Taguchi, Grey Relational Analysis, and ANOVA Optimization of TIG Welding Parameters to Maximize Mechanical Performance of Al-6061 T6 Alloy

Abstract

This study presents a comprehensive investigation into optimizing Tungsten Inert Gas (TIG) welding parameters to enhance the mechanical performance of the widely used Al-6061 T6 alloy, specifically in a double V joint configuration with a plate thickness of 6 mm, for aerospace applications. The Taguchi method was employed to design the experiments, providing a robust framework for analyzing the influence of the electrical current, voltage, and gas flow rate on weld quality. Additionally, a Grey Relational Analysis (GRA) and an Analysis of Variance (ANOVA) were used to validate the optimal welding parameters and quantify the significance of each factor. The optimized parameters were determined to be an amperage of 180 A, a voltage of 18 V, and a gas flow rate of 10 L/min, resulting in significant improvements of up to 40% in tensile strength and 23% in hardness, demonstrating the effectiveness of the optimized conditions. The findings provide valuable insights into welding metallurgy, offering practical guidelines for enhancing high-performance welded joints in critical industrial applications. This study underscores the potential of combining Taguchi, GRA, and ANOVA methodologies to achieve superior mechanical properties and reliability in welded structures.

1. Introduction

Welding is an essential process in manufacturing and construction, enabling the permanent joining of materials through fusion and coalescence. There are multiple welding methods, each with its advantages and limitations, with the choice of method depending on the type of material, application, and required mechanical properties of the final joint. Among these methods, Tungsten Inert Gas (TIG) welding stands out for its ability to produce high-quality welds in a wide variety of materials, offering superior control over the welding process and resulting in cleaner, stronger joints [1,2]. The mechanical properties of TIG welds, such as tensile strength, hardness, and ductility, are highly sensitive to variations in welding parameters. Several studies have demonstrated that the welding current, arc voltage, and shielding gas flow rate can significantly affect the quality of the weld. For instance, increasing the welding current tends to improve penetration and tensile strength but may also increase the risk of defects such as porosity if not properly controlled [3,4]. Meanwhile, the arc voltage influences the shape of the weld bead and the heat input, with higher voltages typically leading to wider welds but potentially reducing hardness [5]. The shielding gas flow rate plays a key role in preventing oxidation and porosity, with an optimal flow rate being essential for weld cleanliness and mechanical performance [6]. Optimizing welding parameters is fundamental to improving the quality of joints and process efficiency. Recent research has shown that optimizing parameters such as the electrical current, voltage, and gas flow rate can lead to significant improvements in the mechanical properties and durability of welded joints. Studies have addressed the optimization of welding processes in various alloys, demonstrating the importance of this approach for improving the quality of the final product [7,8]. TIG welding is widely used in applications where joint quality and integrity are critical, such as the aerospace industry and the manufacture of medical components [9,10,11,12].

The aluminum alloy Al-6061 T6 is widely used due to its excellent combination of strength, ductility, and corrosion resistance. In the automotive and aerospace industries, this alloy is used to manufacture lightweight but strong structural components, improving fuel efficiency and vehicle safety [13,14,15]. Achieving optimal mechanical properties in welded joints of Al-6061 T6 is crucial for maintaining the performance and reliability of the final products. TIG welding is particularly effective in joining aluminum alloys, allowing for joints with excellent mechanical properties. Recent studies have demonstrated that optimizing TIG welding parameters can significantly improve the tensile strength and hardness of joints in aluminum alloys. Works by Yadav et al. (2024) and Santhosh et al. (2022) have shown the importance of precise parameterization in achieving high-quality welds in aluminum alloys using the Gas Tungsten Arc Welding (GTAW) process, also known as Tungsten Inert Gas (TIG) welding [16,17]. This process is central to our study as well, focusing on optimizing parameters such as the current, voltage, and gas flow rate to improve the tensile strength and hardness of Al-6061 T6 welds.

Various statistical methodologies, such as the Taguchi method, Grey Relational Analysis (GRA), and Analysis of Variance (ANOVA), have been successfully implemented to optimize welding processes by systematically evaluating welding parameters. These techniques have been shown to significantly enhance the mechanical properties of welds, providing practical and reproducible approaches for future studies and transforming industrial practices [18,19,20]. In this study, we employed the Taguchi method to design experiments and analyze the effects of welding parameters on the mechanical properties of Al-6061 T6 welds. Additionally, a GRA and an ANOVA were used to validate the optimal parameters and quantify the significance of each factor, offering robust frameworks for systematically optimizing welding processes [21,22].

