# Investigation of Machinability Characteristics of EDMed Inconel 825 Alloy under Multidimensional Parametric Modeling by Using Holistic Grey-PCA Statistical Models

Authors: Nitin Kumar Sahu; Mukesh Kumar Singh; Bupe Getrude Mutono-Mwanza; Atul Kumar Sahu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The current social and industrial communities exceedingly demanded the materials that dealt with rich mechanical properties, i.e., the rich strength, hardness, reliability, high resistance against corrosion and oxidation, and high toughness and refractoriness. Recently, the researchers ascertained the comprehensive applications of these difficult to machine materials in the domain of automotive, aeronautical, nuclear industries etc. It is claimed that it is quite hard and expensive for machining these superadvanced materials by traditional machining operations. In the present study, worldwide promising nickel-based superalloy Inconel 825 material is used due to its outstanding mechanical and thermal properties at eminent temperatures and also having broad application in imperative engineering fields. The authors probed that machining cost and smart machinability index have become the gigantic concern in EDM operation; however, these can be minimized by adapting a conduit of evaluation of the optimum setting among multiple input parameters. It was a challenging task, which is respected by authors as the research gaps to be sorted out. To fulfill research gaps, the authors encountered imperative significant EDM input parameters, i.e., spark gap (Sg), gap voltage (Vg), pulse on time (Ton), pulse off time (Toff), Peak Current (Ip), Servo feed (Sf), Depth of Cut (Dc) and difficulty index (Di) corresponding to output responses, i.e., power consumption (Pc), machining time (Mt), and material removal rate (MRR) for framing the machinability index/model for conducting experiments and collecting objectives/responses/outputs. Next, the authors conducted experiments using the Taguchi L27 orthogonal array model in the nonvibratory domain for recording output responses. Later, to potentially access the results, the authors integrated the computational Taguchi methodology with dual models which is called as Taguchi-grey relational analysis (T-GRA) and Taguchi-principal component analysis (T-PCA). The optimum setting condition among considered inputs is discussed in the conclusion section. Later, confirmatory test gratified the evaluated optimum settings which is yielding an improvement of 0.16262 and 0.34398 score in executing T-GRA and T-PCA, respectively. In continuation, the current research evidenced that pulse off time is the chief significant process parameter havingp values 0.005 and 0.001 for T-GRA and T-PCA, respectively. It is also seen that the depth of cut is also another important significant process parameter having p values 0.061 and 0.073 for T-GRA and T-PCA, respectively. Moreover, the current research work also investigated the effect of variation of momentous input process parameters over the surface topography and their utility in improving surface integrity and eliminating the micropores and cracks.


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## Body

## 1. Introduction

Electrical discharge machining (EDM) has recently gained the high momentum among the various nontraditional manufacturing machining operations due to its less maintenance cost and rapid machining operations. EDM is capable for shaping, chamfering, drilling etc., of hard, tough, and refractory materials. EDM is turned out to be the most renowned nontraditional manufacturing machines at global standard due to its thermoelectric machining process. In EDM, the material removal phenomenon establishes by a series of discrete electrical discharges between the work piece and electrode immersed in a dielectric fluid. In EDM, the tiny material removes from the work piece and flushes away along with a continuously flowing dielectric fluid at a controlled rate. EDM is especially worldwide prioritized for cutting complex/intricate shapes and delicate cavities in various moulds or dyes that might be difficult with other conventional machining processes. A general structure of EDM is shown in Figure1, which is used to remove the metal by means of electric spark erosion. Here, an electric pulse generates electric spark that is used as the cutting tool to erode the work piece and produce the finished work piece in the form of a customized shape as shown in Figure 2.Figure 1
Schematic of sparking occurs at the nearest point in the EDM experimental setup.Figure 2
Typical EDM pulse current train for controlled pulse generator.Currently, Inconel 825 (nickel-chromium-based superalloys) is invented and designed to provide outstanding resistance at numerous critical working environments. This material reveals the excellent resistance to oxidation and corrosion and also possesses well resiliency against tremendous high heat and pressure. Inconel 825 preserves its potency over an extensive range of temperature and is suitable for high temperature applications as shown by Prabhu and Vinayagam [1]. This superalloy has been become more demanding in the current scenario due to their inherent application in various engineering sectors such as nuclear, power, chemical, and production of moulds and dyes. However, shaping and machining operations of Inconel superalloys has become incredibly hard and costly via conventional machining processes. The conventional machining processes are found in the line of uneconomic production in machining the hard Inconel superalloys due to the grounds of excessive heat generation; rapid tool wear; and short tool life at the work-tool interfaces. It is probed that the conventional machining process also affected the properties of Inconel 825 superalloy such as high wear resistance, high hardness, high temperature strength, and high tendency to weld to the conventional cutting tool reported by Rajyalakshmi and Ramaiah [2]. In numerous observations, the conventional machining process also resulted in changes of work material characteristics and mechanical properties. Owing to aforesaid problems, it seemed to be an enormous challenge in front of current researchers for machining Inconel superalloys by conventional machining processes. Therefore, the necessity of nontraditional machining operations for finishing the Inconel superalloys is really experienced by the current manufacturing communities. Nowadays, EDM is found in the area of nontraditional machining process and widely employed in industries for obtaining high accuracy in machining Inconel 825 superalloys and all variety of conductive materials (regardless of their hardness) such as graphite, metals, metallic alloys, and even some ceramic materials.


## 2. Motivation and Research Objective

As we know that, in EDM operations, both work piece and the tool electrode are submerged inside a dielectric fluid. A spark channel is established in between the electrode and work piece at high temperature about 10,000°C, which enables EDM for machining the hard materials. It is found by systematic literature survey that extensive research documents are floated in the different domains of EDM; a few are briefly discussed to find superior models and EDM parameters and building the machinability index.Prasad et al. [3] carried out their work on EN-42 spring steel using zinc-coated brass wire and distilled water as a dielectric in wire electrical discharge machining. The authors added WS2 powder in distilled water to evaluate the impact of dielectric on metal removal rate and surface roughness. It is found that the concentration of powder suspended in dielectric that flows in the gap between a work piece and electrode plays a leading role for improving the surface integrity. It is a well-known fact that efficient flushing rate between the tool and work piece drastically affects the machining conditions of the EDM process. Furthermore, it is also probed that exploration of different dielectric fluids might have marvelous effect over material removal depth, the surface roughness, the electrode wear rate, and other output parameters. Singh and Singh [4] focused on statistical data modeling of various machining parameters to obtain the best combination of parameters for desired machining performances in the EDM process. It is determined via experimental auditing that the size of particle, particle concentration, the electrical resistivity, the particle density, and the thermal conductivity of powders drastically affect the various machining performance and operations of EDM reported by Chow et al. [5]. Appropriate mixing of powders into the dielectric fluid greatly influences the TWR as well as MRR. Guo et al. [6] utilized Ti-6Al-4V work material, acoustic emission (AE) sensor and compressed air, and kerosene and water-based emulsion as a dielectric medium to investigate the material removal process based on expansion and contraction of gas bubble around the discharge plasma. Goyal et al. [7] utilized normal diffused and cryogenic treated diffused wires as electrode on Inconel 625 to investigate the effects of tool electrode, peak current, pulse on time, pulse off time, wire feed and wire tension on the response MRR.Recently, numerous number of researches divert their senses to use the statistical mathematical models and multiobjective evolutionary algorithms (MOEAs) for evaluating and optimizing the multiple objectives/responses vs. input parameters under EDM operations discussed by Golshan et al. [8]. Yang et al. [9] proposed the counterpropagation neural network for examining the experimental data against input variables for maximizing the material removal rate in parallel to minimize the surface roughness. Singh et al. [10] proposed the multiple statistical mathematical models such as adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) with back-propagation algorithm, and response surface methodology (RSM) for computing and anticipating the MRR and SR for D3 die steel material. Jampana et al. [11] performed thermal investigation to identify the effects of powder having different thermo physical properties in powder-mixed EDM (PMEDM) process. There, the authors have modeled the machining characteristic by utilizing artificial neural networks and FEM for determining optimal selection of process variables. Nas et al. [12] selected AISI D2 cold work tool steel and utilized grey relational degree to identify the impact of crucial machining parameters on output responses, where it is found that amperage and pulse on time significantly affects the surface roughness and hole diameter in EDM. Devarasiddappa et al. [13] utilized the modified teaching learning-based optimization algorithm to experimentally investigate Ti6Al4V alloy in WEDM process by varying the process parameters, i.e., wire speed, current, pulse on time, and pulse off time to identify their impact on surface roughness. Kulkarni and Kulkarni [14] applied the heuristic grey wolf Optimizer algorithm in wire electrical discharge machining (WEDM) for optimizing pulse on time, pulse off time, wire feed, wire tension, upper flush, and lower flush on high carbon high chromium steel material. Kumar and Narasimhamu [15] studied the effect of WEDM parameters, i.e., wire feed rate, pulse on time, pulse off time, and water pressure on Inconel 750 alloy by embedding TOPSIS with grey wolf optimizer in estimating cutting speed and surface roughness. Abed et al. [16] proposed a sequential discharge model based on FEM simulation for EDM. Their results are experimentally validated, and it is found that simulated results and experimental results have relative error, and thus there is need to develop appropriate mathematical modeling to minimize the extent of errors. Saffaran et al. [17] employed metaheuristics algorithms, i.e., artificial neural network (ANN) along with particle swarm optimization (PSO) and simulated annealing (SA) on AISI2312 hot worked steel parts in order to carry out optimization of surface roughness, tool wear rate, and material removal rate in electrical discharge machining (EDM) process. Yunus and Alsoufi [18] investigated the effect of pulse on duration, pulse off duration, current, and voltage on MRR and SR in WEDM on nitinol alloys by utilizing particle swarm optimization, where the authors found significant effects of process parameters on responses. Sen et al. [19] tried to establish a correlation between pulse on time, pulse off time, peak current, and servo voltage and wire tension by means of neural network model in order to optimize performance characteristics, i.e., surface roughness, cutting speed, and kerf width.Optimization of the responses such as MRR, surface roughness, and tool wear rate etc., depends on the crucial evaluation and selection of inputs process parameters as Aich et al. [20] and Tanveer et al. [21] mentioned. Moreover, the examination and evaluation of optimum condition setting among multiple control parameters is so complex process in the context of nontraditional machining process as Luan et al. [22] and Jain and Parashar [23] mentioned. The satisfactory evaluation as well as selection of manufacturing conditions is one of the significant aspects to be focused for optimizing the multiple responses in EDM environment reported by Wang et al. [24]. The balance between the machining inputs and outputs in the context of EDM is very important to achieve desired objective as discussed by Gostimirovic et al. [25]. It is significant to determine the crucial machining characteristics and optimum setting for extracting elevated outputs from the group of inputs [26, 27]. Additionally, it is fruitful to evaluate multiple outputs for assuming effectiveness and efficacy from implicated resources [28, 29]. Kumar et al. [30] proposed the RSM accompanied with GRA on Inconel 825 in order to optimize multiple output objectives during wire-cut EDM. Prakash et al. [31] investigated the hybrid composites (Al-Si12/B4C/fly ash) in WEDM to identify the effect of WEDM process parameters on the material removal rate (MRR) and surface roughness (SR) responses and found that the MRR can be increased by increasing pulse on time and reinforcement. It is also found that increase in gap voltage, pulse on time, pulse off time, wire feed, and reinforcement increases the SR. Manikandan et al. [32] proposed the grey relational analysis for electrochemical drilling on Inconel 625 to analyze the effect of machining variables such as feed rate, flow rate, and concentration of electrolyte on MRR, SR, and other geometric measures. Muni et al. [33] performed experimental analysis on rice husk ash/Cu/Mg-reinforced hybrid Al-0.7Fe-0.6Si-0.375Cr-0.25Zn metal matrix nanocomposites in EDM and identified the effects of various process parameters on output objectives. It is found that MRR and SR, both are decreasing with increased content of rice husk ash. Mouralova et al. [34] carried out their investigation on pure aluminum 99.5 to optimize machined surface integrity and kerf width for precision machining. Perumal et al. [35] examined the effect of pulse on duration, wire tension, and wire feed on MRR and SR while performing machining of Ti-6Al-2Sn-4Zr-2Mo (α-β) alloy using the grey relational approach in WEDM, where significant thrust has been received by the authors to review the process parameters for sustainable outcomes. Sharma et al. [36] applied the hybrid approach on Inconel 706 for optimizing the material removal rate and surface roughness. The authors have also carried out energy dispersive X-ray spectroscopy (EDAX) for topography analysis of EDMed material. Mouralova et al. [37] used a transmission electron microscope to study the impact of the orientation direction of the cut on cutting speed and machined surface quality in wire electrical discharge machining (WEDM). Singh et al. [38] carried out their investigation on copper, SS-EN 24, and Ti-6Al-4V material for understanding the effect of thermophysical properties of workpiece materials on MRR.The aim of the present study is to provide robust decision modeling and valuable insights to the current manufacturing organization for processing smart alloys. Moreover, the present study can be used by the manufacturing organization to decide significant levels of process parameters that provides efficient working condition, enhances profitability and productivity, and takes environmental responsibility, while performing machining operation in EDM. It is found that EDM is an advanced machining operation and requires driving fuels and mechanical energy. Thus, the present study has considered the green and productivity aspects in the form of appropriate selection of machining parameters as their proper selection against desired output which is very prominent and plays a keen role in reducing power consumption, enhancing productivity, and reducing machining time. Appropriate selection of process parametric setting enables the EDM in the direction of correct utilization of resources, reduction in negative environmental loads, and reduces wastes. The modeling proposed in the present study assists in the reduction of power consumption in EDM, which will lead towards less consumption of natural resources/fossil fuels and participates in environmental responsiveness. Additionally, the reduction in machining time leads in the faster manufacturing of the components and results in profitability and less cost and supports in gaining competitive advantage, which is the major achievement of the present study.It is summarized that evaluation and selection of the outstanding optimum condition setting among multiple machining inputs parameters in addressing to minimize the power consumption, machining time, and maximize the material removal rate has become so critical occupation. From systematic literature review, it is accessed that a few authors are fruitfully attempted towards parametric modeling and optimization of outputs for evaluating the best optimum condition setting among input parameters under EDM considering Inconel 825 materials. Furthermore, it is also observed that few research documents are published and dealt with multiobjective optimization of limited or single or two outputs with respect to inadequate inputs variables/parameters for Inconel 825 with EDM operation. No authors are available which have considered the spark gap (Sg), gap voltage (Vg), pulse on time (Ton), pulse off time (Toff), peak current (Ip), servo feed (Sf), depth of cut (Dc), and difficulty index (Di) as inputs parameters for optimizing power consumption (Pc), machining time (Mt), and material removal rate (MRR) in multiobjective optimization realm in addition to surface topography analysis. The presented work has considered the optimization of EDM input parameters on Inconel 825 in order to optimize the responses using Taguchi-based grey relational analysis (T-GRA) accompanied with principal component analysis (T-PCA). Twenty-seven experiments are conducted systematically using Taguchi-basedL27 orthogonal array model to fullfill aforesaid agendas.


