1 Introduction

The heat treatable Al–Mg–Si alloys conforming to aluminum alloy 6061 has adequate strength along with its welding properties as compared to high strength aluminum alloys. The AA6061 is very difficult to join using butt or lap joints through conventional arc welding techniques due to high thermal conductivity. As the result, such designated welding procedure would become difficult to incorporate high-quality defect-free welding under favorable process parameters. The mechanical properties such as machinability, weldability, etc. of AA6061 have wide applications in the aerospace industry and ship building resulting the corrosion resistance over other aluminum alloys [1, 2].

Friction Stir Welding (FSW) involves the adequate solid-state joining technique resulting the melting point below of the order of 80% of the liquidus temperature of the parent metal [3]. This technique incorporates rotating non-consumable tool resulting heat generation without filler or fusion material. FSW is performed by butt joining of two plates and traversing the rotating tool at the interface of the plates. Welding controlled through a combined action of stirring process of rotating tool and frictional heating. The welding process widely applicable in numerous fields of engineering involving automotive industries, aerospace, ship-building, railways etc. due its low construction cost reduced welding distortion and enhanced mechanical properties as compared to other solid state welding processes [4].

Owing to numerous investigations carried out for FSW process over the last three-decade focusing on the mechanical-metallurgical properties of welding. These processes largely depend on the operating parameter such as tool profile and tool movement. Sun and Fujji [5] experimentally verified the role of tool pin profile in improving the weld quality and reducing weld defects. Lui et al. [6] considered the parametric effect on weld geometry and localized heating. Elangovan et al. [7] investigated the influence of pin profile and fabricated the butt joints at different welding operating parameters. Palanivel et al. [8] conducted FSW on dissimilar aluminum alloy (AA5083H111-AA6351T6) and proposed a mathematical relationship for the processes parameter and wear resistant. Patil and Soman[9] carried friction stir welding on AA6082-O aluminum alloys to analysis the tool pin profiles and welding speed on butt weld. They confirmed the relationship between welding speedwith ultimate tensile stress and tool pin profile with elongation. The visual appearance of the weld was found satisfactory with no defect. Taper screw thread pin produced joints exhibit superior tensile properties. Cabibbo et al. [10] evaluated micro-structuraland mechanical behavior of AA6056-T6 friction stir welded aluminum alloy. They observed that the weld depicted lower ultimate tensile and yield strength, leading to the weld region having lower ductility in comparison to the parent material.

Chen [11] implemented Taguchi technique to determine the working speed and rotation speed to obtain optimum tensile strength for friction stir welded AA6061.Jayaraman et al. [12] conducted a FSW experimentation work for A319 to optimize tensile strength for different variables like rotational speed, axial force, and linear velocity. The Taguchi techniques has adopted by various researchers to obtain the optimum working condition [13,14,15].

As per the above discussion, it is evident that FSW can be used advantageously to weld aluminium alloys. It is clearly observed that the properties greatly depend on the operating parameters. Therefore, FSW involves several variable process parameters which affect the mechanical properties. Therefore, it becomes necessary to analyze and predict an appropriate value of the process parameter to obtain an optimal mechanical property. Owing to referred article, the researchers did not investigate material characteristic and process parameters of FSW butt joint. The present investigation deals with the controlled parameters with tensile strength, hardness and temperature distribution for FSW butt joint of AA6061. The developed regression analysis with experimental values is validated with optimized process parameters obtained from Taguchi method.

2 Experimentation

2.1 Weld setup, tool and process parameters

The FSW experimental investigation was conducted with modified heavy duty milling machine, having a capacity of 7.5HP motor. Suitable collate was used to mount the tool in vertical arbor of the milling machine. The space between horizontal bed and plates to be joined was set to zero root gaps resulting no slip of the plates during tool movement. The workpiece is allowed to have movement along the interface and tool remains just above the interface. The spindle speed and transverse speed of the bed was set prior to welding. The rotating tool was plunged into the workpiece at one end of the interface. The contact between plate surface and tool shoulder was verified then bed movement in translation direction is provided. The annealed aluminum alloy AA6061-T6 plates of 5 mm thickness was cut to rectangular plate of dimension 120 mm × 75mm with the help of electron discharge machining. The experimental setup and chemical composition of AA6061-T6 aluminum alloys are depicted in Fig. 1 and Table 1 respectively. For welding of the two similar plates, four different tool geometries namely straight cylindrical, straight square pin, straight triangular pin, and tapered pin have been used and geometry of tool pin profile is depicted in Fig. 2. The welding has been done at different rotation speed and transverse speed of the tool, the rotational speed varying from 400 to 1600 rpm and traverse speed varying from 10 to 63 mm/min.

