UDK 621.791:669.715
Original scientific article/Izvirni znanstveni članek
ISSN 1580-2949 MTAEC9, 44(4)205(2010)
APPLICATION OF GREY RELATION ANALYSIS (GRA)
AND TAGUCHI METHOD FOR THE PARAMETRIC OPTIMIZATION OF FRICTION STIR WELDING (FSW)
PROCESS
UPORABA GREYJEVE ANALIZE (GRA) IN TAGUCHIJEVE METODE ZA PARAMETRIČNO OPTIMIZACIJO VARJENJA Z VRTILNO-TORNIM PROCESOM (FSW)
Hakan Aydin1, Ali Bayram2, Ugur Esme3*, Yigit Kazancoglu4, Onur Guven5
1'2Uludag University, Faculty of Engineering and Architecture, Department of Mechanical Engineering, 16059, Gorukle-Bursa/Turkey 3Mersin University Tarsus Technical Education Faculty Department of Mechanical Education, 33480, Tarsus-Mersin/Turkey 4Izmir University of Economics, Department of Business Administration, 35330, Balcova-Izmir/Turkey 5Mersin University, Engineering Faculty, Department of Mechanical Engineering, 33400, Mersin/Turkey
uguresme@gmail.com
Prejem rokopisa - received: 2010-02-15; sprejem za objavo - accepted for publication: 2010-02-25
This study focused on the multi-response optimization of friction stir welding (FSW) process for an optimal parametric combination to yield favorable tensile strength and elongation using the Taguchi based Grey relational analysis (GrA). The objective functions have been selected in relation to parameters of FSW parameters; rotating speed, welding speed and tool shoulder diameter. The experiments were planned using Taguchi's L8 orthogonal array. Multi-response optimization was applied using Grey relation analysis and Taguchi approach to solve the problem. The significance of the factors on overall quality characteristics of the welding process has also been evaluated quantitatively by the analysis of variance (ANOVA) method. Optimal results have been verified through confirmation experiments. This study has also showed the application feasibility of the Grey relation analysis in combination with Taguchi technique for continuous improvement in welding quality.
Keywords: Friction stir welding, Grey relation analysis, Taguchi method, optimization
Cilj raziskave je bila večodgovorna optimizacija procesa varjenja z vrtilnim trenjem (FSW) za kombinacijo parametrov za dosego ugodnih raztržne trdnosti in raztezka z uporabo Taguchi-Greyjeve racionalne analize. Primerne funkcije so bile izbrane v povezavi s FSW-parametri: hitrost vrtenja, hitrost varjenja in premer ramen orodja. Preizkusi so bili izvršeni z uporabo Taguchijeve ortogonalne mreže L8. Odgovori so bili optimizirani z uporabo Greyjeve analize s Taguchijevim približkom. Pomen dejavnikov splošnih značilnosti procesa varjenja je bil kvantitativno analiziran z analizo variance (ANOvA). Optimalni rezultati so bili preverjeni s preizkusi. Raziskava je tudi pokazala uporabnost Greyjeve analize v povezavi s Taguchijevo tehniko za stalno izboljšanje tehnike varjenja.
Ključne besede: vrtilno torno varjenje, Greyjeva analiza odvisnosti, Taguchijeva metoda, optimizacija
1 INTRODUCTION
In today's manufacturing world, quality is of vital importance. Quality can be defined as the degree of customer's satisfaction as provided by the procured product. The product quality depends on the desired requirements gained in the product that suits its functional requirements in various areas of application.1
In the field of welding, weld quality mainly depends on the welding type, mechanical properties of the weld metal and heat affected zone (HAZ), which in turn is influenced by metallurgical characteristics and chemical compositions of the weld.1 Moreover, these mechanical-metallurgical features of the weldment directly related to welding process parameters. In other words, weld quality depends on welding process parameters.1
The welding of aluminum and its alloys has always represented a great challenge for designers and technolo-gists.2 Friction stir welding (FSW) is a welding tech-niaue, patented in 1991 by TWI.3 4
