OPTIMIZATION OF SURFACE ROUGHNESS, CIRCULARITY
DEVIATION AND SELECTION OF DIFFERENT ALLUMINIUM ALLOYS DURING DRILLING FOR
AUTOMOTIVE AND AEROSPACE INDUSTRY
Reddy Sreenivasulu
R.V.R&J.C College of Engineering (A), India
E-mail: rslu1431@gmail.com
Chalamalasetti SrinivasaRao
College of Engineering (A), Andhra University, India
E-mail: csr_auce@yahoo.co.in
Submission:
08/12/2015
Revision: 19/12/2015
Accept: 24/12/2015
ABSTRACT
This paper presents the influence of cutting parameters like cutting
speed, feed rate, drill diameter, point angle and clearance angle on the
surface roughness and circularity deviation of Alluminium alloys during drilling on CNC vertical machining center. A plan of experiments
based on Taguchi method has been used to acquire the data. An orthogonal array,
signal to noise (S/N) ratio and analysis of variance (ANOVA) are employed to
investigate machining characteristics of Alluminium alloys using HSS twist drill bits of variable tool geometry and maintain
constant helix angle of 45 degrees. Confirmation tests have been carried out to
predict the optimal setting of process parameters to validate the
proposed approach and obtained the values 3.7451µm, 0.1076 mm for surface roughness and circularity deviation respectively. Finally, the output
results of Taguchi method fed as input to the AHP and TOPSIS. The results
generated in both AHP and TOPSIS suggests the suitable alternative of aluminum
alloy, which results in better surface roughness and less error in circularity.
Keywords: Alluminium Alloys, Drilling, Taguchi
method, S/N ratio, ANOVA, AHP, TOPSIS
1. INTRODUCTION
The surface quality is an important
parameter to evaluate the productivity of machine tools as well as machined
components. Hence, achieving the desired surface quality is of great importance
for the functional behavior of the mechanical parts. A reasonably good surface
finish is desired for improving the tribological properties, fatigue strength,
corrosion resistance and aesthetic appeal of the product.
Excessively better surface finish
may involve more cost of manufacturing. The surface roughness and roundness
error are affected by several factors including cutting tool geometry, cutting
speed, feed rate, the microstructure of the work piece and the rigidity of the
machine tool. These parameters affecting the surface roughness and drilled hole
qualities (roundness, cylindricality and hole diameter) can be optimized in
various ways such as Taguchi method.
A number of Researchers have been
focused on an appropriate prediction of surface roughness and roundness error.
The Taguchi method has been widely used in engineering analysis and is a
powerful tool to design a high quality system. Moreover, the Taguchi method
employs a special design of orthogonal array to investigate the effects of the
entire machining parameters through the small number of experiments.
Baychi et al. (1993) and Phadke
(1989) discussed the application of Taguchi method in several industrial
fields, and research works in their text books. By applying this Taguchi technique,
the time required for experimental investigations can be significantly reduced,
as it is effective in the investigation of the effects of multiple factors on
performance as well as to study the influence of individual factors to determine
which factor has more influence, which one less.
Chen and Hwang (1992) mentioned in their
lecture notes applicability of fuzzy techniques in decision making systems.
Korkut et al. (2010) also applied
Taguchi method to determine circularity deviation in bored hole experimentally.
Yang and Chen (2001) used the Taguchi parameter design in order to identify
optimum surface roughness performance on an aluminum material with cutting
parameters of depth of cut, cutting speed, feed rate and tool diameter. It was
found that tool diameter is not a significant cutting factor affecting the
surface roughness.
Davim and Reis (2003) presented an
approach using the Taguchi method and ANOVA to establish a correlation between
cutting speed and feed rate with the de lamination in a composite laminate. A
statistical analysis of hole quality was performed by Furness, Wu and Ulsoy
(1996). They found that feed rate and cutting speed have a relatively small
effect on the measured hole quality features. With the expectation of hole
location error, the hole quality was not predictably or significantly affected
by the cutting conditions.
Tsao and Hocheng (2008)
performed the prediction and evaluation of thrust force and surface roughness
in drilling of composite material. The approach used Taguchi and the artificial
neural network methods. The experimental results show that the feed rate and
the drill diameter are the most significant factors affecting the thrust force,
while the feed rate and spindle speed contribute the most to the surface
roughness.