This study highlights the potential of combining the Taguchi method, GRA, and ANOVA to achieve superior mechanical properties and reliability in welded structures. The methodologies and results presented herein contribute to advancing the field of welding metallurgy, promoting the development of high-quality, durable welded joints for critical applications.

2. Experimental Procedure

2.1. Materials and Method

In this study, Al6061-T6 aluminum alloy plates with dimensions of 300 × 75 mm and a thickness of 6 mm were utilized, and ER4043 filler rods with a 1.6 mm diameter were selected due to their compatible mechanical properties with the base aluminum alloy [23]. The chemical composition and mechanical properties of both materials are presented in

Table 1. Chemical composition.

Chemical Composition of Base Metal and Filler Material (wt.%)
Alloy	Al	Si	Fe	Cu	Mn	Mg	Cr	Ti	Pb
Al 6061-T6	97.17	0.65	0.64	0.19	0.07	1	0.21	0.02	0.05
ER4043	92.9	5.6	0.8	0.30	0.05	0.05	0	0.02	0

and

Table 2. Base material properties.

Mechanical Properties	Values
Ultimate tensile strength (MPa)	290
Yield strength (MPa)	240
Modulus of elasticity (GPa)	70
Hardness Vickers (HV)	77

. The preparation of the plates involved brushing the surfaces with a steel brush followed by cleaning with acetone to ensure the removal of any surface impurities.

The plates were placed on a backing bar and clamped at the ends to maintain alignment, ensuring a gap of half the plate thickness to prevent any distortion during welding. The Tungsten Inert Gas (TIG) welding was performed using a double V joint, welding perpendicular to the rolling direction of the plates. The welds were centrally located on the joints of the machined specimens and prepared for tensile and hardness testing, as schematically illustrated in Figure 1, which shows the placement of the weld bead and test specimens. A 3/16” pure tungsten electrode (W-Green) was used for the welding process. The parameters used for TIG welding are detailed in

Table 3. Parameters.

Parameters	TIG
Welding current (A)	160, 180, 200
Arc voltage (V)	16, 18, 20
Gas flow rate (L/min)	10, 15, 20
Welding speed	Constant
Shielding gas	Argon
Current	AC

. No preheating was applied.

Design of Experiments (DOE)

The design of experiments (DOE) plays an essential role in research development and industrial applications, providing a structured approach to systematically investigate the effects of multiple factors on desired outcomes. The DOE allows for the efficient exploration of relationships between variables, process optimization, and product quality improvement. This is particularly relevant in the optimization of welding processes. In this study, the DOE is used as a framework to evaluate the influence of welding parameters such as the current (A), voltage (B), and shielding gas flow rate (C) on the mechanical performance of the Al-6061 T6 alloy, each evaluated at three distinct levels, as shown in

Table 4. Parameters and levels.

Parameters	Units	Symbol	Level 1	Level 2	Level 3
Welding current	A	A	160	180	200
Arc voltage	V	B	16	18	20
Gas flow rate	L/min	C	10	15	20

. To optimize the weld’s tensile strength and hardness, the experiments were designed using Taguchi’s L9 orthogonal array, and the results are analyzed using Minitab^® 18 software [24].

Table 5. Taguchi’s L9 orthogonal array.

S. No	Sample No.	Input Parameter
		A	B	C
1	SA01	160	16	10
2	SA02	160	18	15
3	SA03	160	20	20
4	SA04	180	16	15
5	SA05	180	18	20
6	SA06	180	20	10
7	SA07	200	16	20
8	SA08	200	18	10
9	SA09	200	20	15

outlines the selected parameter combinations for experimentation, detailing the input parameters and their respective levels.

To ensure the integrity of the experimental design, certain parameters were held constant, ensuring a manageable scope for the study. This approach minimized the number of trials and the complexity of the analysis, allowing us to focus on the key welding parameters that impact mechanical performance. By streamlining the design, we enhanced the reliability of the results, contributing to a better understanding of the factors affecting the quality of welded joints in the Al-6061 T6 alloy.

