Friction stir welding of Al-Mg alloy: comparison of process parameter optimization between single and multi response using taguchi methodology.
Vijayan, S. ; Raju, R. ; Rao, S.R.K. 等
Introduction
The AA 5083 is Al-Mg based alloy, which possess many interesting
characteristics such as structural material, moderately high strength,
good corrosion resistance, and low price. These advantages of the alloy
are quite attractive in the automobile industries and marine
applications. [1]. Convectional welding process are found inadequate in
welding Aluminum alloys because of their higher conductivity, hot
cracking and high incidence of porosity. And another important issue in
welding aluminum--magnesium alloys is the pronounced vaporization of
alloying elements. The selective vaporization of volatile alloying
elements, especially magnesium, causes a metal composition change in the
joint, thus affecting the mechanical properties and the corrosion
resistance of the weld. [2]. Laser welding and Friction Stir Welding are
the feasible solutions to overcome this problem as characterized as
lower heat input welding techniques. [3]
Friction Stir Welding (FSW)
FSW is an emerging solid state joining process in which the
materials that is being welded does not melt and recast. [4]. And it has
the ability to weld the unweldable alloys. [5] The basic concept of FSW
is remarkably simple. A non-consumable rotating tool with a specially
designed pin and shoulder is inserted into the abutting edges of sheets
or plates to be joined and traversed along the line of joint (Fig. 1).
[6] The tool serves two primary functions: (a) heating of work piece,
and (b) movement of material to produce the joint. The heating is
accomplished by friction between the tool and the work piece and plastic
deformation of work piece. The localized heating softens the material
around the pin and combination of tool rotation and translation leads to
movement of material from the front of the pin to the back of the pin.
As a result of this process a joint is produced in 'solid
state'. Because of various geometrical features of the tool, the
material movement around the pin can be quite complex [7]. During FSW
process, the material undergoes intense plastic deformation at elevated
temperature, resulting in generation of fine and equiaxed recrystallized
grains [8-11]. The fine microstructure in friction stir welds produces
good mechanical properties. Friction stir welding of aluminum alloys
gains its importance in the present scenario among all other
conventional fusion welding process for its Metallurgical Environmental
and Energy benefits.
[FIGURE 1 OMITTED]
Though research work applying taguchi methods have been used in
many literatures, the optimization of FSW process parameter of AA 5083
using taguchi method has not been reported yet.
FSW Process Parameters
The tool geometry, welding parameters, joint designs are the
significant parameters which significant effect on the material flow
pattern and temperature distribution, thereby influencing the micro
structural evolution of material. [6]. The detailed list of FSW process
parameters are listed bellow and the FSW tool dimension is shown in the
fig 2.
FSW process parameters
(1) Rotational speed (rpm)
(2) Welding speed (mm/s)
(3) Axial force (KN)
(4) Tool geometry
(i) D/d ratio of tool
(ii) Pin length (mm)
(iii) Tool shoulder diameter, D (mm)
(iv) Pin diameter, d (mm)
(v) Tool inclined angle ([degrees])
[FIGURE 2 OMITTED]
In this investigation rotational speed, transverse speed and axial
load are taken into consideration. The levels of the process parameter
are listed in table no 1.
Taguchi method
Taguchi addresses quality in two main areas: off-line and on-line
quality control. Both of these areas are very cost sensitive in the
decisions that are made with respect to the activities in each. Offline
quality control refers to the improvement in quality in the product and
process development stages. On-line quality control refers to the
monitoring of current manufacturing processes to verify the quality
levels produced [12]. The most important difference between a classical
experimental design and a Taguchi-method-based robust design technique
is that the former tends to focus solely on the mean of the quality
characteristic while the later considers the minimization of the
variance of the characteristic of interest. Although, the Taguchi method
has drawn much criticism due to several major limitations, it has been
able to solve single response problems effectively.
The following are the steps to be followed for process parameter
optimization for single response problem [13]
Step 1: Determine the quality characteristic to be optimized
Step 2: Identify the Noise factors and Test conditions
Step 3: Identify the control factors and their Alternative Levels
Step 4: Design the Matrix Experiment and Define the data analysis
procedure.
Step 5: Conduct the matrix Experiment
Step 6: Analyze the Data and determine optimum levels for control
factors
Step 7: Predict the performance at these levels.