## 3. Materials And Methods

### 3.1. Work Piece Material

In today’s era of industry 4.0, technologies and competitiveness enforced industries to more focus on optimization of the EDM process by executing optimization methodologies and models reported by Zhou et al. [39]. The authors found that EDM operation is subjected to multiple limitations along with controllable inputs parameters discussed by Baldin et al. [40]. A vigilant evaluation and selection of inputs machining parameters with right value leads to achieve the optimum output or smatter machining results discussed by Muthuramalingam et al. [41]. In the current market, various super-advanced material, composite, and other materials encompass the high resistance against heating as well as corrosion; rich mechanical properties with least machining cost are demanded with curiosity by different industrial sectors for fabricating various customized goods reported by Payal et al. [42]. It is ascertained that EDM operation is faster and feasible among all nontraditional machining operations discussed by Kumar and Rao [43]. Therefore, in the presented research forum, Inconel 825, composed by mixing the nickel-iron-chromium alloy with molybdenum and copper as well, is chosen due to its unique and exceptional characteristics such as rich hardness and strength, resiliency against reducing and oxidizing acids, voiding stress-corrosion cracking, and neutralizing the localize attack (pitting and crevice cavitations and rusting). Currently, the said Inconel 825 material is highly respected at global standard by many sectors such as chemical processing, aerospace, missile, nuclear fuel reprocessing, chemical and petrochemical, and marine. The material and EDM process evaluation and selection is respected preliminary so that sustainable manufacturing practices can be pushed out in manufacturing firms by evaluating and finding the best inputs or machining parameters at different values.


### 3.2. EDMed Controllable Parameters and Output Responses

(i)
Spark Gap (Sg): it is an appropriate “gap” between electrode and work part to produce the spark under EDM process. Spark gap is needed to be maintained for generating the spark and is controllable by servo system setup.(ii)
Gap Voltage (Vg): it is gained by maintaining the potential gap or difference between the electrode and work piece. Gap voltage is known as the total energy of the spark. Increase in the gap voltage outcomes the improvement in flushing conditions and material removal rate and straightly supports to stabilize the machining.(iii)
Pulse on Time (Ton): it reflects the spark generation over short-timing or pulse timing. It is also known as the period (per cycle) in performing the machining operation, i.e., the current is allowed to flow through the discharge gap. The machining process is straightly proportional to Ton and becomes rapid in nature and thus results in augmentation in material removal rate.(iv)
Pulse off Time (Ton): it is the time consumed between the two consecutive sparks on nonsupply of current to the electrodes. During the period of pulse off time, deionization of dielectric occurs as well as dielectric also flushes the machining debris.(v)
Peak Current (Ip): peak current is the maximum current and occurs against each pulse on power supply. It is found that an expansion in peak discharge current fosters the intensification of input heat rate, which results in increased material removal rate and tool wear rate. It is also called as the peak discharge current in EDM operation.(vi)
Servo Feed (Sf): it maintains and controls the working gap corresponding to the set value. It also represents the distance, maintained the between the tool electrode and the work-piece in the appropriate manner on EDM machine process to avoid the inefficient sparking. Currently, EDMs are assisted by a servo feed mechanism, which automatically manages the servo feed.(vii)
Depth of Cut (Dc): it reflects the total quantity of the metal, which left from work part upto defined depth over each pass of the tool. Generally, it is expressed in mm.(viii)
Difficulty Index (Di): the difficulty index is the proportion or probability that the machine provides to an experimental test for reading input correctly. It ranges between 0 and 100%, and its higher value indicates effectiveness of the machine.(ix)
Power consumption (Pc): it is the consumption of AC/DC electrical energy per unit time by EDM machine. It is basically mapped in the unit of watt (W) or kilowatts (kW). Mathematically, PowerW=V∗I(x)
Machining Time (Mt): it is the amount of time, consumed by EDM machine to shape the work piece in meeting the given dimensions. It is typically mapped in minutes.(xi)
Material Removal Rate (MRR): it states the amount of material removed from the work part over per unit time. It can be computed by weighing the volume of material removal from work part or by measuring the weight of work part prior to and after EDM machining operation. Here, MRRmg/min=initial weight of work piece−final weight of work piece/machining time


### 3.3. Taguchi Model

It is known that the invention of innovative and novel materials is a ceaseless process. Various kind of new conductive, hard, and tough materials are introduced recently due to industrial and market demand. It is observed that empirical optimization and hypothetical auditing of input parameters of EDM process reflects the unreliable and inconsistent results as shown by Shao and Rajurkar [44]. The necessity of statistical mathematical models has been comprehensively realized, which can interpret the structured experimental data discussed by Reddy et al. [45] and Li et al. [46]. Shabgard and Khosrozadeh [47] reported that the Taguchi’s models are most reliable and consistent in nature for executing experiments designs. Taguchi’s model is used to frame the favorable setting of input process parameters against unavoidable variations or external noise on the experiments reported by Singh et al. [48] and Werner [49]. The signal to noise (S/N) ratio is an idyllic metric nomenclature under Taguchi’s model that eliminates the variability and carries forward the improvement of measurement as discussed by Choudhury et al. [50]. The S/N ratios are bifurcated into three standards: lower the better (LB), higher the better (HB), and nominal is the best (NB), as shown in equations (1)–(3), respectively, by Zhang et al. [51]. Furthermore, under the curriculum of Taguchi’s model, the ANOVA analysis is also executed on experimental data towards accessing the most significant and influencing input parameters with respect to output responses.


#### 3.3.1. Lower the Better (LB)

This machining characteristic is associated with minimum is better (objective). Lower values are desirable corresponding to objectives or outputs, i.e., power consumption, machining time, etc.(1)SNLB=−10Log1n∑j=1nyj2.


#### 3.3.2. Higher the Better (HB)

This machining characteristic is associated with maximum is better (objective). High values are desirable corresponding to objectives or outputs, i.e., material removal rate etc.(2)SNHB=−10Log1n∑j=1n1yj2.


#### 3.3.3. Nominal the Best (NB)

This machining characteristic is associated with nominal is better (objective). Nominal values are desirable corresponding to objectives or outputs, i.e., dimensions etc.(3)SNNB=−10Log1n∑j=1nyj−y02,where yj = characteristic value in an observation j, y0 = characteristic nominal value, and n = total experiment conducted.


### 3.4. Theory of Grey Relational Analysis

Prof. Deng’s has designed the grey incidence analysis model or grey relational analysis model. He proposed the model to analysis the black and white information simultaneously, i.e., in any contingency, the situation has no information is represented as black and has complete information is represented as white discussed by Rajyalakshmi and Ramaiah [2] and Kumar et al. [30]. However, the realistic engineering problems usually dealing with partial information and can be fruitfully undertaken by the grey theory by Singh and Singh. The Grey relational analysis (GRA) model is executed to undertake the unsure, vague, imprecise, and inexact information by Manikandan et al. [32]. Hoverer, GRA model also has advanced features analysis and synchronizes the statistical or experimental data and has aptitude to provide the efficient solution to real social problems and manufacturing operations. The subsequent steps are engaged in the GRA model:Step 1.
Data preprocessing
In information preprocessing, the mapped machining characteristics are normalized from 0 to 1, which is called as grey relational generation. In grey relational generation, the normalized objective values corresponding to experimental data; lower the better (LB) and larger-the-better can be calculated by executing (4) and (5), respectively,(4)xik=maxyik−yikmaxyik−minyik,(5)xik=yik−minyikmaxyik−minyik,where xik  = the normalized value, minyik is the minimum value of yik for the kth response, and maxyik) is the maximum value of yik for the kth response.Step 2.
Evaluation ofΔoi
It illustrates the divergence from the ideal sequence for the experimental responses/objectives(6)Δoidifference of the absolute value=x0k−xik,where x0k (k = 1, 2, 3, ..., 9) for the experimental responses.Step 3.
Grey relational coefficient
The grey relational coefficientξik can be estimated as(7)ξik=Δmin+ψΔmaxΔ0ik+ψΔmax,where ψ is the distinguishing coefficient 0≤ψ≤1; Δmin=∀jmin∈i∀kminx0k−xjk is the smallest value of Δoi; Δmax=∀jmax∈i∀kmaxx0k−xjk is the largest value of Δoi.Step 4.
Grey relational gradeγi
Grey relational gradeγi can be computed by using (8) as(8)γi=1n∑ξik,where n = number of output responses.


