A Hybrid RSM–PSO Approach for Enhancing Machining Performance in Nanofluid-Assisted Hard Turning

Hard turning of heat-treated steels has emerged as a cost-effective alternative to grinding for producing high-quality components with tight dimensional tolerances and superior surface finishes. SKD11 steel, a high-carbon, high-chromium cold work tool steel, is widely used in the mold and die industry due to its excellent hardness and wear resistance after heat treatment [1]. However, machining such hardened materials (≥ 55 Rockwell Hardness, Scale C (HRC)) remains challenging due to elevated cutting forces, rapid tool wear, and the risk of thermal damage to both tool and workpiece surfaces [2, 3].

To overcome these issues, Minimum Quantity Lubrication (MQL) has gained attention as an eco-friendly and efficient cooling-lubrication technique [4, 5]. The integration of nanoparticles into MQL fluids significantly enhances the lubrication and cooling properties by improving heat dissipation and reducing friction at the tool–chip interface [6, 7]. This method not only improves surface quality and tool life but also aligns with green manufacturing initiatives [8].

Recent studies have explored various strategies to improve the machinability of hardened steels under MQL conditions using nanofluids. Nanoparticles such as Al₂O₃, SiO₂, CuO, and TiO₂ have been reported to significantly reduce surface roughness (Ra) and cutting temperature while enhancing tool life and chip morphology [9-11]. Among them, Al₂O₃ is known for its high thermal conductivity [12, 13], while SiO₂ offers excellent dispersion stability and tribological behavior in the cutting zone [14, 15].

Building on these individual benefits, recent research has focused on hybrid nanofluids, which combine two or more nanoparticle types to achieve synergistic improvements in lubrication and heat dissipation. Kuntoglu [16] provided a comprehensive review on the application of hybrid nanofluids in machining, highlighting their superior performance in cutting temperature control, tool wear reduction, and surface finish enhancement. Experimental studies have confirmed these advantages in practice. For example, Merga et al. [17] reported significant improvements in Ra and tool life when turning AISI 4140 steel using an Al₂O₃–CuO nanofluid under MQL conditions. Likewise, Safiei et al. [18] demonstrated that a tri-hybrid nanofluid composed of SiO₂, Al₂O₃, and ZrO₂ effectively reduced Ra and cutting temperature in the end milling of aluminum alloys.

In grinding applications, Li [19] showed that an Al₂O₃/SiC hybrid nanofluid outperformed conventional coolants in achieving better surface integrity. Specifically for the Al₂O₃–SiO₂ combination, Salameh et al. [20] applied fuzzy modeling and Particle Swarm Optimization (PSO) to optimize its thermophysical properties, indicating its potential for high-performance machining environments. These findings collectively support the viability of hybrid nanofluids—particularly those combining Al₂O₃ and SiO₂ - for enhancing MQL-assisted machining operations. The Al₂O₃–SiO₂ hybrid was chosen due to the complementary properties of the two nanoparticles. Al₂O₃ offers high thermal conductivity, which enhances heat dissipation at the tool–chip interface, while SiO₂ provides excellent dispersion stability and tribological behavior, acting as a solid lubricant to reduce friction. This combination enables synergistic effects that improve both thermal control and surface finish.

Despite growing interest in hybrid nanofluids, there is a clear lack of research applying dual-nanoparticle MQL (particularly Al₂O₃–SiO₂) in hard turning of high-hardness steels (≥ 55 HRC). Moreover, most studies focus on single-response optimization, whereas few have explored integrated optimization of both Ra and MRR, which is essential for balancing quality and productivity in industrial machining.

While previous studies have demonstrated the benefits of hybrid nanofluids in various machining processes, the integration of dual-nanoparticle systems such as Al₂O₃ and SiO₂ in hard turning of high-hardness tool steels under MQL conditions remains limited. Moreover, most current research has mainly focused on assessing surface roughness or certain other machining criteria individually, without integrating both quality and efficiency objectives into a unified optimization framework.

Additionally, although Response Surface Methodology (RSM) has been widely employed to model the influence of cutting parameters, it is often constrained in global search capabilities, especially in complex or multi-objective optimization scenarios. To address this, hybrid RSM–PSO frameworks have been successfully applied in various machining contexts. For instance, Gupta et al. [21] combined RSM and PSO to optimize surface roughness and tool wear in MQL turning of titanium alloys. Malghan et al. [22] applied this hybrid approach for optimizing milling of aluminum matrix composites, while Nguyen et al. [23] compared RSM–DA and PSO–TOPSIS methods in optimizing MQL turning of 9XC steel. These studies highlight the effectiveness of RSM–PSO combinations in solving nonlinear and multi-response machining problems.