Methodology to solve Multi Response problem using Taguchi method
In DOE the numbers of experiments increases when the levels and
factors of the process increases. Taguchi has used the orthogonal array
to study the entire process parameter window by conducting less number
of experiments. Taguchi has derived the three important signals to noise
ratios (S/N) depending on the type of the quality characteristics. They
are Nominal the best, Smaller the better, Higher the better. The Higher
the better is used for maximization, while Smaller the better is used
for minimization quality characteristics problem. In this study the
input energy and tensile strength of the welded joints are taken into
consideration. Both has conflicting objective i.e., the tensile strength
of the FSW has to be maximized while the input energy should be
minimized. In this study the Assignment of Weight method is used to
solve the multi response problem. [14]. The individual loss function is
integrated into overall loss function by assigning weights to each loss
function. The value of the overall loss function is further transformed
into signal to noise ratio. Based on the quality characteristics of the
response intended the S/N ratio for each level of process parameter is
calculated. Higher the S/N ratio implies better the quality,
irrespective to maximization or minimization. Therefore the highest S/N
ratio corresponds to the optimal level of the parameter. ANOVA is
performed to find the significant process parameter. A confirmation test
is conducted to validate the predicted optimal levels found out from the
analysis. The methodology used to solve multi response problem using
taguchi is taken from the literature of Jeyapaul and Sathya [15-16]. The
methodology is described by the following steps.
Step 1
The S/N ratio is computed based on the quality character tics of
the response. The tensile strength of the FSW welded joints has to be
maximized so Larger the best S/N ratio is to be used and the input power
has to be minimized, hence smaller the better S/N ratio is to be used.
The formula to compute the SN ratios are given bellow.
Larger the Best
S/N Ratio ([eta]) = -10 [log.sub.10] 1/n [n.summation over (i = 1)]
1/[y.sup.2.sub.ij]
Smaller the Best
S/N Ratio ([eta]) = -10 [log.sub.10] 1/n [n.summation over (i = 1)]
[y.sup.2.sub.ij]
Step 2
The S/N ratio values are normalized to the scale of 0 to 1. The
normalization is helpful to interpret the scatter the data and it will
be used for further analysis. The formula used for normalization is
given bellow.
[Z.sub.ij] = [y.sub.ij] - min([y.sub.ij], i =
1,2,3,........n)/max([y.sub.ij], 1,2,3,......n) - min([y.sub.ij],
1,2,3,.........n)
[To be used for larger the best S/N Ratio]
[Z.sub.ij] = max([y.sub.ij], i = 1,2,3,........n) -
[y.sub.ij]/max([y.sub.ij], i = 1,2,3,......n) - min ([y.sub.ij], i =
1,2,3,.........n)
[To be used for smaller the better S/N Ratio]
Step 3
The weights are assigned to the responses and the multiple
responses are converted into the single response index. Three cases of
weights were considered and the weights are shown in table 2
Step 4
The weighted SN ratio is calculated from the weights assigned. The
weighted S/N Ratio is given as
[WSN.sub.i] = [W.sub.1] [Z.sub.11] + [W.sub.2][Z.sub.12] +
............................ + [W.sub.j][Z.sub.ij]
Step 5
The optimum combination levels of the factors are determined.
Maximization of SN ratio results in better product quality; therefore,
on the basis of weighted SN ratio, the factor is estimated and the
optimal level for each controllable factor is determined. For example,
to estimate the effect of factor i, we calculate the average of weighted
SN ratio values (WSN) for each level j, denoted as WSN ij, then the
effect [E.sub.i] is defined as:
[E.sub.i] = max ([WSN.sub.ij]) - min ([WSN.sub.ij])
If the factor j is controllable, the best level j*, is determined
by J * = [max.sub.j]([WSN.sub.ij])
Step 6
Perform ANOVA for identifying significant factors.
Step 7
Calculate the predicted optimum condition using the following
additive model.
[bar.[eta]] = [[eta].sub.m] + [q.summation over (i = 1)]
([bar.[eta]] - [[eta].sub.m.]
Step 8
Conduct the confirmation experiments.