Yang and Chen (2001) performed a
study of the Taguchi design application to optimize surface quality in a CNC
face milling operation. Taguchi design was successful in optimizing milling
parameters for surface roughness.
Nalbant, Gokkaya and
Sur (2007) utilized the Taguchi technique to determine the optimal cutting
parameters for surface roughness in turning of AISI 1030 steel with Ti N coated
inserts.
Risbood et al. (2003)
also applied Taguchi Method to predict the surface roughness and dimensional
deviations experimentally.
Three cutting parameters such as
insert radius, feed rate, and depth of cut, are optimized for minimum surface
roughness. Kurt, Bagci and Kaynak (2009) employed the Taguchi method in the
optimization of cutting parameters for surface finish and hole diameter
accuracy in dry drilling processes. The validity of the Taguchi approach to
process optimization was well established.
The objective of this study is to investigate
the effects of the drilling parameters on surface roughness and circularity
error, and is to determine the optimal drilling parameters using the Taguchi
method later the results fed to multiple attributes in decision making
techniques (AHP and TOPSIS) are applied to optimal selection of Aluminum alloys
during drilling process.
1.1.
Multi-Attribute
Decision Making Technique:
Decision making is the study of
identifying and choosing alternatives based on the values and preferences of
the decision maker. Making a decision implies that there are alternative
choices to be considered, and in such a case, not only as many of these
alternatives as possible are identified but also the best one is chosen to meet
the decision maker’s goals, objectives, desires, and values.
Thus, every decision making process
produces a final choice. The selection decisions are complex, as decision
making is more challenging now a days. For obtaining the best decision in
conjunction with the real-time requirements, a number of MADM approaches are
available. MADM methods (OLSON, 2004; SAATY, 2000) are generally discrete, with
a limited number of pre-specified alternatives.
These methods require both intra and
inter-attribute comparisons, and involve explicit tradeoffs that are appropriate
for the problem considered. Most commonly used MADM approaches (YOON et al.,
1995) are weighted sum method (WSM), weighted product method (WPM), Analytic
hierarchy process (AHP), Technique for order preference by similarity to ideal
solution (TOPSIS), and Compromise ranking method (VIKOR), Graph theoretic
approach (GTA).
The main objective of this paper is
to explore the basic concepts of MADM methods. From the literature it is clear
that Analytic hierarchy process (AHP), Technique for order preference by
similarity to ideal solution (TOPSIS) approach as a decision making method is
relatively new, and offers a generic, simple, easy, and convenient decision
making method that involves less computation.
1.2.
Back
ground of Aluminum Alloys:
At present, alluminium is used in
the aviation industry everywhere in the world. The casing of the first Soviet
satellite was made of aluminum alloys. The body casing of American ‘Avant-garde’
and ‘Titan’ rockets used for launching the first American rockets into the
orbit, and later on – spaceships, was also made of aluminum alloys.
They are used for manufacturing
various components of spaceship equipment: brackets, fixtures, chassis, covers
and casing for many tools and devices. Alluminium alloys have a certain advantage
for creating space equipment units. High values of specific strength and the
specific rigidity of the material enabled the tanks, inter-tank and casing of
the rocket to be manufactured with high longitudinal stability.
The advantages of alluminium alloys
also include their high performance under cryogen temperatures in contact with
liquid oxygen, hydrogen, and helium. The so-called cryogen reinforcement
happens in these alloys, i.e. the strength and flexibility increase parallel to
the decreasing temperature. Engineers and manufacturers never cease to study
the properties of alluminium, developing more and more new alloys for
construction of aircraft and spaceships. 2xxx, 5xxx, 6xxx, and 7xxx series
alloys are widely used in automotive and aviation industries.
2. Experimental Procedure:
2.1.
Material
Alluminium 2014, 6069, 6061, and 7075 alloys used in the
aircraft and automotive components, marine fittings, bicycle frames, camera
lenses, brake components, electrical fittings and connectors, valves, couplings
etc.
