1 Introduction

High strength, hardness, and impact resistance materials are in high demand in the mechanical sectors. These materials are challenging when using traditional techniques like turning, drilling, milling, etc. [1, 2]. The progress of a new invention of materials results from the search for novel, lightweight materials with better strength and durability. These characteristics can frequently pose significant difficulties while machining [3]. From its humble beginnings as an essential technique for crafting tools and dies, wire electrical discharge machining (WEDM) has undergone a remarkable transformation, emerging as the ultimate solution for fabricating micro-scale components with unparalleled precision in dimensions and surface finish [4]. An unconventional thermoelectric process called WEDM makes use of isolated sparks between the work electrode and tool electrode that are separated by a small layer of dielectric fluid to erode material from the workpiece.[5,6,7,8]. Controlled erosion can erode the metal tool by applying sparks between the metal tool and workpiece. The workpiece melts and vaporizes due to the intense thermal conditions that the spark's heat energy creates. The problem known as electrode wear (EW) occurs when the electrode melts and evaporates as a result of the elevated temperatures of the sparks [9, 10]. The EW process and the material removal mechanism are comparable since the EDM electrode and workpiece surface are viewed as electrodes. Because of this wear, electrodes get smaller, which affects how accurately cavities are created [11]. EDM's two most crucial output parameters are material removal rate (MRR) and tool wear rate (TWR). EDM is a unique metal-cutting technique for making intricate dies and mechanical components used in space vehicles, automobiles, and many other industries. [12]. Superalloys and high-strength materials are hard to cut conventionally due to tool edge chipping or fracture, tool attrition wear, and poor thermal diffusivity. Moreover, these new materials' high production costs, poor MRRs, and surface quality present challenges for traditional cutting [13]. Several machining techniques, Advanced Machining Processes (AMPs) and Non-Conventional Machining Processes (NCMP) were created to solve these problems. Advanced machining techniques like EDM remove material electrothermally [14]. Purohit et al. reported employing GRA based on taguchi to optimize process parameters, including MRR and EWR [15]. Mandalio et al. investigated the influence of many EDM process parameters utilizing Design of experiments and Regression analysis employing tungsten-thorium electrodes [16]. Mohanty et al. used particle swarm optimization to optimize further the Inconel 718 work material's numerous performance parameters for the EDM process. Tool material, pulse duration, and discharge current were discovered to impact machinability substantially [17]—Choudhary et al. compared electrodes treated with cryogenic and noncryogenic temperatures for Hastelloy EDM [18]. Compared to noncryogenic treated electrodes, it was found that tool electrodes that had undergone cryogenic treatment produced a superior surface polish. The EDM surface carbon content was discovered using a tool electrode that had yet to be cryogenically treated. Zhang et al. investigated brass tube electrode-based fabricating micro-holes with different outside diameters [19]. Sonawane and Kulkarni studied multi-objective Nimonic 75 optimization using the Taguchi method, and the principal component analysis approach was carried out on the WEDM process. Confirmatory trials demonstrated that the SF, MRR, and overcut anticipated response values closely matched the outcomes of the experiments [20]. Vikas K. Shukla et al. reported machining performance and multi-criteria optimization of novel metal‑Nimonic 80A using EDM. They identified that pulse-on time and peak current are significant parameters for MRR [21].

In this study, the MRR, TWR, and ROC performance characteristics were multi-objectively optimized by varying possible input process parameters over a specified range in the EDM process. This study examines grey relational analysis based on Taguchi for multi-objective optimization of machining properties of EDM on Nimonic-80A. This research contributes to advanced machining by addressing the challenges associated with high-strength materials, offering innovative solutions, and presenting a comprehensive approach to multi-objective optimization in the EDM process on Nimonic-80A.

