Bn33393401

Md Sarfaraz Alam, Md Tabish Haque / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.393-401
393 | P a g e
Expert modeling and multi objective optimization of laser trepan
drilling of titanium alloy sheet
1
. Md Sarfaraz Alam*, 2
Md Tabish Haque
1,2,3
Motilal Nehru National Institute of Technology, Allahabad-211004, Uttar Pradesh, India
ABSTRACT
Nowadays laser machining became an
attractive machining process for difficult to cut
materials like ceramics, composites and super
alloys. Titanium alloys specially Ti-6Al-4V
(grade 5) is most widely used for different
technologically advanced industries due to their
superior performance characteristics such as
high strength and stiffness at elevated
temperatures, high strength to weight ratio,
high corrosion resistance, fatigue resistance, and
ability to withstand moderately high
temperatures without creeping. Laser trepan
drilling (LTD) being a thermal and non contact
nature and having the ability to produce micro
dimensions with required level of accuracy.
However laser drilled holes are inherently
associated with a number of defects like non
circularity of hole, spatter thickness and hole
taper. The present paper investigate the laser
trepan drilling(LTD) process performance
during trepanning of titanium alloy (Ti-6Al-4V)
by modeling and simultaneous optimization of
three important performance challenges such as
hole taper (HT), circularity at entrance
(CIRentry) and circularity at exit (CIRexit). A
hybrid approach of artificial neural network
(ANN)-genetic algorithm (GA) and grey
relational analysis (GRA) has been proposed for
multi-objective optimization. The verification
results are in the close agreements with the
optimization results.
Keywords: ANN, GA, GRA and LTD.
1. INTRODUCTION
The laser drilling process is one of the
most widely used thermal energy based non-
contact type advance machining process which can
be applied across a wide range of materials.
Nowadays laser drilling is finding increasingly
widespread application in the industries. Laser
beam machining is based on the conversion of
electrical energy into light energy and then into
thermal energy to remove the material from work
piece. The material removal process is by focusing
laser beam onto the work material for melting and
vaporizing the unwanted material to create a hole.
CO2 laser drilling has been widely used in
industries because of its high production rate and
abilities on rapidly varying holes size, drilling
holes at shallow angle, and drilling hard-to-work
material such as high strength materials, ceramic
and composite. Laser drilled holes are inherently
associated with a number of defects. Non
circularity of hole, spatter thickness, and hole taper
are some defects associated with laser drilling. As a
result, the quality of the drilled holes is the main
issue in the laser drilling process. There are two
types of laser drilling: trepan drilling and
percussion drilling. Trepan drilling involves cutting
around the circumference of the hole to be
generated, whereas percussion drilling is carried
out by utilizing a focused laser spot to heat, melt
and vaporize the target material such that a desired
hole is formed through the work piece with no
relative movement of the laser or work material
[1,2]. Fig. 1 shows a schematic of laser beam
drilling [2]
Fig. 1: Schematic of laser beam drilling

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A Number of researchers have performed the
experimental studies to investigate into the process
of laser percussion drilling by considering some
significantly affecting factors/ process parameters,
without applying any scientifically designed
experimentation technique, further analyzing the
impact of every parameter on observed process
performance characteristics. Tongyu and Guoquan,
[3] performed a study to investigate the relationship
of laser beam parameters (energy, power, pulse
width, pulse frequency) with the hole geometrical
quality characteristics and to find feasibility of high
carbon steel to investigate the heat affected zone in
laser drilling. Laser percussion drilling of alumina
ceramics was investigated by Kacar et al, [4] to
determine the effect of peak power (2-11 kw) and
pulse duration (0.5-7 ms) on geometrical features
of drilled holes such as diameter at entrance and
exit, crater (Initial cavity before getting through
hole) diameter and hole taper angle. The crater
diameter and the hole exit diameters shows
proportional changes with the Pulse duration and
peak power, although, the entrance hole diameter
do not changes much with them. The reason they
found, after morphological investigation with the
help of optical microscope that the resolidified
material at the entrance side increases with the
increase in pulse duration and peak power, which
ultimately reduces the entrance hole diameter even
after larger crater diameter. Also due to the same
reason there is a decrease in taper angle at the same
conditions, which further becomes negative for
