Parametric optimization in micro-EDM drilling of Ti–46.5Al–5Nb–2Mo–0.3B alloy using teaching-learning-based optimization algorithm

Titanium aluminides are renowned for their outstanding properties like excellent high-temperature strength, low density and superior oxidation resistance. These properties make them highly advantageous and extremely suitable for aerospace and automotive applications (Jiajun et al., 2024). Their ability to maintain structural integrity under extreme conditions, combined with their light weight, contributes to improved fuel efficiency and durability in components exposed to high temperatures and oxidative environments such as turbine engines, exhaust systems and other high-performance engine parts (Wenlu et al., 2024). Despite their notable properties, titanium aluminides face significant challenges in machining due to their intrinsic brittleness and poor machinability. Due to brittleness, these alloys are more prone to cracking and fracturing during processing, while their low thermal conductivity and high hardness further complicate machining operations. These factors lead to increased tool wear, inferior surface quality and reduced machining efficiency. Due to these factors, they are difficult to processed using conventional machining methods and necessitates specialized techniques to achieve the desired precision. Non-conventional machining processes like electrochemical machining (ECM), electrical discharge machining (EDM) and laser beam machining (LBM) offer significant advantages, especially when working with hard and brittle materials like titanium aluminides. These methods avoid direct tool–material contact thereby reducing tool wear and thermal damage (Sreeram et al., 2024; Nikolaos et al., 2024; Kechagias et al., 2023). These processes are also capable of producing precise geometries and fine surface finishes, making them ideal for manufacturing complex components with high hardness and brittleness. Among the various non-conventional machining, micro-electrical discharge drilling (micro-EDD) is a suitable solution for cutting difficult to machine materials such as titanium alloys.

Micro-EDD is a non-contact thermal erosion process that utilizes series of repetitive electrical discharges to remove material and effectively eliminates the mechanical stresses faced in traditional machining methods. Solidification behavior of γ-aluminide Ti–46.5Al–xNb–yCr–zMo–0.3B alloys was investigated by Neelam et al. (2019). They observed that the alloys solidify in the L + β phase field, with β as the primary phase and α and γ as secondary phases, forming various microstructures. Multiple rounds of melting in a vacuum arc furnace improved homogeneity. Adding β-stabilizing elements altered the solidification path, resulting in a finer microstructure and guiding further alloy development. Neelam et al. (2020) also studied the phase transformations in γ-aluminide alloys, Ti–46.5Al–xNb–yCr–zMo–0.3B, where, x = 3.5, 5; y, z = 0, 1, 2; y + z = 2. It was observed that the alloy system is in a two-phase α + β field between 1,430 °C and 1,288–1,272 °C, with a three-phase region below, where the eutectoid temperature ranges from 1,155 to 1,076 °C. The β/B2 phase volume fraction is higher in water-quenched alloys, as furnace cooling allows more time for phase decomposition, reducing hardness. Oliker et al. (2005) studied phase formation in detonation coatings sprayed from Ti - 50 at. % Al powders, produced by crushing and mechanical alloying. The use of mechanically alloyed powders enhances phase control in coatings. It was found that the detonation spraying method leads to coatings based on Al₂TiO₅ from oxidation and titanium aluminides with TiN inclusions from nitriding, inheriting the phase composition of the γ-TiAl powder. Bache et al. (2003) investigated characterization of foreign object damage and fatigue strength in titanium-based aerofoil alloys. Simulated foreign object damage was applied to Ti–6Al–4V and γ titanium aluminide Ti–45Al–2Mn–2Nb alloys for compressor aerofoils. Damage was characterized before fatigue testing at room and elevated temperatures. While γ titanium aluminide showed lower fatigue endurance at room temperature, it has clear advantages in high-temperature performance. Bhowal et al. (1995) studied the effect of processing and microstructure on properties of Ti–47Al–3Nb–1W and 46Al–2.5Nb–2Cr–0.2B γ titanium aluminides. Two γ aluminide compositions, 47Al–3Nb–1W and 46Al–2.5Nb–2Cr–0.2B, were tested for tensile and creep properties in different microstructures. It was found that the necklace microstructure improved ductility and creep resistance in the 47Al–3Nb–1W alloy, while boron addition in the 46Al–2.5Nb–2Cr–0.2B alloy refined the lamellar microstructure, enhancing room temperature ductility and maintaining creep resistance at 760 °C. A review study by Yang et al. (2022) suggested that the TiAl alloys offer high strength and lightweight properties but face challenges with brittleness and microstructure stability at high temperatures. Reinforcing TiAl with carbides improves mechanical properties. They demonstrated the effect of carbon on TiAl alloys, focusing on its role in forming solid solutions and carbide precipitates. Adding carbon enhances tensile properties, flexural strength and hardness, and significantly reduces the minimum creep rate when close to the solubility limit. Neelam et al. (2021) examined the effect of Nb on the microstructure and mechanical properties of two γ-TiAl alloys: Ti–46.5Al–2Cr–3.5Nb–0.3B and Ti–46.5Al–2Cr–5.0Nb–0.3B. The alloys were heat-treated, and their microstructure was analyzed. The compression properties at room temperature as well as high temperature and creep properties at 800 °C and 300 MPa of applied stress were evaluated. It was found that increasing the Nb content enhanced the β-phase fraction and improved creep properties at 800 °C and 300 MPa, though there was no significant change in compression strength at room or high temperatures.