As a solid-state process, FSW can avoid the formation of solidification cracking and porosity associated with fusion (FSW) welding processes and significantly improve the weld properties of aluminum alloys.4 5 As illustrated in Figure 1, this technique involves a non-con-
Figure 1: Schematic representation of FSW Slika 1: Shematična predstavitev FSW
sumable, cylindrical, rotating tool (usually hardened steel) which moves between the seam of two butted plates and stirs them together.2-6 The effect of friction stir welding on the material is both on heat flow and plastic strain. The heat is generated by friction between the tool shoulder and the top of the sheets.
When compared to traditional welding techniques, FSW strongly reduces the presence of distortions and residual stresses.8-11 The fSw process is a solid state process and therefore a solidification structure is absent in the weld. A detailed description of the FSW process is present in the literature.7-16 The process can be easily monitored and replicated. In addition, it does not produce any major safety hazards, such as fume or radiation.17 This process is used to bond metals without fusion or filler materials.18 FSW of aluminum has several advantages over fusion welding processes. Problems arising from fusion welding of aluminum alloys, such as solidification cracking, liquation cracking and porosity, are eliminated with fSw, due to its solid-state nature.17-23
The Taguchi method is very popular for solving optimization problems in the field of production engineering.24 25 The method utilizes a well-balanced experimental design (allows a limited number of experimental runs) called orthogonal array design, and signal-to-noise ratio (sS/N ratio), which serve the objective function to be optimized (maximized) within experimental domain.24 However, traditional Taguchi method cannot solve multi-objective optimization problem. To overcome this, the Taguchi method coupled with Grey relational analysis has a wide area of application in manufacturing processes. This approach can solve multi-response optimization problem simultaneously.26,27
Planning the experiments through the Taguchi orthogonal array has been used quite successfully in process optimization by Chen and Chen,28 Fung and Kang,29 Tang et al,30 Vijian and Arunachalam31 as well as Zhang et al.32 Therefore, this study applied a Taguchi L8 orthogonal array to plan the experiments on FSW welding process. Three controlling factors including rotating speed (w), welding speed (V) and shoulder diameter (d) were selected. The Grey relational analysis is then applied to examine how the welding process factors influence the tensile strength (TS) and percent elongation (e). An optimal parameter combination was then obtained. Through analyzing the Grey relational grade matrix, the most influential factors for individual quality targets of FSW welding process can be identified. Additionally, the analysis of variance (ANOVA) was also utilized to examine the most significant factors for the tensile strength and elongation in FSW welding process.
2 GREY RELATIONAL ANALYSIS (GRA)
2.1 Data Preprocessing
In Grey relational analysis, experimental data i.e., measured features of quality characteristics are first nor-
malized ranging from zero to one. This process is known as Grey relational generation. Next, based on normalized experimental data, Grey relational coefficient is calculated to represent the correlation between the desired and actual experimental data. Then overall Grey relational grade is determined by averaging the Grey relational coefficient corresponding to selected responses.26 The overall performance characteristic of the multiple response process depends on the calculated Grey relational grade. This approach converts a multiple response process optimization problem into a single response optimization situation with the objective function is overall Grey relational grade. The optimal parametric combination is then evaluated which would result highest Grey relational grade. The optimal factor setting for maximizing overall Grey relational grade can be performed by Taguchi
