# Comparative Study on EDM Parameter Optimization for Adsorbed Si3N4–TiN using TOPSIS and GRA Coupled with TLBO Algorithm

Authors: V. P. Srinivasan; Ch. Sandeep; C. Shanthi; A. Bovas Herbert Bejaxhin; R. Anandan; M. Abisha Meji
Journal: Adsorption Science & Technology
 (2022)

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## Abstract

Electrical discharge machining is a thermo-physical-based material removal technique. 25 combinations of process variables were formulated with the aid of Taguchi technique for EDM of adsorbed Si3N4–TiN. Machining variables like pulse current, pulse-on time, pulse-off time, dielectric pressure, and spark gap voltage varied, and impact of each variables on the performance metrics (MRR, EWR, SR, ROC, θ, CIR, and CYL) was assessed. MCDM strategies like grey relational analysis and TOPSIS are utilized to find out the ideal arrangement of machining parameters to achieve most acute productivity of the multitude of reactions. Likewise, metaheuristic algorithm in particular GRA combined with teaching-learning-based optimization algorithm is utilized for getting global optimized input factors. Important factors like pulse current, pulse-on time, and spark gap voltage characteristically affect the outputs. It is recognized that the pulse-on time and the pulse current are the most significant input factors than others. The ideal machining parameters in view of GRA and TOPSIS techniques for acquiring better output factors are I, 12 amps; PON, 7 μsec; POFF, 4 μsec; DP, 12 kg/cm2; and SV, 36 volts.


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## Body

## 1. Introduction

Thermo-physical-based material removal technique named EDM is a modern machining methodology with phenomenal capacity of noncontact machining of profoundly hard and brittle workpieces with accurate three-dimensional complex shapes. Conceivably, surface attributes of the materials can be altered by the EDM process. The predominant problem associated with electrical discharge machining is a poor surface finish. By employing compacted electrodes, particles during the machining process will be settled on the material surface and limit the microcracks, voids, recast layer, and so forth [1–3]. The electrical discharge machining process guarantees legitimate carbonation and surface heat-treatment, and a superior material hardness was acquired with an elevated peak current and reduced duty factor [4]. The electrodischarge machining of each nonconductive workpiece relies upon large variables. Nickel and carbon intensify structure harmful mixtures like Ni (CN)2 and (C5H5) NiNO. Nitrogen-containing ceramic materials (nitrides AlN, SiAlON, and Si3N4) are not being handled in hydrocarbons with a nickel holding assistive electrode [5]. Material transmits by powder metallurgy electrodes and by powder particles suspended in the dielectric liquid; these two techniques offer practical option in contrast to the next right now utilized costly strategies for surface modifications like ion implantation and laser surface processing [6]. Both EDM and powder-mixed EDM can support the deposition of surface layers having novel trademark with unrivaled capability as far as mechanical, metallurgical, and tribological characteristics [7]. To accomplish green and healthy production, save resources, reduce the number of experimental trails, and improve the efficiency of experimental work, CuSn CLEs were employed [8]. Gap-active EDM is another methodology which gives a gap-detectable and automatic adjustable electrode retraction set up to facilitate improved textual attribute with reduced indentation, solidified-agglomerates, and crack [9]. Selecting permissible dielectric fluid is additionally indispensable in EDM since it has influence on the surface roughness. Using water as dielectric fluid advances a safe environment. Also, the electrode wear rate will be less, and surface finish will be better. On the other hand, hydrocarbon oil such as kerosene will break down and deliver harmful vapors like CO and CH4 during EDM [10]. Also, vegetable oil-based dielectric liquids, namely, sunflower and jatropha oils, have homogeneous dielectric properties and erosion procedure when correlated with the traditional dielectric fluid. For sustainable manufacturing, biodegradable and ecofriendly vegetable oil-based dielectric liquid shall be selected [11]. TLBO algorithm is a novel population-based nature exhilarated breakthrough, and it has two stages specifically “teacher phase” and “learner phase.” The modified TLBO technique also has two phases and exploits a new population class system into a traditional TLBO technique. The modified TLBO technique delineates an enhanced result quality and quick intermingling ratio than traditional TLBO. Statistical investigations on the trial results elucidated an extensive performance for proposed changes [12–14]. The TLBO algorithm has an extensive likely when contrasted with the combinatorial optimization complexity, like job-shop scheduling problems and flow-shop scheduling problems [15]. In joint optimization of TLBO, PSO, and GA, TLBO conferred impressive has surpassing amount of combination and within the fixed trails of iterations [16].Square profiles in silicon nitride–titanium nitride are made using square tungsten-copper electrodes, and the machining input factors like I, PON, POFF, DP, and SV are optimized using various methodologies like GRA, TOPSIS, and GRA coupled with TLBO algorithm [1]. Adsorbed silicon nitride–titanium nitride CMCs are best suited for high temperature applications because of their admirable properties. Contributions by numerous researchers in the area of mechanism of electrical discharge machining, influence of EDM parameters, selection of tool electrode, selection to dielectric fluid, influence of powder particles mixed with dielectric fluid, after machining surface morphology, etc., were considered for identifying the research gap in the previous work. In continuation to the previous work, currently circular profiles are made in silicon nitride–titanium nitride using cylindrical tungsten-copper electrodes, and the machining input factors like I, PON, POFF, DP, and SV are optimized using joint optimization techniques. The response factors like MRR, EWR, SR, ROC, θ, CIR, and CYL are considered. The optimum electrical discharge machining ranges were attained by means of the Taguchi optimization technique for circular profiles. The optimal group of electrical discharge machining factors was attained through MCDM techniques like GRA and TOPSIS. Also, global optimization approach GRA coupled with the TLBO algorithm was preferred. The optimal combination model bestows more prominent anticipated outcomes than estimated.


## 2. Experimental Procedure

Figure1 depicts flawless exploration procedure of which the experimental work and electrical discharge machining parameter optimization are done. Commercially available silicon nitride–titanium nitride composites are used as workpiece material for the current research. Usually, silicon nitride–titanium nitride composites are fabricated by hot pressing and SPS process by mixing of Si3N4 and Ti powders at 1350°C temperature [17–19]. Si3N4–TiN has been selected because of its superior properties like high melting point, increased thermal shock resistance, high strength retention at elevated temperatures, excellent corrosion and wear resistance, improved surface hardness, and low density. It finds extensive applications in wear resistant parts, heat exchangers, gas turbines, extrusion dies, ball bearings, shot blast nozzle, level sensors in molten metal, and aircraft engines parts. In the Si3N4–TiN workpiece, electrical discharge machining is led utilizing electronic die-sinker (500×300 series) ED machine. Circular holes of 3 mm diameter are shaped on the Si3N4–TiN workpiece which is of 2 mm thickness and 50 mm diameter. The machining process was finished with tungsten-copper (W-Cu) material electrode of 3 mm diameter and 15 mm length. The Si3N4–TiN workpiece subsequent to the process is delineated in Figure 2. For every circular pocket, one new cylindrical-shaped electrode was chosen, and the tool electrodes before and after processing are shown in Figures 3(a) and 3(b), respectively. The deionized water is employed as dielectric liquid for safe environment [10].Figure 1
Proposed research plan (Srinivasan et al. [1]).Figure 2
Machined Si3N4–TiN workpiece.Figure 3
Cylindrical shaped electrodes: (a) before machining; (b) after machining.
(a)(b)


### 2.1. Design of Experiments

The design of experiments is an organized way for regulating the correlation in dispersion through input factors impacting the process and output factors of that cycle. DOE facilitates to get convenient data around the process by directing least number of trails. The experimentations were accomplished using five input parameters differed at five positions as shown in Table1. The DOE with 25 machining run order as obtained from the Taguchi methodology was produced using Minitab 19.0 statistical tool [1]. The order on which the experimental work is carried out and also the time taken for machining is shown in Table 2. The experimental results are portrayed in Table 3.Table 1
Experimental input parameters.
VariablesSymbolsUnitsLevels12345Pulse currentIamps4681012Pulse-on timePONμsec56789Pulse-off timePOFFμsec246810Dielectric pressureDPkg/cm21214161820Spark gap voltageSVVolts2830323436Table 2
Table design and time taken for machining.
RunInput machining factorsMachining time (t) in minIPONPOFFDPSV1452122829.092464143027.333476163224.454488183421.3654910203619.536654163430.297666183628.048678202826.2596810123023.4710692143220.2511856203032.2512868123230.12138710143425.4314882163623.4515894182819.23161058143628.291710610162826.32181072183024.11191084203221.35201096123418.252112510183231.23221262203427.25231274123623.45241286142819.58251298163017.45Table 3
Experimental results for responses after EDM.
RunMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)10.002980.000981.440.300.04880.07440.128220.002400.000320.710.240.08100.04910.029930.001720.000532.530.230.09850.04360.054540.004440.001110.560.180.08480.05250.068550.002200.000584.800.150.31400.02600.027260.001390.000650.870.380.06120.17520.154970.002800.000731.510.150.56220.01900.009480.002750.000832.870.190.35400.03760.039290.004090.000801.690.200.36670.04410.0748100.001920.000690.920.160.05500.14650.0520110.001980.000851.380.190.12290.04290.0763120.002560.000793.990.200.06110.03200.0496130.002040.000403.830.170.51500.11210.0973140.002810.001161.270.210.02680.05090.0313150.003120.001450.690.230.08930.05730.0818160.001990.000593.260.200.07610.02050.0203170.001510.000622.600.200.08710.01830.0320180.002550.001231.150.120.08770.03030.0410190.002070.000731.170.180.09510.01680.0277200.001830.000292.520.190.02100.04730.0230210.001170.000600.930.210.02440.07780.0307220.000930.000790.650.060.04860.05570.0313230.002190.000580.770.150.10980.03090.0120240.002670.000401.420.240.20730.01370.0231250.001860.000373.440.190.03550.01110.0216


### 2.2. Measurements and Calculations of Response Factors

The MRR and the EWR were determined using Equation (1) and Equation (2), respectively. The radial overcut and taper angle were calculated using Equation (3) and Equation (4), respectively.
(1)Materialremovalrate,MRR=Winitial−WfinalMTgm/min,(2)Electrodeerosionrate,EWR=WBM−WAMMTgm/min,(3)Radialovercut,ROCmm=tan−1DT–DE2,(4)Taperangle,θdeg=tan−1DT–DB2t,where Winitial and Wfinal are the weights of the workpiece before and after machining (g), WBM and WAM are the weights of the electrode before and after machining (g), MT is the time taken for machining (min), DT is the top diameter of drilled hole (mm), DB is the bottom diameter of drilled hole (mm), and DE is the diameter of electrode (mm).The SR is measured using Mitutoyo (SURFTEST SJ-210) surface roughness tester. The geometrical tolerance results obtained from PC-DMIS metrology software are depicted in Figure4 that is utilized to quantify the circularity and cylindricity for circular holes contrived in Si3N4–TiN workpiece.Figure 4
Circularity and cylindricity measurement.