The welds were prepared according to the conditions established in the experimental design, and to minimize any systematic errors in the experimentation, the selected conditions were assigned randomly. This randomization ensures that the experimental results are not biased by any uncontrolled variables and enhances the reliability of the findings [25]. After the welds were prepared, all joints were subjected to visual inspection based on standard guidelines to verify that they conform to quality standards. This inspection ensures the welds are free from surface defects such as cracks, porosity, and incomplete fusion, thus guaranteeing the validity and reliability of the experimental outcomes. Welds that passed this inspection were then machined for hardness and tensile testing. The inherent variations in welding parameters naturally affect the occurrence of defects, which is central to this study as we aim to optimize these parameters to improve weld quality and mechanical performance.

2.2. Mechanical Testing

The samples for tensile and Vickers hardness tests were cut transversely from the midsection of each weld joint and machined in accordance with ASTM E8 and ASTM E18 standards [26,27], respectively. For the tensile tests, an INSTRON Model 4206 testing machine was employed, ensuring precise measurement of the mechanical properties. The Vickers hardness tests were conducted using a Shimadzu hardness tester, with measurements taken at numerous points from the weld centerline, across the heat-affected zone (HAZ), and into the base material (BM). Although hardness varies significantly between these zones due to differences in thermal exposure, using the average value for each set provides a balanced representation of the overall weld performance. The average hardness captures the combined influence of the welding parameters on the entire joint, making it a useful indicator for optimizing mechanical performance. To ensure accuracy and repeatability, the mean value of three measurements from each zone (WZ, HAZ, and BM) was reported for each parameter set, as shown in

Table 6. Tensile and hardness test results.

	Uncoded Matrix			Average Results
S. No	A	B	C	UTS (MPa)	H (HV)
1	160	16	10	95	78
2	160	18	15	105	72
3	160	20	20	115	70
4	180	16	15	120	68
5	180	18	20	110	75
6	180	20	10	125	60
7	200	16	20	100	80
8	200	18	10	128	55
9	200	20	15	89	85

. Similarly, for tensile strength (UTS), the average of three measurements was reported for each parameter set. This approach allowed for comprehensive data collection, facilitating a thorough evaluation of the mechanical properties.

2.3. Taguchi Method

The Taguchi method, a specialized approach within the DOE, is employed in this study to streamline the experimental process by reducing the number of required experiments through the use of orthogonal arrays (OAs). This method is particularly effective when dealing with a high number of variables and resource constraints. It organizes experiments so that each row in an OA corresponds to a specific experiment, while each column represents a factor with different levels, ensuring that all possible combinations are tested efficiently [28].

A key component of the Taguchi method is the Signal-to-Noise (S/N) ratio, which measures the robustness of a process against variability. The S/N ratio has two main scenarios: the “Larger-the-Better” scenario, used when the objective is to maximize the response (e.g., tensile strength), and the “Smaller-the-Better” scenario, used when minimizing undesirable outcomes (e.g., hardness). For the “Larger-the-Better” scenario, the S/N ratio is calculated using Equation (1):

$$S/N=-10\mathrm{l}\mathrm{o}\mathrm{g} \left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{\displaystyle \frac{1}{y_i^2}}\right)$$

(1)

For the “Smaller-the-Better” scenario, the S/N ratio is calculated using Equation (2):

$$S/N=-10\log \left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{y}_i^2\right)$$

(2)

In these formulas, $n$ represents the number of observations and $y_i$ is the observed data point, such as the tensile strength or hardness value for a specific experiment. These equations ensure that the experimental results are robust and reliable by systematically evaluating the impact of various factors on the desired output. By integrating these methodologies, our investigation aims to optimize the TIG welding parameters to enhance the mechanical performance of the Al-6061 T6 alloy, thereby achieving superior weld quality and reliability.

2.4. Grey Relational Analysis (GRA)

The Grey Relational Analysis (GRA) is a powerful tool for multi-response optimization, frequently used in complex industrial processes such as welding. The GRA evaluates the relationships between multiple factors and responses, aiding in comprehensive decision making [29]. This methodology is integral to our study on optimizing TIG welding parameters for the Al-6061 T6 alloy, particularly because it allowed for the evaluation of both tensile strength and hardness simultaneously. This approach enabled a more complete decision-making process when determining the optimal welding conditions. By using the GRA, we ensured that the selected parameters not only enhanced individual properties but also maximized overall weld performance, making it highly relevant to aerospace applications.