method.26,33
In Grey relational generation, the normalized E corresponding to the smaller-the-better (SB) criterion which
can be expressed as:
max yi (k) - yi (k)
^i (k)=-vk—^^ (1)
i max y^ (k) - min y^ (k)
TS should follow the larger-the-better (LB) criterion, which can be expressed as:
y^ (k) - min y^ (k)
Xi (k) =
max yi (k) - min y^ (k)
(2)
where xi(k) is the value after the Grey relational generation, min yi(k) is the smallest value of yi(k) for the kth response, and max yi(k) is the largest value of yi(k) for the klh response.26 An ideal sequence is xo(k) (k = 1, 2, 3...... , 8 for the responses. The definition of Grey relational grade in the course of Grey relational analysis is to reveal the degree of relation between the 16 sequences [xo(k) and xi(k), i = 1, 2, 3.......,8]. The Grey relational coefficient # can be calculated as:
^i(k)=
A min - „
A 0 i (k) + ^A „
(3)
where =
x o(k) - xi (k)
= difference of the absolute
value xo(k) and xi(k); ^ is the distinguishing coefficient
0 ^^ ^ 1; A mi„ =V/
smallest value of Aoi; and
; iVk"
'||x o( k)-xj (k)
= the
A=Vjma" eiVk|xo(k)-xj (k)\ = largest value of
Aoi. After averaging the Grey relational coefficients, the Grey relational grade yi can be computed as:
1 ^
gi = -1 ^ i (k) n k=1
(4)
where n is the number of process responses. The higher value of Grey relational grade corresponds to intense relational degree between the reference sequence xo(k) and the given sequence xi(k). The reference sequence xo(k) represents the best process sequence; therefore,
Table 1: Chemical and mechanical properties of AA1050 aluminum alloy Tabela 1: Kemi~na sestava in mehanske lastnosti zlitine AA1050
Chemical composition w/%	Al	Mg	Si	Mn	Zn	Fe	Ti	Sn
	Balance	0.007	0.18	0.05	0.033	0.30	0.009	0.182
Mechanical properties	Yield strength (MPa)		Tensile strength (MPa)		Elongation (%)		Vickers Hardness (HV)	
	155		175		4		50	
Table 2: Process parameters and their limits Tabela 2: Parametri in limite procesa
Parameters	Notation	Unit	Levels of factors			
			1	2	3	4
Rotating speed	w	r/min	740*	1070	1520	2140
Welding speed	V	mm/min	80*	224	—	-
Shoulder diameter	d	mm	15*	20	-	-
*Initial factor settings
Table 3: Orthogonal array L8 of the experimental runs and results Tabela 3: Ortogonalna mreža L8 eksperimentalnih varkov in rezultatov
Run no	Experimental results					
	w	V	d	TS/ MPa	E/%	Fracture location HAZ: Heat affected zone TMAZ: Thermo-mechanically affected zone NZ: Nugget zone BM: Base metal
1	1	1	1	93	14.8	The interface between HAZ and TMAZ on the retreating side
2	1	2	2	65	5.50	NZ
3	2	1	1	90	17.3	BM
4	2	2	2	89	13.5	HAZ on the retreating side
5	3	1	2	92	18.3	BM
6	3	2	1	93	14.5	HAZ on the advancing side
7	4	1	2	94	19.1	BM
8	4	2	1	92	14.1	HAZ on the advancing side
higher Grey relational grade means that the corresponding parameter combination is closer to the optimal. The mean response for the Grey relational grade with its grand mean and the main effect plot of Grey relational grade are very important because optimal process condition can be evaluated from this plot.26
3 EXPERIMENTAL PROCEDURE AND TEST RESULTS
3.1 Experimental Details
AA1050-H22 aluminum alloy material was used as a workpiece material with the thickness of 4 mm. The workpieces were machined out in 360 mm lengths and 200 mm widths. The mechanical properties and percent composition of workpiece material is listed in Table 1.
1.2367 (X38CrMoV5-3) hardened and threaded (left screw with 0.8 mm pitch) pins with the shoulder diameters of 15 mm and 20 mm were used as welding tools. The dimensions of the welding tools are shown in Figure 2.
