# Bi-objective Optimization of Process Parameters in Electric Discharge Machining of SS630 Using Grey Relation Analysis

Authors: Venkata N. Raju Jampana; P. S. V. Ramana Rao; Anubhav Kumar
Journal: Journal of Nanomaterials
 (2022)

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## Abstract

One of the most former and widely utilized unconventional machining is known as the process of electric discharge machining (EDM). This is a procedure, where a serialized set of electric discharges are applied to eliminate the material from a workpiece (i.e., electrically conductive). This article proposes a bi-objective optimization of process arguments in machining of stainless steel of 630 (SS630) grade using both experimentation and thermal investigation. Here, flushing pressure (PF), pulse on-time (TON), peak current (Ip), and pulse off-time (TOFF) are assumed as the input process parameters to conduct a series of experiments on die-sinking EDM (DS-EDM) of SS630 to predict the output characteristics of machining optimization using grey relation analysis (GRA). Both material removal rate (MRR) and surface roughness (SR) are used for evaluating the output response obtained using the machining performance. In addition, thermal investigation is performed using finite element method (FEM) analysis to compute theoretical MRR (T-MRR) for the distribution of temperature on workpiece. Further, GRA is employed to obtain the optimal process parameter combination for best output responses. From the confirmation test results, the optimal combination obtained using GRA approach is at Ip=6A, TON=35μs, TOFF=90μs, and PF=4MPa.


