Performance optimization of wire EDM of Nitinol shape memory alloy using BBD RSM and TLBO with alumina nano graphene and MWCNT Powder mixed dielectric

TL;DR

This study improves the machining of a shape memory alloy using nano-powders and optimization techniques to enhance material removal and surface quality.

Contribution

A novel hybrid approach combining BBD RSM and TLBO with MWCNT powder improves WEDM performance for Nitinol.

Findings

MWCNT powder outperformed alumina and nano-graphene in material removal rate and surface roughness.

Optimized parameters increased MRR by 60.57% and reduced SR by 75.81% compared to conventional WEDM.

SEM analysis showed MWCNT-based machining produced smoother surfaces with fewer defects.

Abstract

The present study investigated the performance optimization of Wire Electrical Discharge Machining (WEDM) of Nitinol Shape Memory Alloy (SMA) using a hybrid design approach combining Box-Behnken design and Teaching–Learning based optimization (TLBO). A comparative study of three nano-powders, namely, alumina, nano-graphene, and multi-walled carbon nanotubes (MWCNTs), was conducted to investigate their effect on material removal rate (MRR), surface roughness (SR), and surface morphology. The influence of key process parameters, discharge current (Ip), pulse-off time (Toff), and pulse-on time (Ton) has been systematically evaluated through experimental trials. Non-linear regression models were developed for both MRR and SR responses, and their statistical adequacy was validated using ANOVA and R² values, all exceeding 96%, confirming strong model accuracy. ANOVA further identified discharge current as the most significant factor, with the highest F-values for MRR and SR. Among all powders, MWCNTs consistently outperformed, achieving the highest MRR (3.6353 g/min) and lowest SR (2.12 μm) due to superior spark stability and thermal conductivity. The simultaneous optimization for MWCNT-based WEDM process has given the optimal parametric settings of Ip of 4 A, Toff of 20 µs, and Ton of 42 µs with the response values of MRR and SR as 2.8144 g/min and 3.06 μm, respectively. Additionally, a comparative experimental at optimized variables revealed that MWCNT-assisted WEDM yielded a 60.57% increase in MRR and a 75.81% reduction in SR over conventional WEDM. SEM analysis further shown that MWCNT-based machining produced the smoothest surfaces with minimal defects, while conventional EDM exhibited extensive pitting and re-solidified debris. This integrated experimental and optimization study provides a robust framework for improving the machinability and surface integrity of Nitinol SMA using advanced nano-powder-assisted WEDM.

Figures

SEM of machined surface for conventional WEDM

FESEM micrographs of (a) Al₂O₃, (b) nanographene, and (c) MWCNTs^[44](#CR44)–[46](#CR46)^

TLBO process flowchart^[44](#CR44)^

TLBO process flowchart^[44](#CR44)^

Effect of input factors on MRR response

Effect of input factors on SR response

Pareto graph for MRR vs. SR

SEM of machined surface for MWCNT-based WEDM

SEM of machined surface for graphene-based WEDM

SEM of machined surface for alumina-based WEDM

Full text

Introduction

The advancement in materials science and manufacturing systems has shown various industrial revolutions. Introduction of shape memory alloys (SMAs) is of that revolution due to its development due to its applications^1,2^. SMAs has an ability to come back to their initial shape and size once they get heated at their defined transformation temperatures^3^. Nickel-titanium alloy commonly known as Nitinol is one the type of SMAs. Nitinol possesses superior properties of super elasticity, and biocompatibility^4^. It is widely preferred material for high-performance applications such as aerospace parts, automotive components, surgical instruments etc^5,6^. Owing to the exceptional biocompatibility of Nitinol, it generates a protective titanium oxide layer, which restricts the discharge of toxic nickel ions into the adjacent blood or tissue^7^. Thus, it requires accurate machining techniques of Nitinol SMAs. However, conventional machining processes possesses various limitations as they generates extreme heat and leads to phase changes owing to the higher hardness of Nitinol^8,9^. Another difficulties associated with conventional machining are tool wear, poor surface finish, and higher surface defects. Thus, non-traditional machining techniques like Wire-electrical discharge machining (WEDM) process has shown precise machining capabilities as they can be used to cut complex geometries with less heat-affected zones and an excellent surface finish^10^. In WEDM process, electrical discharges gets created among the work-tool interfaces^11^. The generated sparks melts and vaporizes the work material, which allows precise material removal without mechanical stress^12^.

Many studies have been done to improve machining characteristics during WEDM of nickel and titanium-based alloys. WEDM process consists of various input process parameters like pulse-on-time (T_on_), duty cycle, wire tension, wire speed, pulse-off-time (T_off_), discharge current (I_p_), etc. Thus, it is essential to control these variables. Box-Behnken design (BBD) approach of response surface methodology (RSM) systematically analyzes the effect of input factors on the selected responses with the least number of trials^13,14^. Compared to Central Composite Design (CCD), BBD offers a distinct advantage for machining studies involving high-energy discharge processes such as WEDM. BBD does not include factorial points at the extreme corners of the design space, thereby avoiding experimental runs at potentially unsafe or unstable parameter combinations^15^. Moreover, BBD approach needs less number of experimental trials for three input factors as compared to CCD for developing the full quadratic models. While dealing with multiple responses such as material removal rate (MRR) and surface roughness (SR), conflicting situations arise during machining operations. It can be effectively tackled by using a multi-objective optimization approach^16^. Teaching-learning based optimization (TLBO) is one such metaheuristic optimization technique that has been effectively used for various engineering applications^17,18^. It operates on the fundamental principle of teaching and learning activities in a classroom. The TLBO approach is easy to implement and useful for solving complex problems^19^. TLBO was selected over other popular metaheuristic algorithms owing to their parameter-less structure, computational efficiency, and ease of implementation. Some of the other algorithms requires careful tuning of multiple algorithm-specific parameters, and improper tuning can significantly affect convergence behavior and solution quality.

