Cutting feed 9.26208 0.30958 29.918 0.000

Spindle speed 0.00009 0.00005 2.017 0.047

S = 0.0881180; R-Sq = 95.69% ; R-Sq(adj) = 95.46%

Table 6. Linear regression model for ln(torque).

ln(Torque) = 1.408 + 0.374 Al2O3 (vol%) − 0.254 Gr (vol%)+ 8.933

Cutting feed (mm/rev) + 0.0002 Spindle speed (rpm)

Term Coef SE Coef T p-value

Constant 1.40802 0.114153 12.334 0.000

Al2O3 0.37386 0.015232 24.545 0.000

Gr −0.25409 0.015232 −16.682 0.000

Cutting feed 8.93298 0.786467 11.358 0.000

Spindle speed 0.00019 0.000119 1.616 0.110

S = 0.223857; R-Sq = 93.02%; R-Sq(adj) = 92.65%

speed is considered marginal, but still important in this

model with p-value less than 0.05. The final regression

model is:

12

34

ln3.813 0.1370.0976

9.262 0.0001

th

F

XX

XX

(14)

where Fth represents thrust force, X1 represents Al2O3

(vol%), X2 represents Gr (vol%), and X3 represents cut-

ting feed and X4 represents spindle speed.

Similarly for (ln(torque)) model, the final regression

model is:

12

ln Torque1.4080.3740.254+8.9333

X

XX (15)

where X1 represents Al2O3 (vol%), X2 represents Gr

(vol%), X3 represents cutting feed (mm/rev), and X4 re-

presents spindle speed (rpm).

The signs of the parameters in the model presented in

Tables 5 and 6 were examined. Positive signs mean the

response output (either thrust force or torque) values go

in the same direction as the parameter, and negative signs

imply the opposite.

To test the prediction performance of the ln(thrust

force) and ln(torque) regression models, the absolute re-

lative errors were computed based on experimental and

predicted values. The absolute relative error (ARE) was

computed based on the following equation:

Predicted valueExperimental value

ARE %Experimental value

(16)

Average absolute relative errors (ARE) were 12.59% and

7.10% for ln(thrust force) and ln(torque), respectively.

Although these error levels could be accepted in some

cases, better prediction models may give better predi-

ctability and lower error values. This leads us to use

ANN for prediction purposes instead of MRA because it

performs well and gives a better mapping between inputs

and outputs.

5.2. Artificial Neural Network Results

The ANN was implemented using fully developed feed

forward backpropagation network. The models for cut-

ting forces are identified by using the alumina (Al2O3)

particles contents, graphite (Gr) particles contents, cutting

feeds (f) and spindle speeds (N) as input data and thrust

force and cutting torque as the output data. An 4-10-2

ANN topology was used, which consists of four input

nodes, one hidden layer (10 neurons in the) and two out-

puts (thrust force and torque).

The inputs in ANN nodes must be a numerical value

and fall in the closed interval [0,1]. The input data were

normalized n the range between 0 and 1 using the follow-

ing formula:

Normalized value

input valueminimum value

maximum valueminimum value

(17)

Output values resulting from ANN were also in the

range [0,1] and converted to their equivalent values

based on reverse method of normalization technique.

All of the original 81 machining conditions were ran-

domly divided into three datasets including a training,

validation and testing datasets. The training set contained

57 (70%) data points were used to build the network, 12

data points (15%) were used to measure network gene-

ralization and another 12 points (15%) were used as a

testing set of the neural network. Sigmoid activation fun-

ction was selected to be the transfer function in the

hidden layer and linear function was used between hidden

layer and output layer (Figure 9). After many trials,

learning rate and momentum were experimentally se-

lected to be 0.03 and 0.9, respectively. Levenberg-

Marquardt training algorithm was used to train this ANN.

Training, testing and validation process were terminated

after 106 cycles and further iterations had insignificant

effect on error reduction. The obtained MSE value was

0.00182. Hence, one can conclude that a simple archite-

cture can be used efficiently without loss of prediction

accuracy. Table 7 summarizes ANN training and valida-

tion parameters as well final training error.

