Modeling and optimization of cutting parameters in high speed dry machini

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME
242
MODELING AND OPTIMIZATION OF CUTTING PARAMETERS IN
HIGH-SPEED DRY MACHINING OF INCONEL 718 ALLOY
B.Satyanarayanaa
, G. Ranga Janardhanab
and D. Hanumantha Raoc
a
Department of Mechanical Engineering, VNR Vignana Jyothi Institute of Engineering &
Technology, Hyderabad, India,
b
Director, Foreign University Relations, J N T U, Kakinada, India,
c
Principal, Matrusri Engineering College, Hyderabad, India,
ABSTRACT
The aim of this research paper is to develop mathematical model and optimize the
machining conditions during high speed dry turning of nickel based super alloy Inconel 718
with coated tungsten-carbide tool insert. Surface roughness(SR) is considered as a
performance measure. The effectiveness of experimental values and the effect of input
process parameters such as cutting speed, feed rate and depth of cut on the performance
measure were determined by multiple regression analysis with the use of analysis of variance
(ANOVA). Based on the experimental results, second order surface roughness mathematical
model was developed in terms of input process parameters. The developed mathematical
model is used as an objective function in Genetic Algorithm (GA) to determine the optimal
parameter values that gives minimum SR. The GA predicted value is confirmed with that of
experimental value.
Keywords: Inconel 718, High Speed Machining, Multiple Regression Analysis,
Genetic Algorithm.
1. INTRODUCTION
Among the nickel based heat resistant super alloys (HRSA), Inconel 718 is the most
extensively used alloy [1], principally because it maintains excellent mechanical properties
and is corrosion resistant over a wide temperature range (−250 to 705 °C) [2]. This alloy
exhibit high strength to weight ratio, high resistance to corrosion, erosion, and wear and are
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243
also capable of retaining their mechanical properties such as hardness at elevated
temperatures relative to steel and stainless steel alloys [3].
In any machining operation, it is an important task to select cutting parameter values
for achieving high-quality cutting performance [4]. Increase in productivity and reduction in
costs could be achieved with optimum selection of cutting conditions. [5]. A good
understanding of the behaviour and the relationship between the work piece material, cutting
tool material, cutting conditions and the process parameters is an essential requirement for the
optimization of the cutting process [6].
Recently, the use of higher cutting speeds has shown promise in the reduction in
cutting forces and less use of coolant and thus improving the machined surface quality to
some extent [7, 8]. Thus, high- speed dry machining is expected to provide a suitable
technology for the bulk material removal in machining of the aerospace components of this
material. In this context, it is important to understand the cutting temperature, tool wear and
the mechanics at higher cutting speeds, which govern the quality and integrity of machined
surfaces [9–11].
2. LITERATURE SURVEY
D.G. Thakur et. al. [12] measured the surface roughness in high speed dry machining
of Inconel 718 using carbide tool inserts(K20). They found that the surface finish was found
to be optimum in the cutting range of 45–55 m/min for the feed rate of 0.08 mm/rev and 0.5
mm and also observed the grain deformation and refinement after machining. Taguchi S/N
ratio was used to find the optimal cutting conditions.
M.Z.A.Yazid et. al. [13] reported the results of an experimental works on surface
integrity during finish turning of Inconel 718, under three cutting conditions (DRY, MQL 50
mL/h and MQL 100 mL/h). The parameter ranges are: cutting speed (90-150 m/min), feed
rate (0.1-0.15 mm/rev) and cutting depth (0.3 to 0.5 mm. The results of this study show that
MQL possibly improve the surface integrity characteristics.
A. Devillez et. al. [14] focused on the effect of dry machining of Inconel 718 on
surface integrity with semi-finished cutting conditions using a triangular shaped coated
carbide tool insert. The observation is the surface quality is effected by the deposition of parts
of built up edge to the machined surface; this is due to the higher temperatures generated.
V. Bushlya et.al. [15] presented the results of superalloy machinability study on
surface integrity of Inconel 718 with uncoated and coated PCBN round tools under wet
cutting environment aiming on increased speed and efficiency. The parameters are: speed
(250-350m/min), feed rate (0.1-0.2 mm/rev) and depth of cut constant at 0.3mm. The finding
was the surface roughness has higher values for coated tools as a result of increased edge
radius.
Sahoo.P, [16] has successfully applied Response Surface Methodology (RSM) and
Genetic Algorithm (GA) to optimize turning parameters for surface roughness during
machining of AISI 1040 mild steel. The developed models through RSM shows good
agreement with the experimental results. The optimal parameters obtained through GA
matches with the confirmatory test results.
The literature reveals that, there is a scope for optimizing the cutting conditions
during high speed dry turning of Inconel 718 with coated carbide tool using regression
analysis and Genetic Algorithm. Hence, in the present study, second order mathematical
model was developed using multiple regression analysis for surface roughness and the