Xu et al. (2022) investigated the effect of three dielectrics: kerosene, EDM oil and deionized water on electrical discharge assisted milling (EDAM) performance of titanium alloy. Discharge signals, surface morphology and electrode composition were analyzed under various machining conditions. Results witnessed that kerosene and EDM oil provided a higher discharge frequency than deionized water. Prolonged discharge led to debris and carbide formation, affecting microhardness and discharge stability. EDM oil achieved the best surface integrity, reducing surface roughness as compared to kerosene, deionized water and conventional milling. EDAM also reduced microhardness by minimizing surface plastic deformation. Ramazan (2022) analyzed keyway machining on titanium alloy (Ti–6Al–4V) using die-sinking EDM, following DIN 6885 standards. Effect of discharge current, pulse on time and pulse off time was studied on MRR, TWR and SR in a kerosene environment. Discharge current and pulse on time were found to significantly affect all the output parameters. SEM and EDS revealed surface and subsurface changes, with the heat-affected zone reaching a depth of 60 µm due to the alloy’s low thermal conductivity. Artificial neural networks (ANN) provided predictions that were more accurate and closer to experimental results than RA. Mithilesh et al. (2023) performed EDM of titanium alloy, based on RSM and optimized the process using NSGA-II. A quadratic model was used to predict MRR and Ra using peak current, pulse on time and pulse off time. It was observed that peak current had the most significant effect, influencing MRR and Ra witnessing increased in MRR with peak current, while Ra increased and then decreased after a certain point. Good accuracy was showed by optimization results and confirmation experiments yielding errors of only 6% for MRR and 4.8% for Ra. Xu et al. (2024) applied ultrasonic vibration–assisted multi-objective optimization. Second-order quadratic models for MRR and TWR were developed and the effect of peak voltage, peak current, pulse width, frequency, ultrasonic amplitude and rotation speed as input parameters was analyzed. A desirability function approach was applied for multi-objective optimization and optimized parameters were used to machine micro-holes, resulting in a significant improvement in surface quality. Chitrasen et al. (2024) explored EDM as an alternative for machining titanium alloy. This study focused on using copper electrodes to optimize four key EDM parameters: peak current, duty cycle, discharge current and pulse-on time. A Taguchi design and the RAMS-RATMI method was used to improve machining efficiency and reliability. Optimized settings resulted in better MRR, lower TWR and smoother surfaces. Surface analysis showed fewer microcracks and a thinner recast layer. ANOVA confirmed the robustness of the process. The findings offered valuable guidance for industrial EDM applications on titanium alloys. Farooq et al. (2024) explored micro-machining error reduction in EDM of titanium alloy using nonionic liquids and cryogenically treated tool electrodes. A Full Factorial experimental setup was conducted: 12 unmodified experiments with kerosene and 108 modified ones using nonionic liquids, varying concentrations, treated electrodes and pulse on and pulse off times. All nonionic liquid-based setups outperformed the conventional dielectric. In the unmodified process, aluminum and graphite showed errors of 151.9 µm and 75 µm, respectively. The best result showing 17.75 µm error was achieved using cryogenically treated graphite, S-60 nonionic liquid at 25 g/L and a 50:50 µSec pulse. This setup had a desirability index of 98.60%, confirming its effectiveness. Kebede et al. (2024) investigated micro-electric discharge drilling (µEDD) on titanium grade 2 using a 496 µm tungsten carbide tool. Capacitance, voltage and feed rate were varied using a full factorial design and performance was measured in terms of overcut, MRR, circularity and hole taper. An overall evaluation criteria (OEC) approach was used for multi-objective optimization and results were compared with a multi-objective genetic algorithm (MOGA), showing similar optimal parameters. Lower capacitance and voltage led to reduced burrs, recast layers and circularity errors. Surface topology and composition were further examined using FESEM and EDS analyses. Bhaskar et al. (2025) investigated the wire EDM machining of Ni50.3Ti29.7Hf20, a high-temperature shape memory alloy known for its strength, hardness and corrosion resistance. WEDM was used to achieve high precision with minimal material damage due to its challenging machinability. Pulse on time, pulse off time, gap voltage (GV) and wire speed (WS) were optimized using TOPSIS and GWO techniques. The optimal settings T_on = 123.8 µs, T_off = 50 µs, WS = 2, GV = 25 produced a predicted MRR of 4.22 mm³/min and surface roughness of 3.62 µm. Experimental results closely matched predictions, confirming the method’s effectiveness.

