# EDM of Ti-6Al-4V under Nano-Graphene Mixed Dielectric: A Detailed Investigation on Axial and Radial Dimensional Overcuts

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## Abstract

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_{DE}) and radial errors (R

_{DE}). The developed optimal settings ensure 4.4- and 6.3-times reduction in R

_{DE}and A

_{DE}, respectively. In comparison to kerosene, graphene-based dielectric yields 10.2% and 19.4% reduction in R

_{DE}and A

_{DE}, respectively.

## 1. Introduction

^{2}hybridization [5]. It is worthy to mention that nano-graphene has admirably captured the research focus in EDM, owing to its excellent electrical characteristics which makes the achievement of a high material rate possible in EDM. However, its addition also creates certain challenges in terms of dimensional overcuts, as the dispersion of these particles widen the plasma channel during the electroerrosion process, which eventually translates in compromised dimensional accuracy. This aspect has not been explicitly studied so far in regard to the nanographene mixed dielectric, which is the core focus in this work.

_{OC}) using the response surfaces method (RSM) during machining of Inconel 800. In the same way, Bhaumik et al. [33] developed a semi-empirical model for R

_{OC}and found a correlation between numerical and experimental results. It was also claimed that dimensional accuracy has a significant impact on product aesthetics. In another work, the influence of the tool rotation on the magnitude of overcut was investigated. It was reported that high tool rotation affects the overcut value [34]. Kumar et al. [35] indicated that discharge current, spark voltage, and pulse off time have a significant impact on overcut (OC) in EDM of EN19 workpiece. Multiple studies were carried out to analyze the effect of different EDM parameters, including discharge current, spark voltage, pulse-on time, pulse-off time, flushing time, electrode types, and polarity on the OC [36,37,38,39]. However, the significant factors which noticeably affect the magnitude of OC are discharge current and pulse-on time [38,39]. Researchers have reported that the size of OC is reduced by increasing discharge current and pulse-on time due to the high amount of spark energy affiliated with them [40,41]. Contrarily, a reverse trend (i.e., low intensity of discharge current yielded poor dimensional accuracy) was noted between OC and discharge current during EDM of Ti-6Al-4V [42]. Prasanna et al. [43] assessed the impact of different input parameters, including peak current, duty factor, and pulse-on time on OC and tool wear rate (TWR) during EDM of Ti-6Al-4V using copper electrode coated with Al

_{2}O

_{3}-TiO

_{2}. They concluded that peak current is the principal factor controlling the TWR and OC. Furthermore, it was claimed that the proposed parametric setting provided 92% and 62.5% reduction in TWR and OC, respectively. Another investigation inferred that tool material and pulse on time are the most critical parameters for deciding the OC magnitude [44]. In another research conducted on EDM of Ti-6Al-4V, analysis of variance and grey relational analysis was performed. It was concluded that spark voltage is the significant input parameter which affects OC value [45]. The role of cryogenic treatment was also examined in the context of OC during EDM. It was stated that cryo-treated electrode enhances the radial overcut value. Another experimental study analyzed the effect of mixing aluminum, graphite, and silicone particles in the dielectric on the EDM of Inconel 625 done with copper electrode. It was demonstrated that R

_{OC}was minimized in case of silicone powder mixed dielectric because of its high electrical resistivity (6.4 × 10

^{2}Ω/m) followed by aluminum (2.8 × 10

^{8}Ω/m) and graphite (1 × 10

^{5}Ω/m) [46]. Batish et al. [47] studied the effect of using different concentrations (0 g/L, 5 g/L, and 10 g/L) of powder mixed dielectric on OC during machining of AISI 1045 steel; three different electrodes (i.e., graphite, brass, and tungsten copper) were considered. They concluded that the size of OC increases for higher powder concentration as it causes an intense discharging between the working tool and workpiece.

