have applied ANN for modeling fractal dimension in CNC
turning of aluminium, brass and mild steel using coated carbide tool (titanium
nitrate coating) and compared with response surface model. They have concluded
that the ANN models predict fractal dimension with better accuracy than the
RSM models. Very few researchers have worked on prediction and optimization
of process parameters in machining of MMCs (particularly Albased MMC).
Basavarajappa et al. (2007) studied the variation
of surface roughness on the drilling of metal matrix composites using carbide
tool and found that the surface roughness decreases with the increase in cutting
speed and increases with the increase in feed rate. Arokiadass
et al. (2011) have used response surface model to predict surface
roughness in end milling of AlSiC_{p} MMC. It is reported that R_{a
}is mainly influenced by feed rate and spindle speed. Apart from conventional
modeling neural network based prediction modeling becomes popular and found
effective. In this study a surface roughness prediction model for end milling
of AlSiC_{p }MMCs using artificial neural network and its evaluation
is carried out.
DESCRIPTION OF THE PROBLEM
Apart from composites manufacturing, modeling and optimization of machining
of composite materials is gaining importance among researchers. Much attention
is paid for the development of prediction model for surface roughness during
the machining process such as turning and milling. Among the different prediction
strategies neural network modeling has been found effective for surface roughness
prediction. In this work, an artificial neural network based surface roughness
prediction model for end milling of MMCs having LM25 Aluminium alloy matrix
reinforced with Silicon Carbide (SiC) milled with carbide tool is developed
and results are compared with response surface model. Also the effect of various
parameters is studied. In addition to the three basic machining parameters viz.
spindle speed, N (rpm), feed rate, f (mm. rev^{1}) and depth of cut,
d (mm) another variable SiC percentage, S (% wt) is considered in the study.
The level of the parameters considered is given in the Table 1.
Table 1: 
Levels of parameters 

X_{1}: Spindle speed, N (rpm), X_{3}: Depth
of cut, d (mm), X_{2}: Feed rate, f (mm. rev^{1}), X_{4}:
SiC content, S (%wt) 
The experimental data sets of Arokiadass et al.
(2011) are used in this work for ANN modeling. The surface roughness depends
on spindle speed, N (rpm), feed rate, f (mm. rev^{1}) and depth of
cut, d (mm) and SiC percentage, S (% wt).
DEVELOPMENT OF ANN MODEL
Neural network or artificial neural network is network/combination of a number
of interconnected processing elements/units/nodes called the neurons. The ANN
can be used to determine the input and output relationship of a complex process.
It is therefore, considered as the non linear statistical data modeling tool.
The neural network system can thus acquire, store and utilize the knowledge
gained from the experience. ANN models motivated from the working of human brain
can be trained with the experimental data to describe the non linear and interaction
effects of the process variables on the response. A properly trained neural
network can predict the response parameter value for unknown input variables
with reasonable accuracy.
In the present study, ANN predictive model is developed using 25 data sets
and given in the Table 2.
Table 2: 
Experimental design matrix and experimental values of R_{a} 

The ANN is modeled using Neural Network toolbox available in MATLAB^{®}
version 7.8 to predict the surface roughness as a function of four input parameters
viz.., spindle speed, feed rate, depth of cut and SiC percentage.
A MLP with one hidden layer having fourteen neurons with logsig transfer function
is used in the present work. Four input neurons, each representing one input
variable constitute the input layer while the output layer consists of one neuron
with purelin activation function, corresponding to one response variable i.e.,
surface roughness. Figure 1 shows architecture of twolayer
feed forward neural network used in the present study. Figure
2 shows the graphical representation of the transfer functions used in building
the network.
Table 3 shows the testing error and the corresponding MSE
obtained in arriving at optimum number of neurons and transfer function used
in hidden layer. Optimum number of neurons and transfer function for the hidden
layer is selected based on the least MSE in the testing data sets after training
network until one of the stopping criteria is achieved.
Table 3: 
Optimal number of neurons and transfer function for the hidden
layer 

*Average percentage error 

Fig. 2(ab): 
Transfer functions used; (a) Hidden layer and (b) Output
layer 

Fig. 3: 
Average percentage testing error vs. No. of neurons in the
hidden layer 
The testing error and MSE of the network are recorded starting from minimum
five (05) neurons and number of neurons is increased gradually in steps of one
till a maximum of twenty (20) neurons. The fourteen neurons with logsig transfer
function giving least average percentage testing error of 0.453% (MSE = 0.001128)
is found to be optimum in the present work. Figure 3 and 4
show the plot of average percentage testing error and MSE recorded for different
number of neurons used with logsig and tansig transfer function.
In the present study, the total number of data sets available is limited to
25 only. As in early stopping, dividing these data sets into three subsets would
result in only 15 data sets for training; 5 data sets each for validation and
testing. With this division of data sets, the trainlm (LevenbergMarquardt back
propagation) training function did not produce a network with good generalization
performance with absolute testing error recording as high as 35% and the average
testing error being close to 20%.
Therefore, the network is trained with trainbr (Bayesian regulation back propagation)
training function that uses the Bayesian regularization.