Building upon this foundation, the present study proposes a hybrid RSM–PSO optimization approach to enhance the performance of nanofluid-assisted hard turning of SKD11 steel. Al₂O₃ and SiO₂ nanoparticles are dispersed in canola oil to formulate an eco-friendly hybrid nanofluid used under MQL conditions. The main objectives are: to develop a predictive model for surface roughness using RSM based on experimental data; to optimize the machining parameters for minimum Ra using PSO; and to perform multi-objective optimization of both Ra and MRR to achieve a balance between surface quality and material removal efficiency. This study advances sustainable and high-performance machining by integrating a hybrid optimization algorithm based on RSM and PSO with environmentally friendly MQL techniques.

To systematically achieve these objectives, a research framework has been developed, as illustrated in Figure 1. The study begins with the description of the experimental setup and the preparation of the hybrid nanofluids. This is followed by the development of a predictive RSM model and the application of PSO for optimization. Finally, the results are discussed, and conclusions are drawn along with suggestions for future work.

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Figure 1. Research framework of the present study

This section presents and discusses the results obtained from the hard turning experiments of SKD11 steel using hybrid Al₂O₃–SiO₂ nanofluids under MQL conditions. The experimental data were analyzed using RSM to develop regression models for surface roughness, followed by optimization using PSO. The effects of input parameters on machining performance and the optimal conditions for improving surface quality and productivity are discussed.

The complete set of experimental results is summarized in Table 2. Ra values ranged from 0.60 µm to 1.10 µm across the experiments. The lowest Ra of 0.60 µm was observed in Run 6 under a cutting speed of 100 m/min, feed rate of 0.1 mm/rev, depth of cut of 0.4 mm, with 2 wt.% Al₂O₃ and 0.5 wt.% SiO₂ concentrations. Conversely, the highest Ra value of 1.10 µm was recorded in Run 38 under a cutting speed of 80 m/min, feed rate of 0.15 mm/rev, and a depth of cut of 0.6 mm without nanoparticle addition.

Table 2. Experimental results for Ra and MRR

Regarding material removal rate, values varied between 1200 mm³/min and 9000 mm³/min. The maximum MRR of 9000 mm³/min was achieved in Run 32 under high cutting speed and feed conditions, while the minimum MRR of 1200 mm³/min was obtained in Run 25 under lower cutting parameters. These variations highlight the strong influence of cutting conditions and nanoparticle concentrations on machining performance, which will be further analyzed in the following sections.

3.1 RSM modeling results

RSM was employed to develop a predictive model for Ra as a function of the cutting parameters and nanoparticle concentrations. The analysis of variance (ANOVA) results for Ra are summarized in Table 3.

Table 3. The ANOVA results for Ra

The ANOVA results indicate that the developed quadratic model is statistically significant at a 95% confidence level, with a p-value less than 0.05. The model exhibits a high coefficient of determination as shown in Table 4, with R² = 99.84%, adjusted R² = 99.72%, and predicted R² = 99.63%, demonstrating excellent agreement between the experimental and predicted values. The relatively low standard deviation (S = 0.0063 µm) further supports the precision of the model.

Table 4. Model summary

The "Model" term and all linear and quadratic terms were found to be significant, while most of the two-way interaction terms were statistically insignificant (p > 0.05). The lack-of-fit test was also found to be insignificant, confirming that the model adequately fits the experimental data without systematic error.

The resulting regression equation for Ra (in uncoded form) is presented as follows:

Ra = 0.4818 – 0.1153A + 0.1281B + 0.01496V_c – 5.75f – 0.5181a_p + 0.01713A² – 0.1552B² – 0.000103V_c² + 42.15f² + 0.8495a_p² + 0.00473A*B + 0.0500A*f + 0.00625A*a_p– 0.167f*a_p

where, A and B are the concentrations of Al₂O₃ and SiO₂ nanoparticles, respectively (wt.%), V_c is the cutting speed (m/min), f is the feed rate (mm/rev), a_p is the depth of cut (mm).

To improve the transparency and robustness of the RSM model, Table 5 presents the estimated coefficients and their corresponding 95% confidence intervals for the statistically significant terms (p < 0.05). The narrow CI ranges indicate high confidence in the regression estimates and further support the stability and accuracy of the developed model.