Selection of Orthogonal Array (OA)
The selection of which orthogonal array to use predominately
depends on these items in order of priority: [17]
(i) The number of factors and interactions of interest
(ii) The number of levels for the factors of interest
(iii)The desired experimental resolution or cost limitations
As three levels and three factors are taken into consideration, L9
OA is used in this investigation. Only the main factor effects are taken
into consideration and not the interactions. The degrees of freedom
(dof) for each factor is 2(No of levels 1,ie 3-1=2) and therefore the
total degrees of freedom will be 3x2=6.Generally the dof of the OA
should be greater than the total dof of the factors. As the dof of L9 is
8 it can be suitable for the study.
Experimental procedure
Single pass butt welds were produced in 5 mm thick plates of
aluminum alloy 5083 using indigenously designed friction stir welding
machine. The machine can rotate the tool at up to 3000 RPM, apply an
axial load of 30 KN and the transverse speed can be 500mm/min. A
wattmeter is connected to the motors of the FSW machine to measure the
power consumed by the machine. A cylindrical taper tool (M2 tool steel)
of hardness 50-55 VHN with shoulder diameter 15 mm and pin diameter 5 mm
is used for this work. The length of the tool pin is 4.5 mm. The
chemical composition and mechanical properties of the plate are given in
the table 2and 3 respectively.
The rolled plates of 5 mm thickness plate were cut into required
shapes (300 mm x 150 mm) using shaper and milling machine. The
mechanical clamps are used to clamp the plate in the work table of the
machine. The butt joints were fabricated normal to the rolling
direction. The experiments were conducted using parameters of the
designed matrix. The American Society for Testing Materials (ASTM -E8)
guidelines were followed for preparing the tensile test specimens. The
wire cut EDM is used to cut the smooth profile tensile specimens. To
minimize the machining error (noise) three specimens were prepared at
each levels of the designed matrix. The 27 prepared tensile specimens
were subjected to tensile test and its ultimate tensile strength is
evaluated. The experiments were conducted according to the designed L9
OA. The following table no 4 will give the values of designed
experimental layout.
[FIGURE 3 OMITTED]
Results and discussion
Single objective optimization
The following will describes the optimization of the process
parameters with single objective function. The tensile strength of the
FSW joints is the response taken into consideration.
Signal to noise Ratio
The SN Ratio is calculated based on the quality of the
characteristics intended. The objective function described in this
investigation is maximization of the tensile strength so, the Larger the
best SN ratio is to calculated. The formula used for calculating the SN
ratio is given bellow
Larger the Best
S/N Ratio ([eta]) = -10 [log.sub.10] 1/n [n.summartion over (i =
1)] 1/[y.sup.2.sub.ij]
The Tensile strength of the Friction Stir welding joints values is
analyzed to study the effects of the FSW process parameters. The
experimental data's are converted into mean and SN ratio. The
calculated mean and SN ratio values are tabulated in the table 7. The
main effects, average mean and SN ratio values of all levels are
calculated and listed in the table 8, 9 & 10. Irrespective of the
objective function whether maximization or minimization the larger SN
Ratio corresponds to the better quality characteristics [18]. Based on
both mean and SN ratio values the optimal level setting is
[RS.sub.2][TS.sub.1][AF.sub.3] ie., the rotational speed is to set at
65o rpm, the transverse speed has to be set at 115mm/min and the axial
force is to be 17 KN based on the experimental results.
Analysis of Variance (ANOVA)
The purpose of ANOVA is to find the significant factor
statistically. It gives a clear picture how far the process parameter
affects the response and the level of significance of the factor
considered. The ANOVA table for both mean and SN ratios are calculated
and listed in the table no 11 & 12.The main effects for mean and SN
ratio is plotted in the Figure 4&5. The F test is being carried out
to study the significances of the process parameter. The high F value
indicates that the factor is highly significant in affecting the
response of the process. In our investigation, for the material AA 5083
the rotational speed is highly significant factor and plays a major role
in affecting the tensile strength of the weld. The effect of axial force
doesn't make any impact in the responses.
[FIGURE 4 & 5 OMITTED]
Predicted value of tensile strength
Based on the experiments, the optimum level settings is
[RT.sub.2][TS.sub.1][AF.sub.3].The additive model to evaluate the
predicted tensile strength is taken from the literature. [18]. The
average values of the factors at their levels are taken from the table 7
and the predicted value of the response is given bellow.