The composition of Alluminium
alloy 2014 consists of Chromium:
0.1%, Copper:
3.9% - 5%, Iron:
0.5% ,Magnesium:
0.2% - 0.8%,Manganese:
0.4 - 1.2%, Silicon:
0.5% - 0.9Titanium:
0.15%, Titanium :
0.2% Zinc:
0.25% and remaining is alluminium.
The composition of Alluminium Alloy
6069 consists of Magnesium (Mg) 1.2 - 1.6%, Si 0.6 - 1.2%, Copper 0.55 - 1.0%,
Vanedium 0.1 - 0.3 %, Cr 0.05 - 0.3%, Titanium- 0.1% , Iron - 0.4%, Manganese - 0.05%, Zinc - 0.05%, Strancium - 0.05%.
The composition of Alluminium alloy
6061consists of 0.63% Silicon, 0.096% Copper, 0.091% Zinc, o.466% Iron, 0.179%
Manganese, 0.53% Magnesium, 0.028% Titanium, 0.028% Chromium, and remaining alluminium.
The composition of Alluminium alloy
7075 consists of Alluminium (Al) 87.2 to 91.4 %, Zinc (Zn)5.1 to 6.1
%,Magnesium (Mg)2.1 to 2.9 %, Copper (Cu)1.2 to 2.0 %, Iron (Fe)0 to 0.5 %,
Silicon (Si)0 to 0.4 %, Manganese (Mn)0 to 0.30 %, Chromium (Cr)0.18 to 0.28 %,
Zirconium (Zr)0 to 0.25 %, Titanium (Ti)0 to 0.2 %, Residuals 0 to 0.15 %. In
this study 600x50x10mm rectangular bar was used.
2.2.
Schematic
machining:
In this study, the experiments were
carried out on a CNC vertical machining center (KENT and ND Co. Ltd, Taiwan make) shown in Figure.1
to perform different size of holes on Alluminium 2014, 6069, 6061, and 7075
alloy work pieces by alter the point and clearance angles on standard HSS twist
drill bits and maintain constant helix angle of 45 degrees. Furthermore the
cutting speed (m/min), the feed rate (mm/rev) and percentage of cutting fluid
mixture ratio are regulated in this experiment.
Figure 1: Drilling of Aluminum alloys
Figure 2: Alteration of drill tool geometry using Tool and Cutter
grinder
Figure3: Coordinate Measuring Machine and surface analyser of Talysurf
50
2.3.
Measuring
Apparatus
After drilling on all Alluminium
alloy work pieces, the surface roughness(R1) and circularity deviation(R2) of
drilled holes measured by a surface analyzer of Talysurf 50 (Taylor Hobson Co
Ltd) and coordinate measuring machine (CMM) respectively.
3. MOTIVATION OF THE PRESENT WORK
3.1.
Methodology
The orthogonal array forms the basis
for the experimental analysis in the Taguchi method. The selection of
orthogonal array is concerned with the total degree of freedom of process
parameters. Total degree of freedom (DOF) associated with five parameters is
equal to 10 (5X2).
The degree of freedom for the
orthogonal array should be greater than or at least equal to that of the
process parameters. There by, a L27 orthogonal array having degree of freedom
equal to (27-1) 26 has been considered, which is used to optimize the cutting
parameters for surface roughness and circularity deviation using the S/N ratio
and ANOVA for machining of Alluminium alloys of 2014,6069,6061,7075 and
predicted results were nearer to the experimental results.
Although similar to design of
experiment (DOE), the Taguchi design only conducts the balanced (orthogonal)
experimental combinations, which makes the Taguchi design even more effective
than a fractional factorial design. By Taguchi techniques, industries are able
to greatly reduce product development cycle time for design and production,
therefore reducing costs and increasing profit.
Confirmation test have been carried
out to compare the predicted values with the experimental values confirm its
effectiveness in the analysis of surface roughness and circularity deviation.
Later the results fed to multiple attributes in decision-making techniques (AHP
and TOPSIS) are applied to optimal selection of Alluminium alloys during
drilling process.
3.2.
Experimentation
as per Taguchi method
A plan of experiments based on Taguchi
technique has been used to acquire the data. An orthogonal array, signal to
noise (S/N) ratio and analysis of variance (ANOVA) are employed to investigate
the drilling characteristics of Aluminum alloys using HSS twist drill bits. The
complete procedure in Taguchi design method can be divided into three stages:
system design, parameter design, and tolerance design.