The machining performance of the WEDM process can be significantly improved with the addition of suspended nano-powders to the dielectric fluid in an appropriate amount^20,21^. To enhance the EDM machining process, many researchers have employed various nano-powders, such as Ti, alumina (Al_2_O_3_), Al, Si, SiC, multi-walled carbon nanotubes (MWCNTs), Cu, W, Cr, nano-graphene, etc^22–24^. The key characteristic of nano-particles, such as size, density, and amount, electrical and thermal conductivity, plays an important role in their performance^25^.

Ramesh and Jenarthanan^26^ used cobalt, zinc, and molybdenum nano-powders for machining of Nimonic 75 alloy by utilizing tungsten, brass, and copper tools. Since cobalt and zinc have low melting points, and due to their early uniform distribution in the dielectric, the MRR response was found to be higher. Rajaguru et al.^27^ utilized a composite electrode made by fusing carbon nanotubes on a copper tool for enhancing the efficiency of EDM for machining of high-carbon high-chromium steel. It was observed that MRR is 2.5 times higher than normal copper electrode, as the composite tool has high electrical conductivity. The SR was improved by 13% due to a large spark gap, causing debris to flush out and improve surface texture. Rao et al.^28^ investigated the EDM process of AISI D2 steel with a copper tungsten electrode by using Al_2_O_3_ nano-powder in a sunflower oil dielectric. The output responses indicated that powder-mixed EDM (PMEDM) gave the lower SRs with enhanced MRR, and reduced TWR. Davis et al.^29^ conducted surface modification of medical-grade nitinol with a micro-copper and micro-brass tool. It was concluded that the concentration of powder dissolved in the dielectric determines the machining quality. Concentration of 6 g/L Zn-powder proved to be the optimal amount. Below this, machining time was increased with more dimensional deviation due to low powder particles between the tool and workpiece, and above 6 g/L resulted in unstable sparks and powder particles and debris attaching to the machined surface. A study conducted by Ishfaq et al.^30^ showed that the addition of nanographene powder improved the SR by 70%. This was because the nano-particles arrange themselves in a chain between the tool and the workpiece, creating a bridging gap which enhances thermal conductivity of the dielectric medium. They concluded that the flushing efficiency of dielectric was improved by the incorporation of nano-graphene, which is essential for clearing debris and ensuring a clear machining zone. The machining process was more stable as a result of this improved flushing action, which lowers the possibility of arcing and short circuits. Gattu et al.^31^ compared different nanopowders for the machining of tungsten carbide. They observed that the MRR was enhanced with the addition of all powders, with carbon nano-fiber significantly improving MRR due to its favorable electrical properties. When compared to oil EDM, surface texture improved for all nano-powders and concentrations at higher voltages (100 and 110 V). Sabbar et al.^32^ showed that nanographene-coated copper electrodes exhibited a TWR improvement of 15.10% and MRR increased by 29.67%. The machined surfaces from copper-nanographene electrodes showed fewer defects (micro-cracks, micro-pores). Behera et al.^33^ concluded that the use of copper tool electrodes in conjunction with nanographene oxide mixed dielectric significantly enhances the machinability of Nimonic alloy with a concentration of 5 g/L. Dutta and Sharma^34^ investigated the effect of nano-graphene for the machining of Hastealloy C-276. They found that nano-graphene powder concentration of 0.21 g/L increases MRR, but after this, due to particle accumulation in the machining gap, there is machining instability, which lowers MRR. Sharma et al.^35^ incorporated MWCNTs and graphene nanopowders into the dielectric fluid during EDM of Inconel 825. Graphene-based EDM demonstrated a higher MRR (0.2468 g/min) compared to MWCNTs, as it possesses superior thermal conductivity (5000 W/m.K). MWCNTs are also conductive but have lower thermal conductivity (3000 W/m·K) due to their tubular structure and potential defects, which can hinder effective heat dissipation. Darji et al.^36^ has observed an enhancement in MRR response by 19%, and decrement in TWR by 8.51% by using CNT nanopowders. Chaudhari et al.^21^ investigated the impact of alumina and nanographene on MRR, and SR response. Their findings has revealed an improvement of 45.81%, and 37.22% for MRR, and SR respectively by using nano-graphene. The alumina has also shown the enhancement in MRR, and SR by 35.19% and 18.27%, respectively. The higher conductivity of nano-graphene powders has shown better performance than alumina nano-powder. The machining of AI6061 conducted by Sana et al.^37^ using alumna powder has observed an enhancement in MRR by 87.42%, and drop in SR by 3.4%. Rouniyar and Shandilya^38^ investigated surface crack density and microhardness for EDM of Al6061 with alumina powder. Optimal machining parameters resulted in an SCD of 0.0063 μm/µm², indicating enhanced surface integrity.

The effect of dielectric composition and machining parameters of Nitinol SMAs were investigated in recent studies using other machining processes. Chaurasia et al.^39^ investigated powder-mixed micro-electrical discharge milling of NiTi SMA. Their results reported that appropriate powder additives in the dielectric can significantly affect surface morphology and in vitro biocompatibility metrics, linking process parameters to post-machined cell viability and surface chemistry. Another study by Chaurasia and Debnath^40^ focused on microchannel fabrication in biomedical-grade Nitinol SMA using µ-ED milling with sustainable vegetable oils as dielectrics; the work demonstrates that eco-friendly dielectric selection can improve microchannel quality and surface integrity important for biomedical applications. Complementing the NiTi studies, a Box–Behnken Design (BBD)–RSM investigation on EDM of Incoloy 925 showed that RSM provides accurate predictive models for key responses (e.g., MRR and Ra) and is effective for parametric optimization in alloy machining, but it is typically applied as a single-objective technique^41^. The above mentioned studies reveals the advantages of dielectric modification and statistical modelling in EDM processes, they also shows two limitations. Firstly, majority of works focuses on process-to-surface mapping or on single-technique optimization, and secondly, comparative evaluations across different nano-additives within the same experimental/optimization framework are limited. To address these gaps, the present work integrates BBD–RSM for model identification with Teaching-Learning-Based Optimization (TLBO) for parameter-free, multi-objective optimization (MRR vs. SR) and provides a direct experimental comparison among alumina, nano-graphene and MWCNT additives under the same validated framework.