## 2. Materials and Methods

_{DE}) and axial dimensional error (A

_{DE}). Six input parameters, i.e., tool polarity (TP), type of electrode (E), spark voltage (SV), discharge current (DC), pulse time ratio (PTR), and flushing time (FT) have been selected herein to comprehensively investigate the Ti-6Al-4V machinability issue. The selection of these input parameters was based on two criteria, i.e., either the impact of a particular variable on the defined responses is yet not assessed, or it has well-proven effect with respect to the output variables. For instance, DC, PTR and SV significantly affect the defined responses [49]. Whereas, the impact of TP, E and FT has not been thoroughly investigated yet for the set responses and hence are considered here for investigation. The rest of control factors (servo-sensitivity, spark time, and powder concentration) were set as constant parameters in this research.

_{DE}) and axial dimension error (A

_{DE}) are simply defined as the difference between diametric values along the radial/axial directions of the machined impression and the diameter of the electrode. The schematic of R

_{DE}and A

_{DE}is presented in Figure 2. The radial and axial diametric values were measured using a CMM (see Figure 3). Errors R

_{DE}and A

_{DE}were determined as:

_{DE}and A

_{DE}, the results have been broadly investigated using a statistical approach based on parametric plots. The values of R

_{DE}and A

_{DE}were noted against all parametric levels of the selected control variables. Since polarity may have two states (i.e., positive or negative polarity), nine experiments were conducted at positive polarity and the other nine at negative polarity.

_{DE}and A

_{DE}have been evaluated against input parameters. Thus, according to the relationship, the smaller value of both is rated as best. Thereof, the smaller the best criterion is picked as depicted in Equation (2):

_{ij}= performance of j-th attribute in the ith alternative—denoted by Yi = (Y

_{i1}, Y

_{i2},….., Y

_{ij}….Y

_{in}), and X

_{i}= comparability sequence.

_{o}(X

_{o1}, X

_{o2}, ….., X

_{oj},…..X

_{on}) has been taken as (1, 1,….., 1….1). After that, the comparability sequence is calculated by comparing it with the reference sequence.

_{oj}and X

_{ij}are akin to each other.

## 3. Results and Discussion

_{DE}) and axial dimensional error (A

_{DE}) are evaluated against the selected EDM input parameters. After obtaining the results, parametric plots were drawn to envisage the trend of the control variable for the set responses (R

_{DE}and A

_{DE}).

_{DE}response during EDM of Ti-6Al-4V is illustrated in Figure 5. It can be seen that the tool polarity slightly affects the mean value of R

_{DE}when graphene mixed dielectric is used for the cutting of Ti-6Al-4V. Negative tool polarity allows on average to achieve smaller values of R

_{DE}than in the case of positive polarity. The comparison between positive and negative polarity against selected electrodes is also displayed in Figure 6. For instance, aluminium electrode with negative polarity provided the minimal magnitudes of 0.045 and 0.034 mm for R

_{DE}and A

_{DE}, respectively. Contrarily, large values for both errors (i.e., R

_{DE}= 0.341 mm and A

_{DE}= 0.392 mm) were found for positive polarity, as far as aluminium electrode is concerned. It is mentioned in the literature that less energy is generated between the tool and workpiece gap at negative polarity. Thus, a lower amount of material can be eroded from the central region of the workpiece as well as from the cutting edges of machined cavity. This generated less deep craters on the specimen surface (see Figure 7b); such a result is consistent with the literature [18]. Conversely, for positive polarity, the nano-particles present in the dielectric liquid intensify spark energy and the intense heat generated disintegrates the material thus creating deep craters in the workpiece’s surface (see Figure 7a). This leads to increase R

_{DE}error.

_{DE}. Three distinct electrodes (aluminum, brass and copper) were employed in this study, as mentioned previously. The effect of each electrode on the R

_{DE}is shown in Figure 5. Moreover, the comparison of selected electrodes against each response’s magnitude is provided in Figure 8. The decreasing trend is perceived for R

_{DE}from aluminium to copper electrode. This is because of the higher thermal conductivity of copper (385 W/mK) with respect to brass (109 W/mK) and aluminum (205 W/mK) electrodes. The greater magnitude of R

_{DE}seen for the Al electrode is attributed to its lower thermal conductivity which resists the dissipation of heat energy in the tool surface. Thereof the heat stays in the cutting regime and causes the severe melting and vaporization of the workpiece. This effect results in the generation of deep craters with re-cast layer on the workpiece. Since more melting and vaporization of the workpiece material occurs, this tends to increase the R

_{DE}as highlighted in Figure 9 [54].