244
developed model is used to find the optimal cutting parameters using GA during high speed
dry machining of Inconel 718 using coated carbide tool. The surface roughness obtained with
the optimal conditions obtained from GA, was verified with that of measured values from
experiments for the feasibility of optimization process.
3. METHODOLOGY
A multiple regression analysis using analysis of variance (ANOVA) is conducted to
determine the performance of experimental measurements and to show the effect of cutting
parameters on the response. By using the experimental results, the second-order mathematical
model in terms of cutting parameters are developed for the response with the help of
Response Surface Methodology (RSM). The developed mathematical model was used as an
objective function and the optimization was carried out with the help of Genetic Algorithm.
3.1 Mathematical formulation
Response Surface methodology (RSM) is a collection of mathematical and statistical
techniques useful for developing, improving and optimizing processes [17]. This is
extensively used in the environment where a number of input variables influence the
response, with the aim to establish the relationship between response and independent
variables (input variables). In general the relationship is represented by:
y = f (VC, f ,d) + ε (1)
where y is the machining response, f is the response function and VC, f and d are turning
variables and ε is the statistical error which is often assumed to be normally distributed about
the observed response y with mean zero. The relationship between the response variable
surface roughness Ra, and the independent variables can be represented as:
Ra = C (VC)a
f b
dc
(2)
where C represents constant and a, b and c represents exponents.
To assist the determination of exponents and constants, the mathematical model has to be
linearized by applying logarithmic transformation. This can be represented as:
ln( Ra) = lnC + a ln VC +b ln f +c ln d (3)
The second order polynomial model developed from the equation (3) using method of least
squares, can be represented as:
y2 =y - ε= b0 x0 + b1 x1 + b2 x2 + b3 x3 + b12 x1 x2 + b23 x2 x3 + b31 x3 x1 + b11 x1 x1 + b22 x2 x2
+b33 x3 x3
(4)
where y2 is the estimated response based on the second order polynomial equation. y
is the measured response on a logarithmic scale, x0 =1, x1, x2 and x3 are logarithmic
transformations of cutting speed, feed rate and depth of cut respectively, ε is the experimental
error and 'b' values are to be estimated by the method of least squares.

245
3.2 Optimization by Genetic Algorithm (GA)
Optimization problems can be effectively solved by a powerful and robust tool,
Genetic Algorithm (GA) [18]. GA performs a multi directional search by maintaining a
population of potential solutions and encourages information formation and exchange
between these directions. The population undergoes a simulated evolution: at each generation
the relatively “good "solutions reproduce, while the relatively “bad” solutions die. To
distinguish between different solutions it has been used an objective (evaluation) function
which plays the role of an environment [19].
4. EXPERIMENTAL DETAILS
4.1 Design of experiment
The design of experiments technique is a vital tool, which allow us to carry out the
modeling and analysis of the influence of input process variables on the response. In the
present study, the controllable turning parameters such as cutting speed, feed rate and depth
of cut are considered as design factors. The range of values of each factor was set at three
different levels based on the available machining data on Inconel 718 from hand books,
literature and from preliminary experimentation as shown in Table 1. A full factorial design
(L27 orthogonal array) is used to design factors to increase the accuracy of the developed
model.
Table. 1 Process parameters and their levels
Parameters
Levels
1 2 3
Cutting speed, VC (m/min) 50 65 80
Feed, f (mm/rev) 0.05 0.125 0.2
Depth of cut, d (mm) 0.2 0.4 0.6
4.2 Work material, equipment and cutting tool used
The work material used was Inconel 718 rod (Ni = 54.48 %, Cr = 17.5%, Nb = 4.9%,
Al = 0.66 %, Ti = 0.96% balance are Fe and other). The machine used for turning tests is a
ACE make CNC Super jobber 500 turning centre with 12 kW motor. For generating the
turned surfaces, CNC part programs for tool paths were created with specific commands.
The surface roughness of a machined surface was recorded using Mitutoyo make
standard profilometer SJ 301. As per the ISO 3685 standards, surface roughness of arithmetic
average roughness, Ra (µm) was recorded. The sampling length used was 0.8mm.
Sandvik make SNMG 120408 coated carbide tool was used in the experimentation.
The working tool geometry in combination with tool holder and insert is given in Table 2.
For each machining experiment, a new cutting edge was used. Readings are taken at least
twice and the average values are considered.
Table 2: Working tool geometry
Orthogonal
rake angle
(γ)
Orthogonal
Clearance
angle (α)
Inclination
angle (λ)
Auxiliary
cutting
edge
angle
Approach
angle (ψ)
Included
angle (β)
Nose
radius
(r) mm
-6 °
6°
-6°
15°
75°
90°
0.8