## 2.1. Design of Experiments

The design of experiments is an organized way for regulating the correlation in dispersion through input factors impacting the process and output factors of that cycle. DOE facilitates to get convenient data around the process by directing least number of trails. The experimentations were accomplished using five input parameters differed at five positions as shown in Table1. The DOE with 25 machining run order as obtained from the Taguchi methodology was produced using Minitab 19.0 statistical tool [1]. The order on which the experimental work is carried out and also the time taken for machining is shown in Table 2. The experimental results are portrayed in Table 3.Table 1
Experimental input parameters.
VariablesSymbolsUnitsLevels12345Pulse currentIamps4681012Pulse-on timePONμsec56789Pulse-off timePOFFμsec246810Dielectric pressureDPkg/cm21214161820Spark gap voltageSVVolts2830323436Table 2
Table design and time taken for machining.
RunInput machining factorsMachining time (t) in minIPONPOFFDPSV1452122829.092464143027.333476163224.454488183421.3654910203619.536654163430.297666183628.048678202826.2596810123023.4710692143220.2511856203032.2512868123230.12138710143425.4314882163623.4515894182819.23161058143628.291710610162826.32181072183024.11191084203221.35201096123418.252112510183231.23221262203427.25231274123623.45241286142819.58251298163017.45Table 3
Experimental results for responses after EDM.
RunMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)10.002980.000981.440.300.04880.07440.128220.002400.000320.710.240.08100.04910.029930.001720.000532.530.230.09850.04360.054540.004440.001110.560.180.08480.05250.068550.002200.000584.800.150.31400.02600.027260.001390.000650.870.380.06120.17520.154970.002800.000731.510.150.56220.01900.009480.002750.000832.870.190.35400.03760.039290.004090.000801.690.200.36670.04410.0748100.001920.000690.920.160.05500.14650.0520110.001980.000851.380.190.12290.04290.0763120.002560.000793.990.200.06110.03200.0496130.002040.000403.830.170.51500.11210.0973140.002810.001161.270.210.02680.05090.0313150.003120.001450.690.230.08930.05730.0818160.001990.000593.260.200.07610.02050.0203170.001510.000622.600.200.08710.01830.0320180.002550.001231.150.120.08770.03030.0410190.002070.000731.170.180.09510.01680.0277200.001830.000292.520.190.02100.04730.0230210.001170.000600.930.210.02440.07780.0307220.000930.000790.650.060.04860.05570.0313230.002190.000580.770.150.10980.03090.0120240.002670.000401.420.240.20730.01370.0231250.001860.000373.440.190.03550.01110.0216


## 2.2. Measurements and Calculations of Response Factors

The MRR and the EWR were determined using Equation (1) and Equation (2), respectively. The radial overcut and taper angle were calculated using Equation (3) and Equation (4), respectively.
(1)Materialremovalrate,MRR=Winitial−WfinalMTgm/min,(2)Electrodeerosionrate,EWR=WBM−WAMMTgm/min,(3)Radialovercut,ROCmm=tan−1DT–DE2,(4)Taperangle,θdeg=tan−1DT–DB2t,where Winitial and Wfinal are the weights of the workpiece before and after machining (g), WBM and WAM are the weights of the electrode before and after machining (g), MT is the time taken for machining (min), DT is the top diameter of drilled hole (mm), DB is the bottom diameter of drilled hole (mm), and DE is the diameter of electrode (mm).The SR is measured using Mitutoyo (SURFTEST SJ-210) surface roughness tester. The geometrical tolerance results obtained from PC-DMIS metrology software are depicted in Figure4 that is utilized to quantify the circularity and cylindricity for circular holes contrived in Si3N4–TiN workpiece.Figure 4
Circularity and cylindricity measurement.


## 3. Results and Discussions

### 3.1. Taguchi Methodology for Response Factors

In this investigation, negative polarity is selected as it increments the MRR and reduces the EWR by bombarding the electrode by electrons present in the discharge section and workpiece by positive ions [1]. The MRR increases as the PON and the pulse current increments. It is ascertained that the dielectric pressure and the POFF does not impact mostly on the output factor and also the SV has average output factor. To get increased material removal rate, the pulse current and the PON should be increased. The EWR has effects similar to that of MRR. In this scenario also, as the PON and the pulse current increments, the electrode erosion rate reduces. It is noticed that the dielectric pressure and the POFF does not impact much on the output factor and SV has average impact. To decrease the electrode erosion rate, moderate pulse-on time and pulse current are enforced. To achieve good surface, moderate pulse-on time and high gap voltage are enforced. From the main effect plot, it is evident that the surface quality decreases as the pulse current increments. The gap voltage increases the overall ROC, and the top radial would be reduced by employing lower discharge current and DP and higher SV. The θ could be reduced by decreasing pulse current and average DP. It is also observed that the low pulse current increases the taper angle drastically. To decrease the circularity, moderate discharge current and PON are employed, and the voltage should be maintained low. The effect of the DP and the POFF is high in circularity. The cylindricity is less at moderately high pulse current, and the main effect plot proves that decreasing pulse current increments the cylindricity profoundly. On the other hand, the lower PON increases the cylindricity, and SV should be continued low.


### 3.2. GRA Optimization

Grey relational analysis transforms the single-objective condition into an individual response optimization [1]. The GRA proceeds through the accompanying advances.Step 1.
Normalization is done for all the experimental output parameters by the successive equations.
Normalization for higher-the-better,(5)xik=gik−mingikmaxgik−mingik.
Normalization for lower-the-better,(6)xik=maxgik−gikmaxgik−mingik,where xik is normalized value for obtained response, mingik is the least value of gik for kth response, maxgik is the highest value of gik for kth response, “i” is the experimental number, and “k” is the comparability sequence.Step 2.
Grey relational coefficient delineates the correlation among the desired and actual normalized experimental response. The GRC value is determined as follows:(7)φik=∆min+φ∆max∆oik+φ∆max,where Δk is a deviation sequence, i.e., Δoik=gik–xik; φ is a unique coefficient which sustains between 0 and 1 (usually assumed as φ=0.5); k is a GRC; Δmin (least deviation sequence) is the lowest value of Δk; and Δmax (highest deviation sequence) is the highest value of Δoik.Step 3.
The grey relational grade is obtained from average value of GRC. The GRG is calculated as follows:(8)θi=1n∑i=1nφik,where θi is the GRG of ith trial, n is a number of trials, and φik is a GRC.In GRA, the GRG which is highest was given top ranking, and lower GRG is given last rank [1]. The calculated GRG for 25 experimental run orders is shown in Table 4. Figure 5 outlines the GRG for 25 experimental run orders, and Table 4 portrays the impact of input factor on the GRG. From Tables 4 and 5, it is evident that A5B3C2D1E5 are the optimal input factor levels. Consequently, the 23rd experimental run order is the optimized group of input factors for best output response.Table 4
Grey relational analysis.
RunNormalizationGrey relational coefficientGRGRankMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)MRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)10.100210.998890.707370.247140.948670.614260.901250.357200.997780.630810.399090.906890.564500.835070.670191520.071760.999730.861050.432500.889170.768430.859110.350080.999450.782540.468380.818560.683470.780160.697521030.038470.999460.477890.463390.856830.801950.690030.342110.998920.489190.482340.777400.716280.617310.631942240.171480.998720.892630.617860.882150.747710.593810.376360.997450.823220.566800.809250.664640.551760.684211450.061740.9993900.710530.458630.909200.877660.347640.998790.333330.633340.480140.846310.803420.6347121610.999300.8273700.925750010.998610.743350.333330.870710.333330.333330.658951670.091310.999210.692630.7105300.9518610.354940.998420.619300.633340.333330.9121710.693071280.088870.999080.406320.586960.384710.838510.795190.354330.998170.457170.547620.448320.755870.709410.610132390.154370.999110.654740.556070.361250.798900.550520.371570.998230.591530.529700.439080.713170.526600.5957024100.048300.999260.816840.679640.937160.174890.707220.344420.998530.731900.609490.888350.377330.630690.6543917110.051230.999060.720000.586960.811740.806220.540210.345120.998110.641030.547620.726470.720690.520950.6428620120.079480.999130.170530.556070.925940.872640.723710.351980.998260.376090.529700.870990.796990.644090.6525918130.0543610.204210.648750.087220.384520.395880.3458710.385870.587370.353910.448240.452850.5105925140.091800.998660.743160.525180.989260.757460.849480.355060.997320.660640.512910.978980.673370.768620.706706150.106960.998290.865260.463390.873830.718460.502410.358930.996600.787730.482340.798510.639770.501210.6521519160.051820.999380.324210.556070.898220.942720.925090.345260.998750.425250.529700.830870.897210.869700.699538170.028260.999350.463160.556070.877950.956120.844670.339730.998700.482230.529700.803800.919330.762980.6909213180.079090.998570.768420.803210.876790.883000.782820.351890.997150.683450.717580.802290.810370.697170.722844190.055780.999200.764210.617860.863210.965270.874230.346210.998400.679540.566800.785180.935040.799010.730032200.043900.999760.480000.5869610.779400.906530.343380.999510.490200.5476210.693870.842500.702447210.011640.999370.814740.525180.993750.593540.853610.335940.998750.729650.512910.987660.551600.773520.6985892200110.949040.728210.849480.333330.33333110.907500.647850.768620.712955230.061500.999400.848420.710530.835950.879340.982130.347580.998800.767370.633340.752960.805600.965490.753021240.084760.999630.711580.432500.655790.984160.905840.353300.999260.634180.468380.592270.969290.841530.6940311250.045370.999660.286320.586960.9732410.916150.343730.999320.411970.547620.9492110.856390.729753Figure 5
GRG for experimental run.Table 5
Factor effect on GRG.
ParameterGrey relational gradeOptimal levelDifferenceRank12345I0.663710.642450.632980.709150.7176650.084691PON0.674020.682130.689410.641220.6746930.048192POFF0.693410.698330.692870.675240.6661020.032244DP0.690170.661210.674790.683650.6661310.028965SV0.663490.677730.673500.653830.6974150.033923


