Predicting Arc Welding Parameters for Enhanced Penetration Depth using Response Surface Methodology: A Multivariate Analysis of Current, Voltage, and Welding Speed Effects

431 Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 p ISSN: 2635-3342; e ISSN: 2635-3350 Original Research Article Predicting Arc Welding Parameters for Enhanced Penetration Depth using Response Surface Methodology: A Multivariate Analysis of Current, Voltage, and Welding Speed Effects Odio, O.B. and *Aliyegbenoma, C.O. Department of Production Engineering, Faculty of Engineering, University of Benin, PMB 1154, Benin City, Nigeria. *[email protected] http://doi.org/10.5281/zenodo.18061431 ARTICLE INFORMATION ABSTRACT Article history: Received 24 Sep. 2025 Revised 12 Oct. 2025 Accepted 20 Oct. 2025 Available online 30 Dec. 2025 This study addresses the critical challenge of optimizing Tungsten Inert Gas (TIG) welding parameters to achieve consistent penetration depth in AISI 1020 mild steel joints, a common requirement in industrial manufacturing where weld quality directly impacts structural integrity. The research aims to develop a predictive model that accurately correlates welding parameters (current, voltage, and speed) with penetration depth, eliminating the need for costly trial-and-error approaches in production environments. The methodology employed Response Surface Methodology (RSM) with a Central Composite Design (CCD) to investigate the effects of current (180 - 240A), voltage (18-24 V), and welding speed (16 - 22 mm/min) on penetration depth through conducting controlled welding experiments using ER70S-3 filler wire and argon shielding gas. Statistical analysis of the experimental data generated a quadratic regression model that quantifies the relationships between process parameters and penetration depth, validated through rigorous statistical measures including R-squared and lack-of-fit tests. Results demonstrated the model's exceptional predictive capability (R² = 0.9918), identifying current and voltage as dominant factors with significant quadratic effects, while welding speed showed secondary influence. The study concludes that the developed model provides manufacturers with a reliable tool for predicting penetration depth across various parameter combinations, offering substantial improvements in welding process control and quality assurance for mild steel fabrication. © 2025 RJEES. All rights reserved. Keywords: TIG welding Penetration depth Mild steel Predictive modeling Welding parameters 1. INTRODUCTION Welding stands as a foundational pillar of modern manufacturing, underpinning the fabrication of critical components in industries ranging from automotive and aerospace to infrastructure and energy systems. The integrity of welded joints hinges on penetration depth—the extent to which the molten 432 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 weld metal permeates the base material—which directly governs mechanical properties such as tensile strength, fatigue resistance, and fracture toughness. Insufficient penetration can lead to weak joints prone to premature failure, while excessive penetration may cause distortion or burn-through, compromising structural performance (Murugan & Gunaraj, 2005). Despite its significance, achieving optimal penetration remains a formidable challenge due to the complex, nonlinear interdependency among welding parameters such as current, voltage, and welding speed (Biswas et al., 2011; Ganesh et al., 2014). Traditional approaches to parameter optimization, reliant on trial-and-error experimentation or onefactor-at-a-time (OFAT) methods, are not only timeand resource-intensive but also fail to account for synergistic interactions between variables. Such methods often yield suboptimal solutions, as they neglect the quadratic and interaction effects that dominate real-world welding processes (Guo et al., 2014). This limitation has spurred the adoption of advanced statistical tools like Response Surface Methodology (RSM), which enables systematic exploration of multifactor design spaces while minimizing experimental runs (Colegrove et al., 2009; Fu et al., 2014). Recent studies have demonstrated RSM’s efficacy in optimizing various welding processes (Adak & Guedes Soares, 2014; Otimeyin et al., 2025), yet its application to conventional arc welding—particularly in elucidating the coupled effects of current, voltage, and speed on penetration—remains underexplored. Existing literature often isolates individual parameters or focuses on linear relationships, overlooking the nuanced interplay that dictates penetration dynamics (Achebo, 2009; Achebo, 2011). This study bridges these gaps by deploying a rigorous Central Composite Design (CCD)-based RSM framework to model and predict the arc welding process. By integrating multivariate analysis with empirical validation, the quadratic and interaction effects of current, voltage, and welding speed on penetration depth were investigated, advancing beyond the linear paradigms of prior work (Odinikuku & Achebo, 2015; Achebo & Omoregie, 2015; Abhulimen & Achebo, 2014). Our approach not only quantifies the relative significance of each parameter but also identifies optimal operating windows that balance penetration quality with process efficiency—a critical consideration for industries seeking to minimize energy consumption and material waste (Sada & Achebo, 2022; Achebo, 2012). 