Tensile strength (predicted) = RT 2 + TS1 + AF3 - 2T
= 270 + 211.7 + 199.7 - 2(191.5889)
= 298.222 Mpa
Where
RT2 : Average mean value of rotational speed at 2 level
TS1 : Average mean value of Transverse speed at 1 level
AF3 : Average mean value of Axial Force at 3 level
T : Overall Mean
Confirmation Run
The confirmation experiments were carried out by setting the
process parameter at optimum levels. The rotational speed, Transverse
speed, and axial force were set at 650 rpm, 115 mm/min and 17 KN
respectively. Three tensile specimens were subjected to tensile test and
the average value of the Friction Stir welded AA 5083 was 301Mpa.
Multi objective optimization
The following will describes the optimization of the process
parameters with multi objective function. The tensile strength of the
FSW joints and the power input are the response taken into consideration
Results and discussion
The SN ratio for the tensile strength and input power is computed
and normalized. The weighted SN ratios for all the nine experiments were
calculated and listed in the table 13. The effects of normalized SN
ratio for each level were summarized and listed in the table 14, 15,
& 16.
From the SN responses tables 14 -16 the predicted levels of
friction stir welding parameters for case 1 and case 2 are A2B1C1.ie,
the rotation speed of the tool is to be set at 650 rpm, the transverse
speed at 115 mm/min and the axial force is at 9 kN. And A2B1C2 is the
predicted levels of the parameter for the case 3. The rotational speed,
transverse speed and the axial force is set at 650 rpm, 115 mm/min, and
9 kN respectively. The confirmation experiments were carried out by
setting the levels of the process parameters at their predicted levels.
Analysis of Variance (ANOVA)
The purpose of ANOVA is to find the significant factor
statistically. It gives a clear picture how far the process parameter
affects the response and the level of significance of the factor
considered. The ANOVA tables for the three cases are listed in the table
17 -19. The F test is being carried out to study the significances of
the process parameter. The high F value indicates that the factor is
highly significant in affecting the response of the process. In our
investigation, for the material AA 5083 the rotational speed is highly
significant factor and plays a major role in affecting the tensile
strength of the weld.
Predicted SN value
Based on the experiments, the optimum level settings isA2B1C1 fie
case 1 &2 and A2B1C2 for case 3. The additive model to evaluate the
predicted tensile strength is taken from the literature. [18]. The
average values of the factors at their levels are taken from the table 7
and the predicted value of the response for all the cases is given
bellow.
Case 1
SN Ratio (predicted) = RT 2 + TS1 + AF1 - 2T1
= 0.7512 + 0.5275 + 0.5610 - 2 * 0.448
= 0.9437
Case 2
SN Ratio (predicted) =RT 2 + TS1 + AF1 - 2T2
= 0.8005 + 0.5403 + 0.5062 - 2 * 0.4445
= 0.958
Case 3
SN Ratio (predicted) =RT 2 + TS1 + AF2 - 2T3
= 0.8496 + 0.55313 + 0.45176 - 2 * 0.4442
= 0.96609
Where
RT2: Average SN Ratio value of rotational speed at 2nd level
TS1: Average SN Ratio value of Transverse speed at 1st level
AF1: Average SN ratio value of Axial Force at 1st level
AF2: Average SN ratio value of Axial Force at 2nd level
T [1, 2, 3]: verall Mean SN ratio at level 1, 2, and 3
Confirmation Run
The confirmation experiments were carried out by setting the
process parameter at optimum levels. The result of the confirmation run
is given in the table 20.The results of the confirmation run is
converted into SN Ratios and the comparisons of predication and
confirmation is shown in the table 21.
Comparison between single and multi objective optimization
In the case of single objective optimization the optimized FSW
process parameters are the rotational speed of the tool is 650 rpm, the
Transverse speed is 115 mm/min, and axial force is 17 kN. Three tensile
specimens were subjected to tensile test and the average value of the
Friction Stir welded AA 5083 was 301Mpa.
In the case of multi objective optimization the FSW process
parameter are the rotational speed of the tool is 650 rpm, the
Transverse speed is 115 mm/min, and axial force is 9,13 kN. When the
axial force is 9 kN & 13 kN the tensile strength of the FSW joints
are 270 &286 Mpa, provided other two process parameter remain the
same.
Conclusion
(1) The L9 Taguchi orthogonal designed experiments of Friction Stir
Welding on Aluminum Alloy AA 5083 were successfully conducted.
(2) The FSW process parameters are optimized towards the tensile
strength of the joint and the optimum level of settings were found out.