2.4.1. Normalization of Data

The first step in the GRA is data normalization, which scales the data within a range to facilitate comparison. Normalization transforms the data so that they fall between 0 and 1. For “Larger-the-Better” characteristics, the normalized value $x_i\left(k\right)$ is calculated using Equation (3):

$$x_i\left(k\right)={\displaystyle \frac{x_i\left(k\right)-\mathrm{m}\mathrm{i}\mathrm{n}{x}_i\left(k\right)}{\mathrm{m}\mathrm{a}\mathrm{x}{x}_i\left(k\right)-\mathrm{m}\mathrm{i}\mathrm{n}{x}_i\left(k\right)}}$$

(3)

For “Smaller-the-Better” characteristics, the normalization formula is given by Equation (4):

$$x_i\left(k\right)={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}{x}_i\left(k\right)-x_i\left(k\right)}{\mathrm{m}\mathrm{a}\mathrm{x}{x}_i\left(k\right)-\mathrm{m}\mathrm{i}\mathrm{n}{x}_i\left(k\right)}}$$

(4)

Here, $x_i\left(k\right)$ represents the normalized value, and $\mathrm{m}\mathrm{a}\mathrm{x}{x}_i\left(k\right)$ and $\mathrm{m}\mathrm{i}\mathrm{n}{x}_i\left(k\right)$ are the maximum and minimum values of the $k$-th response, respectively. The index i refers to the specific experimental trial, while k corresponds to the response variable under consideration, such as tensile strength or hardness.

2.4.2. Deviation of Data

After normalization, the deviation sequence, which measures the absolute difference between the normalized values and the reference sequence (ideal value), is calculated. The deviation sequence ${\mathsf{\Delta }}_{0}i\left(k\right)$ is defined by Equation (5):

$${\mathsf{\Delta }}_{0}i\left(k\right)=\left|x_0\left(k\right)-x_i\left(k\right)\right|$$

(5)

where ${\mathsf{\Delta }}_{0}i\left(k\right)$ is the deviation sequence for the $i$-th trial at the $k$-th response variable, $x_0\left(k\right)$ is the reference (or ideal) value for the k-th response, and $x_i\left(k\right)$ is the normalized value for the i-th trial and k-th response variable. The index i refers to the specific experimental trial, while k corresponds to the response variable being analyzed (such as tensile strength or hardness). This deviation sequence provides a measure of how far each experimental run is from the ideal condition.

2.4.3. Grey Relational Coefficient

The Grey Relational Coefficient (GRC) quantifies the relationship between the reference and comparability sequences. The GRC is calculated using Equation (6):

$${\xi }_i\left(k\right)={\displaystyle \frac{{\mathsf{\Delta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}+\zeta {\mathsf{\Delta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathsf{\Delta }}_{0}i\left(k\right)+\zeta {\mathsf{\Delta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(6)

In this equation, ${\xi }_i\left(k\right)$ is the GRC for the $i$-th response at the $k$-th condition, ${\mathsf{\Delta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathsf{\Delta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are the minimum and maximum deviation sequences, and $\zeta$ is the distinguishing coefficient, typically set to 0.5.

2.4.4. Grey Relational Grade

The Grey Relational Grade (GRG) provides a single value representing the overall performance of each experimental condition. The GRG is calculated using Equation (7):

$${\gamma }_i={\displaystyle \frac{1}{n}}\sum _{k=1}^n{\xi }_i\left(k\right)$$

(7)

where ${\gamma }_i$ is the GRG for the $i$-th experiment and $n$ is the number of responses.

In our study, the GRA is applied to analyze and optimize TIG welding parameters, including the welding current (A), voltage (V), and gas flow rate (L/min). These parameters are varied systematically, and their effects on tensile strength and Vickers hardness are evaluated. By normalizing the data, calculating deviation sequences, and determining the GRC and GRG, we identify the optimal welding parameters. This ensures robust welding processes that yield superior mechanical properties, enhancing weld quality and reliability.

