Optimization of Process Parameters in Powder-Mixed EDM

Abstract

Electrical discharge machining (EDM) finds wide application all around the world for producing complex contour on very hard metals and alloys. It finds numerous applications in automobile, die making, aerospace, and electronic industries. Low volumetric material removal rate and reduced surface quality are few limitations of the process. Powder-mixed electro-discharge machining (PMEDM) is a novel advancement to EDM that has enhanced the machining capabilities of the process. The present chapter deals with the investigations on the effect of process variables like powder concentration (C _p ), peak current (I _p ), pulse-on-time (T_on), duty cycle (DC), and gap voltage (V _g ) on output responses like material removal rate (MRR), tool wear rate (TWR), electrode wear ratio (EWR), surface roughness (SR), recast layer thickness (RLT), and microhardness (HVN) for PMEDM of H-11 hot work tool steel. The work material possesses excellent mechanical characteristics and finds huge application in various industries. Taguchi’s L₂₇ orthogonal array has been implemented to conduct the experiments using graphite powder-mixed dielectric with the copper tool. Single-objective optimization has been performed to determine the optimum set of input parameters. Analysis of variance (ANOVA) has been implemented to determine the effect of each process parameter and to establish the optimal setting of process parameters. Multi-objective optimization using technique for an order of preference by similarity to ideal solution (TOPSIS) was used to determine the optimum set of process variables to obtain maximum MRR and HVN with minimum TWR, EWR, SR and RLT simultaneously. Predicted results on verification with confirmation tests improve the preference values by 0.1021 with TOPSIS. The recommended settings of process parameters is found to be C _p  = 6 g/l, I _p  = 3 A, T_on = 200 µs, DC = 80% and V _g  = 50 V from TOPSIS. The microstructures were examined with scanning electron microscope (SEM) to find the presence of surface defects and identify modifications on the surface.

1 Introduction

Novel manufacturing theory makes use of non-conventional sources of energy like light, sound, chemical, electrical, mechanical, ions and electrons. The technical and industrial advancement has led to the growth of very hard materials which are difficult to machine but are widely used in nuclear, aerospace and other industries. With the progress in the field of material science, advancement of latest metallic, ceramic materials and composite materials has been witnessed which possess excellent mechanical properties, thermal characteristics and electrical conductivity. Spark erosion machining techniques or non-traditional machining processes are used for machining such exotic materials. Non-traditional machining processes do not employ any conventional tools for material removal. The intricacy of the contour, size, requirement of product accurateness and high surface quality can be overcome by implementing non-traditional methods. Presently, non-conventional processes acquire infinite capabilities, but exhibit poor material removal rates. Enormous developments have taken place in the past few years for the improvement of MRR. With increase in removal rate, the cost efficiency of the process gets maximized, leading to greater application of non-traditional techniques for machining. Electrical discharge machining (EDM) is widely used for making tools, dies and parts with higher accuracy. Modern electric discharge machines have been established globally as a benchmark in manufacturing. They are proficient of machining geometrically complex components such as composites, superalloys, ceramics, heat-treated tool steels, heat-resistant steels, carbides etc. which find application in mould making industries, aeronautics, aerospace and nuclear industries. EDM has reached the recent fields of sports, optics, medicinal and surgical instruments, automotive and R&D areas.

The process of EDM came into existence in 1943, with its foundation in Moscow by the Russian scientists Boris and Natalya Lazarenko. The researchers reported that by immersing the electrodes in oil, steady sparks were generated than air. The phenomenon was inverted and controlled sparks were used for erosion. EDM machine was first developed during war by Lazarenkos. It was very useful for the erosion of metals like tungsten or tungsten carbide. Advancement for understanding the erosion phenomenon evolved in the 1950s. In 1960s, the growth in semiconductor industry endorsed substantial development in EDM machines with increased reliability that produced surfaces with superior quality. The development then led to the design of generators, automation, servo-control and robotics. During 1980s micro-machining using EDM gained a good deal of interest. The EDM process became globalized during this period. Subsequently, advancements to EDM emerged in the 1990s using neural networks, response surface methodology, fuzzy control, central composite design, Taguchi optimization etc. The research in this field is still in progress with innovative ideas of adding additives to the dielectric fluid like conductive powders, nano-sized particles, carbon nanotubes etc.

In EDM process the tool and workpiece material are separated by a small gap in the presence of a dielectric medium. High-frequency-controlled pulses are generated which creates a plasma channel due to the continuous movement of electrons and ions. The temperature in the discharge gap rises to a range of 8000–12,000 °C which causes melting and vaporization. PMEDM improves the process capabilities of EDM by producing surfaces with superior finish and less cracks. Adding fine powders to the dielectric decreases its insulating strength by increasing the inter-electrode gap. The removal of debris becomes easier in the presence of powders. On applying a voltage of 80–320 V an electric field is formed in the range of 10⁵–10⁷ V/m generating positive and negative charges on powder particles. This energizes powder particles and they move in zigzag manner forming clusters in the sparking area. Bridging occurs under the sparking area creating several discharges in a single pulse. The rapid sparking and erosion from the workpiece surface improve the machining rate. Widening of plasma channel produces stable sparks which form craters with improved surface finish. Material is removed from both the electrodes which combine with the powder particles and modifies the surface properties of the machined surface. Consequently, the MRR increases, TWR reduces and uniform sparks produce corrosion-resistant surfaces. The presence of abrasive powder changes the sparking pattern and improves the surface properties, increases the microhardness gets increased and micro-cracks get minimized. Added powders may be aluminium, chromium, graphite, silicon, titanium etc.

Pecas and Henriques (2008) reported that PMEDM process performance depends upon powder type, concentration, grain size, electrode area, constituents of the tool and workpiece material. Kumar et al. (2009) reviewed the outcome of mixing the dielectric fluid with various powders and additives. Assarzadeh and Ghoreishi (2013) implemented response surface methodology with desirability technique to model and optimize the process parameters during EDM of CK-45 die steel using Al₂O₃ powder-mixed dielectric to improve the MRR. Singh et al. (2012) investigated the effect of process parameters on SR for machining H-11 with the copper tool in the presence of Al powder in the dielectric. Negative polarity of the tool electrode reduced the SR. Talla et al. (2015) conducted multi-objective optimization of PMEDM using Taguchi, GRA and Principal Component Analysis (PCA) to control the process parameters. Lal (2015) performed multi-objective optimization with Taguchi-based GRA for wire EDM. Sidhu et al. (2014) reported the optimal process setting for machining of three types of MMCs using PMEDM. MRR, TWR, SR and surface integrity were examined to determine the significant process parameters. The responses were jointly optimized using technique for order of preference by similarity to ideal solution (TOPSIS) and optimal process conditions were recognized. Singh et al. (2015) examined the outcome of adding graphite powder to the dielectric on the surface properties of superalloy Super Co 605. The results showed that an optimization between microhardness and surface finish can be achieved by this method of machining. Batish and Bhattacharya (2012) studied the material migration occurring between electrode and powder-suspended dielectric fluid for enhancing the surface properties in terms of microhardness for H-11 and H-13 steels. Aluminium, copper, graphite and tungsten powders were added to kerosene, EDM oil, and refined mineral oil as dielectric. Sidhu et al. (2014) optimized MRR, TWR, SR and surface integrity for three different metal matrix composites using TOPSIS and the ranking was done as per the severity of surface defects. Gadakh (2012) applied TOPSIS method for solving multiple criteria optimization problem in wire electrical discharge machining (WEDM) and obtained the most suitable set of process parameters.