Of the three design stages, the
second stage – the parameter design – is the most important stage. Taguchi’s
orthogonal array (OA) provides a set of well-balanced experiments (with less
number of experimental runs), and Taguchi’s signal-to-noise ratios (S/N), which
are logarithmic functions of desired output in the optimization process. Taguchi
method uses a statistical measure of performance called signal-to-noise ratio.
The S/N ratio takes both the mean
and the variability into account. The S/N ratio is the ratio of the mean
(Signal) to the standard deviation (Noise). The ratio depends on the quality
characteristics of the product/process to be optimized. The machining
parameters and their levels are given in Table1. Plan of experiments based on Taguchi
orthogonal array and observed responses shown in Table 2.
Table1: Machining parameters and their levels
LEVELS |
FACTORS |
||||
Cutting Speed (rpm) |
Feed Rate (mm/min) |
Drill Diameter (mm) |
Point Angle (Degrees) |
Clearance Angle (Degrees) |
|
A |
B |
C |
D |
E |
|
1 |
600 |
0.3 |
8 |
118 |
4 |
2 |
800 |
0.5 |
10 |
110 |
6 |
3 |
1000 |
0.6 |
12 |
100 |
8 |
Table 2: Plan of experiments based on Taguchi
orthogonal array and observed responses
Runs |
A |
B |
C |
D |
E |
Al
6061 Measured
Responses |
Al 2014 Measured
Responses |
Al 5035 Measured
Responses |
Al
7075 Measured
Responses |
S/N Ratio h |
||||
R1 |
R2 |
R1 |
R2 |
R1 |
R2 |
R1 |
R2 |
|||||||
1 |
1 |
1 |
1 |
1 |
1 |
0.28 |
0.18 |
0.21 |
0.26 |
0.34 |
0.35 |
0.36 |
0.41 |
-1.6278 |
2 |
1 |
1 |
1 |
1 |
2 |
0.27 |
0.16 |
0.24 |
0.34 |
0.38 |
0.46 |
0.44 |
0.37 |
4.4320 |
3 |
1 |
1 |
1 |
1 |
3 |
0.30 |
0.18 |
0.29 |
0.44 |
0.31 |
0.52 |
0.33 |
0.46 |
-7.0672 |
4 |
1 |
2 |
2 |
2 |
1 |
0.29 |
0.20 |
0.35 |
0.38 |
0.43 |
0.44 |
0.35 |
0.44 |
3.7360 |
5 |
1 |
2 |
2 |
2 |
2 |
0.25 |
0.16 |
0.28 |
0.23 |
0.44 |
0.45 |
0.38 |
0.50 |
-4.5433 |
6 |
1 |
2 |
2 |
2 |
3 |
0.26 |
0.19 |
0.22 |
0.31 |
0.41 |
0.40 |
0.43 |
0.41 |
-5.4292 |
7 |
1 |
3 |
3 |
3 |
1 |
0.19 |
0.15 |
0.19 |
0.37 |
0.39 |
0.30 |
0.45 |
0.54 |
-6.1495 |
8 |
1 |
3 |
3 |
3 |
2 |
0.35 |
0.23 |
0.23 |
0.43 |
0.33 |
0.34 |
0.52 |
0.33 |
-4.8008 |
9 |
1 |
3 |
3 |
3 |
3 |
0.24 |
0.18 |
0.34 |
0.38 |
0.48 |
0.34 |
0.51 |
