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Experimental characteristic evaluation of micro hole EDM drilling of Ni51.58Ti48.34 alloy with copper electrode and response optimization using GRG assisted with GA


Nitinol, a biocompatible material, is gradually becoming famous for its superelasticity, shape memory and corrosion resistance behaviours. However, the lower machinability due to the strain-hardening effect and lower thermal conductivity is contrary to its adventitious properties. Therefore, EDM is a preferable machining process for materials like Nitinol. EDM, thermal processing, raises the concern of processing Nitinol with minimal variation of its well-known properties and economical machining process. Therefore, this article deals with multi-objective optimization through GRG-assisted GA of µ-EDM drilling of Ni51.58Ti48.34 alloy using a copper electrode and distilled water. It was found that discharge current and servo voltage significantly influence the responses. The GA, with the assistance of GRG, optimized the multiple responses (viz. MRR, TWR and DoT) and yielded a discharge current of 12 A, gap voltage of 40 V, discharge time of 2 µs, charging time of 9 µs and flushing pressure of 50 kg/cm2. The confirmatory experiment yielded MRR of 0.0036 g/min, TWR of 0.0038 g/min and DoT of 0.0089 radians. There were variations of the predicted and experimentally validated responses by − 2.78, 26.32 and 35.96% for MRR, TWR and DoT, respectively.


Nitinol is a biocompatible material suited for various devices in medical uses [1]. It is well recognized for its superelasticity behaviour and smartness properties, like shape memory, which finds applications such as actuators and fasteners [2]. It is an almost equiatomic composition of nickel and titanium and is an intermetallic compound. However, Nitinol is hard to cut because of its high ductility, low thermal conductivity and strain-hardening effect [3]. EDM is an unconventional technique dealing with material removal by the sparks generated in the electrode-work gap. EDM can remove material from electrically conductive materials, including hard-to-cut ones like Nitinol [4]. Various researchers investigated EDM operations on exotic materials to evaluate their performance and characterize them [5,6,7,8,9].

Chakala et al. [10] studied the optimization of WEDM for Nitinol through RSM and desirability approach and found that uneven surfaces due to craters and recast layers directly vary with current and exposure time.

Kim et al. [11] studied and optimized electropolishing of Nitinol stent and found improved corrosion resistance characteristics at lower roughness. Lee and Shin [12] experimented with laser-direct deposition of Nitinol and stated that precipitates are incoherent with the matrix after the ageing heat treatment that raises the transformation temperature. Li et al. [13] underwent a biocompatibility study of Nitinol through the micro- or nanostructures created using a nanosecond laser, and the oxide films of titanium and nickel were produced to provide better cell growth on the implant. Chaudhari et al. [14] analysed the WEDMed Nitinol surface and found that surface roughness rises with discharge energy. Lojen et al. [15] tried continuous casting of Nitinol and verified the presence of various compounds like Ti2Ni, TiNi and TiNi3 under different casting conditions. Datta et al. [16] optimized the process of LBW of Nitinol through various metaheuristic practices and found satisfactory predicted results validated by experimentation for minimum variation of micro-hardness of the weld. Ikeuchi et al. [17] investigated EDM characteristics for LaB6 work material and found that material fracturing leads to material removal along with common causes such as melting and evaporation. Ming et al. [18] compared the behaviour of magnetic-assisted EDM on ferromagnetic and diamagnetic materials. They concluded that the MRR rises for both, and the higher rise of MRR was seen for ferromagnetic work material. Ilani and Khoshnevisan [19] investigated the PM-EDM on titanium grade-5 alloy using an FDMed copper electrode and found enhancements in MRR, TWR and surface finish with the most remarkable improvement in the surface quality. Paswan et al. [20] investigated EDM operations on MMC using steam as dielectric instead of kerosine in the die-sinking method and found improvement concerning the recast layer and yield as a sustainable process. Baran and Polanski [21] verified the microstructure of Nitinol through laser processing of net shape products and stated that at low scanning speed, it yielded lower superelasticity and shape memory behaviour, whereas the axial grains formed at higher scanning speed. Pelton et al. [22] optimized the process and the properties of Nitinol and stated that the shape memory property could be retained by accurately fixing the transformation temperature through a selective ageing heat-treatment process. Roy and Mandal [23] studied WEDM through surface integrity of Nitinol and concluded that the crack density rises with the rise in the flow of the dielectric that quenches the material efficiently, and recast layers on it confirmed that the higher flow was unable to flush the removed material properly. Lee and Shin [24] completed electrochemical polishing of Nitinol for the machinability study and stated that at a higher current and lower interelectrode gap, the surface finish is better. Kowalczyk and Nizankowski [25] experimented with the turning of Nitinol materials and studied their machinability through a weighted radar diagram and found that the machinability of β-Nitinol is better than α-Nitinol.

