the MADM. Apart from burr size strength and temperature are also
considered as attributes. Finally, the results generated in MADM suggests the
suitable alternative of aluminium alloy,
which results in less debugging cost, high strength and high resistance at
elevated temperatures.
Keywords: Drilling, Aluminium alloys, Grey based Taguchi
method, AHP, TOPSIS.
1.
INTRODUCTION
Most of the industries perform a
huge number of drilling operations in shop floor. The drilling technology has
been discussed to improve the cutting performance with optimizing the cutting
parameters and the drill geometry. However, burr size is sometimes formed when
the drill exits the work piece and the exit burrs have to be removed in the
debugging process. The control of exit burr formation, therefore, has been
strongly required to reduce the post process of the drilling operation.
A burr is formed due to incompleteness of cutting
mechanism during machining process in general. Machining is not necessarily
only the process creating the burr but it is the most concerned process in the
burr related industry and academic researchers. All machining processes intend
to process a raw material or partially shaped work piece material into a
designed shape with a specific size and tolerance. Fundamental weaknesses in
machining processes that a cutting always requires sustainable work piece
materials, however, causes bending or break-off of the work piece material.
The
result of the former is the burr and that of the latter is the edge break.
Therefore, the burr, an unintended outcome of machining processes (PANDE;
RELEKAR, 1986; LAUDERBAUGH, 2008),
has been a widely recognized problem to the industry. It ruins the integrity of
design of the part, requires additional processes to assemble it, causes safety
hazards, and results in malfunction of the product. All these side effects
causes unnecessary cost to the industry in various forms such as additional
machining, compensation, service, redesign, and collateral damage on the
company goodwill.
Therefore,
in most cases, it is a must either to remove or to secure the burr in order to
prevent it from being detached from the part. Traditionally, burr problems had
been considered unavoidable so that most efforts had been made on removal of
the burr as a post process. Naturally, many de
burring processes have been developed (KO; LEE, 2001) and for their effectiveness and competitiveness, many
researchers have been conducted.
Nowadays,
a trend of manufacturing is an integration of the whole production flow from
design to end product. Manufacturing problem issues are handled in various
stages, even from design stage. Therefore, the methods of describing the burr
are getting much attention in recent years for the systematic approach to
resolve the burr problem at various manufacturing stages.
Figure 1: Effect of deburring cost in to part cost
2.
BACK GROUND OF ALUMINIUM ALLOYS:
At
present, aluminium is used in the aviation industry everywhere in the world.
The casing of the first Soviet satellite was made of aluminium 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 aluminium alloys. They are used for manufacturing various components of
spaceship equipment: brackets, fixtures, chassis, covers and casing for many
tools and devices.
Aluminium
alloys (HAMADE; ISMAIL, 2005) 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 aluminium
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 aluminium, developing more and more new
alloys for construction of aircraft and spaceships. 2xxx, 5xxx, 6xxx, and 7xxx
series alloys are widely used in aviation.
3.
METHODOLOGY
3.1.
Grey based – taguchi method:
The
integrated grey based Taguchi method combines advantages of both grey
relational analysis and Taguchi method (DENG, 1989; MONTGOMERY, 2007). This
method was successfully applied to optimize the multi response of complicated
problems in manufacturing processes. Furthermore, ANOVA is performed to see
which process parameters are statistically significant. The integrated grey
based Taguchi method combines the algorithm of Taguchi method and grey
relational analysis to determine process parameters for multiple responses.
Figure 2: Influential Factors on burr formation in
drilling &block diagram of MADM integrated with grey based-Taguchi
method
3.2.
Multi-Attribute Decision Making (MADM)
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 (HWANG; YOON, 1982; CHEN; HWANG, 1992; YOON; HWANG, 1995).
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 (SAATY, 2000; OLSON, 2004; KUMAR; SUMAN, 2014) 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
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.
The main procedure of
the combined TOPSIS and AHP method is as follows:
·
Step 1:
Determine the objective and evaluation attributes. In the present case, 2xxx, 5xxx, 6xxx, and 7xxx series of aluminium alloys on the basis of the attributes such as deburring cost, strength and
temperature satisfying the requirements.