Although numerous studies have explored powder-mixed WEDM using various nano-powders and optimization techniques, a systematic comparative analysis of advanced powders, specifically alumina, nano-graphene, and MWCNTs for machining Nitinol remains underexplored. Furthermore, the integrated approach of BBD-RSM design with metaheuristic TLBO techniques for performance enhancement was not explored in depth, along with the comparative analysis of nano-powders. The present study fills this critical gap by experimentally investigating and comparing the influence of these powders on key machining responses of MRR and SR during WEDM of Nitinol SMA. A novel hybrid approach combining BBD-RSM and TLBO is employed to model, optimize, and analyze the process parameters. Scanning electron microscopy (SEM) was employed to assess the surface morphology under different powder conditions. This comprehensive investigation provides valuable insights into the machinability of Nitinol using advanced nano-powders and offers an effective framework for multi-objective optimization in powder-mixed WEDM processes.

Materials and methods

Preparations of nano-powders with synthesis

In our study, three types of nanomaterials, namely nano-graphene, multi-walled carbon nanotubes (MWCNTs), and Al₂O₃ nanoparticles, were synthesized using standard and widely reported chemical and hydrothermal methods^21,42,43^. These methods are commonly adopted in nanomaterials research because they provide good control over particle size, morphology, and structural quality, while remaining practical and cost-effective for engineering applications.

Nano-graphene was prepared using a modified Hummers method. In this process, graphite was oxidized using concentrated sulfuric acid and sodium nitrate, followed by the controlled addition of potassium permanganate while maintaining a low temperature using an ice bath. The mixture was continuously stirred for two days and subsequently subjected to hydrothermal treatment at 150 °C for 12 h in Teflon-lined autoclaves. The resulting product was repeatedly washed with distilled water and ethanol to remove residual impurities and then dried in a vacuum oven at 60 °C to obtain fine graphene powder^42^.

MWCNTs were synthesized through a hydrothermal reaction using a solution containing polyethylene glycol, ethanol, sodium hydroxide, and distilled water. The solution was stirred for one hour, sealed in a reactor, and heated at temperatures ranging from 120 °C to 200 °C for 24 h. After synthesis, the material was thoroughly washed until a neutral pH was achieved and then dried in a vacuum oven at 75 °C. This method produced MWCNTs with lengths of 5–10 μm^43^.

Al₂O₃ nanoparticles were synthesized using a sol–gel route, which is a well-established and widely reported method for producing oxide nanoparticles, as discussed in our earlier studies^21^. Aluminum nitrate nanohydrate was first dissolved in deionized water, followed by the gradual addition of triethanolamine under continuous stirring. Citric acid was then introduced at 75 °C, leading to the formation of a viscous sol. The sol was heated at 150 °C for 90 min to initiate gelation. The resulting gel was subsequently calcined at 1200 °C for 3 h, producing Al₂O₃ nanoparticles with an average particle size of approximately 110 nm.

The morphology and crystal structure of all synthesized nanomaterials were examined using FESEM, TEM, XRD, and Raman spectroscopy. The results confirmed the successful formation of nanostructured, crystalline materials suitable for advanced engineering applications. Detailed characterization results, including morphology and structural analysis, have been reported in our earlier studies^44–46^. Figure 1a-c presents FESEM micrographs of Al₂O₃, nano-graphene, and MWCNT powders, while Table 1 summarizes the key properties of the nanomaterials used in the present work.

Fig. 1FESEM micrographs of (a) Al₂O₃, (b) nanographene, and (c) MWCNTs^44–46^

Table 1. Comparison of Nanomaterials: Nanographene, MWCNT, and Al₂O₃^47–49^PropertyNanographeneMWCNTAl₂O₃ NanoparticlesStructure2D sheet of sp²-bonded carbon atomsCylindrical tubes of concentric graphene layersSpherical/irregular oxide particlesDensity (g/cm³)~ 2.2~ 1.3–1.4~ 3.95Specific Surface AreaUp to 2630 m²/g~ 200–400 m²/g~ 100–150 m²/gElectrical Conductivity~ 10³–10⁴ S/cm~ 10⁴–10⁵ S/cm~ 10⁻¹¹–10⁻¹³ S/cmThermal Conductivity~ 2000 W/m·K~ 3000 W/m·K~ 10–30 W/m·KYoung’s Modulus (GPa)~ 1000~ 1000~ 300–400Tensile Strength (GPa)~ 130~ 60–150~ 1–2Melting PointSublimates at ~ 3650 °C> 3000 °C~ 2072 °CApplicationsSensors, flexible electronics, coatingsComposites, transistors, EMI shieldingCatalysts, thermal materials, dielectrics

Experimental plan

The experiments for the present study were conducted by using a Concord DK7732 make Wire-EDM machine. Nitinol SMA with 55.8% element composition of Ni and the remainder as Ti was employed as the work material with a reusable wire electrode of molybdenum having of 0.18 mm of diameter. Figure 2a shows the methodology employed, while Fig. 2b shows the enlarged view of the machining zone of the WEDM process used in the present study. For each experiment run, a 2 mm-thick slice was cut from a nitinol square bar, having a cross-sectional area of 10 mm². The dielectric fluid of EDM oil was combined with alumina, nano-graphene, and MWCNTs nano-powders at a concentration of 1 g/L. In all the experimental trials, EDM was combined with nanopowders (1 g/L) which was homogenized using ultrasonic agitation for 20 min to ensure uniform suspension. The concentration of nano-powders was selected on the basis of the results of preliminary trials and past studies. Along with nano-particles, the input factors of T_on_, T_off_, and I_p_ were investigated on the output responses of MRR and SR. Table 2 shows the input conditions employed for the experimental work. All the input variables were varied at three levels. Again, the selection of input factors and their levels was decided from the results of preliminary trials, past studies, and machine limits. The BBD-RSM approach of design of experiments was used to design the experimental matrix. The BBD approach systematically analyses the effect of input factors on the selected responses with the least number of trials. The BBD is a more extensive statistical approach that constructs second-order quadratic models (as illustrated in Eq. 1) to evaluate both the main effects and the interactions among process variables.

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Where, Xi represents the coded factors (T_on_, T_off_, I_p_), βi represents regression coefficients, and α represents random error. The coefficients were estimated using least-squares fitting in Minitab v17, and model adequacy was verified through ANOVA and residuals.