Past studies showed that although few authors have investigated titanium aluminide but the composition of titanium aluminide used in the study is completely different. Moreover, earlier studies are primarily focused on discussing the phase transformation, effect of the alloying element in the whole alloy and material characterization. The machining behavior of titanium aluminides is rarely investigated. The present study is thus completely focused towards studying the machining behavior of Ti–46.5Al–5Nb–2Mo–0.3B is rarely investigated. Experimental design was done using the Taguchi L27 orthogonal array (OA) considering five important process parameters: tool rotational speed, discharge current, pulse-on length, pulse-off time and power. Present optimization approach offers systematic investigation of the parameter space, resulting in an efficient trade-off between MRR and TWR.

Trial machining experiments showed that machining of Ti–46.5Al–5Nb–2Mo–0.3B possesses other challenges such as increased tool wear and reduced material removal rates (MMRs), necessitating the optimization of process parameters to achieve an optimal balance between MRR and tool wear rate (TWR). Optimizing machining parameters is essential for improving productivity and maintaining the quality of machined components (Surya, 2024). Supplementary Table 1 reflected few commonly used conventional optimization techniques used for parametric optimization for EDM of titanium alloys. Conventional optimization techniques frequently encounter difficulties due to the intricate, nonlinear characteristics of machining operations.

In this regard, metaheuristic algorithms have gained significance for their capacity to effectively traverse extensive search spaces and ascertain ideal solutions. TLBO (Teaching-Learning-Based Optimization) was chosen over other metaheuristic algorithms due to its simplicity, efficiency and parameter-less nature. Unlike algorithms such as Genetic Algorithm (GA) or Particle Swarm Optimization (PSO), TLBO does not require algorithm-specific parameters like crossover rates or inertia weights, making it easier to implement and tune. It offers a good balance between exploration and exploitation through its two-phase learning mechanism, leading to faster convergence and robust performance across a wide range of optimization problems.

TLBO method has demonstrated potential in numerous manufacturing applications. Inspired by the educational process within a classroom, TLBO enhances solutions iteratively by mimicking the impact of a teacher on students and the interactions among the students themselves. TLBO is rapidly being used to enhance machining parameters in unconventional machining processes such as abrasive water jet machining, grinding and milling, demonstrating its ability to produce better outcomes than other optimization techniques. Nevertheless, application of TLBO in micro-EDM or micro-EDD, notably for titanium aluminides, have been rarely investigated. Due to the specific challenges associated with machining titanium aluminides, it is essential to investigate TLBO algorithm in optimizing machining parameters for the alloy (Rao et al., 2011). This study not only enhances the use of TLBO in micro-EDM, but it also offers practical insights for machining sophisticated materials like titanium aluminides. Thus, this work is novel in its application of the TLBO algorithm for optimizing the micro-EDD process of titanium aluminide alloys, which are known for their challenging machinability.

Titanium aluminides are distinguished by their superior high-temperature stability, low density and oxidation resistance, rendering them particularly appropriate for aerospace and automotive applications. The precise formulation of this alloy is designed to improve its mechanical characteristics and machinability. Niobium (5%) and molybdenum (2%) are used to enhance high-temperature strength and creep resistance, while a minor addition of boron (0.3%) refines the grain structure, leading to increased mechanical performance and machinability (Supplementary Table 2). The alloy is procured from Defence Metallurgical Research laboratory. Hyderabad, India.

The alloy’s microstructure as shown in Supplementary Figure 1 was examined microscopically and was shown to have a fine-grained duplex structure consisting of the γ (TiAl) phase and the α2 (Ti3Al) phase. This dual-phase microstructure is essential for optimizing strength, ductility and machinability. The lamellar structure observed in the micrograph improves fracture toughness and heat resistance, rendering the alloy a viable option for high-performance applications. The use of boron in the alloy yields finer grains, enhancing surface quality and precision in machining operations.

Supplementary Table 3 presented the properties of Ti–46.5Al–5Nb–2Mo–0.3B (Naga et al., 2020). This titanium aluminide alloy, with a density of roughly 4.0 g/cm³, serves as a lightweight substitute for traditional nickel-based superalloys, providing considerable benefits in weight-sensitive applications. The thermal conductivity varies between 11 and 16W/mK, while the melting point of roughly 1,460°C guarantees stability and efficacy in harsh situations. The alloy demonstrates an ultimate tensile strength of 400–600 MPa, an elastic modulus of around 150GPa and improved fracture toughness attributed to niobium and boron content.