### 3.5. Principal Component Analysis (PCA)

The purpose of principal component analysis (PCA) is to interpret and recognize the variance as well as covariance of entire performance characteristics or output objectives by integrating them linearly by Payal et al. [42]. The key benefit of PCA is that data can be compressed once the pattern is recorded, i.e., dimensional reduction without sacrificing accuracy as discussed by Saha and Mondal [52]. The steps are associated with the PCA model which is explained by Kasdekaret al. [53] as follows:(1)
Getting some data(2)
Normalization of data(3)
Computation of covariance matrix(4)
Analysis and interpretation of covariance matrixStep 5.
Construct a variance-covariance matrixM via executing the normalized data, illustrated as follows:(9)M=N1,1N1,2…N1,uN2,1N2,2…N2,p⋮⋮…⋮Nq,1Nq,2…Nq,p,where u reflects the number of machining characteristics and p reflects the number of experimental runs.Step 6.
The correlation coefficient array can be written as follows:(10)Nk,l=CovYi,k∗,Yi,l∗VarYi,k∗VarYi,l∗,where CovYi,k∗,Yi,l∗ expressed the covariance of sequence Yi,k∗ and Yi,l∗. VarYi,k∗ is the standard deviation of Yi,k∗, VarYi,l∗ is the standard deviation of Yi,l∗ and Nk,l is the correlation coefficient.Step 7.
Evaluation of Eigen vectors and Eigen values of matrixM are denoted by VJ⟶ and λj, respectively.
In the PCA model, the eigenvectorVJ⟶ expresses the weighting factor of j number of machining characteristics of the jth principal component. For example, if Qj expresses the jth machining characteristic, then the jth principal component ψj can be respected as a quality indicator along with the operating machining characteristic and might be calculated by equation (11). It is to be understood that each principal component ψj depicts a certain degree of clarification of the variation of machining characteristics such as the accountability proportion AP. AP of machining characteristics increase in the case of numerous gathering of principal components which is called as cumulative accountability proportion CAP. Evaluation and selection of individual principal components ψj, those need to be associated with composite machining indicator ψ depends on their individual accountability proportion.(11)ψj=V∗J1Q+1V∗J2Q,2V∗JJQ=JVJ⟶.Q⟶.
In the conducted research work, the composite principal componentψ is defined as the combination of principal components with their individual eigen values, and it serves as the representative of multiresponses, called as multi/composite response indicators.
If a machining characteristicQj is robustly governed by the jth principal component, this principal component becomes the chief indicator of such a machining characteristic. It ought to be sensed that one machining indicator might frequently represent entire multimachining characteristics.Step 8.
After computing the individual principal components, the composite machining indicator must be defined, which is the representative of multicharacteristics of the output responses. In the presented research work, the composite principal componentψ can be calculated as follows:(12)ψ=ψ2i2+ψ2i2+ψ3i2+ψ4i2,1/2where i is the experiment conducted.


## 3.1. Work Piece Material

In today’s era of industry 4.0, technologies and competitiveness enforced industries to more focus on optimization of the EDM process by executing optimization methodologies and models reported by Zhou et al. [39]. The authors found that EDM operation is subjected to multiple limitations along with controllable inputs parameters discussed by Baldin et al. [40]. A vigilant evaluation and selection of inputs machining parameters with right value leads to achieve the optimum output or smatter machining results discussed by Muthuramalingam et al. [41]. In the current market, various super-advanced material, composite, and other materials encompass the high resistance against heating as well as corrosion; rich mechanical properties with least machining cost are demanded with curiosity by different industrial sectors for fabricating various customized goods reported by Payal et al. [42]. It is ascertained that EDM operation is faster and feasible among all nontraditional machining operations discussed by Kumar and Rao [43]. Therefore, in the presented research forum, Inconel 825, composed by mixing the nickel-iron-chromium alloy with molybdenum and copper as well, is chosen due to its unique and exceptional characteristics such as rich hardness and strength, resiliency against reducing and oxidizing acids, voiding stress-corrosion cracking, and neutralizing the localize attack (pitting and crevice cavitations and rusting). Currently, the said Inconel 825 material is highly respected at global standard by many sectors such as chemical processing, aerospace, missile, nuclear fuel reprocessing, chemical and petrochemical, and marine. The material and EDM process evaluation and selection is respected preliminary so that sustainable manufacturing practices can be pushed out in manufacturing firms by evaluating and finding the best inputs or machining parameters at different values.


## 3.2. EDMed Controllable Parameters and Output Responses

(i)
Spark Gap (Sg): it is an appropriate “gap” between electrode and work part to produce the spark under EDM process. Spark gap is needed to be maintained for generating the spark and is controllable by servo system setup.(ii)
Gap Voltage (Vg): it is gained by maintaining the potential gap or difference between the electrode and work piece. Gap voltage is known as the total energy of the spark. Increase in the gap voltage outcomes the improvement in flushing conditions and material removal rate and straightly supports to stabilize the machining.(iii)
Pulse on Time (Ton): it reflects the spark generation over short-timing or pulse timing. It is also known as the period (per cycle) in performing the machining operation, i.e., the current is allowed to flow through the discharge gap. The machining process is straightly proportional to Ton and becomes rapid in nature and thus results in augmentation in material removal rate.(iv)
Pulse off Time (Ton): it is the time consumed between the two consecutive sparks on nonsupply of current to the electrodes. During the period of pulse off time, deionization of dielectric occurs as well as dielectric also flushes the machining debris.(v)
Peak Current (Ip): peak current is the maximum current and occurs against each pulse on power supply. It is found that an expansion in peak discharge current fosters the intensification of input heat rate, which results in increased material removal rate and tool wear rate. It is also called as the peak discharge current in EDM operation.(vi)
Servo Feed (Sf): it maintains and controls the working gap corresponding to the set value. It also represents the distance, maintained the between the tool electrode and the work-piece in the appropriate manner on EDM machine process to avoid the inefficient sparking. Currently, EDMs are assisted by a servo feed mechanism, which automatically manages the servo feed.(vii)
Depth of Cut (Dc): it reflects the total quantity of the metal, which left from work part upto defined depth over each pass of the tool. Generally, it is expressed in mm.(viii)
Difficulty Index (Di): the difficulty index is the proportion or probability that the machine provides to an experimental test for reading input correctly. It ranges between 0 and 100%, and its higher value indicates effectiveness of the machine.(ix)
Power consumption (Pc): it is the consumption of AC/DC electrical energy per unit time by EDM machine. It is basically mapped in the unit of watt (W) or kilowatts (kW). Mathematically, PowerW=V∗I(x)
Machining Time (Mt): it is the amount of time, consumed by EDM machine to shape the work piece in meeting the given dimensions. It is typically mapped in minutes.(xi)
Material Removal Rate (MRR): it states the amount of material removed from the work part over per unit time. It can be computed by weighing the volume of material removal from work part or by measuring the weight of work part prior to and after EDM machining operation. Here, MRRmg/min=initial weight of work piece−final weight of work piece/machining time


## 3.3. Taguchi Model

It is known that the invention of innovative and novel materials is a ceaseless process. Various kind of new conductive, hard, and tough materials are introduced recently due to industrial and market demand. It is observed that empirical optimization and hypothetical auditing of input parameters of EDM process reflects the unreliable and inconsistent results as shown by Shao and Rajurkar [44]. The necessity of statistical mathematical models has been comprehensively realized, which can interpret the structured experimental data discussed by Reddy et al. [45] and Li et al. [46]. Shabgard and Khosrozadeh [47] reported that the Taguchi’s models are most reliable and consistent in nature for executing experiments designs. Taguchi’s model is used to frame the favorable setting of input process parameters against unavoidable variations or external noise on the experiments reported by Singh et al. [48] and Werner [49]. The signal to noise (S/N) ratio is an idyllic metric nomenclature under Taguchi’s model that eliminates the variability and carries forward the improvement of measurement as discussed by Choudhury et al. [50]. The S/N ratios are bifurcated into three standards: lower the better (LB), higher the better (HB), and nominal is the best (NB), as shown in equations (1)–(3), respectively, by Zhang et al. [51]. Furthermore, under the curriculum of Taguchi’s model, the ANOVA analysis is also executed on experimental data towards accessing the most significant and influencing input parameters with respect to output responses.


### 3.3.1. Lower the Better (LB)

This machining characteristic is associated with minimum is better (objective). Lower values are desirable corresponding to objectives or outputs, i.e., power consumption, machining time, etc.(1)SNLB=−10Log1n∑j=1nyj2.


### 3.3.2. Higher the Better (HB)

This machining characteristic is associated with maximum is better (objective). High values are desirable corresponding to objectives or outputs, i.e., material removal rate etc.(2)SNHB=−10Log1n∑j=1n1yj2.


### 3.3.3. Nominal the Best (NB)

This machining characteristic is associated with nominal is better (objective). Nominal values are desirable corresponding to objectives or outputs, i.e., dimensions etc.(3)SNNB=−10Log1n∑j=1nyj−y02,where yj = characteristic value in an observation j, y0 = characteristic nominal value, and n = total experiment conducted.


## 3.3.1. Lower the Better (LB)

This machining characteristic is associated with minimum is better (objective). Lower values are desirable corresponding to objectives or outputs, i.e., power consumption, machining time, etc.(1)SNLB=−10Log1n∑j=1nyj2.


## 3.3.2. Higher the Better (HB)

This machining characteristic is associated with maximum is better (objective). High values are desirable corresponding to objectives or outputs, i.e., material removal rate etc.(2)SNHB=−10Log1n∑j=1n1yj2.


## 3.3.3. Nominal the Best (NB)

This machining characteristic is associated with nominal is better (objective). Nominal values are desirable corresponding to objectives or outputs, i.e., dimensions etc.(3)SNNB=−10Log1n∑j=1nyj−y02,where yj = characteristic value in an observation j, y0 = characteristic nominal value, and n = total experiment conducted.


## 3.4. Theory of Grey Relational Analysis

Prof. Deng’s has designed the grey incidence analysis model or grey relational analysis model. He proposed the model to analysis the black and white information simultaneously, i.e., in any contingency, the situation has no information is represented as black and has complete information is represented as white discussed by Rajyalakshmi and Ramaiah [2] and Kumar et al. [30]. However, the realistic engineering problems usually dealing with partial information and can be fruitfully undertaken by the grey theory by Singh and Singh. The Grey relational analysis (GRA) model is executed to undertake the unsure, vague, imprecise, and inexact information by Manikandan et al. [32]. Hoverer, GRA model also has advanced features analysis and synchronizes the statistical or experimental data and has aptitude to provide the efficient solution to real social problems and manufacturing operations. The subsequent steps are engaged in the GRA model:Step 1.
Data preprocessing
In information preprocessing, the mapped machining characteristics are normalized from 0 to 1, which is called as grey relational generation. In grey relational generation, the normalized objective values corresponding to experimental data; lower the better (LB) and larger-the-better can be calculated by executing (4) and (5), respectively,(4)xik=maxyik−yikmaxyik−minyik,(5)xik=yik−minyikmaxyik−minyik,where xik  = the normalized value, minyik is the minimum value of yik for the kth response, and maxyik) is the maximum value of yik for the kth response.Step 2.
Evaluation ofΔoi
It illustrates the divergence from the ideal sequence for the experimental responses/objectives(6)Δoidifference of the absolute value=x0k−xik,where x0k (k = 1, 2, 3, ..., 9) for the experimental responses.Step 3.
Grey relational coefficient
The grey relational coefficientξik can be estimated as(7)ξik=Δmin+ψΔmaxΔ0ik+ψΔmax,where ψ is the distinguishing coefficient 0≤ψ≤1; Δmin=∀jmin∈i∀kminx0k−xjk is the smallest value of Δoi; Δmax=∀jmax∈i∀kmaxx0k−xjk is the largest value of Δoi.Step 4.
Grey relational gradeγi
Grey relational gradeγi can be computed by using (8) as(8)γi=1n∑ξik,where n = number of output responses.