The pre-machined aluminum plates were fixed rigidly on the table of the vertical semiautomatic milling machine for lap joint of FSW as shown in Figure 3.
The rotating tool was fixed to the spindle of the milling machine and then the spindle of the milling machine was adjusted at an angle of 2-3° away from the spindle travel path. To generate the required pre-frictional heating, the shoulder of the rotating tool was held in its ini-
Figure 2: Dimensions of the welding tools used in the experiments: a) 20 mm shoulder diameter, b) 15 mm shoulder diameter Slika 2: Dimenzije pri preizkusih uporabljenih varilnih orodij: a) premer ramena 20 mm, b) premer ramena 15 mm
Figure 4: Dimensions of tensile test specimens Slika 4: Dimenzije raztržnesa preizkušanca
Figure 3: FSW applications on conventional vertical milling machine;
1	milling head, 2 welding tool, 3 aluminum plates, 4 Steel backing plate, 5 clamping setup, 6 machine table
Slika 3: Uporaba FSW na pokončnem vrtalnem stroju;1 vrtalna glava,
2	varilno orodje, 3 aluminijevi plošči, 4 jeklena oporna plošča, 5 pri-jemno orodje, 6 delovna miza stroja
tial position for 30 s rubbing with the surface of the workpiece.
Figure 4 shows the dimensions of the tensile test specimens prepared according to TS138 EN10002-1 standard. The tensile tests were carried out at a room temperature and crosshead speed of 10 mm/min using using a ZWICK Z-050 tensile testing machine. Each tensile test is the average of four specimens cut from the same joint.
3.2 Process Parameters and Test Results
In full factorial design, the number of experimental runs exponentially increases as the number of factors as well as their level increases. This results huge experimentation cost and considerable time.26 So, in order to compromise these two adverse factors and to search the optimal process condition through a limited number of experimental runs, Taguchi's L8 orthogonal array consisting of 8 sets of data has been selected to optimize the multiple performance characteristics of FSW. Experiments have been conducted with the process parameters given in Table 2, to obtain butt welding on AA1050-H22 aluminum 4 mm thickness with (360 x 200) mm dimensions by FSW welding process.
Table 3 shows the selected design matrix based on Taguchi L8 orthogonal array consisting of 8 sets of coded conditions and the experimental results for the responses of TS and E. All these data have been utilized for analysis and evaluation of optimal parameter combination required to achieve desired quality weld within the experimental domain.
4 PARAMETRIC OPTIMIZATION OF FSW PROCESS
4.1 Evaluation of Optimal Process Condition
First, by using Eqs. (1) and (2), experimental data have been normalized to obtain Grey relational genera-tion.26 The normalized data and A0i for each of the responses have been furnished in Table 4 and Table 5 respectively. For TS larger-the-better (LB) and for E smaller-the-better (SB) criterion has been selected.
Table 4: Grey relational generation of each performance characteristics
Tabela 4: Generiranje Greyjeve odvisnosti za značilnosti vsakega preizkusa
Run no
Ideal sequence
TS
Larger-the-better
1
0.966
0.000
0.862
0.828
0.931
0.966
1.000
0.931
E
Smaller-the-better
1
0.463
1.000
0.132
0.412
0.059
0.338
0.000
0.368
Table 5: Evaluation of a0i for each of the responses Tabela 5: Ocena a0i za vsak odgovor
Run no
Ideal sequence
1
8
Ra
1
0.034
1.000
0.138
0.172
0.069
0.034
0.000
0.069
HV
1
0.537
0.000
0.868
0.588
0.941
0.662
1.000
0.632
Table 6 shows the calculated Grey relational coefficients (with the weights of ^ts = 0.7 and ^e = 0.3) of each performance characteristic using Eq. (3).
Table 6: Grey relational coefficient of each performance characteristics (^TS = 0.7, ^e = 0.3)
Tabela 6: Greyjevi koeficienti odvisnosti za značilnosti vsakega preizkusa (^TS = 0.7, = 0.3)
Run no
Ideal sequence
1
TS
1
0 953
0.412
0.829
0.795
0.906
0.951
1.000
1.000
E
1
0.359
1.000
0.564
0.741
0.531
0.685
0.507
0.706
1