This alloy is generally produced using sophisticated metallurgical methods like vacuum arc melting, guaranteeing consistent composition and reduced impurities. Heat treatments are frequently utilized to enhance the equilibrium between the γ and α2 phases for certain purposes. This alloy is extensively utilized in turbine blades, automotive engine valves and other components that demand high strength-to-weight ratios and exceptional thermal resistance due to its superior qualities. The microstructural examination of the alloy reveals a refined lamellar structure with distinct grain boundaries, essential for its machinability in micro-electrical discharge machining (micro-EDM) procedures.

The distinctive amalgamation of qualities and microstructural characteristics renders the Ti–46.5Al–5Nb–2Mo–0.3B alloy an optimal material for precision machining and high-performance applications.

The methodology section is divided into a number of subsections and each subsection is discussed in detail in the following text.

The experimental studies were conducted using an EDM drilling machine (Supplementary Figure 2) manufactured by Sparkonix India Private Limited. The machine’s reliability and precision make it a preferred choice for machining operations involving titanium alloys, which are known for their challenging machinability due to their high strength and heat resistance. Based on findings from pilot experiments and existing literature, five critical process parameters were identified for variation during the experimental studies. These parameters include tool rotational speed (N), discharge current (A), pulse-on time (T_on), pulse-off time (T_off) and power (W). These variables were systematically varied to optimize machining performance and evaluate their effects on chosen performance measures, that is MRR and TWR. This setup was carefully designed to ensure the accurate analysis of the machining behaviour of titanium aluminides, providing valuable insights into optimizing micro-EDM parameters for high-performance alloys. Table 1 presented the input parameters and their levels. RPM directly affects the efficacy of flushing and the removal of debris in the machining area. A substantially influences the MRR and TWR. T_on regulates the duration of energy transmission during a singular discharge. T_off dictates the cooling interval between consecutive discharges, influencing the stability of the EDM process. W integrates the effects of voltage and current, affecting the energy intensity of the discharges. The parameters and their levels in Table 1 are selected based on trial experiment, past studies and experiences and manufacturer recommendations.

Experimental runs were designed by the Taguchi L27 OA. Minitab 16 (Student’s version) was used for designing the experimental runs. Taguchi design is a robust experimental design tool used to optimize processes by evaluating the effects of multiple factors simultaneously. It reduces the number of experiments needed by using only 27 trials instead of testing all possible combinations. This array ensures orthogonality, meaning the factors' effects are independent, allowing for a clear analysis of their individual impact.

L27 OA is a fractional factorial design, offering an efficient way to study complex systems with limited resources. It is widely applied in fields like manufacturing, engineering and product design to improve quality and performance. The L27 array, with its enhanced resolution, facilitates accurate examination of parameter effects and interactions, rendering it ideal for optimizing micro-EDM machining of titanium aluminides. The experimental design in uncoded form is shown in Supplementary Table 4.

A titanium aluminide (Ti–46.5Al–5Nb–2Mo–0.3B) is a completely new γ alloy selected for investigation in the present research. Ti–46.5Al–5Nb–2Mo–0.3B possesses challenges such as increased tool wear and reduced MMRs, necessitating the optimization of process parameters to achieve an optimal balance between MRR and TWR. It is extensively utilized in aerospace and automotive sectors. The alloy samples were prepared by cutting them into rectangular blocks with dimensions of 70 × 45 × 15 mm using a Wire EDM setup (Supplementary Figure 3). This ensured accurate dimensions and uniformity across all samples for consistent mounting and machining during the EDD process. Milling of the samples is done to obtain uniform shapes (Supplementary Figure 4) and the final obtained sample is shown in Supplementary Figure 5.

Electrolytic (EC) grade copper was selected as the electrode material for the study. This decision was based on its superior electrical conductivity, which ensures efficient spark generation and stable machining performance, leading to higher MMRs and improved surface finishes (Mahajan et al., 2018). Copper’s excellent thermal conductivity enables efficient heat dissipation, minimizing the risk of thermal damage to both the electrode and the workpiece during machining. Its ability to provide consistent sparks ensures smoother surface finishes compared to graphite, which often produces rougher surfaces, or brass, which provides reasonable but inferior surface quality. While copper electrodes may experience moderate tool wear, they exhibit significantly lower wear rates than graphite and offer better overall performance in terms of cost-effectiveness due to their extended lifespan and reduced need for post-machining operations. The choice of copper electrodes was particularly critical for machining the Ti–46.5Al–5Nb–2Mo–0.3B alloy. This alloy’s high niobium and molybdenum content contributes to its exceptional strength and heat resistance. Copper’s high conductivity and thermal properties were essential in effectively managing the machining of this material, ensuring efficient heat dissipation, precise machining and excellent surface quality. A 0.5 mm diameter hollow copper electrode was selected for the experiments, with an inner diameter of 0.2 mm as shown in Supplementary Figure 6.