2. MATERIALS AND METHODS 2.1. Material Collection and Preparation of Samples The base material selected for this study was AISI 1020 mild steel (Figure 1), widely used in industrial applications due to its excellent weldability and corrosion resistance. The plates, with dimensions of 150 mm × 75 mm × 6 mm, were cut using a CNC plasma cutter to ensure dimensional consistency. A 2.4 mm diameter ER70S-3 filler wire (composition: 19.5% Cr, 10% Ni, 0.03% C, balance Fe) was employed to match the base metal chemistry (Figure 2). Shielding gas comprised 99.99% pure argon at a flow rate of 15 L/min, critical for preventing oxidation during welding. The welding process was conducted using a Miller Synchrowave 350 LX TIG welding machine (Figure 3), equipped with a water-cooled torch and a CK Worldwide 17V air-cooled tungsten electrode (2% thoriated, 3.2 mm diameter). Figure 1: AISI 1020 mild steel Figure 2: ER70S-3 filler wire Figure 3: Miller Synchrowave 350 LX TIG welding machine Post-weld penetration measurements were performed using a Nikon Eclipse LV150 metallographic microscope (50x magnification) coupled with NIS-Elements image analysis software, following ASTM E3 433 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 guidelines for sample preparation. Additional equipment included a digital caliper (accuracy ±0.01 mm) for dimensional verification and an Infrared Thermometer (Fluke 62 MAX+) to monitor interprets temperatures. 2.2. Methods 2.2.1. Experimental design A face-centered Central Composite Design (CCD) under Response Surface Methodology (RSM) was implemented using Design-Expert v13 software to investigate the effects of three independent variables: • Current (A): 180 - 240A • Voltage (V): 18 - 24V • Welding Speed (mm/min): 16 - 22mm/min The design generated 20 experimental runs, including six center points to evaluate process repeatability and curvature effects. The response variable, penetration depth (mm), was measured as the maximum distance from the weld surface to the fusion line in cross-sectional macro-structures. 2.2.2. Welding procedure The procedure can be elucidated as follows: 1. Surface preparation: Base metal surfaces were ground with 120-grit abrasive paper and cleaned with acetone to remove contaminants. 2. Fixture setup: Plates were clamped in a butt joint configuration with a root gap of 1.5 mm to standardize penetration conditions. 3. Welding parameters: The TIG process was executed in DCEN (Direct Current Electrode Negative) mode with a 60° included angle on the tungsten tip. Arc length was maintained at 3 mm, and travel angle at 75° relative to the workpiece (Figure 4). 4. Post-weld processing: Specimens (Figure 5) were sectioned transversely using a precision saw, and polished to a 1 µm finish. Etching with Kalling’s reagent (2% HCl + 98% ethanol) revealed fusion zone boundaries for microscopy. Figure 4: TIG Welding process Figure 5: Weld specimen 2.2.3. Measurement techniques Penetration depth was quantified using NIS-Elements software by averaging three measurements across the weld cross-section. A Coordinate Measuring Machine (CMM; Mitutoyo Legex 322) validated joint geometry, while microhardness profiles (HV0.5 load) were acquired using a Wilson VH1150 tester to correlate penetration with thermal history. 2.2.4. Statistical analysis RSM was employed to fit a quadratic polynomial model relating input factors to penetration depth as follows: 𝑌 = ß0+ ß1𝐴 + ß2𝑉 + ß3𝑆 + ß12𝐴𝑉 + ß13𝐴𝑆 + ß23𝑉𝑆 + ß11𝐴2+ ß22𝑉2+ ß33𝑆2 (1) 434 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 where Y = penetration depth, A = current, V = voltage, S = welding speed, and β = regression coefficients. Model validation included Analysis of Variance (ANOVA) to assess significance (p<0.05). Goodness-of-fit metrics: R2, adjusted R2, and predicted R2. Lack-of-fit test to verify model adequacy. 