### 3.3. TOPSIS Optimization

Technique for order of preference by similarity to ideal solution is an ordinary MCDM optimization methodology that assists with selecting the better input factors among the enormous number of options which is having the shortest point from positive ideal solution and the largest point from negative ideal solution [1]. The MCDM using the TOPSIS methodology proceeds through the accompanying advances.Step 1.
First, all the information gathered from experimental run was utilized for developing decision matrix which comprises ofn number of response factors which are complexions and m number of experimental runs that are the substitute result.
(9)Dm=a11a12a13⋯⋯a1na21a22a23⋯⋯a2n⋮⋮⋮⋮⋮⋮am1am2am3⋯⋯amn,where aij is the measure of jth attribute to ith alternative.Step 2.
The accompanying condition gives the result for normalization of decision matrix.(10)γij=aij∑i=1maij2,where γij is normalized solution for i=1,2,3,⋯,m and j=1,2,3,⋯,n.Step 3.
The weights of every characteristic are fixed, and for the whole attributes, the total sum of weightage should be equivalent to 1. By utilizing the accompanying condition, the weighted normalized decision matrix is determined.(11)φij=wjγij,where ∑j=1nwj=1.Step 4.
The positive ideal solution (PIS) and negative ideal solution (NIS) can be determined by(12)φ+=φ1+,φ2+,⋯.φn+=maxφijj∈J1,minφijj∈J2,i=1,2,⋯n,(13)φ−=φ1−,φ2−,⋯.φn−=minφijj∈J1,maxφijj∈J2,i=1,2,⋯n,where J1 and J2 are sets of beneficial attribute and nonbeneficial attribute, respectively.Step 5.
Separation proportions of the entire options are determined from PIS and NIS(14)Si+=∑j=1nφij−φi+2,(15)Si−=∑j=1nφij−φi−2,where i=1,2,3,⋯,m.Step 6.
The relative similarity index (SI) of every parameter is determined utilizing the accompanying equation(16)SI=Si−Si+−Si−.In TOPSIS, the first part is to change the outcomes to a decision matrix comprising of output responses (attributes) in columns and exploratory trials (alternatives) in rows as delineated in Equation (9). By utilizing Equation (10), the decision matrix is normalized, and relative weightage is doled to all entities. Then, equivalent relative weightage is fixed to entire seven responses, viz., material removal rate, electrode wear rate, surface roughness, radial overcut, taper angle, circularity, and cylindricity. The weighted normalization numbers were determined by using Equation (11). Using Equations (12) and (13), the positive ideal solution and negative ideal solution are obtained from the normalization matrix. Equations (14) and (15) are utilized to ascertain the separation measures of every alternative from PIS and NIS. Likewise, Equation (16) is employed to ascertain the similarity index for all the options by finding the separation measures [1].Based on the TOPSIS optimization, the normalized matrix, weighted-normalized matrix, separation evaluated data, and SI of every option are delineated in Table6. The alternative result with highest SI value is the predominant, and the trails are ranked depending upon the SI. The 23rd experimental run is the good run, and the 13th is the poor among every one of the other options. Table 7 displays the determined mean similarity index of all the input factors at all the levels.Table 6
TOPSIS.
RunNormalizationWeighted normalized matrixSeparationSIRankMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)MRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)S+S-10.135960.282220.052640.167130.081120.142940.199240.019440.040360.007530.023900.011600.020440.028490.555004.841440.897152320.125240.204370.158860.185700.350770.120070.217570.017910.029220.022720.026550.050160.017170.031110.539834.821920.89932930.084270.236940.074260.046420.053850.132320.162010.012050.033880.010620.006640.007700.018920.023170.552564.840250.897542140.086040.295440.119380.194980.025660.138580.091040.012300.042250.017070.027880.003670.019820.013020.545414.833050.898591450.058790.174210.086480.148560.052640.398860.151250.008410.024910.012370.021240.007530.057040.021630.551114.836330.897702060.063480.186650.109980.167130.090920.045740.080570.009080.026690.015730.023900.013000.006540.011520.545804.833980.898551570.060630.215610.129720.176410.117560.116800.221930.008670.030830.018550.025230.016810.016700.031740.543524.829780.898851180.095540.368670.064860.213550.085420.156010.237930.013660.052720.009270.030540.012220.022310.034020.554314.839050.897222290.073490.080880.066740.222830.077480.133680.086970.010510.011570.009540.031870.011080.019120.012440.551114.839240.8977619100.091310.248910.135360.278540.046680.202560.372890.013060.035590.019360.039830.006680.028970.053320.544154.828240.8987112110.067060.146190.072380.139270.105030.084130.034900.009590.020910.010350.019920.015020.012030.004990.551044.839360.8977718120.078080.312730.108100.111420.083890.082490.119250.011170.044720.015460.015930.012000.011800.017050.547654.834750.8982516130.654970.165920.081780.352820.058540.477000.450550.093660.023730.011690.050450.008370.068210.064430.559094.834450.8963325140.084210.209760.269780.176410.338620.102370.114020.012040.030000.038580.025230.048420.014640.016300.523714.806960.901755150.035830.151790.087420.194980.023340.211820.089300.005120.021710.012500.027880.003340.030290.012770.549164.837160.8980517160.056040.074620.236880.176410.020110.128780.066900.008010.010670.033870.025230.002880.018420.009570.527324.816690.901337170.085740.184490.141940.139270.537780.051730.027340.012260.026380.020300.019920.076900.007400.003910.544204.823110.8986113180.062590.025880.360020.157840.492630.305200.283010.008950.003700.051480.022570.070450.043640.040470.513634.790460.903163190.078330.200580.375060.185700.058450.087120.144270.011200.028680.053630.026550.008360.012460.020630.508104.796350.904212200.046240.156490.244400.185700.083290.049820.093080.006610.022380.034950.026550.011910.007120.013310.526394.814790.901456210.052640.134040.237820.213550.094220.118710.158520.007530.019170.034010.030540.013470.016970.022670.527114.814640.901328220.061000.151080.306440.185700.072790.055810.059050.008720.021600.043820.026550.010410.007980.008440.517464.806300.902804230.067210.147900.451200.139270.300360.070790.079120.009610.021150.064520.019920.042950.010120.011310.497484.782510.905781240.081630.100710.133480.222830.198290.037300.067190.011670.014400.019090.031870.028360.005330.009610.541614.828410.8991410250.654970.165920.081780.352820.058540.477000.450550.093660.023730.011690.050450.008370.068210.064430.559094.834450.8963424Table 7
Mean similarity index of each parameter at entry level.
ParameterSimilarity indexOptimal levelDifferenceRank12345I0.898060.897220.898430.901080.9017550.004531PON0.899220.896570.900290.900010.8984530.003732POFF0.900720.901180.898950.898350.8983520.002834DP0.900080.898970.898560.899990.8999410.001115SV0.898030.897870.900010.899550.9010850.003213