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## Body

## 1. Introduction

Manufacturing is experiencing many changes because of the frequent demands of the customers for qualitative, reliable, and superior components and merchandises in the most advanced and technological climate. To meet these demands, manufacturers around the globe are working toward cheaper cost solutions to maintain their competitiveness on machined parts and manufactured goods. It is not feasible to procure device products for cutting materials like stainless steel, Nimonics, titanium, satellites, and ceramics. Generation of intricate shapes on such materials is also difficult by traditional techniques. Advanced machining methods have come into existence to match such needs. Such advanced machining methods have unique qualities compared to conventional machining methods. EDM is one of such advanced machining methods, to generate parts with excellence, finesse, and dimensional accuracy [1]. The advanced machining methods are essential as several workpiece materials are actively employed in the automotive enterprises, aerospace part, medical appliances, and molding, and die manufacturing industries. A regulated erosion by a sequence of electric sparks necessitates removing the material in EDM, and the two conductors are immersed in a dielectric medium [2]. For electrical discharge sparking, both conductors are separated by the distance, known as a spark gap. The spark gap is maintained with the help of the servo controller [3]. The transmitted electrons strike with dielectric particles existing in the spark gap so that the plasma channel formed. The plasma channel permits the current to cross the conductors to produce sparks. A significant quantity of heat produced due to which a few portions of conductors melted and dissipated. After this, the material is melted and vaporized. During the process, several sparks are created, and the workpiece material gets the shape of the electrode. The flushing process can remove the melted material in the air gap [4]. Figure 1 displays the principal schematic picture of the EDM process.Figure 1
Schematic of EDM process.In [5], the authors executed a full scale electrothermal visualization of variable effect on the attributes of solitary spark corrosion used in the procedure of EDM. Additionally, they have also performed theoretical analysis in differentiation with experiment validation. Jithin et al. [6] assumed the equations of Gaussian heat flux and thermal conductivity as temperature relaying properties for finding the experimental radius of carter, which are then compared with predicted carter radius. In [7], the authors performed an improvement on modelling of EDM with the adjoining process of the deformed characteristic of geometry and the thermal study of heat transfer. Due to the proportionality of deformation rate computation with the spark corrosion, the outcome is more accurate and naturalistic result and further validated the simulated outputs by managing examination on AISI OI work steels with the change in the procedure variable of machine such asTONandIp. In [8], ANSYS FEM coding is used to calculate the propagation of temperature, and then prediction of volume discarded on account of solitary spark is reckoned from the temperature profiles. Further, T-MRR values are compared with the values of E-MRR. The recent investigation [9] of machining on H13 die steel assumed process variables such as substances of cathodes, anodes, TON, and Ip for conducting a series of experiments, and the machining process is evaluated using output responses like TWR, MRR, and SR. In addition, Taguchi approach is employed as an optimization of EDM parameters. In [10], MRR is verified on DS-EDM of structural machining of SKD11 die steel with process variables like TON, Ip, and gap voltage (VG). Further, the effects of these process parameters also analyzed using response surface methodology (RSM). In [11], the influence of different input process arguments in DS-EDM is experimented and examined with the usage of couple of electrodes such as copper and graphite with both polarities (i.e., positive, and negative) to obtain maximum response of MRR and minimum of SR.Chekuri et al. [12] studied the DS-EDM on supper alloy made of Nimonic C-263 with graphite electrode using Taguchi L25 orthogonal array by considering input process parameters such as Ip, TON, TOFF, and PF to obtain the output response characteristics like MRR, TWR, and SR, respectively. Rajamanickam and Prasanna [13] examined the EDM for drilling of small hole on Inconel 718 workpiece with brass electrode (diameter of 300 μm). The authors employed RSM and TOPSIS approaches for describing the significant input process parameters that influence the output response characteristics like MRR, EWR, ovrcut, taper angle and circularity etc. In [14, 15], the authors introduced optimization techniques based on evolutionary algorithms to obtain optimal process parameter combination to reduce the machining time and improving the machining efficiency with enhanced performance. In [16], the concept of artificial intelligence called artificial neural networks is employed to predict the output response parameters such as MRR, SR, and TWR after machining the Nimonic C-263 using DS-EDM process.Kavimani and Soorya [17] proposed T-GRA-PCA to assess the effect of process variables over the measured machining performance of WEDM performed on magnesium based MMCs. Chaudhari et al. [18] implemented a unique and integrated design for optimizing the control variables such as discharge current, TON, and TOFF in wire cut EDM process using an approach of GRA. The authors found an optimal combination of input control variables at 6 μsec, 4 μsec, and 6A of TON, TOFF, and discharge current, respectively. Further, the validation has proven the closest association of optimal outcome as compared to the experimental response. In [19], the authors performed an experimental evaluation with optimization of input control variables in DS-EDM of AISI D2 steel, where the optimal combination is obtained using integrated RSM with GRA technique. The obtained optimal combination of process variables such as discharge current, gap of spark, dielectric liquid, and electrode polarity are 15A, 6 mm, kerosene oil, and positive polarity, respectively. The confirmation test results have been verified and validated the enhancement in machining process. Mitra et al. [20] performed an induration process by creating a highly nonlinear model with twenty-two dimensional principles and implemented an architecture of neural network with multilayer perceptron for solving an optimization issue with multiple objectives. In [21], the authors experimented and validated the impact of various control variables such as VG, TON, and Ip on DS-EDM of SS with grade AISI420 material. They have measured MRR and electrode wear rate as output response attributed for performance validation. Additionally, the integrated Taguchi with GRA is applied to find the best possible combination for optimal machining on DS-EDM. Jampana and Ramana Rao [22] investigated an experimental analysis of DS-EDM on SS630 grade with machining control variable optimization using a design approach of Taguchi for an output response attributes such as MRR, and SR. However, the machining parameter optimization is still a challenging job for improving the productivity and reducing the labor time which influences the overall production cost in the applications of manufacturing filed. In substance, the main problems arisen in DS-EDM process are due to the generation of heat. Therefore, addressing the temperature alterations in workpiece material is essential to enhance the performance before starting the machining process, which can be achieved using thermal investigation techniques like FEM analysis [23, 24]. Recently, Chekuri et al. [25] studied the experimental and numerical investigation of DS-EDM on Nimonic C-263 as workpiece material with an electrode tool of copper-tungsten. In addition, hybrid optimization approach called the cuckoo search-based whale optimization algorithm is implemented for obtaining the optimal combination of machining control variables for increased performance. However, none of the works addressed in the literature have not examined FEM analysis of DS-EDM on SS630 grade. In addition, it is quite sturdy to do machining of a workpiece made of SS630 grade material because of its properties such as lesser thermal conductivity, higher erosive resistance, and higher built-up edge tendency. Further, this product has a variety of applications in industries such as pharmaceutical, pumping production, and other device paradigms.Hence, this article addresses a thermal and experimental evaluation of DS-EDM on a workpiece made of using SS630 grade material with an electrode tool of copper-tungsten. Initially, the temperature distribution profiles are observed using the FEM analysis, and T-MRR is computed using an isotherm of temperature. Additionally, GRA technique is employed as a solution for solving the optimization problem, which predicts the optimal combination of machining control variables.