The hollow structure of the electrode offered several advantages over solid electrodes, particularly in micro-EDM processes. These include improved flushing efficiency, enhanced debris removal, better cooling and reduced tool wear. The hollow design also contributed to better surface integrity and precision, making it suitable for high-precision applications requiring small, accurate holes and intricate geometries. Additionally, the consistent control over the machining environment allowed for higher precision and machining speeds, making it possible to achieve tight tolerances in complex geometries.

In the present study, two output responses MRR and TWR are selected for investigation. Both are critical machining performance indicators that directly impact process efficiency, tool life and surface quality. Precisely quantifying MRR and TWR is essential for enhancing machining parameters, as increased MRR boosts productivity, whereas reduced TWR prolongs tool longevity and preserves accuracy. The study methodically analyses these values to achieve an optimal equilibrium among machining efficiency, tool durability and overall process stability.

Material removal rate: MRR measures the volume of material extracted from the workpiece per unit of time, offering insights into the efficiency of the machining process. To ascertain MRR, the workpiece is initially weighed prior to cutting with a high-precision digital balance (Model: Mettler PM1200, Make: India). Subsequent to machining, the workpiece is meticulously cleaned to eliminate any waste and is then reweighed. The weight differential pre- and post-machining indicates the mass of material extracted. Eq. (1) is used for calculation of MRR (Equbal et al., 2019).

Where, M_i and M_f are the weight (in g) of the workpiece pre- and post-machining, respectively which were measured using a weighing machine and t is the machining time (in min), which was recorded using stopwatch of the mobile phone.

Tool wear rate: TWR is assessed to determine the lifespan of the tool electrode during machining. The tool is weighed prior to machining and machining was performed. After machining it was subsequently cleaned and reweighed to ascertain the material loss attributable to wear. TWR is calculated using Eq. (2) (Equbal et al., 2019).

where, m_i and m_f are the weight (in g) of the electrode pre- and post-machining that were taken with the help of a weighing machine (Model: Mettler PM1200; Make: India) and t is machining time (in min) which was recorded using stopwatch of the mobile phone.

The TLBO algorithm is a population-based, metaheuristic optimization technique inspired by the educational process. TLBO operates without requiring specific algorithm-dependent parameters, making it computationally efficient and robust in solving complex engineering optimization problems (Equbal et al., 2024; Rao, 2016). TLBO is applied in manufacturing to optimize processes such as machining parameters, production scheduling and inventory management. TLBO is also used to solve complex multi-objective optimization problems, balancing various conflicting objectives in manufacturing systems. Its adaptability and ability to handle diverse scenarios make it a valuable tool for manufacturing optimization. In this study, TLBO was applied to optimize the process parameters of micro-EDM for the Ti–46.5Al–5Nb–2Mo–0.3B alloy. The various steps in TLBO algorithm are:

• Step 1: Generate an initial population based on the experimental data from the L27 array, with each individual representing a set of process parameters.

• Step 2: Define a composite fitness function to balance MRR and TWR. This is given in Eq. (3).

where,

$Ftotal$ is the total function value,

1. $w1$ and $w2$ are the weighting factors. Here $w1$ = $w2$ = 0.5,

2. max (MRR) and min (MRR) are the maximum and minimum values of MRR, respectively.

3. max (TWR) and min (TWR) are the maximum and minimum values of TWR, respectively.

4. Step 3: Teacher Phase: For each individual X_i Eq. (4) is given as

Here,

1. R is the Random number [0,1]

2. $XT$ is the Teacher Position

3. $TM$ is the Teaching Factor

4. Mean is Mean of the population

5. Step 4: Learner Phase: For each individual $Xi$⁠, randomly select another variable $Xnew:i$ as shown in Eq. (4).

Here, $Fi$ and $Fj$ are the fitness values of $Xi$ and $Xj$ respectively.

• Step 5: Repeat the Teacher and Learner phases until convergence criteria are met, such as a maximum number of iterations or a satisfactory fitness level.