_{DE}was obtained. This happens because the graphene nanoparticles included in the dielectric pose a hindrance in front of the spark. Consequently, carbon particles are released in the pool due to the interaction of the plasma with nano-graphene. These particles stick to the electrode surface and hamper the spark strength: hence, the R

_{DE}is reduced. Thus, the electrode of Cu would be a preferred choice to have a lower magnitude of R

_{DE}in EDM of Ti-6Al-4V.

_{DE}is presented in Figure 5. It can be seen that R

_{DE}increases almost linearly with the magnitude of SV. Therefore, the smallest level (3 V) of SV is considered as the most reliable choice for getting high geometric precision of the manufactured parts. In fact, at low voltage, limited discharging occurs in the gap between workpiece and tool, thus reducing the material erosion rate [32]. Consequently, the size of R

_{DE}is reduced as it appears from Figure 10. Whereas, at a large value (i.e., 5 V), the nano-particles present in the dielectric liquid increased the current flow in the machining region. The higher current amplitude enlarged the effective width of plasma channel thus generating a larger amount of discharge energy in the cutting zone. The plasma channel was dispersed beyond the cut dimensions owing to the presence of tiny graphene particles. The resulting overcut yield higher values of R

_{DE}and A

_{DE}.

_{DE}is illustrated by Figure 5. It is understood that, at higher DC values, the presence of graphene nanoparticles in the dielectric enhanced the strength of the spark, which transfers more energy to the machining zone. Hence, melting of the workpiece is more pronounced and this increases the R

_{DE}. Besides worsening R

_{DE}, the high temperature established between the electrode and workpiece also caused larger and wider craters to form on the workpiece surface, as displayed in Figure 11 [55]. However, an interesting phenomenon is seen passing from 8 to 10 A, the R

_{DE}–DC curve becomes approximately horizontal (see Figure 5), which means that there is no further appreciable change in R

_{DE}. Hence, 6 A is the best DC value for maximizing accuracy of EDM machining of Ti-6Al-4V.

_{DE}with respect to pulse time ratio (PTR) also can be analyzed looking at Figure 5. In this research, the value of pulse-off time (50 µs) remained constant for all experiments. The R

_{DE}increased as PTR passed from 0.5 to 1.0 and then decreased sharply when PTR passed from 1 to 1.5. The initial increase of R

_{DE}was related with the spark energy generated in the cutting regime [55]. A greater magnitude of spark energy is realized for PTR = 1 as the pulse-ontime increased from 25 to 50 µs. This liberated more heat in the spark gap that increased the melting of material. However, increasing further the pulse-ontime to 75 µs, R

_{DE}was significantly reduced due to the discharge of graphene particles at the higher energy peak. This led to the deposition of the particles’ layer onto the tool surface. This layer acts as a shield over the tool periphery and hence the sparking efficacy of the electrode is compromised. Subsequently, a lesser amount of material is eroded and this allows a reduction of the R

_{DE}. Furthermore, high PTR values also ensure the existence of the melt pool for a longer period, which minimizes the probability of debris re-deposition. However, too large values of PTR (i.e., 1.5) cause the formation of deep craters on the workpiece surface (see Figure 12).

_{DE}value is obtained for the very large value of FT. Interestingly, the 1st level of FT (i.e., 4 µs) also allowed to obtain a very small R

_{DE}value but yet larger than that achieved for FT = 8 µs. The highest value of R

_{DE}was obtained for FT = 6 µs. Such a value probably allowed to efficiently remove debris without a significant quenching. Hence, a larger amount of material was removed from the target surface, thus increasing R

_{DE}. However, for FT = 8 µs, the graphene particles present in the dielectric were deposited on the tool surface because the tool and workpiece are submerged in the dielectric. As FT becomes longer, the probability of re-deposition on the machined area increases as quenching might occur both in the tool and workpiece. This reduces the spark intensity concentration and the material erosion rate, thus leading to have a lower value of R

_{DE}.