Fig. 2**(a)**Flowchart of the methodology employed in the present study. (b) Enlarged view of machining zone of WEDM process

Table 2. Experimental conditions of the WEDM processInput factors for PMEDMValues/LevelsDischarge Current, I_p_ (A)2; 4; 6Pulse-off-time, T_off_ (µs)15; 20; 25Pulse-on-time, T_on_ (µs)30; 40; 50Tool electrodeMolybdenum wire (0.18 mm of dia.)Type of nano-powdersAlumina, Graphene, MWCNTsAmount of nano-powders (g//L)1

Testing and characterization

The MRR response was used to assess the efficiency of the process, and it was measured in grams per minute in the present study. A Metler ME204 analytical weighing scale with a reading of 0.1 mg was used to calculate the weight of the workpiece both before and after machining. SR serves as a crucial metric for assessing the quality of a machined surface. In this study, a Mitutoyo Surftest-410 instrument was employed to measure SR at various locations on the machined samples. The average surface roughness (Ra) obtained from these measurements was used for analysis. SEM was employed to assess the surface morphology of the machined parts under different powder conditions.

Optimization

In the present work, the Teaching-Learning-Based Optimization (TLBO) method was used to find optimal solutions for response variables. The multi-objective optimization using TLBO was performed with a population size of 50 and 100 iterations, using a convergence criterion of a change in the fitness function less than or equal to 0.01%, and adaptive weight assignments ranging from 0 to 1. The algorithm is inspired by the influence of a teacher on students’ performance in a classroom. It operates in two phases: the teacher phase and the student phase. This is a population-based process where different design variables are treated as subjects taught to learners. In the teacher phase, the teacher imparts knowledge about various subjects or design parameters to the students. The teacher continuously works to educate all students in the class. The student phase follows, where students randomly interact with each other to further exchange and improve the knowledge they have gained. The performance or fitness of each student is represented by the marks they score. Thus, TLBO is employed to obtain optimal objective functions or results for a given population. After the teaching-learning process, the student’s ability is aligned with the fitness value of an objective function. The best result is achieved by the teacher. In this phase, the teacher works to improve the overall class average from an initial value (M_1_) to a better level (M_2_). The solution in the teacher phase is updated for both the old and new means in each iteration, where Mi represents the class mean, as illustrated below. A detailed process flow chart of the TLBO has been represented in Fig. 3.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:DM_i\:=\:r_i\:(M_{new}\:-\:T_F\:M_i)\:\:\:\:$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:T_F\:=\:round\:\left(1\right)\:+\:rand\:(0,\:1)\:\:\:\:$$\end{document}

Where TF is the teaching factor, ri is a random number between 0 and 1.

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In the students phase, taking two random learners X_k_ and X_k_ where j ≠ k

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{I}\mathrm{f}\:\mathrm{f}\:\left(\mathrm{X}_\mathrm{j}\:\right)\hspace{0.17em}<\hspace{0.17em}\mathrm{f}\:\left(\mathrm{X}_\mathrm{k}\:\right),\:\:\:\:\:$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X_{new,j}} = {\text{ }}{X_{old,j}} + {\text{ }}{r_j}({X_j} - {X_k})$$\end{document}

Otherwise

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Fig. 3TLBO process flowchart^44^

Thus, the current work is focused on implantation of a hybrid BBD-based RSM model with TLBO for multi-response optimization of powder-mixed WEDM process of Nitinol. The current study has used BBD approach to generate statistically validated quadratic models for MRR, and SR responses, while TLBO was preferred to optimize these conflicting responses. The hybridization of these techniques ensures the model accuracy as well as robustness of algorithmic by representing a methodological advancement over a single-objective optimization approach.

Results and discussions

DOE results through BBD-RSM approach

In the current work, the experimental matrix was designed by following the BBD-RSM approach by considering three input factors at three levels. A total of fifteen experiments were planned as per the BBD-RSM approach. These fifteen experimental matrices were planned for each type of nano-powder. Each of these experimental tests was repeated three times, and the average value was taken for analysis purposes. The repeatability of experiments provides more robust and reliable results. Table 3 shows the results of experimental trials for output measures of MRR and SR. The derived results were then analyzed through statistical methods of ANOVA and the coefficient of determination (R^2^). The effect of input factors and nano-particles on output measures was investigated by using main effect plots.

Table 3. Experimental matrix and results as per the BBD-RSM approachRun orderI_pT_off_T_on_MRRSRNano-powder typeAlumina Nano-powder (Al_2_O_3)1625402.21335.47Al_2_O_3_2420401.85934.42Al_2_O_3_3615402.49715.90Al_2_O_3_4220301.56213.69Al_2_O_3_5620502.48685.89Al_2_O_3_6220501.86374.40Al_2_O_3_7620302.16715.52Al_2_O_3_8420401.89354.37Al_2_O_3_9415502.12785.02Al_2_O_3_10420401.79814.32Al_2_O_3_11415302.09614.92Al_2_O_3_12425301.65213.72Al_2_O_3_13215401.73354.08Al_2_O_3_14225401.42133.50Al_2_O_3_15425502.19115.14Al_2_O_3_ Nano-graphene powder 1625402.61174.71Graphene2420402.19403.81Graphene3615402.94665.09Graphene4220301.84333.18Graphene5620502.92115.07Graphene6220502.19923.79Graphene7620302.55724.76Graphene8420402.23433.77Graphene9415502.51094.33Graphene10420402.17523.72Graphene11415302.47344.24Graphene12425301.94953.21Graphene13215402.04563.52Graphene14225401.67713.02Graphene15425502.58554.43Graphene MWCNTs 1625403.18633.75MWCNTs2420402.67663.05MWCNTs3615403.59484.07MWCNTs4220302.24882.54MWCNTs5620503.61524.06MWCNTs6220502.68303.03MWCNTs7620303.11983.81MWCNTs8420402.73413.02MWCNTs9415503.06323.46MWCNTs10420402.67112.98MWCNTs11415303.01753.39MWCNTs12425302.37842.57MWCNTs13215402.49562.82MWCNTs14225402.03142.42MWCNTs15425503.15433.54MWCNTs

Regression equations

The experimental results attained through BBD were analyzed through Minitab v17 software. Second-order polynomial regression equations have been generated for MRR, and SR. The generated regression equations for alumina, graphene, and MWCNTs particles were represented in Eqs. 2–8 for MRR and SR respectively.