·
Step 2:
Formulate a decision matrix with each alternative as a row and each column to
one attribute. Therefore, an element dij of the decision matrix “D” gives the
value of the jth attribute in original real values, that is, non-normalized
form and units, for the ith alternative. Thus, if the number of alternatives is
“M” and the number of attributes in “N”, then the decision matrix is an M×N
matrix can be represented as:
·
Step 3:
Obtain the normalized decision matrix, Rij. This can be represented
- Step 4: 1. Find out the relative importance of different attributes with
respect to the objective. To do so, one has to construct a pair-wise
comparison matrix using a scale of relative importance. The results are
entered using the fundamental scale of the analytic hierarchy process. An attribute (material) compared
with it is always assigned the value 1 so the main diagonal entries of the
pair-wise comparison matrix are all 1. The numbers 3, 5, 7, and 9
correspond to the verbal judgments “less importance”, “medium importance”,
“more importance”, and “ideal importance” (with 2, 4, 6, and 8 for
compromise between the previous values). Assuming N attributes, the pair
wise comparison of attribute i with attribute j yields a square matrix A N
× N where aij denotes the comparative importance of attribute i with
respect to attribute j. In the matrix, aij=1 when i=j and aji=1 / aij.. This can be
described as
The relative
normalized weight (Wj) of each attribute by (i) calculating the geometric mean
of ith row and (ii) normalizing the geometric means of rows in the
comparability matrix. This can be represented as
and
The geometric mean
method of AHP is used in the present work to find out the relative normalized
weights of the attributes because of its simplicity and easiness to find out
the maximum Eigen value and to reduce the inconsistency in judgments.
2. Calculate matrix A3 and A4 such that
A3=A1×A2 and A4=A3 / A2, where A2= [W1, W2... WN] T.
3. Find out the maximum Eigen value λmax that is the average of matrix A4.
4. Calculate the consistency index CI= (λmax − N) / (N − 1). The smaller the value of CI, the smaller is the
deviation from the consistency.
5. Obtain the random index (RI) for the
number of attributes used in decision making.
6. Calculate the consistency ratio
CR=CI/RI. Usually, a CR of 0.1 or less is considered as acceptable and it
reflects an informed judgment that could be attributed to the knowledge of the
analyst about the problem under study.
- Step 5: Obtain the weighted normalized matrix Vij. This is obtained by
the multiplication of each element of the column of the matrix Rij with
its associated weight Wj. Hence, the elements of the weighted normalized
matrix Vij are expressed as Vij = Wj Rij.
- Step 6: Obtain the Ideal (best) and Negative-Ideal (worst) solutions in
this step. The ideal (best) and negative ideal (worst) solution can be
expressed as
- Step 7:
Obtain the separation measures. The separation of each alternative from
the ideal one is given by Euclidean distance by the following equations.
- Step 8:
The relative closeness of a particular alternative to the ideal solution
can be expressed in this step as follows.
- Step 9:
A set of alternatives is made in the descending order in this step,
according to the preference value indicating the most preferred and least
preferred feasible solutions.
- Step 10:
Take a final decision keeping in view the practical considerations. All
possible constraints likely to be experienced by the user are looked in
during this stage.
4.
OBSERVATIONS AND RESULTS:
In this study, the
experiments were carried out on a CNC vertical machining center (KENT and ND Co. Ltd, Taiwan make) to perform
different size of holes on Al6061, 2014, 5035, 7075 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. The burr size (thickness, R1 and height, R2) is measured by
digital profile projector. 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 (mm/min) |
Feed
Rate (mm/min) |
Drill
Diameter (mm) |
Point
Angle (Degrees) |
Clearance
Angle (Degrees) |
|
|
A |
B |
C |
D |
E |
|
|
1 |
15.08 |
0.3 |
8 |
118 |
4 |
|
2 |
25.13 |
0.5 |
10 |
110 |
6 |
|
3 |
37.7 |
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 |
||||
|