_{DE}are: polarity = negative, tool material = copper, SV = 3 V, DC = 6 A, PTR = 1.5, and FT = 8 µs.

_{DE}are described by Figure 13 for the EDM set up including the graphene particles mixed dielectric. As mentioned earlier, two types of polarity (i.e., positive and negative) were considered. The averaged experimental results obtained for different polarities indicate that the value of A

_{DE}decreases when polarity turns from positive to negative (see Figure 13). For positive polarity, the energy produced in the dielectric is absorbed by the graphene nanoparticles. This stabilizes the sparking in the spark gap [56] and more material is removed from the workpiece, thus raising the magnitude of A

_{DE}. Conversely, at negative polarity, less material is removed because the nano-particles present in the dielectric medium cause dispersion of heat in all directions, and thus A

_{DE}is reduced.

_{DE}(see Figure 13) is similar to the observed trend for R

_{DE}(see Figure 5). The dimensional error decreased passing from the aluminum electrode to the copper electrode. The Cu electrode is the most efficient one because the carbon particles produced by the discharging stick to the electrode surface and make material removal rate decrease. However, the surface of the Cu tool deteriorated because of the discharging of graphene particles over the surface, which produced more irregularities on it (see Figure 14).

_{DE}values. Since sparking occurs in an unstable manner in graphene mixed dielectric that has a capability to uplift the spark potential, the quality of the machined surface is compromised and presents large and deep craters (see Figure 15a). However, Cu-electrode caused the formation of shallow craters (see Figure 15b) due to the adhesion of small carbon and graphene particles onto the tool surface, which lead to stable discharging between the work-electrode gap. Consequently, A

_{DE}improved. The experimental results gathered in this study prove that, under the powder mixed dielectric, copper tool is more effective in terms of mean R

_{DE}and A

_{DE}in the cutting of Ti-6Al-4V.

_{DE}and R

_{DE}errors sharply increase with SV. A similar effect of SV was also noted while investigating the TWR of the EDM setup with nanographene mixed dielectric (see Reference [48]). At the 1st level selected for SV (i.e., 3 V), the rate of ionization for graphene particles is low. Hence, a lower discharge energy is produced which causes plasma density to decrease in the region comprised between workpiece and tool. Due to minimal plasma density in the machining gap, the amount of material removed is smaller. Consequently, the value of A

_{DE}is significantly reduced. However, at the 3rd selected level for SV (i.e., 5 V), spark intensity is enhanced in the dielectric medium. Such a rise in the strength of discharge energy led towards a greater pool of ions due to the increase in ionization of graphene nano-particles over the machined surface. These ions strike the surface of workpiece and erode more material; hence, A

_{DE}is increased [57]. Thus, 3 V is the optimal level for achieving high surface integrity with the precise dimensions of the workpiece.

_{DE}is also sensitive to the variation of DC if Ti-6Al-4V is machined through EDM with graphene mixed dielectric (see Figure 13). Increasing DC from 6 to 8 A allowed A

_{DE}to be reduced. This is due to the presence of graphene nano-particles that influence the discharging process by creating hindrance in front of sparks. The hurdle created by particles decreases the discharge energy. This reduced the MRR leaving small size craters on the workpiece surface (see Figure 16a). Hence, the magnitude of A

_{DE}drops down as DC increases. However, A

_{DE}sharply increased to its maximum value for DC = 10 A due to an intense heat generation in the discharge gap. At 10 A, more material is detached from the workpiece due to a large heat input because of powerful sparking in the machining gap [58]. Hence, the discrete sparking hits more strongly on the surface of the workpiece and creates the large craters shown in Figure 16b. In summary, the presence of large craters caused the sudden increase in A

_{DE}value.

_{DE}is also evaluated against different values of PTR under graphene-based dielectric. Experimental results are plotted in Figure 13. The 3rd level selected for PTR (1.5) yield the lowest dimensional error A

_{DE}. The effect of PTR appears to be similar for both types of cutting errors R

_{DE}and A

_{DE}. Therefore, the variations of A

_{DE}with respect to PTR can be explained with the previous arguments developed for R

_{DE}.