Fig. 4: 
Mean squared error vs. No. of neurons in the hidden layer 

Fig. 5: 
Network performance parameters of the converged network 
The inputs and outputs are scaled to lie in the range (1 1) using mapminmax
function. A different data set (80%) randomly selected using dividerand function
is presented to the network every time it is initialized and trained. The training
is continued until specified stopping criteria is achieved. The network is tested
with data sets (20%) which are also randomly selected. The effective number
of parameters (weight and biases), Sum Squared Error (SSE) and Sum Squared Weights
(SSW) are recorded at the end of each training. The network is considered as
converged with effective number of parameters and SSW remaining constant at
20 and 22.5857, respectively over 110 epochs. The testing SSE recorded approximately
0.0200249 remained constant over the entire range of iterations. The SSE during
training is found to be very small (1.14504x10^{18}). Figure
5 shows the network performance parameters of the converged network.

Fig. 6: 
Predictive performance of ANN model 
The post training analysis of the ANN model shows that the model prediction
exhibits close relationship with the experimental result with the correlation
coefficient R = 0.9988. Figure 6 shows the predictive performance
of ANN model.
RESULTS AND DISCUSSION
The predicted values of surface roughness from the ANN model are compared with
the experimental result and also with the surface roughness predicted by response
surface model. The comparison of prediction performance of both the models with
the experimental result is given in Table 4. The response
surface model developed by Arokiadass et al. (2011)
using second order polynomial equation found that the model is statistically
significant with 95% confidence level. It is also reported that the input parameter
feed rate has more influence on the response followed by spindle speed, SiC_{p}
percentage and depth of cut.
The maximum absolute percentage error in ANN model prediction is 2.31% while
for the RSM it is 1.39%, when compared with the experimental result. However,
the average percentage error in ANN prediction is 0.31% and is less than that
involved in RSM prediction which is 0.51%. The neural network based surface
roughness prediction model is found better than the response surface model in
end milling of AlSiC_{p} metal matrix composites using carbide tool.
Table 4: 
Performance comparison of ANN model and RSM with experimental
result 


Fig. 7: 
Correlation between the predicted values of R_{a}
and experimental result 
The graphical representation of the predicted values of R_{a} from
both the ANN model and RSM is shown in the Fig. 7. The prediction
of both ANN model and RSM show high correlation with the experimental result.
The generalization performance of the ANN predictive model is further examined
on completely new 256 hypothetical data sets obtained by taking the average
of the two levels of the original parameters as given in Table
5.
The functional dependence of surface roughness for all the possible combinations
of input variables is analyzed by surface plots.
Table 5: 
New levels of parameters 

X_{1}: Spindle speed, N (rpm), X_{3}: Depth
of cut, d (mm), X_{2}: Feed rate, f (mm. rev^{1}), X_{4}:
SiC content, S (%wt.) 

Fig. 8: 
Surface plot of R_{a} with spindle speed and feed
rate 

Fig. 9: 
Surface plot of R_{a} with spindle speed and depth
of cut 
Figure 8 depicts the variation of surface roughness with
spindle speed and feed rate for constant values of depth cut (0.75 mm) and SiC
percentage (7.5%). It can be inferred from the plot that surface roughness increases
as the feed rate increases whereas it decreases with increase in the spindle
speed.
The variation of R_{a }with spindle speed and depth of cut for constant
values of f = 0.025 rev. mm^{1} and SiC = 7.5% is shown in Fig.
9.

Fig. 10: 
Surface plot of R_{a} with feed rate and depth of
cut 

Fig. 11: 
Surface plot of R_{a} with depth of cut and SiC percentage 

Fig. 12: 
Surface plot of Ra with spindle speed and SiC percentage 
It shows that the depth of cut has least influence in predicting R_{a}
and it also can be inferred from Fig. 10 and 11.
Figure 12 depicts the variation of surface roughness with
spindle speed and SiC percentage for constant values of feed (0.045 mm. rev^{1})
and depth of cut (2.25 mm).

Fig. 13: 
Surface plot of R_{a} with feed rate and SiC percentage 
It shows that the variation of R_{a} is directly proportional to the
SiC percentage and it also can be inferred from Fig. 13.
CONCLUSIONS
In the present study, an artificial neural network based surface roughness
prediction model for AlSiC_{p} MMC milling with carbide tool is developed.
The performance of the predictive model is found to be very encouraging with
average percentage error being 0.31% when compared with the experimental data
sets. The performance of the ANN model is also compared with the response surface
model and found that the ANN model outperforms RSM. The surface roughness mainly
depends upon feed rate, spindle speed and SiC percentage of AlSiC_{p}
MMC. It is observed that the depth of cut has least influence on the response
variable.
The surface roughness varies directly as the input parameters feed rate and
SiC percentage whereas it bears inverse relationship with spindle speed. Thus
suitable combination of machining parameters for the desired surface roughness
can be obtained. However, improved tool life should be aimed for economical
production of MMCs components.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial help provided by All India
Council for Technical Education (AICTE) from the project AICTE: 8023/RID/BOIII/NCP
(21) 20072008, Project Id at Indian Institute of Technology, Guwahati being
ME/P/USD/4.