Fig. 1
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Experimental setup of the FSW process

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Table 1 Chemical analysis of workpiece (AA6061-T6)
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Fig. 2
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FSW tool pin profiles a Cylindrical b Square c Triangular and d Tapered

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The tool used for welding aluminium alloy is made of tool steel (AISI H13) with constituent element provided in Table 2. The oil quenching of tool resulted to increase its hardness (55HRC). The tool consisting 18 mm shoulder diameter and 4.7 mm pin length used FSW.

Table 2 Constituent element of toolsteel
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2.2 Orthogonal array

The L16 orthogonal Taguchi design consisting of 4 levels and 3 factors depicted in Table 3 is implemented for obtaining an optimized value of the FSW parameter. The controlled parameters of FSW for the analysis of welding are tool rotational speed, traverse speed, and tool geometry. The S/N analysis is performed for individual level of process parameter based on the obtained results by Taguchi method. The highest value of the S/N ratio corresponds to the optimized value of the experiment achieved for regardless of the category for the quality characteristic [16].

Table 3 Control variables and their levels
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2.3 Tensile strength test

The welded specimen AA6061-T6 used in CNC Milling machine has been prepared as per instruction of ASTM E8M-04 standards [17] to evaluate tensile properties of the welded portion. The dimensions of the prepared welded specimen for the tensile test aredepicted in Figs. 3 and 4 respectively. The prepared specimenis tested inUniversal Testing Machine with load capacity of 100kN for the tensile strength and percentage elongation with constant crosshead displacement of 0.5 mm/min.

Fig. 3
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ASTM E8 sub size specimen; Tensile specimen

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Fig. 4
figure 4

Specimens for welded plates

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2.4 Measurement of micro-hardness

The micro hardness of the welded joints was determined with help of a micro-hardness machine (Fig. 5), with 0.2 kg of test load for 15 s of loading time. The indentation was performed at mid-section of the welded region of the plates across the joint.

Fig. 5
figure 5

Micro-hardness machine

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3 Optimization methodology

Today, world is witnessing customer driven market which leads to manufacturing and unique product. The product should be more and more reliable, robust, compact and processes should be progressively matured. The optimization of operating parameters and composition of materials has become essential for product features [18,19,20]. The simplest and systematic approach for FS welding optimization techniques is Taguchi's method which is used to obtain high quality, low cost and excellent design for performance with acceptable results.

The controlled parameters like percentage elongation, tensile strength, and hardness were analyzed and optimized for FSW process. The signal to noise (S/N) ratios for each control factor performance is calculated and served as the objective functions for optimization. The predicated optimum results were evaluated for the criterion of the “larger-the-better” which chosen for S/N ratio to maximize the response from Eq. 1.

$$ S/N = - 10\log_{10} \frac{1}{N}\sum\limits_{i = 1}^{n} {\frac{1}{{X_{i}^{2} }}} $$
(1)

where, \(X_{i}\) is the function of tensile strength, percentage elongation and hardness for the ith test, \(N\) is the total number of data points, and \(n\) is the number of tests.

4 Result and discussion

4.1 Analysis of S/N ratio

By means of the experimental design through Taguchi techniques, tensile strength (TS), percentage elongation (PE) and hardness (H) were calculated for individual combination of control factors and S/N ratios were optimized for calculated control factors with the "larger-the-better" condition. The significant values tool geometry (TG), welding speed (WS) and rotating speed(RS) emphasized to tensile strength, percentage elongation and hardness resulting product quality improvement and lower cost production.

The S/N ratio graphs in Figs. 6, 7 and 8 depicted optimal welding parameters for minimizing the TS, PE and H. The optimal levels for each control factor were computed as per the S/N ratio highest value. The tool geometry (Level 1, S/N = 44.32), rotation speed (Level 4, S/ N = 43.69) and rotation speed (Level 4, S/N = 45.07) were achieved for optimum value for tensile strength. Similarly, for square pin profile, the optimum Tensile Strength value was obtained at a rotation speed (RS4) of 1600 rpm and at a feed rate (WS4) of 63 mm/min (Fig. 6), Corresponding to the tool geometry (Level 1, S/N = 18.22), rotation speed factor (Level 4, S/N = 17.68) and rotation speed factor (Level 4, S/N = 18.79) and optimal percentage elongation achieved for S/N ratios12.59%.