higher values of process parameters. Ghoreishi et
al. [5] investigated the relationships and parameter
interactions between laser peak power, laser pulse
width, pulse frequency, number of pulses, assist
gas pressure and focal plane position on the hole
taper and circularity in laser percussion drilling of
stainless steel and mild steel. The central composite
design was employed to plan the experiments in
order to obtain required information. The process
performance was evaluated in terms of equivalent
entrance diameter, hole taper and hole entrance
circularity. They found that the pulse frequency
had a significant effect on the hole entrance
diameter and hole circularity in drilling stainless
steel unlike the drilling of mild steel, where the
pulse frequency had no significant effect on the
hole characteristics. Benyounis and Olabi [6] did a
comprehensive literature review of the applications
of design of experiments, evolutionary algorithms
and computational networks on the optimization of
different welding processes through mathematical
models. According to their review of various
literatures, they were of the opinion that there was
considerable interest among the researchers in the
adaption of response surface methodology (RSM)
and artificial neural network (ANN) to predict
responses in the welding process. For a smaller
number of experimental runs, they noted that RSM
was better than ANN and genetic algorithm (GA)
in the case of low order non-linear behavior of the
response data. In the case of highly non-linear
behavior of the response data, ANN was better than
other techniques. They also observed that the
Taguchi approach of S/N ratio might lead to non-
optimal solutions with less flexibility and the
conducting of needless experiments. Some recent
attempts have been made to control the laser drilled
hole taper through the development of drilling
techniques [7, 8]. Ng and Li [9] assessed the effect
of laser peak power and pulse width on the hole
geometry repeatability in Nd:YAG laser percussion
drilling of 2 mm thick mild steel sheets. Thirty-five
holes were drilled and analyzed for each set of
identical laser parameters. They found that higher
peak power and shorter pulse width gave better
hole geometry repeatability. The circularity of the
entrance hole ranged from 0.94 to 0.87, and was
found to correlate with repeatability.
Titanium and its alloys are most widely
used for different technologically advanced
industries such as aerospace, marine, chemical,
food processing and medical due to their superior
performance characteristics such as high strength
and stiffness at elevated temperatures, high strength
to weight ratio, high corrosion resistance, fatigue
resistance, and ability to withstand moderately high
temperatures without creeping [10]. The Ti-6Al-4V
is an alloy (grade 5) of Ti, has extensively used in
aerospace, marine, chemical processing, medical
and automobile sectors for making different
components such as airframes, fastener
components, vessels, cases, hubs, forgings, bone
plates, rods, expendable ribs cages, finger and toe
replacements, spinal fusion cages and dental
implants, pistons and piston rings. Ti and its alloys
cannot be cut easily by conventional cutting
methods due to their improved mechanical
properties, poor thermal conductivity, low elastic
modulus and high chemical affinity at elevated
temperatures. Due to the poor thermal conductivity
of these alloys, the heat generated during the
cutting cannot dissipated properly which results
very high temperature at the tool–work piece
interface and melting of the tool tip. Thus adversely
affects the tool life. Ti is chemically reactive at
elevated temperatures due to which the tool
material either rapidly dissolves or chemically
reacts during the cutting process, resulting
premature tool life [11]. The low elastic modulus of
Ti alloys permits greater deflection of workpiece
during machining and complexity of the machining
increases. While machining the Ti alloys, the
contact length between the tool and chip has been
found very small due to which high cutting
temperatures and high cutting stresses are
concentrated near the tool tip which results the
melting of tool tip and finally tool life reduces. Due
to the thermal plastic instability, the shear strains in

395 | P a g e
the chips are not uniform which promotes the
formation of serrated chips. These serrated chips
create fluctuations in the cutting force (generates
vibrational forces) which are responsible for sever
flank wear of cutting tools [12]. Thus there is a
crucial need for reliable and effective cutting
process for Ti and its alloys. Alternatively for the
cutting of these materials advanced cutting
processes such as Electric discharge machining,
ultrasonic machining, laser beam machining may
be used with some limitations. But for using these
advanced cutting methods, a lot of research work
has been required so that the required objectives
may be fulfilled by controlling different process
parameters.
