Thermal Modelling and Multi Decision Making Optimization of EDM of Non Conductive SiC-CNT Ceramic Composite Used for Li-ion Battery and Sensor

Electrical discharge machining (EDM) is a highly effective method for producing complicated moulds and machining hard materials. A voltage is applied between two electrodes, the instrument and the work piece, which are tightly spaced within a liquid dielectric medium. When this voltage is applied, an electric spark discharge occurs between the electrodes, causing enough heat to melt and even vaporise the machined workpiece material. During the discharge phase, a plasma channel forms between the anode and cathode, allowing electrons and ions to pass into it, displace the dielectric fluid, and induce a significant volume of pressure on the work piece surface, preventing the molten substance from flowing. As the spark collapses, the abrupt release of pressure causes a violent ejection of the liquid and vaporised material from the workpiece floor, the gushing of the dielectric to fill the vacuum, and the forming of small craters at material removal sites.

The primary fundamental phenomenon causing material removal in the EDM phase is the electric discharges produced between the tool and the workpiece. The substance removal process is a result of the fusion of two processes (Dibitonto et al. [1];Schumacher [2]; Shuvra Das et al. [3]). The first is thermal in nature, caused by electric discharges that generate high energy densities of approximately 1017 W/m2 (Ekmekci et al. [4]), resulting in the rapid melting and even evaporation of material. The second form is hydrodynamic erosion, which occurs as a result of the gas bubble collapsing and expelling a portion of the molten liquid. Dibitonto et al. [1] quantified this expelled fraction experimentally using a parameter called plasma flushing quality (PFE).

Earlier published works mostly used computational models (Snoeys and Van Dijck [5]; Van Dijck and Dutre [6]; Beck [7, 8]; Jilani and Pandey [9, 10]; Erden and Kaftanoglu [11]; Lhiaubet and Meyer [12]; Lhiaubet et al. [13]; Pandey and Jilani [14]; Dibitonto et al. [1]; Patel et al. [15]). These models allowed prediction of the temperature distribution chart, material removal rate (MRR), and shape of the crater on the machined workpiece. These experiments used a variety of different types of thermal loading. Snoeys and Van Dijck [5], Beck [7], Jilani and Pandey [10] all used a constant-radius disc heat source. Dibitonto et al. [1] simulated cathode erosion using a point heat source and a decreased plasma radius during the discharge. The majority of the authors cited above believe that 50% of heat power (Fc=0.5) is transmitted to the workpiece; only Dibitonto et al. [1] believed it was equivalent to 18.3% at the cathode. In the majority of these experiments, the thermal properties of machined material is assumed to be stable. At the end of the discharge, the crater's morphology and volume is determined using the isothermal curve that separates the liquid and solid portions of the workpiece material. SiC/CNT has an excellent electrical and thermal conductivity due to which it can be used as electrode support for electrochemical energy devices as Polymer Electrolyte Membrane Fuel Cells on Li-ion battery [14,15]. Yeo et al. [16] conducted a thorough analysis and review of prior models, and they were found to be inconsistent with experimental findings. As a conclusion, he demonstrated that the model established by DiBitonto et al. [1] has the strongest agreement with experimental data. Recently published papers (Shuvra Das et al. [3]; Kansal et al. [17]; Marafona and Chousal [18]; Ghanem et al. [19]; Salah, N.B et al. [20, 21]; Bhondwe et al. [22]; Vinod Yadav et al. [23]) have advanced the field of computational simulation of the EDM method. The assumptions of these experiments have been significantly changed. In both of these experiments, the Gaussian form of the heat flux distribution was assumed, as was the temperature-dependent evolution of the thermal properties of machined material. The value of the power fraction transmitted to the workpiece continues to be a source of contention. Shuvra Das et al. [3], Ghanem et al. [19], and Salah et al. [20, 21] recommended an 18% value, while Vinod Yadav et al. [23] recommended an 8% value. Marafona and Chousal [18] assume that the fraction of energy transmitted to the workpiece is 50%. According to Kansal et al. [17] and Bhondwe et al. [22], the powder fraction (Fc) is dependent on the dielectric fluid used.