Alumina nano-powder:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \:\mathrm{M}\mathrm{R}\mathrm{R}\:=&4.770+0.1740\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.1259\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.1172\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\\&+0.001018\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.002536\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\:\mathrm{S}\mathrm{R}=&13.30+0.070\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.4725\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.2679\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.0680\cdot\:{\mathrm{I}}_{\mathrm{p}}\cdot\:{\mathrm{I}}_{\mathrm{p}}\\&+0.002328\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.00395\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.00424\cdot\:{\mathrm{I}}_{\mathrm{p}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.00655\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}} \end{aligned}$$\end{document}

Graphene nano-powder:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\:\mathrm{M}\mathrm{R}\mathrm{R}\:=&5.498+0.2045\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.1485\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.1311\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\\&+0.001108\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.002993\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}} \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\:\mathrm{S}\mathrm{R}=&11.45+0.067\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.4079\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.2305\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\\&+0.0582\cdot\:{\mathrm{I}}_{\mathrm{p}}\cdot\:{\mathrm{I}}_{\mathrm{p}}+0.002004\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}} \end{aligned}$$\end{document}

MWCNTs nano-powder:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\:\mathrm{M}\mathrm{R}\mathrm{R}\:=&6.75+0.2536\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.1816\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.1632\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\\&+0.00140\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.003651\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}} \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\:\mathrm{S}\mathrm{R}=&9.17+0.0563\cdot\:{\mathrm{I}}_{\mathrm{p}}-0.3235\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.1860\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.04608\cdot\:{\mathrm{I}}_{\mathrm{p}}\cdot\:{\mathrm{I}}_{\mathrm{p}}+0.001623\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}\\&+0.00265\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}-0.0030\cdot\:{\mathrm{I}}_{\mathrm{p}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}}+0.004520\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{f}\mathrm{f}}\cdot\:{\mathrm{T}}_{\mathrm{o}\mathrm{n}} \end{aligned}$$\end{document}

Analysis of variance (ANOVA)

The effect of input factors of the WEDM process was examined on MRR and SR responses by using ANOVA analysis. The ANOVA tables were generated to understand the statistical significance, non-significance, and adequacy of the developed models. Through ANOVA, R^2^ values, and Adj. R^2^ values were also assessed to check the adequacy, data fitness, and reliability of the generated regressions. To check the significance/non-significance of machining variables, P-values of ANOVA were used, while the largest contributing factors were identified through the F-value. A 95% confidence level was used in the present study. As per the confidence level, the P-value of the model or variable should be lower than 0.05 to have a significant impact on the output measure^50^. Tables 4 and 5 show the ANOVA for MRR and SR responses, respectively, in the case of all nano-particles.

Table 4 shows the ANOVA results for MRR response for all three nano-particles (alumina, nano-graphene, and MWCNTs). The regression model terms were found to be highly significant (P-value < 0.001) for all three nano-powders, showing their robust predictive competency. Among the linear terms, I_p_ had the most dominant effect on MRR across all powders, as their F-values were observed to the highest compared to others: 183.27 (alumina**)**, 219.94 (graphene), and 247.23 (MWCNTs). The T_off_ and T_on_ were also significant, though with comparatively lower influence. The square terms and 2-way interaction model terms were also found to be statistically significant for all powders. This shows that nonlinear and interaction effects among the input variables also play a key role. The insignificance of lack-of-fits for all three models confirms that the empirical models adequately captured the variability in the experimental data without significant model error^51,52^. The coefficients of determination obtained for all nano-particles show near unity: (Alumina: R^2^ = 96.64%, Adj. R^2^ = 94.47%), (Graphene: R^2^ = 97.17%, Adj. R^2^ = 95.60%), and (MWCNTs: R^2^ = 97.48%, Adj. R^2^ = 96.08%). The R-square values of the models, all approaching 100%, indicated the excellent model fit and demonstrated the high suitability of the regression models for accurately representing the experimental data^53–55^.

Table 5 depicts the ANOVA results for SR response for all three nano-powders of alumina, graphene, and MWCNTs. The ANOVA results show that the generated quadratic empirical models were statistically significant in all three cases, showing a robust correlation among the input factors and SR response. All the linear terms have shown a significant contribution across all the nanoparticles. Among them, I_p_ had the maximum impact on deciding the SR values, followed by T_on_ and T_off_ due to their highest F-values as shown in Table 5. The square terms and 2-way interaction model terms were also found to be statistically significant for all powders. This shows that nonlinear and interaction effects among the input variables also play a key role. The insignificance of lack-of-fits for all three models confirms that the empirical models adequately captured the variability in the experimental data without significant model error. All the model terms also show higher R^2^ values, higher than 99% along with all Adj. R^2^ values close to 98.5%. This shows the outstanding predictive accuracy of the model terms.

Overall, the ANOVA results for both the responses for each type of nano-powder have shown that the regression models were adequate, robust, and reliable.

Table 4ANOVA of MRR for alumina, graphene, and MWCNTs nano-powdersSourceAluminaNano-grapheneMWCNTsAdj. SSF-ValueP-valueAdj. SSF-ValueP-valueAdj. SSF-ValueP-value Model 1.368551.790.0001.881961.880.0002.899969.690.000 Linear 1.265579.820.0001.746595.710.0002.6934107.870.000 I p 0.9686183.270.0001.3378219.940.0002.0577247.230.000 T off 0.119322.570.0010.166127.30.0010.252430.320.000 T on 0.177633.610.0000.242739.890.0000.383446.060.000 Square 0.03877.320.0240.04587.530.0230.07328.80.016 2-way inter. 0.064312.170.0070.089614.730.0040.133316.020.003 Lack-of-fit 0.04292.620.3040.05298.290.1120.07258.510.109 Pure error 0.0047--0.0018--0.0024 Total 1.4160--1.9366--2.9748R^2^ valuesR^2^ = 96.64%; Adj. R^2^ = 94.47%R^2^ = 97.17%; Adj. R^2^ = 95.60%R^2^ = 97.48; Adj. R^2^ = 96.08%