Table 5. Estimated regression coefficients and their 95% confidence intervals for significant terms in the RSM model for Ra

3.2 Effect of process parameters on surface roughness

The main effects of cutting parameters and nanoparticle concentrations on Ra are illustrated in Figure 3.

The concentration of Al₂O₃ nanoparticles (A) exhibited a significant negative effect on Ra. As shown in Figure 3, increasing the Al₂O₃ concentration considerably decreased the surface roughness. This trend is consistent with previous studies, where Al₂O₃ nanofluids have been reported to enhance lubrication and cooling at the cutting zone, resulting in improved surface finish [12, 13].

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Figure 3. Main effects plot for surface roughness

This stronger influence of Al₂O₃ can be attributed to its superior thermal conductivity, which facilitates efficient heat dissipation at the tool–chip interface. This in turn reduces adhesion, thermal softening, and built-up edge formation—ultimately producing smoother surfaces. These findings align with prior research on thermal-assisted lubrication in nanoparticle-enhanced MQL environments.

Similarly, the concentration of SiO₂ nanoparticles (B) also showed a slight negative effect on Ra. A moderate decrease in surface roughness was observed with increasing SiO₂ concentration, which can be attributed to the improved dispersion stability and friction-reducing effects of SiO₂ nanoparticles [14, 15]. The relatively smaller effect of SiO₂, despite its excellent tribological behavior, may be due to its lower thermal conductivity compared to Al₂O₃. The spherical morphology of SiO₂ particles may contribute a “ball-bearing” mechanism, acting as nano-rollers that reduce friction at the tool–workpiece interface.

Cutting speed (V_c) had a strong negative effect on Ra. As the cutting speed increased, the surface roughness decreased noticeably. This behavior aligns with the findings of Asiltürk and Akkuş [24] and Aouici et al. [25], who reported that higher cutting speeds reduce built-up edge formation and facilitate smoother chip flow, thereby enhancing surface finish quality during hard turning.

In contrast, the feed rate (f) exerted the most substantial positive effect on Ra. Increasing the feed rate significantly deteriorated the surface quality, which is consistent with earlier reports [25, 26]. Larger feed values increase the distance between consecutive tool paths, resulting in deeper valleys and rougher surfaces.

The depth of cut (a_p) displayed a mild positive effect on Ra. Surface roughness slightly increased with greater depths of cut, possibly due to higher cutting forces and potential tool deflection or vibration [24, 25]. However, the overall influence of ap was limited. This is likely due to the high rigidity of the CNC lathe and the clamping setup, which minimized vibration and maintained machining stability even at higher cutting depths.

Overall, the results highlight that optimizing feed rate and cutting speed, along with careful selection of nanoparticle concentrations, are critical strategies for achieving superior surface finishes in nanofluid-assisted hard turning processes.

3.3 Optimization results using PSO

PSO was applied to determine the optimal machining parameters that minimize surface roughness while achieving a balanced trade-off with material removal rate. The optimization was conducted using regression models derived from the RSM analysis.

PSO was selected over the traditional desirability-based approach in RSM due to its superior capability in solving non-linear, multi-dimensional problems and avoiding local optima. PSO offers higher flexibility and better performance in exploring complex design spaces, which is particularly beneficial for simultaneous optimization of conflicting objectives like Ra and MRR.

3.3.1 Single-objective optimization for Ra

This section details the implementation of PSO in Python to achieve single-objective optimization of surface roughness in the hard turning of SKD11 steel under hybrid nanofluid-Al₂O₃/SiO₂ MQL conditions. Building on the regression model (1) for Ra developed through RSM in Section 3, PSO was employed to determine the optimal combination of Al₂O₃ concentration (A), SiO₂ concentration (B), cutting speed (V_c), feed rate (f), and depth of cut (a_p) that minimizes Ra.

The PSO algorithm was implemented using Python 3.13 and the Pyswarm Library. A swarm consisting of 30 particles was initialized within the defined parameter bounds: A (0–2 wt.%), B (0–1 wt.%), V_c (60–100 m/min), f (0.10–0.15 mm/rev), and a_p (0.2–0.6 mm). Each particle represented a potential solution, and its objective function value (Ra) was evaluated based on the developed regression equation. The PSO parameters were set as follows: inertia weight (w) = 0.7, cognitive coefficient (c₁) = 2.0, and social coefficient (c₂) = 2.0. The optimization process was performed over 100 iterations to ensure convergence.