Many authors have been considered the constant thermal properties for the thermal analysis. Numerical study of Metal matrix composite (MMC) or Ceramic matrix composite has not been significantly performed. Least work has been done to show the Effect of Specific Discharge Energy (SDE) for removing material by EDM.  The combined effect of SDE & Latent heat on the material erosion process has not been performed till now. The present work has been focused on the numerical modeling of the SiC (6vol% of CNT) machined by EDM.  For this analysis Gaussian heat flux has been taken as heat source. A comparison study of MRR for experimental results and varying thermal properties has been done.

1.1 Introduction to Specific Discharge Energy

A novel technique The specific discharge energy (SDE) of a wire electrical discharge machining process is defined as the actual energy needed to extract a unit volume of a specific material. As shown, current forecasting methods are insufficient to satisfy the needs of EDM processes, and a new approach for predicting EDM efficiency with sufficient precision and cost is warranted. Liao [27] pioneered the idea of specific discharge energy (SDE) in wire-cut electric discharge machining (WEDM) in order to demonstrate the relationship between material properties and EDM efficiency. Liao simplifies the complex interaction between material properties and efficiency by computing the SDE of a variety of materials.

SDE offers a quantitative and straightforward method for describing the properties of materials and assists in effectively estimating the efficiency of different materials. Materials with comparable SDE have been shown to perform similarly under the same conditions, while materials with a lower SDE appear to be extracted more quickly but perform poorly. The theory is validated and applied to the optimization of parameters for various materials in WEDM [28]. However, despite the fact that SDE offers special advantages in wire-EDM, acquiring its worth is difficult. According to Liao's research, not all energy transmitted to the workpiece is used to erode the substance [27]. Thus, an additional L18 mixed orthogonal Taguchi quality design tool must be used to determine the proportion of total energy currently used for metal removal under different circumstances, necessitating an extraordinary amount of work and effectively impeding further implementation of SDE. Indeed, the EDM mechanism can be thought of as a single spark compounded by the discharge frequency. The energy transmitted in the heat influenced region during the previous pulse, which Liao ignores, has a direct effect on the subsequent pulse. But for the energy dissipated in the tens of micrometres deep heat-affected region over the course of an EDM phase, the actual energy needed to extract the substance is the overall energy spread on the surface. To obtain the SDE value more precisely and effectively, this analysis establishes a computational approach based on the simulation model. The equivalent temperature and proportion of energy distribution have been considered concurrently in this analysis. SDE can be defined mathematically as the ratio of material removal energy to material removal volume. Finally, the numerical value of SDE was validated by comparing it to experimental data.

In the present study the thermal modelling of Ceramic matrix Composite has been conducted with necessary experimental validation. According to the mechanism of EDM the modelling can be done by considering the requisite Plasma diameter along with the appropriate material properties. As from the previous literature survey it can be inferred the Gaussian heat flux is the most suitable heat source for machining by EDM as the temperature distribution inside the Spark plasma channel is not uniform in nature.

The temperature distribution along the depth of the crater still depends on time interval and is somewhat similar to the Gaussian function [13]. This is the reason the geometry shape of the crater crated after simulation (by taking Gaussian heat source) resemble to the experimental crater after machining. Hence in this analysis Gaussian heat flux has been applied to the spark radius section. Fig.2 shows the 2D domain for single spark EDM of ceramic. In the following section all the technique has been covered and are used for modelling.

3.1 Modeling Assumption

The numerical model of machining SiC/CNT Ceramic Composite can be designed by considering the discharge phenomena, which involves heating of the work piece by the incident high energy plasma. That incident area is known as Spark Radius. As the analysis is considered as transient analysis so the heat flux increases with respect to time. Both the electrodes has been considered as the isotropic in nature and subjected to Gaussian heat flux. In the following section some specific assumption has been considered to simplify the electro-thermal analysis.

Modeling involves the use of some simplifying assumptions

• Homogeneity of both tool and workpiece electrode.