The optimum levels of the rotational speed, Transverse speed, and axial
force are 650 rpm, 115 mm/min and 17 kN respectively.
(3) The FSW process parameters are optimized towards the tensile
strength of the joint and input power. The optimal levels of the
rotational speed, Transverse speed, and axial force is 650 rpm, 115
mm/min and 9 kN respectively.
(4) The rotational speed of the tool is the highly significant
factor
(5) The input power increases significantly with increase in the
axial force
Acknowledgements
The authors are grateful to the Department of Mechanical
Engineering, SSN College of Engineering, Kalavakkam, chennai, Tamil
Nadu, India for extending the facilities of Workshop and Materials
Testing Laboratory to carry out this investigation. The authors also
wish to express their sincere thanks to Naval Research Board (NRB),
Ministry of Defense, New Delhi for the financial support to carry out
this investigation through sponsored project No.DNRD/05/4003/NRB/82.
References
[1] M. Czechowski, (2005) Low-cycle fatigue of friction stir welded
Al-Mg alloys, J.Mater. Proc. Tech. 164/165 1001-1006.
[2] Hecht RL, Kannan K. In: Ghosh AK, Bieler TR, (1995) Super
plasticity and super plastic forming. PA: Warrendale; p. 259
[3] H. Zhao, et al., (1999) Current issues and problems in laser
welding of automotive aluminum alloys, Int. Mater. Rev. 44 (6) 238-266.
[4] COLLIGAN K. (1999) Material flow behavior during friction stir
welding of aluminum [J]. Welding Journal, 7: 229-237.
[5] LIU H J, FUJI H, MAEDA M, NOGI K. Mechanical properties of
Friction stir welded joints of 1050-H 24 aluminum alloy [J]. Science and
Technology of Welding and Joining, 2003, 8: 450-454
[6] R.S. Mishra, Z.Y. Ma (2005)/Materials Science and Engineering R
50 1-78
[7] B. London, M. Mahoney, B. Bingel, M. Calabrese, D. Waldron,
(2001) in: Proceedings of the Third International Symposium on Friction
Stir Welding, Kobe, Japan, 27-28 September.
[8] C.G. Rhodes, M.W. Mahoney, W.H. Bingel, R.A. Spurling, C.C.
Bampton, (1997) Scripta Mater. 36 69.
[9] G. Liu, L.E. Murr, C.S. Niou, J.C. McClure, F.R. Vega, (1997)
Scripta Mater. 37 355.
[10] V. Jata, S.L. Semiatin, Scripta Mater. 43 (2000) 743.
[11] S. Benavides, Y. Li, L.E. Murr, D. Brown, J.C. McClure, (1999)
Scripta Mater. 41 809.
[12] Ross PJ (1996) Taguchi Techniques for Quality Engineering.
McGraw-Hill, Singapore.
[13] Saurav Datta, Asish Bandyaopadhyay, Pradip kumar Pal (2006)
Int. J. Adv. Manufacturing Technology. Springer
[14] R. Jeyapaul P. Shahabudeen K. Krishnaiah (2005) Quality
management research by considering multi-response problems in the
Taguchi method--a review Int J Adv Manuf Technol 26: 1331-1337
[15] R. Jeyapaul. P. Shahabudeen. K. Krishnaiah Simultaneous
optimization of multi-response problems in the Taguchi method using
genetic algorithm Int J Adv Manufuring Technology (2006) 30: 870-878
[16] Paulraj Sathiya, S. Aravindan A. Noorul Haq (2006)
Optimization for friction welding parameters with multiple performance
characteristics Int J Mech Mater Des 3:309-318
[17] Ross PJ (1996) Taguchi Techniques for Quality Engineering.
McGraw-Hill, Singapore.
[18] K. LAKSHMINARAYANAN, V. BALASUBRAMANIAN Process parameters
optimization for friction stir welding of RDE-40 aluminium alloy using
Taguchi technique. Transactions of non ferrous metal society of china18
(2008)548-554
S. Vijayan (1), R. Raju (2) and S.R.K. Rao (3)
(1) Department of Mechanical Engineering, SSN college of
Engineering, Chennai, Tamilnadu, India.
(2) Department of Industrial Engineering, Anna University, Chennai,
Tamilnadu, India
(3) Principal, Tagore Engineering College, Chennai, Tamilnadu,
India (1) E-mail: vijayans@ssn.edu.in
Table 1: FSW parameters and their Levels.