Most of the previous works related to hole
drilling used the percussion drilling process where
with intense laser burst, the hole size was the size
of the beam that was varied by focusing. The
present study focuses on the alternative trepan
drilling. This paper reports the multi-objective
optimization of hole geometrical qualities such as
HT, CIRentry and CIRexit in the pulsed Nd:YAG
laser trepanning of Titanium alloy sheet. The
motivation for the investigation is the fact that
Titanium alloys being increasingly used in different
industries and engineers of these industries are
trying to obtain best qualities of these materials in
the laser drilling. In this investigation, Ti-6Al-4V
(Titanium alloy sheet grade 5) sheet has been
selected because it is known for its exceptional
performance characteristics and is one of the
mostly used Titanium alloys. Due to higher
material costs, the Ti alloys require such type of
drilling methods in which minimum wastage of
materials is obtained with satisfactory trepanned
qualities. But the reported research works show
that poor qualities are obtained by use of air or
nitrogen assist gases due to low thermal
conductivity and high chemical reactivity at
elevated temperatures. The use of costlier inert
gases may further increase the cutting cost.
Therefore, the aim of present research is to obtain
good quality of trepanned hole by using N2 as assist
gas. ANN has been applied for the modeling of HT,
CIRentry and CIRexit with the help of data obtained
by the L27 orthogonal array experimentation. The
hybrid approach of ANN, GA and GRA based
entropy measurement technique has been applied
for modeling and multi-objective optimization of
HT, CIRentry and CIRexit. The predicted optimum
results have been verified by confirmation tests.
2. EXPERIMENTAL SETUP AND DESIGN
OF EXPERIMENTS
The experiments have been performed on
200W pulsed Nd:YAG laser cutting system with
CNC work table supplied by SIL Pune, India. The
assist gas used is Nitrogen and it is passed through
a nozzle of 1 mm diameter, which remains constant
throughout the experiments. The focal length of the
lens is 50 mm and the standoff distance is 1 mm.
The Titanium alloy sheet (Ti-6Al-4V) of thickness
1.4 mm is used as work material. The chemical
compositions of the Ti-6Al-4V are shown in Table
1. Pulse width or pulse duration, pulse frequency,
assist gas pressure and cutting speed have been
selected as input process parameters (control
factors). An exhaustive pilot experimentation has
been performed in order to decide the range of each
control factors for complete through cutting. The
different control factors and their levels are shown
in Table 2. The quality characteristics or responses
selected for the analyses are HT, CIRentry and
CIRexit. 1 mm diameter holes are made with two
repetitions for the each experimental run. The hole
diameters at the entrance and exit were measured at
six orientations at an interval of 300
. Diameters are
measured by using optical microscope with 10X
magnification supplied by Radical instruments,
India. The HT, CIRentry and CIRexit were calculated
by following formula:
Hole taper  
   
t
dd exitfentrancef 
 ,
(Since α =tan α, for small value of α) Where
(df) entrance and (df) exit are mean Feret’s diameters at
the entrance and exit, respectively and (t) is the
drilled hole depth.
Circularity at entry/exit
where (df) Min and (df) Max are minimum and
maximum Feret’s diameters at entrance or exit side
of drilled hole.
The total number of experiments can be
substantially reduced with the help of a well
designed experimental plan without affecting the
accuracy during the experimental study of any
manufacturing process. Taguchi have suggested
that it is better to make the process robust rather
than equipments and machinery just by nullifying
the effects of variations through selection of
appropriate parameter level. Taguchi has suggested
properly designed experimental matrices known as
orthogonal arrays (OAs) to conducts the
experiments. In this present research work four
control factors with three levels of each have been
considered. Hence experiments can be performed

396 | P a g e
by using simplest L9 OA. But authors have selected L27 OA for high resolution factor [13].
Table 1: Composition of titanium alloy sheet (grade-5) (% volume)
Table 2: Control factors and their levels
3. METHODOLOGY
3.1. ARTIFICIAL NEURAL NETWORK (ANN)
ANN is information processing paradigm
inspired by biological nervous systems like our
brain. In neural network a large number of highly
interconnected processing elements (neurons) are
working together. Like people, they learn from
experience. In a biological system, learning
involves adjustments to the synaptic connections
between neurons; the same is true for ANNs [14].
In the network, each neuron receives total input
from all of the neurons in the preceding layer as
(1)
Where the total or net input and N is
are the numbers of inputs to the rth neuron in the
forward layer. is the weight of the connection
to the qth neuron in the forward layer from the rth
neuron in the preceding layer , is the input
from the rth neuron in the preceding layer to the
forward layer and the bias to qth neuron . A
neuron in the network produces its output ( )
by processing the net input through an activation
function Ғ , such as log sigmoid function and pure
linear function chosen in this study as below
(2)
&
(3)
In calculation of connection weights, often
known as network training, the weights are given
quasi-random initial values. They are then
iteratively updated until converges to the certain
value using the gradient descent method. Gradient
descent method updates weights so as to minimize
the mean square error between the network output
and the training data set. For simultaneous
optimization of more than one quality
characteristics, sometimes it is desirable to
normalize the quality characteristics. So the
training data set, i.e. the experimental values of
quality characteristics have been normalized using
following formula:
(4)
Where the normalized value of the kth
response is during ith observation, is the
maximum value of for the kth response.