Table 5ANOVA of SR for alumina, graphene, and MWCNTs nano-powdersSourceAluminaNano-grapheneMWCNTsAdj. SSF-ValueP-valueAdj. SSF-ValueP-valueAdj. SSF-ValueP-value Model 8.6297103.520.0006.3897101.980.0004.0747109.160.000 Linear 7.7167246.850.0005.7129243.150.0003.6425260.230.000 I p 6.3268607.160.0004.6818597.780.0002.9768638.010.000 T off 0.547752.560.0000.409552.290.0000.267957.420.000 T on 0.842180.820.0000.621679.370.0000.397885.270.000 Square 0.454714.550.0040.335114.260.0040.213415.250.003 2-way inter. 0.458321.990.0020.341721.820.0020.218723.440.001 Lack-of-fit 0.05715.210.1670.04295.280.1660.02544.880.177 Pure error 0.0055--0.0041--0.0026 Total 8.6922--6.4367--4.1027R^2^ valuesR^2^ = 99.28%; Adj. R^2^ = 98.32%R^2^ = 99.27; Adj. R^2^ = 98.41%R^2^ = 99.32%; Adj. R^2^ = 98.41%

Effect of EDM factors and nano-powder on response measures

The impact of EDM factors was studied on response measures of MRR and SR by using main effect plots along with the comparative analysis of alumina, nano-Graphene, and MWCNT Powders.

The material removal per discharge is related to the energy deposited into the workpiece during each spark. The energy offered for erosion (E) is nearly proportional to the voltage, discharge current, and pulse-on-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\mathrm{E}\:\propto\:\:\mathrm{V}\:\times\:\mathrm{I}\mathrm{p}\:\times\:\:\mathrm{T}\mathrm{o}\mathrm{n})$$\end{document} . The resulting crater volume (V_c_), and subsequently MRR depends on how efficiently this energy is transferred into the workpiece material, which is influenced by the dielectric medium and plasma channel behavior. This relationship can be expressed qualitatively as:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:\mathrm{V}\mathrm{c}\:\propto\:\:\left[\right(\mathrm{E})/(\hspace{0.17em}\times\:\hspace{0.17em}\mathrm{L}\left)\right]\:$$\end{document}

Where ρ is the density and L is the effective latent/evaporation energy of the material. Additives that alter the dielectric breakdown, plasma stability, or heat transfer efficiency effectively modify this energy-transfer efficiency, thereby changing both the MRR and the resulting surface morphology. Powders influence the efficiency of this coupling via dielectric and plasma effects. Thus, two powders exposed to the same nominal E can produce different crater volumes (hence different MRR) and crater morphologies (hence different SR).

Figure 4a depicts the main effect plot for MRR response. The effect of discharge current, as shown in Fig. 4a, shows a strong positive correlation with MRR. The increase in current has shown an enhancement in MRR values for all three powders. At the higher discharge current values, the energy obtained per spark increases. The increase in higher thermal energy enhances the melting and vaporization of the work material, thereby enhancing the MRR value. The MWCNT-based dielectric has shown the largest value of MRR, followed by nano-graphene and alumina powders. The reason behind this is the superior electrical and thermal conductivity of MWCNTs, which helps in faster spark initiation and removes the debris more efficiently^56,57^. Although graphene particles are also highly conductive, with a slightly lower aspect ratio and surface area compared to MWCNTs, this results in a slightly lower enhancement of MRR^58^. Alumina, being a ceramic with poor electrical conductivity, offers the least improvement in spark efficiency, thus yielding the lowest MRR^59^. Figure 4b of T_off_ vs. MRR depicts the decrease in MRR values as T_off_ increases from 15 µs to 25 µs for all three powder types. The MWCNT-based dielectric has again shown the highest MRR, followed by nanographene and alumina. An increase in the T_off_ value reduces the interval between the two successive sparks and also increases it. So, larger values of T_off_ reduce the number of active sparks per unit time, giving lower values of MRR response. Lower T_off_ values increase the MRR as it leads to more frequent sparking. The superior performance of MWCNT-based dielectric is attributed to its ability to maintain spark stability and reduce arcing even at lower T_off_ values due to its enhanced thermal and electrical conductivity^60^. An increase in T_on_ from 30 µs to 50 µs leads to an increase in MRR for all powders, with MWCNT again providing the highest MRR as shown in Fig. 4c. The higher T_on_ value allows the sparks to keep them active for a longer duration, which enhances the energy transferred per discharge. This, in turn, forms deeper and wider craters and increases the material removal. MWCNTs assist in maintaining spark stability and uniformity during prolonged discharge, leading to the highest MRR observed in comparison with nanographene and alumina^61,62^.

In addition to the higher electrical conductivity of MWCNTs, a synergistic modification of the dielectric behavior and plasma channel dynamics also assists it for the improvement in MRR. The addition of well-dispersed MWCNTs decreases the dielectric breakdown strength by means of establishing the conductive lanes among the work material and tool. This enables the former spark commencement and steady discharges. The energy utilization in each discharge gets improved through the stabilized plasma channel due to the tubular morphology and high aspect ratio of MWCNTs. Additionally, the excellent thermal conductivity of MWCNTs assist in faster elimination of molten material which avoids localized overheating and thus, maintains consistency of spark. A constant diffusion of MWCNTs also avoids particle clustering. Subsequently, these combined characteristics of MWCNTs like dielectric breakdown strength, thermal conductivity, particle dispersion stability, and plasma channel dynamics increases the MRR compared to alumina and nano-graphene.