## 3.5. Principal Component Analysis (PCA)

The purpose of principal component analysis (PCA) is to interpret and recognize the variance as well as covariance of entire performance characteristics or output objectives by integrating them linearly by Payal et al. [42]. The key benefit of PCA is that data can be compressed once the pattern is recorded, i.e., dimensional reduction without sacrificing accuracy as discussed by Saha and Mondal [52]. The steps are associated with the PCA model which is explained by Kasdekaret al. [53] as follows:(1)
Getting some data(2)
Normalization of data(3)
Computation of covariance matrix(4)
Analysis and interpretation of covariance matrixStep 5.
Construct a variance-covariance matrixM via executing the normalized data, illustrated as follows:(9)M=N1,1N1,2…N1,uN2,1N2,2…N2,p⋮⋮…⋮Nq,1Nq,2…Nq,p,where u reflects the number of machining characteristics and p reflects the number of experimental runs.Step 6.
The correlation coefficient array can be written as follows:(10)Nk,l=CovYi,k∗,Yi,l∗VarYi,k∗VarYi,l∗,where CovYi,k∗,Yi,l∗ expressed the covariance of sequence Yi,k∗ and Yi,l∗. VarYi,k∗ is the standard deviation of Yi,k∗, VarYi,l∗ is the standard deviation of Yi,l∗ and Nk,l is the correlation coefficient.Step 7.
Evaluation of Eigen vectors and Eigen values of matrixM are denoted by VJ⟶ and λj, respectively.
In the PCA model, the eigenvectorVJ⟶ expresses the weighting factor of j number of machining characteristics of the jth principal component. For example, if Qj expresses the jth machining characteristic, then the jth principal component ψj can be respected as a quality indicator along with the operating machining characteristic and might be calculated by equation (11). It is to be understood that each principal component ψj depicts a certain degree of clarification of the variation of machining characteristics such as the accountability proportion AP. AP of machining characteristics increase in the case of numerous gathering of principal components which is called as cumulative accountability proportion CAP. Evaluation and selection of individual principal components ψj, those need to be associated with composite machining indicator ψ depends on their individual accountability proportion.(11)ψj=V∗J1Q+1V∗J2Q,2V∗JJQ=JVJ⟶.Q⟶.
In the conducted research work, the composite principal componentψ is defined as the combination of principal components with their individual eigen values, and it serves as the representative of multiresponses, called as multi/composite response indicators.
If a machining characteristicQj is robustly governed by the jth principal component, this principal component becomes the chief indicator of such a machining characteristic. It ought to be sensed that one machining indicator might frequently represent entire multimachining characteristics.Step 8.
After computing the individual principal components, the composite machining indicator must be defined, which is the representative of multicharacteristics of the output responses. In the presented research work, the composite principal componentψ can be calculated as follows:(12)ψ=ψ2i2+ψ2i2+ψ3i2+ψ4i2,1/2where i is the experiment conducted.


## 4. Experimentation Setup Details

### 4.1. Detail of Experimental Setup and Problem Formulation

In current investigation, experiments are robustly conducted upon EDM using Inconel 825 material specimen Both the mechanical properties and chemical composition of composed Inconel 825 are tabulated in Tables1 and 2, respectively.Table 1
Chemical composition of Inconel 825 properties.
Chemical compositionElementSNiCuAlCrSiFeMnTiMoCWeight (%)0.0338–461.5–3.00.219.5–23.50.52210.6–1.22.5–3.50.05Table 2
Mechanical properties of Inconel 825.
Mechanical propertiesPropertiesModulus of elasticityMelting pointDensityCoefficient of expansionThermal conductivityModulus of rigidityPoisson’s ratioSpecific heatTensile strengthValues196 kN/mm21400°C8.14 g/cm314.0 m/m/°C (20–100°C)12.3 W/moC at 100°C75.9 N/mm20.29440 Joules/kg-C550 N/mm2To conduct experiments, the authors availed the EDM setup (manufacturer: Electronica India Limited, model no: Electronica Electrapuls PS 50ZNC), provided by Central Institute of Petrochemicals Engineering and Technology (CIPET), Raipur, C.G, India. The specification of EDM setup is tabulated in Table3. Figure 3 depicts the flow chart of conducted experiments for EDMed Inconel 825 specimen. To attain the high degree of precision in experiments, it was highly concern to assess irregularities or roughness of electrode’s bottom surface.Table 3
Specification of EDM setup.
Item (s)Value/rangeItem (s)Value/rangeMounting surface (length × width)600 × 400 mmMaximum work piece height250 mmWidth of the work tank900 mmMaximum job weight50 kgDepth of the work tank600 mmHeight of the work tank400 mmX-axis travel400 mmCurrent range (Ip)0–50 AY-axis travel300 mmPulse on time range (ton)0.5–3000μsTransverse (X,Y, Z)400, 300, 250 mmDuty factor range (τ)8–100%Open circuit voltage range (Vg)0–100 VFigure 3
Flow chart of conducted experimental research for EDMed Inconel 825 material.The copper was prioritized as a tool material which was having surface irregularities and is requisite for machining. Copper electrode (dimensions: diameter 10 mm and length 35 mm) along with its mechanical properties and images at various orientations and stages are depicted in Table4 and Figure 4, respectively. The work piece size of 150∗100∗10 mm (length∗width∗thickness) was employed for experiments.Table 4
Mechanical properties of pure copper electrode.
Physical propertiesElectrical resistivity (μΩ/cm)Thermal conductivity (W/m·K)Melting point (°C)Specific gravity at 20°C (g/cc)Density (g/cc)Value1.96268.38910838.98.92Figure 4
Electrode images at various stages. (a) Image of requisite machining performed on lathe on copper tool electrode. (b) Image of copper tool electrode after requisite machining performed and before starting experiment 1.
(a)(b)Prior to conduct the experiments on EDM, initial weight of copper electrode and Inconel 825 specimen was measured by executing the Chemico Complete Lab Ware White Weighing Scale (digital capacity: 200gm, accuracy: 1 mg). The weight of electrode and work piece was found as 60.91 gm and 785.24 gm, respectively. Commercial grade EDM oil at freezing point = 94°C and specific gravity = 0.763 was employed as dielectric fluid with a constant flushing pressure of Fp = 2.1 bar in the EDM operation. Work piece and electrode has been kept at a positive and negative polarity, respectively, throughout the experimentation.After finishing the aforesaid prerequisite, the process parameters optimization problem is formulated or machinability assessing index was framed. The experiments were conducted on EDMed Inconel 825 specimen with considering eight controllable EDM input process parameters, i.e., spark gap (Sg), gap voltage (Vg), pulse on time (Ton), pulse off time (Toff), peak current (Ip), servo feed (Sf), depth of cut (Dc), and difficulty index (Di). Each input parameter is varied at three discrete levels as shown in Table5. The authors are supposed to conduct many experiments under compliance of the full factorial rule for optimizing inputs. But because of many challenges and constraints, i.e., framing more specimens, time, operating cost, and machining cost, the authors evaluated the twenty-seven (27) experiments by executing the statistical Taguchi’s based L27 orthogonal array model. The total number of 27 experiments to be conducted corresponding to eight controllable EDM input process parameters at three discrete levels are shown in Table 6. Figure 5 shows the images for experiment 1 and 2, after data entry of process parameters into control panel or computer, embedded with EDM machine.Table 5
Domain of experiments: bounded machining process parameters.
ParametersSpark gapGap voltagePulse on timePulse off timePeak currentServo feedDepth of cutDifficulty indexNotations(Sg)(Vg)(Ton)(Toff)(Ip)(Sf)(Dc)(Di)Unitsmmvμsμsampmm/minmm—Level of variations10.05255001015400.53020.0755075020306016030.17510003045801.590Table 6
Taguchi’sL27 orthogonal array structure.
Exp no.Spark gap (Sg)Gap voltage (Vg)Pulse on time (Ton)Pulse off Time (Toff)Peak current (Ip)Servo feed (Sf)Depth of cut (Dc)Difficulty index (Di)δ10.05255001015400.530δ20.0525500103060160δ30.05255001045801.590δ40.05507502015400.560δ50.0550750203060190δ60.05507502045801.530δ70.057510003015400.590δ80.05751000303060130δ90.057510003045801.560δ100.075257503015601.530δ110.075257503030800.560δ120.07525750304540190δ130.0755010001015601.560δ140.0755010001030800.590δ150.075501000104540130δ160.075755002015601.590δ170.075755002030800.530δ180.07575500204540160δ190.1251000201580130δ200.12510002030401.560δ210.12510002045600.590δ220.150500301580160δ230.1505003030401.590δ240.1505003045600.530δ250.175750101580190δ260.1757501030401.530δ270.1757501045600.560Figure 5
Images showing details of experimentation 1 and experimentation 2. (a) Experiment 1 (run 1). (b) Experiment 2 (run 2).
(a)(b)The responses/objectives, i.e., power consumption, machining time, and material removal rate corresponding to entered inputs parameters are tabulated in Table7. After performing the twenty-seven experiments, the captured image of EDMed Inconel 825 specimen is depicted in Figure 6. The presented research has intention to determine the effective conditions of favorable input process parameters for Inconel 825, which might aid the manufacturers for producing their products at least cost with high production.Table 7
Design of experiment (L27) orthogonal array and collected response experimental data.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Power consumption (KW)1.1254.6257.1001.2507.6259.7504.2507.50010.0001.8758.75012.5002.6255.1507.5004.5006.2258.5002.0005.0009.8755.1259.0009.5002.5004.4386.000Machining time (min)6.9002.4502.4802.1302.7004.6702.9203.9503.93010.3002.2303.8808.8300.9800.7653.6201.5002.10011.2705.1201.77010.9805.1901.3703.2803.4201.150MRR (mg/min)32.394232.653370.96867.265159.259209.85048.077149.36783.96966.990116.592153.84695.130193.878168.831204.420373.333328.00065.661172.862101.69559.199161.654153.285201.22295.322356.522Figure 6
Images of EDMed Work piece after completion of 27 experimentation.
(a)(b)