From the available literature it is evident that several researchers have reported results using different powders mixed during EDM, but performance characteristics of H-11 during PMEDM needs investigation. The quality of the machined component is defined by various output characteristics such as MRR, TWR, SR, recast layer thickness, microhardness obtained on the machining surface etc. Thus, investigating the significance of the process variables in relation to the output performance characteristics becomes vital. Therefore the problem of PMEDM can be considered as a multi-objective optimization problem. The aim of this study is to obtain a single-optimal setting of various input parameters to obtain a single-output characteristic as a whole. Multi-attribute decision-making techniques like TOPSIS have not yet been used to find the optimal setting during PMEDM of H-11. The present work is a stride in this direction. Taguchi design of experiments is used to conduct the experiments using an L₂₇ orthogonal array. An effort has been made to find an optimal set of process variables by using multi-objective optimization using TOPSIS to get maximum MRR and minimum TWR, EWR, SR, RLT and maximum HVN by adding graphite powder to the dielectric in different concentrations. ANOVA has been used to create a relationship among the significant input parameters on the output responses. A comparative study for the EDM and PMEDM surface characteristics has been done using scanning electron microscope. The optimal parameter setting obtained from Taguchi and TOPSIS can be used for quality improvement in industrial applications involving PMEDM.

2 Materials and Methods

The machines, materials and design of experiment technique adopted for the estimation of output responses are highlighted in this section. The procedure used for optimization has also been presented in this section.

2.1 EDM Machine Set-up

The electric discharge machine, model ELECTRONICA-ELECTRAPULS PS 50ZNC has been used for the experiments. Commercial-grade EDM oil has been used as a dielectric fluid. To facilitate the generation of a rectangular form of current pulses for discharging, dielectric fluid was energized by “Current Pulse Generator” and associate controller. The current and voltage waveforms were recorded on a “Digital Storage Oscilloscope”. Figure 1 shows the machine used in the present study.

Fig. 1

EDM machine used for the experiment

Working tank of the machine had a capacity of 300 L for the circulation of dielectric fluid. The powder particles were required to be added in different concentrations for which changing the entire dielectric fluid and removing the powder particles from the circulating system would have been difficult. The existing circulation system might have choked due to the presence of powders and debris. To minimize the cost, avoid the wastage of dielectric and for effective use of powder particles, a separate machining tank has been designed with a capacity of 20 L. It consists of a machining tank to perform the operation placed in the working tank of EDM. A workpiece fixture assembly was placed in it to hold the workpiece. The machining tank was filled up with the dielectric fluid. A pump was installed to ensure proper distribution of powder in dielectric fluid. To avoid the powder from settling down, a stirring arrangement was installed. Each run was carried out for a time duration of 15 min. The setup of the tank is shown in Fig. 2.

Fig. 2

PMEDM setup (Tripathy and Tripathy 2017b, c)

2.2 Selection of Materials

The mechanical properties and composition of the workpiece and tool material used for the present experiment have been discussed in this section.

2.2.1 Workpiece Material

H-11 hot work tool steel is the workpiece material. This steel possesses very high strength, abrasion resistance, wear resistance, compressive strength, hardenability, toughness and it is not susceptible to hot cracking. The presence of chromium in the H-11 steel resists oxidization whereas molybdenum prevents corrosion in non-oxidizing environments. The mechanical properties of the H-11 steel are given in Table 1. Applications of H-11 is found in aircraft components, structural use, die casting dies, extrusion tooling, forging dies, piercing tools, hot work punches, tool holders, ejector pins etc. The properties cause a great challenge during machining by conventional methods. The chemical composition of this material as obtained by glow discharge-optical emission spectrometer is given in Table 2. Each surface of the workpiece and tool were machined using CNC-milling machine to get smooth mirror-like surfaces. The electrodes were subjected to surface grinding for proper contact and alignment of surfaces during machining. The dimension of the workpiece used for this EDM operation was 120 × 60 × 25 mm.

Table 1 Mechanical properties of H-11 steel

Table 2 Chemical composition of H-11 steel

2.2.2 Tool Material

Electrolytic copper electrode (99.9%) has been used as the tool electrode material. A square tool of dimension 20 × 20 × 60 mm has been used to perform the machining operation. The mechanical properties of the tool material are given in Table 3. The work material was mounted on the T-slot table and positioned at the desired place and clamped. The electrode was clamped and its alignment was checked. The machining was performed for time duration of 15 min. Finally the essential power switches were switched ‘ON’ for operating the desired machine settings.

Table 3 Properties of tool electrode material

2.3 Process Parameters

The process parameters chosen for the present research work are powder concentration (C _p ), peak current (I _p ), pulse on time (T_on), duty cycle (DC) and gap voltage (V _g ) to study their effect on output parameters e.g. material removal rate (MRR), tool wear rate (TWR), electrode wear ratio (EWR), surface roughness (SR), recast layer thickness (RLT) and microhardness (HVN) based upon the significant effect on the EDM and PMEDM process and the extensive literature review presented. The methodology to assess the performance characteristics are discussed below.

2.3.1 Material Removal Rate

High material removal rate is the most desirable output response for any machining process which leads to increased productivity. After each machining operation, the workpiece material was taken out and weighed to find out the weight loss. Weight of the workpiece before and after the experiment was measured using an electronic balance with a least count of 0.001 g. The time duration of each experimental run was recorded using a digital stop watch. From the weight loss obtained, the material removal rate was calculated for different experimental runs. MRR is calculated using the volume loss from the workpiece material as cubic millimetre per minute (mm³/min). The MRR is expressed as:

$$ \begin{aligned} & {\text{MRR }}\left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = \frac{\text{Wear weight of the work piece }}{{\rho \, \times {\text{time}}}} \\ & {\text{MRR}} = w_{i} - w_{f} /\rho *T \\ \end{aligned} $$

(1)

where w _i and w _f are initial and final weights of the workpiece before and after the machining process, ρ is density of the workpiece material and T is the machining time in minutes.