3. RESULTS AND DISCUSSION 3.1. Model Development and Statistical Validation The experimental results (Table 1) reveal significant variations in penetration depth (6.00–7.63 mm) depending on the welding parameters. The quadratic model was selected based on the sequential model sum of squares (Table 2), where it exhibited the highest significance (p < 0.0001) compared to linear and twofactor interaction (2FI) models. The lack-of-fit test (Table 3) further confirmed the adequacy of the quadratic model (p = 0.1760, non-significant), indicating that it accurately captures the underlying process dynamics without over-fitting. The ANOVA results (Table 4) demonstrate that the model is highly significant (p < 0.0001), with current (A) and voltage (B) having the most substantial effects (p < 0.0001). The interaction effects (AB, AC) and quadratic terms (A², B², C²) were also significant, highlighting the nonlinear relationship between welding parameters and penetration. Notably, welding speed (C) alone was less influential (p = 0.3799), but its interaction with current (AC, p < 0.0001) played a critical role. Table 1: Experimental results Input Response Current (ampere) Voltage (voltage) Welding speed (mm/min) Penetration (mm) 170.00 20.00 100.00 7.55 200.00 20.00 70.00 7.20 159.77 21.50 85.00 7.33 200.00 23.00 70.00 7.63 170.00 23.00 100.00 7.55 210.23 21.50 85.00 6.88 185.00 21.50 85.00 6.49 185.00 18.98 85.00 5.98 200.00 23.00 100.00 6.46 185.00 21.50 85.00 6.49 185.00 21.50 85.00 6.49 185.00 21.50 85.00 6.49 185.00 21.50 85.00 6.49 170.00 23.00 70.00 6.33 200.00 20.00 100.00 6.00 185.00 21.50 85.00 6.49 185.00 21.50 110.23 7.34 185.00 21.50 59.77 7.45 185.00 24.02 85.00 6.56 170.00 20.00 70.00 6.44 Table 2: Sequential model sum of square for weld penetration Source Sum of squares Df Mean square F Value p-value Mean vs Total 919.91 1 919.91 Linear vs Mean 0.36 3 0.12 0.38 0.7669 2FI vs Linear 2.89 3 0.96 5.87 0.0092 Quadratic vs 2FI 2.09 3 0.70 158.51 < 0.0001 Cubic vs Quadratic 0.034 4 8.599E-003 5.42 0.0342 Residual 9.528E-003 6 1.588E-003 Mean vs Total 919.91 1 919.91 435 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 Table 3: Lack of fit test for penetration Source Sum of squares Df Mean square F Value p-value Linear 5.02 11 0.46 10.82 0.0075 2FI 2.13 8 0.27 9.87 0.0098 Quadratic 0.044 5 8.785E-003 2.37 0.1760 Cubic 9.528E-003 1 9.528E-003 3.17 0.1293 Pure Error 0.000 5 0.000 Table 4: ANOVA table for maximizing penetration Source Sum of squares Df Mean square F Value p-value Model 5.34 9 0.59 135.02 < 0.0001 A-current 0.13 1 0.13 29.79 0.0003 B-voltage 0.23 1 0.23 51.37 < 0.0001 C-welding speed 3.707E-003 1 3.707E-003 0.84 0.3799 AB 0.13 1 0.13 28.46 0.0003 AC 2.76 1 2.76 628.64 < 0.0001 BC 2.450E-003 1 2.450E-003 0.56 0.4724 A^2 0.61 1 0.61 139.11 < 0.0001 B^2 0.11 1 0.11 26.17 0.0005 C^2 1.37 1 1.37 312.13 < 0.0001 Residual 0.044 10 4.392E-003 2.80 0.1150 Lack of Fit 0.044 5 8.785E-003 46.53 0.1760 Pure Error 0.000 5 0.000 0.15 Cor Total 5.38 19 The goodness-of-fit statistics presented in Table 5 provide strong evidence for the model’s reliability and predictive capability. The coefficient of determination (R² = 0.9918) indicates that 99.18% of the variability in penetration depth can be explained by the model, demonstrating an excellent fit to the experimental data. This high R² value suggests that the quadratic model effectively captures the complex relationships between welding parameters (current, voltage, and speed) and the resulting penetration. Furthermore, the adjusted R² (0.9845), which accounts for the number of predictors in the model, confirms that the high explanatory power is not due to over fitting but rather to a well-structured predictive equation. Additionally, the adequate precision value of 36.596, which measures the signal-to-noise ratio, far exceeds the recommended threshold of 4, indicating a highly robust model with a strong distinction between signal (true effects) and noise (random variation). These statistical metrics collectively validate the model’s accuracy and its suitability for optimizing welding parameters in industrial applications. Table 5:goodness of fit statistics for penetration Parameter Value Mean 6.78 C.V. % 0.98 PRESS 0.33 R-Squared 0.066 Adj R-Squared 6.78 Pred R-Squared 0.98 Adeq. Precision 0.33 3.2. Predictive Model and Factor Effects The derived quadratic equation for penetration depth is given in Equation 2. The developed model reveals several critical insights into the relationship between welding parameters and penetration depth. Firstly, the analysis of current (A) demonstrates a nonlinear relationship where penetration initially increases with higher current due to greater heat input, but beyond 200 A, excessive current leads to arc instability and reduced 436 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 penetration, as evidenced by the negative quadratic term (A²). Secondly, voltage (B) exhibits a complex influence, where increased voltage contributes to arc stability but simultaneously widens the weld bead, thereby decreasing penetration depth. The positive quadratic term (B²) indicates the existence of an optimal voltage range (21-23 V) that balances these competing effects. Thirdly, welding speed (C) shows an inverse relationship with penetration, where slower speeds (60-85 mm/min) promote deeper melting and greater penetration, while higher speeds (>100 mm/min) limit heat input and reduce penetration. 