### 4.2. Parametric Optimization of EDMed Inconel 825

#### 4.2.1. Evaluation of Optimal Process Condition

It is undoubtedly required to convert the multiobjective responses into single response, i.e., multiresponse performance indicator (MRPI) in order to calculate the optimal process condition. To transform the variety of dimensions of investigational data into comparable platform, (4) and (5) are employed in the case of grey relational analysis, whereas (9) is applied in the case of principal component analysis.After computing single response/MRPI, the authors executed equations (6)–(8) towards estimating the overall grey relational grade (OGRG), and the sequential tables are depicted in Tables 8–11.Table 8
Assessment of Δ0i for each of the responses.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc0.00000.30770.52530.01100.57140.75820.27470.56040.78020.06590.67031.00000.13190.35380.56040.29670.44840.64840.07690.34070.76920.35160.69230.73630.12090.29120.4286Mt0.58400.16040.16330.12990.18420.37170.20510.30320.30130.90770.13950.29650.76770.02050.00000.27180.07000.12711.00000.41460.09570.97240.42120.05760.23940.25270.0366MRR1.00000.41260.00690.89770.62790.47950.95400.65690.84870.89850.75300.64380.81600.52640.59980.49540.00000.13300.90240.58800.79670.92140.62090.64540.50480.22880.0493Table 9
Grey relational coefficientξi (k) of each machining characteristics (with ψ = 0.5).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.00000.61900.48770.97850.46670.39740.64540.47150.39060.88350.42720.33330.79130.58560.47150.62760.52720.43540.86670.59480.39390.58710.41940.40440.80530.63190.5385Mt0.46130.75710.75390.79370.73080.57360.70910.62250.62400.35520.78190.62770.39440.96071.00000.64790.87720.79730.33330.54670.83940.33960.54280.89670.67620.66420.9317MRR0.33330.54790.98630.35770.44330.51050.34390.43220.37070.35750.39900.43710.37990.48720.45460.50231.00000.78990.35650.45960.38560.35180.44610.43650.49760.6860.9102Table 10
Data preprocessing of each machining characteristic (grey relational generation).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.0000.6920.4750.9890.4290.2420.7250.4400.2200.9340.3300.0000.8680.6460.4400.7030.5520.3520.9230.6590.2310.6480.3080.2640.8790.7090.571Mt0.4160.8400.8370.8700.8160.6280.7950.6970.6990.0920.8610.7030.2320.9801.0000.7280.9300.8730.0000.5850.9040.0280.5790.9420.7610.7470.963MRR0.0000.5870.9930.1020.3720.5200.0460.3430.1510.1010.2470.3560.1840.4740.4000.5051.0000.8670.0980.4120.2030.0790.3790.3550.4950.7710.951Table 11
Grey relational grade.γi
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Grey relational gradeγi0.598190.641340.742610.709980.546920.493800.566120.508740.461760.532070.536060.466070.521880.677810.642040.592580.801490.674230.518840.533680.539640.426150.469400.579230.659710.660740.79347S/N ratio (higher-the-better)−4.46315−3.85817−2.58473−2.97504−5.24156−6.12890−4.94190−5.87016−6.71170−5.48061−5.41578−6.63098−5.64852−3.37787−3.84875−4.54508−1.92202−3.42387−5.69930−5.45438−5.35794−7.40875−6.56920−4.74303−3.61296−3.59933−2.00942Moreover, equations (10)–(12) are employed towards estimating composite principal components (CPC), and sequential tables are depicted in Tables 12–14. Evaluated OGRG and CRC were subjected to maximization function, and therefore, their higher value is respected close to the optimal objective index. The mean response against OGRG and CRC with main effect plot, S/N plot, interaction plot, matrix plot, and residual plots are depicted in Figures 7–10 and Figures 11–14, respectively.Figure 7
Interaction plot for the composite principal component.Figure 8
Matrix plot for the composite principal component.Figure 9
Interaction plot for overall grey relational grade (OGRG).Figure 10
Matrix plot for overall grey relational grade (OGRG).Table 12
Principal componentψj for L27 OA experimental observations.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1 (1st PC)−0.414840.461940.77318−0.184030.357180.419050.070320.296800.19018−0.153240.311000.33866−0.002820.608240.693360.358720.855710.72844−0.138900.283140.329510.030120.313210.483340.256860.538650.88861ψ2 (2nd PC)−0.55547−0.27027−0.15886−0.70430−0.23583−0.09294−0.32774−0.16474−0.17979−0.31664−0.29907−0.13699−0.23188−0.68027−0.84864−0.20054−0.34162−0.21551−0.29394−0.15086−0.37607−0.13539−0.10702−0.46145−0.31615−0.16828−0.48658ψ3 (3rd PC)0.734340.502230.686060.663440.313160.408900.205990.319780.178360.522110.210120.284470.447560.300560.153960.482490.655930.578430.494930.424850.151550.241340.335190.213940.612440.641390.59272Table 13
(Analysis of covariance matrix) eigen values, eigenvectors, accountability proportion (AP) and cumulative accountability proportion (CAP) computed for EDM major quality measures.
Principle componentψ1ψ2ψ3Eigen vectors(−0.527, 0.445, 0.724)(−0.476, −0.860, 0.183)(0.705, −0.248, 0.655)Eigen value0.108260.038170.03426AP0.5990.2110.190CAP0.5990.811.00Table 14
Composite principal componentψ for EDMed machining characteristics and corresponding S/N ratios.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1.009900.733941.045810.984920.530340.592820.393440.466360.316710.629560.479920.463010.504070.960761.106640.633791.131010.954810.592150.532380.522470.278360.471070.701660.735530.854311.17375S/N ratio0.08554−2.686750.38904−0.13199−5.50885−4.54157−8.10248−6.62566−9.98679−4.01930−6.37669−6.68815−5.95022−0.347700.88011−3.961091.06935−0.40170−4.55130−5.47556−5.63878−11.10799−6.53833−3.07749−2.66795−1.367721.39153Figure 11
Main effect plot and S/N plot for overall grey relational grade (OGRG).Figure 12
Residual plots for overall grey relational grade (OGRG).Figure 13
Main effect plot and S/N plot for composite principal component.Figure 14
Residual plots for the composite principal component.The total mean of OGRG and CRC for each level of parameter is computed and depicted in Tables15 and 16, respectively. Figures 11–14 resulted the optimal parametric setting such as Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1.Table 15
Response table (mean) for grey relational grade.
Grey Relational GradeParametersSgVgTonToffIpSfDcDiLevel 10.585500.567610.613910.659760.569500.591160.644660.59279Level 20.604910.563020.599870.601240.597350.583980.564890.58873Level 30.575650.635430.552280.505060.599210.590910.556500.58454Delta0.029260.072400.061640.154690.029700.007180.088160.00826Mean ofγi  = 0.58869Delta = range, i.e., maximum – minimum.Table 16
Response table (mean) for composite principal componentψ.
Composite Principal ComponentParametersSgVgTonToffIpSfDcDiLevel 10.674910.667680.773370.902750.640190.752270.817540.78716Level 20.762620.681180.716020.719410.684450.65510.651240.66209Level 30.65130.739970.599440.466670.764190.681450.620060.63958Delta0.111320.072280.173930.436070.1240.097170.197480.14758Mean ofψ = 0.69628Delta = range, i.e., maximum – minimum.


#### 4.2.2. Analysis of Variance (ANOVA)

After assurance or confirmatory against evaluated/predicted optimal condition among multiple input parameters, the authors focused on evaluating the effectual and significant (important) input among multiple input parameters and is called as factor (input parameters) analysis. The authors’ fruitfully adapted analysis of variance (ANOVA) statistical model. ANOVA assisted the authors to interpret the output responses (data) for evaluating the most significance input parameters. The evaluation of most important input guides the EDM operator to focus and control more the identified most important input, as low controlling or nonstrong traceability on identified input might cause the bad quality of goods. The total variability of the global desirably value is measured by sum of squared deviations about the grand mean of global desirability value is shown as follows. Thus,(13)SST=SSF+SSE,SST=∑j=1pγj−γm2.where SST = total sum of squared deviations about the mean, γj  = jth experiment mean response, γm  = grand mean of the response, P = number of experiments in the orthogonal array, SSF = sum of squared deviations due to each factor, and SSE = sum of squared deviations due to error.In ANOVA table mean square deviation is defined as(14)SS=SSsum of squared deviationDFdegree of freedom.F-value of Fisher’s F ratio (variance ratio) is defined as(15)F=MS of a termMS for the error term.Equations (13)–(16) are employed for estimating ANOVA for OGRG and CPC are shown in Tables 17 and 18, respectively. After assessing the F value, probability of significance, i.e., p value is determined and estimated by MINITAB-16 software release 13.1. It is probed that p value for pulse off time is found such as 0.005 and 0.001 corresponding to OGRG and CPC, respectively.Table 17
ANOVA forγi using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.0039910.0039910.0019960.350.712Vg20.0295850.0295850.0147932.610.123Ton20.0187830.0187830.0093921.650.239Toff20.1098100.1098100.0549059.670.005Ip20.0049840.0049840.0024920.440.656Sf20.0002990.0002990.0001490.030.974Dc20.0426190.0426190.0213093.750.061Di20.0003070.0003070.0001530.030.973Error100.0567510.0567510.005675Total260.267129Table 18
ANOVA for composite principal componentψ using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.061930.061930.030961.050.385Vg20.026590.026590.013290.450.649Ton20.141390.141390.070702.400.141Toff20.862940.862940.4314714.640.001Ip20.071070.071070.035541.210.339Sf20.045460.045460.022730.770.488Dc20.202880.202880.101443.440.073Di20.113780.113780.056891.930.195Error100.294640.294640.02946Total261.82067Therefore, it is ascertained and marked that pulse off time is the key significant among multiple input parameters. In addition to that depth of cut is found the second significant input parameter, while the influences of other six factors were found insignificant. Furthermore, proportion of contribution encountered by each process parameters is also estimated for both T-GRA AND T-PCA and tabulated in Table19.Table 19
Proportion of contribution encountered by the process parameters.
ParametersUnitγMRPIGRGψMRPIPCAAdj SSPercentage contribution (%)Adj SSPercentage contribution (%)Spark gapmm0.003991.490.061933.40Gap voltagev0.0295911.080.026591.46Pulse on timeµs0.018787.030.141397.77Pulse off timeµs0.1098141.110.8629447.40Peak currentamp0.004981.870.071073.90Servo feedmm/min0.00030.110.045462.50Depth of cutMm0.0426215.950.2028811.14Difficulty index—0.000310.110.113786.25


#### 4.2.3. Confirmatory Experiment and Validation

After determining the optimal process conditions/parametric setting of EDMed Inconel 825 material, the authors were not potentially sure to implement and install evaluated optimal parametric setting for machining on EDM. Therefore, the authors reconducted one more experiment on same material to confirm the obtained optimal parametric setting, i.e.,Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1. Thereafter, the contrast between the obtained results and the predicted theoretical results is critically audited by employing (16), as shown in Tables 20 and 21. The estimated index γ∧ of the optimal parametric setting of the design parameters is calculated as(16)γ∧=γm+∑i=10γi−−γm,where γm and γi− expressed the total means and mean at the optimal level, corresponding to GRG and CPC as well. 0 expressed the number of core design parameters might be responsive for good and poor quality characteristics of work part. After statistical interpretation and analysis, it is determined that there is the best synergy and compliance among OGRG and CPC. It is concluded that the proposed models are valid to evaluate the optimal parametric setting amongst multiple input parameters in addressing the multiple objectives/responses.Table 20
Results of confirmatory experiment for overall grey relational grade (OGRG).
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofγMRPIGRG−4.46315−1.71286−2.48370γMRPIGRG0.598190.821030.75130Improvement inγMRPIGRG = 0.16262.Table 21
Results of confirmatory experiment for composite principal componentψ.
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofψMRPIPCA0.085543.081870.34283ψMRPIPCA1.009901.425921.04026Improvement inψMRPIPCA = 0.34398.