246
5. RESULTS AND DISCUSSION
From the experimental results, the unknown regression coefficients were determined
through Design expert software and empirical equation has been obtained to estimate surface
roughness (Ra) with the input process parameters considered i.e. cutting speed, feed rate and
depth of cut. The second-order polynomial equations for the response variable surface
roughness (Ra) is expressed as
222
0556.09383.120012.0
5.10053.00089.07056.01383.01677.09062.5
)(
dfV
dfdVfVdfV
RRoughnessSurface
c
ccc
a
−+
++−++−−+
=
(5)
5.1 Model accuracy and significance of the individual model coefficients
Analysis of variance(ANOVA) is conducted to check the model accuracy and to know
the significance of individual coefficients shown in Table 3. The Table 3 shows that the
regression model, cutting speed, feed, depth of cut, higher order terms of speed and feed are
significant which influence the surface roughness (Ra) as their p-values are less than that of a
significance level of α = 0.05.
Multiple regression correlation coefficients R2
for the second order polynomial
model was quite satisfactorily as
R2
= 97.5% R2
(pred) = 93.2% R2
(adj) = 96.24%
Table 3 Analysis of Variance (ANOVA) for surface roughness (Ra)
After eliminating the insignificant coefficient terms, the equation (5) is modified as:
22
9383.120012.07056.01383.01677.09062.5
)(
fVdfV
RRoughnessSurface
cc
a
+++−−+
=
(6)
The normal probability plot of the residuals for the surface roughness is shown in Fig
1. It shows that the residuals are placed on a straight line, indicates that the errors are
Source Sum of
Squares
DF Mean square F
Value
p-value
Prob > F
Model 3.51 9 0.39 75.79 < 0.0001 Significant
Vc 1.02 1 1.02 197.94 < 0.0001
F 1.84 1 1.84 357.27 < 0.0001
D 0.19 1 0.19 36.58 < 0.0001
Vc x f 8.333E-004 1 8.333E-004 0.16 0.6923
Vc x d 2.408E-003 1 2.408E-003 0.47 0.5029
f x d 5.208E-003 1 5.208E-003 1.01 0.3283
Vc x Vc 0.42 1 0.42 82.30 < 0.0001
f x f 0.033 1 0.033 6.37 0.0218
d x d 7.407E-006 1 7.407E-006 1.441E-
003
0.9702
Residual 0.087 17 5.141E-003
Total 3.59 26

247
distributed normally and the developed model is fairly well fitted with the experimental
values.
Fig. 1 Probability plot of the residuals
The variation of experimental surface roughness (Ra) values with the predicted values
obtained from equation (6) is shown in the Fig. 2. It was seen that predicted and experimental
values follows the close path which shows the adequacy of developed model.
Fig. 2. Comparison of experimental results and predicted values for surface roughness
5.2 Validation of the model
Additional experiments were conducted to check the accuracy of the developed model
with the different input process parameter values selected randomly are shown in Table 4.
The experimental and model values with percentage error is shown in Table 5. The
percentage error associated with each experiment is observed to be less than 3%. The
experimental values and predicted values are close together, which indicates the suitability of
the developed model.