Symbol Welding Unit Level 1 Level 2 Level 3
parameter
A Rotational rpm 500 650 800
speed
B Transverse mm/min 115 135 155
Speed
C Axial Load kN 9 13 17
Table 2: Weightage of output variables.
Case No Tensile strength Input Power
Weights Weights
1 0.7 0.3
2 0.8 0.2
3 0.9 0.1
Table 3: Chemical Composition of the plate AA 5083, wt %.
Material Mg Mn Fe Si Cu Cr Zn
AA 5083 4.15 0.73 0.31 0.13 < 0.025 < 0.01 < 0.01
Material Ti Al
AA 5083 < 0.01 Remaining
Table 4: Mechanical properties of the base plate AA 5083.
AA 5083 Yield Ultimate % Elongation % Reduction
Strength/Mpa Tensile in Area
Strength/Mpa
Base Metal 260.67 291.67 26.42 23.77
Table 6: Experimental Layout using L9 orthogonal Array response table.
Sl.No Rotational Transverse Axial Mean Tensile Mean Input
speed Speed load Strength power Watts
rpm mm/min KN Mpa
1 1 1 1 188.333 746.67
2 1 2 2 171.667 1033.33
3 1 3 3 149.000 1206.67
4 2 1 2 282.000 1073.33
5 2 2 3 286.333 1266.67
6 2 3 1 228.000 783.33
7 3 1 3 156.333 1266.67
8 3 2 1 129.000 776.67
9 3 3 2 133.667 1026.67
Table 7: Mean value and SN value.
Sl No Input Parameter Response Mean
RS TS AF T1 T2 T3 value SN Ratio
1 500 115 9 191 186 188 188.3 45.4970
2 500 135 13 171 175 169 171.667 44.6910
3 500 155 17 147 154 146 149.0 43.4564
4 650 115 13 287 280 279 282.0 49.0029
5 650 135 17 295 280 284 286.333 49.1311
6 650 155 9 228 231 225 228.0 47.1572
7 800 115 19 157 156 156 156.333 43.8809
8 800 135 9 127 129 131 129.0 42.2097
9 800 155 13 130 135 136 133.667 42.5154
Table 8: Main effects of the process parameters.
Process Level Mean SN Ratio
Parameter A(RS) B(TS) C(AF) A(RS) B(TS) C(AF)
Average L1 169.7 211.7 182.0 44.54 46.23 44.95
value L2 270.0 197.7 196.0 48.57 45.38 45.37
L3 138.0 168.3 199.7 42.76 44.26 45.55
Main L2-L1 100.3 -14 14 4.03 -0.85 0.42
effects L3-L2 -31.7 -43.4 3.7 -5.81 -1.12 0.18
Table 9: Response Table for Signal
to Noise Ratios.
level RS TS AF
1 44.54 46.23 44.95
2 48.57 45.38 45.37
3 42.76 44.26 45.55
Delta 5.81 1.97 0.60
Rank 1 2 3
The optimal setting is [RS.sub.2]
[TS.sub.1][AF.sub.3] based on SN ratio
Table 10: Response Table for Means.
level RS TS AF
1 169.7 211.7 182.0
2 270.0 197.7 196.0
3 138.0 168.3 199.7
Delta 132 43.3 17.7
Rank 1 2 3
The optimal setting is [RS.sub.2]
[TS.sub.1][AF.sub.3] based on Mean
Table 11: Analysis of Variance for Means.
Source DoF Seq SS Adj SS Adj MS F % Contribution
RS 2 25893.4 25893.4 12946.7 45.78 88.6363
TS 2 2317.4 2317.4 1158.7 4.10 7.9327
AF 2 436.6 436.6 218.3 0.77 1.4945
Residual 2 565.7 565.7 282.8 1.9365
Error
Total 8 29213.1 29213.1 100
Table 12: Analysis of Variance for SN Ratio.
Source DoF Seq SS Adj SS Adj MS F % Contribution
RS 2 14.584 14.584 7.292 1.83 45.67777
TS 2 4.848 4.848 2.424 0.61 15.18416
AF 2 4.544 4.544 2.272 0.57 14.23202
Residual 2 7.952 7.952 3.976 24.90604
Error
Total 8 31.928 31.928 100
DoF--Degrees of freedom, Seq SS--Sequencial sum of squares,
Adj SS--Adjusted sum of square, Adj MS--Adjusted mean square,
SS'--Pure sum of squares, F--Fisher ratio
Table 13: The Weighted SN Ratio.