The optimal machining parameters obtained for minimum Ra were: A = 2.0 wt.%, B = 1.0 wt.%, V_c = 100 m/min, f = 0.10 mm/rev, and a_p = 0.307 mm. Under these conditions, the predicted minimum Ra was 0.5443 µm. These results indicate that a combination of high nanoparticle concentrations, high cutting speed, low feed rate, and moderate depth of cut is favorable for achieving superior surface finishes in hard turning operations.

While the predicted Ra was 0.5443 µm, the lowest experimentally observed Ra was 0.60 µm. This minor deviation (< 10%) confirms the accuracy of the RSM model and the effectiveness of the PSO-based optimization in identifying near-optimal machining parameters.

The effectiveness of the proposed RSM–PSO hybrid approach demonstrates its effectiveness in capturing the optimal parameter set for enhancing machining performance, providing a flexible and robust tool for improving surface quality under nanofluid-assisted MQL conditions.

3.3.2 Multi-objective optimization for Ra and MRR

Following the single-objective analysis, a multi-objective optimization was conducted to simultaneously minimize Ra and maximize MRR during the hard turning of SKD11 steel under hybrid nanofluid-Al₂O₃/SiO₂ MQL conditions. The regression equations developed in Section 3 for Ra and MRR were utilized as objective functions.

The multi-objective optimization was implemented using Python 3.13 and the Pyswarm Library. A swarm of 30 particles was initialized within the predefined parameter bounds: A (0–2 wt.%), B (0–1 wt.%), V_c (60–100 m/min), f (0.10–0.15 mm/rev), and a_p (0.2–0.6 mm). Each particle represented a potential solution, and the objective function was defined as a weighted sum, minimizing 0.5×Ra + 0.5×(1/MRR), to balance the conflicting goals of achieving low surface roughness and high productivity. The PSO parameters were set as: inertia weight (w) = 0.7, cognitive coefficient (c₁) = 2.0, social coefficient (c₂) = 2.0, and a maximum of 100 iterations was used to ensure convergence.

The optimal machining parameters identified through the multi-objective PSO approach were: A = 2.0 wt.%, B = 1.0 wt.%, V_c = 100 m/min, f = 0.10 mm/rev, and a_p = 0.523 mm. Under these conditions, the predicted Ra was approximately 0.584 µm, and the predicted MRR was approximately 5230 mm³/min.

This solution demonstrates a practical and balanced trade-off between achieving high surface integrity and maintaining reasonable machining productivity. The successful application of the RSM–PSO hybrid approach to multi-objective optimization underscores its effectiveness and flexibility in enhancing machining performance under nanofluid-assisted MQL conditions.

The weights of 0.5 for both Ra and MRR in the objective function were selected to reflect an equal emphasis on machining quality and productivity, which aligns with typical industrial trade-offs. The PSO algorithm typically converges within 100 iterations. Based on the problem size and swarm configuration, the total runtime is generally less than one minute on a standard laptop (e.g., Intel i7, 16 GB RAM), indicating the computational efficiency of the proposed approach.

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Figure 4. Pareto front showing the trade-off between Ra and MRR

Figure 4 illustrates the Pareto front generated from the multi-objective PSO optimization, depicting the trade-off relationship between surface roughness and material removal rate in the nanofluid-assisted hard turning of SKD11 steel. As shown, achieving lower Ra values generally corresponds to lower MRR values, while higher MRR levels are associated with increased surface roughness. This trend highlights the fundamental trade-off between surface integrity and machining productivity.

The Pareto front provides valuable insights into the selection of machining parameters based on specific production priorities. If superior surface finish is prioritized, solutions located toward the lower Ra region should be selected, albeit with a sacrifice in material removal rate. Conversely, for applications where higher productivity is essential, solutions with higher MRR and slightly higher Ra may be more appropriate. The RSM–PSO hybrid approach effectively captures this trade-off, offering practical flexibility for optimizing machining performance under various operational requirements.

For instance, in Table 2, Run 32 exhibits a high MRR but a relatively moderate Ra. This observation is consistent with the Pareto trade-off curve, where higher material removal rates tend to coincide with increased surface roughness. Such points lie along the mid to high MRR segment of the Pareto front and highlight the real-world compromise between performance metrics.

It is acknowledged that this study did not include an analysis of tool wear, which is an important factor in evaluating the long-term effects of nanoparticle-based lubrication. Future work should incorporate tool wear assessment to comprehensively validate the benefits of hybrid nanofluid-assisted MQL in hard turning.