However, the main quality indicator of a neural net-

work is its generalization ability, in other words, its abi-

lity to predict accurately the output of unseen data; this

was achieved by testing dataset. Absolute relative errors

Copyright © 2012 SciRes. JMMCE

A. MAYYAS ET AL.

Copyright © 2012 SciRes. JMMCE

1046

Figure 10 shows the comparison between experi-

mental torque and thrust force values and corresponding

ANNs outputs for the total dataset (training, validation

and testing). These figures show that the significant por-

tion of points clusters along the diagonal line, which in

turn is a good indication of performance of training algo-

rithm. The correlation coefficients (R2) between experi-

mental and predicted outputs—values exceed 0.99 for all

training, testing and validating datasets. These values

show the accuracy of prediction ability obtained from

ANN.

Figure 9. Architecture of ANN with 4-10-2 topology.

5.3. Comparison between MRA and ANN

Prediction Models

between experimental and predicted values from ANN

were used to evaluate the performance of the proposed

ANN in prediction technique. The mean absolute relative

errors for the second ANN were: 1.66% for torque and

0.78% for thrust force for testing dataset. These levels of

error are satisfactory and smaller than errors that nor-

mally arise due to experimental variation and instrument-

tation accuracy.

A visual comparison was established between the fitted

and experimental values (Figures 11 and 12) for testing

and validation datasets of ANN, respectively. Both fi-

gures show that the predicted values from ANN appro-

ximate the experimental values much more than the

Figure 10. Comparisons between experimental thrust force values and corresponding ANN outputs (4-10-2 structure).

A. MAYYAS ET AL. 1047

Table 7. Summary of ANN parameters.

Neural network parameters

Network type Feed forward BP (Levenberg-

Marquardt training algorithm)

Network architecture 4-10-2

Number of hidden layer 1

Number of hidden neuron One hidden layer: 10

Transfer function Sigmoid: input hidden layer);

(Linear: hidden layeroutput layer)

Number of training examples 57

Number of testing examples 12

Number of validating examples 12

Learning rate 0.03

Momentum factor 0.9

Number of epochs 106

Mean squared error (MSE) 0.00182

MRA model does. This was also proved by getting smaller

absolute relative errors. Experimental value columns in

Figures 11 and 12 represent the actual values with 10%.

When compared to the experimental values with predi-

cted values, it can be seen that ANN outputs lie in good

prediction ranges compare to MRA outputs.

Now, which prediction method is better and when

should each one be used to predict and optimize the

drilling process in this situation? In the case of develop-

ing empirical relations, MRA model is preferred over

ANN model because it is an explicit model while the

ANN model is a black box. In the other direction, when

data are sparse or not generated from designed experi-

ments, MRA may not be able to produce a better model

than ANN; then the ANN modeling method and its asso-

ciated model may be preferred to the MRA method and

its model if such a model is available.

6. Conclusions

Two modeling techniques were used to predict the thrust

force and torque, namely multiple regression analysis

(MRA) and artificial neural network (ANN). Modeling

the drilling process using MRA and ANN approach pro-

vides a systematic and effective methodology for the

prediction. Both MRA and ANN revealed that rein-

forcement fractions were the important factors that in-

fluence the responses (i.e. thrust force and torque) fol-

lowed by the cutting feed rate. However, spindle speed

seemed insignificant in both models.

Many ANN architectures have been used to model the

collected experimental data. The best neural network

configuration was (4-10-2) which was trained using 57

training examples, tested using 12 examples and vali-

dated using 12 examples.

The results of ANN models showed close matching

(a)

(b)

Figure 11. Experimental vs. predicted values from ANN

and MRA for testing dataset: (a) thrust force; and (b) tor-

que.

(a)

(b)

Figure 12. Experimental vs. predicted values from ANN

and MRA for validation dataset: (a) thrust force; and (b)

torque.

Copyright © 2012 SciRes. JMMCE

A. MAYYAS ET AL.

1048

between the model outputs and the measured outputs.

The mean absolute relative errors were 0.82% for torque

and 2.89% for thrust force models, while MRA model

error values were 7.10% and 12.59%, respectively.