0.56 |
-1.2765 |
10 |
2 |
1 |
2 |
3 |
1 |
0.31 |
0.24 |
0.33 |
0.40 |
0.39 |
0.43 |
0.48 |
0.36 |
-4.4935 |
11 |
2 |
1 |
2 |
3 |
2 |
0.22 |
0.15 |
0.36 |
0.39 |
0.37 |
0.44 |
0.41 |
0.46 |
-1.0965 |
12 |
2 |
1 |
2 |
3 |
3 |
0.32 |
0.20 |
0.27 |
0.33 |
0.39 |
0.42 |
0.43 |
0.40 |
4.9026 |
13 |
2 |
2 |
3 |
1 |
1 |
0.23 |
0.15 |
0.30 |
0.34 |
0.42 |
0.46 |
0.49 |
0.49 |
-4.2749 |
14 |
2 |
2 |
3 |
1 |
2 |
0.20 |
0.15 |
0.38 |
0.28 |
0.41 |
0.51 |
0.52 |
0.51 |
-5.1270 |
15 |
2 |
2 |
3 |
1 |
3 |
0.18 |
0.16 |
0.35 |
0.38 |
0.48 |
0.43 |
0.56 |
0.36 |
2.0188 |
16 |
2 |
3 |
1 |
2 |
1 |
0.33 |
0.22 |
0.31 |
0.18 |
0.36 |
0.37 |
0.53 |
0.37 |
-5.0137 |
17 |
2 |
3 |
1 |
2 |
2 |
0.21 |
0.14 |
0.32 |
0.21 |
0.39 |
0.41 |
0.57 |
0.42 |
-1.8190 |
18 |
2 |
3 |
1 |
2 |
3 |
0.24 |
0.21 |
0.25 |
0.22 |
0.36 |
0.39 |
0.47 |
0.36 |
-6.8348 |
19 |
3 |
1 |
3 |
2 |
1 |
0.21 |
0.23 |
0.21 |
0.37 |
0.39 |
0.52 |
0.41 |
0.50 |
-3.2417 |
20 |
3 |
1 |
3 |
2 |
2 |
0.23 |
0.18 |
0.24 |
0.43 |
0.33 |
0.44 |
0.43 |
0.41 |
-3.3032 |
21 |
3 |
1 |
3 |
2 |
3 |
0.18 |
0.24 |
0.29 |
0.38 |
0.48 |
0.45 |
0.49 |
0.54 |
-4.6847 |
22 |
3 |
2 |
1 |
3 |
1 |
0.24 |
0.15 |
0.35 |
0.40 |
0.39 |
0.40 |
0.35 |
0.33 |
-3.8870 |
23 |
3 |
2 |
1 |
3 |
2 |
0.33 |
0.20 |
0.28 |
0.39 |
0.37 |
0.30 |
0.38 |
0.56 |
-3.6437 |
24 |
3 |
2 |
1 |
3 |
3 |
0.32 |
0.15 |
0.19 |
0.33 |
0.39 |
0.34 |
0.43 |
0.36 |
1.5171 |
25 |
3 |
3 |
2 |
1 |
1 |
0.36 |
0.16 |
0.23 |
0.34 |
0.42 |
0.34 |
0.45 |
0.41 |
-2.7075 |
26 |
3 |
3 |
2 |
1 |
2 |
0.27 |
0.18 |
0.34 |
0.26 |
0.39 |
0.43 |
0.52 |
0.37 |
-4.7936 |
27 |
3 |
3 |
2 |
1 |
3 |
0.24 |
0.20 |
0.33 |
0.34 |
0.42 |
0.44 |
0.51 |
0.46 |
-5.1176 |
3.3.
Analysis
of the S/N Ratio
In Taguchi method, the term ‘signal’
represents the desirable value (mean) for the output characteristic and the
term ‘noise’ represents the undesirable value (Standard Deviation) for the
output characteristic. S/N ratio used to measure the quality characteristic
deviating from the desired value.
The S/N ratio h = -10 log (M.S.D), Where M.S.D is the mean square
deviation for the output characteristic. Table 2 shows the experimental results
for observed responses. The S/N ratio table for observed responses is shown in
Table 3.