Table 2 presented the experimental results for the EDD process under the varying input parameters as discussed in Supplementary Table 4. A total of 27 experiments were conducted using different parameter combinations to systematically observe their effects on the output responses (designed using Minitab 16 software). MRR and TWR are critical indicators of machining efficiency and tool longevity. The MRR and TWR values were calculated in accordance with Eq. (1) and Eq. (2) respectively. It is to be noted that the machining time was calculated for the machining depth of 10 mm in the titanium aluminide workpiece used. The results reveal that higher current and optimized power levels generally lead to an increase in MRR, indicating improved machining efficiency. However, TWR does not follow a linear trend and is influenced by complex interactions among current, pulse durations and power levels. Additionally, variations in tool rotational speed also exhibit noticeable effects on both MRR and TWR, suggesting its role in enhancing flushing efficiency and spark stability. These experimental findings are essential for understanding the behavior of the EDD process and serve as a valuable dataset for optimization, which can effectively identify the most favorable parameter combinations for maximizing performance and minimizing tool wear.

To methodically identify the most influential process parameters affecting the MRR and TWR, ANOVA (Analysis of variance) was conducted using the experimental data. ANOVA helps to statistically discern the significance of each parameter by comparing the variance attributed to each parameter against the residual variance. ANOVA table for MRR and TWR is presented in Supplementary Table 5 and Supplementary Table 6. From Supplementary Table 5 for MRR, it is clearly evidenced that T_on emerged as the most significant parameter with a p-value of 0.003, indicating its strong statistical influence on MRR. T_on substantially influences the duration for which electrical energy is applied, directly correlating with the thermal energy available for material removal. Extended T_on allows greater heat generation, facilitating higher MRR but with the trade-off of increased thermal stresses. However, the other process parameters, including tool rotational speed, current, Pulse-off time and Power were found to have relatively insignificant impacts on MRR (p-values above 0.05). This indicates that, within the tested ranges, these parameters alone do not prominently influence the efficiency of material removal. Nevertheless, their interactions could indirectly affect process stability and must be considered carefully when integrated into optimization strategies.

Supplementary Table 6 depicts the ANOVA result for TWR. According to the ANOVA results, the discharge current (A) demonstrated the highest statistical significance on TWR, with a p-value of 0.0006. Higher current settings substantially increase electrical and thermal loads on the electrode, thus accelerating tool degradation and material loss from the electrode surface. Furthermore, the tool rotational speed was also found to be statistically significant with a p-value of 0.044. It plays a vital role in effectively flushing debris from the machining zone. Increased rotational speed facilitates better evacuation of debris and heat, thus directly contributing to reduced tool wear. Additionally, power showed marginal statistical significance with a p-value of 0.054, indicating its influence on tool wear is considerable, albeit slightly above the traditional significance threshold.

This marginal significance underscores the fact that power settings should still be selected carefully to optimize tool longevity. Conversely, T_on and T_off appeared statistically insignificant, suggesting limited direct influence within the range investigated.

The variation of output responses with each input parameters is shown in Figure 1 (drawn using Python). In Figure 1(a) –Figure 1(e), solid lines represent MRR whereas dashed lines showed the variation in TWR. Figure 1(a) showed the variation of MRR and TWR with tool rotational speed (N) in RPM. N has a considerable impact on machining performance. It can be observed from the figure that MRR is high at higher speed whereas tool wear decreases. At lower speeds (60 RPM), MRR is inconsistent due to insufficient debris removal, increasing the risk of tool damage. As the speed increases to 120 RPM and 180 RPM, MRR stabilizes while TWR lowers, indicating more efficient machining (Zhang et al., 2016). According to the findings, greater rotational speeds improve flushing efficiency, resulting in less debris and heat accumulation in the machining zone. Figure 1(b) presented the variation of MRR and TWR with pulse on time (T_on). It showed that MRR increases with T_on due to higher energy generation whereas TWR initially decreases with T_on and then increases at high T_on. TWR initially decreases with an increase in T_on, but subsequently increases at higher T_on. This behavior is attributed to the increased spark energy associated with longer T_on, which results in greater material erosion from the tool’s bottom surface exposed to the machining process. As a result, the enhanced spark energy at elevated T_on leads to an increase in tool wear. The increase in spark energy with increase in T_on erodes more material from the tool bottom surface exposed to machining and it leads to increase in the TWR (Sood and Equbal, 2020).

Figure 1(c) depicts the variation in output with power (W). Power settings have a considerable impact on the output. It can be observed from Figure 1(c) that higher power levels (3000 W) result in a higher MRR but dramatically increased TWR (Nieslony et al., 2023; Equbal et al., 2021). Lower power levels (2000 W) produce a better mix of MRR and TWR, making them appropriate for applications that value precision and tool longevity. The trade-off between productivity and tool wear is an important factor to consider when determining the optimal power level.