Shiek et al. [26] experimented with the PMEDM process to enhance MRR for Ti alloy and stated that the powder concentration up to 4 g/positively impacts MRR. Sharma et al. [27] reported EDM operation on stainless steel and stated that copper electrodes were better than brass electrodes regarding hole circularity. Quarto et al. [28] reported optimization of the micro-EDM using PSO and ANN and indicated that the two-step method provides operator flexibility to select the parameter required to optimize the process for the best solution. Abhilash and Chakradhar [29] completed multi-attribute optimization of WEDM of Inconel 718 through GRA-TOPSIS and emphasized that the entropy-weighted TOPSIS provides a better process concerning the TOPSIS alone. Naik and Sathisha [30] optimized micro-channelling using the EDM process on silicon wafer and stated that PSO gave the required convergence for the machining conditions using sodium hydroxide and potassium hydroxide as the mixed dielectric fluid. Ram et al. [31] experimented with WEDM operation on MMC based on Al6351 and stated that discharge time and current were the best factors controlling kerf width and surface roughness concerning wire feed. Pandey et al. [32] conducted a vibration-assisted EAM process on aluminium and boron carbide MMC and stated that a single objective optimization process based on the AI approach significantly improved MRR. Sisodiya et al. [33] studied Maglev EDM on pure titanium and found improvements compared to the traditional EDM procedure. Kiran et al. [34] examined the consequences of powder material used along with the bio-dielectric fluid on the exterior of Ti-grade 5 alloy and found the dielectric and the tool materials on the substrate confirmed through EDX analysis. Baroi et al. [35] reviewed EDM’s sustainability and safety issues and stated that the truly eco-friendly dielectric was water based, and selection and recirculation of dielectric with suspended powder were difficult. Ablyaz et al. [36] studied the composite electrode’s impact on the steel-copper bi-metallic material and stated that micro-holes formed during the processing of the steel zone and enlarged holes formed during the processing of the other zone. Rajguru et al. [37] studied the accomplishment of a composite copper-CNT electrode on the EDM process and found that MRR and surface finish enhanced due to the modification in the tool material and possessed higher TWR. Kumar and Davim [38] investigated the impact of silicon powder mixed with the dielectric of MMC and reported that improvement in surface quality and MRR happened with a particular powder concentration. Fasina et al. [39] investigated boring on steel through comparative optimization studies and indicated that the hybrid TLBO provided better surface roughness estimation.

Muralidharan et al. [40] experimented with laser machining Nitinol and concluded a rise in micro-surface irregularity with laser energy and reduced cutting speed. Hung and Yang [41] experimented with ultrasonic-assisted electrochemical machining of Nitinol wire for micro-slots and confirmed that the slot width rises with the electrolyte concentration by the enhanced process efficiency due to the vibration assistance. Sahu et al. [42] stated the impact of an electrode on the surface finish of the EDMed Nitinol work material and found that a healthier surface finish was accomplished by the AlSiMg electrode prepared by a selective laser sintering process compared with the copper electrode. Kulkarni et al. [43] completed the optimization of multiple responses of WEDM of Nitinol and confirmed the genuinely significant process control parameter was wire feed rate, considering material removal rate and surface quality as the responses. Pradhan et al. [44] studied micromachining of Nitinol using Nd:YAG laser and concluded that the lower width deviation falls with the rise in the pulse frequency. Liu et al. [45] analysed the formation of white layer while machining Nitinol shape memory alloy using EDM and emphasized that the nano hardness rises and the modulus of white layer falls concerning the base material. Duerig et al. [46] explored the transformation temperature of Nitinol and found that the transformation temperature can be reduced by making the material’s triple point higher. Sahoo et al. [47] experimented with EDM and optimized for Nitinol through Taguchi analysis and GRG and found that the discharge time and inter-work-electrode gap voltage were the process’s very influencing process parameters. Kılıç [48] utilized ANN and GIS to predict wind energy potential.