## 4.1. Detail of Experimental Setup and Problem Formulation

In current investigation, experiments are robustly conducted upon EDM using Inconel 825 material specimen Both the mechanical properties and chemical composition of composed Inconel 825 are tabulated in Tables1 and 2, respectively.Table 1
Chemical composition of Inconel 825 properties.
Chemical compositionElementSNiCuAlCrSiFeMnTiMoCWeight (%)0.0338–461.5–3.00.219.5–23.50.52210.6–1.22.5–3.50.05Table 2
Mechanical properties of Inconel 825.
Mechanical propertiesPropertiesModulus of elasticityMelting pointDensityCoefficient of expansionThermal conductivityModulus of rigidityPoisson’s ratioSpecific heatTensile strengthValues196 kN/mm21400°C8.14 g/cm314.0 m/m/°C (20–100°C)12.3 W/moC at 100°C75.9 N/mm20.29440 Joules/kg-C550 N/mm2To conduct experiments, the authors availed the EDM setup (manufacturer: Electronica India Limited, model no: Electronica Electrapuls PS 50ZNC), provided by Central Institute of Petrochemicals Engineering and Technology (CIPET), Raipur, C.G, India. The specification of EDM setup is tabulated in Table3. Figure 3 depicts the flow chart of conducted experiments for EDMed Inconel 825 specimen. To attain the high degree of precision in experiments, it was highly concern to assess irregularities or roughness of electrode’s bottom surface.Table 3
Specification of EDM setup.
Item (s)Value/rangeItem (s)Value/rangeMounting surface (length × width)600 × 400 mmMaximum work piece height250 mmWidth of the work tank900 mmMaximum job weight50 kgDepth of the work tank600 mmHeight of the work tank400 mmX-axis travel400 mmCurrent range (Ip)0–50 AY-axis travel300 mmPulse on time range (ton)0.5–3000μsTransverse (X,Y, Z)400, 300, 250 mmDuty factor range (τ)8–100%Open circuit voltage range (Vg)0–100 VFigure 3
Flow chart of conducted experimental research for EDMed Inconel 825 material.The copper was prioritized as a tool material which was having surface irregularities and is requisite for machining. Copper electrode (dimensions: diameter 10 mm and length 35 mm) along with its mechanical properties and images at various orientations and stages are depicted in Table4 and Figure 4, respectively. The work piece size of 150∗100∗10 mm (length∗width∗thickness) was employed for experiments.Table 4
Mechanical properties of pure copper electrode.
Physical propertiesElectrical resistivity (μΩ/cm)Thermal conductivity (W/m·K)Melting point (°C)Specific gravity at 20°C (g/cc)Density (g/cc)Value1.96268.38910838.98.92Figure 4
Electrode images at various stages. (a) Image of requisite machining performed on lathe on copper tool electrode. (b) Image of copper tool electrode after requisite machining performed and before starting experiment 1.
(a)(b)Prior to conduct the experiments on EDM, initial weight of copper electrode and Inconel 825 specimen was measured by executing the Chemico Complete Lab Ware White Weighing Scale (digital capacity: 200gm, accuracy: 1 mg). The weight of electrode and work piece was found as 60.91 gm and 785.24 gm, respectively. Commercial grade EDM oil at freezing point = 94°C and specific gravity = 0.763 was employed as dielectric fluid with a constant flushing pressure of Fp = 2.1 bar in the EDM operation. Work piece and electrode has been kept at a positive and negative polarity, respectively, throughout the experimentation.After finishing the aforesaid prerequisite, the process parameters optimization problem is formulated or machinability assessing index was framed. The experiments were conducted on EDMed Inconel 825 specimen with considering eight controllable EDM input process parameters, i.e., spark gap (Sg), gap voltage (Vg), pulse on time (Ton), pulse off time (Toff), peak current (Ip), servo feed (Sf), depth of cut (Dc), and difficulty index (Di). Each input parameter is varied at three discrete levels as shown in Table5. The authors are supposed to conduct many experiments under compliance of the full factorial rule for optimizing inputs. But because of many challenges and constraints, i.e., framing more specimens, time, operating cost, and machining cost, the authors evaluated the twenty-seven (27) experiments by executing the statistical Taguchi’s based L27 orthogonal array model. The total number of 27 experiments to be conducted corresponding to eight controllable EDM input process parameters at three discrete levels are shown in Table 6. Figure 5 shows the images for experiment 1 and 2, after data entry of process parameters into control panel or computer, embedded with EDM machine.Table 5
Domain of experiments: bounded machining process parameters.
ParametersSpark gapGap voltagePulse on timePulse off timePeak currentServo feedDepth of cutDifficulty indexNotations(Sg)(Vg)(Ton)(Toff)(Ip)(Sf)(Dc)(Di)Unitsmmvμsμsampmm/minmm—Level of variations10.05255001015400.53020.0755075020306016030.17510003045801.590Table 6
Taguchi’sL27 orthogonal array structure.
Exp no.Spark gap (Sg)Gap voltage (Vg)Pulse on time (Ton)Pulse off Time (Toff)Peak current (Ip)Servo feed (Sf)Depth of cut (Dc)Difficulty index (Di)δ10.05255001015400.530δ20.0525500103060160δ30.05255001045801.590δ40.05507502015400.560δ50.0550750203060190δ60.05507502045801.530δ70.057510003015400.590δ80.05751000303060130δ90.057510003045801.560δ100.075257503015601.530δ110.075257503030800.560δ120.07525750304540190δ130.0755010001015601.560δ140.0755010001030800.590δ150.075501000104540130δ160.075755002015601.590δ170.075755002030800.530δ180.07575500204540160δ190.1251000201580130δ200.12510002030401.560δ210.12510002045600.590δ220.150500301580160δ230.1505003030401.590δ240.1505003045600.530δ250.175750101580190δ260.1757501030401.530δ270.1757501045600.560Figure 5
Images showing details of experimentation 1 and experimentation 2. (a) Experiment 1 (run 1). (b) Experiment 2 (run 2).
(a)(b)The responses/objectives, i.e., power consumption, machining time, and material removal rate corresponding to entered inputs parameters are tabulated in Table7. After performing the twenty-seven experiments, the captured image of EDMed Inconel 825 specimen is depicted in Figure 6. The presented research has intention to determine the effective conditions of favorable input process parameters for Inconel 825, which might aid the manufacturers for producing their products at least cost with high production.Table 7
Design of experiment (L27) orthogonal array and collected response experimental data.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Power consumption (KW)1.1254.6257.1001.2507.6259.7504.2507.50010.0001.8758.75012.5002.6255.1507.5004.5006.2258.5002.0005.0009.8755.1259.0009.5002.5004.4386.000Machining time (min)6.9002.4502.4802.1302.7004.6702.9203.9503.93010.3002.2303.8808.8300.9800.7653.6201.5002.10011.2705.1201.77010.9805.1901.3703.2803.4201.150MRR (mg/min)32.394232.653370.96867.265159.259209.85048.077149.36783.96966.990116.592153.84695.130193.878168.831204.420373.333328.00065.661172.862101.69559.199161.654153.285201.22295.322356.522Figure 6
Images of EDMed Work piece after completion of 27 experimentation.
(a)(b)


## 4.2. Parametric Optimization of EDMed Inconel 825

### 4.2.1. Evaluation of Optimal Process Condition

It is undoubtedly required to convert the multiobjective responses into single response, i.e., multiresponse performance indicator (MRPI) in order to calculate the optimal process condition. To transform the variety of dimensions of investigational data into comparable platform, (4) and (5) are employed in the case of grey relational analysis, whereas (9) is applied in the case of principal component analysis.After computing single response/MRPI, the authors executed equations (6)–(8) towards estimating the overall grey relational grade (OGRG), and the sequential tables are depicted in Tables 8–11.Table 8
Assessment of Δ0i for each of the responses.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc0.00000.30770.52530.01100.57140.75820.27470.56040.78020.06590.67031.00000.13190.35380.56040.29670.44840.64840.07690.34070.76920.35160.69230.73630.12090.29120.4286Mt0.58400.16040.16330.12990.18420.37170.20510.30320.30130.90770.13950.29650.76770.02050.00000.27180.07000.12711.00000.41460.09570.97240.42120.05760.23940.25270.0366MRR1.00000.41260.00690.89770.62790.47950.95400.65690.84870.89850.75300.64380.81600.52640.59980.49540.00000.13300.90240.58800.79670.92140.62090.64540.50480.22880.0493Table 9
Grey relational coefficientξi (k) of each machining characteristics (with ψ = 0.5).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.00000.61900.48770.97850.46670.39740.64540.47150.39060.88350.42720.33330.79130.58560.47150.62760.52720.43540.86670.59480.39390.58710.41940.40440.80530.63190.5385Mt0.46130.75710.75390.79370.73080.57360.70910.62250.62400.35520.78190.62770.39440.96071.00000.64790.87720.79730.33330.54670.83940.33960.54280.89670.67620.66420.9317MRR0.33330.54790.98630.35770.44330.51050.34390.43220.37070.35750.39900.43710.37990.48720.45460.50231.00000.78990.35650.45960.38560.35180.44610.43650.49760.6860.9102Table 10
Data preprocessing of each machining characteristic (grey relational generation).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.0000.6920.4750.9890.4290.2420.7250.4400.2200.9340.3300.0000.8680.6460.4400.7030.5520.3520.9230.6590.2310.6480.3080.2640.8790.7090.571Mt0.4160.8400.8370.8700.8160.6280.7950.6970.6990.0920.8610.7030.2320.9801.0000.7280.9300.8730.0000.5850.9040.0280.5790.9420.7610.7470.963MRR0.0000.5870.9930.1020.3720.5200.0460.3430.1510.1010.2470.3560.1840.4740.4000.5051.0000.8670.0980.4120.2030.0790.3790.3550.4950.7710.951Table 11
Grey relational grade.γi
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Grey relational gradeγi0.598190.641340.742610.709980.546920.493800.566120.508740.461760.532070.536060.466070.521880.677810.642040.592580.801490.674230.518840.533680.539640.426150.469400.579230.659710.660740.79347S/N ratio (higher-the-better)−4.46315−3.85817−2.58473−2.97504−5.24156−6.12890−4.94190−5.87016−6.71170−5.48061−5.41578−6.63098−5.64852−3.37787−3.84875−4.54508−1.92202−3.42387−5.69930−5.45438−5.35794−7.40875−6.56920−4.74303−3.61296−3.59933−2.00942Moreover, equations (10)–(12) are employed towards estimating composite principal components (CPC), and sequential tables are depicted in Tables 12–14. Evaluated OGRG and CRC were subjected to maximization function, and therefore, their higher value is respected close to the optimal objective index. The mean response against OGRG and CRC with main effect plot, S/N plot, interaction plot, matrix plot, and residual plots are depicted in Figures 7–10 and Figures 11–14, respectively.Figure 7
Interaction plot for the composite principal component.Figure 8
Matrix plot for the composite principal component.Figure 9
Interaction plot for overall grey relational grade (OGRG).Figure 10
Matrix plot for overall grey relational grade (OGRG).Table 12
Principal componentψj for L27 OA experimental observations.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1 (1st PC)−0.414840.461940.77318−0.184030.357180.419050.070320.296800.19018−0.153240.311000.33866−0.002820.608240.693360.358720.855710.72844−0.138900.283140.329510.030120.313210.483340.256860.538650.88861ψ2 (2nd PC)−0.55547−0.27027−0.15886−0.70430−0.23583−0.09294−0.32774−0.16474−0.17979−0.31664−0.29907−0.13699−0.23188−0.68027−0.84864−0.20054−0.34162−0.21551−0.29394−0.15086−0.37607−0.13539−0.10702−0.46145−0.31615−0.16828−0.48658ψ3 (3rd PC)0.734340.502230.686060.663440.313160.408900.205990.319780.178360.522110.210120.284470.447560.300560.153960.482490.655930.578430.494930.424850.151550.241340.335190.213940.612440.641390.59272Table 13
(Analysis of covariance matrix) eigen values, eigenvectors, accountability proportion (AP) and cumulative accountability proportion (CAP) computed for EDM major quality measures.
Principle componentψ1ψ2ψ3Eigen vectors(−0.527, 0.445, 0.724)(−0.476, −0.860, 0.183)(0.705, −0.248, 0.655)Eigen value0.108260.038170.03426AP0.5990.2110.190CAP0.5990.811.00Table 14
Composite principal componentψ for EDMed machining characteristics and corresponding S/N ratios.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1.009900.733941.045810.984920.530340.592820.393440.466360.316710.629560.479920.463010.504070.960761.106640.633791.131010.954810.592150.532380.522470.278360.471070.701660.735530.854311.17375S/N ratio0.08554−2.686750.38904−0.13199−5.50885−4.54157−8.10248−6.62566−9.98679−4.01930−6.37669−6.68815−5.95022−0.347700.88011−3.961091.06935−0.40170−4.55130−5.47556−5.63878−11.10799−6.53833−3.07749−2.66795−1.367721.39153Figure 11
Main effect plot and S/N plot for overall grey relational grade (OGRG).Figure 12
Residual plots for overall grey relational grade (OGRG).Figure 13
Main effect plot and S/N plot for composite principal component.Figure 14
Residual plots for the composite principal component.The total mean of OGRG and CRC for each level of parameter is computed and depicted in Tables15 and 16, respectively. Figures 11–14 resulted the optimal parametric setting such as Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1.Table 15
Response table (mean) for grey relational grade.
Grey Relational GradeParametersSgVgTonToffIpSfDcDiLevel 10.585500.567610.613910.659760.569500.591160.644660.59279Level 20.604910.563020.599870.601240.597350.583980.564890.58873Level 30.575650.635430.552280.505060.599210.590910.556500.58454Delta0.029260.072400.061640.154690.029700.007180.088160.00826Mean ofγi  = 0.58869Delta = range, i.e., maximum – minimum.Table 16
Response table (mean) for composite principal componentψ.
Composite Principal ComponentParametersSgVgTonToffIpSfDcDiLevel 10.674910.667680.773370.902750.640190.752270.817540.78716Level 20.762620.681180.716020.719410.684450.65510.651240.66209Level 30.65130.739970.599440.466670.764190.681450.620060.63958Delta0.111320.072280.173930.436070.1240.097170.197480.14758Mean ofψ = 0.69628Delta = range, i.e., maximum – minimum.