3.2. GENETIC ALGORITHM (GA) FOR
OPTIMIZATION
Genetic algorithms (GA) are the global
optimization technique which is quite suitable for
non-linear optimization problems. GA is based on
the Darwin’s principle of “survival of fittest” .The
algorithm starts with the creation of random
population. The individual with best fitness are
selected to form the mating pair and then the new
population is created through the process of cross-
over and mutation. The new individuals are again
tested for their fitness and this cycle is repeated
until some termination criteria are satisfied [14].
3.3 GREY RELATIONAL ANALYSIS (GRA)
A common difficulty with multi-objective
optimization is the appearance of an objective
conflict; none of the feasible solution allows
simultaneous optimal solution for all objectives.
The individual optimal solutions of each objective
are usually different. To get the solution of multi-
objective optimization problem, using classical
methods, all the objectives are converted into
single objective function. There are many methods
of transforming multi-objective optimization
problem into single objective optimization problem
and objective weighting method is one of the
popular methods. In objective weighting method,
multi-objective functions are combined into one
overall objective function by assigning different
weigh to different objective [15]. The
determination of weight is a critical aspect, which
sometimes is decided by designer’s experience or
some mathematical techniques. In this study, the
GRA coupled with entropy measurement technique
[16] has been used to find the weight of each
quality characteristics for multi-objective
Al Fe Sn V Ti
6.22 0.187 0.56 3.35 89.6
Symbol Factors Level 1 Level 2 Level 3
X1 Pulse width (ms) 0.8 1.2 1.6
X2 Pulse frequency (Hz) 13 17 21
X3 Gas pressure (kg/cm2
) 6 8 10
X4 Trepanning speed (mm/s) 0.1 0.2 0.3

397 | P a g e
optimization. The working of the GRA and entropy
measurement technique has been explained with
the help of block diagram in Fig. 2.
Fig. 2: Block diagram for GRA and Entropy measurement technique
The normalized value of the quality characteristics have been calculated using Eqs. (4), and have been shown in
the Fig.3.
4. MODELING
The optimal neural network architecture
used for normalized hole taper (NHT), normalized
circularity at entry (NCIRentry) and normalized
circularity at exit (NCIRexit) is shown in Fig. 4. The
network for all three NHT, NCIRentry and NCIRexit
consists of one input, one hidden and one output
layer. The input and output layers have four and
one neuron respectively. The neurons in input layer
are corresponded to Pulse width, Pulse frequency,
Gas pressure and Trepanning speed. Output layer
corresponds to NHT, NCIRentry and NCIRexit. The
hidden layer has five neurons in case of all. The
activation function used for the hidden layer and
output layer was log sigmoid and pure linear
respectively. In this work, a commercially available
software package MATLAB was used for the
training of ANN .The values of the weights, and
biases, after network getting fully trained are
shown in the Table 3 for all the NHT, NCIRentry and
NCIRexit.
0
0.2
0.4
0.6
0.8
1
1.2
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Normalizedvalues
Experiment Number
Experimental values for NHT
Experimental values for
NCIRentry
Experimental values for
NCIRexit
Input layer
Hidden layer
X1
X2
X3
X4
Output layer
wqr bq
NHT/ NCIRentry/
NCIRexit
Normalization of
data
Calculation of grey
relational coefficient
Calculation of the sum of the
grey relational coefficient
Evaluation of the
normalized coefficient
Calculation of the entropy of
each quality characteristics
Calculation of the sum
of entropy
Calculation of the weight of
each quality characteristic
Fig. 4: Architecture of artificial neural network for NHT, NCIRentry
and NCIRexit
Fig. 3: Normalized values of quality characteristics

398 | P a g e
Table 3: Final values of Weights and Biases for NHT, NCIRentry and NCIRexit
So, in the mathematical form, the ANN model for
NMRR can be represented as follows:
NHT/NCIRentry/NCIRexit (5)
Where and corresponded to weight and
bias to output layer and is the net input to the
output layer from hidden layer and it is given by,
q=1, 2… 5
The results of the experimental data and neural
network predicted data for NHT, NCIRentry and
NCIRexit have been compared in the Table 4. It is
evident that ANN prediction is in good agreement
with the experimental results. It is found that ANN
with mean square error of 0.000037%, 0.0000186%
and 0.000125% respectively, appears to constitute
a workable model for predicting the characteristics
under given set of input parameters for LTD.