### 3.4. TLBO Algorithms

TLBO algorithms depict the teaching, and learning phenomenon takes place in the classroom [1]. The current work was centered on maximization of material removal rate and minimization of electrode erosion rate, SR, ROC, θ, circularity, and cylindricity, respectively. The regression equation for maximization and minimization of output factors is delineated in Equation (17) to Equation (23). Additionally, the parametric bounds are delineated in Equation (24) to Equation (28).Maximization:(17)MRR=0.00047+0.000367I+0.000214PON–0.000039POFF–0.000050DP–0.000025SV.Minimization:(18)EWR=–0.000535+0.000106I+0.000065PON–0.000014POFF–0.000007DP+0.000004SV,(19)SR=0.35–0.0242I+0.0076PON+0.0660POFF+0.0492DP+0.0029SV,(20)ROC=0.118–0.00210I–0.00200PON+0.00010POFF+0.00320DP+0.00180SV,(21)θ=0.367–0.03776I+0.0086PON+0.00444POFF+0.00327DP–0.00182SV,(22)CIR=–0.090+0.00021I–0.00397PON+0.00182POFF+0.00060DP+0.00459SV,(23)CYL=0.003–0.00411I+0.00295PON+0.00159POFF–0.00010DP+0.00163SV.Parameter bounds:(24)Pulsecurrent:4≤I≤12,(25)Pulse‐ontime:5≤PON≤9,(26)Pulse‐offtime:2≤POFF≤10,(27)Dielectricpressure:12≤DP≤20,(28)Sparkgapvoltage:28≤SV≤36.The TLBO is carried through the accompanying advances.Step 1.
Set the population size,Np=25.Step 2.
Based on DOE, the design matrix is embraced, and the same is ranked utilizing the GRG as delineated in Table8.Step 3 (teacher phase).
New solution is generated as delineated in Table9.
(29)Xnew=X+rXbest–Tf∗Xmean,where Xnew is a recent solution, X is a current solution, r is a random value between 0 and 1, Xbest is a teacher, Tf is a teaching entity either 1 or 2, and Xmean is a mean of the population.Step 4.
Here, the bounded input factors are joined with the actual parameters taken from design of experiments. Table10 delineates the combined population.Step 5.
Here, ranks 1 to 25 (50% of higher order rankings) are selected from the combined population table, and the same is optimized through the GRG. Ranks 1 to 25 acquired from the combined population are delineated in Table11.Step 6 (learner phase).
Creation of new solution is developed by means of a partner response which is haphazardly chosen from the population is delineated in Table12.
(30)Xnew=X+rX–Xp,where Xp is a partner solution.Table 8
Initial random population.
RunInput parameterResponseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL145212280.002980.000981.440.300.04880.07440.12820.6701915246414300.002400.000320.710.240.08100.04910.02990.6975210347616320.001720.000532.530.230.09850.04360.05450.6319422448818340.004440.001110.560.180.08480.05250.06850.68421145491020360.002200.000584.800.150.31400.02600.02720.6347121665416340.021390.000650.870.380.06120.17520.15490.6589516766618360.002800.000731.510.150.56220.01900.00940.6930712867820280.002750.000832.870.190.35400.03760.03920.61013239681012300.004090.000801.690.200.36670.04410.07480.59570241069214320.001920.000690.920.160.05500.14650.05200.65439171185620300.001980.000851.380.190.12290.04290.07630.64286201286812320.002560.000793.990.200.06110.03200.04960.652591813871014340.002040.000103.830.170.51500.11210.09730.51059251488216360.002810.001161.270.210.02680.05090.03130.7067061589418280.003120.001450.690.230.08930.05730.08180.652151916105814360.001990.000593.260.200.07610.02050.02030.699538171061016280.001510.000622.600.200.08710.01830.03200.690921318107218300.002550.001231.150.120.08770.03030.04100.72284419108420320.002070.000731.170.180.09510.01680.02770.73003220109612340.001830.000292.520.190.02100.04730.02300.702447211251018320.001170.000600.930.210.02440.07780.03070.69858922126220340.000930.790000.050.060.04860.05570.03130.71295523127412360.002190.000580.770.150.10980.03090.01200.75302124128614280.002670.000401.420.240.20730.01370.02310.694031125129816300.001860.000373.440.190.03550.01110.02160.729753Mean8761632Table 9
Teacher phase–updated process parameter and responses.
S. noNew input parameterBounded input parameterNew responseGRGRankIPONPOFFDPSVIPONPOFFDPSVMRREWRSRROCθCIRCYL12.23.9-0.6924.643.9212280.006660.013220.560.310.04500.09500.11650.605152322.25.452.712.528.345.452.712.528.30.005590.038500.930.290.07500.08580.10340.697521032.276163247616320.004450.030602.020.220.20270.06720.07200.631942142.28.559.319.535.748.559.319.535.70.003320.022703.120.160.33040.04860.04060.684211452.210.112.62339.4491020360.002940.030603.350.150.35370.04390.03490.634712065.13.92.71635.75.13.92.71635.70.007200.117130.840.230.11710.09210.08140.658951575.15.45619.539.45.15.45619.5360.005540.098171.780.190.22300.06820.05940.693071285.179.32324.65.179.320280.002700.033762.490.210.25860.03730.06540.610132295.18.5512.6928.35.18.5510928.30.002130.240743.510.270.22310.05160.07100.5957024105.110.1-0.612.5325.19212.5320.003710.036921.310.220.08870.07530.06410.65439161183.962328.383.962028.30.004320.115551.080.230.12530.04970.07400.64286191285.459.393285.459.312320.003700.058252.810.240.18740.05450.06140.6525917138712.612.535.7871012.535.70.003160.056673.350.200.23920.05070.03880.51059251488.55-0.61639.488.55216360.003510.102911.120.160.08980.06460.03390.70670615810.12.719.524.6892.719.5280.001700.076840.810.180.07710.04070.04630.65215181610.93.99.312.539.410.93.99.312.5360.004320.051562.660.210.16470.05430.04350.6995381710.95.4512.61624.610.95.451016280.001820.008112.480.210.15870.02600.04850.69092131810.97-0.619.528.310.97219.528.30.002170.167690.260.180.00920.03990.04360.7228441910.98.552.7233210.98.552.720320.001630.169270.790.130.06100.03610.02110.7300322010.910.16935.710.996935.70.001830.034552.560.180.09930.05150.02070.7024472113.83.912.619.532123.91019.5320.002900.136882.240.180.17890.02700.03590.6985892213.85.45-0.62335.7125.4522035.70.003920.275920.340.140.03410.05230.02650.7129552313.872.7939.41272.79360.003350.068941.360.190.00140.06670.03210.7530212413.88.55612.524.6128.55612.5280.000380.015591.910.200.05140.02970.03320.69403112513.810.19.31628.31299.31628.30.000600.017172.700.170.15060.01010.01860.729753Table 10
Combined population.
RunCombined input parameterNew responseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL145212280.002980.000981.440.300.04880.07440.12820.6701949246414300.002400.000320.710.240.08100.04910.02990.6975221347616320.001720.000532.530.230.09850.04360.05450.6319446448818340.004440.001110.560.180.08480.05250.06850.68421235491020360.002200.000584.800.150.31400.02600.02720.6347138665416340.021390.000650.870.380.06120.17520.15490.6589519766618360.002800.000731.510.150.56220.01900.00940.693076867820280.002750.000832.870.190.35400.03760.03920.61013409681012300.004090.000801.690.200.36670.04410.07480.59570441069214320.001920.000690.920.160.05500.14650.05200.65439241185620300.001980.000851.380.190.12290.04290.07630.64286411286812320.002560.000793.990.200.06110.03200.04960.652594713871014340.002040.000103.830.170.51500.11210.09730.51059481488216360.002810.001161.270.210.02680.05090.03130.70670271589418280.003120.001450.690.230.08930.05730.08180.652153716105814360.001990.000593.260.200.07610.02050.02030.6995334171061016280.001510.000622.600.200.08710.01830.03200.690923918107218300.002550.001231.150.120.08770.03030.04100.722841619108420320.002070.000731.170.180.09510.01680.02770.730032020109612340.001830.000292.520.190.02100.04730.02300.7024431211251018320.001170.000600.930.210.02440.07780.03070.698582222126220340.000930.790000.050.060.04860.05570.03130.712951723127412360.002190.000580.770.150.10980.03090.01200.75302224128614280.002670.000401.420.240.20730.01370.02310.694032525129816300.001860.000373.440.190.03550.01110.02160.72975362643.9212280.006660.013220.560.310.04500.09500.11650.60515432745.452.712.528.30.005590.038500.930.290.07500.08580.10340.69752122847616320.004450.030602.020.220.20270.06720.07200.63194352948.559.319.535.70.003320.022703.120.160.33040.04860.04060.684211830491020360.002940.030603.350.150.35370.04390.03490.6347133315.13.92.71635.70.007200.117130.840.230.11710.09210.08140.6589526325.15.45619.5360.005540.098171.780.190.22300.06820.05940.6930714335.179.320280.002700.033762.490.210.25860.03730.06540.6101342345.18.5510928.30.002130.240743.510.270.22310.05160.07100.5957045355.19212.5320.003710.036921.310.220.08870.07530.06410.65439283683.962028.30.004320.115551.080.230.12530.04970.07400.64286323785.459.312320.003700.058252.810.240.18740.05450.06140.652592938871012.535.70.003160.056673.350.200.23920.05070.03880.51059503988.55216360.003510.102911.120.160.08980.06460.03390.70670840892.719.5280.001700.076840.810.180.07710.04070.04630.65215304110.93.99.312.5360.004320.051562.660.210.16470.05430.04350.69953104210.95.451016280.001820.008112.480.210.15870.02600.04850.69092154310.97219.528.30.002170.167690.260.180.00920.03990.04360.7228454410.98.552.720320.001630.169270.790.130.06100.03610.02110.7300334510.996935.70.001830.034552.560.180.09930.05150.02070.70244946123.91019.5320.002900.136882.240.180.17890.02700.03590.698581147125.4522035.70.003920.275920.340.140.03410.05230.02650.712957481272.79360.003350.068941.360.190.00140.06670.03210.75302149128.55612.5280.000380.015591.910.200.05140.02970.03320.6940313501299.31628.30.000600.017172.700.170.15060.01010.01860.729754Table 11
Candidate solution based on the nondominance rank.
S. noCombined input parameterNew responseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL11272.79360.006580.000581.360.190.00140.06670.03210.7530212127412360.002190.000580.770.150.10980.03090.01200.742522310.98.552.720320.005730.000790.790.130.06100.03610.02110.73003341299.31628.30.006100.000652.700.170.15060.01010.01860.729754510.97219.528.30.005420.000100.260.180.00920.03990.04360.722845666618360.002800.000731.510.150.56220.01900.00940.7212067125.4522035.70.005300.000590.340.140.03410.05230.02650.712957888.55216360.005020.000831.120.160.08980.06460.03390.706708910.996935.70.006480.000622.560.180.09930.05150.02070.7024491010.93.99.312.5360.004500.000292.660.210.16470.05430.04350.699531011123.91019.5320.004300.000532.240.180.17890.02700.03590.69858111245.452.712.528.30.002950.000800.930.290.07500.08580.10340.697521213128.55612.5280.006520.000401.910.200.05140.02970.03320.6940313145.15.45619.5360.002480.000851.780.190.22300.06820.05940.69307141510.95.451016280.004640.000732.480.210.15870.02600.04850.690921516107218300.002550.001231.150.120.08770.03030.04100.689451617126220340.000930.790000.050.060.04860.05570.03130.68706171848.559.319.535.70.002680.001163.120.160.33040.04860.04060.68421181965416340.021390.000650.870.380.06120.17520.15490.681721920108420320.002070.000731.170.180.09510.01680.02770.67799202146414300.002400.000320.710.240.08100.04910.02990.6761221221251018320.001170.000600.930.210.02440.07780.03070.67015222348818340.004440.001110.560.180.08480.05250.06850.66312232469214320.001920.000690.920.160.05500.14650.05200.663002425128614280.002670.000401.420.240.20730.01370.02310.6593325Table 12
Learner phase–new process variables and objective values after interaction.
S.noNew input parameterBounded input parameterNew responseGRGRankInteractionIPONPOFFDPSVIPONPOFFDPSVMRREWRSRROCθCIRCYL1126.751.5456.7540.4126.75212360.003500.131350.960.180.00170.06390.03000.60641141 and 25212.726.564.6611.1238.2126.564.6612360.003150.092321.680.180.05730.05580.02720.59075192 and 24311.7288.6710.95120.8830.911.7288.67122030.90.001240.182810.530.130.02700.03290.01970.6672263 and 234129.889.06915.1226.2651299.06915.12280.000560.029562.670.170.13840.01220.02120.60127174 and 22511.7287.221.3421.9227.36511.7287.22220280.001690.182830.210.170.00040.03420.03750.62493115 and 2165.525.566.6617.1238.25.525.566.6617.12360.005320.055042.090.200.21890.06870.05920.60589156 and 20712.725.5491.3421.7636.63512.725.549220360.003670.288100.340.130.02630.04950.02090.6992637 and 1988.488.55-0.40914.4636.1658.488.55214.46360.003420.086161.190.170.07410.06580.03370.61784138 and 18910.7689.667.324.1636.63510.76897.3212360.001550.007762.780.160.15010.04200.01380.6739059 and 171011.0083.21811.70910.0839.311.00851012360.003490.016933.020.200.18280.04810.03530.597441810 and 161112.1323.5591021.0434.212.1325102034.20.002490.146872.440.150.20070.02450.02090.582062211 and 15123.8685.451.6119.4224.06545.45212280.005690.033260.750.290.05440.08870.10610.63567912 and 1413128.8917.08914.0423.6128.8917.08914.04280.005760.001860.960.180.08690.02150.01670.73367113 and 1144.2725.1096.6622.8364.2725.1096.6620360.005880.087951.920.190.25060.06960.06460.621631214 and 21510.94.76812.40914.2425.810.951014.24280.002170.012502.530.230.14590.03140.05440.546702415 and 3169.766.56-0.40918.8830.9359.766.56218.8830.9350.003260.167650.410.180.03630.05170.04670.604281616 and 41712.1325.78220.2237.13512.1325.78220360.003720.275160.390.130.03620.05100.02270.68916417 and 5188.59.11110.38920.1635.5358.59.111102035.5350.001320.035073.160.120.28660.02460.01000.70768218 and 6195.284.9014.6614.2433.0655.2854.6614.2433.0650.005770.023001.490.240.13860.07990.08020.64285819 and 72010.247.8794.6621.7629.810.247.8794.662029.80.001570.121101.180.160.09660.03150.03240.584182120 and 8213.1725.343.3416.226.86545.343.3416.2280.005330.009220.880.270.10800.07610.09800.64698721 and 92212.1325.24210.23120.4229.812.1325.242102029.80.001650.108282.270.170.17400.01660.03140.542002522 and 10233.048.9027.3417.3435.148.9027.3417.3435.10.003450.036162.700.180.27210.05720.04640.580762323 and 11246.249.7811.76914.6634.0356.249.781214.6634.0350.003070.018961.330.180.10240.06630.04320.635131024 and 1225127.879614.6628127.879614.66280.000710.029141.700.190.05960.02800.03420.584802025 and 13Based on the TLBO technique, the global optimal values were identified. The optimal set of input factors are acquired from the learner phase based on the top ranking [1]. This ranking is produced after interaction between parameters as displayed in Table 12. The SEM images of the hole made using optimal machining parameters are delineated in Figure 6. From the micrograph, it is evident that the machined area of the Si3N4–TiN ceramic matrix composite workpiece exhibits good surface finish.Figure 6
SEM micrographs of machined Si3N4–TiN.