## 2. Prerequisite for FEM Analysis

This paragraph states the various inspection of DS-EDM procedure utilizing the scanning of the FEM, which is preferred for replicating single spark with the EDM by obtaining numerous properties such as variable spark radius, cathode energy fraction, and evenly distributing the equation for Gaussian heat flux. The following are the considerations for numerical analysis:(i)
Workpiece substance is homogeneous and isotropic(ii)
Vitality fragment is depending onTON(iii)
297 K: required temperature(iv)
Modeling for solitary spark(v)
100%: effective flushingThe equation properties of Fourier heat condition are employed to derive the governing equation that operates FEM.


### 2.1. Governing Equation

The differential equations stated below are employed to manage the conduction of thermal generated heat in axisymmetric model:(1)ρCp∂T∂t=1r∂∂rKtr∂T∂r+∂∂zKt∂T∂z.Cp is denoted as specific heat, ρis workpiece, Tis temperature, and Kt is thermal conductivity. The r and z are denoted by cylindrical workpiece.


### 2.2. Boundary Conditions

Figure2 represents the 2D axisymmetric model which is introduced with frontier conditions that is on the north side of XY surface. The properties of nature Gaussian distribution are utilized by spark radius aimed overall with the ignition on heat flux time. Heat transfer beyond the spark radius is the convective generation of cooling effect of dielectric. Here, the value of heat flux is considered as negligible almost zero. XW is denoted as axisymmetric boundary, and WZ and YZ are two other boundaries, which are far from the radius of spark, severally.Figure 2
2D symmetric axis sharing its partition with DS-EDM process.


### 2.3. Heat Input

In general, DS-EDM has some significant factors such as workpiece heat input and the measure of thermophysical properties, where the preference of these parameters impacts the estimation of MRR values. The approximation of generated heat from plasma of transitory model is done using Gaussian heat distribution as formulated below:(2)qwr=4.45PVGIpπRs2exp−4.5rRs2,whereVG is denoted as the gap voltage, Rsisrepresentedas spark radius, Ip is denoted as peak current, P is denoted as amount of temperature gained by the workpiece, and qw is represented as the temperature quantity in the workpiece through the sparking operation.


### 2.4. Spark Radius

In real-time cases, it is a tough task to calculate short pulse duration with the spark radius. Thus, for calculation of this spark radius constructively, numerous methods had been listed in the literature. In those, Erden23 has shown that the discharge power and time are directly proportional to spark radius, which is expressed as follows:(3)Rs=ZPmTonn,wherem, n, and Z are represented as empirical constants; Ton denotes pulse on-time; and P and Rs represent the power and spark radius, respectively.


### 2.5. Solution Methodology for Thermal Analysis

With the implementation of FEM, control equation specified in Equation (1) can be resolved by acquiring the ANSYS 15.0 visualization domain. The size of the workpiece for thermal analysis is assumed as 15×10×3 mm, where element size is assumed as 1 μm and then the model mesh and dimensions are created. FEM is an application to gain the organizing of the heat quotient on the workpiece, and the values of MRR are calculated from the workpiece as shown below:
(4)MRR=Cv×60TON+TOFFsec,whereCvisdenoted crater volume and TON and TOFF are represented as pulse on-time and pulse off-time.