2.5. Analysis of Variance (ANOVA)

The Analysis of Variance (ANOVA) is a critical statistical tool used to evaluate the relative impact of various process parameters and to assess experimental errors. The ANOVA provides a quantifiable measure of each factor’s contribution, offering a clearer understanding of the comparative effects on the output variables. This method is essential for detecting any error variability in factor effects and the discrepancy in prediction errors. The primary goal of an ANOVA is to identify which design parameters significantly influence quality characteristics. Typically, this analysis is performed at a 5% significance level, corresponding to a 95% confidence level [30].

2.5.1. Central Limit Theorem (CLT)

The Central Limit Theorem (CLT) asserts that the sum (or average) of a substantial number of independent and identically distributed variables will approximate a normal distribution, irrespective of the initial distribution of the variables. This theorem is essential in statistics because it enables sample mean distributions to be treated as normal, which simplifies hypothesis testing and the estimation of confidence intervals. The following equations are used to perform the calculations:

2.5.2. Sum of Squares Total (SST)

$$SST=\sum _{i=1}^n{\left(Y_i-\bar{Y}\right)}^2$$

(8)

where $Y_i$ is the individual observation and $\bar{Y}$ is the overall mean.

2.5.3. Sum of Squares Between Groups (SSB)

$$SSB=\sum _{j=1}^k{n}_j{\left({\bar{Y}}_j-\bar{Y}\right)}^2$$

(9)

where ${\bar{Y}}_j$ is the mean of group j, $n_j$ is the number of observations in group j, and k is the number of groups.

2.5.4. Sum of Squares Within Groups (SSW)

$$SSW=\sum _{j=1}^k\sum _{i=1}^{n_j}{\left(Y_{ij}-{\bar{Y}}_j\right)}^2$$

(10)

where $Y_{ij}$ is the observation in group j.

2.5.5. Mean Square Between Groups (MSB)

$$MSW={\displaystyle \frac{SSW}{n-k}}$$

(11)

2.5.6. Mean Square Within Groups (MSW)

$$MSB={\displaystyle \frac{SSB}{k-1}}$$

(12)

2.5.7. F-Test

The F-test is a statistical test used to compare variances between groups. In the context of an ANOVA, it tests the null hypothesis that the means of several groups are equal. The F-test calculates the ratio of between-group variance to within-group variance. A large F-value indicates that the group means are significantly different, suggesting that at least one group mean is different from the others. The F value is calculated using Equation (13):

$$F={\displaystyle \frac{MSB}{MSW}}$$

(13)

2.5.8. Percentage of Contribution in ANOVA

In an ANOVA, the percentage of contribution indicates the relative importance of each factor in influencing the response variable. It is calculated by Equation (14):

$$\% \mathrm{Contribution} =\left({\displaystyle \frac{ \mathrm{SS} \mathrm{Factor} }{SST}}\right)\times 100$$

(14)

In the current study, an ANOVA was utilized to analyze the percentage contribution of key input process parameters, such as the welding current (amps) {A}, arc voltage (volts) {B}, and gas flow rate (L/min) {C}, on the output variables of the welding process. This approach enabled a detailed understanding of how each parameter influences the mechanical properties of the welds, thereby facilitating the optimization of the TIG welding process for the Al-6061 T6 alloy.

3. Results and Discussion

3.1. Taguchi Method

As shown in

Table 7. S/N ratio response table.

Larger is better	UTS	Level	Welding current	Arc voltage	Gas flow rate
		1	40.4	40.38	41.21
		2	41.45	41.13	40.33
		3	40.38	40.71	40.68
		Delta	1.07	0.75	0.88
		Rank	1	3	2
Smaller is better	Hardness	Level	Welding current	Arc voltage	Gas flow rate
		1	−37.3	−37.52	−36.07
		2	−36.57	−36.49	−37.46
		3	−37.15	−37.02	−37.49
		Delta	0.73	1.03	1.42
		Rank	3	2	1

, the welding current emerged as the most influential parameter for UTS, with a delta of 1.07. This indicates that variations in the welding current significantly affect the tensile strength of the welds. The gas flow rate was the second most influential parameter, with a delta of 0.88, followed by an arc voltage with a delta of 0.75. Each value in the table represents the mean S/N ratio at each parameter level, helping to determine the optimal settings to maximize UTS. The delta value reflects the difference between the highest and lowest S/N ratios for each parameter, where a larger delta indicates a greater influence on the response. The rank column highlights the relative significance of each parameter, with the welding current ranked as the most impactful, followed by the gas flow rate and arc voltage. The “Larger-the-Better” criterion was applied to obtain the S/N ratio values for tensile strength, as outlined in Equation (1).