2.3.2 Tool Wear Rate

The tool material for machining is selected based upon the principle that the material should have low resistance to electricity and high melting point. The tool electrode was taken out and weighed after each machining operation to find out the weight loss. Weight of the tool before and after the experiment was measured to determine the tool wear rate. The TWR is expressed as:

$$ \begin{aligned} & {\text{TWR }}\left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = \frac{\text{Wear weight of the tool}}{{\rho \times {\text{time}}}} \\ & {\text{TWR}} = t_{i} - t_{f} /\rho *T \\ \end{aligned} $$

(2)

where t _i and t _f are initial and final weights of the tool before and after the machining process, ρ is density of the tool and T is the machining time in minutes.

2.3.3 Electrode Wear Ratio

The electrode wear ratio is dependent on the material removal rate and the tool wear rate. Lower EWR is desirable to enhance the productivity of the process. EWR can be defined as “the ratio of weight of the electrode wear to the weight of the workpiece wear after machining” and is expressed as:

$$ \begin{aligned} & {\text{EWR}}\, (\% )= \frac{{{\text{`` }} {\text{Wear weight of the tool}}^{\text{'' }} }}{{{\text{``}} {\text{Wear weight of the work piece}}^{\text{'' }} }} \times 100 \\ & {\text{EWR}} = w_{t} /w_{w} *100 \\ \end{aligned} $$

(3)

where w _t and w _w are the wear weights of the tool and workpiece material measured after the machining operation is carried out in relation to the TWR and MRR.

2.3.4 Surface Roughness

Larger is the vertical deviation, rougher is the surface. The surface roughness is measured based upon various statistical descriptors out of which centre line average method is mostly used. SR is the arithmetic mean of the deviations from the mean line. The expression for R _a is given as:

$$ R_{a} = \left( {\frac{1}{L}} \right)\mathop \smallint \limits_{0}^{L} \left| {y\left( x \right)} \right|{\text{d}}x $$

(4)

where, L is the sampling length, y is the profile curve sampled by the set of N points and x is the profile direction. The roughness of the surface was measured using a surface roughness tester (Talysurf, Rank Taylor Hobson, England, Model-Surtronic S-100 series).

2.3.5 Recast Layer Thickness

During the machining process, a small amount of material gets re-solidified after being melted due to the refrigeration effect of the dielectric fluid. This layer is known as the recast layer. Material transfer also takes place from the powder suspended in the dielectric fluid and also from the electrode to the machined surface. Beyond this layer lies the heat-affected zone and the base material. In order to find out the structural features present below the machined surface and the distribution of cracks in the recast layer, specimens were cut from the machined surface in a traverse direction and were then mounted for metallographic studies. The recast layer thickness was measured using a scanning electron microscope (FESEM, model: Supra 55, Zeiss, Germany) for all the experiments by taking three sets of readings for a particular experiment and considering the average of the three values as the average recast layer thickness.

2.3.6 Microhardness

After the metallographic analysis, the samples were measured for hardness in a microhardness tester (LM 247AT of LECO) under a load of 10 mgf. The purpose of obtaining the microhardness of the material before and after machining was to examine the change in hardness and its effect on the machining surface due to the addition of the powder particles during machining. The microhardness was measured at three different locations and the average value was considered to be the microhardness of the machined specimen.

2.4 Design of Experiments

Taguchi’s technique uses a philosophy and methodology to improve the quality of the process and minimizes the cost involved to carry out the process by optimizing the product design using statistical concepts. The effect of various machining process parameters such as concentration of powder (C _p ), peak current (I _p ), pulse on time (T_on), duty cycle (DC) and gap voltage (V _g ) on various output responses like material removal rate (MRR), tool wear rate (TWR), electrode wear ratio (EWR), surface roughness (SR), recast layer thickness (RLT) and microhardness (HVN) on H-11 hot work tool steel was investigated using Taguchi’s parameter design and Analysis of variance (ANOVA) helps to determine the statistically significant parameters affecting the responses. Predicted results obtained by Taguchi’s technique were verified through confirmatory tests for validation and minimization of errors. Taguchi prescribes the use of orthogonal arrays (OA) for experiments. The design of experiments involves the assignment of important and influencing parameters to appropriate columns in the array with the use of linear graphs or triangular tables as suggested by Taguchi. The use of array in the design provides almost identical experimental runs. The most important stage in the DOE lies in the selection of control factors and their levels. The results are further analysed to establish the optimal condition for a product or process, estimation of the contribution of individual parameters affecting the response, and to determine the optimum response under the best condition. The best condition may be determined by analysing the behaviour of minimum effects of each of the parameters which provides the trend of each parameter and its influence on the process. ANOVA is applied to the results which help to determine the percentage contribution of each parameter for a stated level of confidence. The ANOVA table suggests which parameters need to be controlled. Taguchi suggests two ways to carry out the complete analysis. In the first case, the results of a single run or the average of repetitive runs are analysed through main effects plot and ANOVA (raw data analysis). The second approach uses signal-to-noise (S/N) ratio to the previous steps. The S/N ratio is a concurrent quality metric linked to the loss function. As S/N ratio maximizes, the loss associated gets minimized. S/N ratio provides the robust set of operating conditions for the process. S/N ratio is defined as “the ratio of the mean of the signal to the standard deviation of the noise”. It is denoted by ‘η’ and it has the unit of dB. The present analysis involves the use of Taguchi’s orthogonal array to conduct the experiments and the optimum setting is obtained by analyzing the main effect plot aided by the raw data analysis aided by S/N data analysis followed by ANOVA. Based upon the trial experiments and extensive literature survey, the significant machining parameters taken into consideration are concentration of powder (C _p ), peak current (I _p ), pulse on time (T_on), duty cycle (DC) and gap voltage (V _g ) and their effect on the output responses has been investigated. Three sets of experimental runs have been performed at each condition. The control factors were selected based on the literature survey and some preliminary investigations. L₂₇ Taguchi’s orthogonal array was used for the experiments as shown in Table 4.