Figure 1(d) depicts the variation in output with pulse off time (T_off). Figure 1(d) depicts that MRR initially increases and then decreases at higher T_off. As the value of T_off increases, the interval between successive discharges becomes greater, allowing more time for the solidification of previously melted material that was not fully removed. This material will be cleared in the next cycle, resulting in a reduction in the MRR. A higher T_off also offers ample time for the dielectric strength to be restored. However, during the subsequent cycle, some energy is consumed in overcoming the regained dielectric strength, which further leads to a decrease in the MRR (Kebede et al., 2024). The link between pulse-on and pulse-off times is also important. The optimal machining performance with high MRR and low TWR is observed when the T_on is around 9 µs and the T_off is 6 µs. Shorter T_off results in insufficient dielectric recovery, causing unstable machining, whereas long T_off increases thermal stress, causing tool damage. This balance of pulse-on and pulse-off periods is crucial for maintaining stable and efficient machining conditions.

Figure 1(e) presented the variations in output with the change in discharge current (A). It can be observed that MRR increases with larger A. It has a direct impact on the energy delivered to the machining zone, which allows for better material removal. However, this comes at the expense of a greater TWR, as increased temperature and electrical stress on the tool increases wear (Kebede et al., 2024). It is important to know that in Figure 1, the variation of MRR and TWR is presented with respect to individual machining parameters such as tool speed, power, pulse-on time, pulse-off time and current. It is obvious that MRR and TWR are influenced by the combined effect of all five variables, each subfigure in Figure 1 isolates the impact of a single parameter by assuming the remaining four variables are held constant at their central or reference values. This approach is commonly used in response surface methodology (RSM) and regression analysis to study the effect of one variable independently, without the influence of interactions with other variables. The curves shown are typically generated from fitted second-order models rather than raw experimental data, and they represent predicted responses under fixed conditions. Therefore, the trends in each subfigure demonstrate that the variations in MRR and TWR are expected to change when only the selected parameter is varied, offering a clearer understanding of its individual impact on machining performance.

The TLBO algorithm, being parameter-less, does not require crossover or mutation rates. In the present research, number of generations used was set to 10 (as evident in Supplementary Table 7 and Figure 2), the population size chosen was 27, corresponding to the L27 OA used in the experimental design. The calculations for Average Fitness and Best Fitness were derived at each iteration based on the composite fitness function described in Eq. (4). Supplementary Table 7 summarizes the fitness development observed during the optimization process utilizing the TLBO algorithm. This table includes two critical measures for each iteration: Average Fitness and Best Fitness. Average Fitness is the mean fitness value determined from all 27 experiments in a given iteration. It reflects the overall improvement in population fitness caused by the TLBO algorithm’s iterative parameter adjustments. In contrast, best fitness tracks the highest fitness value achieved by a single experiment in each iteration. This statistic tracks the progress of the “teacher” experiment, which is critical in driving the optimization process to the global optimum.

The fitness progression table shows a constant increase in both average fitness and best fitness values throughout iterations, demonstrating the algorithm’s effectiveness in improving parameter settings. By the tenth iteration, the average and best fitness measures have stabilized, indicating that the algorithm has successfully converged to an optimal solution (Figure 2).

The resulting best fitness value of 0.962 is consistent with the recommended machining settings for micro-EDM drilling the Ti–46.5Al–5Nb–2Mo–0.3B alloy. These settings strike a balance between boosting MRR and lowering TWR, making them acceptable for use in precision machining. The parameter combination associated with the final fitness value of 0.962 was selected as the optimal setup for micro-EDM drilling of the Ti–46.5Al–5Nb–2Mo–0.3B alloy. These parameters represent the best trade-off between MRR and TWR. The optimal parameters are shown in Supplementary Table 8.

From Table 2 it can be deduced that higher rotational speed improves the flushing of debris from the machining zone, contributing to better machining stability. A lower discharge current minimizes tool wear and reduces the thermal load, leading to improved tool life and better dimensional accuracy. This value provides sufficient time for effective material removal without excessive heat generation, balancing MRR and TWR. A suitable off-time allows the dielectric to deionize and cool down the machining zone, ensuring stable machining conditions. Lower power settings are ideal for precision machining, reducing the risk of excessive tool wear and thermal damage to the workpiece. Figure 2 witnessed that the best fitness value increased consistently from iteration 1 to 10, the rate of improvement has significantly decreased in the later iterations. As seen in Figure 2, the curve begins to flatten after iteration 7, indicating that the algorithm is approaching convergence. The minimal increase in fitness value between iterations 9 and 10 suggests that further iterations (such as 11 and 12) are unlikely to produce meaningful gains. Therefore, continuing beyond 10 iterations may not be necessary, as the optimization has effectively stabilized and reached near-optimal performance.

The optimized machining parameters produced from the TLBO method were validated using an experiment. This validation process was critical to ensuring that the recommended parameter settings not only worked well conceptually, but also produced dependable and consistent outcomes in real-world situations. The validation technique compared the expected machining reactions generated by the TLBO algorithm to the actual experimental results. The errors between predicted and experimental values for both MRR and TWR are well within acceptable limits for machining process validations, indicating the robustness of the TLBO optimization method (Supplementary Table 9).