2 Materials and experimental setup

In EDM, tool material plays a very vital role in the Machining. In this present study, a Copper electrode coated with Silver (3 µ) thickness is used. The electrode dimensions are 10 mm in diameter and 50 mm in length, respectively. In this present study, Nimonic 80A serves as the work material. The dimensions of rectangular workpiece material are 15 mm*5 mm. Figure 1 shows the electrode and workpiece. The powder used in the present study is Aluminum metal powder of 325 meshes, which is used to mix in the dielectric—aluminum powder concentration in the dielectric ranges from 3 to 9 g/l.

Fig. 1
figure 1

a Workpiece and electrode, b EDM setup, c Arrangement of workpieces

Full size image

All experiments used an EDM model ARD ARTM30D (Die-sinking type). The dielectric fluid employed was white kerosene. The EDM machine tool can be observed in Fig. 1. Aluminum powder is added to the dielectric to examine the effect on responses. As the powder concentration is taken as one of the input variables, it is not easy to maintain the total tank with a 200 L capacity. To minimize this, a separate tray of 1 l capacity was prepared, and the different concentration levels were examined. The workpieces are fitted with the help of Glue.

3 Cutting condition and experimental design

The selection of optimal EDM machining characteristics is a crucial component. Taguchi Optimization is a single-parameter optimization method centered upon that signal-to-noise ratio [22]. GRA improves parameters with many outcomes using grey relational grade [23]. ANOVA is also conducted to ascertain whether process factors are statistically significant [24,25,26]. The process parameters chosen and the levels of the variables are tabulated in Table 1. The response variables affected concerning the process parameters are Material Removal Rate (MRR), Tool Wear rate (TWR), and Radial overcut (ROC). The Experiments were carried out in accordance with L27 OA using a random approach generated using MINITAB. A different electrode (Silver Coated Copper Electrode) is used for each experiment. The machining time considered for Nimonic 80A is 5 min. The arrangement of the experiments according to the L27 Orthogonal array is tabulated in Table 2 with the actual values.

Table 1 Process parameters levels
Full size table
Table 2 Design of experiments with actual value
Full size table

4 Results and discussions

The experiments were conducted on all the 27 specimens with 5 min of machining time. The specimens and the electrodes are to be weighed before and after conducting the experiments. The electrode’s diameter at the tip of the machining and the hole diameter produced are to be measured for every specimen using vernier calipers. The weights and Diameters measured before and after the experiments are tabulated. The response variables (MRR, TWR, ROC) are calculated and are tabulated. Table 3 displays measured weights, tool, and workpiece diameter, and the measured response variables. The Eqs. (1–13) for calculation are given below.

Table 3 Response values
Full size table

Material Removal Rate (MRR):

$$ {\text{MRR }} = \frac{{{\text{W}}_{{\text{b}}} - {\text{W}}_{{\text{a}}} }}{{\text{t}}}\;{\text{g}}/{\text{min}} $$
(1)

Tool Wear Rate (TWR):

$$ {\text{TWR }} = \frac{{{\text{W}}_{{{\text{tb}}}} - {\text{W}}_{{{\text{ta}}}} }}{{\text{t}}}\;{\text{g}}/{\text{min}} $$
(2)

Radial over Cut (ROC):

$$ {\text{C }} = \frac{{{\text{D}}_{{\text{h}}} - {\text{D}}_{{\text{t}}} }}{2}\;{\text{mm}} $$
(3)

Where Wb & Wa = Weight of the workpiece prior to and after Machining.Wtb & Wta = Weight of Tool Prior to and after Machining.Dt & Dh = Diameter of Tool and Hole respectively.t = time taken for Machining.

Any process must use the optimum process parameter combination to get desired output response while utilizing the fewest resources possible. The Analysis of Variance (ANOVA) approach is employed for calculating the Optimum Response Variables and the Effect of Process Parameters on the Response Variables.