## 2.1. Governing Equation

The differential equations stated below are employed to manage the conduction of thermal generated heat in axisymmetric model:(1)ρCp∂T∂t=1r∂∂rKtr∂T∂r+∂∂zKt∂T∂z.Cp is denoted as specific heat, ρis workpiece, Tis temperature, and Kt is thermal conductivity. The r and z are denoted by cylindrical workpiece.


## 2.2. Boundary Conditions

Figure2 represents the 2D axisymmetric model which is introduced with frontier conditions that is on the north side of XY surface. The properties of nature Gaussian distribution are utilized by spark radius aimed overall with the ignition on heat flux time. Heat transfer beyond the spark radius is the convective generation of cooling effect of dielectric. Here, the value of heat flux is considered as negligible almost zero. XW is denoted as axisymmetric boundary, and WZ and YZ are two other boundaries, which are far from the radius of spark, severally.Figure 2
2D symmetric axis sharing its partition with DS-EDM process.


## 2.3. Heat Input

In general, DS-EDM has some significant factors such as workpiece heat input and the measure of thermophysical properties, where the preference of these parameters impacts the estimation of MRR values. The approximation of generated heat from plasma of transitory model is done using Gaussian heat distribution as formulated below:(2)qwr=4.45PVGIpπRs2exp−4.5rRs2,whereVG is denoted as the gap voltage, Rsisrepresentedas spark radius, Ip is denoted as peak current, P is denoted as amount of temperature gained by the workpiece, and qw is represented as the temperature quantity in the workpiece through the sparking operation.


## 2.4. Spark Radius

In real-time cases, it is a tough task to calculate short pulse duration with the spark radius. Thus, for calculation of this spark radius constructively, numerous methods had been listed in the literature. In those, Erden23 has shown that the discharge power and time are directly proportional to spark radius, which is expressed as follows:(3)Rs=ZPmTonn,wherem, n, and Z are represented as empirical constants; Ton denotes pulse on-time; and P and Rs represent the power and spark radius, respectively.


## 2.5. Solution Methodology for Thermal Analysis

With the implementation of FEM, control equation specified in Equation (1) can be resolved by acquiring the ANSYS 15.0 visualization domain. The size of the workpiece for thermal analysis is assumed as 15×10×3 mm, where element size is assumed as 1 μm and then the model mesh and dimensions are created. FEM is an application to gain the organizing of the heat quotient on the workpiece, and the values of MRR are calculated from the workpiece as shown below:
(4)MRR=Cv×60TON+TOFFsec,whereCvisdenoted crater volume and TON and TOFF are represented as pulse on-time and pulse off-time.


## 3. Materials and Methods

Here, SS630 grade material is selected as a workpiece due to low risk of distortion at reduced temperatures. It has 8 mm thickness and70×40 mm rectangular dimensions. Additionally, it is a best choice for an experimentation on DS-EDM when there is a necessity of erosion and higher strength. The electrode material used in this work is a copper-tungsten mixture since they are not mutually solvable.The electrode length is about 21.5 mm and 12.5 mm diameter. The chemical composition of workpiece material and the properties of electrode material are listed in Tables1 and 2, respectively.Table 1
Workpiece material compositions with corresponding weight.
Name of component% of weightSilicon (Si)0.40 maxNickel (Ni)10.00-14.00Manganese (Mn)0.60-1.00 maxCarbon (C)0.036-0.44 maxChromium (Cr)16.00-18.00Sulphur (S)0.030 maxNitrogen (N)0.10 maxPhosphorus (P)0.05 maxMolybdenum (Mo)2.00-3.00Iron (Fe)BalanceTable 2
Fundamental attributes of composition of electrode material.
Name of compositionDensity (g/cm3≥)Hardness (Kgf/mm2)Resistivity (μΩcm)W50/Cu5011.849114.993.199