248
Table 4 Cutting conditions for validation of model
Test
No
Cutting Speed (Vc)
(m/min)
Feed (f)
(mm/rev)
Depth of cut (d)
(mm)
1 60 0.08 0.25
2 75 0.15 0.45
3 60 0.1 0.5
4 75 0.175 0.3
Table 5 Validation test results
Test No
surface roughness (Ra)
Model value Experiment value % Error
1 0.311012 0.32 2.808
2 0.538038 0.53 1.513
3 0.498248 0.51 2.304
4 0.592528 0.61 2.864
Mean 2.37
5.3 Effect of Cutting parameters on surface roughness
Surface plots have been drawn using Design expert software for the convenience of
understanding the effect of cutting parameters on the response and selecting the best
combinations of cutting parameters. The surface roughness variation for different
combinations of cutting parameters are shown in Fig. 3.
The surface roughness variation with cutting speed and feed rate at 0.4mm depth of
cut is shown in Fig. 3 (a). It shows that, the surface roughness is increasing greatly with
increase in feed than decrease in cutting speed. It was also observed that feed has more effect
on surface roughness than other control factors. The combination of low feed rate and high
speed gives better surface finish.
The effect of feed rate and depth of cut at a speed of 50m/min on surface roughness is
shown in Fig. 3 (b). It was observed that, surface roughness is better at low values of feed
rate and depth of cut. Surface roughness is increasing with the increase of feed and depth of
cut.
The effect of cutting speed and depth of cut at a feed rate of 0.125 mm/rev on surface
roughness is shown in Fig. 3 (c). It was found that, at lower value of depth of cut and higher
value of cutting speed, the surface roughness is minimum.

249
(a) (b)
(c)
Fig. 3 Surface plots of speed, feed and depth of cut
6. OPTIMIZATION THROUGH GA
The model would be optimized using GA optimization tool in MATLAB software
[20]. In this context an effort has been made to optimize the process variables that produce
the best possible output parameter value within the assumed variable bounds. The
optimization problem consists of a minimization function defined by the second order
equation given by (6) and the following variable bounds.
50 m/min ≤ x1 ≤ 80 m/min
0.05 mm/rev ≤ x2 ≤ 0.2 mm/rev
0.2 mm ≤ x3 ≤ 0.6 mm
xil ≤ xi ≤ xiu
where xil and xiu are the lower and upper bounds of process variables xi and x1, x2, x3 are
logarithmic transformation of cutting speed, feed rate and depth of cut.
The main parameters of the GA are the mutation, population size, number of generations and
cross over function. In the present study, population size 100, adaptive feasible mutation, two
point crossover function and number of generations 500 are judiciously taken. The
convergence of GA to the minimum objective function value for the optimization problem is
shown in Fig. 4. The results found by GA are compared with those obtained from
conformation experiments and given in Table 6. They show fairly good agreement with each
other.
Table 6. Optimization results
Output parameters
Cutting parameters Predicted
value
(GA)
Experiment
al value
Vc
(m/min)
f
(mm/rev)
d
(mm)
Surface roughness (µm) 70 0.05 0.2 0.133 0.13

250
Fig. 4. Convergence graphs of GA for the optimization problems
It can be justified that, the surface roughness is directly proportional to the square of
feed rate [21]. At higher speeds the formation of built up edge (BUE), if any, disappears and
observed improved surface finish. Therefore, the surface roughness is low at higher speeds
and lower feed rates and depth of cuts. The same phenomenon was observed in high speed
dry turning of Inconel 718 with coated cemented carbide tools.
7. CONCLUSIONS
A mathematical model based on experimental results was developed for
obtaining a surface roughness using the response surface methodology. The
predicted values of the surface roughness from the model are compared with
the values obtained experimentally and found a good closeness between them.
The surface roughness is increasing greatly with increase in feed than decrease
in cutting speed. Feed shows more effect on surface roughness than other
control factors. The combination of low feed rate and high speed are giving
better surface finish.
Surface roughness is better at low values of feed rate and depth of cut.
At lower value of depth of cut and higher value of cutting speed, the surface
roughness was observed minimum.
The optimal cutting conditions were obtained for the best possible values of
surface roughness during high speed turning of Inconel 718 through GA.
Confirmation experiment results, when machining with optimal cutting
conditions, shows good agreement with the predicted values obtained from
GA.
0 20 40 60 80 100
0.1
0.2
0.3
0.4
0.5
0.6
Generation
Surfaceroughnes
Best: 0.13351 Mean: 0.13357
Best fitness
Mean fitness

251
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