### 3.5. Verification Test

The GRG for different optimization methods is calculated for electrodischarge machining of Si3N4–TiN ceramic matrix composite workpiece. A point by point correlation is made for the GRG acquired from joint optimization techniques and is outlined in Table 13. Finally, a confirmatory experiment was done for the final TLBO optimized values, and the outcomes are great in contention. Table 14 portrays the outcomes obtained for optimal input machining factors.Table 13
Comparison of various optimization techniques.
S. noOutput parametersTaguchiGRATOPSISTLBOGRG—0.753020.905780.73367Setting level—I: 12 ampsI: 12 ampsI: 12 ampsPON: 7μsecPON: 7μsecPON: 8.89μsecPOFF: 4μsecPOFF: 4μsecPOFF: 7.09μsecDP: 12 kg/cm2DP: 12 kg/cm2DP: 14.04 kg/cm2SV: 36 voltsSV: 36 voltsSV: 28 volts(A5B3C2D1E5)(A5B3C2D1E5)1MRR (g/min)0.004400.002190.002190.005762EWR (g/min)0.000320.000580.000580.001863SR (μm)0.560.770.770.964ROC (mm)0.060.150.150.185θ (deg)0.02100.10980.10980.08696CIR (mm)0.01110.03090.03090.02157CYL (mm)0.00940.01200.01200.0167Table 14
Comparison of verification test for various optimization techniques.
S.noOutput parametersGRATOPSISTLBO1MRR (g/min)Trial 10.002240.001990.00498Trial 20.001980.002210.00591Trial 30.002270.002300.00544Trial 40.002220.002040.00561Trial 50.002090.002190.00553Average0.002160.002150.005492EWR (g/min)Trial 10.000550.000620.00092Trial 20.000610.000610.00190Trial 30.000570.000560.00181Trial 40.000610.000590.00199Trial 50.000620.000600.00177Average0.000590.000600.001683SR (μm)Trial 10.770.790.82Trial 20.710.760.9Trial 30.80.810.89Trial 40.790.740.96Trial 50.750.780.95Average0.760.780.904ROC (mm)Trial 10.140.150.16Trial 20.160.160.19Trial 30.170.160.14Trial 40.150.140.15Trial 50.150.130.19Average0.150.150.175θ (deg)Trial 10.10890.11020.0910Trial 20.10990.10990.0891Trial 30.11010.10970.0852Trial 40.10890.10960.0888Trial 50.10950.10920.0869Average0.10950.10970.08826CIR (mm)Trial 10.03080.03080.0301Trial 20.02810.03140.0210Trial 30.03130.03060.0202Trial 40.03040.02790.0289Trial 50.03350.03280.0221Average0.03080.03070.02457CYL (mm)Trial 10.01210.01280.0152Trial 20.01320.01230.0159Trial 30.01290.01200.0182Trial 40.01150.01120.0181Trial 50.01220.01280.0170Average0.01240.01220.0169


## 3.1. Taguchi Methodology for Response Factors

In this investigation, negative polarity is selected as it increments the MRR and reduces the EWR by bombarding the electrode by electrons present in the discharge section and workpiece by positive ions [1]. The MRR increases as the PON and the pulse current increments. It is ascertained that the dielectric pressure and the POFF does not impact mostly on the output factor and also the SV has average output factor. To get increased material removal rate, the pulse current and the PON should be increased. The EWR has effects similar to that of MRR. In this scenario also, as the PON and the pulse current increments, the electrode erosion rate reduces. It is noticed that the dielectric pressure and the POFF does not impact much on the output factor and SV has average impact. To decrease the electrode erosion rate, moderate pulse-on time and pulse current are enforced. To achieve good surface, moderate pulse-on time and high gap voltage are enforced. From the main effect plot, it is evident that the surface quality decreases as the pulse current increments. The gap voltage increases the overall ROC, and the top radial would be reduced by employing lower discharge current and DP and higher SV. The θ could be reduced by decreasing pulse current and average DP. It is also observed that the low pulse current increases the taper angle drastically. To decrease the circularity, moderate discharge current and PON are employed, and the voltage should be maintained low. The effect of the DP and the POFF is high in circularity. The cylindricity is less at moderately high pulse current, and the main effect plot proves that decreasing pulse current increments the cylindricity profoundly. On the other hand, the lower PON increases the cylindricity, and SV should be continued low.


## 3.2. GRA Optimization

Grey relational analysis transforms the single-objective condition into an individual response optimization [1]. The GRA proceeds through the accompanying advances.Step 1.
Normalization is done for all the experimental output parameters by the successive equations.
Normalization for higher-the-better,(5)xik=gik−mingikmaxgik−mingik.
Normalization for lower-the-better,(6)xik=maxgik−gikmaxgik−mingik,where xik is normalized value for obtained response, mingik is the least value of gik for kth response, maxgik is the highest value of gik for kth response, “i” is the experimental number, and “k” is the comparability sequence.Step 2.
Grey relational coefficient delineates the correlation among the desired and actual normalized experimental response. The GRC value is determined as follows:(7)φik=∆min+φ∆max∆oik+φ∆max,where Δk is a deviation sequence, i.e., Δoik=gik–xik; φ is a unique coefficient which sustains between 0 and 1 (usually assumed as φ=0.5); k is a GRC; Δmin (least deviation sequence) is the lowest value of Δk; and Δmax (highest deviation sequence) is the highest value of Δoik.Step 3.
The grey relational grade is obtained from average value of GRC. The GRG is calculated as follows:(8)θi=1n∑i=1nφik,where θi is the GRG of ith trial, n is a number of trials, and φik is a GRC.In GRA, the GRG which is highest was given top ranking, and lower GRG is given last rank [1]. The calculated GRG for 25 experimental run orders is shown in Table 4. Figure 5 outlines the GRG for 25 experimental run orders, and Table 4 portrays the impact of input factor on the GRG. From Tables 4 and 5, it is evident that A5B3C2D1E5 are the optimal input factor levels. Consequently, the 23rd experimental run order is the optimized group of input factors for best output response.Table 4
Grey relational analysis.
RunNormalizationGrey relational coefficientGRGRankMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)MRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)10.100210.998890.707370.247140.948670.614260.901250.357200.997780.630810.399090.906890.564500.835070.670191520.071760.999730.861050.432500.889170.768430.859110.350080.999450.782540.468380.818560.683470.780160.697521030.038470.999460.477890.463390.856830.801950.690030.342110.998920.489190.482340.777400.716280.617310.631942240.171480.998720.892630.617860.882150.747710.593810.376360.997450.823220.566800.809250.664640.551760.684211450.061740.9993900.710530.458630.909200.877660.347640.998790.333330.633340.480140.846310.803420.6347121610.999300.8273700.925750010.998610.743350.333330.870710.333330.333330.658951670.091310.999210.692630.7105300.9518610.354940.998420.619300.633340.333330.9121710.693071280.088870.999080.406320.586960.384710.838510.795190.354330.998170.457170.547620.448320.755870.709410.610132390.154370.999110.654740.556070.361250.798900.550520.371570.998230.591530.529700.439080.713170.526600.5957024100.048300.999260.816840.679640.937160.174890.707220.344420.998530.731900.609490.888350.377330.630690.6543917110.051230.999060.720000.586960.811740.806220.540210.345120.998110.641030.547620.726470.720690.520950.6428620120.079480.999130.170530.556070.925940.872640.723710.351980.998260.376090.529700.870990.796990.644090.6525918130.0543610.204210.648750.087220.384520.395880.3458710.385870.587370.353910.448240.452850.5105925140.091800.998660.743160.525180.989260.757460.849480.355060.997320.660640.512910.978980.673370.768620.706706150.106960.998290.865260.463390.873830.718460.502410.358930.996600.787730.482340.798510.639770.501210.6521519160.051820.999380.324210.556070.898220.942720.925090.345260.998750.425250.529700.830870.897210.869700.699538170.028260.999350.463160.556070.877950.956120.844670.339730.998700.482230.529700.803800.919330.762980.6909213180.079090.998570.768420.803210.876790.883000.782820.351890.997150.683450.717580.802290.810370.697170.722844190.055780.999200.764210.617860.863210.965270.874230.346210.998400.679540.566800.785180.935040.799010.730032200.043900.999760.480000.5869610.779400.906530.343380.999510.490200.5476210.693870.842500.702447210.011640.999370.814740.525180.993750.593540.853610.335940.998750.729650.512910.987660.551600.773520.6985892200110.949040.728210.849480.333330.33333110.907500.647850.768620.712955230.061500.999400.848420.710530.835950.879340.982130.347580.998800.767370.633340.752960.805600.965490.753021240.084760.999630.711580.432500.655790.984160.905840.353300.999260.634180.468380.592270.969290.841530.6940311250.045370.999660.286320.586960.9732410.916150.343730.999320.411970.547620.9492110.856390.729753Figure 5
GRG for experimental run.Table 5
Factor effect on GRG.
ParameterGrey relational gradeOptimal levelDifferenceRank12345I0.663710.642450.632980.709150.7176650.084691PON0.674020.682130.689410.641220.6746930.048192POFF0.693410.698330.692870.675240.6661020.032244DP0.690170.661210.674790.683650.6661310.028965SV0.663490.677730.673500.653830.6974150.033923