### 4.2.2. Analysis of Variance (ANOVA)

After assurance or confirmatory against evaluated/predicted optimal condition among multiple input parameters, the authors focused on evaluating the effectual and significant (important) input among multiple input parameters and is called as factor (input parameters) analysis. The authors’ fruitfully adapted analysis of variance (ANOVA) statistical model. ANOVA assisted the authors to interpret the output responses (data) for evaluating the most significance input parameters. The evaluation of most important input guides the EDM operator to focus and control more the identified most important input, as low controlling or nonstrong traceability on identified input might cause the bad quality of goods. The total variability of the global desirably value is measured by sum of squared deviations about the grand mean of global desirability value is shown as follows. Thus,(13)SST=SSF+SSE,SST=∑j=1pγj−γm2.where SST = total sum of squared deviations about the mean, γj  = jth experiment mean response, γm  = grand mean of the response, P = number of experiments in the orthogonal array, SSF = sum of squared deviations due to each factor, and SSE = sum of squared deviations due to error.In ANOVA table mean square deviation is defined as(14)SS=SSsum of squared deviationDFdegree of freedom.F-value of Fisher’s F ratio (variance ratio) is defined as(15)F=MS of a termMS for the error term.Equations (13)–(16) are employed for estimating ANOVA for OGRG and CPC are shown in Tables 17 and 18, respectively. After assessing the F value, probability of significance, i.e., p value is determined and estimated by MINITAB-16 software release 13.1. It is probed that p value for pulse off time is found such as 0.005 and 0.001 corresponding to OGRG and CPC, respectively.Table 17
ANOVA forγi using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.0039910.0039910.0019960.350.712Vg20.0295850.0295850.0147932.610.123Ton20.0187830.0187830.0093921.650.239Toff20.1098100.1098100.0549059.670.005Ip20.0049840.0049840.0024920.440.656Sf20.0002990.0002990.0001490.030.974Dc20.0426190.0426190.0213093.750.061Di20.0003070.0003070.0001530.030.973Error100.0567510.0567510.005675Total260.267129Table 18
ANOVA for composite principal componentψ using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.061930.061930.030961.050.385Vg20.026590.026590.013290.450.649Ton20.141390.141390.070702.400.141Toff20.862940.862940.4314714.640.001Ip20.071070.071070.035541.210.339Sf20.045460.045460.022730.770.488Dc20.202880.202880.101443.440.073Di20.113780.113780.056891.930.195Error100.294640.294640.02946Total261.82067Therefore, it is ascertained and marked that pulse off time is the key significant among multiple input parameters. In addition to that depth of cut is found the second significant input parameter, while the influences of other six factors were found insignificant. Furthermore, proportion of contribution encountered by each process parameters is also estimated for both T-GRA AND T-PCA and tabulated in Table19.Table 19
Proportion of contribution encountered by the process parameters.
ParametersUnitγMRPIGRGψMRPIPCAAdj SSPercentage contribution (%)Adj SSPercentage contribution (%)Spark gapmm0.003991.490.061933.40Gap voltagev0.0295911.080.026591.46Pulse on timeµs0.018787.030.141397.77Pulse off timeµs0.1098141.110.8629447.40Peak currentamp0.004981.870.071073.90Servo feedmm/min0.00030.110.045462.50Depth of cutMm0.0426215.950.2028811.14Difficulty index—0.000310.110.113786.25


### 4.2.3. Confirmatory Experiment and Validation

After determining the optimal process conditions/parametric setting of EDMed Inconel 825 material, the authors were not potentially sure to implement and install evaluated optimal parametric setting for machining on EDM. Therefore, the authors reconducted one more experiment on same material to confirm the obtained optimal parametric setting, i.e.,Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1. Thereafter, the contrast between the obtained results and the predicted theoretical results is critically audited by employing (16), as shown in Tables 20 and 21. The estimated index γ∧ of the optimal parametric setting of the design parameters is calculated as(16)γ∧=γm+∑i=10γi−−γm,where γm and γi− expressed the total means and mean at the optimal level, corresponding to GRG and CPC as well. 0 expressed the number of core design parameters might be responsive for good and poor quality characteristics of work part. After statistical interpretation and analysis, it is determined that there is the best synergy and compliance among OGRG and CPC. It is concluded that the proposed models are valid to evaluate the optimal parametric setting amongst multiple input parameters in addressing the multiple objectives/responses.Table 20
Results of confirmatory experiment for overall grey relational grade (OGRG).
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofγMRPIGRG−4.46315−1.71286−2.48370γMRPIGRG0.598190.821030.75130Improvement inγMRPIGRG = 0.16262.Table 21
Results of confirmatory experiment for composite principal componentψ.
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofψMRPIPCA0.085543.081870.34283ψMRPIPCA1.009901.425921.04026Improvement inψMRPIPCA = 0.34398.


## 4.2.1. Evaluation of Optimal Process Condition

It is undoubtedly required to convert the multiobjective responses into single response, i.e., multiresponse performance indicator (MRPI) in order to calculate the optimal process condition. To transform the variety of dimensions of investigational data into comparable platform, (4) and (5) are employed in the case of grey relational analysis, whereas (9) is applied in the case of principal component analysis.After computing single response/MRPI, the authors executed equations (6)–(8) towards estimating the overall grey relational grade (OGRG), and the sequential tables are depicted in Tables 8–11.Table 8
Assessment of Δ0i for each of the responses.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc0.00000.30770.52530.01100.57140.75820.27470.56040.78020.06590.67031.00000.13190.35380.56040.29670.44840.64840.07690.34070.76920.35160.69230.73630.12090.29120.4286Mt0.58400.16040.16330.12990.18420.37170.20510.30320.30130.90770.13950.29650.76770.02050.00000.27180.07000.12711.00000.41460.09570.97240.42120.05760.23940.25270.0366MRR1.00000.41260.00690.89770.62790.47950.95400.65690.84870.89850.75300.64380.81600.52640.59980.49540.00000.13300.90240.58800.79670.92140.62090.64540.50480.22880.0493Table 9
Grey relational coefficientξi (k) of each machining characteristics (with ψ = 0.5).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.00000.61900.48770.97850.46670.39740.64540.47150.39060.88350.42720.33330.79130.58560.47150.62760.52720.43540.86670.59480.39390.58710.41940.40440.80530.63190.5385Mt0.46130.75710.75390.79370.73080.57360.70910.62250.62400.35520.78190.62770.39440.96071.00000.64790.87720.79730.33330.54670.83940.33960.54280.89670.67620.66420.9317MRR0.33330.54790.98630.35770.44330.51050.34390.43220.37070.35750.39900.43710.37990.48720.45460.50231.00000.78990.35650.45960.38560.35180.44610.43650.49760.6860.9102Table 10
Data preprocessing of each machining characteristic (grey relational generation).
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Pc1.0000.6920.4750.9890.4290.2420.7250.4400.2200.9340.3300.0000.8680.6460.4400.7030.5520.3520.9230.6590.2310.6480.3080.2640.8790.7090.571Mt0.4160.8400.8370.8700.8160.6280.7950.6970.6990.0920.8610.7030.2320.9801.0000.7280.9300.8730.0000.5850.9040.0280.5790.9420.7610.7470.963MRR0.0000.5870.9930.1020.3720.5200.0460.3430.1510.1010.2470.3560.1840.4740.4000.5051.0000.8670.0980.4120.2030.0790.3790.3550.4950.7710.951Table 11
Grey relational grade.γi
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27Grey relational gradeγi0.598190.641340.742610.709980.546920.493800.566120.508740.461760.532070.536060.466070.521880.677810.642040.592580.801490.674230.518840.533680.539640.426150.469400.579230.659710.660740.79347S/N ratio (higher-the-better)−4.46315−3.85817−2.58473−2.97504−5.24156−6.12890−4.94190−5.87016−6.71170−5.48061−5.41578−6.63098−5.64852−3.37787−3.84875−4.54508−1.92202−3.42387−5.69930−5.45438−5.35794−7.40875−6.56920−4.74303−3.61296−3.59933−2.00942Moreover, equations (10)–(12) are employed towards estimating composite principal components (CPC), and sequential tables are depicted in Tables 12–14. Evaluated OGRG and CRC were subjected to maximization function, and therefore, their higher value is respected close to the optimal objective index. The mean response against OGRG and CRC with main effect plot, S/N plot, interaction plot, matrix plot, and residual plots are depicted in Figures 7–10 and Figures 11–14, respectively.Figure 7
Interaction plot for the composite principal component.Figure 8
Matrix plot for the composite principal component.Figure 9
Interaction plot for overall grey relational grade (OGRG).Figure 10
Matrix plot for overall grey relational grade (OGRG).Table 12
Principal componentψj for L27 OA experimental observations.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1 (1st PC)−0.414840.461940.77318−0.184030.357180.419050.070320.296800.19018−0.153240.311000.33866−0.002820.608240.693360.358720.855710.72844−0.138900.283140.329510.030120.313210.483340.256860.538650.88861ψ2 (2nd PC)−0.55547−0.27027−0.15886−0.70430−0.23583−0.09294−0.32774−0.16474−0.17979−0.31664−0.29907−0.13699−0.23188−0.68027−0.84864−0.20054−0.34162−0.21551−0.29394−0.15086−0.37607−0.13539−0.10702−0.46145−0.31615−0.16828−0.48658ψ3 (3rd PC)0.734340.502230.686060.663440.313160.408900.205990.319780.178360.522110.210120.284470.447560.300560.153960.482490.655930.578430.494930.424850.151550.241340.335190.213940.612440.641390.59272Table 13
(Analysis of covariance matrix) eigen values, eigenvectors, accountability proportion (AP) and cumulative accountability proportion (CAP) computed for EDM major quality measures.
Principle componentψ1ψ2ψ3Eigen vectors(−0.527, 0.445, 0.724)(−0.476, −0.860, 0.183)(0.705, −0.248, 0.655)Eigen value0.108260.038170.03426AP0.5990.2110.190CAP0.5990.811.00Table 14
Composite principal componentψ for EDMed machining characteristics and corresponding S/N ratios.
δiδ1δ2δ3δ4δ5δ6δ7δ8δ9δ10δ11δ12δ13δ14δ15δ16δ17δ18δ19δ20δ21δ22δ23δ24δ25δ26δ27ψ1.009900.733941.045810.984920.530340.592820.393440.466360.316710.629560.479920.463010.504070.960761.106640.633791.131010.954810.592150.532380.522470.278360.471070.701660.735530.854311.17375S/N ratio0.08554−2.686750.38904−0.13199−5.50885−4.54157−8.10248−6.62566−9.98679−4.01930−6.37669−6.68815−5.95022−0.347700.88011−3.961091.06935−0.40170−4.55130−5.47556−5.63878−11.10799−6.53833−3.07749−2.66795−1.367721.39153Figure 11
Main effect plot and S/N plot for overall grey relational grade (OGRG).Figure 12
Residual plots for overall grey relational grade (OGRG).Figure 13
Main effect plot and S/N plot for composite principal component.Figure 14
Residual plots for the composite principal component.The total mean of OGRG and CRC for each level of parameter is computed and depicted in Tables15 and 16, respectively. Figures 11–14 resulted the optimal parametric setting such as Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1.Table 15
Response table (mean) for grey relational grade.
Grey Relational GradeParametersSgVgTonToffIpSfDcDiLevel 10.585500.567610.613910.659760.569500.591160.644660.59279Level 20.604910.563020.599870.601240.597350.583980.564890.58873Level 30.575650.635430.552280.505060.599210.590910.556500.58454Delta0.029260.072400.061640.154690.029700.007180.088160.00826Mean ofγi  = 0.58869Delta = range, i.e., maximum – minimum.Table 16
Response table (mean) for composite principal componentψ.
Composite Principal ComponentParametersSgVgTonToffIpSfDcDiLevel 10.674910.667680.773370.902750.640190.752270.817540.78716Level 20.762620.681180.716020.719410.684450.65510.651240.66209Level 30.65130.739970.599440.466670.764190.681450.620060.63958Delta0.111320.072280.173930.436070.1240.097170.197480.14758Mean ofψ = 0.69628Delta = range, i.e., maximum – minimum.