## 4. Experimental Setup

This section contains numerous process variables with all ideal levels and experimental setup. All the experimental trials are performed using FORMATICS 50 on an apparatus of DS-EDM model, which is embedded with ELECTONICA PRS 20 to analyze the effects of various elements of process variables such asTOFF, TON, PF, and Ip on the SR of machine drilled hole. In addition, MRR also computed during the process of DS-EDM of SS 630 grade with copper-tungsten electrode. Before starting themachining process of DS-EDM , the experimentation tools like electrode, and workpiece are well polished and cleaned. The control variables of input to the DS-EDM are listed in Table 3 with their number of levels, while the working conditions and their explanation for setting up the experimentation is listed in Table 4, respectively. Additionally, the SR is measured on machined surfaces with the direction of transverse on machine surface of cutoff length as 0.8 mm using Talysurf SR tester. The final values of SR are measured using the iterative mechanism, where it was tested thrice and considered the averaged value as final SR.Table 3
Input control variables with their corresponding levels.
ParameterNo. of levelsLevel 1Level 2Level 3Level 4Ip (A)6101418TON (μs)15253545TOFF (μs)20507090PF (Mpa)2468Table 4
Working circumstances for setting up the experimentation.
NameDescriptionWorkpiece materialSS630 grade70×40×8mmElectrode materialCopper-tungsten (21.5 mm length with a diameter of 12.5 mm)Dielectric oilCommercial EDM oil grade SAE 450Sign of polarityNormalSupply voltage110 VGap voltage70 VTime of machining5 mins


### 4.1. Thermal Investigation Using FEM

In practice, the commercial FE code is integrated in DS-EDM process to estimate the distribution of temperature and the deformation of molten material using the plasma pressure. On the other hand, FE code is employed by ANSYS for verifying the solutions for real-time problems. The complicated interlinkage of numerous material phenomenon is intricated in DS-EDM which is again a complex thermal process. Therefore, FEM analysis is applied to simulate the distribution of temperature and stress analysis into the workpiece; here, an advanced software, i.e., ANSYS, is utilized for upgrading the DS-EDM model with FEM analysis for all complex parameters processing. This can be utilized with various models and determine any complex geometry which consists various capacities of FEM varying from thermal system, and fluid mechanics, simple linear structure to static analysis of nonlinear complex structures, structural mechanics, varying dynamic survey, and electromagnetics.This work considered ANSYS 14.5 workbench for simulating the results on modelling of DS-EDM with SS630 grade with the development of geometrical work via precise constraints of boundary and employing variable loads. An approach called mapped meshing is utilized for meshing the domain of workpiece. As it is shown in Figures3–5, there are four different regions with distinct colors such as red, light green, light blue, and blue, whereas the red and blue colors denote the region of boiling and solid metal, while the light green and light blue denote the zones of liquid and heat affected, respectively. Usually, the distribution of temperature on workpiece relies on input control variables such as input heat percentage, TON, Ip, TOFF, and VG along with the change in phase. Figure 3 demonstrates the distribution of temperature attained for 18A of current intensity with 45 μsec of pulse duration, where the maximum and minimum distributed temperatures are about 800 K and 295.16 K. Figure 4 illustrates the amount of material removed for the same current intensity with pulse duration, where the maximum and minimum heat flux is about 11.337 w/mm2 and 1.26 w/mm2. The structural error is demonstrated in Figure 5.Figure 3
Distribution of temperature distribution attained for 18A of current intensity and 45μsec of pulse duration.Figure 4
Amount of material removed for 18A of current intensity and 45μsec of pulse duration.Figure 5
Structural error.


### 4.2. Results

Figure6 illustrates the processing of machining with DS-EDM on SS630 grade, while Figure 7 demonstrates the workpiece after machining of SS630. As mentioned earlier, MRR and SR are used as he output response parameters for evaluating the performance of DS-EDM on SS630 grade. Table 5 lists with the obtained results of output response parameters with varying of input control parameters.Figure 6
Machining procedure of DS-EDM.Figure 7
Illustration of SS630 grade workpiece after machining.Table 5
Obtained experimental values of MRR, and SR for the input process variables.
Experiment no.Ip (A)TON (μs)PF (MPa)TOFF (μs)E-MRR (mm3/min)SR (μm)16152201.3723.29210154505.0153.92314156702.4124.12418158903.4214.45514254205.5224.56618252506.1015.1276258702.5853.12810256903.9214.21918356203.8125.311014358504.9124.921110352708.1564.72126354909.1213.561310458204.1254.31146456503.9123.8415184547010.1215.541614452909.3125.62