_{DE}increased. On the other hand, increasing further PTR to 1.5 allowed A

_{DE}to be reduced because graphene particles burned smoothly and built a re-cast layer on the electrode’s surface (see Figure 17c). This re-cast layer acted as a shield protecting the specimen surface from further damage: consequently, the value of A

_{DE}became lower. Therefore, for PTR = 1.5, the EDM process was more uniform, and it was possible to achieve high geometric accuracy.

_{DE}with respect to the flushing time parameter FT is shown in Figure 13. A

_{DE}dropped down as FT raised from 4 µs to 6 µs but then increased for FT = 8 µs. As mentioned before, longer FT means that more time is provided to the EDM equipment to flush away the debris over the machined surface. The efficient removal of the debris from the machining regime helps to achieve better dimensional control. Hence, the magnitude of A

_{DE}could be reduced by increased FT up to 8 µs. However, for FT = 8 µs, the opposite occurred, and A

_{DE}increased. Basically, the larger flushing time improved the probability that debris quench on the cut profile. Graphene nanoparticles also contributed to this phenomenon. The re-solidification occurs at the machined cavity in a random manner. Moreover, its effect was more prominent at the cutting periphery of the machined cavity. Therefore, the A

_{DE}error increased for the very large value of FT. The re-deposition on the cut surface (machined at FT = 8 µs) is also visible in the SEM micrograph of Figure 18. After having discussed in great detail the effects of EDM process parameters on dimensional errors R

_{DE}and A

_{DE}, the optimal combination of input parameters was developed.

_{DE}and A

_{DE}are different in magnitude and also the influence of some of the parameters is dissimilar for them. Therefore, the grey relational approach (GRA), which is a multi-objective optimization methodology, was used in this research to find the optimal variables’ combination. GRA results are tabulated in Table 5. Based on the findings shown in the said Table 5, the best alternate that can provide lower values of both the errors i.e., A

_{DE}and R

_{DE}is alternate no. 10. The proposed optimal setting of EDM parameters reported in Table 6 was also tested through confirmatory trials. In order to compare the proposed nano-graphene mixed dielectric EDM setup with the traditional kerosene oil based dielectric setup, the optimal setting yielding the minimum values of R

_{DE}and A

_{DE}was used also for the traditional kerosene-based set up. Table 7 shows that both errors R

_{DE}and A

_{DE}achieved by the proposed graphene-mixed EDM set up could be significantly reduced using the optimal setting. In particular, the minimum errors R

_{DE}and A

_{DE}were respectively 4.4-times and 6.3-times lower than average values while the error difference δ decreased by a factor 4.

_{DE}and A

_{DE}. In fact, the minimum dimensional errors R

_{DE}and A

_{DE}achieved by the proposed EDM set up using mixed-graphene were reduced, respectively, by 50% (i.e., only 0.045 vs. 0.091 mm) and 66% (i.e., only 0.034 vs. 0.100 mm) with respect to their counterpart achieved by traditional kerosene-based EDM set up. Furthermore, R

_{DE}found with the traditional EDM set up was 10.2% higher than that achieved by the proposed EDM set up at the defined optimal settings mentioned in Table 6. In the same way, A

_{DE}was 19.4% larger in magnitude for the traditional EDM set up employing kerosene dielectric. In summary, the proposed mixed-graphene EDM set up achieved significantly higher manufacturing accuracy for Ti-6Al-4V alloy than the classical EDM set up.

## 4. Conclusions

_{DE}) and axial (A

_{DE}) dimensional errors against six EDM process parameters. Experiments were performed using three electrodes (Al, Brass, Cu) based on Taguchi’s (L18) approach. Experimental results were thoroughly analyzed via statistical tests and microscopy-based inspections. The optimal setting that minimizes dimensional errors in both the cutting orientations with respect to target impression sizes was developed using GRA approach. Based on experimental results, the following conclusions are drawn:

- i.
- The Cu electrode outperforms other electrodes in terms of mean values of R
_{DE}and A_{DE}errors. - ii.
- Amongst the other EDM parameters, spark voltage and pulse-time ratio significantly affect the magnitude of dimensional errors in axial and radial machining orientations. The very small value of spark voltage (i.e., 3 V) helps to restrain the spark discharges in a localized machining region. This allows lowering of the R
_{DE}and A_{DE}values down to 0.045 and 0.034 mm, respectively_{.}The very large pulse-time ratio (1.5) also allows minimization of machining errors in both cutting directions. - iii.
- The negative tool polarity allows a reduction of the values of R
_{DE}and A_{DE}when the Al electrode is employed in the EDM of Ti-6Al-4V with the graphene-mixed dielectric. However, the reverse occurs if a brass electrode is used. - iv.
- The desired levels of parameters for minimizing R
_{DE}and A_{DE}as well as the difference between errors were developed using GRA approach. The adequacy of the proposed setting i.e., polarity = negative, Tool material = Al, SV = 3V, DC = 6 A, PTR = 0.5, and FT = 4 µs, also was validated by carrying out confirmation experiments. - v.
- The minimum values of R
_{DE}and A_{DE}achieved by the novel EDM set up for the optimal setting of process parameters were respectively 4.4 and 6.3 times smaller than the corresponding average values: 0.045 mm vs. 0.244 mm for R_{DE}and 0.034 mm vs. 0.247 mm for A_{DE}. - vi.
- The classical EDM set up using a conventional dielectric liquid such as kerosene achieved a poor geometric accuracy during cutting of Ti-6Al-4V through EDM. In particular, mean values of R
_{DE}and A_{DE}achieved by the conventional EDM set up were, respectively, 10.2% and 19.4% larger than those obtained by the graphene-mixed dielectric EDM set up. Hence, the blending of graphene particles in the dielectric of EDM has been proven as a good choice for achieving high dimensional accuracy in the machining of Ti-6Al-4V workpieces.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**EDM setup: (

**a**) schematic of EDM process under graphene mixed dielectric; (

**b**) actual machining environment.

**Figure 3.**Coordinate measuring machine: (

**a**) workpiece setting on CMM, (

**b**) dimensional measurement of machined surfaces.

**Figure 5.**Average experimental results obtained for the radial dimensional error by varying each control parameter for the EDM process including graphene-based dielectric fluid.

**Figure 7.**Micrographs representing surface morphology of Ti-6Al-4V specimens machined with Al-electrode at two different tool polarities: (

**a**) positive polarity; (

**b**) negative polarity.

**Figure 9.**Experimental results for Al-electrode at positive polarity: (

**a**) actual machined surface representing a high value of overcut; (

**b**) deep craters are present on the workpiece surface; (

**c**) SEM image shows re-cast layers formed on the specimen’s surface.

**Figure 10.**Experimental outcomes for Al-electrode with 3 V spark voltage: (

**a**) actual machined surface characterized by R

_{DE}= 0.045 mm and A

_{DE}= 0.034 mm; (

**b**) micrograph showing the smaller number of craters present on workpiece surface; (

**c**) micrograph of the electrode surface showing the presence of only one or two craters.

**Figure 11.**Micrographs showing size of craters in the specimen surface treated with brass electrode: (

**a**) Small and deep craters formed at 6A discharge current; (

**b**) Large and wide craters formed at 8 A discharge current.

**Figure 12.**Experimental results obtained for the Cu-electrode and PTR = 1.5: (

**a**) machined surface of workpiece; (

**b**) micrograph of Ti-6Al-4V showing the presence of deep craters on the workpiece surface; (

**c**) recast layers occurred on tool surface.

**Figure 13.**Average experimental results obtained for the axial dimensional error by varying each control parameter for the EDM process including graphene-based dielectric fluid.