• Average physical thermal characteristics (Table 1) are applied across the temperature spectrum.

• Only by the conduction is heat transferred to the surface of the electrode.

• There is insignificant radiation and convective heat loss.

• A percentage of anode- and cathode-based discharge energy is stable.

• As a heat source, the Gaussian heat flow is used.

The remainder are lost in the dielectric convection and radiation. • A fraction of the overall spark energy is disbursed as heat in the part.

• The quality of flushing shall be considered 100%. The recast coating on the machined surfaces is not deposited.

• Flushing efficiency is considered to be 100 %. There is no deposition of the recast layer on the machined surfaces.

• Temperature analysis is considered to be of transient type.

• The workpiece is free from any type of stress before EDM.

• Only one spark is considered in the analysis.

• The capacitor is fully charged and discharged during the process.

3.2 Governing Equation

In EDM process two types of heat transfer mechanism occurred which are Conduction & Convection. As the EDM mechanism starts from Penetrating the Plasma channel in to the work piece Surface, So Conduction has been considered as the main mode of heat transfer in EDM.  Therefore the Fourier heat conduction equation (Eqn.1) has been solved for the analysis of the thermal modeling with no internal heat generation.

$\frac{1}{\alpha }\frac{\partial T}{\partial t}=\left[ \frac{{{\partial }^{2}}T}{\partial {{r}^{2}}}+\left( \frac{1}{r}\frac{\partial T}{\partial r} \right)+\frac{{{\partial }^{2}}T}{\partial {{z}^{2}}} \right]$         (1)

where, T is temperature, t is time, and r and z are coordinate axes. ά is the thermal diffusivity which can be represented by eqn. (2)

$\alpha =\frac{{{K}_{t}}}{\rho {{C}_{p}}}$              (2)

3.3 Heat Input to the Work Piece

In EDM process the electrical energy gets converted to the thermal energy in form of Plasma which melts the material from the work piece surface. The total energy of the plasma is the function of three variables which are Spark radius, Amount of heat flux and lastly the energy within the gap between electrodes. The detail of the three parameters of modeling has been discussed below.

3.3.1 Shape and size of plasma channel

The critical aspect for a proper numerical simulation of the EDM mechanism is determining the sparking region where the heat source must be applied. Since the mathematical model represents a single pulse, the funnelling radius can hardly be experimentally determined. There is also an aspect that is very much lower, i.e. in micro second (μS), depend on the time of pulse or pulse. The interaction of the spark radius w.r.t with the current and pulse time suggested by Ikai and Hashigushi has been used in this present analysis  [9].

$R(\mu m)=2.04\times {{I}^{0.43}}\times To{{n}^{0.44}}$                 (3)

where, R is in µm, I in Amp & Ton in µS.

3.3.2 Selection of heat source

For the analysis of the thermal Models of EDM, the heat source is most essential factor. Many studies have already been conducted on computational modelling of EDM using three types of heat sources, namely disc, point, and Gaussian heat sources [3-11]. Gaussian heat flux has been shown to coincide with the real case of EDM among the three forms of heat sources [4, 5, and 6]. As the heat flux that varies with time in this work, a Gaussian heat source has been used. The heat flux (q(r)) for a Gaussian heat source is given by Eqn. (4).

$q(r)=\frac{4.45{{F}_{c}}VI}{\prod {{R}^{2}}}\exp (-4.5*{{(\frac{r}{R})}^{2}})$            (4)

where F_c is the fraction of heat transferred to work piece, V and I are the discharge voltage and the supplied current respectively.

3.3.3 Estimation of fraction of heat

Due to the ultra short pulse length in a single discharge, the energy transmitted in the form of radiation and convection may be skipped. The bulk of the energy is thus transported by heat conduction to the cathode, anode, and dielectric, therefore a precise calculation of the energy ratio transmitted to the cathode is essential for reducing thermal model errors. Singh [31] showed that a portion of energy transmitted to a workpiece (Fc), which varies with current and pulse durations, is the result of pulse length, current, polarity of electrodes and a mixture of workpiece and tool electrodes.