Table3. Signal to Noise Ratios for Smaller is better
Level |
Aluminum alloy 2014 |
||||
cutting speed(rpm) A |
feed rate (mm/min) B |
drill diameter(mm) C |
point angle(Deg) D |
clearance angle(Deg) E |
|
1 |
-3.01518 |
-2.42151 |
-2.25041 |
-2.72382 |
-2.48101 |
2 |
-2.40537 |
-1.76045 |
-3.12840 |
-4.05336 |
-3.71325 |
3 |
-3.31212 |
-3.07968 |
-3.42063 |
-3.61682 |
-3.67003 |
Delta |
1.40265 |
3.04105 |
2.85124 |
2.91623 |
2.00203 |
Rank |
5 |
1 |
3 |
2 |
4 |
Level |
Aluminum alloy 6069 |
||||
cutting speed(rpm) A |
feed rate (mm/min) B |
drill diameter(mm) C |
point angle(Deg) D |
clearance angle(Deg) E |
|
1 |
-2.62382 |
-2.68011 |
-3.51302 |
-1.79783 |
-2.70312 |
2 |
-3.05136 |
-3.61305 |
-3.75534 |
-2.18147 |
-2.45034 |
3 |
-4.61288 |
-3.76003 |
-2.39812 |
-4.27928 |
-3.65602 |
Delta |
2.51623 |
2.23053 |
1.25623 |
2.48145 |
1.15623 |
Rank |
1 |
4 |
3 |
2 |
5 |
Level |
Aluminum
alloy 6061 |
||||
cutting speed(rpm) A |
feed rate (mm/min) B |
drill diameter(mm) C |
point angle(Deg) D |
clearance angle(Deg) E |
|
1 |
-3.15041 |
-2.52518 |
-2.44130 |
-3.11352 |
-2.66049 |
2 |
-2.12840 |
-2.41537 |
-2.74395 |
-3.42034 |
-2.17144 |
3 |
-3.46140 |
-3.31802 |
-3.07333 |
-2.09641 |
-3.42665 |
Delta |
2.91126 |
0.90265 |
0.63203 |
1.55623 |
1.25522 |
Rank |
1 |
4 |
5 |
2 |
3 |
Level |
Aluminum
alloy 7075 |
||||
cutting speed(rpm) A |
feed rate (mm/min) B |
drill diameter(mm) C |
point angle(Deg) D |
clearance angle(Deg) E |
|
1 |
-3.57514 |
-1.79783 |
-4.63041 |
-2.10312 |
-3.24031 |
2 |
-4.21302 |
-2.18147 |
-3.16164 |
-3.45934 |
-1.94792 |
3 |
-3.34812 |
-4.27928 |
-3.42205 |
-2.69612 |
-4.16343 |
Delta |
2.60265 |
2.48145 |
2.75122 |
1.35623 |
1.73203 |
Rank |
2 |
3 |
1 |
5 |
4 |
Table4: Optimal combination of parameters to optimize surface roughness and circularity deviation by Taguchimethod
Material |
Optimal combination
of parameters |
Surface Roughness(
µm) |
Circularity
Deviation(mm) |
Al 2014 |
A5B1C3D2E4 |
0.25 |
0.21 |
Al 6069 |
A1B4C3D2E5 |
0.34 |
0.24 |
Al 6061 |
A1B4C5D2E3 |
0.26 |
0.34 |
Al7075 |
A2B3C1D5E4 |
0.19 |
0.27 |
4. RESULTS AND DISCUSSIONS
The optimum parameter combination
for surface roughness, circularity deviations are tabulated in table4
corresponding to the largest values of S/N ratio for all control parameters of
different Aluminum alloys. From Table 4, it is observed that feed rate, point
angle, drill diameter, cutting speed and clearance angle has the order of
influence on surface roughness and circularity deviation during drilling of Alluminium
alloys.
Figure
4: Interaction plot of surface roughness with
effect of other parameters
Figure
5: Interaction plot of circularity deviation with effect of other parameters
4.1.
Results
of ANOVA
The purpose of the analysis of
variance (ANOVA) is to investigate which design parameters significantly affect
the quality characteristic. Table 5 and 6 shows the results of ANOVA for both
surface roughness and , circularity deviation , cutting speed, feed rate, point
angle and clearance angle are the significant cutting parameters for affecting
the both responses for Alluminium 2014 alloy. Same procedure applied for
remaining Aluminum alloys.