Mishra et al. [49] investigated the kerf quality of laser cutting of FRP. They optimized the process using GRA and found improvements by enhancing kerf width. Taskan et al. [50] examined the suitability of Nitinol as anode in microbial fuel cells and concluded that thick electroactive biofilm formed on the anode was suitable for achieving higher power density. Guo et al. [51] researched the machinability aspects of Nitinol. They stated that the white layer formed due to higher plastic deformation during the milling operation, whereas it is due to melting and quenching in EDM operation. Mishra et al. [52] optimized the kerf deviation of laser cutting operation using GRA and indicated improvement in cut quality with stand-off distance as the significant parameter. Paszkowicz [53] studied the application of genetic algorithm (GA) in the related fields of material science and stated that GA is an efficient tool to optimize problems with a higher number of process control parameters having several local maxima or minima. Bhoskar et al. [54] reviewed the utilization of GA in mechanical engineering and concluded that GA, a stochastic approach, is a nondeterministic method for searching for the optimum value through nature-inspired evolution and natural selection. Reddy et al. [55] utilized GA to optimize laser machining operation on Hastelloy C-276 and stated that the pulsated laser frequency has a more momentous impact on the surface unevenness, whereas the scanning speed of the laser influences the milling depth more than the other parameters. Kilickap et al. [56] used GA to optimize drilling operation on AISI 1045 steel for surface roughness by a TiN-coated HSS drill through the response surface methodology. Gautam and Mishra [57] evaluated the geometric features of laser cutting of KBFRP hybrid composite using GRGA and found 31.23% overall improvements in the cut quality characteristics. Guo et al. [58] purported a new deformation method prediction by changing early residual stress based on regression analysis of support vector and GA and confirmed that the residual stress lowered to 15.45% from 31.1%.

The biocompatible, superelastic, and shape memory material, i.e. Nitinol, needs to be machined using advanced machining processes like EDM for better product accuracy. The heat of the spark in the EDM operation is responsible for material removal, which has consequences on the Nitinol product’s behaviour. Hence, the EDM drilling of Nitinol needs an optimized process to enhance the economy and the accuracy of the processed product. The optimization also considers the required properties essential for using Nitinol material. Therefore, micro EDM drilling on Nitinol has been reported in this manuscript, including its characterization and optimization using a genetic algorithm assisted with the grey relational grade for tri-response analysis considering material removal rate, tool wear rate and degree of hole taper as the responses.


This experimental work was completed using a three-phase methodology, as shown in Fig. 1. The first phase consists of experimental trial runs to select the levels of process parameters. In the next step, the Box-Behnken design (BBD) was used for the experimental design, in which five process control parameters with their three different levels were selected along with six replications of the centre point, a total of 46 experiments. In the next step, the experimental work was carried out concerning the BBD DOE, and the responses were evaluated for their mathematical modelling to check their suitability. The grey relational analysis (GRA) was completed in the second phase. The second phase includes normalization, calculation of grey relational grades (GRG) and mathematical modelling of GRG. A genetic algorithm (GA) was implemented in the last phase to optimize the response.

Fig. 1
figure 1

Graphical representation of the work

The Sparkonix EDM machine was used to carry out the experimental work. The actual photograph of the machine is demonstrated in Fig. 2. There are five process control parameters such as discharge current ranging from 1 to 25 A with steps of 1 A, servo-controlled gap voltage ranging from 10 to 100 V with steps of 10 V, the charging and discharging times ranging from 1 to 10 μs with steps of 1 μs and discharge pressure of dielectric fluid up to 100 kg/cm2.