5 Calculation of S/N ratio for MRR

Taguchi's signal-to-noise ratio is the logarithmic function of the intended output.. The S/N ratio is the mean-to-standard deviation ratio. The term mean relates to the signal, and standard deviation refers to the noise. The quality of the product or process being optimized determines the value of this ratio [27]. As the material removal rate is the response, which is to be maximum, the larger is better will be considered in calculating the S/N ratios. The Higher the MRR indicates that the machining performance will be maximum. The computed values of "Larger the Better S/N ratios" for MRR in negative signs are tabulated [28].

$$ \left( \frac{S}{N} \right)_{HB} = - 10log_{10} (MSD_{HB} )dB $$
(4)
$$ MSD_{HB} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \frac{1}{{Y_{i}^{2} }} $$
(5)

6 Calculation of S/N ratio for TWR

A low tool rate will permit an increase in the tool's life, which means the tool can be used for extended periods without changing the accuracy while machining. The sound-to-noise ratios for the TWR are found to be smaller, the better. The sound-to-noise ratios for TWR are calculated and tabulated.

\({\left(\frac{S}{N}\right)}_{LB}\)=—10 \({log}_{10}\)(MS \({D}_{LB}\)) dB (6)

$${\mathrm{MSD}}_{\mathrm{LB}}=\frac{1}{\mathrm{n}}\sum_{\mathrm{i}=1}^{\mathrm{n}}\frac{1}{{\mathrm{Y}}_{\mathrm{i}}^{2}}$$
(7)

7 Calculation of S/N ratio for ROC

Radial overcut is an error which is generated during the machining. It shouldn’t be large as it may result in the improper contours. The smaller the better formula was utilized to calculate the S/N Ratio’s for the Radial Overcut and these values are presented in a table. (Table 4)

$$ \left( \frac{S}{N} \right)_{LB} = - 10log_{10} (MSD_{LB} )dB $$
(8)
$$ MSD_{LB} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \frac{1}{{Y_{i}^{2} }} $$
(9)
Table 4 S/N ratios of MRR, TWR & ROC
Full size table

MSD = Mean Square Data.

Yi = Response value of ith experiment,

n = Number of Replicants.

8 Effect of process parameters on MRR

The extent to which the input variables affect the responses is to be identified. This is done by generating the response table using Minitab 18 Statistical Software [29,30,31,32]. The Main effects plot is generated by taking the input variables with 3 levels in the Abcissa and Response variable (MRR) on the ordinate. (Fig. 2)

Fig. 2
figure 2

Main effects plot for MRR

Full size image

The process parameters thus selected should be in such a way that MRR should be maximum. The levels at which the process parameters give maximum MRR are generated using Taguchi’s technique. The obtained values are tabulated in response Tables. (Table 5)

Table 5 Response table for MRR
Full size table

Rankings are generated for various process parameters at distinct levels. The maximum values of the levels are considered as the MRR follows the Larger the better concept. The optimized parameters for MRR are Current is15 A, Ton = 300 µs, Powder concentration is 6 g/l, Toff is 90 µs and IEG is 2 mm. (Table 6)

Table 6 Response table for TWR
Full size table

9 Effect of process parameters on TWR:

The optimized parameters for TWR are Current is 12 A, Powder concentration is 3 g/l, Ton is 300 µs, IEG is 1 mm and Toff is 30 µs. (Table 7)

Table 7 Response table for ROC
Full size table

10 Effect of process parameters on ROC

Rankings are generated for various process parameters at distinct levels. The minimum values of levels are considered as the TWR follows the smaller the better concept. The optimized parameters for ROC are Current is 6 A, Powder Concentration is 3 g/l, Toff is 90 µs, Ton is 600 µs and IEG is 3 mm. (Figs. 3), 4

Fig. 3
figure 3

Main effects plot for TWR

Full size image
Fig. 4
figure 4

Main effects plot for roc

Full size image

11 ANOVA for response variable

ANOVA, a statistical method, is employed to discover variations in average performance of the test set of items [33, 34]. ANOVA at a 95% confidence interval can be used to specify the significant impact of process factors on response parameters. A Two-way ANOVA was employed to generate mean square value and sum of squares. F and P values are thus generated. The contribution table is also generated using ANOVA in Minitab. (Tables 8, 9, 10)