## 3.3. TOPSIS Optimization

Technique for order of preference by similarity to ideal solution is an ordinary MCDM optimization methodology that assists with selecting the better input factors among the enormous number of options which is having the shortest point from positive ideal solution and the largest point from negative ideal solution [1]. The MCDM using the TOPSIS methodology proceeds through the accompanying advances.Step 1.
First, all the information gathered from experimental run was utilized for developing decision matrix which comprises ofn number of response factors which are complexions and m number of experimental runs that are the substitute result.
(9)Dm=a11a12a13⋯⋯a1na21a22a23⋯⋯a2n⋮⋮⋮⋮⋮⋮am1am2am3⋯⋯amn,where aij is the measure of jth attribute to ith alternative.Step 2.
The accompanying condition gives the result for normalization of decision matrix.(10)γij=aij∑i=1maij2,where γij is normalized solution for i=1,2,3,⋯,m and j=1,2,3,⋯,n.Step 3.
The weights of every characteristic are fixed, and for the whole attributes, the total sum of weightage should be equivalent to 1. By utilizing the accompanying condition, the weighted normalized decision matrix is determined.(11)φij=wjγij,where ∑j=1nwj=1.Step 4.
The positive ideal solution (PIS) and negative ideal solution (NIS) can be determined by(12)φ+=φ1+,φ2+,⋯.φn+=maxφijj∈J1,minφijj∈J2,i=1,2,⋯n,(13)φ−=φ1−,φ2−,⋯.φn−=minφijj∈J1,maxφijj∈J2,i=1,2,⋯n,where J1 and J2 are sets of beneficial attribute and nonbeneficial attribute, respectively.Step 5.
Separation proportions of the entire options are determined from PIS and NIS(14)Si+=∑j=1nφij−φi+2,(15)Si−=∑j=1nφij−φi−2,where i=1,2,3,⋯,m.Step 6.
The relative similarity index (SI) of every parameter is determined utilizing the accompanying equation(16)SI=Si−Si+−Si−.In TOPSIS, the first part is to change the outcomes to a decision matrix comprising of output responses (attributes) in columns and exploratory trials (alternatives) in rows as delineated in Equation (9). By utilizing Equation (10), the decision matrix is normalized, and relative weightage is doled to all entities. Then, equivalent relative weightage is fixed to entire seven responses, viz., material removal rate, electrode wear rate, surface roughness, radial overcut, taper angle, circularity, and cylindricity. The weighted normalization numbers were determined by using Equation (11). Using Equations (12) and (13), the positive ideal solution and negative ideal solution are obtained from the normalization matrix. Equations (14) and (15) are utilized to ascertain the separation measures of every alternative from PIS and NIS. Likewise, Equation (16) is employed to ascertain the similarity index for all the options by finding the separation measures [1].Based on the TOPSIS optimization, the normalized matrix, weighted-normalized matrix, separation evaluated data, and SI of every option are delineated in Table6. The alternative result with highest SI value is the predominant, and the trails are ranked depending upon the SI. The 23rd experimental run is the good run, and the 13th is the poor among every one of the other options. Table 7 displays the determined mean similarity index of all the input factors at all the levels.Table 6
TOPSIS.
RunNormalizationWeighted normalized matrixSeparationSIRankMRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)MRR (g/min)EWR (g/min)SR (μm)ROC (mm)θ (deg)CIR (mm)CYL (mm)S+S-10.135960.282220.052640.167130.081120.142940.199240.019440.040360.007530.023900.011600.020440.028490.555004.841440.897152320.125240.204370.158860.185700.350770.120070.217570.017910.029220.022720.026550.050160.017170.031110.539834.821920.89932930.084270.236940.074260.046420.053850.132320.162010.012050.033880.010620.006640.007700.018920.023170.552564.840250.897542140.086040.295440.119380.194980.025660.138580.091040.012300.042250.017070.027880.003670.019820.013020.545414.833050.898591450.058790.174210.086480.148560.052640.398860.151250.008410.024910.012370.021240.007530.057040.021630.551114.836330.897702060.063480.186650.109980.167130.090920.045740.080570.009080.026690.015730.023900.013000.006540.011520.545804.833980.898551570.060630.215610.129720.176410.117560.116800.221930.008670.030830.018550.025230.016810.016700.031740.543524.829780.898851180.095540.368670.064860.213550.085420.156010.237930.013660.052720.009270.030540.012220.022310.034020.554314.839050.897222290.073490.080880.066740.222830.077480.133680.086970.010510.011570.009540.031870.011080.019120.012440.551114.839240.8977619100.091310.248910.135360.278540.046680.202560.372890.013060.035590.019360.039830.006680.028970.053320.544154.828240.8987112110.067060.146190.072380.139270.105030.084130.034900.009590.020910.010350.019920.015020.012030.004990.551044.839360.8977718120.078080.312730.108100.111420.083890.082490.119250.011170.044720.015460.015930.012000.011800.017050.547654.834750.8982516130.654970.165920.081780.352820.058540.477000.450550.093660.023730.011690.050450.008370.068210.064430.559094.834450.8963325140.084210.209760.269780.176410.338620.102370.114020.012040.030000.038580.025230.048420.014640.016300.523714.806960.901755150.035830.151790.087420.194980.023340.211820.089300.005120.021710.012500.027880.003340.030290.012770.549164.837160.8980517160.056040.074620.236880.176410.020110.128780.066900.008010.010670.033870.025230.002880.018420.009570.527324.816690.901337170.085740.184490.141940.139270.537780.051730.027340.012260.026380.020300.019920.076900.007400.003910.544204.823110.8986113180.062590.025880.360020.157840.492630.305200.283010.008950.003700.051480.022570.070450.043640.040470.513634.790460.903163190.078330.200580.375060.185700.058450.087120.144270.011200.028680.053630.026550.008360.012460.020630.508104.796350.904212200.046240.156490.244400.185700.083290.049820.093080.006610.022380.034950.026550.011910.007120.013310.526394.814790.901456210.052640.134040.237820.213550.094220.118710.158520.007530.019170.034010.030540.013470.016970.022670.527114.814640.901328220.061000.151080.306440.185700.072790.055810.059050.008720.021600.043820.026550.010410.007980.008440.517464.806300.902804230.067210.147900.451200.139270.300360.070790.079120.009610.021150.064520.019920.042950.010120.011310.497484.782510.905781240.081630.100710.133480.222830.198290.037300.067190.011670.014400.019090.031870.028360.005330.009610.541614.828410.8991410250.654970.165920.081780.352820.058540.477000.450550.093660.023730.011690.050450.008370.068210.064430.559094.834450.8963424Table 7
Mean similarity index of each parameter at entry level.
ParameterSimilarity indexOptimal levelDifferenceRank12345I0.898060.897220.898430.901080.9017550.004531PON0.899220.896570.900290.900010.8984530.003732POFF0.900720.901180.898950.898350.8983520.002834DP0.900080.898970.898560.899990.8999410.001115SV0.898030.897870.900010.899550.9010850.003213