The values of , , and are shown in Table 3.
I: Experiment No. II: Pulse width III: Pulse frequency IV: Gas pressure
V: Trepanning speed VI: Experimental Hole taper VII: Experimental Circularity VIII:
Experimental Circularity
at entry at exit
IX: ANN predicted Hole taper X: ANN predicted Circularity XI: ANN predicted Circularity XII: % error
in prediction of
at entry at exit Hole taper
XIII: % error in prediction of XIV: % error in prediction of
Circularity at entry Circularity at exit
Table 4: Comparison of ANN predicted result with the experimental result for NHT, NCIRentry and NCIRexit
I II III IV V VI VII VIII IX X XI XII XIII XIV
1 0.500 0.619 0.600 0.333 0.433 0.914 0.966 0.433 0.914 0.952 0.055 0.005 1.468
2 0.500 0.619 0.800 0.667 0.736 0.927 0.942 0.736 0.927 0.952 0.051 0.005 1.096
3 0.500 0.619 1.000 1.000 0.992 0.973 0.963 0.991 0.973 0.961 0.027 0.004 0.150
4 0.500 0.810 0.600 0.667 0.539 0.902 0.970 0.539 0.902 0.971 0.079 0.003 0.100
5 0.500 0.810 0.800 1.000 0.691 0.910 0.955 0.691 0.910 0.955 0.049 0.004 0.033
Weights to hidden layer from
input layer
Bias to
hidden
layer
Weights to output layer
Bias to
output
layer
NHT [122.7035 -28.3073 16.9694 -
33.6773;
-4.8487 -22.6453 -32.7136 -
10.3398;
2.8113 -2.9929 5.8978 0.53677;
3.9119 3.3126 0.68229 0.29932;
-2.7571 2.4243 -5.7577 -0.61036]
[-
81.9011;
58.7437;
-1.1352;
-4.0345;
0.56399]
[0.33548 -0.44801 -43.5783 -2.3246 -
105.1382]
[46.4105
]
NCIRentry [-3.0176 -4.1509 60.4266 -
0.77578;
1.0815 6.3481 1.2684 1.7164;
-1.1774 -6.0712 -1.3746 -1.6547;
41.2793 -1.1825 8.5567 -34.2151;
5.5617 -56.9911 1.8769 2.2187]
[-
29.6378;
-8.1871;
8.1269;
-3.1741;
51.2141]
[-0.094972 -4.8731 -5.0107 -0.046963 -
0.074669]
[6.129]
NCIRexit [19.7725 6.0393 -7.3166 -1.7965;
0.26041 67.3029 -70.1356
78.0474; -45.1386
185.994 64.4417 66.0488;
-57.4946 0.24336 0.11946 -
0.53196;
20.0861 -59.1983 24.6627 -
61.9418]
[-13.606;
-9.8892;
-225.056;
64.2284;
64.7269]
[-0.074678 0.047406 -0.045112 -66.1898 -
0.048632]
[67.1431
]

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6 0.500 0.810 1.000 0.333 0.584 0.914 0.935 0.584 0.914 0.935 0.001 0.095 0.004
7 0.500 1.000 0.600 1.000 1.000 0.971 0.954 1.000 0.971 0.954 0.000 0.002 0.043
8 0.500 1.000 0.800 0.333 0.703 0.902 0.904 0.704 0.902 0.906 0.038 0.001 0.201
9 0.500 1.000 1.000 0.667 0.900 0.942 0.942 0.899 0.942 0.943 0.043 0.003 0.055
10 0.750 0.619 0.600 0.667 0.337 0.935 0.927 0.338 0.935 0.926 0.015 0.003 0.132
11 0.750 0.619 0.800 1.000 0.372 0.956 0.960 0.371 0.956 0.961 0.116 0.000 0.121
12 0.750 0.619 1.000 0.333 0.437 0.957 0.901 0.437 0.958 0.901 0.002 0.069 0.001
13 0.750 0.810 0.600 1.000 0.437 0.952 0.962 0.436 0.952 0.964 0.181 0.006 0.117
14 0.750 0.810 0.800 0.333 0.293 0.919 0.919 0.292 0.918 0.921 0.398 0.113 0.176
15 0.750 0.810 1.000 0.667 0.670 0.944 0.921 0.670 0.943 0.922 0.067 0.110 0.120
16 0.750 1.000 0.600 0.333 0.555 0.937 0.884 0.555 0.937 0.884 0.038 0.002 0.003
17 0.750 1.000 0.800 0.667 0.696 0.925 0.902 0.696 0.925 0.901 0.011 0.002 0.160
18 0.750 1.000 1.000 1.000 0.668 0.985 0.946 0.669 0.985 0.945 0.165 0.001 0.105
19 1.000 0.619 0.600 1.000 0.335 0.974 1.000 0.335 0.974 0.999 0.009 0.006 0.090
20 1.000 0.619 0.800 0.333 0.517 0.961 0.947 0.518 0.960 0.947 0.179 0.061 0.001