Many analytical models [1, 2, 3, 4, 5] set the proportion of heat distribution as a fixed value, resulting in lower precision in predicting the MRR and surface roughness. The regression model of fc versus pulse current (I) and pulse length (Ton) represented in Eqn.(5), according to Ming's analysis [26], resembles the actual case of energy sharing to the work piece surface.

f_c(%)=5.672+0.2713×I^0.5598T_on^0.4602           (5)

3.3.4 Boundary and initial condition

The following boundary conditions constrain the system (Fig.2) by equation 6:

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Figure 2. Schematic 2D work domain with boundary Condition

$\begin{align}  & \frac{\partial T(X,z,t)}{\partial r}=0 \\ & -K\frac{\partial T}{\partial z}(r,0,t)=\{{{E}_{0}}\text{ for 0rR, 0 for RrX }\!\!\}\!\!\text{ } \\ & \text{T(r,}\infty \text{,t)}\to {{\text{T}}_{0}} \\\end{align}$            (6)

where, E₀ is the Energy density

T₀ is the room temperature

X is the total width of the work domain

The Initial condition of the system is represented by $T(r,z,0)={{T}_{0}}$.

Section 1, 2 & 5 are fully insulated and the heat flux has been applied within $0\le r\le R$.

Eqn. (7) can be For the Gaussian heat source which has a finite duration of time period t, the temperature profile can be obtained using the Laplace transformation as follows by eqn. (7):

$T(r,z,t)=\frac{{{E}_{0}}{{R}^{2}}{{k}^{1/2}}}{K{{\prod }^{1/2}}}\int\limits_{0}^{t}{\frac{d{{t}^{I}}}{{{t}^{{{I}^{1/2}}}}(4K{{t}^{I}}+{{R}^{2}})}X\exp [\frac{-{{z}^{2}}}{4K{{t}^{I}}}}-\frac{{{r}^{2}}}{4K{{t}^{I}}+{{R}^{2}}}]$                  (7)

Eqn. (7) has been manipulated in this study for considering the Latent heat of fusion and specific heat to make it valid for the phase change of work piece by plasma channel. This can be done by the following Eqn.-8.

${{K}^{I}}=\frac{K}{\rho }\frac{1}{{{C}^{I}}}\text{ where }{{\text{C}}^{I}}=C+\frac{m}{{{T}_{m}}}$                    (8)

where, K^I and C^I are the adaptive thermal diffusivity and adaptive specific heat.

3.4 Latent Heat for Phase Change

The material removal mechanism in EDM mainly involves two types of mechanism firstly melting and secondly Vaporization phenomena. However the effect of Vaporization is negligible due to the significant dynamic pressure of the plasma channel. This pressure also restricts the effect of evaporation [31, 32]. The Vaporization effect is directly proportional to the Latent heat of fusion. Earlier many researcher neglect the Latent heat effect [6-10].  In this study to enhance the accuracy of the electro-thermal modeling. The latent heat of fusion has been considered in this study by considering all the thermal properties vary according to temperature.  Table-1 represents the variation of Specific heat and conductivity with respect to temperature increase. The specific heat C_P has been denoted as C_Peff and the mathematical formula to estimate the C_Peff has been denoted below by equation-8:

${{C}_{peff}}={{C}_{p}}+\frac{{{L}_{H}}}{\Delta T}$                  (9)

where L_H is the workpiece latent heat of melting and ∆T=T_m-T₀ the temperature difference between melting point temperature and dielectric temperature.

Table 3. Temperature Dependent [Properties of SiC -6% CNT Ceramic matrix Composite

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The FEM model of SiC/CNT Ceramic composite has been validated with the experimental result in the above section. To know the effect of parameters (Peak Current, Voltage & Pulse-On time) on the process parameters (MRR & Crater geometry) it is necessary to carry out the parametric study. The numerical model (FEM Model) has been used for the parametric study. To determine the metal erosion rate it has been necessary to obtained temperature profile by simulating the work model using proper boundary condition. The significance of this parametric study is to understand the quality of how a parameter affects the MRR of SiC/CNT Ceramic Composite while working under different machining conditions of EDM.