Fig. 2
figure 2

Photograph of Sparkonix EDM drilling machine

The EDM drilling can be easily comprehended through the schematic shown in Fig. 3. The schematic shows all the essential components of EDM drilling, including the sparking between the tool-work gap, removal work material, electrode wear, recast layer, hole tapper, and dielectric flushing.

Fig. 3
figure 3

Representation of EDM drilling operation

This experimental work used Nitinol with a substance composition of 51.58% Ni and 48.34% Ti and 6-mm thickness. The copper tubular electrodes used for drilling were 0.5 mm in diameter. The BBD design used five process parameters with three levels due to its non-linear sensitivity of the responses considered. The BBD yielded 46 sets of experiments, including 6 centre-point repetitions. The process parameters and their levels considered in the experimental work are given in Table 1.

Table 1 Process parameters and their levels used for the experimental work

The weight measurements before and after the EDM drilling were completed during the experimentation for the electrode and the workpiece. A weighing machine with a precision of 0.001 g was used. Also, the action times were recorded with a precision of 0.001 s to estimate the material removal rate (MRR) and tool wear rate (TWR) as two responses. Furthermore, the third response degree of hole taper (DoT) was evaluated by measuring both side hole diameters with a precision of 0.01 mm. The diameters were evaluated as the average of six measurements at different orientations of the drilled holes. The responses considered are MRR, TWR and DoT, calculated using Eqs. 1, 2 and 3 and tabulated in Table 2. Figure 4 shows the photographs of the workpiece on both sides, indicating the corresponding experiment numbers.

Table 2 Experiments as per BBD with responses (MRR, TWR & DoT)
Fig. 4
figure 4

Images of both sides of EDM drilled workpiece


The mathematical analysis of the results had been completed before moving to the optimization process using GA. In this work, three responses were recorded as MRR, TWR and DoT, from which MRR needs to be maximized and TWR and DoT need to be minimized. In addition, the different goals for each response needed to be unified to have one optimisation goal. Therefore, grey relational analysis was considered the unified mathematical mechanism [29] where the responses were normalized per their requirements. Hence, Eqs. 4 and 5 were used to maximize MRR and minimize TWR and DoT, respectively.


where XNi, Xin, Xmax and Xmin are the normalized ith response, ith response, top value of responses and bottom value of responses, respectively.

The deviation sequences of each experimental set for each response were calculated as the deviation of the maximum and the corresponding values. After that, the grey relational coefficients (GRCs) for each response were calculated using Eq. 6. Finally, the unified responses as the grey relational grades (GRGs) were estimated using Eq. 7. The normalized responses, GRCs and GRGs, are tabulated in Table 3.

$$GR{C}_{i}=\frac{\Delta {X}_{{\text{min}}.}+\zeta \times \Delta {X}_{{\text{max}}.}}{\Delta {X}_{in}+\zeta \times \Delta {X}_{{\text{max}}.}}$$

where ΔXmin, ΔXmax and ΔXin are the minimum, maximum and ith deviation sequence of each response for each experimental set, respectively. ζ = 0.5, average importance to each, generally varying between 0 and 1. The GRGs were found by averaging the GRCs of each experimental set, i.e. equal weight to each response considered.

Table 3 Normalized values, GRCs and GRGs of each experiment

The GRGs of the experimental sets were then used to get the mathematical modelling using multi-regression analysis as a quadratic model, as shown in Eq. 8. Furthermore, the ANOVA of GRG is shown in Table 4. The ANOVA shows that the tri-regression model is significant, with a lower p-value [59]. The ANOVA provides that the GRG model’s process parameters that influence the most are servo voltage (V) and discharge current (I). The terms of the model with higher p-values have a lower influence on the GRG response. As the lack of fit is insignificant, the model does not overfit. It can be well understood through the fit statistics, which provide a difference of less than 0.2 between the adjusted R2 and the predicted R2 values, and the signal-to-noise ratio is greater than the 4 required.