Table 8 ANOVA for MRR
Full size table
Table 9 ANOVA for TWR
Full size table
Table 10 ANOVA for ROC
Full size table

If the P value is below 0.05, they are considered to affect the response variable significantly. Thus, the Percentage contributions of the process parameters on the response variables are found. Significant ANOVA percentage of contribution for MRR, current is the primary factor, contributing 91.06%. In TWR variance analysis, current dominates, contributing 34.81%. Current is the foremost factor in ROC variance analysis, contributing 37.94%.

12 Multi objective optimization by grey relational analysis (GRA)

Any process must use the optimum process parameter combinations to achieve the desired output response while utilizing the fewest resources possible. The ideal parameter choice for one response may harm other replies.

In order to determine the best parameter configuration, it is necessary to find a middle ground and conduct multi-objective optimization [25]. Over the years, many optimization approaches have evolved to optimize the parameters by solving numerous objective functions [26]. One such technique is GRA. Multiple performance characteristics have been explored using the Grey Relational technique in Grey Relational Analysis. GRA allows the examination of multiple performance attributes, converting them into a unified metric known as the Grey Relational Grade (GRG). The GRG plays a vital role in grey relational analysis as it demonstrates the connection between sequences. When both sequences are identical, the GRGe value is 1. Moreover, the GRG indicates the impact of the comparison sequence on the reference sequence. Therefore, when a specific comparison sequence exerts a more substantial influence on the reference sequence compared to others, its GRG with the reference sequence will be greater than the GRGs of the others.

Normalizing the S/N values For higher the better

$$ {\text{Z}}_{{{\text{ij}}}} = \frac{{{\text{y}}_{{{\text{ij}}}} - {\text{min}}\left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right)}}{{\max \left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right) - {\text{min}}\left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right)}} $$
(10)

Normalizing the S/N values For Smaller the better

$$ {\text{Z}}_{{{\text{ij}}}} = \frac{{{\text{min}}\left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right) - {\text{y}}_{{{\text{ij}}}} }}{{\max \left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right) - {\text{min}}\left( {{\text{y}}_{{{\text{ij}}}} ,{\text{i}} = 1,2, \ldots {\text{n}}} \right)}} $$
(11)

The highest and lowest values for MRR, TWR & ROC are taken respectively in the Eqs. 10 and 11 for normalization. The normalized values are tabulated in Table 11.

Table 11 Grey relational coefficient
Full size table

Calculation of Grey Relational Coefficient

$${\upxi }_{\mathrm{i}}\left(\mathrm{k}\right)=\frac{{\Delta }_{\mathrm{min}}+\upzeta {\Delta }_{\mathrm{max}}}{{\Delta }_{\mathrm{Oi}}(\mathrm{k})+\upzeta {\Delta }_{\mathrm{max}}}$$
(12)

where ∆ is the Deviation sequence, Where Δ0i(k) is the deviation sequence of the reference sequence and compatibility sequence.\(\upzeta \) is identified coefficients. The value of \(\upzeta \) is the lesser and recognized ability is the larger.\(\upzeta \) =0.5 is usually utilized.

Calculation of GRG

$$ \gamma _{i} = \frac{1}{n}\sum\limits_{{k = 1}}^{n} {\xi _{i} \left( k \right)} $$
(13)

The Grey Relational grades are ranked as per their value and are tabulated in Table 12. The ideal solution for getting the Maximum MRR, Minimum TWR, and ROC is represented by rank 1. The optimized properties thus obtained are Current at 15 A, Inter Electrode Gap at 2 mm, Powder concentration in dielectric at 9 g/l, Pulse on time at 300 µs &Pulse off time at 90 µs.