Table 4 Selection of levels for the factors

2.4.1 Signal-to-Noise Ratio

Establishment of the loss function with its appropriate k value and to use it as a figure of merit is not easy and cost-effective. Thus, the loss function is transformed to S/N ratio. S/N ratio being a concurrent statistics uses two or more characteristics of distribution and converts them into a single figure of merit. A higher value of S/N ratio implies that signal is much higher than the random effect of noise factors. The equations for calculating S/N ratios for “lower-the-better (LB), higher-the-better (HB) and nominal-the-best (NB)” type of characteristics are:

$$ {\text{LB}}{:}\;{\text{S/N Ratio}} = - 10\log_{10} \,\left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} y_{i}^{2} } \right] $$

(5)

$$ {\text{HB}}{:}\;{\text{S/N Ratio}} = - 10\log_{10} \,\left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} y_{i}^{ - 2} } \right] $$

(6)

$$ {\text{NB}}{:}\;{\text{S/N Ratio}} = - 10\log_{10} \left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} (y_{i} - y_{0} )^{2} } \right] $$

(7)

where

y :

sample mean

z :

standard deviation for the number of observations in each trial.

y _o :

nominal value of the characteristic

2.4.2 Selection of Orthogonal Array and Parameter Assignment

Selection of orthogonal array depends on the number of controllable parameters, their interactions with each other, and the number of levels to be selected. The number of controllable parameters with their levels considered in the present work is shown in Table 4. The minimum DOF required for the experiment are the sum of all the degrees of freedom of the factors. In the present experimental investigation, five three-level factors are considered for the study. As per Taguchi’s experimental design philosophy, a set of three levels assigned to each parameter has two degrees of freedom. Thus, total DOF of the experiment becomes 10. The OA to be used should have more than 10 DOF. Hence, an L₂₇ OA was chosen which has 27 trials and 26 DOF, assuming the interaction effect of process parameters negligible as shown in Table 5. The additional DOF may be used to measure the random error. Twenty-seven experiments each were conducted for three different powders mixed with the dielectric fluid using Taguchi’s experimental design methodology, repeating each experiment three times. The designs, plots, and analysis have been carried out with MINITAB 15 software.

Table 5 Taguchi’s L₂₇ standard orthogonal array

2.4.3 Analysis of Variance

Analysis of variance (ANOVA) was performed to determine the significant effect of process parameters on performance characteristics. The main effect plots for factors show the trend of the influence of factors toward the process. The importance of process variables with respect to output responses helps to determine the optimum set of parameters using ANOVA from Minitab15 software. Various steps involved in the analysis are:

• Step 1: Total of all results (T):

  $$ T = \mathop \sum \limits_{i = 1}^{n} \mathop \sum \limits_{j = 1}^{R} y_{ij} , $$

  (8)

  where, y _ij is the value of the characteristic in the ith trial and jth repetition.

• Step 2: Correction Factor (C.F.):

  $$ {\text{C}}.{\text{F}}. = T^{2} /N,{\text{ where }}N{\text{ is the total number of experiments i}}.{\text{e}}.\;3 \, \times { 27} = 8 1. $$

  (9)

• Step 3: Total sum of squares (SS _T ):

  $$ {\text{SS}}_{T} = \mathop \sum \limits_{i = 1}^{n} \mathop \sum \limits_{j = 1}^{R} y_{ij} - {\text{C}}.{\text{F}} . $$

  (10)

• Step 4: Sum of squares of parameter A (SS _A ):

  $$ {\text{SS}}_{A} = \left[ {\frac{{A\left( 1 \right)^{2} }}{{N_{A1} }} + \frac{{A\left( 2 \right)^{2} }}{{N_{A2} }} + \frac{{A\left( 3 \right)^{2} }}{{N_{A3} }}} \right] - {\text{C}}.{\text{F}} . $$

  (11)

  where, N_A1, N_A2 and N_A3 are the number of experiments with parameter A at levels 1, 2 and 3, respectively. The sums of squares for all the factors are calculated similarly.

• Step 5: Error sum of squares:

  $$ {\text{SS}}_{e} = {\text{SS}}_{T} {-}\left( {\text{Summation of sum of squares of all the parameters}} \right) $$

  (12)

  where, e stands for the error.

• Step 6: Degrees of freedom:

  $$ {\text{Total DOF}} = \left( {{\text{total number of trials}} - 1} \right) = \left( {R \, \times \, n \, - 1} \right) = 80 $$

  (13)

  DOF of each parameters = (Number of levels of each parameter − 1) = 2

  The DOF for all parameters are calculated in the similar way.

• Step 7: Mean square of variance (V):

  $$ V_{A} = {\text{Variance due to parameter }}A = \frac{{\text{SS}}_{A}}{\text{fA}} $$

  (14)

  Variance for the other parameters is obtained in the similar manner.

• Step 8: Percentage contribution (P):

  P _A  = Percentage contribution of parameter A towards mean of the response

  $$ P_{A} = \left( {\frac{{{\text{SS}}_{A} }}{{{\text{SS}}_{T} }}} \right) \times 100 $$

  (15)

  Similarly, the percentage contribution of all other parameters is calculated.

• Step 9: F-ratios:

  The F-ratio is defined as the ratio of variance due to a parameter and due to its error.

  $$ F_{A} = \frac{{V_{A} }}{{V_{e} }} $$

  (16)

The F-ratio is calculated for all the parameters in the similar manner.

2.5 Multi-objective Optimization

Taguchi’s experimental philosophy is focused on optimizing the process parameters in the perspective of a single quality criterion which does not give sufficient idea about the influence on other performance characteristics involved. The performance of the product is evaluated by various response parameters. Taguchi technique cannot solve a multi-response optimization problem. Hence, multi-objective optimization techniques are implemented wherein the quality characteristics are optimized and the results for the best levels are obtained. Taguchi technique is often combined with multi-objective optimization techniques to switch a multi-decision-making technique to a single-objective optimization problem. The decision maker assigns different priority weights to the responses basing upon their relative importance.

2.5.1 Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

The present study focuses on finding the most suitable set of process variables for PMEDM using TOPSIS to obtain maximum MRR and HVN along with minimum TWR, EWR SR, and RLT with graphite powder-mixed dielectric. The optimum set of input parameters should be identified to improve the machining process for performance characteristics and surface quality and improve the machining characteristics of H-11 tool steel. Analysis of variance (ANOVA) helps to identify the statistically significant input parameters that affect the performance parameters. TOPSIS is a capable multi-objective decision-making tool for solving complex decision-making problems in manufacturing domain where number of criteria, alternatives and their interactions play a significant role and their simultaneous effect influences the process to a great deal. TOPSIS uses preference grades with ranking order to find the most suitable set of input variables for the performance measures. TOPSIS can be used suitably for solving any type of decision-making problems. TOPSIS is a multi-optimization technique used to find the best alternative from a finite set. The technique is based upon the principle that the chosen criteria should have the shortest distance from the positive ideal solution and greatest distance from the negative ideal solution, the best solution being the closest to the ideal solution. The steps involved in carrying out the procedure of TOPSIS are:

• Step 1 The decision matrix is the first step of TOPSIS which consist of ‘n’ attributes and ‘m’ alternatives and is represented as (Tripathy and Tripathy 2017b, c):

  $$ D_{m} = \left[ {\begin{array}{*{20}c} {x_{11} } & {x_{12} } & {x_{13} } & \cdots & \cdots & {x_{1n} } \\ {x_{21} } & {x_{22} } & {x_{23} } & \cdots & \cdots & {x_{2n} } \\ {x_{31} } & {x_{32} } & {x_{33} } & \cdots & \cdots & {x_{3n} } \\ \vdots & \vdots & \vdots & \ddots & \ddots & \vdots \\ \vdots & \vdots & \vdots & \ddots & \ddots & \vdots \\ {x_{m1} } & {x_{m2} } & {x_{m3} } & \cdots & \cdots & {x_{mn} } \\ \end{array} } \right] $$

  (17)

  where $x_{ij}$ is the performance of ith alternative with respect to jth attribute.