## 4.2.2. Analysis of Variance (ANOVA)

After assurance or confirmatory against evaluated/predicted optimal condition among multiple input parameters, the authors focused on evaluating the effectual and significant (important) input among multiple input parameters and is called as factor (input parameters) analysis. The authors’ fruitfully adapted analysis of variance (ANOVA) statistical model. ANOVA assisted the authors to interpret the output responses (data) for evaluating the most significance input parameters. The evaluation of most important input guides the EDM operator to focus and control more the identified most important input, as low controlling or nonstrong traceability on identified input might cause the bad quality of goods. The total variability of the global desirably value is measured by sum of squared deviations about the grand mean of global desirability value is shown as follows. Thus,(13)SST=SSF+SSE,SST=∑j=1pγj−γm2.where SST = total sum of squared deviations about the mean, γj  = jth experiment mean response, γm  = grand mean of the response, P = number of experiments in the orthogonal array, SSF = sum of squared deviations due to each factor, and SSE = sum of squared deviations due to error.In ANOVA table mean square deviation is defined as(14)SS=SSsum of squared deviationDFdegree of freedom.F-value of Fisher’s F ratio (variance ratio) is defined as(15)F=MS of a termMS for the error term.Equations (13)–(16) are employed for estimating ANOVA for OGRG and CPC are shown in Tables 17 and 18, respectively. After assessing the F value, probability of significance, i.e., p value is determined and estimated by MINITAB-16 software release 13.1. It is probed that p value for pulse off time is found such as 0.005 and 0.001 corresponding to OGRG and CPC, respectively.Table 17
ANOVA forγi using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.0039910.0039910.0019960.350.712Vg20.0295850.0295850.0147932.610.123Ton20.0187830.0187830.0093921.650.239Toff20.1098100.1098100.0549059.670.005Ip20.0049840.0049840.0024920.440.656Sf20.0002990.0002990.0001490.030.974Dc20.0426190.0426190.0213093.750.061Di20.0003070.0003070.0001530.030.973Error100.0567510.0567510.005675Total260.267129Table 18
ANOVA for composite principal componentψ using adjusted SS for tests.
SourceDFSequential SSAdj SSAdj MSFpSg20.061930.061930.030961.050.385Vg20.026590.026590.013290.450.649Ton20.141390.141390.070702.400.141Toff20.862940.862940.4314714.640.001Ip20.071070.071070.035541.210.339Sf20.045460.045460.022730.770.488Dc20.202880.202880.101443.440.073Di20.113780.113780.056891.930.195Error100.294640.294640.02946Total261.82067Therefore, it is ascertained and marked that pulse off time is the key significant among multiple input parameters. In addition to that depth of cut is found the second significant input parameter, while the influences of other six factors were found insignificant. Furthermore, proportion of contribution encountered by each process parameters is also estimated for both T-GRA AND T-PCA and tabulated in Table19.Table 19
Proportion of contribution encountered by the process parameters.
ParametersUnitγMRPIGRGψMRPIPCAAdj SSPercentage contribution (%)Adj SSPercentage contribution (%)Spark gapmm0.003991.490.061933.40Gap voltagev0.0295911.080.026591.46Pulse on timeµs0.018787.030.141397.77Pulse off timeµs0.1098141.110.8629447.40Peak currentamp0.004981.870.071073.90Servo feedmm/min0.00030.110.045462.50Depth of cutMm0.0426215.950.2028811.14Difficulty index—0.000310.110.113786.25


## 4.2.3. Confirmatory Experiment and Validation

After determining the optimal process conditions/parametric setting of EDMed Inconel 825 material, the authors were not potentially sure to implement and install evaluated optimal parametric setting for machining on EDM. Therefore, the authors reconducted one more experiment on same material to confirm the obtained optimal parametric setting, i.e.,Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1. Thereafter, the contrast between the obtained results and the predicted theoretical results is critically audited by employing (16), as shown in Tables 20 and 21. The estimated index γ∧ of the optimal parametric setting of the design parameters is calculated as(16)γ∧=γm+∑i=10γi−−γm,where γm and γi− expressed the total means and mean at the optimal level, corresponding to GRG and CPC as well. 0 expressed the number of core design parameters might be responsive for good and poor quality characteristics of work part. After statistical interpretation and analysis, it is determined that there is the best synergy and compliance among OGRG and CPC. It is concluded that the proposed models are valid to evaluate the optimal parametric setting amongst multiple input parameters in addressing the multiple objectives/responses.Table 20
Results of confirmatory experiment for overall grey relational grade (OGRG).
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofγMRPIGRG−4.46315−1.71286−2.48370γMRPIGRG0.598190.821030.75130Improvement inγMRPIGRG = 0.16262.Table 21
Results of confirmatory experiment for composite principal componentψ.
Initial factor settingOptimal process conditionPredictionExperimentLevel of factorsSg1Vg1Ton1Toff1 Ip1Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1Di1Sg2Vg3Ton1Toff1 Ip3Sf1Dc1DiPower consumption (Pc)1.1256.125Machining time (Mt)6.9001.950Material removal rate (MRR)32.394355.610S/N ratio ofψMRPIPCA0.085543.081870.34283ψMRPIPCA1.009901.425921.04026Improvement inψMRPIPCA = 0.34398.


## 5. Analysis of Surface Topography

After, evaluation of optimal process condition, confirmatory test and ANOVA analysis, the authors acted to investigate the topography of the machined surface of EDMed Inconel 825 specimen using an Optical Microscope (Model-Carl Zeiss Microscope AXIO). The investigation of work part topography aids the authors to redesign the inputs and adapt the other robust optimal process condition evaluation models. To investigate topography, at first, preliminary invigilation is conducted on evaluated initial parametric settingSg1Vg1Ton1Toff1Ip1Sf1Dc1Di1 which had low value of constrained process parameters for the evaluation of metallurgical structure and cracks. It has been found that initial parametric setting will have an acceptable metallurgical structure and crack. Tiny or very small amount of microvoids, resolidified debris, droplets, and molten pool are examined and depicted in Figure 15. Moreover, increasing value of spark gap allows vast amount of electrical current transferred to the work piece and results in higher thermal energy generation at projected surface which ultimately results in high material removal and lower machining time. However, on the other hand, it increases the deep craters and deposition of molten metal along with tendency of more crack formation on the machined surface as depicted in Figure 16 for parametric setting Sg3Vg1Ton3Toff2Ip1Sf3Dc2Di1.Figure 15
Analysis of surface topography for experimental run 1 using the initial parametric.Figure 16
Analysis of surface topography for experimental run 19 using the parametric setting.Moreover, it is also observed from surface topography snapshots analysis that increased value in peak current also allowed enormous amount of thermal energy on the work piece that results in the generation of spherical globules and acceleration in molten metal deposition. Hence, in order to trim down these irregularities, the authors advised to increase the dielectric flashing circulation pressure in conjunction with increased value of process parameters as in present investigation, it was set at constant Fp = 2.1 bar. Also, increase in gap voltage results in spacious gap between the electrode and work piece, which delivers the extra efficient flushing rate of melted metal and debris. Hence, in the present investigation, the surface topography reconfirmed the results of ANOVA analysis, it is recertified that pulse off time as well as depth of cut broadly enhanced the surface integrity of the EDMed surface. Parallel enhancement in both pulse off time and depth of cut results in the efficient improvement in removal of the debris and melted metal which ultimately enhance material removal rate and decrease machining time. Moreover, efficient flushing can take place during pulse off time which reduces the thermal stress on the EDMed surface that generated due to extreme heat and cooling rates.


## 6. Conclusions

EDM is searched as a challenging, dynamic, and majestic machine and has short payback period for investors. EDM became the honeywell for entire production communities industry 4.0 in the current era. In the presented research forum, Taguchi-basedL27 orthogonal array model is fruitfully adapted for conducting the experiments on Inconel 825 specimen using EDM operation. Preliminary, to conclude the reliable optimum setting among defined eight input parameters, a novel integrated Taguchi-grey relational analysis (T-GRA) and principal component analysis (T-PCA) is implemented. Two MRPIs are calculated by executing the T-GRA and T-PCA models over triple responses, i.e., Pc, Mt, and MRR. The computed MRPIs are examined for determining the optimum condition setting among eight input parameters which is found as Sg2Vg3Ton1Toff1Ip3Sf1Dc1Di1. Next, evaluated optimum setting is reconfirmed and validated with 100% assurance after conducting one more experiment on the same specimen with the same identical setup against evaluated optimum setting. The upshots of the confirmation test yielded an improvement of 0.16262 and 0.34398 corresponding to evaluated MRPIs by T-GRA and T-PCA, respectively, as a part first contribution or finding.Furthermore, the analysis of variance (ANOVA) statistical model is adapted to find the priority ratings against eight inputs. The pulse off time and depth of cut is prioritized as the first and second significant input factor, respectively, on resultedp value as 0.005, 0.001, and 0.061, 0.073 in application of T-GRA and T-PCA, respectively, respected as a part second contribution/finding. Pulse off time is found as a most significant parameter by both T-GRA and T-PCA methodologies, where T-GRA reflected 41.11%% of contribution while T-PCA reflected 47.40% of contribution of pulse off time, respectively. In addition to this, the authors audited the effects of varying values of input parameters over the surface topography such as metallurgical structure, deep craters, and cracks, as discussed in Section 5; however, to overcome awful surface topography, a few remediates are proposed by authors as a part of third contribution/finding.The research works is constrained or limited up to discussed problems, namely, the optimum parameters setting, significance inputs, and surface topography evaluation problems. The problems such as linear, programmable, and alternative evaluation problems is not in the curriculum of research work. From industrial value and applications perspectives, the nontraditional material scholars and investigators can prolifically adapt the proposed insights, models, methodology to audit the same materials with different nontraditional machines such as ECM and LBM. From the future scope standing point, the proposed integrated models, T-GRA and T-PCA in conjunction with ANOVA models can be employed to investigate the smart or forthcoming materials with different nontraditional machining process/operations. From the point of interdisciplinary view, the same protocol of the proposed research forum can be executed by the researchers of chemistry, physics, civil, electronic engineering etc., realms.



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