Hence, these models can be used efficiently for predic-

tion potentials for non-experimental patterns which, in

turn, save experimental time and cost. It was shown that

ANN performs well in mapping nonlinear relationships

between inputs and outputs. If both MRA and ANN

models are considered they will provide statistically sat-

isfactory prediction results. ANN methodology consumes

less time and gives higher accuracy. Hence, modeling the

drilling process using ANN is more effective compared

with MRA. The two proposed models are good in mod-

eling and predicting the drilling forces, which in turn can

provide a valuable tool for many similar applications of

modeling methods in engineering design and manufac-

turing. The developed modeling methods in this paper

can aid the prediction, optimization, and improvement of

drilling processes and the selection of cutting parameters

in the case of drilling aluminum-based materials.

REFERENCES

[1] J. P. Davim. “Study of Drilling Metal-Matrix Composites

Based on the Taguchi Techniques,” Journal of materials

processing technology, Vol. 132, No. 1-3, 2003, pp. 250-

254. doi:10.1016/S0924-0136(02)00935-4

[2] N. Altinkok and R. Koker. “Use of Artificial Neural Net-

work for Prediction of Physical Properties and Tensile

Strengths in Particle Reinforced Aluminum Matrix Com-

posites,” Journal of Materials Science, Vol. 40, No. 7,

2005, pp. 1767-1770. doi:10.1007/s10853-005-0689-5

[3] N. Altinkok and R. Koker, “Modeling of the Prediction of

Tensile and Density Properties in Particle Reinforced

Metal Matrix Composites by Using Neural Networks,”

Materials & Design, Vol. 27, No. 8, 2006, pp. 625-631.

doi:10.1016/j.matdes.2005.01.005

[4] A. M. Hassan, M. Hayajneh and M. Al-Omari, “The Ef-

fect of the Increase in Graphite Volumetric Percentage on

the Strength and Hardness of Al-4wt%Mg Graphite

Composites,” Journal of Materials Engineering and Per-

formance, Vol. 11, No. 3, 2002, pp. 250-255.

doi:10.1361/105994902770344024

[5] A. M. Hassan, A. Alrashdan, M. T. Hayajneh, A. T. May-

yas, “Prediction of Density, Porosity and Hardness in

Aluminum-Copper-Based Composite Materials Using

Artificial Neural Network,” Journal of materials proc-

essing technology, Vol. 209, No. 2, 2009, pp. 894-899.

doi:10.1016/j.jmatprotec.2008.02.066

[6] S. Kalpakjian and S. R. Schmid, “Manufacturing Engi-

neering and Technology,” 4th Edition, Addison-Wesley,

Boston, 2000.

[7] M. Ramulu, P. N. Rao and H. Kao, “Drilling of

(Al2O3)p/6061 Metal Matrix Composites,” Journal of ma-

terials processing technology, Vol. 124, No. 1-2, 2002,

pp. 244-254. doi:10.1016/S0924-0136(02)00176-0

[8] J. F. Kelly and M. G. Cotterell, “Minimal Lubrication

Machining of Aluminum Alloys,” Journal of Materials

Processing Technology, Vol. 120, No. 1-3, 2002, pp. 327-

334. doi:10.1016/S0924-0136(01)01126-8

[9] M. Tash, F. H. Samuel, F. Mucciardi, H. W Doty and S.

Valtierra, “Effect of Metallurgical Parameters on the Hard-

ness and Microstructural Characterization of As-Cast and

Heat-Treated 356 and 319 Aluminum Alloys,” Materials

Science and Engineering: A, Vol. 443, No. 1-2, 2007, pp.

185-201. doi:10.1016/j.msea.2006.08.054

[10] M. Nouari, G. List, F. Girot and D. Coupard, “Experi-

mental Analysis and Optimisation of Tool Wear in Dry

Machining of Aluminium Alloys,” Wear, Vol. 255, No.

7-12, 2003, pp. 1359-1368.

doi:10.1016/S0043-1648(03)00105-4

[11] G. Tosun and M. Muratoglu, “The Drilling of Al/SiCp

Metal-Matrix Composites. Part II: Workpiece Surface In-

tegrity,” Composites Science and Technology, Vol. 64,

No. 10-11, 2004, pp. 1413-1418.

doi:10.1016/j.compscitech.2003.07.007

[12] G. Tosun and M. Muratoglu, “The Drilling of an Al/SiCP

Metal-Matrix Composites. Part I: Microstructure,” Com-

posites Science and Technology, Vol. 64, No. 2, 2004, pp.