## 3.4. TLBO Algorithms

TLBO algorithms depict the teaching, and learning phenomenon takes place in the classroom [1]. The current work was centered on maximization of material removal rate and minimization of electrode erosion rate, SR, ROC, θ, circularity, and cylindricity, respectively. The regression equation for maximization and minimization of output factors is delineated in Equation (17) to Equation (23). Additionally, the parametric bounds are delineated in Equation (24) to Equation (28).Maximization:(17)MRR=0.00047+0.000367I+0.000214PON–0.000039POFF–0.000050DP–0.000025SV.Minimization:(18)EWR=–0.000535+0.000106I+0.000065PON–0.000014POFF–0.000007DP+0.000004SV,(19)SR=0.35–0.0242I+0.0076PON+0.0660POFF+0.0492DP+0.0029SV,(20)ROC=0.118–0.00210I–0.00200PON+0.00010POFF+0.00320DP+0.00180SV,(21)θ=0.367–0.03776I+0.0086PON+0.00444POFF+0.00327DP–0.00182SV,(22)CIR=–0.090+0.00021I–0.00397PON+0.00182POFF+0.00060DP+0.00459SV,(23)CYL=0.003–0.00411I+0.00295PON+0.00159POFF–0.00010DP+0.00163SV.Parameter bounds:(24)Pulsecurrent:4≤I≤12,(25)Pulse‐ontime:5≤PON≤9,(26)Pulse‐offtime:2≤POFF≤10,(27)Dielectricpressure:12≤DP≤20,(28)Sparkgapvoltage:28≤SV≤36.The TLBO is carried through the accompanying advances.Step 1.
Set the population size,Np=25.Step 2.
Based on DOE, the design matrix is embraced, and the same is ranked utilizing the GRG as delineated in Table8.Step 3 (teacher phase).
New solution is generated as delineated in Table9.
(29)Xnew=X+rXbest–Tf∗Xmean,where Xnew is a recent solution, X is a current solution, r is a random value between 0 and 1, Xbest is a teacher, Tf is a teaching entity either 1 or 2, and Xmean is a mean of the population.Step 4.
Here, the bounded input factors are joined with the actual parameters taken from design of experiments. Table10 delineates the combined population.Step 5.
Here, ranks 1 to 25 (50% of higher order rankings) are selected from the combined population table, and the same is optimized through the GRG. Ranks 1 to 25 acquired from the combined population are delineated in Table11.Step 6 (learner phase).
Creation of new solution is developed by means of a partner response which is haphazardly chosen from the population is delineated in Table12.
(30)Xnew=X+rX–Xp,where Xp is a partner solution.Table 8
Initial random population.
RunInput parameterResponseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL145212280.002980.000981.440.300.04880.07440.12820.6701915246414300.002400.000320.710.240.08100.04910.02990.6975210347616320.001720.000532.530.230.09850.04360.05450.6319422448818340.004440.001110.560.180.08480.05250.06850.68421145491020360.002200.000584.800.150.31400.02600.02720.6347121665416340.021390.000650.870.380.06120.17520.15490.6589516766618360.002800.000731.510.150.56220.01900.00940.6930712867820280.002750.000832.870.190.35400.03760.03920.61013239681012300.004090.000801.690.200.36670.04410.07480.59570241069214320.001920.000690.920.160.05500.14650.05200.65439171185620300.001980.000851.380.190.12290.04290.07630.64286201286812320.002560.000793.990.200.06110.03200.04960.652591813871014340.002040.000103.830.170.51500.11210.09730.51059251488216360.002810.001161.270.210.02680.05090.03130.7067061589418280.003120.001450.690.230.08930.05730.08180.652151916105814360.001990.000593.260.200.07610.02050.02030.699538171061016280.001510.000622.600.200.08710.01830.03200.690921318107218300.002550.001231.150.120.08770.03030.04100.72284419108420320.002070.000731.170.180.09510.01680.02770.73003220109612340.001830.000292.520.190.02100.04730.02300.702447211251018320.001170.000600.930.210.02440.07780.03070.69858922126220340.000930.790000.050.060.04860.05570.03130.71295523127412360.002190.000580.770.150.10980.03090.01200.75302124128614280.002670.000401.420.240.20730.01370.02310.694031125129816300.001860.000373.440.190.03550.01110.02160.729753Mean8761632Table 9
Teacher phase–updated process parameter and responses.
S. noNew input parameterBounded input parameterNew responseGRGRankIPONPOFFDPSVIPONPOFFDPSVMRREWRSRROCθCIRCYL12.23.9-0.6924.643.9212280.006660.013220.560.310.04500.09500.11650.605152322.25.452.712.528.345.452.712.528.30.005590.038500.930.290.07500.08580.10340.697521032.276163247616320.004450.030602.020.220.20270.06720.07200.631942142.28.559.319.535.748.559.319.535.70.003320.022703.120.160.33040.04860.04060.684211452.210.112.62339.4491020360.002940.030603.350.150.35370.04390.03490.634712065.13.92.71635.75.13.92.71635.70.007200.117130.840.230.11710.09210.08140.658951575.15.45619.539.45.15.45619.5360.005540.098171.780.190.22300.06820.05940.693071285.179.32324.65.179.320280.002700.033762.490.210.25860.03730.06540.610132295.18.5512.6928.35.18.5510928.30.002130.240743.510.270.22310.05160.07100.5957024105.110.1-0.612.5325.19212.5320.003710.036921.310.220.08870.07530.06410.65439161183.962328.383.962028.30.004320.115551.080.230.12530.04970.07400.64286191285.459.393285.459.312320.003700.058252.810.240.18740.05450.06140.6525917138712.612.535.7871012.535.70.003160.056673.350.200.23920.05070.03880.51059251488.55-0.61639.488.55216360.003510.102911.120.160.08980.06460.03390.70670615810.12.719.524.6892.719.5280.001700.076840.810.180.07710.04070.04630.65215181610.93.99.312.539.410.93.99.312.5360.004320.051562.660.210.16470.05430.04350.6995381710.95.4512.61624.610.95.451016280.001820.008112.480.210.15870.02600.04850.69092131810.97-0.619.528.310.97219.528.30.002170.167690.260.180.00920.03990.04360.7228441910.98.552.7233210.98.552.720320.001630.169270.790.130.06100.03610.02110.7300322010.910.16935.710.996935.70.001830.034552.560.180.09930.05150.02070.7024472113.83.912.619.532123.91019.5320.002900.136882.240.180.17890.02700.03590.6985892213.85.45-0.62335.7125.4522035.70.003920.275920.340.140.03410.05230.02650.7129552313.872.7939.41272.79360.003350.068941.360.190.00140.06670.03210.7530212413.88.55612.524.6128.55612.5280.000380.015591.910.200.05140.02970.03320.69403112513.810.19.31628.31299.31628.30.000600.017172.700.170.15060.01010.01860.729753Table 10
Combined population.
RunCombined input parameterNew responseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL145212280.002980.000981.440.300.04880.07440.12820.6701949246414300.002400.000320.710.240.08100.04910.02990.6975221347616320.001720.000532.530.230.09850.04360.05450.6319446448818340.004440.001110.560.180.08480.05250.06850.68421235491020360.002200.000584.800.150.31400.02600.02720.6347138665416340.021390.000650.870.380.06120.17520.15490.6589519766618360.002800.000731.510.150.56220.01900.00940.693076867820280.002750.000832.870.190.35400.03760.03920.61013409681012300.004090.000801.690.200.36670.04410.07480.59570441069214320.001920.000690.920.160.05500.14650.05200.65439241185620300.001980.000851.380.190.12290.04290.07630.64286411286812320.002560.000793.990.200.06110.03200.04960.652594713871014340.002040.000103.830.170.51500.11210.09730.51059481488216360.002810.001161.270.210.02680.05090.03130.70670271589418280.003120.001450.690.230.08930.05730.08180.652153716105814360.001990.000593.260.200.07610.02050.02030.6995334171061016280.001510.000622.600.200.08710.01830.03200.690923918107218300.002550.001231.150.120.08770.03030.04100.722841619108420320.002070.000731.170.180.09510.01680.02770.730032020109612340.001830.000292.520.190.02100.04730.02300.7024431211251018320.001170.000600.930.210.02440.07780.03070.698582222126220340.000930.790000.050.060.04860.05570.03130.712951723127412360.002190.000580.770.150.10980.03090.01200.75302224128614280.002670.000401.420.240.20730.01370.02310.694032525129816300.001860.000373.440.190.03550.01110.02160.72975362643.9212280.006660.013220.560.310.04500.09500.11650.60515432745.452.712.528.30.005590.038500.930.290.07500.08580.10340.69752122847616320.004450.030602.020.220.20270.06720.07200.63194352948.559.319.535.70.003320.022703.120.160.33040.04860.04060.684211830491020360.002940.030603.350.150.35370.04390.03490.6347133315.13.92.71635.70.007200.117130.840.230.11710.09210.08140.6589526325.15.45619.5360.005540.098171.780.190.22300.06820.05940.6930714335.179.320280.002700.033762.490.210.25860.03730.06540.6101342345.18.5510928.30.002130.240743.510.270.22310.05160.07100.5957045355.19212.5320.003710.036921.310.220.08870.07530.06410.65439283683.962028.30.004320.115551.080.230.12530.04970.07400.64286323785.459.312320.003700.058252.810.240.18740.05450.06140.652592938871012.535.70.003160.056673.350.200.23920.05070.03880.51059503988.55216360.003510.102911.120.160.08980.06460.03390.70670840892.719.5280.001700.076840.810.180.07710.04070.04630.65215304110.93.99.312.5360.004320.051562.660.210.16470.05430.04350.69953104210.95.451016280.001820.008112.480.210.15870.02600.04850.69092154310.97219.528.30.002170.167690.260.180.00920.03990.04360.7228454410.98.552.720320.001630.169270.790.130.06100.03610.02110.7300334510.996935.70.001830.034552.560.180.09930.05150.02070.70244946123.91019.5320.002900.136882.240.180.17890.02700.03590.698581147125.4522035.70.003920.275920.340.140.03410.05230.02650.712957481272.79360.003350.068941.360.190.00140.06670.03210.75302149128.55612.5280.000380.015591.910.200.05140.02970.03320.6940313501299.31628.30.000600.017172.700.170.15060.01010.01860.729754Table 11
Candidate solution based on the nondominance rank.
S. noCombined input parameterNew responseGRGRankIPONPOFFDPSVMRREWRSRROCθCIRCYL11272.79360.006580.000581.360.190.00140.06670.03210.7530212127412360.002190.000580.770.150.10980.03090.01200.742522310.98.552.720320.005730.000790.790.130.06100.03610.02110.73003341299.31628.30.006100.000652.700.170.15060.01010.01860.729754510.97219.528.30.005420.000100.260.180.00920.03990.04360.722845666618360.002800.000731.510.150.56220.01900.00940.7212067125.4522035.70.005300.000590.340.140.03410.05230.02650.712957888.55216360.005020.000831.120.160.08980.06460.03390.706708910.996935.70.006480.000622.560.180.09930.05150.02070.7024491010.93.99.312.5360.004500.000292.660.210.16470.05430.04350.699531011123.91019.5320.004300.000532.240.180.17890.02700.03590.69858111245.452.712.528.30.002950.000800.930.290.07500.08580.10340.697521213128.55612.5280.006520.000401.910.200.05140.02970.03320.6940313145.15.45619.5360.002480.000851.780.190.22300.06820.05940.69307141510.95.451016280.004640.000732.480.210.15870.02600.04850.690921516107218300.002550.001231.150.120.08770.03030.04100.689451617126220340.000930.790000.050.060.04860.05570.03130.68706171848.559.319.535.70.002680.001163.120.160.33040.04860.04060.68421181965416340.021390.000650.870.380.06120.17520.15490.681721920108420320.002070.000731.170.180.09510.01680.02770.67799202146414300.002400.000320.710.240.08100.04910.02990.6761221221251018320.001170.000600.930.210.02440.07780.03070.67015222348818340.004440.001110.560.180.08480.05250.06850.66312232469214320.001920.000690.920.160.05500.14650.05200.663002425128614280.002670.000401.420.240.20730.01370.02310.6593325Table 12
Learner phase–new process variables and objective values after interaction.
S.noNew input parameterBounded input parameterNew responseGRGRankInteractionIPONPOFFDPSVIPONPOFFDPSVMRREWRSRROCθCIRCYL1126.751.5456.7540.4126.75212360.003500.131350.960.180.00170.06390.03000.60641141 and 25212.726.564.6611.1238.2126.564.6612360.003150.092321.680.180.05730.05580.02720.59075192 and 24311.7288.6710.95120.8830.911.7288.67122030.90.001240.182810.530.130.02700.03290.01970.6672263 and 234129.889.06915.1226.2651299.06915.12280.000560.029562.670.170.13840.01220.02120.60127174 and 22511.7287.221.3421.9227.36511.7287.22220280.001690.182830.210.170.00040.03420.03750.62493115 and 2165.525.566.6617.1238.25.525.566.6617.12360.005320.055042.090.200.21890.06870.05920.60589156 and 20712.725.5491.3421.7636.63512.725.549220360.003670.288100.340.130.02630.04950.02090.6992637 and 1988.488.55-0.40914.4636.1658.488.55214.46360.003420.086161.190.170.07410.06580.03370.61784138 and 18910.7689.667.324.1636.63510.76897.3212360.001550.007762.780.160.15010.04200.01380.6739059 and 171011.0083.21811.70910.0839.311.00851012360.003490.016933.020.200.18280.04810.03530.597441810 and 161112.1323.5591021.0434.212.1325102034.20.002490.146872.440.150.20070.02450.02090.582062211 and 15123.8685.451.6119.4224.06545.45212280.005690.033260.750.290.05440.08870.10610.63567912 and 1413128.8917.08914.0423.6128.8917.08914.04280.005760.001860.960.180.08690.02150.01670.73367113 and 1144.2725.1096.6622.8364.2725.1096.6620360.005880.087951.920.190.25060.06960.06460.621631214 and 21510.94.76812.40914.2425.810.951014.24280.002170.012502.530.230.14590.03140.05440.546702415 and 3169.766.56-0.40918.8830.9359.766.56218.8830.9350.003260.167650.410.180.03630.05170.04670.604281616 and 41712.1325.78220.2237.13512.1325.78220360.003720.275160.390.130.03620.05100.02270.68916417 and 5188.59.11110.38920.1635.5358.59.111102035.5350.001320.035073.160.120.28660.02460.01000.70768218 and 6195.284.9014.6614.2433.0655.2854.6614.2433.0650.005770.023001.490.240.13860.07990.08020.64285819 and 72010.247.8794.6621.7629.810.247.8794.662029.80.001570.121101.180.160.09660.03150.03240.584182120 and 8213.1725.343.3416.226.86545.343.3416.2280.005330.009220.880.270.10800.07610.09800.64698721 and 92212.1325.24210.23120.4229.812.1325.242102029.80.001650.108282.270.170.17400.01660.03140.542002522 and 10233.048.9027.3417.3435.148.9027.3417.3435.10.003450.036162.700.180.27210.05720.04640.580762323 and 11246.249.7811.76914.6634.0356.249.781214.6634.0350.003070.018961.330.180.10240.06630.04320.635131024 and 1225127.879614.6628127.879614.66280.000710.029141.700.190.05960.02800.03420.584802025 and 13Based on the TLBO technique, the global optimal values were identified. The optimal set of input factors are acquired from the learner phase based on the top ranking [1]. This ranking is produced after interaction between parameters as displayed in Table 12. The SEM images of the hole made using optimal machining parameters are delineated in Figure 6. From the micrograph, it is evident that the machined area of the Si3N4–TiN ceramic matrix composite workpiece exhibits good surface finish.Figure 6
SEM micrographs of machined Si3N4–TiN.