21 1.000 0.619 1.000 0.667 0.710 1.000 0.979 0.710 1.000 0.978 0.021 0.000 0.094
22 1.000 0.810 0.600 0.333 0.513 0.969 0.949 0.514 0.969 0.949 0.222 0.002 0.049
23 1.000 0.810 0.800 0.667 0.526 0.946 0.960 0.526 0.947 0.962 0.093 0.124 0.267
24 1.000 0.810 1.000 1.000 0.834 0.980 0.967 0.834 0.980 0.968 0.006 0.010 0.100
25 1.000 1.000 0.600 0.667 0.656 0.991 0.986 0.656 0.991 0.986 0.007 0.000 0.015
26 1.000 1.000 0.800 1.000 0.664 0.970 0.978 0.665 0.971 0.977 0.107 0.009 0.069
27 1.000 1.000 1.000 0.333 0.914 0.977 0.904 0.913 0.977 0.903 0.186 0.003 0.152
5. MULTI OBJECTIVE OPTIMIZATION
Using GRA coupled with entropy
measurement, the weight for NHT, NCIRentry and
NCIRexit have been found as 0.33, 0.33 and 0.34
respectively. Now the multi-objective optimization
problem can be transformed into single objective
optimization problem. In the present case, both the
objective functions are of conflicting nature
because the aim is to maximize HT the and
minimize the NCIRentry, NCIRexit. Thus, the
objective function of optimization problem can be
stated as below:
Find: X1, X2, X3 and X4
Minimize:
(6)
Where = 0.33, 0.33 and = 0.34 NHT,
NCIRentry and NCIRexit Eq. (5) ,with range of
process input parameters:
0.8≤ ≤1.6
13≤ ≤21
6≤ ≤10
0.1≤ ≤0.3
The critical parameters of GA are the size
of the population, cross-over rate, mutation rate,
and number of generations. After trying different
combinations of GA parameters, the population
size 20, cross-over rate 0.8, mutation rate 0.01 and
number of generation 40, have been taken in the
present study. The objective function in Eq. (6) has
been solved without any constraint. The
generation-fitness graphics have been shown in the
Fig.5. The fitness function is optimized when the
mean curve converges to the best curve after 7
generation. The corresponding values of Pulse
width, Pulse frequency, Gas pressure and
Trepanning speed have been found as1.3 ms, 17
Hz, 8 kg/cm2
and 0.2 mm/s.

400 | P a g e
Fig. 5: The generation-fitness graphics
6. DISCUSSION
Achieving a good compromise between
objective functions in multi-objective optimization
problem is a big challenge due to existence of
multiple solutions, known as Pareto-optimal
solutions. To overcome it, in the present work,
weights for each quality characteristics have been
calculated first, to get optimal solution.
7. CONCLUSIONS
The multi-objective optimization of laser
trepan drilling of Ti-6Al-4V using hybrid approach
of artificial neural network, genetic algorithm and
grey relational analysis with entropy measurement
technique has been done. Following conclusions
have been drawn on the basis of results obtained:
(1) The developed models for HT, CIRentry and
CIRexit, with mean square error of 0.000037%,
0.0000186% and 0.000125% respectively, are well
in agreement with the experimental result.
(2) The optimum levels of control factors are Pulse
width, Pulse frequency, Gas pressure and
Trepanning speed have been found as 1.3 ms, 17
Hz, 8 kg/cm2
and 0.2 mm/s respectively.
(3) Validation has been performed in order to
verify the result, which shows a good agreement
between the optimized and experimental result.
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