Table 4 ANOVA table of GRG

The next step of analysing the result as the mathematical multi-regression model was to optimize the process. The GRG model is a unified model that requires maximizing. Therefore, the genetic algorithm (GA) was employed for the tri-objective optimization through GRA. GA is a population-based method of optimization inspired by nature [60, 61]. The first step defined the population size (PS), crossover (PCO) and mutation (PMU) probabilities and crossover (ICO) and mutation (IMU) indices. The number of iterations required to evaluate the unified function (GRG) was required as the termination criteria. On the contrary, the termination was taken within the iteration number where all the population members carry the same value. Each iteration consists of a selection of a mating pool, crossover to generate an equal number of offspring, mutation of the offspring and, at last, the survival of the fittest.

The binary tournament selection was considered for getting the mating pool. Each member of the population should have to go through the tournament selection process twice, and one member should be selected based on the relative fitness values. In this step, the member with the best fitness was selected twice for the mating pool. The next step was the crossover, and simulated binary crossover (SBX) was selected. Based on the value of random numbers, the crossover is either to be there or the parents considered as offspring.

In this SBX crossover, two members from the mating pool were selected randomly. Then, based on another random number (R), the crossover was decided with respect to the probability of crossover (PCO) [62, 63]. If R ≥ PCO, the crossover is not required, and the parents were moved further as the two offspring. Otherwise, a crossover is required to have the two offspring. Hence, a pool (U) of n random numbers was selected that depends on variable counts (n) considered for the problem and shown as Eq. 9. Finally, the pool of random numbers was used to calculate the βin values for each variable for the crossover using Eq. 10. Then, two offspring are generated using Eq. 11 and corner-bounding the offspring to bring them inside the solution space. Corner-bounding is required either for the variable higher than its upper bound or lower than its lower bound.


After each member of the mating pool crossover, the polynomial mutation was considered as per the mutation probability (PMU) and index of mutation (IMU). Then, each offspring was checked for the possibility of mutation depending on PMU and a random number [64, 65]. No offspring mutation existed if the random number was more than the PMU. Otherwise, the mutation happens to the offspring. The mutation requires a pool of random numbers (r) equal to the number of variables considered, as shown in Eq. 12. The δin was calculated as per the value of the ri using Eq. 13 and then the mutated offspring (Om) using Eq. 14 through the use of the uber bound (UB) and the lower bound (LB) of each variable.


Then, all the parents and offspring were considered together for the natural selection of survival of the fittest. The best PS members were selected from the 2PS solutions depending on their fitness values in the next iteration. The optimized process control parameters were found when all the PS members had the same fitness values and each member’s variables were the same.

Results and discussion

As this article deals with a hybrid optimisation approach, i.e. GA assisted by GRA, the various behaviours of GRG are discussed first. Therefore, Fig. 5 shows the interaction plots for GRG’s truly influential process parameters found using ANOVA, shown in Table 2. The interaction plot concerns the influences of discharge current (I), servo voltage (V) and the rest of the process parameters at constant values found through GA’s optimisation process.

Fig. 5
figure 5

Interaction plots for GRG concerning its most influential process parameters

The other process parameters are the discharge time of the spark (TON), the charging time of the capacitor blanks (TOFF) and dielectric pressure (DP) at 2 μs, 9 μs and 50 kg/cm2, respectively. The graph shows that the GRG falls by raising the servo gap voltage (V) and vice versa. It also shows that at V of 40 V and I of 12 A, the predicted GRG was 0.9888, whereas it was at 0.7413 at V = 40 V and I = 22 A. Hence, the GRG also falls by raising the discharge current. At higher servo gap voltage, the GRG falls concerning the rise of the discharge current, but its fall is lower than low servo gap voltage.

Figure 6 shows the predicted and actual values variation of GRG. The graph shows a maximum of 14.87% more prediction of GRG than the actual GRG at experimental set 41. Conversely, at experimental set 37, a maximum of 18.73% less prediction of GRG than the actual. There is an average of 0.55% more prediction of GRG than the actual one.