Table 12 Grey relational coefficient and ranking of GRG for the design of experiments
Full size table

13 Microstructure analysis

The optical microstructure analysis of EDM performed on Nimonic 80A alloy reveals critical insights into the material's structural changes. Under the EDM process, the alloy's microstructure exhibits distinct characteristics, including recast layers and micro-cracks formation. The recast layers, composed of re-solidified material, can vary in thickness based on EDM parameters such as pulse energy, duration, and sparking frequency. Micro-cracks indicate localized material removal, demonstrating the EDM process's thermal influence. Studying these optical microstructures provides valuable information for optimizing EDM parameters and understanding how they impact the surface quality and material properties of Nimonic 80A alloy components. Figure 5 reveals a significant presence of surface defects, including excessive melted material deposition, microcracks, clusters of debris globules, as well as micro-pores on the machined surface, where an aluminum powder concentration of 9 g/L was introduced, displays a noticeable reduction in surface defects compared to aluminum powder concentration of 3 g/L). The enhancement in surface morphology becomes more pronounced, incorporating an aluminum powder concentration of 6 g/L, demonstrating a substantial decrease in surface defects.

Fig. 5
figure 5

Optical microstructure of EDM on Nimonic 80A Alloy, a Sample 1 b Sample 5, c Sample 12, d Sample 20

Full size image

Figure 5 shows a significant decrease in the deposition of molten material and the occurrence of micro-cracks, debris globules, and micro-pores. The introduction of aluminum powder has significantly mitigated surface defects. These nanoparticles promote consistent sparking between work and tool interface, effectively diminishing micro-cracks. Furthermore, it widens the IEG and enhances the heat dissipation of the dielectric fluid through the formation of small craters, thereby reducing plasma heat flux and mitigating issues related to melted material deposition and globule formation, as well as micro-pore formation. Adding aluminum powder also facilitates improved debris flushing within the machining zone, forming smaller ridges and an overall enhancement in surface quality. These Micro pores likely correspond to points where individual discharges penetrated deeply into the workpiece. When a high-energy pulse is applied, it could potentially vaporize a substantial quantity of metal during the initial discharge. Following smaller current discharges, the initial removal of metal may be less, but a larger portion is heated to its melting point and subsequently redeposited on the surface as a recast layer. Moreover, multiple built-up layers can be observed.

Increasing pulse-on time produces more powerful explosions and higher discharge energy production. This, in turn, enhances material removal rates (MRR) but also speeds the consumption of the brass wire. Residual brass wire particles can adhere to the cutting surface, resulting in rougher surfaces. Higher peak currents amplify the influence of discharge energy on the workpiece surface, exacerbating erosion and deterioration of surface roughness.

14 Conclusions

In this research, the effects of machining response are MRR, TWR, and ROC of NIMONIC 80A with silver-coated copper electrode have been investigated using the EDM process by varying IEG, Powder concentration in dielectric, Current, Pulse On time, and Pulse OFF time. GRA is used to optimize the process parameters for MRR, TWR, and ROC combined effects. From the experimental investigation, the following conclusions were drawn:

  • Current is the most predominant parameter on Material Removal Rate (0.168 g), Tool Wear Rate (0.013 g), and Radial Over Cut (0.128 mm).

  • For MRR, the best process parameters are Current at 15 A, Ton at 300 μs, Powder concentration in dielectric at 6 g/l, Toff at 90 μs, and IEG at 2 mm.

  • The best process parameters to obtain the minimum tool wear rate are Current at 15 A, Powder concentration in dielectric at 9 g/l, Ton at 600 μs, IEG at 1 mm, and Toff at 30 μs.

  • The best process parameters to obtain the minimum radial overcut Current at 6 A, Powder concentration in dielectric at 3 g/l, Toff at 90 μs, Ton at 600 μs, and IEG at 3 mm.

  • Multi-objective optimization is carried out using Grey Relational Analysis, yielding the optimal values as follows: Current-15 A, Inter Electrode Gap-2 mm, and Powder concentration in dielectric—9 g/l, Ton—300 μs and Toff—90 μs.