## 4.1. Thermal Investigation Using FEM

In practice, the commercial FE code is integrated in DS-EDM process to estimate the distribution of temperature and the deformation of molten material using the plasma pressure. On the other hand, FE code is employed by ANSYS for verifying the solutions for real-time problems. The complicated interlinkage of numerous material phenomenon is intricated in DS-EDM which is again a complex thermal process. Therefore, FEM analysis is applied to simulate the distribution of temperature and stress analysis into the workpiece; here, an advanced software, i.e., ANSYS, is utilized for upgrading the DS-EDM model with FEM analysis for all complex parameters processing. This can be utilized with various models and determine any complex geometry which consists various capacities of FEM varying from thermal system, and fluid mechanics, simple linear structure to static analysis of nonlinear complex structures, structural mechanics, varying dynamic survey, and electromagnetics.This work considered ANSYS 14.5 workbench for simulating the results on modelling of DS-EDM with SS630 grade with the development of geometrical work via precise constraints of boundary and employing variable loads. An approach called mapped meshing is utilized for meshing the domain of workpiece. As it is shown in Figures3–5, there are four different regions with distinct colors such as red, light green, light blue, and blue, whereas the red and blue colors denote the region of boiling and solid metal, while the light green and light blue denote the zones of liquid and heat affected, respectively. Usually, the distribution of temperature on workpiece relies on input control variables such as input heat percentage, TON, Ip, TOFF, and VG along with the change in phase. Figure 3 demonstrates the distribution of temperature attained for 18A of current intensity with 45 μsec of pulse duration, where the maximum and minimum distributed temperatures are about 800 K and 295.16 K. Figure 4 illustrates the amount of material removed for the same current intensity with pulse duration, where the maximum and minimum heat flux is about 11.337 w/mm2 and 1.26 w/mm2. The structural error is demonstrated in Figure 5.Figure 3
Distribution of temperature distribution attained for 18A of current intensity and 45μsec of pulse duration.Figure 4
Amount of material removed for 18A of current intensity and 45μsec of pulse duration.Figure 5
Structural error.


## 4.2. Results

Figure6 illustrates the processing of machining with DS-EDM on SS630 grade, while Figure 7 demonstrates the workpiece after machining of SS630. As mentioned earlier, MRR and SR are used as he output response parameters for evaluating the performance of DS-EDM on SS630 grade. Table 5 lists with the obtained results of output response parameters with varying of input control parameters.Figure 6
Machining procedure of DS-EDM.Figure 7
Illustration of SS630 grade workpiece after machining.Table 5
Obtained experimental values of MRR, and SR for the input process variables.
Experiment no.Ip (A)TON (μs)PF (MPa)TOFF (μs)E-MRR (mm3/min)SR (μm)16152201.3723.29210154505.0153.92314156702.4124.12418158903.4214.45514254205.5224.56618252506.1015.1276258702.5853.12810256903.9214.21918356203.8125.311014358504.9124.921110352708.1564.72126354909.1213.561310458204.1254.31146456503.9123.8415184547010.1215.541614452909.3125.62