The slight differences can be attributed to practical factors such as: slight differences in dielectric fluid conditions or temperature during the experiments, minor inconsistencies in the material properties of the tool or workpiece, minor deviations caused by limitations in the measurement devices used to record MRR and TWR.

The SEM image of a hole machined at optimized machine setting shows a smooth and uniform surface, indicating effective and better material removal (Supplementary Figure 7). This homogeneity is due to the tool rotational speed (180 RPM), which improves debris draining and reduces uneven deposition (Kuppan et al., 2008). The moderate T_on (9 µs) allows for controlled energy input, resulting in effective machining while reducing the risk of localized overheating or uneven crater formation (Gostimirović et al., 2018). The heat-affected zone is limited, with no signs of thermal cracking or surface discoloration. This result shows the impact of the discharge current (4 A), which balances the energy given to the machining zone and prevents excessive thermal stress. The T_off of 6 µs allows for adequate recovery time for the dielectric fluid, optimizing heat dissipation and minimizing thermal damage (Tawfiq and Abbas, 2018).

The lack of microcracks and apparent imperfections on the machined surface demonstrates the accuracy of the TLBO-optimized parameters. The comparatively low power (1000 W) eliminates excessive energy input, lowering the risk of thermal stresses that contribute to cracking (Sahoo and Barman, 2012). Furthermore, the fast tool rotating speed inhibits debris from collecting and functioning as crack initiation sites, which helps to maintain surface integrity. The craters found are finer and more consistent than previous samples, indicating a well-controlled sparking process. This crater geometry demonstrates the achieved balance between MRR and TWR. The optimized T_on (9 µs) and T_off (6 µs) provide accurate energy bursts and appropriate cooling, resulting in well-defined craters with no overlap or material redeposition. Minimal material formation is observed, confirming the efficiency of the tool rotational speed (180 RPM). The quick rotation aids in debris evacuation from the machining zone, lowering the possibility of secondary discharges and providing a clean surface finish.

The present study explores the parametric optimization of micro-EDD for Ti–46.5Al–5Nb–2Mo–0.3B. A series of experiments were conducted based on a Taguchi L27 OA design, taking five key machining parameters: N, A, T_on, T_off and W. The study aimed to evaluate machining efficiency and tool performance through two critical output responses: MRR and TWR. To optimize the EDD process, the TLBO algorithm was employed. The TLBO algorithm was applied to balance the conflicting objectives of maximizing MRR while minimizing TWR. The study was also validated by performing machining at optimal parameter setting and analyzing its metallurgical aspect. Key conclusions drawn from the present study are:

1. Greater rotational speeds improve flushing efficiency, resulting in less debris and heat accumulation in the machining zone. At higher value of N, MRR is higher and TWR is comparatively lower.

2. The MRR increases with T_on due to the higher energy generated during the discharge process. On the other hand, TWR initially decreases with an increase in T_on, but subsequently increases at higher T_on. This behaviour is attributed to the increased spark energy associated with longer T_on.

3. The effect of power settings (W) on the output responses evident that higher power leads to an increase in the MRR, but at the cost of a significant rise in TWR. On the other hand, lower power settings provide a more balanced combination of MRR and TWR.

4. MRR initially increases with T_off, but begins to decrease at higher values of T_off. With increase in T_off, the interval between successive discharges becomes longer, providing more time for the solidification of previously melted material that was not fully removed. This solidified material is cleared in the subsequent discharge cycle, leading to a reduction in MRR.

5. MRR increases with higher discharge current (A), as it directly influences the energy delivered to the machining zone, thereby enhancing material removal. However, this improvement in MRR is accompanied by a higher TWR.

6. The research effectively illustrated the efficacy of the TLBO algorithm in optimizing process parameters for micro-EDD of the Ti–46.5Al–5Nb–2Mo–0.3B alloy. The TLBO algorithm determined the optimal parameter set, which showed a tool rotational speed of 180 RPM, current of 4 A, T_on of 9 µs, T_off of 6 µs and power of 1000 W, resulting in a fitness value of 0.962.

7. The experimental validation of the TLBO-optimized parameters showed a strong correlation between predicted and observed values for MRR and TWR, with percentage errors remaining under 5%. The strong correlation confirms the reliability of the TLBO method for multi-objective optimization.

8. The metallurgical analysis of the machined samples confirmed the effectiveness of the TLBO optimization. The surface morphology displayed smoothness and uniformity, with minimal heat-affected zones (HAZ) and no micro-cracks, consistent with the anticipated machining results.

The supplementary material for this article can be found online.