Fig. 6
figure 6

Effect of process parameters on average S/N ratio for TS

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Fig. 7
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Effect of process parameters on average S/N ratio for PE

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Fig. 8
figure 8

Effect of process parameters on average S/N ratio for H

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The optimum levels and S/N ratios were determined for the optimal result of hardness corresponding to tapered pin profile factor (Level 4, S/N = 40.94), RS factor (Level 1, S/N = 40.72) and WS factor (Level 3, S/N = 40.58). The optimum hardness value was achieved at rotation speed of 400 rpm and at a feed rate of 40 mm/min for tapered pin profile as depicted in Fig. 8. The S/N response for optimal values of TS, PE and H are depicted in Table 4. The S/N ratio values for tensile strength, percentage elongation and hardness are represented in Table 5.The average S/N ratio was determined as 43.31 dB, 16.3 dB and 40.17 dB for 148.53 MPa of tensile strength, 6.95% percentage elongation and 102.44HV hardness respectively, at the end of the welding experiments.

Table 4 S/N ratio for TS, PE and H factor
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Table 5 The similar friction stir welding results of experimental and S/N ratios values
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\(P_{TS}\) (Tensile strength total mean value) = 148.53 MPa

\(P_{TS - S/N}\)(Tensile strength S/N ratio total mean value) = 43.31 dB

\(P_{PE}\) (Percentage elongation total mean value) = 6.95%

\(P_{PE - S/N}\)(Percentage elongation S/N ratio total mean value) = 16.3 dB

\(P_{H}\) (Hardness total mean value) = 102.44HV

\(P_{H - S/N}\)(Hardness S/N ratio total mean value) = 40.17 dB

4.2 Analysis of variance method

ANOVA is a statistical approach that is used in the experimental design to control the access of individual interactions within the vicinity domain of working parameters. The physical significance of ANOVA analysis deprecates the experimental inaccuracy units to a great extent. The ANOVA techniques used for executing the optimum decisions for homogeneous set of experimental units [24, 25].

The present study implemented the ANOVA table to examine the influence of tool geometry, rotational speed and welding speed on TS, PE and H respectively. The experimental observations for TS, PE and H for identical metal alloys are shown in Table 6.

Table 6 ANOVA analysis for TS, PE and H
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The percent contributions of factors i.e., tool geometry, rotation speed and welding speed to the tensile strength is found to be of 33.4%, 4.69% and 58.39% respectively. The results depict that taper tool geometry contributes to the maximum amount of heat distribution to the intermetallic compounds during FSW as compare other tool geometries.

The rotational speed play’s significant role in the generation and crystallization of intermetallic compounds due to friction between tool and workpiece causing consequently high temperatures. Additionally, welding speed drives the time spent by the tool per unit area: at low welding speed, friction between tool and workpiece lasts a longer time in a certain region results to increasing temperature [26].

It is observed that welding speed (58.39%) plays significant role influencing the tensile strength. Similarly, the percentage contributions of tool geometry, rotation speed and welding speed on percentage elongation is found to be 35.08%, 14.29% and 38.28% respectively. The observation concluded that welding speed is the most influential factor for percentage elongation. In addition, the percent contributions of the tool geometry, rotation speed and welding speed on hardness reported as 50.1%, 19.36% and 20.49%respectively. This concluded that tool geometry is the most effective factor for hardness.

4.3 Estimation of optimum tensile strength, hardness and percentage elongation

The optimum levels of control factors were determined with the help of S/ N ratio and mean response features. The expected average of quality characteristics, i.e., tensile strength, percentage elongation and hardness, is therefore calculated using the Eq. 2 to Eq. 4 [19]. The authors also put efforts to enhance the characteristic to of welding and other process by using the design of experiment methodology [20,21,22,23].