Fig. 4. Effect of input factors on MRR response

Figure 5a shows the influence of EDM factors on SR response. The effect of discharge current, as shown in Fig. 5a, shows a larger negative impact on the SR response. The increase in current has shown a considerable rise in SR values for all three powders. At the higher discharge current values, the energy obtained per spark increases. This, in turn, forms the deeper and larger craters on the machined surface and thus increases the SR. MWCNT-based dielectric fluids produce more uniform and controlled sparks due to their superior electrical and thermal conductivity, leading to smaller and more consistent craters and thus smoother surfaces^63^. Nanographene offers moderate control over spark energy distribution. Alumina, being non-conductive, cannot effectively moderate spark energy, leading to random, uncontrolled discharges and higher SR^64^. Figure 5b of T_off_ vs. SR depicts the decrease in SR response as T_off_ increases from 15 µs to 25 µs for all three powder types. The MWCNT-based dielectric has again shown the lowest SR, followed by nanographene and alumina. A larger value of T_off_ allows more time for the dielectric to flush away debris and for the work-tool gap to recover thermally. This reduces abnormal discharges and short-circuiting, leading to more consistent sparking and improved surface finish. MWCNTs enhance flushing efficiency and spark gap stability, resulting in the least SR^65,66^. Alumina fails to promote such stability due to its insulating nature, resulting in erratic sparks and rougher surfaces. An increase in T_on_ from 30 µs to 50 µs leads to an increase in SR for all powders, with MWCNT again providing the lowest SR, as shown in Fig. 5c. The longer duration of the T_on_ generated the high spark energy with larger exposure of the surface to heat. This forms larger molten pools and craters, and thereby increases SR. MWCNTs assist in distributing the thermal load and maintaining plasma uniformity, which reduces crater irregularity and minimizes SR, while nanographene helps to a lesser extent, while Alumina allows heat buildup and inconsistent spark behavior, leading to coarse surfaces^20,22^.

A comparative analysis among alumina, nano-graphene, and MWCNTs was made through main effect plots to assess the influence of individual nanopowders. The findings has revealed a progressive improvement in machining performance for nano-powders. Alumina nano-powder has shown the modest enhancement in output responses due to their least conductivity, while nano-graphene has shown moderate enhancement. The addition of nano-powders significantly enhances EDM performance, with MWCNT-based dielectric consistently achieving the highest MRR and lowest SR across all process parameters. This superior performance is attributed to MWCNTs’ excellent electrical and thermal conductivity, which promotes uniform spark distribution, efficient energy transfer, and controlled crater formation^67–69^.

Fig. 5. Effect of input factors on SR response

Optimization using TLBO algorithm

The TLBO algorithm was employed for the optimization of MRR and SR responses by using the comprehensive experimental analysis and developed regression models. The obtained results of experimental trials for comparative performance of three nano-powders (alumina, nano-graphene, and MWCNTs), along with main effect plots, have clearly shown the outperformance of MWCNTs. Thus, the findings obtained for MWCNTs have been selected for an optimization study for output measures of MRR and SR. The optimization was performed using the same input parameter levels as in the experimental matrix: I_p_ in between 2 and 6 A, T_on_ in between 30 and 50 µs, and T_off_ in between 15 and 25 µs. The multi-objective optimization was performed with a population size of 50 and 100 iterations, using a convergence criterion of a change in the fitness function less than or equal to 0.01%, and adaptive weight assignments ranging from 0 to 1.

The optimization was carried out at the initial stage independently for MRR and SR. For maximum MRR, the optimal parameters were identified as: I_p_ of 6 A, T_off_ of 25 µs, and T_on_ of 50 µs, giving the response value of MRR as 3.6353 g/min. Conversely, for minimum SR, the TLBO algorithm has shown a different optimal setting: I_p_ of 2 A, T_off_ of 25 µs, and T_on_ of 30 µs, giving the response value of SR as 2.12 μm. The different input parameter settings for MRR and SR clearly show the conflicting nature of the two responses, wherein increased discharge energy enhances MRR but also deteriorates the surface quality. Thus, independent optimization of these conflicting responses is not practical for real-world applications that need a balance between productivity and surface integrity. Such conflicting scenarios can be tackled by using simultaneous multi-objective optimization, assigning appropriate weightage to response measures. An objective function was formulated as shown in Eq. 8, wherein MRR was normalized and maximized, and SR was normalized and minimized simultaneously. By considering the equal importance of both the responses, 0.5 weightage (w_1_ and w_2_) was assigned to MRR and SR for the objective shown in the Eq. 

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{O}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\:\left(\mathrm{V}1\right)={\mathrm{W}}_{1}\cdot\:\mathrm{M}\mathrm{R}\mathrm{R}+{\mathrm{W}}_{2}\cdot\:\mathrm{S}\mathrm{R}$$\end{document}

The simultaneous optimization for the above function has led to the optimal parametric settings of I_p_ of 4 A, T_off_ of 20 µs, and T_off_ of 42 µs with the response values of MRR and SR as 2.8144 g/min and 3.06 μm, respectively. The obtained results have demonstrated a practical trade-off, achieving optimal MRR along with a good surface quality. Another trial with conventional WEDM (without nano-powder) was conducted to determine the effectiveness of MWCNT-assisted WEDM at these optimal parametric settings. The obtained results for conventional WEDM have shown optimal response values of MRR and SR of 1.1097 g/min and 5.38 μm, respectively. The results clearly show a substantial enhancement of MRR and SR by 60.57% and 75.81% respectively, for the MWCNT-based WEDM process in comparison with the conventional WEDM process. This shows the superior capability of MWCNTs in enhancing process efficiency and surface integrity.

In addition to the objective function, various Pareto points were generated by using the TLBO algorithm, which represents the set of non-dominated optimal solutions. Each solution offered by Pareto points gives a unique balance between the high MRR and low SR values. The Pareto points offer additional benefits for users to select machining settings based on their specific requirement (high MRR/low SR/optimal). Figure 6 shows the Pareto graph of these optimal solutions for MRR vs. SR response. To validate the effectiveness of the obtained results of TLBO-based optimization, a set of 7 random confirmatory trials were conducted as shown in Table 6. The set of random confirmatory trials were selected from the obtained Pareto points. The comparison of all the predicted and actual has shown a deviation of less than 5%. These findings demonstrate the accuracy and robustness of the optimization approach. Thus, the TLBO algorithm has shown outstanding abilities in handling the multi-objective nature of the WEDM process without requiring algorithm-specific parameters. Overall, the TLBO-driven optimization reinforces the viability of MWCNT-assisted WEDM for high-performance machining of Nitinol SMA.