## 5. Optimization Using GRA

In a problem of multiresponse, the influence and relationship between different parameters are complex and not clear. This is termed as grey which signifies poor and uncertain information. The proposed GRA analyzes this complicated uncertainty among the multiresponses in each system and optimizes it with the help of grey relational grade (GRG). Therefore, a multiresponse optimization problem is reduced to a single response optimization problem called single relational grade. The detailed procedure of GRA is described as below:Step 1: The first step of GRA involves in the normalization of output response parameters such as MRR and SR for avoiding distinct units and variability mitigation. This is essential due to that differentiation in one data varies from another data. An actual value is utilized to gain an appropriate value which makes the array in the range of [0, 1]. Usually, this is an approach of transforming the actual data into a corresponding data. If the required observation is to be minimized, the smaller-the-better attributes are proposed for the normalization to surmount it into a satisfactory range using the below formulation:(5)x∗ik=maxxik−xikmaxxik−minxik,i=1,⋯,m;k=1,⋯,n,where the desired value is denoted with x. The data quantity of experiments and the corresponding response are referred to m and n. The actual and preprocessed sequence are denoted as xik, and x∗ik, respectively. The maximum and minimum values of actual data are represented as maxxik, and minxik. Table 6 demonstrates the grey relation generation values for output attributes named MRR and SR where maximum is better and minimum is better, respectively.Table 6
Grey relation generation values for output response parameters obtained using DS-EDM of SS630 with Cu-W electrode.
Ideal seq.MRR (mm3/min)SR (μm)Larger the betterSmaller the better100.93220.416390.6830.1188710.640.2341980.46850.474340.42460.5405190.270.138644180.2913480.56490.2788890.124100.4046180.28110.7754030.36120.8857010.824130.3146650.524140.2903190.7121510.032160.9075320Step 2: The second step is to compute the grey relation coefficient (GRC) denoted asξik from the obtained normalized values in Step 1. The computation of GRC is as follows:
(6)ξik=∆min+ξ∆max∆0ik+ξ∆max,where ∆0ik denotes the deviation sequence of the reference sequence and ∆0i=x0k−xik represents the sequence of comparability, where the reference and comparability sequences are termed as x0k, and xik, respectively.The larger and smaller values of absolute differences of all the comparability sequences are represented as∆min and ∆max. The coefficient of identification is denoted as ξ with the range of 0,1. In general, this value will be considered as 0.5.Step 3: This step computes the grey relation grade (GRG) as shown below:(7)γi=1n∑k=1nξik,where the required GRG is represented as γi for ith experiment and n denotes the response attributes quantity. In general, this GRG determines the level of association between the sequences of reference and comparability. On the other side, it also represents the overall illustration of all the quality attributes. Therefore, the optimization problem of multiple responses can be transformed into a solitary optimization issue using the design approach of Taguchi with integration of GRA technique. Table 7 lists the obtained GRC and GRG with ranking values for the bi-objective optimization of MRR and SR responses.Table 7
Obtained GRC and GRG values with their corresponding ranks.
Ideal Seq.Deviation seq.GRCGRGRankMRR (mm3/min)SR (μm)MRR (mm3/min)SR (μm)110.0680.3333330.8802820.606808420.583610.320.4614210.6097560.535588730.8811290.40.3620230.5555560.4587891240.7658020.5320.3950070.4844960.4397511450.525660.5760.4874910.4646840.476087960.4594810.80.5211150.3846150.4528651370.86135600.36728110.68364280.7086520.4360.4136840.5341880.4739361090.7211110.8760.4094630.3633720.38641816100.5953820.720.4564620.4098360.43314915110.2245970.640.6900390.4385960.5643186120.1142990.1760.8139360.7396450.7767911130.6853350.4760.4218220.5122950.46705811140.7096810.2880.4133320.6345180.52392581500.96810.3405990.67033160.09246810.8439280.3333330.5886315Step 4: Now, this stage determines the control variables optimal level using the maximum GRG which designates an improved quality of product. To get this, the aggregated grade values of all machining control variables should be derived as listed in Table8, which is called a table of mean responses where the maximum of average grade values are selected as an optimal machining control variable combination for multiple responses.Table 8
Response table for mean GRG.