• Step 2 Normalized matrix is obtained by the following expression:

  $$ r_{ij} = \frac{{x_{ij} }}{{\sqrt {\sum\nolimits_{i = 1}^{m} {x_{ij}^{2} } } }}\quad j = 1,2, \ldots,n. $$

  (18)

• Step 3 The weight of each attribute was assumed to be $w_{j}$ (j = 1, 2, …, n). Weighted normalized decision matrix V = [$v_{ij}$] may be obtained as:

  $$ V = w_{j } r_{ij} $$

  (19)

  where, $\sum\nolimits_{j = 1}^{n} {w_{j} = 1} .$

• Step 4 The most suitable and least suitable solutions may be obtained from the following expressions:

  $$ \begin{aligned} V^{ + } = & \left\{ {\left( {\sum\limits_{i}^{\hbox{max} } {v_{ij} } \left| {j \in J} \right.} \right),\left. {\left( {\sum\limits_{i}^{\hbox{min} } {\left| {j \in J} \right.} } \right. | i = 1,2, \ldots m } \right)} \right\} \\ = & \left\{ {v_{1}^{ + } ,v_{2}^{ + } ,v_{3}^{ + } , \ldots ,v_{n}^{ + } } \right\} \\ \end{aligned}$$

  (20)
  $$ \begin{aligned} V^{ - } = & \left\{ {\left( {\sum\limits_{i}^{\hbox{max} } {v_{ij} } \left| {j \in J} \right.} \right),\left. {\left( {\sum\limits_{i}^{\hbox{min} } {\left| {j \in J} \right.} } \right. | i = 1,2, \ldots m } \right)} \right\} \\ = & \left\{ {v_{1}^{ - } ,v_{2}^{ - } ,v_{3}^{ - } , \ldots ,v_{n}^{ - } } \right\} \\ \end{aligned} $$

  (21)

• Step 5 The separation of alternatives from positive ideal solution is given by:

  $$ S_{i}^{ + } = \sqrt {\mathop {\sum\nolimits_{j = 1}^{n} {\left( {v_{ij} - v_{j}^{ + } } \right)^{2} } }\limits_{{}}^{{}} } ,\quad i = 1,2, \ldots m $$

  (22)

  The separation of alternatives from negative-ideal solution is given by:

  $$ S_{i}^{ - } = \sqrt {\mathop {\sum\nolimits_{j = 1}^{n} {\left( {v_{ij} - v_{j}^{ - } } \right)^{2} } }\limits_{{}}^{{}} } ,\quad i = 1,2, \ldots m $$

  (23)

• Step 6 The relative closeness of the alternative to the ideal solution is calculated and expressed as:

  $$ P_{i} = \frac{{S_{i}^{ - } }}{{S_{i}^{ + } + S_{i}^{ - } }}\quad i = 1,2, \ldots m $$

  (24)

• Step 7 The $P_{i}$ value was ranked in descending order to identify the set of alternatives having the preferred solutions.

Preference value of alternatives can be calculated from their nearness to ideal solution. The ratio of negative ideal separation measure divided by the sum of negative ideal separation measure and the positive ideal separation measure gives the relative closeness. The normalized matrix, weighted normalized decision matrix, separation of alternatives from positive and negative ideal solutions and preference values for TOPSIS for the runs with the ordered rankings are presented in Tables 25, 26, 27 and 28 respectively. The most suitable value of performance measure is the one which is close to the ideal solution of the performance measure and has the maximum preference value with the highest rank.

3 Results and Discussions

Experimental results obtained by varying the chosen set of input parameters for the selected output responses have been presented in this section. The discussion of the obtained results and the variations in their behaviour has also been detailed in the present section.

3.1 Experimental Results

Experiments were conducted using Taguchi’s L₂₇ orthogonal array. The results are represented in Table 6.

Table 6 L₂₇ experimental design with response variables

3.2 Effect of Process Parameters on Response Characteristics

The influence of input parameters on response characteristics has been highlighted in the present section. The variation of the output response with each input parameter has been discussed with the help of respective graphs.

3.2.1 Effect of Process Parameters on Material Removal Rate

The goal of machining is high material removal and low tool wear. The MRR is the volume of material being removed per minute during machining. Experimental results show that machining without powder increases the MRR as I _p and T_on increase whereas the TWR, SR and RLT increase hampering the surface texture. Addition of powder in varying concentration modifies the surface properties. It causes a decrease in insulating strength of the dielectric fluid while increasing the inter-electrode gap making the removal of debris easier. Rapid sparks are generated due to the bridging effect which erodes material faster from the workpiece and increases the machining rate. Widening of plasma channel generates consistent sparks creating shallow craters on the machined region with superior surface finish. When graphite powder is added in C _p of 0 g/L, the MRR varies in a range of 2.564–10.940 mm³/min. When C _p increases to 3 g/L, the MRR shows slight increase from 2.87–11.04 mm³/min. Further increase of C _p to 6 g/L improves the MRR in a range of 5.56–12.54 mm³/min. The variation of MRR with the input parameters is shown in Fig. 3a–e. As the I _p increases, the MRR increases significantly as more thermal energy is produced in the discharge channel as the electrical power increases. As T_on increases, the MRR slightly decreases and then tends to increase with the increase in discharge energy and heat transferred to the section. The decrease in MRR is due to the constant flushing pressure which is not sufficient to remove the molten material causing redeposition on the surfaces. The abrasive property of the powder promotes makes the removal of debris easier. The discharge gap distance increases with V _g , which consequently increases the material deposition on the surface which may be minimized under proper flushing conditions.