Fig. 6. Pareto graph for MRR vs. SR

Table 6. Confirmatory trial runs for validationSr. NoI_p_T_off_T_on_Predicted values by TLBOExperimental values% deviationMRRSRMRRSRMRRSR1225301.81942.131.87232.222.914.222625503.63534.243.54814.372.393.063325312.08652.342.18932.274.922.994518423.12453.483.19853.612.363.735420422.81443.072.88753.152.592.616416483.05473.342.94673.213.533.897320362.44672.682.56212.814.724.85

Surface morphology

The surface morphology of the machined samples was investigated by using SEM at the optimal parametric conditions (I_p_ of 4 A, T_off_ of 20 µs, and T_on_ of 42 µs). The experiments were conducted at optimized parameters for all three powder particles of alumina, nano-graphene, and MWCNT. The machined surface was then analysed for these three powder types along with the machined surface produced without any powder (conventional EDM) at optimized parameters. Figures 7, 8, 9 and 10 depicts the SEM of the machined surfaces obtained for MWCNT, nano-graphene, alumina, and conventional EDM. All SEM images were analyzed based on identical scale bars of 20 μm and that variations in magnification were employed only to improve visual readability of specific features. Figure 7shows the SEM of the machined surface obtained for the MWCNT-based dielectric fluid. It has produced the smoothest surface with the least number of surface defects, such as micro-cracks, re-solidified layers, and debris accumulation. The obtained findings were consistent with the results reported by Shabgard et al^70^. and Sharma et al^71^.. This is attributed to the excellent thermal and electrical conductivity of MWCNTs, which enables uniform spark distribution, rapid heat dissipation, and efficient flushing of molten material from the spark gap. These characteristics minimize thermal stress and result in uniform and shallow craters, enhancing surface integrity. In contrast, surfaces machined with nanographene-mixed dielectric, as shown in Fig. 8, exhibited moderate surface defects, including some micro-voids and uneven recast layers. Although graphene offers good conductivity and heat transfer properties, its relatively lower aspect ratio and particle dispersion stability compared to MWCNTs slightly reduce its effectiveness in spark control and plasma uniformity^72^. The specimen machined with alumina powder, as depicted in Fig. 9, showed larger surface defects, including deeper craters, irregular recast layers, and micro-cracking. This is due to the insulating nature of alumina, which hampers spark uniformity and heat transfer, leading to inefficient melting and expulsion of material. The worst surface morphology, as shown in Fig. 10, was observed on the sample machined with conventional EDM, where the surface exhibited maximum defects, such as extensive pitting, re-solidified debris, and heat-affected zones. The absence of conductive particles leads to poor spark stability, uneven energy concentration, and higher thermal loading on the surface, which significantly deteriorates surface quality.

Thus, the incorporation of MWCNT nanoparticles into the EDM dielectric fluid exhibits a novel and synergistic improvement in machining performance by simultaneously enhancing MRR, reducing SR, and minimizing surface defects. Their superior electrical and thermal conductivity, along with high aspect ratio, promote stable and uniform spark discharges, efficient energy transfer, and rapid heat dissipation. As a result, MWCNT-based EDM yields faster machining with smoother surfaces and significantly fewer micro-cracks, craters, and re-solidified debris compared to both conventional EDM and other powder additives.

Fig. 7SEM of machined surface for MWCNT-based WEDM

Fig. 8SEM of machined surface for graphene-based WEDM

Fig. 9SEM of machined surface for alumina-based WEDM

Fig. 10SEM of machined surface for conventional WEDM

Conclusions

A comprehensive experimental and optimization study was carried out to investigate the effect of nano-powder-mixed dielectric fluids of alumina, nano-graphene, and MWCNTs on the WEDM performance of Nitinol SMA. The Box-Behnken design with TLBO algorithm to model and optimize process parameters of MRR and SR.

ANOVA results confirmed discharge current as the most influential factor for MRR and SR in case of all three types of nano-powder-mixed dielectric fluids. All regression models showed strong predictive performance, with R² values close to 98%.

Main effect plots revealed that higher discharge current and pulse-on time enhanced MRR, while an increase in pulse-off time led to reduced SR. Among all powders, MWCNTs exhibited superior performance due to their excellent thermal and electrical conductivity, which enhanced spark stability and crater uniformity. Among the nano-powders evaluated, MWCNTs provided the highest performance, achieving a maximum MRR of 3.6353 g/min and minimum SR of 2.12 μm during single-response optimization, outperforming both nano-alumina and nano-graphene.

Multi-objective TLBO with equal weightage successfully yielded a balanced parameter combination (I_p_ = 4 A, T_off_ = 20 µs, T_on_ = 42 µs) with a corresponding MRR of 2.8144 g/min and SR of 3.06 μm. A comparison with conventional WEDM under the same optimal conditions demonstrated a 60.57% increase in MRR and a 75.81% reduction in SR, confirming the superior performance of MWCNT-based WEDM. Pareto points were also generated by using the TLBO algorithm, which represents the set of non-dominated optimal solutions.

Surface morphology examined via SEM confirmed that MWCNT-assisted machining produced the most uniform and defect-free surfaces, with minimal micro-cracks, shallow craters, and negligible debris. Nano-graphene provided moderate improvement, while alumina showed deeper craters and more surface defects. The poorest surface integrity was observed in the conventional EDM setup without any powder, with extensive pitting and recast layer formation.

This study validates the novel use of MWCNTs as an effective dielectric additive for precision machining of Nitinol SMA, offering enhanced material removal, superior surface finish, and improved surface integrity. The integrated BBD-RSM and TLBO framework further provides a reliable tool for multi-objective optimization in powder-mixed WEDM applications.

The investigation of the current work was restricted to a fixed powder concentration of 1 g/L limiting the effects of different amount of powder concentrations. Also, only two output response were studied in the current study i.e. MRR, and SR. The future study will be explored with the varied powder concentrations and their impact on multiple response outputs such as MRR, SR, TWR, and RLT etc. The future study will also be focused on comprehensive surface and subsurface analysis (microhardness, recast layer thickness, microstructural evolution, and corrosion resistance) to correlate machining conditions with functional performance.