## 3.5. Verification Test

The GRG for different optimization methods is calculated for electrodischarge machining of Si3N4–TiN ceramic matrix composite workpiece. A point by point correlation is made for the GRG acquired from joint optimization techniques and is outlined in Table 13. Finally, a confirmatory experiment was done for the final TLBO optimized values, and the outcomes are great in contention. Table 14 portrays the outcomes obtained for optimal input machining factors.Table 13
Comparison of various optimization techniques.
S. noOutput parametersTaguchiGRATOPSISTLBOGRG—0.753020.905780.73367Setting level—I: 12 ampsI: 12 ampsI: 12 ampsPON: 7μsecPON: 7μsecPON: 8.89μsecPOFF: 4μsecPOFF: 4μsecPOFF: 7.09μsecDP: 12 kg/cm2DP: 12 kg/cm2DP: 14.04 kg/cm2SV: 36 voltsSV: 36 voltsSV: 28 volts(A5B3C2D1E5)(A5B3C2D1E5)1MRR (g/min)0.004400.002190.002190.005762EWR (g/min)0.000320.000580.000580.001863SR (μm)0.560.770.770.964ROC (mm)0.060.150.150.185θ (deg)0.02100.10980.10980.08696CIR (mm)0.01110.03090.03090.02157CYL (mm)0.00940.01200.01200.0167Table 14
Comparison of verification test for various optimization techniques.
S.noOutput parametersGRATOPSISTLBO1MRR (g/min)Trial 10.002240.001990.00498Trial 20.001980.002210.00591Trial 30.002270.002300.00544Trial 40.002220.002040.00561Trial 50.002090.002190.00553Average0.002160.002150.005492EWR (g/min)Trial 10.000550.000620.00092Trial 20.000610.000610.00190Trial 30.000570.000560.00181Trial 40.000610.000590.00199Trial 50.000620.000600.00177Average0.000590.000600.001683SR (μm)Trial 10.770.790.82Trial 20.710.760.9Trial 30.80.810.89Trial 40.790.740.96Trial 50.750.780.95Average0.760.780.904ROC (mm)Trial 10.140.150.16Trial 20.160.160.19Trial 30.170.160.14Trial 40.150.140.15Trial 50.150.130.19Average0.150.150.175θ (deg)Trial 10.10890.11020.0910Trial 20.10990.10990.0891Trial 30.11010.10970.0852Trial 40.10890.10960.0888Trial 50.10950.10920.0869Average0.10950.10970.08826CIR (mm)Trial 10.03080.03080.0301Trial 20.02810.03140.0210Trial 30.03130.03060.0202Trial 40.03040.02790.0289Trial 50.03350.03280.0221Average0.03080.03070.02457CYL (mm)Trial 10.01210.01280.0152Trial 20.01320.01230.0159Trial 30.01290.01200.0182Trial 40.01150.01120.0181Trial 50.01220.01280.0170Average0.01240.01220.0169


## 4. Conclusions

The input factors influencing electrodischarge machining of adsorbed Si3N4–TiN workpiece using cylindrical-shaped W-Cu electrode were examined. The experimental runs for directing the experiments were arranged utilizing statistical tool by design of experiments methodology. The disparate mixture of input factors like I, PON, POFF, DP, and SV is chosen in this research. The outputs like MRR, EWR, SR, ROC, θ, CIR, and CYL are determined. Here, various optimization methodologies like Taguchi methodology, grey relational analysis, TOPSIS, and TLBO are engaged to obtain the combination of optimized factors to increase material removal rate and to decrease EWR, SR, taper angle, ROC, circularity, and cylindricity. From the experimental results and calculations, the accompanying conclusions were obtained:
(i)
The outcomes determined for grey relational analysis and TOPSIS are comparative. The best output factors are obtained forI=12 amps, PON=7 μsec, POFF=4 μsec, DP=12 kg/cm2, and SV=36 volts (A5B3C2D1E5).(ii)
The execution of GRA coupled with TLBO a global optimization technique gave the preferred outcomes over that of other methodologies. The accompanying combination was achieved from GRA coupled with TLBO algorithmI=12 amps, PON=8.89 μsec, POFF=7.09 μsec, DP=14.04 kg/cm2, and SV=28 volts.


### 4.1. Future Scopes of the Research

(i)
This study can be further extended for nanocomposites and microstructure studies on machined surface of adsorbed Si3N4–TiN composites.(ii)
Other shape of electrodes like rectangle, hexagon, and octagon can be employed.(iii)
Furthermore, in the future, different electrode materials can be employed to characterize the surface integrity, fatigue performance, and dry sliding wear behaviour of adsorbed Si3N4–TiN. Also, different polishing methods can be imparted for better surface finish and fatigue life, higher wear resistance, and microhardness.(iv)
Optimization techniques like genetic algorithm, simulated annealing, particle swarm optimization, and ant bee colony optimization can be employed to find out significant parameters.


## 4.1. Future Scopes of the Research

(i)
This study can be further extended for nanocomposites and microstructure studies on machined surface of adsorbed Si3N4–TiN composites.(ii)
Other shape of electrodes like rectangle, hexagon, and octagon can be employed.(iii)
Furthermore, in the future, different electrode materials can be employed to characterize the surface integrity, fatigue performance, and dry sliding wear behaviour of adsorbed Si3N4–TiN. Also, different polishing methods can be imparted for better surface finish and fatigue life, higher wear resistance, and microhardness.(iv)
Optimization techniques like genetic algorithm, simulated annealing, particle swarm optimization, and ant bee colony optimization can be employed to find out significant parameters.



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*Source: 4112448-2022-09-30.xml*