$$ {\text{TS}}_{{{\text{opt}}}} = \, P_{TS} + (TG_{1} - P_{TS} ) + (RS_{4} - P_{TS} ) + (WS_{4} - P_{TS} ) $$
(2)
$$ PE_{{{\text{opt}}}} = \, P_{PE} + (TG_{1} - P_{PE} ) + (RS_{4} - P_{PE} ) + (WS_{4} - P_{PE} ) $$
(3)
$$ H_{{{\text{opt}}}} = \, P_{H} + (TG_{4} - P_{H} ) + (RS_{1} - P_{H} ) + (WS_{4} - P_{H} )\\ $$
(4)

where \(P_{TS} , \, P_{PE} \;and \, P_{H}\) is mean value for performance characteristics corresponding to TS, PE and H respectively.\(P_{TS} ,{\text{ P}}_{PE} {\text{ and P}}_{H}\) represents the predicted mean of the tensile strength, percentage elongation and hardness at optimum conditions. The optimum average values for tensile strength, percentage elongation and hardness, i.e.,\((TG_{1} , \, RS_{4} {, }WS_{4} )\), \((TG_{1} , \, RS_{4} , \, WS_{4} )\) and \((TG_{4} , \, RS_{1} {, }WS_{4} )\) respectively shown in Table 7. Substituting these values in Eq. (2) to (4), the mean optimum value of the tensile strength, percentage elongation and hardness was achieved as \(TS_{opt} = 202.94MPa\), \(PE_{opt} = 12.23\%\) and \(H_{opt} = 115.1HV\) respectively.

Table 7 Mean response for TS, PE, H and WR factor
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The Taguchi optimization technique validated with optimized condition with confidence interval of 95% and predicted result is obtained with the help of Eq. 5 and Eq. 6.

$$ {\text{CI }} = \, \sqrt {{\text{F}}\left( {\alpha ,1,{\text{f}}_{{\text{e}}} } \right) \, \times {\text{ V}}_{{\text{C}}} \, \left| {\frac{1}{{{\text{n}}_{{{\text{eff}}{.}}} }} + \frac{1}{{\text{R}}}} \right|} $$
(5)
$$ {\text{n}}_{{{\text{eff}}{.}}} { = }\frac{{\text{N}}}{{\left( {{\text{1 + T}}_{{{\text{dof}}}} } \right)}} $$
(6)

where \(F(\alpha ,1,f_{e} )\) is the F-ratio required for \(100(1 - \alpha )\) percent confidence interval,

Degree of freedom (DOF) for error, \(f_{e}\) = 6,

The error variance, \(V_{c}\) = 357.5,

The number of replications for confirmation experiments, R = 3,

Effective number of replications,\(n_{eff}\).

Total number of experiments, N = 48 (16 × 3)

The total degrees of freedom associated with the mean optimum, \(T_{dof}\) = 9 (3 × 3),

Ross et al. [19] recommended F-ratio for \(\alpha = 0.05\) as \(F(0.05,\;1,\;6) = 5.99\) from standard statistical table. Substituting these values in Eqs. (4) and (5), we reported \(n_{eff} = 4.8\) and \(CI = 34.05\) for Tensile strength, \(CI = 6.47\) for percentage elongation and \(CI = 21.58\) for hardness.

The predicted average optimal tensile strength at 95% confidence interval is expressed as;

$$ \begin{gathered} \left[ {TS_{opt} - CI_{TS} } \right] < TS\left[ {TS_{opt} + CI_{TS} } \right]_{exp.} \hfill \\ \left[ {202.94 - 34.05} \right] < 192.58 < \left[ {\left[ {202.94 + 34.05} \right]} \right] \hfill \\ { }168.89 < 192.58 < 236.99 \hfill \\ \end{gathered} $$
$$ \begin{gathered} \left[ {PE_{opt} - CI_{PE} } \right] < PE\left[ {PE_{opt} + CI_{PE} } \right]_{exp.} \hfill \\ \left[ {12.23 - 4.75} \right] < 12.59 < \left[ {\left[ {12.23 + 4.75} \right]} \right] \hfill \\ {7}{\text{.48}} < 12.59 < 16.98 \hfill \\ \end{gathered} $$
$$ \begin{gathered} \left[ {H_{opt} - CI_{H} } \right] < H\left[ {H_{opt} + CI_{H} } \right]_{exp.} \hfill \\ \left[ {115.1 - 21.58} \right] < 114.5 < \left[ {\left[ {115.1 + 21.58} \right]} \right]{ } \hfill \\ {93}{\text{.52}} < 114.5 < 136.68 \hfill \\ \end{gathered} $$

It is concluded from the above discussion that the experimental values obtained for \(TS_{\exp }\), \(PE_{\exp }\) and \(H_{\exp }\) lies within domain of the confidence interval limits and the system optimization for tensile strength is achieved at 0.05of significance level.