299-308. doi:10.1016/S0266-3538(03)00290-2

[13] J. T. Lin, D. Bharracharyya and V. Kecman, “Multiple

Regression and Neural Networks Analysis in Composite

Machining,” Composite Science and Technology, Vol. 63,

No. 3-4, 2003, pp. 539-548.

doi:10.1016/S0266-3538(02)00232-4

[14] M. T. Hayajneh, A. M. Hassan, A. Alrashdan and A. T.

Mayyas, “Prediction of Tribological Behavior of Alumi-

num-Copper Based Composite Using Artificial Neural

Network,” Journal of Alloys and Compounds 2009, Vol.

470, No. 1-2, 2009, pp. 584-588.

doi:10.1016/j.jallcom.2008.03.035

[15] S. Frouzan and A. Akbarzadeh, “Prediction of Effect of

Thermo-Mechanical Parameters on Mechanical Properties

and Anisotropy of Aluminum Alloy AA3004 Using Arti-

ficial Neural Network,” Materials & Design, Vol. 28, No.

5, 2007, pp. 1678-1684.

doi:10.1016/j.jallcom.2008.03.035

[16] K.Genel, S. C. Kurnaz and M. Durman, “Modeling of

Tribological Properties of Alumina Fiber Reinforced

Zinc-Aluminum Composites Using Artificial Neural Net-

work,” Materials Science and Engineering: A, Vol. 363,

No. 1-2, 2003, pp. 203-210.

doi:10.1016/S0921-5093(03)00623-3

[17] D. Montgomery and G. C. Runger, “Applied Statistics

and Probability for Engineers,” John Wiley and Sons,

New York, 2003.

[18] M. Negnevitsky, “Artificial Intelligence,” 2nd Edition,

Addison-Wesley, Boston, 2005.

[19] J. R. Rogier and M. W. Geatz, “Data Mining: A Tuto-

rial-Based Primer,” Addison-Wesley, Boston, 2003.

[20] Z. Zhang, K. Friedrich and K. Velten, “Prediction on

Tribological Properties of Short Fiber Composites Using

Artificial Neural Networks,” Wear, Vol. 252, No. 7-8,

2002, pp. 668-675. doi:10.1016/S0043-1648(02)00023-6

[21] S. Kumanan, S. K. N. Saheb and C. P. Jesuthanam, “Pre-

Copyright © 2012 SciRes. JMMCE

A. MAYYAS ET AL.

Copyright © 2012 SciRes. JMMCE

1049

diction of Machining Forces Using Neural Networks

Trained by a Genetic Algorithm,” Institution of Engineers

Journal, Vol. 87, No. 3, 2006, pp. 11-15.

[22] M. M. Hamasha, A. T. Mayyas, A. M. Hassan and M. T.

Hayajneh, “The Effect of Time, Percent of Copper and

Nickel on Naturally Aged Al-CuNi Cast Alloys,” Journal

of Minerals & Materials Characterization & Engineering,

Vol. 11, No. 2, 2012, pp. 117-131.

[23] A. T. Mayyas, M. M. Hamasha, A. Alrashdan, A. M.

Hassan and M. T. Hayajneh, “Effect of Copper and Sili-

con Carbide Content on the Corrosion Resistance of

Al-Mg Alloys in Acidic and Alkaline Solutions,” Journal

of Minerals & Materials Characterization & Engineering,

Vol. 11, No. 4, 2012, pp. 435-452.

[24] M. M. Hamasha, A. T. Mayyas, A. M. Hassan and M. T.

Hayajneh, “The Effect of Time, Percent of Copper and

Nickel on the Natural Precipitation Hardness of Al-Cu-Ni

Powder Metallurgy Alloys Using Design of Experiments,”

Journal of Minerals & Materials Characterization & En-

gineering, Vol. 10, No. 6, 2011, pp. 479-492.