Table 5: Results of ANOVA for surface roughness (Aluminum
2014 alloy)
Symbol |
Cutting
Parameters |
DO
F |
SS |
MS |
F |
|
A |
Cutting speed |
2 |
2.96 |
1.48 |
3.797 |
significant |
B |
Feed rate |
2 |
4.44 |
2.22 |
5.696 |
significant |
C |
Drill diameter |
2 |
3.40 |
1.7 |
3.362 |
Insignificant |
D |
Point angle |
2 |
3.76 |
1.88 |
4.824 |
significant |
E |
Clearance angle |
2 |
3.43 |
1.715 |
4.4 |
significant |
Error |
|
16 |
6.2353 |
0.3897 |
|
|
Total |
|
26 |
23.3653 |
|
|
|
Significant, F table at
95%confidence level is F0.05, 2, 16 = 3.63, F exp ≥ F
table
Table 6: Results of ANOVA for circularity
deviation (Aluminum 2014 alloy)
Symbol |
Cutting
Parameters |
DOF |
SS |
MS |
F |
|
A |
Cutting speed |
2 |
0.00584 |
0.00292 |
3.74 |
significant |
B |
Feed rate |
2 |
0.00577 |
0.00885 |
3.64 |
significant |
C |
Drill diameter |
2 |
0.00215 |
0.00107 |
1.37 |
Insignificant |
D |
Point angle |
2 |
0.00579 |
0.00289 |
3.71 |
significant |
E |
Clearance angle |
2 |
0.02307 |
0.01153 |
14.78 |
significant |
Error |
|
16 |
0.01248 |
0.00078 |
|
|
Total |
|
26 |
0.0511 |
|
|
|
Significant, F table at 95%confidence
level is F0.05, 2, 16 = 3.63, F exp ≥ F table
Table 7: Optimal values of individual
machining characteristics
Machining
characteristics |
Optimal
combination of parameters |
Significant parameters(at 95% confidence level) |
Predicted
optimum value |
Experimental
value |
Surface
Roughness (R3) µm |
A3B3C3D2E3 |
A,B,D,E |
3.7451 |
4.078 |
Circularity
deviation(R4) mm |
A3B1C1D1E1 |
A,B,D,E |
0.1076 |
0.1654 |
Confirmatory experiments were conducted
for surface roughness and circularity deviation, corresponding their optimal
setting of process parameters to validate the used approach, obtained the
values of 3.7451µm, 0.1076mm for surface roughness and circularity deviation
respectively. Predicted and experimental values of responses are depicted in
Table 7. Same procedure applied for remaining Aluminum alloys.
4.2.
Results
of MADM
The results obtained in integrated
grey based Taguchi method are given into the input for MADM apart from
mechanical properties (resistance to corrosion, resistance to high temperature,
fatigue strength, ultimate tensile strength, hardness) of Al 6061, 7075, 6069,
2014 alloys are also considered for air craft applications from previous
literature, those weights are taken as per the importance of respective
properties.
Then
the Decision Matrix, C =
[0.1600
0.1100 3.0000 1.0000
3.0000 3.0000 2.0000
0.3000
0.2600 2.0000 2.0000
1.0000 1.0000 1.0000
0.2600
0.2400 1.0000 3.0000
4.0000 4.0000 3.0000
0.1700
0.1400 4.0000 4.0000
2.0000 2.0000 4.0000]
Normalized
Matrix (N) =
[1.0000
1.0000 0.7500 0.2500
0.7500 0.7500 0.5000
0.5333
0.4231 0.5000 0.5000
0.2500 0.2500 0.2500
0.6154
0.4583 0.2500 0.7500
1.0000 1.0000 0.7500
0.9412
0.7857 1.0000 1.0000
0.5000 0.5000 1.0000]
Normalized
decision matrix, Ri =
[1.0000
4.0000 2.0000 6.0000
3.0000 4.0000 3.0000
0.2500 1.0000
1.0000 3.0000 6.0000
5.0000 8.0000
0.5000
1.0000 1.0000 2.0000
6.0000 4.0000
4.0000
0.1667
0.3333 0.5000 1.0000