Fig. 6
figure 6

Predicted versus actual GRG

As discussed earlier, Fig. 7 displays the surface chart for the GRG concerning I and V at the optimum set. It is clear from the graphs that at lower servo gap voltage, the GRG is highest at lower discharge current. Whereas at an enormous servo voltage, the GRG is minimal. The variation of GRG is low due to the variation in discharge current at a superior servo voltage.

Fig. 7
figure 7

Surface and contour plots for GRG concerning I and V

Figure 8 indicates the variation MRR as the surface plot involving the GRG’s most influencing process parameters. The graphs show that at higher servo gap voltage and lower discharge current, the MRR is not possible due to insufficient energy available for the material removal. By raising discharge current (I) and lowering the servo voltage, the MRR moves to its higher value, about 0.00904 g/min, whereas at about 21.98 A and 42.06 V, the MRR is at its maximum predicted, 0.0091 g/min. The MRR rises with the discharge current [66]. The higher MRR required is due to the maximum possible energy utilization for the melting and evaporating of the work material.

Fig. 8
figure 8

Surface plot for MRR concerning I and V

Figures 9 and 10 show the surface plots concerning TWR and DoT, the lower, the better responses, respectively, at the optimum control parameters with the variation of the most substantial process parameters I and V. The TWR graphs show that its required lower value is around 0.0044 g/min at about 12.11 A of discharge current and 42.001 V of servo gap voltage. This lower TWR is because the energy the electrode receives from the spark dissipates more promptly through conduction into the electrode and convention into the flushed distilled water, the dielectric fluid. On the contrary, the unwanted rise of TWR is predicted at elevated servo voltage and discharge current and reaches approximately 0.0322 g/min [67]. The DoT graphs also show the same trend type as the TWR.

Fig. 9
figure 9

Surface plot for TWR concerning I and V

Fig. 10
figure 10

Surface plot for DoT concerning I and V

Figure 10 shows the favourable DoT value, i.e. 0 radians bounded by the area between 12 A and 54 V and 22 A and 42 V. The minimum DoT value of 0 radians means that the tool wear raises the work-electrode gap at the hole’s top surface, reducing excessive sparking at the top side of the hole. It led to shelf adjustment of the hole to a predicted perfect right cylindrical hole. In contrast to a perfect predicted hole, the unwanted DoT value reaches a maximum of about 0.0128 radians, approximately at 18 A of discharge current and 60 V of servo gap voltage [68].

The genetic algorithm (GA) optimized the GRG quadratic equation through MATLAB programming. The population was considered to have 20 members, four times the counts of process parameters. The termination criteria for the GA was 20 iterations, and the optimum conditions were reached for each condition within 20 generations. Another set of GA parameters is the crossover (ICO) and mutation (IMU) indices, 20 each; as the values of the indices are higher, the offspring generated closer to their parents. Finally, the crossover (PCO) and mutations (PMU) probabilities were decided through the algorithm, considering that the PCO should be higher and the PMU should be lower. At PCO = 0.5 and PMU = 0.4, the optimum setting after which the results are the same, i.e. all combinations of PCO greater than 0.5 and PMU, varies between 0.1 and 0.5. All the above parametric settings of GA lead to the optimum control process parameters as I of 12 A, V of 40 V, TON of 2 µs, TOFF of 9 µs and DP of 50 kg/cm2.

The assenting experiment checked the boldness of the optimum setting concerning the predicted responses, as provided in Table 5. It can be realized from the table that percentage of variation of the predicted values of the responses with respect to the experimental values; MRR predicts 2.78% less than its experimental value, and the TWR and DoT were predicted at 26.32% and 35.96%, respectively, more than their experimental values. The higher deviations of the TWR and DoT are due to measurement errors. The weight, diameter and time errors are 0.001 g, 0.01 mm and 0.001 s, respectively. These errors are tiny, but the overall weight of the electrode is relatively low, and the diameters of the drilled holes on both sides are low. Therefore, it leads to much higher deviations in the TWR and DoT.