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 |
|
2 |
1 |
2 |
2 |
2 |
2 |
0.27 |
0.16 |
0.24 |
0.34 |
0.38 |
0.46 |
0.44 |
0.37 |
|
3 |
1 |
3 |
3 |
3 |
3 |
0.30 |
0.18 |
0.29 |
0.44 |
0.31 |
0.52 |
0.33 |
0.46 |
|
4 |
2 |
1 |
1 |
2 |
2 |
0.29 |
0.20 |
0.35 |
0.38 |
0.43 |
0.44 |
0.35 |
0.44 |
|
5 |
2 |
2 |
2 |
3 |
3 |
0.25 |
0.16 |
0.28 |
0.23 |
0.44 |
0.45 |
0.38 |
0.50 |
|
6 |
2 |
3 |
3 |
1 |
1 |
0.26 |
0.19 |
0.22 |
0.31 |
0.41 |
0.40 |
0.43 |
0.41 |
|
7 |
3 |
1 |
2 |
1 |
3 |
0.19 |
0.15 |
0.19 |
0.37 |
0.39 |
0.30 |
0.45 |
0.54 |
|
8 |
3 |
2 |
3 |
2 |
1 |
0.35 |
0.23 |
0.23 |
0.43 |
0.33 |
0.34 |
0.52 |
0.33 |
|
9 |
3 |
3 |
1 |
3 |
2 |
0.24 |
0.18 |
0.34 |
0.38 |
0.48 |
0.34 |
0.51 |
0.56 |
|
10 |
1 |
1 |
3 |
3 |
2 |
0.31 |
0.24 |
0.33 |
0.40 |
0.39 |
0.43 |
0.48 |
0.36 |
|
11 |
1 |
2 |
1 |
1 |
3 |
0.22 |
0.15 |
0.36 |
0.39 |
0.37 |
0.44 |
0.41 |
0.46 |
|
12 |
1 |
3 |
2 |
2 |
1 |
0.32 |
0.20 |
0.27 |
0.33 |
0.39 |
0.42 |
0.43 |
0.40 |
|
13 |
2 |
1 |
2 |
3 |
1 |
0.23 |
0.15 |
0.30 |
0.34 |
0.42 |
0.46 |
0.49 |
0.49 |
|
14 |
2 |
2 |
3 |
1 |
2 |
0.20 |
0.15 |
0.38 |
0.28 |
0.41 |
0.51 |
0.52 |
0.51 |
|
15 |
2 |
3 |
1 |
2 |
3 |
0.18 |
0.16 |
0.35 |
0.38 |
0.48 |
0.43 |
0.56 |
0.36 |
|
16 |
3 |
1 |
3 |
2 |
3 |
0.33 |
0.22 |
0.31 |
0.18 |
0.36 |
0.37 |
0.53 |
0.37 |
|
17 |
3 |
2 |
1 |
3 |
1 |
0.21 |
0.14 |
0.32 |
0.21 |
0.39 |
0.41 |
0.57 |
0.42 |
|
18 |
3 |
3 |
2 |
1 |
2 |
0.24 |
0.21 |
0.25 |
0.22 |
0.36 |
0.39 |
0.47 |
0.36 |
Table3: Optimal combination of parameters to minimize
burr size by integrated grey based Taguchi method
|
Material |
Optimal
combination of parameters |
Burr
height ( mm) |
Burr
thickness(mm) |
|
Al
6061 |
A2B2C1D1E3 |
0.16 |
0.11 |
|
Al
7075 |
A3B2C2D2E2 |
0.33 |
0.26 |
|
Al
5035 |
A1B1C3D3E1 |
0.26 |
0.24 |
|
Al2014 |
A1B2C1D1E3 |
0.17 |
0.14 |
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, 5035, 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]
3.1.
AHP Result:
Pair wise comparison
pwc(:,:,1) = pwc(:,:,6) =
1.0000
1.8750 1.6250 1.0625 1.0000 3.0000
0.7500 1.5000
0.5333
1.0000 0.8667 0.5667 0.3333 1.0000
0.2500 0.5000
0.6154
1.1538 1.0000 0.6538 1.3333 4.0000
1.0000 2.0000
0.9412
1.7647 1.5294 1.0000 0.6667 2.0000
0.5000 1.0000
pwc (:,:,2) = pwc(:,:,7) =
1.0000
2.3636 2.1818 1.2727 1.0000 2.0000
0.6667 0.5000
0.4231
1.0000 0.9231 0.5385 0.5000 1.0000
0.3333 0.2500
0.4583
1.0833 1.0000 0.5833 1.5000 3.0000
1.0000 0.7500
0.7857
1.8571 1.7143 1.0000 2.0000 4.0000
1.3333 1.0000
pwc(:,:,3) = pwc(:,:,8) =
1.0000
1.5000 3.0000 0.7500 0.3236 0.1726
0.1992 0.3046
0.6667
1.0000 2.0000 0.5000 0.3749 0.1586
0.1718 0.2946
0.3333
0.5000 1.0000 0.2500 0.3000 0.2000
0.1000 0.4000
1.3333
2.0000 4.0000
1.0000 0.1000 0.2000
0.3000 0.4000
pwc(:,:,4) = 0.3000 0.1000
0.4000 0.2000
1.0000
0.5000 0.3333 0.2500 0.3000 0.1000
0.4000 0.2000
2.0000
1.0000 0.6667 0.5000 0.2000 0.1000
0.3000 0.4000
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
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
AHPdisrank =
4
1 3 2
3.2.
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
TOPSISrank = 4
1 3 2
5.
CONCLUDING REMARKS:
Burr
formation during drilling is a serious problem while assembly of precision
components. Majority of aerospace, automobile and marine industries use
aluminium alloys. In this paper, a study on the optimal selection of aluminium
alloys especially for aerospace industry to minimize the debugging cost (cost
incurred for post processing of burr formation on exit of drilled holes) is
carried out. In this connection, MADM technique is proposed for decision making
regarding selection of suitable material which yields minimal burr size, high
strength and high temperature resistant.
Initially,
the optimum burr size is estimated using grey based- Taguchi method for
different series of aluminium alloys. The output from grey based- Taguchi
method fed as input to the MADM. Apart from burr size strength and temperature
are also considered as attributes. Finally, the results generated in MADM
suggests the suitable alternative choice of
aluminium alloys in a rank wise (2014,6061,5035,7075 in an order) in
both AHP and TOPSIS methods, which results in less debugging cost, high
strength and high resistance at elevated temperatures.
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