4.4 Empirical relationship

The present study involved second order response surface central composite design with the help of Minitab 17software package. The response function i.e., tensile strength (TS), percentage elongation (PE)and hardness (H) are expressed as the functions of tool geometry (TG), rotation speed (RS) and welding speed (WS) respectively and expressed as:

$$ TS = f(TG,RS,WS) $$
(7)
$$ PE = f(TG,RS,WS) $$
(8)
$$ H = f(TG,RS,WS) $$
(9)

The second order polynomial equation that represents the response surface \(^{\prime}Y^{\prime}\) is:

$$ Y = b_{0} + \sum {b_{i} } x_{i} + \sum {b_{ii} } x_{i}^{2} + \sum {b_{ij} } x_{i} x_{j} $$
(10)

Further, the individual responses are expressed in linear and interaction regression functions as:

$$ \begin{aligned} TS & = b_{0} + b_{1} (TG) + b_{2} (RS) + b_{3} (WS) + b_{11} (TG^{2} )\\ &\quad + b_{22} (RS^{2} ) + b_{33} (WS^{2} ) \\ &\quad + b_{12} (TG \times RS) + b_{13} (TG \times WS) + b_{23} (RS \times WS) \\ \end{aligned} $$
(11)
$$ \begin{aligned} PE & = b_{0}^{^{\prime}} + b_{1}^{^{\prime}} (TG) + b_{2}^{^{\prime}} (RS) + b_{3}^{^{\prime}} (WS) + b_{11}^{^{\prime}} (TG^{2} )\\ &\quad + b_{22}^{^{\prime}} (RS^{2} ) + b_{33}^{^{\prime}} (WS^{2} ) \\ &\quad + b_{12}^{^{\prime}} (TG \times RS) + b_{13}^{^{\prime}} (TG \times WS) + b_{23}^{^{\prime}} (RS \times WS) \\ \end{aligned} $$
(12)
$$ \begin{aligned} H & = b_{0}^{^{\prime\prime}} + b_{1}^{^{\prime\prime}} (TG) + b_{2}^{^{\prime\prime}} (RS) + b_{3}^{^{\prime\prime}} (WS) + b_{11}^{^{\prime\prime}} (TG^{2} )\\ &\quad + b_{22}^{^{\prime\prime}} (RS^{2} ) + b_{33}^{^{\prime\prime}} (WS^{2} ) \\ &\quad + b_{12}^{^{\prime\prime}} (TG \times RS) + b_{13}^{^{\prime\prime}} (TG \times WS) + b_{23}^{^{\prime\prime}} (RS \times WS) \\ \end{aligned} $$
(13)

where,\(b_{0} , \, b_{0}^{^{\prime}} \, and \, b_{0}^{^{\prime\prime}} \, \) are responses averages.\(b_{i} , \, b_{i}^{^{\prime}} \, and \, b_{i}^{^{\prime\prime}} \, \) and \(b_{ij} , \, b_{ij}^{^{\prime}} \, and \, b_{ij}^{^{\prime\prime}} \, \) are the coefficients that depend on the respective main and interaction effects of the parameters. The final relationships were established based on the determined coefficients.

The empirical relationship to predict tensile strength, percentage elongation and hardness of friction stir welded AA6061-T6 is obtained from Eq. 14 to Eq. 19.

$$ \begin{aligned} {\text{TS}} = & \, 204.2 - 37.1 {\text{TG}} - 0.0362 {\text{RS}} - 0.70 {\text{WS}} \\ & \quad + 0.0117 {\text{WS}}^{2} + 0.0180 \left( {{\text{TG}} \times {\text{RS}}} \right) \\ &\quad + 0.314 \left( {{\text{TG}} \times {\text{WS}}} \right) \, + 0.000269 \left( {{\text{RS}} \times {\text{WS}}} \right) \\ \end{aligned} $$
(14)