Table 5 Experimental, predicted and percentage of variations of responses at the optimized process control parametric setting

Figure 11 shows the SEM image of the top side of the EDM drilled hole for the optimum parametric setting. More material was removed adjacent to the EDM drilled hole due to the spark’s erratic behaviour. Recast layers are visible in the vicinity, and cracks on them imply a higher rate of cooling of the molten material on the surface of the workpiece. Micro pits are also visible on the drilled hole surface, indicating the impact of the spark. A few macro pits were formed around the micro EDM drilled hole.

Fig. 11
figure 11

SEM image of the micro EDM drilled hole


The shape memory behaviour of Nitinol can be altered during thermal processing. Therefore, thermal processing needs optimization. Hence, this experimental work on micro-EDM drilling operation has been carried out by selecting process parameters such as discharge current (I), discharge time (TON), charging time (TOFF), servo gap voltage (V) and dielectric flushing pressure (DP). The experiment was designed using a Box-Behnken design, and the material removal rate (MRR), tool wear rate (TWR), and degree of hole taper (DoT) were considered as the responses. The tri-response optimization was carried through grey relational grade (GRG)-assisted genetic algorithm (GA) of µ-EDM drilling on Ni51.58Ti48.34 alloy using a copper tubular electrode and demineralized water (dielectric fluid). The following conclusions are drawn:

  1. i.

    The tri-regression analysis using the quadratic GRG model provides the mathematical model’s significance through variance analysis; the spark’s discharge current (I) and the servo voltage (V) were the most substantial process parameters.

  2. ii.

    The GRA-assisted GA offers the optimum parametric set I of 12 A, V of 40 V, TON of 2 µs, TOFF of 9 µs and DP of 50 kg/cm2.

  3. iii.

    The confirmatory experiment at the optimized control parametric setting provides the experimental MRR, TWR and DoT, and their predicted values vary by 2.78, 26.32 and 35.96%, respectively.

The future directions of the research work might include surface quality, hole circularity and heat-affected zones for micro-EDM drilling of the Nitinol, shape memory alloy and the optimization of the responses through other techniques.

Availability of data and materials

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.


MRR (g/min):

Material removal rate

TWR (g/min):

Tool wear rate

DoT (radians):

Degree of hole taper


Box-Behnken design


Design of experiment


Grey relational analysis


Grey relational grades


Genetic algorithm

XNi :

Normalized ith response

Xin :

Ith response

Xmax :

Maximum value of the responses

Xmin :

Minimum value of the responses


Grey relational coefficient

ΔXmin :

Minimum value of deviation sequence

ΔXmax :

Maximum value of deviation sequence


Analysis of variance

I (Amp):

Discharge current

V (volts):

Servo voltage

TON (μs):

Discharge time

TOFF (μs):

Charging time

DP (kg/cm2):

Dielectric flushing pressure

PS :

Population size


Crossover probability


Mutation probability


Index of crossover


Index of mutation


Simulated binary crossover


A random numbers

U, r:

Pools of random numbers


Number of variables

βin, δin :


Uin, ri :

Ith random number of the pools

Oi,in, Om :

Ith offspring and mutated offspring

Pi, Pi+1 :

Ith and (i + 1)th parent


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We are glad to acknowledge the help of Mr. Bhanu Pratap Arya, the lab staff, the Mechanical Engineering Department, JUET, and Guna during the experimental work.


The authors did not receive funding from any organization for the experimental work.

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AKS contributed with preparation of DOE, experimentation, theoretical analysis of the experimental result, conduction of the different testing and validation experiments based on the experimental results. DRM contributed with problem formulation, verification of the confirmation experimental results of the article and review of the manuscript. All authors have read and approved the final manuscript.

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Correspondence to Dhananjay R. Mishra.

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Sahoo, A.K., Mishra, D.R. Experimental characteristic evaluation of micro hole EDM drilling of Ni51.58Ti48.34 alloy with copper electrode and response optimization using GRG assisted with GA. J. Eng. Appl. Sci. 71, 117 (2024).

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