The following set of parametric study has been done for the analysis:

1. Temperature Profile & Crater formation

2. Influence of Specific heat on MRR

3. Effect of Pulse-On time on MRR

4. Effect of Current on Crater Geometry

5.1 The Effect of Heat Fraction on MRR and SR

In this study a comparative review was conducted for the mathematical calculation of MRR and SR. In Figure 4, a comparison of MRR and SR has been made. The research indicates that for high the erosion rate needed for macro machining Fc should be between 7.23% and 9.11%. Likewise, for micro machining, an Fc of less than 6.2% is recommended. However, at a higher MRR and SR also rise as well. This can be accomplished by surface eradication phase of completion. Similarly, when the MRR is big, the surface finish is poor.

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Figure 6. Variation in MRR and SR w.r.t Fc

As a result of Figure 6, it can be inferred that at 6.3 to 6.7% of 'F' the error between the two versions is between 41 and 48%. Similarly, the error falls from 45% to 35% in 7.13 to 7.2'F'. 9.2 percent of 'F' has been counted with the least mistake of 27 percent. As such, itIt can be inferred that when machining SiC-6% vol CNT for EDM, the recommended fraction of heat entering the cathode should be between 9.2 and 10.11%. However, the maximum MRR of 9.74mm³/min was obtained using a statistical model at 3A, 75µS and 30 V, and 9% Dc.

5.2 Temperature Profile & Crater Formation

Fig.6 shows the result of the temperature contour plots after Simulation of SiC/CNT wok domain. From the transient thermal analysis performed, the temperature variation over a period of time can be obtained. The nodes showing the temperature more than the melting point (For SiC/CNT the melting point is around 2242K) were selected and eliminated from the complete mesh of the work domain for MRR calculation. In fig. 6 (d) to (i) the selected nodes of maximum temperature has been eliminated to calculate the volume of crater. From the figures, it can be seen that the change in temperature with time for any point on the radial axis has a similar trend to the case of the vertical axis. For any instance of time, the temperature is highest at the origin and decreases gradually with an increase in distance from the center. This is because the Gaussian heat source, which is closer to real-life situation, is showing steep temperature gradients within the spark radius zone. The highest temperature at 3A and 75µS is 8700K, for which the MRR is 1.01mm³/min. Similarly the lowest MRR for the rise in 2400K temperature is 0.21mm³/min.

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5.3 Influence of Specific Heat on the Erosion Rate

The FE simulation of SiC/CNT has been done to get the temperature contour. From that contour the numerical MRR has been calculated according to eqn. 11. Fig.7 shows a comparative study of the three different thermal properties of numerical MRR and the experimental result. In the first condition the Specific heat varies directly as the Latent heat according to equation-9. In second the C_p remains constant and in third condition C_p changes along with thermal conductivity and Latent heat.  Fig.7 (a), (b) & (c) represent the MRR variation with respect to different input parameters (peak current, Voltage, Pulse-On time). Fig.7 (a) clearly indicates at high current (by keeping other parameter as constant) the numerical value of MRR (C_p varying w.r.t LH & TH) coincides with the experimental results of MRR. The highest MRR at 5A current is 1.8 mm³/min. Similarly in fig.5 (b) there is slight deviation in between the third model (C_p varying w.r.t LH & TH) and experimental results but at high Voltage (by keeping other parameter as constant) the two MRR approaches each other. In fig.7 (c) with varying T_on the deviation between the third model and experimental value is more in comparison to the fig. 7 (a) and (b), but again in high T_on 75µS the numerical MRR and experimental MRR coincide (1.01mm³/min) with each other.

The reason behind the deviation at the low input parameter condition is that, during discharge not all the molten metal can be evacuated at the end of the pulse, which subsequently gets re-solidified. Therefore, the real crater is to some extent shallower than the ideally obtained one.