R-sq = 85.16% and R-sq (adj) = 68.19%

$$ \begin{aligned} {\text{PE}} = & 10.92 - \, 2.58{\text{ TG}} - 0.00576 {\text{RS}} + 0.001 {\text{WS}} \\ & - 0.000001 {\text{RS}}^{2} + 0.00156{\text{ WS}}^{2} + 0.00267 \left( {{\text{TG}} \times {\text{RS}}} \right) \\ & - 0.0226 \left( {{\text{TG}} \times {\text{WS}}} \right) + 0.000065 \left( {{\text{RS}} \times {\text{WS}}} \right) \\ \end{aligned} $$
(15)

R-sq = 84.83% and R-sq (adj) = 67.49%

$$ \begin{aligned} {\text{H}} = & \, 87.5 \, + 6.92 {\text{TG }} + 0.0084 {\text{RS}} + 0.279 {\text{WS}}\\ & - 0.00281 {\text{WS}}^{2} - 0.00294 \left( {{\text{TG}} \times {\text{RS}}} \right) \\ & - 0.013 \left( {{\text{TG}} \times {\text{WS}}} \right) - 0.000248 \left( {{\text{RS}} \times {\text{WS}}} \right) \\ \end{aligned} $$
(16)

R-sq = 59.30% and R-sq (adj) = 12.78%

The quadratic regression models highlighted in Eq. 14 to Eq. 16, the resultant R2 values for tensile strength, percentage elongation and hardness as 85.16%, 84.83% and 59.30% respectively. Similarly, R2 values for linear regression model in Eq. 17 to Eq. 19 were obtained for tensile strength, percentage elongation and hardness as 70.69%, 68.61% and 56.49% respectively. Hence, the quadratic regression model is more intensive and reliable as compared to that of linear regression model through obtained predicted values.

$$ {\text{TS }} = { 142}.{1} - {11}.{81} {\text{TG }} + 0.00{812} {\text{RS }} + 0.{828} {\text{WS}} $$
(17)

R-sq = 70.69% and R-sq (adj) = 63.36%

$$ {\text{PE }} = { 6}.{34} - {1}.{313} {\text{TG }} + 0.00{1782} {\text{RS}} + 0.0{66}0 {\text{WS}} $$
(18)

R-sq = 68.61% and R-sq (adj) = 60.77%

$$ {\text{H }} = { 99}.{38} + {5}.{34} {\text{TG }} - 0.00{646} {\text{RS }} - 0.{128}0 {\text{WS}} $$
(19)

R-sq = 56.49% and R-sq (adj) = 45.61%

4.5 Confirmation tests

For Taguchi and regression model equations at optimum values are considered by the confirmation tests of the operating parameters [27, 28]. Table 8 shows the comparison of the experimental results and predicted results carried out by the Taguchi and developed empirical relationship through regression model. The experimental results validated with predicted results showing good convergence.

Table 8 confirmation tests by the Taguchi and regression model empirical relationship
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4.6 The comparison between Taguchi method and regression equations

The experimental results and predicted values obtained by Taguchi method and linear & quadratic regression model are shown in Fig. 9 for AA6061-T6. The data points are evaluated through 45° line with scatter point, corresponding to perfect fit of the developed three empirical models. The variation of the predicted and experimental results lies within the limit of 20% indicating good predictive results and adhere to the statistical analysis obtained from literature i.e., error should less than 20% [29,30,31,32,33].

Fig. 9
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Comparison for Taguchi method, linear regression and quadratic regression of similar welding with experimental results for TS, PE and H

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5 Conclusion

The Taguchi technique implemented to evaluate an optimal welding condition for Friction stir welding of AA6061-T6 aluminum alloy. Experimental results were optimized for a set of control factor i.e., tensile strength, percentage elongation and hardness with the help of ANOVA analysis. The following conclusions were carried out with present investigation are:

  • The square pin profile provides the maximum tensile strength of 192.58 MPa and percentage elongation of 12.59%at optimum operating condition of 1600 rpm and 63 mm/min for tool rotation speed and welding speed respectively.

  • The tapered pin profile provides the maximum hardness of 114.5HV at optimum welding condition of welding speed of 63 mm/min and tool rotation speed of 400 rpm.

  • The developed quadratic regression model predicted coefficient of determination (R2) value for tensile strength, percentage elongation and hardness as 85.16%, 84.83% and 59.30% respectively corresponding to 95% confidence level with performed experimentation.

  • The comparison of three method i.e., Taguchi method, linear regression and quadratic regression reveals that the quadratic regression is more suitable amongst other methods because of minimum percentage error between experimental and predicted values for friction stir welded metals.