Tensile strength Input Power S/N S/N
Ex. Ratio for Ratio for
No T1 T2 T3 P1 P2 P3 tensile input
strength power
1 191 186 188 760 720 760 45.497 -57.4653
2 171 175 169 1050 1010 1040 44.691 -60.286
3 147 154 146 1220 1220 1180 43.456 -61.6328
4 287 280 279 1090 1040 1090 49.003 -60.6168
5 295 280 284 1280 1280 1240 49.131 -62.0542
6 228 231 225 800 750 800 47.157 -57.8829
7 157 156 156 1280 1240 1280 43.881 -62.0542
8 127 129 131 800 780 750 42.21 -57.8077
9 130 135 136 1030 1020 1030 42.515 -60.2287
Normalized Normalized
Values of Values of Weighted SN Ratio
Ex.
No SN Ratio SN Ratio 0.7T * 0 0.8T * 0.9T *
for Tensile for Input .3P 0.2P 0.1P
strength Power
1 0.4749 1.0000 0.6325 0.5799 0.5274
2 0.3585 0.3853 0.3665 0.3638 0.3612
3 0.1800 0.0918 0.1536 0.1624 0.1712
4 0.9815 0.3132 0.7810 0.8479 0.9147
5 1.0000 0.0000 0.7000 0.8000 0.9000
6 0.7148 0.9090 0.7730 0.7536 0.7342
7 0.2414 0.0000 0.1690 0.1932 0.2173
8 0.0000 0.9254 0.2776 0.1851 0.0925
9 0.0441 0.3978 0.1502 0.1148 0.0794
Table 14: SN ratio for welding parameters case 1.
Symbol Welding Parameter 1 level 2 level 3 level
A Rotational speed(RS) 0.3842 0.7514 0.1989
B Transverse Speed(TS) 0.5275 0.4480 0.3589
C Axial Load(AF) 0.5610 0.4326 0.3409
Setting A2B1C1
Table 15: SN ratio for welding parameters case 2.
Symbol Welding Parameter 1 2 3
A Rotational speed 0.3687 0.8005 0.1643
B Transverse Speed 0.5403 0.4496 0.3436
C Axial Load 0.5062 0.4422 0.3852
Setting A2B1C1
Table 16: SN ratio for welding parameters case 3.
Symbol Welding Parameter 1 2 3
A Rotational speed 0.35327 0.8496 0.12975
B Transverse Speed 0.55313 0.451232 0.32828
C Axial Load 0.451393 0.45176 0.429502
Setting A2B1C2
Table 17: Case 1 ANOVA.
Symbol Source Degrees of Sum of Mean F
freedom squares square
A Rotational speed 2 0.474256 0.237128 37.84
B Transverse Speed 2 0.042668 0.021334 3.4044
C Axial Load 2 0.073386 0.036693 5.8554
Error 2 0.012533 0.0062665
Total 8 0.602843
Table 18: Case 2 ANOVA.
Symbol Source Degrees of Sum of Mean F
freedom squares square
A Rotational speed 2 0.632869 0.31643 41.652
B Transverse speed 2 0.058174 0.029087 3.8287
C Axial Load 2 0.021986 0.010993 1.4470
Error 2 0.015194 0.007597
Total 8 0.728223
Table 19: Case 3 ANOVA.
Symbol Source Degrees of Sum of Mean F
freedom squares square
A Rotational speed 2 0.814603 0.40730 44.822
B Transverse Speed 2 0.076069 0.03803 4.1855
C Axial Load 2 0.000974 0.00048 0.0535
Error 2 0.018174 0.00908
Total 8 0.909820
Table 20: Experimental results for the optimized parameter.
Ex. No A, Rotational B, Transverse C, Axial Tensile Power
speed(rpm) speed (mm/min) force (kN) Strength Watts
Mpa
1 650 115 9 270 740
2 650 115 1.3 286 1020
Table 21: Comparison between the predicted and
Experimental value.
Predicted value Experimental value
Case 1 0.9437 0.9467
Case 2 0.9580 0.9402
Case 3 0.96609 0.9405