Fig. 3

Variation of MRR with process parameters (Tripathy and Tripathy 2017b, c)

3.2.2 Effect of Process Parameters on Tool Wear Rate

Tool wear rate is determined as the volumetric material removed per minute during machining from the tool surface. The main aim of machining should be less tool wear for more amount of material removed from the workpiece surface. When no powder is added to the dielectric, the tool wear varies within a range of 0.0172–0.5243 mm³/min. With the increase in C _p , the tool wear rate shows reduction. The TWR shows an increase with further increase in the concentration of powder to compensate for the more amount of MRR. With more MRR, TWR also shows an increase irrespective of the concentration of powder added to the dielectric as shown in Fig. 4a. More amount of MRR is observed while the I _p is more. Thus, more TWR occurs when more MRR is achieved with increased I _p . With the addition of 0 g/L of graphite powder, the maximum TWR is 0.5243 mm³/min which reduces to a maximum value of 0.1517 mm³/min when 3 g/L of graphite powder. On addition of 6 g/L of graphite powder, the maximum TWR reaches to a value of 0.2341 mm³/min which is higher than that achieved with a C_p of 3 g/L. When graphite powder is added to the dielectric, more amount of carbon gets deposited on both the tool and workpiece surface. The resolidified layer on the workpiece leads to the recast layer formation and causes damage to the workpiece surface. Increased carbon content can be removed with proper flushing, which if insufficient would lead to increased TWR. Figure 4b–e show that with the increase in current and pulse on time the MRR and the TWR consequently increase due to the increased thermal energy in the discharge channel. This phenomenon is observed irrespective of the increase in the concentration of powders. With the increase in duty cycle, the tool wear rate increases as the material removal rate also show an increase due to the rapid ejection of molten material. The tool wear rate also shows an increase with the increase in gap voltage as the increased discharge gap distance increases the deposition of material on the machined surface and to perform the erosion of material from this deposited layer, the TWR shows an increase. With proper flushing conditions, higher machining rates can be achieved.

Fig. 4

Variation of TWR with process parameters (Tripathy and Tripathy 2017b, c)

3.2.3 Effect of Process Parameters on Electrode Wear Ratio

The characteristic of a perfect tool should be the potential of removing maximum material from the workpiece with the capability to resist self-erosion. When the machining is performed without addition of powder, the increase in I _p and T_on, increases the EWR. With the addition of powder, the EWR decreases which is the result of less tool wear with more material removal from the workpiece. Figure 5a–e show that with the increase in concentration of powder-mixed to the dielectric, the EWR tends to decrease initially up to C _p of 3 g/L of powder but on increasing the C _p to 6 g/L, the EWR increases to a value much lower than that achieved with a C _p of 0 g/L. The nature of the variation of EWR can be related to the machining rates achieved by the addition of powder to the dielectric. The maximum value of EWR at 0, 3 and 6 g/L is 4.7928, 1.2777 and 1.711% respectively. With the increase in I _p , the EWR increases for graphite powder-mixed dielectric. This is because of the more thermal energy generated in the discharge channel. The EWR shows variation in relation to the amount of material removed and the corresponding TWR for the maximum amount of material removed from the workpiece. With the increase in T_on, the EWR shows a decrease followed by a significant increase with the further increase of T_on. With the increase in DC, the EWR tends to decrease initially followed by a significant rise with the increase in DC. This is because of the fact that for a C _p of 3 g/L, the amount of material removed from workpiece is less than that with a C _p of 6 g/L, with a subsequent increase in TWR. Hence, the EWR initially decreases, then increases due to the rapid ejection of molten material with the increase in DC. With the increase in V _g , the EWR increases due to the increase in discharge gap distance which leads to more amount of material deposition on the top surface of the workpiece leading to the increase in TWR for the required amount of MRR in presence of proper flushing.

Fig. 5

Variation of EWR with process parameters

3.2.4 Effect of Process Parameters on Surface Roughness

The SR during PMEDM depends on size of the crater and variation of recast layer. From the experimental results, it can be seen that the roughness of the surface varies within a range of 3.8–6.19 µm without addition of powder. On addition of graphite powder in a C _p of 3 g/L, the SR lies between 1.94 and 5.65 µm. As the C _p increases to 6 g/L, the SR varies in a range of 2.41–6.19 µm. Influence of input parameters on SR is shown in Fig. 6a–e. With the rise in pulse current, the SR increases as the large dispersive energy cause impulsive forces and violent sparks which result in formation of large craters leading to the increase of SR as shown in Fig. 6b. Complete flushing does not occur during the pulse—off-time which increases the SR due to resolidification. Adding foreign particles in proper size and quantities reduce the SR during machining. With the increase in T_on, more heat is transferred to the section causing more material removal and increased SR. During PMEDM, the plasma flushing efficiency increases which improves the surface texture. Material deposition and carbide formation increases the SR. SR increases with increase in V _g as increased discharge gap distance minimizes the effect of induced energy at the workpiece surface thus increasing the deposition on the machined surface producing increased SR.

Fig. 6

Variation of SR with process parameters (Tripathy and Tripathy 2017b, c)

3.2.5 Effect of Process Parameters on Recast Layer Thickness

RLT increases with the increase in machining rate. It can be seen from Fig. 7a–e that increase in I _p increases the RLT. The temperature on the surface thus rises to the melting temperature consequently increasing the amount of material removed. Since the dielectric fluid does not get sufficient time to remove the molten material, the RLT increases. Increasing the C _p also increases the RLT as more amount of material is removed in presence of powder particles and redeposition occurs if flushing is insufficient which tends to increase the RLT. With the increase in T_on, the amount of heat transferred to the section increases. Adding graphite powder while machining and the breakdown of the dielectric fluid increases the carbon content. During PMEDM, as the T_on increases, the RLT tends to increase followed by reduction as the process becomes stable with the increase in discharge rate. Increase in DC, increases the RLT by a subsequent decrease which is due to the conduction of heat into the workpiece with a decrease in discharge duration. The abrasive effect of the powder particles decreases the RLT with the increase in DC. Increase in V _g increases the RLT due to the increase in discharge gap distance, which reduces the effect of induced energy at the workpiece and increases material deposition.

Fig. 7

Variation of RLT with process parameters (Tripathy and Tripathy 2017b, c)

3.2.6 Effect of Process Parameters on Microhardness

The microhardness of the parent material before machining has been found to be 621. The microhardness of the material after PMEDM was nearly double of the value before machining. It can be observed from Fig. 8a–e that the increase in C _p and I _p , increase the HVN values appreciably. Melting and deposition phenomenon increase the HVN. It may be observed that the surface quality is increased with the increase in HVN. The HVN increases while machining without the addition of powder with the increase in the values of I _p and T_on as high current increases the pulse energy. As the discharge column expands at higher pulse on time more heating of the surface occurs which releases the stresses and lowers the HVN at higher pulse on time. Increase in DC decreases the HVN as a consequence of the decrease in HVN with the variation of T_on. As V _g increases HVN also increases due to improper flushing of the debris during the no spark condition.