4
6

8

ä
f.
1
n

/I
f.
n
s
The Grey relational coefficients, given in Table 7, for each response have been accumulated by using Eq. (4) to evaluate Grey relational grade, which is the overall representative of all the features of FSW quality. Thus, the multi-criteria optimization problem has been transformed into a single equivalent objective function optimization problem using the combination of Taguchi approach and Grey relational analyses. Higher is the value of Grey relational grade, the corresponding factor combination is said to be close to the optimal26.
Table 7: Grey relational grade Tabela 7: Stopnje Greyjeve odvisnosti
Run no
Grey relational grade
0.7747
0.5882
0.7493
0.7787
0.7936
0.8710
Rank
Parameter	Degree of Freedom	Sum of Square	Mean Square	F	Contribution (%)
w	3	0.050	0.020	0.88	65.61
V	1	0.015	0.002	0.62	19.68
D	1	0.010	0.010	0.47	13.12
Error	1	0.0012	0.010		1.58
Total	6	0.0762			100
r 1 11
S / N =-10lg-X-«7=1 V
(5)
Figure 5: S/N ratio plot for the overall Grey relational grade Slika 5: Razmerje S/N za splo{no Greyjevo odvisnost
Table 8: S/N ratio for overall Grey relational grade Tabela 8: Razmerje S/N za splo{no Greyjevo stopnjo
Run no
1
S/N
-2.22
-4.61
-2.51
-2.17
-2.01
-1.20
-1.39
-0.80
Table 9: Response table for the mean Grey relational grade Tabela 9: Odgovori za povprečno stopnjo po Greyu
Factors
d
Level 1 Level 2 Level 3 Level 4 Max-Min
0.68
0.79
0.83
Grey relational grade
0.76
0.78
0.75
0.83
0.88
0.20
0.01
0.08
the-better criterion for overall Grey relational grade calculated by using Eq. (5).
where n is the number of measurements, and yt is the measured characteristic value.
Graphical representation of S/N ratio for overall Grey relational grade is shown in Figure 5. The dashed line is the value of the total mean of the S/N ratio.
As indicated in Figure 5, the optimal condition for the FSW of aluminum alloy becomes W4V1d1. Table 9 shows the mean Grey relational grade ratio for each level of the process parameters.
Total mean Grey relational grade = 0.79
4.2 Analysis of Variance (ANOVA)
The purpose of the analysis of variance (ANOVA) is to investigate which welding parameters significantly affect the performance characteristic.26,33,34 This is accomplished by separating the total variability of the grey relational grades, which is measured by the sum of the squared deviations from the total mean of the grey relational grade, into contributions by each welding parameters and the error.26,34 Thus
SS T = SS F + SS e
where
and
SSt Yj
Ym p
SSf SSe
(Y,
i=1
SS T =X (Y i - Y m )
(6)
(7)
Total sum of squared deviations about the mean
Mean response for jth experiment
Grand mean of the response
Number of experiments in the orthogonal array
Sum of squared deviations due to each factor
Sum of squared deviations due to error
In addition, the F test was used to determine which welding parameters have a significant effect on the
Table 10: ANOVA results of FSW process Tabela 10: ANOVA-rezultati FSW-procesa
Paramptpr
V
D
Tnrrnr
Total
Degree of
Prpprlnm
Sum of Square
0.050
0.015
0.010
0.0012
0.0762
Mean Square
0.020
0.002
0.010
0.010
F
0.88
0.62
0.47
Contribu tion (%)
65.61
19 68
13 19
1 58
100

4
6

8
6
2
8
3

V
5
5
4
6
r>
7
8





f.
performance characteristic. Usually, the change of the welding parameter has a significant effect on the performance characteristic when the F value is large. ANOVA for overall Grey relational grade is shown in Table 10.
4.3 Confirmation Test
After evaluating the optimal parameter settings, the next step is to predict and verify the enhancement of quality characteristics using the optimal parametric combination. The estimated Grey relational grade y using the optimal level of the design parameters can be calculated as:
y=y,

(y ; - y m )
(8)
where ym is the total mean Grey relational grade, yi is the mean Grey relational grade at the optimal level, and o is the number of the main design parameters that affect the quality characteristics.26 Table 11 indicates the comparison of the predicted tensile strength and elongation with that of actual by using the optimal welding conditions. Good agreement between the actual and predicted results has been observed (improvement in overall Grey relational grade was found to be as 0.20).
Table 11: Results of confirmation test Tabela 11: Rezultati preizkusov preverjanja
	Initial factor settings	Optimal process condition	
		Prediction	Experiment
Factor levels	w1V1d1	W4V1d1	W4Vidi
TS	93		96
E	14.8		12.3
S/N ratio of overall Grey relational grade	-2.22	-0.58	-1.80
Overall Grey relational grade	0.72	0.89	0.92
Improvement in Grey relational grade = 0.20
In Taguchi method, the only performance feature is the overall Grey relational grade; and the aim should be to search a parameter setting that can achieve highest overall Grey relational grade.26,33 The Grey relational grade is the representative of all individual performance characteristics. In the present study, objective functions have been selected in relation to parameters of tensile strength and elongation. The weight calculations were done by using Analytic Hierarchy Process (AHP) and the weights were found to be as 0.70 and 0.30 for the responses of tensile strength and elongation respectively.
The results showed that using optimal parameter setting (w4V1d1) caused lower elongation with higher tensile strength.
5 CONCLUSION
Taguchi method is a very effective tool for process optimization under limited number of experimental runs. Essential requirements for all types of welding processes are higher tensile strength with lower elongation. This study has concentrated on the application of Taguchi method coupled with Grey relation analysis for solving multi criteria optimization problem in the field of friction stir welding process. Experimental results have shown that tensile strength and elongation of welded AA1050-H22 aluminum alloy are greatly improved by using Grey based Taguchi method.
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