LevelTONTOFFPFIp10.51020.48410.55320.647820.52160.48640.61470.510230.54020.59430.46080.489240.56250.56980.50590.4873Delta0.05220.11020.15390.1605Rank4321Table9 illustrates the response table for signal to noise (S/N) ratios. Figures 8 and 9 disclose the main effect plots of GRG and S/N ratios, respectively.Table 9
Response table for signal to noise ratios (larger is better).
LevelTONTOFFPFIp1-5.916-6.414-5.198-3.8632-5.779-6.296-4.385-5.8733-5.672-4.629-6.782-6.2714-5.076-5.105-6.080-6.437Delta0.8401.7852.3972.575Rank4321Figure 8
Main effect plot of mean GRG.Figure 9
Main effect plot of mean of S/N ratios.Step 5: This stage uses analysis of variance (ANOVA) to determine the relevant factors influencing the different responses with the confidence level of 90%, which provides valuable data about experimental requirements. So, the process of ANOVA avoids the unwanted experimentations by selecting the best combination of EDM performance properties. Further, the ANOVA analysis will be useful in determining the contribution percentage to recognize parameter dependent effects generated from EDM, because the influence of each parameter on multiple response cannot be measured using Taguchi’s design technique. The ANOVA divides the entire variability of the answer such as squared sum deviations generated from grand mean with the error and parameter contributions. Here, probability of significance is considered asP values, and it is calculated using Fisher’s F ratio (F value), which tells the importance of each processing parameter. Further, the range of P values should be less than 0.1, which indicates the significant parameters. If the P value (probability of significance) is less than 0.1, the P value is determined based on the Fvalue or to get information about the importance of the chosen answer. In addition, the mean square (MS) is generated by dividing the degrees of freedom (DF) with available independent data-based sum of squares (SS), i.e., MS=SS/DF. Moreover, in the optimal parameters obtained scenario, F value is equivalent to MS, i.e., F=MS. Table 10 shows the GRG based ANOVA simulation findings with the importance of process parameters on multiple responses.Table 10
Obtained results of ANOVA on GRG of DS-EDM on SS630.
SourceDFAdj. SSAdj. MSF valueP valueRemarksTON30.0062650.0020881.070.479“Insignificant”TOFF30.0386770.0128926.590.078“Significant”PF30.0521210.0173748.870.053“Significant”Ip30.0708040.02360112.060.035“Significant”Error30.0058730.001958Total150.173740Step 6: This step enhances the GRG by investigating confirmation test results. Finally, the GRG predicted values for optimal level can be obtained as follows:(8)γ^=γm+∑i=1oγ¯i−γm,where the total mean GRG is denoted withγm, the mean GRG at the optimal level of each parameter is represented as γi, and o is the number of the significant process parameters. Table 11 lists the obtained values of T-MRR, and E-MRR with machining control variables for L16 orthogonal array. The validation of DS-EDM on SS630 grade is done using the obtained T-MRR computed from isotherm of temperature observed from FEM analysis with the values of E-MRR obtained from experimental analysis. Figure 10 illustrates the comparative analysis of E-MRR and T-MRR which discloses a very close relation between numerical and experimental values of MRR.Table 11
Obtained values of T-MRR and E-MRR with machining control variables.
S. No.Ip (A)PF (MPa)TOFF (μs)TON (μs)E-MRR (mm3/min)T-MRR (mm3/min)16220151.3721.512210450155.0154.912314670152.4122.321418890153.4213.614514420255.5225.23618250256.1015.9076870252.5852.421810690253.9213.672918620353.8123.6121014850354.9125.211110270358.1568.912126490359.1219.4611310820454.1253.671146650453.9123.87615184704510.12111.241614290459.3128.91Figure 10
Comparison of E-MRR and T-MRR obtained using FEM analysis and experimentation of DS-EDM on SS630.


## 6. Conclusion

This article aimed on experimental and thermal investigation of DS-EDM with bi-objective optimization using GRA approach. In addition, FEM analysis also employed to compute the T-MRR using 2-D axisymmetric with its boundary conditions by distributing the Gaussian flux. Further, GRA is used and found the best fit and approximate solutions for obtaining the optimal combination of process parameters such as Ip, TON, TOFF, and PF. From the confirmation test results, the optimal combination obtained using GRA approach is about 12th experiment, i.e., Ip=6A, TON=35μs, TOFF=90μs, and PF=4MPa. The most significant process parameters identified using ANOVA are Ip, PF, and TOFF with 90% confidence values.



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