1.0000 3.0000 3.0000
0.3333
0.1667 0.1667 1.0000
1.0000 2.0000 2.0000
0.2500
0.2000 0.2500 0.3333
0.5000 1.0000 1.0000
0.3333
0.1250 0.2500 0.3333
0.5000 1.0000 1.0000]
4.2.1. AHP
Result:
Pair wise comparison
pwc(:,:,1) =
1.0000 1.8750 1.6250
1.0625
0.5333 1.0000
0.8667 0.5667
0.6154 1.1538
1.0000 0.6538
0.9412 1.7647
1.5294 1.0000
pwc
(:,:,2) = 1.0000 2.3636
2.1818 1.2727
0.4231 1.0000
0.9231 0.5385
0.4583 1.0833
1.0000 0.5833
0.7857 1.8571
1.7143 1.0000
pwc(:,:,3)
= 1.0000 1.5000
3.0000 0.7500
0.6667 1.0000
2.0000 0.5000
0.3333 0.5000
1.0000 0.2500
1.3333 2.0000
4.0000 1.0000
pwc(:,:,4)
= 1.0000 0.5000
0.3333 0.2500
2.0000 1.0000
0.6667 0.5000
3.0000 1.5000
1.0000 0.7500
4.0000 2.0000
1.3333 1.0000
pwc(:,:,5)
= 1.0000 3.0000
0.7500 1.5000
0.3333 1.0000
0.2500 0.5000
1.3333 4.0000
1.0000 2.0000
0.6667 2.0000
0.5000 1.0000
pwc(:,:,6)
= 1.0000 3.0000
0.7500 1.5000
0.3333 1.0000
0.2500 0.5000
1.3333 4.0000
1.0000 2.0000
0.6667 2.0000
0.5000 1.0000
pwc(:,:,7)
= 1.0000 2.0000
0.6667 0.5000
0.5000
1.0000 0.3333 0.2500
1.5000 3.0000
1.0000 0.7500
2.0000 4.0000
1.3333 1.0000
pwc(:,:,8)
= 0.3236 0.1726
0.1992 0.3046
0.3749 0.1586
0.1718 0.2946
0.3000 0.2000
0.1000 0.4000
0.1000 0.2000
0.3000 0.4000
0.3000 0.1000
0.4000 0.2000
0.3000 0.1000
0.4000 0.2000
0.2000 0.1000
0.3000 0.4000
p1
= [0.3236 0.3749
0.3000 0.1000 0.3000
0.3000 0.2000
0.1726 0.1586
0.2000 0.2000 0.1000
0.1000 0.1000
0.1992 0.1718
0.1000 0.3000 0.4000
0.4000 0.3000
0.3046 0.2946
0.4000 0.4000 0.2000
0.2000 0.4000]
AHP
matrix final = 0.3023
0.1662
0.2083
0.3231
AHP
rank = 4 1
3 2
4.2.2. TOPSIS
Method
su
= 0.4605 0.3961
5.4772 5.4772 5.4772
5.4772 5.4772
r
= 0.3474 0.2777
0.5477 0.1826 0.5477
0.5477 0.3651
0.6514 0.6564
0.3651 0.3651 0.1826
0.1826 0.1826
0.5646 0.6059
0.1826 0.5477 0.7303
0.7303 0.5477
0.3691 0.3534
0.7303 0.7303 0.3651
0.3651 0.7303
wm
= 0.3159 0.2287
0.2090 0.0893 0.0680
0.0451 0.0439
vv
= 0.1098 0.0635
0.1145 0.0163 0.0373
0.0247 0.0160
0.2058 0.1501
0.0763 0.0326 0.0124
0.0082 0.0080
0.1783 0.1386
0.0382 0.0489 0.0497
0.0329 0.0241
0.1166 0.0808
0.1527 0.0652 0.0248
0.0165 0.0321
vplus =
0.1098 0.0635 0.1527
0.0652 0.0497 0.0329
0.0321
vminus
= 0.2058 0.1501
0.0382 0.0163 0.0124
0.0082 0.0080
siplus = 0.0658 0.1618
0.1542 0.0351
siminus
= 0.1533 0.0415
0.0648 0.1705
Topsis
matrix = 0.6997 0.2041
0.2960 0.8291
TOPSIS
rank = 4 1
3 2
5. CONCLUSIONS
In this paper, a study on the
optimal selection of alluminium alloys especially for automotive and aerospace
industry to optimize the surface roughness and circularity deviation of drilled
holes is carried out. In this connection, MADM technique is proposed for
decision making regarding selection of suitable material, which yields optimal
values of surface roughness and circularity deviation of drilled holes. The
output from Taguchi method fed as input to the MADM. Finally, the result
generated in MADM suggests the suitable alternative of alluminium alloys in a
rank wise (2014, 6061, 6069, 7075 in an order) in both AHP and TOPSIS methods.
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