For Vickers hardness, the gas flow rate was the most influential parameter, with a delta of 1.42. The arc voltage was the second most influential with a delta of 1.03, while the welding current was the least influential with a delta of 0.73. These delta values indicate the degree of variation in hardness due to changes in each parameter. The gas flow rate had the largest effect, followed by the arc voltage and welding current, as reflected in their rankings. The “Smaller-the-Better” criterion, as described in Equation (2), was applied to calculate the S/N ratio values for hardness, as minimizing hardness was the goal in this case. This highlights the need for the careful optimization of welding parameters based on specific application requirements, as different parameters exert varying degrees of influence on tensile strength and hardness.

From a metallurgical standpoint, the predominance of the gas flow rate in controlling hardness can be explained by its impact on the purity of the welding atmosphere and cooling rates, which influence the formation of hardening precipitates in the Al-6061 T6 alloy. Similarly, the significant influence of the welding current on UTS is linked to the heat input, which affects the penetration and fusion quality in the weld pool.

Figure 2 depicts the S/N ratio for UTS and HV concerning the input process parameters: current, voltage, and gas flow rate. The deviation in the response lines from the horizontal baseline demonstrates the significant impact of these parameters on performance measures. For UTS, the optimal levels were identified as 180 A, 18 V, and 10 L/min, aligning with the “larger-is-better” criterion. For hardness, following the “smaller-is-better” criterion, the same levels were found to be optimal.

The results clearly indicate that the welding current significantly affects tensile strength, while the gas flow rate is crucial for controlling hardness. This aligns with previous research findings where the welding current and gas flow were identified as critical parameters in welding process optimization [31,32]. The optimal balance between tensile strength and hardness is vital for aerospace components, which require high strength for structural integrity and sufficient ductility for forming and fitting operations.

3.2. Grey Relational Analysis (GRA)

The GRA further refined our understanding of the multi-objective optimization problem. The normalized values for UTS and HV were obtained using Equations (3) and (4), respectively. For UTS, the “larger-the-better” criterion was applied, while for HV, the “smaller-the-better” criterion was used. The deviation sequences were calculated using Equation (5). The Grey Relational Coefficients (GRCs) were then determined with a distinguishing coefficient ζ = 0.5 using Equation (6). Finally, the Grey Relational Grades (GRGs) were calculated using Equation (7), representing the overall performance of the welding parameters.

In general, a higher Grey Relational Grade indicates that the corresponding factor combination is closer to the optimal condition. As shown in

Table 8. Grey Relational Analysis.

S. No	Normalized Values		Deviation Sequence		GRC		GRG	S/N GRG	Rank
	UTS	H	UTS	H	UTS	H
1	0.154	0.233	0.846	0.767	0.371	0.395	0.38	−8.33	8
2	0.410	0.433	0.590	0.567	0.459	0.469	0.46	−6.67	6
3	0.667	0.500	0.333	0.500	0.600	0.500	0.55	−5.19	4
4	0.795	0.567	0.205	0.433	0.709	0.536	0.62	−4.12	3
5	0.538	0.333	0.462	0.667	0.520	0.429	0.47	−6.48	5
6	0.923	0.833	0.077	0.167	0.867	0.750	0.81	−1.85	2
7	0.282	0.167	0.718	0.833	0.411	0.375	0.39	−8.12	7
8	1.000	1.000	0.000	0.000	1.000	1.000	1.00	0.00	1
9	0.000	0.000	1.000	1.000	0.333	0.333	0.33	−9.54	9

and Figure 3, the parameter setup for experiment no. 8 achieved the highest Grey Relational Grade. Consequently, experiment no. 8 exhibits the best multiple performance characteristics among all nine experiments. This multi-criteria optimization problem was thus transformed into a single-objective optimization problem using the combined Taguchi and Grey Relational analysis approach. Additionally, the S/N ratio for the overall Grey Relational Grade was calculated using the “larger-the-better” criterion, as outlined in Equation (1).