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Figure 7. (a), (b), (c) Comparison between Simulated Results of numerical MRR with Experimental result by varying Peak current , Voltage and Pulse-On time respectively

5.4 Effect of Pulse-on Timeon Erosion Rate

From the FEM model of machining of EDM it has been clear that Pulse-On time is the most significant parameter for machining by EDM. In fig. 8 (a) & (b) the effect of Pulse-On time on material erosion rate with varying current and Voltage has been shown. At low Current (1and 2A) MRR increases with increase in Ton due to the more Spark On time.  But at 3A above 50µS MRR suddenly decreases due to the low Flushing pressure. At 4A and 5A the rate of increment of MRR also decreases in comparison to the Fig.8 (a) & (b). This reason leads to deposition of white layer due to reduce in Plasma flushing efficiency. The highest MRR recorded at 5A, 30V and 75 µS is 1.70 mm³/min. Similarly the lowest has been calculated for 1A, 30V and 25 µS. In fig. 8 (b) it can be concluded that at high voltage the deviation between the erosion rate between 50V and 70 V is approaches towards each other this is due to the more occurrence of more rate of spark at high voltage.

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Fig.8 (a) MRR Vs. Pulse-On time at different Current  (b) MRR Vs. PulseOn time at different Voltage

5.5 Effect of Discharge Current on Crater Dimension

The effect of discharge current on crater radius and depth is seen in Fig.9 (a) and (b) while the other parameters are kept constant (i.e V-30V). The effects on crater size of the most important parameters modulating the MRR, namely discharge current and discharge length (spark on-time) (radius and depth). Since this characteristic is directly proportional to the size of the crater depth, the results would be crucial in predicting the efficiency (MRR) of the EDM operation. It also aids in the comprehension of how a parameter impacts the MRR when operating under various machining conditions.

As the discharge current is increased from 1 to 5A, the Crater Radius graph still indicates an increase due to the higher amounts of discharge energies emitted during sparking. However, it's worth noting that the developed crater depth to radius (d/r) ratio jumps from 0.83 to 0.89. It means that the crater diameter expands faster than the crater radius, meaning that the melting boundary moves further into the workpiece as a result of strong discharge current to prevent molten material from solidifying again. In other words, as the discharge current is increased, the water ejection quality improves, with more material being removed rather than scattered over the work surface.

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Fig.9 (a) Crater RadiusVs.  Current at different Spark On time                   (b) Crater Depth Vs. Current at different Spark On time

5.6 Optimization by Desirability Analysis (D)

In this study the input parameters I, Ton, Dc, and V has been used to express the results of the output responses. Desirability analyses are carried out in order to refine the input parameters. A number between 0 and 1 is allocated to each answer. The consequence is considered completely needless if the value is 0, and the most desirable or optimal condition if the value is 1. By combining all mean responses, the overall desirability (D) can be calculated and expressed as follows.

D= [d₁₍y₁ )*(d₂(y₂ ))*.........*(d_k(y_k ))]                     (14)

The aim in this study is to optimise MRR, PFE, and decrease SR and Rlt. Any difference in the input parameters influences the output response, as seen in Figure 10 of the desirability analysis. As a result, choosing the right input parameters is crucial for getting the best output response. To achieve high MRR & PFE and low Rlt, SR, multi-objective optimization was used to calculate the optimal values of I, V and  Ton. The optimal values of input parameters can be found by looking at the Figure's desirability analysis, which also shows the average desirability value of 0.0774.

10.png

Figure 10. Desirability test of SiC-CNT composite machining

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Figure 11. SEM image of SiC-6%CNT machined at optimum condition

A validation test has been also performed using the optimal set of input parameters for SiC-6 percent CNT composite machined by EDM, namely I= 3A, V=30V, and Ton= 75µs. It is evident from Figure 11(a) that the crater formed by EDM machining resembles a hemispheric cavity. The thickness of the White film can also be seen on the crater's outer periphery rim. The existence of MWCNT structure within the composite can be seen in the longitudinal grain.