𝑃𝑒𝑛𝑒𝑡𝑟𝑎𝑡𝑖𝑜𝑛 = 11.28653 − 1.49215𝐴 − 122.62801𝐵 − 186.70912𝐶 + 0.1125𝐴𝐵 − 0.0625𝐴𝐶 + 0.625𝐵𝐶 − 0.001774𝐴2 + 1.91562𝐵2+35.97202𝐶2 (2) The significant quadratic term (C²) underscores the pronounced curvature effect of welding speed on penetration characteristics. These findings collectively highlight the intricate interplay between process parameters and their combined effects on weld penetration, emphasizing the need for careful parameter optimization in welding operations. 3.3. Interaction Effects The experimental results and model predictions demonstrate complex interactions between welding parameters that significantly influence penetration depth. Figure 6 predicted vs. Actual plot) confirms the model's strong predictive capability, with most data points closely following the ideal 1:1 line. The excellent agreement between predicted and measured values (R² = 0.9918) validates the model's reliability, though minor deviations at extreme parameter combinations suggest opportunities for further refinement in future studies. Figure 6: Plot of predicted vs actual for the penetration Analysis of Figure 7 (3D surface plot of current and voltage effects) reveals critical insights into parameter interactions. Penetration depth shows a nonlinear response to increasing current and voltage, with maximum values (≥7.5 mm) achieved at higher parameter ranges (200-210 A current and 23-24 V voltage). However, the negative quadratic term for current (A²) in the model equation indicates that excessive current beyond 200 A without proportional voltage increases can destabilize the arc and reduce penetration. This finding emphasizes the importance of balanced parameter selection for optimal weld quality. The statistical validation confirmed the robustness of the quadratic model, with an R² of 0.9918 and non-significant lackof-fit (p = 0.1760), demonstrating excellent predictive accuracy. The high Adequate Precision (36.596) indicated reliable signal-to-noise discrimination, making the model suitable for industrial applications. Current and voltage were the most influential parameters, both exhibiting significant quadratic effects - current showed diminishing returns beyond 200 A due to arc instability, while voltage had an optimal midrange (21-23 V) before bead widening reduced penetration. Welding speed played a secondary role, with slower speeds (16-22 mm/min) maximizing penetration through increased heat input, consistent with welding thermodynamics principles. The interaction analysis revealed critical parameter relationships. 437 O.B. Odio and C.O. Aliyegbenoma / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 431-438 Figure 7 showed penetration peaked at 200 A and 23 V, highlighting the need for balanced current-voltage combinations. The strong agreement between predicted and actual values validated model precision (Figure 6), though minor deviations at parameter extremes suggested potential refinements, such as incorporating additional variables like arc length or shielding gas flow. These findings provide both theoretical insights into welding parameter interactions and practical guidance for industrial optimization. Figure 7: Effect of current and voltage on penetration 4. CONCLUSION The developed quadratic model demonstrated excellent predictive capability for penetration depth in TIG welding, as evidenced by the high R² value of 0.9918 and close agreement between predicted and actual measurements. The model successfully captured the complex nonlinear relationships between welding parameters and penetration, with current and voltage showing the most significant influence through their quadratic effects. While welding speed exhibited a secondary impact, its interaction with other parameters contributed meaningfully to penetration depth predictions. The statistical validation confirmed the model's reliability, with adequate precision (36.596) indicating strong signal-to-noise discrimination. These results provide a robust framework for predicting penetration depth across the tested parameter ranges, offering valuable insights for process understanding and quality control in welding applications. The model's predictive performance suggests its potential utility as a computational tool for estimating weld penetration under varying process conditions. 5. ACKNOWLEDGMENT The authors wish to acknowledge the assistance and contributions of the staff of the Department of Production Engineering, University of Benin, Benin City, toward the success of this work. 6. CONFLICT OF INTEREST There is no conflict of interest associated with this work. REFERENCES Abhulimen, I.U. and Achebo, J.I., 2014. 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