Figure 4 graphically represents the S/N ratio for the overall Grey Relational grade, with the dashed line indicating the total mean S/N ratio value. Consequently, the optimal combination of the welding process parameters to maximize the properties of the welded joints, presenting less variability at these levels, is A2B2C1. The average Grey Relational Grade for each control factor level is listed in the response table (

Table 9. Average of parameter GRG.

Parameters	Levels			Delta	Rank
	1	2	3
Welding Current	0.47	0.64	0.58	0.17	3
Arc Voltage	0.47	0.65	0.56	0.18	2
Gas Flow Rate	0.73	0.47	0.45	0.28	1

).

Given that the Grey relational grade measures the correlation between reference and comparability sequences, a higher Grey Relational Grade indicates a stronger correlation. It is evident that the parameter with the most influence on the performance of UTS and HV is the gas flow rate, followed by the voltage and, lastly, the welding current.

Integrating the Taguchi method with the GRA allowed for a comprehensive optimization of welding parameters for the Al-6061 T6 alloy. The identified optimal settings (180 A, 18 V, and 10 L/min) significantly enhanced the mechanical properties, crucial for aerospace applications requiring a balance of strength and ductility. This method provides a robust framework for systematically evaluating and improving welding processes by combining Taguchi’s design of experiments with a Grey Relational Analysis, offering a comprehensive approach to multi-objective optimization in welding metallurgy.

3.3. Analysis of Variance (ANOVA)

This section presents the Analysis of Variance (ANOVA) results used to identify significant control factors affecting the performance characteristics, specifically ultimate tensile strength (UTS) and Vickers hardness (HV).

The ANOVA results for UTS are summarized in

Table 10. ANOVA for individual responses.

	Source	DoF	Adj SS	Adj MS	F-Value	p-Value	% Contribution
UTS	Welding Current	2	338.7	169.33	0.43	0.701	23.13%
	Arc Voltage	2	130.7	65.33	0.16	0.859	8.93%
	Gas Flow Rate	2	200.7	100.33	0.25	0.798	13.71%
	Error	2	794.0	397.00	--	--	--
	Total	8	--	--	--	--	--
Hardness	Welding Current	2	64.22	32.11	0.19	0.841	8.82%
	Arc Voltage	2	96.22	48.11	0.28	0.780	13.21%
	Gas Flow Rate	2	227.56	113.78	0.67	0.599	31.25%
	Error	2	340.22	170.11	--	--	--
	Total	8	--	--	--	--	--

. The contribution of each factor was calculated using two statistical tools: the Central Limit Theorem and the F-test (Equations (8) to (14)). A high F-value indicates a significant effect of the parameter on the performance characteristic. The welding current emerged as the most significant parameter with a contribution of 23.13%, suggesting its dominant influence on tensile strength. The gas flow rate and arc voltage contributed 13.71% and 8.93%, respectively. These findings indicate that variations in the welding current significantly impact the UTS, while the gas flow rate and arc voltage have lesser but notable effects.

The ANOVA results for HV reveal that the gas flow rate is the most influential parameter, with a contribution of 31.25%. This high percentage underscores its significant role in determining hardness. The arc voltage followed with a 13.21% contribution, while the welding current had the least influence with an 8.82% contribution. The ANOVA method was essential in determining the contributions of each input parameter and validating the results obtained through the Taguchi method.

The ANOVA for the Grey Relational Grade (GRG), which integrates multiple performance characteristics into a single metric, is presented in

Table 11. Analysis of variance for GRG.

Analysis of Variance
Source	Dof	Adj SS	Adj MS	F-Value	p-Value	% Contribution
Welding current	2	0.04429	0.02215	0.28	0.787	11.46%
Arc voltage	2	0.04869	0.02435	0.3	0.767	12.60%
Gas flow rate	2	0.13283	0.06641	0.83	0.547	34.37%
Error	2	0.16086	0.08034	--	--	--
Total	8	--	--	--	--	--

. The gas flow rate had the highest contribution of 34.37%, confirming its overall importance in optimizing the welding process. The arc voltage and welding current had contributions of 12.60% and 11.46%, respectively. These percentages reflect the relative power of each control factor in reducing variability and improving the overall quality of the welds.

The ANOVA results clearly demonstrate the significance of each control factor in affecting the UTS and HV of the welds. The welding current is the primary factor influencing tensile strength, while the gas flow rate is most critical for hardness. These insights are crucial for optimizing welding parameters to achieve desired mechanical properties in aerospace applications.