Fig. 8

Variation of HVN with process parameters

3.3 ANOVA Results for the Output Responses

The ANOVA results of each output response have been discussed in this section. The optimum set of process parameters has also been identified using the main effect plots for S/N ratio and means.

3.3.1 Analysis of Variance for Material Removal Rate

From the main effect plots shown in Fig. 9, the influence of different factors on the process can be visualized. The significance of the process variables in relation to MRR was investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 7 and 8 respectively. MRR being higher-the-better type of quality characteristic, from the response curves as shown in Fig. 9a, it can be revealed that the third level of parameters of C _p , third level of I _p , third level of T_on, third level of DC and third level of V _g may offer maximum MRR. It may be noticed that the parameters C _p , I _p , T_on and V _g show similar trend of variation in both the main effect plots whereas DC shows the best value in the third level from the main effect plot of means and second level as a best value from the main effect plot for S/N ratio. In order to arrive at the final optimal setting, the relative contribution of the mean and S/N values has been considered from the ANOVA table.

Fig. 9

Main effect plot for means and S/N ratio of material removal rate. a Main effect plot for means of MRR (Tripathy and Tripathy 2017a). b Main effect plot for S/N ratio of MRR

Table 7 ANOVA table for means of MRR

Table 8 ANOVA table for S/N ratio of MRR

The relative contribution of DC towards mean value of MRR (0.36%) is lower than that of S/N ratio (2.02%). Therefore, considering the level corresponding to the higher relative contribution, the optimum combination of input parameters for best MRR is the third level of parameters of C _p , third level of I _p , third level of T_on, second level of DC and third level of V _g which has been obtained at the main effect plot of S/N ratio.

The response table for all the process parameters is shown in Table 9. The ranks are based upon delta statistics that evaluate relative magnitude of effects.

Table 9 Response table for means of MRR

3.3.2 Analysis of Variance for Tool Wear Rate

Figure 10 represents the influence of different factors on the process. The significance of the process variables in relation to TWR was investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 10 and 11 respectively.

Fig. 10

Main effect plot for means and S/N ratio of tool wear rate. a Main effect plot for means of TWR (Tripathy and Tripathy 2017a). b Main effect plot for S/N ratio of TWR

Table 10 ANOVA table for means of TWR

Table 11 ANOVA table for S/N ratio of TWR

TWR being lower-the-better type of quality characteristic, the tendency of deviation of the response curves as shown in Fig. 10 demonstrate that the optimal set of parameters for TWR is the second level of parameters of C _p , first level of I _p , second level of T_on, second level of DC, and first level of V _g . The response table for all the process parameters is shown in Table 12.

Table 12 Response table for means of TWR

3.3.3 Analysis of Variance for Electrode Wear Ratio

Figure 11 shows the influence of different factors on the process. The significance of the process variables in relation to EWR was investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 13 and 14 respectively.

Fig. 11

Main effect plot for means and S/N ratio of electrode wear ratio. a Main effect plot for means of EWR. b Main effect plot for S/N ratio of EWR

Table 13 ANOVA table for means of EWR

Table 14 ANOVA table for S/N ratio of EWR

EWR being lower-the-better type of quality characteristic, the trend of deviation of the response curves as shown in Fig. 11 demonstrate that the optimal set of parameters for EWR is the second level of parameters of C _p , first level of I _p , second level of T_on, second level of DC and first level of V _g . The response table for all the process parameters is shown in Table 15.

Table 15 Response table for means of EWR

3.3.4 Analysis of Variance for Surface Roughness

Figure 12 demonstrates the influence of different factors on the process. The significance of the process variables in relation to SR has been investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 16 and 17 respectively.

Fig. 12

Main effect plot for means and S/N ratio of surface roughness. a Main effect plot for means of SR (Tripathy and Tripathy 2017a). b Main effect plot for S/N ratio of SR

Table 16 ANOVA table for means of SR

Table 17 ANOVA table for S/N ratio of SR

SR being lower-the-better type of quality characteristic, the tendency of deviation of the response curves demonstrate that the optimal set of parameters for SR is the second level of parameters of C _p , first level of I _p , first level of T_on, second level of DC and first level of V _g as shown in Fig. 12. The response table for all the process parameters is shown in Table 18.

Table 18 Response table for means of SR

3.3.5 Analysis of Variance for Recast Layer Thickness

Figure 13 shows the influence of different factors on the process. The significance of the process variables in relation to RLT has been investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 19 and 20 respectively.

Fig. 13

Main effect plot for means and S/N ratio of recast layer thickness. a Main effect plot for means of RLT (Tripathy and Tripathy 2017a). b Main effect plot for S/N ratio of RLT

Table 19 ANOVA table for means of RLT

Table 20 ANOVA table for S/N ratio of RLT

RLT being lower-the-better type of quality characteristic, the tendency of deviation of the response curves as shown in Fig. 13, demonstrate that the optimal set of parameters for RLT is the first level of parameters of C _p , first level of I _p , third level of T_on, third level of DC and first level of V _g . The response table for all the process parameters is shown in Table 21.

Table 21 Response table for means of RLT

3.3.6 Analysis of Variance for Microhardness

From the main effect plots shown in Fig. 14, the influence of different factors on the process can be visualized. The significance of the process variables in relation to HVN has been investigated and the optimum combination of parameters was determined from the ANOVA analysis presented in Tables 22 and 23 respectively.

Fig. 14

Main effect plot for means and S/N ratio of microhardness. a Main effect plot for means of HVN. b Main effect plot for S/N ratio of HVN

Table 22 ANOVA table for means of HVN

Table 23 ANOVA table for S/N ratio of HVN

HVN being higher-the-better type of quality characteristic, the tendency of deviation of the response curves as shown in Fig. 14, demonstrate that the optimal setting of parameters for HVN is the third level of parameters of C _p , third level of I _p , first level of T_on, first level of DC and third level of V _g . The response table for all the process parameters is shown in Table 24.

Table 24 Response table for means of HVN

3.4 Multi-objective Optimization Using TOPSIS

The normalized matrix, weighted normalized decision matrix, separation of alternatives from positive and negative ideal solutions and preference values for TOPSIS obtained for experimental runs with ranks are represented in Tables 25, 26, 27 and 28 respectively. The weights given to different parameters are MRR, TWR and SR = 0.2, EWR = 0.1, RLT and HVN = 0.15 (Sum = 1).