**Figure 14.**Experimental results obtained for the Cu-tool: (

**a**) actual machined surface of workpiece showing minimum value of overcut; (

**b**) micrograph showing less craters on the surface of the workpiece; (

**c**) surface of the Cu tool representing wide and dense craters.

**Figure 15.**Micrographs demonstrating different types of craters formed on the workpiece surface with: (

**a**) Al-electrode; (

**b**) Cu-electrode.

**Figure 16.**Micrographs showing the different sizes of craters present on workpiece’s surface machined witha brass tool: (

**a**) small size craters generated for DC = 8 A and positive polarity; (

**b**) large size craters generated for DC = 10 A and negative polarity.

**Figure 17.**Experimental results obtained for the brass electrode: (

**a**) actual machined surface showing a high value of overcut; (

**b**) micrograph showing the presence of small size craters formed on the workpiece surface; (

**c**) SEM micrograph showing the presence of deep craters on the surface of Ti-6Al-4V.

**Figure 19.**Comparison of minimum EDM’s dimensional errors between graphene and kerosene-based dielectric.

Elements | Al | V | C | N | O | H | Fe | Y | Other | Ti |
---|---|---|---|---|---|---|---|---|---|---|

wt % | 6.75 | 4.50 | 0.08 | 0.05 | 0.20 | 0.0125 | 0.30 | 0.005 | 0.40 | Balance |

**Table 2.**Nominal properties of Ti-6Al-4V workpiece (taken from [15]).

Characteristics | Values |
---|---|

Density (kg/m^{3}) | 4428.785 |

Melting Temperature (K) | 1882.59–1933.15 |

Tensile strength (MPa) | 869–924 |

Ultimate tensile strength (MPa) | 832 |

Hardness (HRC) | 28–32 |

Electrical resistivity (Ω/m) | 1.724 × 10^{−}^{6} |

Thermal conductivity (Wm/K) | 6.7 |

Input Parameters | Units | 1st Level | 2nd Level | 3rd Level |
---|---|---|---|---|

Polarity | - | Positive | Negative | - |

Electrode type | - | Al | Brass | Cu |

Spark Voltage | Volt | 3 | 4 | 5 |

Discharge Current | Ampere | 6 | 8 | 10 |

Pulse time ratio | - | 0.5 | 1.0 | 1.5 |

Flushing time | µs | 4 | 6 | 8 |

Properties | Units | Magnitude |
---|---|---|

Density | g/mL | (6–9) × 10^{−}^{2} |

Thickness | nm | 2–10 |

Diameter | μm | 2–10 |

Colour | - | Grey/black powder |

Carbon content | % | >99 |

Electrical conductivity | S/m | 80,000 |

Surface area | m^{2}/g | 20–40 |

Additional impurities | wt % | <1 |

Percentage of water | wt % | <2 |

Exp. No. | Grey Relational Generation | Grey Relational Coefficients Calculation | GRA Grades Calculation and Alternates’ Ranking | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

R_{DE} | A_{DE} | (δ) | R_{DE} | A_{DE} | (δ) | R_{DE} (GC) | A_{DE} (GC) | (δ) (GC) | GRA Grades | GRA Ranking | |

Xo | 1 | 1 | 1 | ||||||||

1 | 0.294 | 0.173 | 0.589 | 0.706 | 0.827 | 0.411 | 0.414 | 0.377 | 0.549 | 0.447 | 15 |

2 | 0.000 | 0.072 | 0.795 | 1.000 | 0.928 | 0.205 | 0.333 | 0.350 | 0.709 | 0.464 | 12 |

3 | 0.158 | 0.069 | 0.696 | 0.842 | 0.931 | 0.304 | 0.372 | 0.349 | 0.622 | 0.448 | 14 |

4 | 0.857 | 0.859 | 0.955 | 0.143 | 0.141 | 0.045 | 0.777 | 0.780 | 0.918 | 0.825 | 2 |

5 | 0.697 | 0.813 | 0.536 | 0.303 | 0.187 | 0.464 | 0.623 | 0.728 | 0.519 | 0.623 | 6 |

6 | 0.578 | 0.333 | 0.143 | 0.422 | 0.667 | 0.857 | 0.542 | 0.428 | 0.368 | 0.446 | 16 |

7 | 0.986 | 0.857 | 0.643 | 0.014 | 0.143 | 0.357 | 0.972 | 0.777 | 0.583 | 0.778 | 4 |

8 | 0.549 | 0.467 | 0.768 | 0.451 | 0.533 | 0.232 | 0.526 | 0.484 | 0.683 | 0.564 | 10 |