3.4. Confirmation Test

A confirmation test is conducted here to verify the analysis once the optimal process parameters have been determined. This test utilizes the optimal levels of the control factors. The Signal-to-Noise (S/N) ratio and the Grey Relational Grade (GRG) can be predicted using Equation (15):

$${\eta }_{\mathrm{opt} }=n_m+\sum _{i=j}^n\left(n_j-n_m\right)$$

(15)

where $n_m$ represents the overall mean of the S/N ratio or GRG, $n_j$ represents the mean S/N ratio or GRG at the optimized level, and n denotes the number of significant welding parameters.

An estimated value in real units is calculated using Equations (16) and (17), applying the inverse formulas corresponding to the “higher is better” and “smaller is better” criteria, respectively:

$${\overline{{\gamma }^2}}_{\mathrm{opt}} = {10}^{{\eta }_{\mathrm{opt}}/10} \mathrm{for} \mathrm{properties} \mathrm{higher} \mathrm{is} \mathrm{better}.$$

(16)

$${\overline{{\gamma }^2}}_{\mathrm{opt}} = {10}^{{-\eta }_{\mathrm{opt}}/10}\mathrm{for} \mathrm{properties} \mathrm{smaller} \mathrm{is} \mathrm{better}.$$

(17)

where ${\overline{\mathsf{\gamma }}}_{\mathrm{opt}}$ is the estimated value in real units and ${\eta }_{\mathrm{opt} }$ is the calculated optimal S/N ratio.

Table 12. Confirmation experiment results.

Response Variables	Initial Conditions	Optimal Condition
		Predicted	Experimental
Level	A1B1C1	A2B2C1	A2B2C1
Ultimate tensile strength (MPa)	95	130	133
Hardness Vickers (HV)	78	57	60
GRG	0.383	0.893	0.875

shows a strong agreement between the actual and predicted results, with the prediction error for the GRG being around 2.0%. The table also shows that the GRG improves by 0.492 compared to the initial values obtained from the standard parameters recommended by the aerospace industry and manufacturer guidelines [33], which authenticates the performance of the optimal configuration. Using these statistical methods together, the multi-performance characteristic of the TIG welding process for Al6061T-6 has been improved. Specifically, UTS increased by 40% and hardness improved by approximately 23%.

These results underscore the importance of the confirmation test in validating the optimal parameters identified through the initial analysis. By calculating the optimal S/N ratio and GRG, and verifying these predictions with actual experimental data, the reliability and effectiveness of the statistical optimization approach are confirmed. The significant improvements in UTS and hardness demonstrate the practical benefits of this methodology in enhancing the welding performance of the Al6061T-6 alloy, making it highly relevant for aerospace applications where both strength and hardness are critical.

4. Conclusions

The present study utilized the Taguchi method, a Grey Relational Analysis (GRA), and an Analysis of Variance (ANOVA) to optimize the TIG welding process parameters for the Al6061T-6 alloy. The primary conclusions drawn from this investigation are summarized below:

• From the Taguchi method, the results show that for UTS, the welding current is the most influential parameter, with the gas flow rate and arc voltage following in significance, whereas for HV, the gas flow rate is the most critical, followed by the arc voltage and welding current, with optimal levels for both being 180 A, 18 V, and 10 L/min.
• Based on the Grey Relational Analysis, the parameter combination that demonstrated the best overall performance is experiment no. 8 (200 A, 18 V, and 10 L/min).
• The optimal parameter combination identified through the multi-response optimization using GRA is A2B2C1.
• According to the ANOVA method, the welding current significantly impacts UTS with a 23.13% contribution, while the gas flow rate is the key factor for HV, contributing 31.25%.
• The ANOVA results indicated that the shielding gas flow rate (34.37%) had the most significant influence on achieving optimal welding results, followed by the arc voltage (12.60%) and weld current (11.46%).
• Following the study using statistical methods (Taguchi, GRG, and ANOVA), significant improvements were found: UTS increased by 40% and hardness by 23%.

These findings underscore the value of using statistical methods to optimize welding processes, improving the mechanical properties of the Al6061T-6 alloy effectively and making it more suitable for aerospace applications that require a balance of high strength and adequate ductility.