Table 25 Normalized matrix

Table 26 Weighted normalized decision matrix

Table 27 Separation of alternatives from positive and negative ideal solutions

Table 28 Estimation of preference value with rank order

It may be observed that the experimental run #21 has the most suitable multiple performance characteristics having the highest preference order followed by #20 and #19. The higher preference values are considered as optimum, therefore, considering the preference values as higher-the-better type of quality characteristic, the third level of parameters of C _p , first level of I _p , third level of T_on, second level of DC and third level of V _g offer maximum grades and are considered to be the optimum set of process parameters. The optimal parametric combination is C_p3I_p1T_on3DC₂V_g3.

3.4.1 Confirmatory Experiment for TOPSIS

After the evaluation of optimal parameter setting, prediction and confirmation for the enhancement of quality characteristic using the optimal setting has been examined. The results have been presented in Table 29.

Table 29 Results of confirmatory experiment

Table 29 shows that the optimum set of parameters obtained from TOPSIS gives an increased MRR with a rise in the value from 2.564 to 9.6 mm³/min. For this subsequent rise in MRR, the TWR exhibits an increase from a value of 0.0172–0.0395 mm³/min. The EWR value decreases from 0.6718 to 0.4115%. The surface roughness increases from 3.8 to 4 μm as more amount of material removal leads to the formation of rough surfaces. The recast layer thickness reduces from 13.8 to 13.2 µm and the microhardness value shows an increase from 784 to 1105 by adding graphite powder. The concentration of graphite powder causing more amount of material removal is 6 g/L. The improvement in preference value for ideal solution = 0.1021.

3.4.2 ANOVA for TOPSIS

The influence of process parameters on performance characteristics may be determined by ANOVA. The result for preference solution using ANOVA is given in Table 30. The results of factor responses are considered by using higher-the-better criteria by means of MINITAB software. Table 31 indicates that C _p , I _p , T_on and DC are parameters which have a significant contribution towards improvement in the value of preference solution while the role of V _g is insignificant.

Table 30 ANOVA table for preference solution

Table 31 Response table for means of preference value

The response table for all the process parameters is shown in Table 31. The table demonstrates the ranks based upon the delta statistics which compare the relative magnitude of effects.

3.5 Microstructure Analysis

The SR has been observed to be dependent on the recast layer distribution. The existing thermal conditions damage the surface and make it irregular. The mechanism of melting and mixing of powder in proper concentrations vary the surface properties of the material resulting in its modification. The presence of foreign particles if added in appropriate quantities reduces the SR of the machined parts. Figure 15a, b represent the microstructures obtained at the optimum set of process parameters with the addition of graphite powder to the dielectric fluid. The surface quality of the machined sample tends to improve as the recast layer thickness and microcracks formation reduce in comparison to machining without the addition of powder. The increase in plasma flushing efficiency during PMEDM results in the ejection of molten material and resolidification. Under constant flushing pressure, with the increase in C _p the SR increases. This is due to the formation of carbide layers resulting from the increased level of carbon from the graphite powder particles. The experimental findings depict that adding powder reduces the SR to a huge extent, but multi-objective optimization helps to determine the most suitable set of parameters with simultaneous optimization of chosen parameters to resulting in improved surface properties of the machined surface.

Fig. 15

SEM of surfaces and sub-surfaces for the machining with graphite powder-mixed dielectric. a Optical microscopy image of recast layer. b SEM micrograph of recast layer

4 Conclusion

The present investigation aims to determine the optimal setting for the process variables to increase the MRR and HVN and minimize the TWR, EWR, SR and RLT simultaneously for H-11 hot work tool steel by adding graphite powder to the dielectric fluid. Taguchi’s technique has been implemented to perform the experiments by altering C _p , I _p , T_on, DC and V _g . Single-objective optimization has been carried out and an optimum set of process parameters have been identified for the response parameters. Further, multi-objective optimization has been performed using TOPSIS to identify the optimum set of input parameters that improve the process performance. The findings from the present work are as follows:

• 1. Maximum MRR can be achieved at C _{p 3} I _{p 3} T _on3 DC ₂ V _{g 3} when machined using PMEDM. I _p , powder concentration, V _g and T_on are the parameters which have significant contribution toward improvement in MRR while the role of DC is insignificant.

• 2. Minimum TWR can be obtained at C _{p 2} I _{p 1} T _on2 DC ₂ V _{g 1} . Parameters which have significant contribution toward improvement in TWR are C _p , I _p , T_on and DC are while the role of V _g is insignificant.

• 3. C _{p 2} I _{p 1} T _on2 DC ₂ V _{g 1} offer minimum EWR when machined using PMEDM. C _p , I _p , T_on and DC are parameters which have significant contribution toward improvement in EWR while the role of V _g is insignificant.

• 4. Minimum SR is obtained at C _{p 2} I _{p 1} T _on1 DC ₂ V _{g 1} . Parameters which have a significant contribution towards improvement in SR are C _p , I _p and V _g are while the role of T_on and DC is insignificant.

• 5. Minimum RLT is obtained at C _{p 1} I _{p 1} T _on3 DC ₃ V _{g 1} . Parameters which have significant contribution towards improvement in RLT is C _p , I _p and V _g are while the role of T_on is insignificant.

• 6. Maximum HVN can be achieved at C _{p 3} I _{p 3} T _on1 DC ₁ V _{g 3} when machined using PMEDM. I _p , powder concentration, DC and T_on are the parameters which have significant contribution toward improvement in HVN while the role of V _g is insignificant.

• 7. The multi-objective optimization results show that C _p of 6 g/L, I _p of 3 A, T_on of 200 µs, DC of 80% and V _g of 50 V i.e. C _{p 3} I _{p 1} T _on3 DC ₂ V _{g 3} is the optimal setting using TOPSIS. The optimal setting obtained can develop the performance of the quality characteristics under consideration.

• 8. Confirmatory test shows improvement of 0.1021 in the preferred values for the optimum set using TOPSIS as compared to the initial setting, which is satisfactory.

• 9. The significant machining parameters affecting the process characteristics at 95% confidence interval were determined using ANOVA. The adjusted R² value was found to be 98.1% which means that 98.1% of the response variables fit the linear model.

• 10. The microstructure analysis was done for the optimal setting which shows improved properties due to less crack formation, lower roughness values and small thickness of recast layer.

• 11. The model is appropriate for use to identify the most suitable set of input parameters for the required performance characteristics. The outcome of the present research work will be a substantial aid to the industries concerned with the use of materials processed through PMEDM.

• 12. Adding powder particles to the dielectric widens the gap, improves the flushing and makes the process stable. However, powders should be added in appropriate concentrations as they tend to settle down in the tank and cause difficulty in stirring.