9 | 0.611 | 0.684 | 0.714 | 0.389 | 0.316 | 0.286 | 0.562 | 0.612 | 0.636 | 0.604 | 7 |

10 | 1.000 | 1.000 | 0.946 | 0.000 | 0.000 | 0.054 | 1.000 | 1.000 | 0.903 | 0.968 | 1 |

11 | 0.902 | 0.734 | 0.482 | 0.098 | 0.266 | 0.518 | 0.836 | 0.653 | 0.491 | 0.660 | 5 |

12 | 0.413 | 0.365 | 0.884 | 0.587 | 0.635 | 0.116 | 0.460 | 0.440 | 0.812 | 0.571 | 9 |

13 | 0.792 | 0.785 | 1.000 | 0.208 | 0.215 | 0.000 | 0.707 | 0.700 | 1.000 | 0.802 | 3 |

14 | 0.222 | 0.337 | 0.598 | 0.778 | 0.663 | 0.402 | 0.391 | 0.430 | 0.554 | 0.459 | 13 |

15 | 0.119 | 0.000 | 0.571 | 0.881 | 1.000 | 0.429 | 0.362 | 0.333 | 0.538 | 0.411 | 17 |

16 | 0.520 | 0.651 | 0.500 | 0.480 | 0.349 | 0.500 | 0.510 | 0.589 | 0.500 | 0.533 | 11 |

17 | 0.654 | 0.550 | 0.696 | 0.346 | 0.450 | 0.304 | 0.591 | 0.526 | 0.622 | 0.580 | 8 |

18 | 0.122 | 0.395 | 0.000 | 0.878 | 0.605 | 1.000 | 0.363 | 0.452 | 0.333 | 0.383 | 18 |

**Table 6.**Optimal parameter settings of graphene-based dielectric EDM set up yielding the lowest values of R

_{DE}and A

_{DE}.

Sr. No. | Control Variables | Graphene Based Dielectric |
---|---|---|

Optimal Value | ||

1 | Polarity | Negative (−) |

2 | Electrode material | Al |

3 | Spark voltage | 3V |

4 | Discharge current | 6 A |

5 | Pulse time ratio | 0.5 |

6 | Flushing time | 4 µs |

**Table 7.**Confirmatory experimental results obtained by implementing optimized EDM’s input parameters.

Responses Magnitude | Radial Dimension Error (R_{DE}) | Axial Dimension Error (A_{DE}) | Error Difference (δ) |
---|---|---|---|

Optimized EDM parameters | 0.045 mm | 0.034 mm | 0.01 |

Average responses’ value | 0.244 mm | 0.247 mm | 0.04 |

Improvement | 4.4 times | 6.3 times | 4 times |

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## Share and Cite

**MDPI and ACS Style**

Ishfaq, K.; Asad, M.; Harris, M.; Alfaify, A.; Anwar, S.; Lamberti, L.; Scutaru, M.L. EDM of Ti-6Al-4V under Nano-Graphene Mixed Dielectric: A Detailed Investigation on Axial and Radial Dimensional Overcuts. *Nanomaterials* **2022**, *12*, 432.
https://doi.org/10.3390/nano12030432

**AMA Style**

Ishfaq K, Asad M, Harris M, Alfaify A, Anwar S, Lamberti L, Scutaru ML. EDM of Ti-6Al-4V under Nano-Graphene Mixed Dielectric: A Detailed Investigation on Axial and Radial Dimensional Overcuts. *Nanomaterials*. 2022; 12(3):432.
https://doi.org/10.3390/nano12030432

**Chicago/Turabian Style**

Ishfaq, Kashif, Muhammad Asad, Muhammad Harris, Abdullah Alfaify, Saqib Anwar, Luciano Lamberti, and Maria Luminita Scutaru. 2022. "EDM of Ti-6Al-4V under Nano-Graphene Mixed Dielectric: A Detailed Investigation on Axial and Radial Dimensional Overcuts" *Nanomaterials* 12, no. 3: 432.
https://doi.org/10.3390/nano12030432