Thermo-physical modeling of die-sinking EDM process

Journal of Manufacturing Processes 12 (2010) 45–56

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Thermo-physical modeling of die-sinking EDM process S.N. Joshi, S.S. Pande ∗ Computer Aided Manufacturing Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai – 400076, India

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Article history: Received 4 November 2009 Received in revised form 27 January 2010 Accepted 13 February 2010 Available online 16 March 2010

abstract This paper reports the development of a thermo-physical model for die-sinking electric discharge machining (EDM) process using finite element method (FEM). Numerical analysis of the single spark operation of EDM process has been carried out considering the two-dimensional axi-symmetric process continuum. The analysis is based on more realistic assumptions such as Gaussian distribution of heat flux, spark radius equation based on discharge current and discharge duration, latent heat of melting, etc., to predict the shape of crater cavity and the material removal rate (MRR). Using the developed model, parametric studies were carried out to study the effect of EDM process parameters such as discharge current, discharge duration, discharge voltage and duty cycle on the process performance. Experimental studies were carried out to study the MRR and crater shapes produced during actual machining. When compared with the reported analytical models, our model was found to predict results closer to the experimental results. The thermo-physical model developed can further be used to carry out exhaustive studies on the EDM process to obtain optimal process conditions. © 2010 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

1. Introduction Electric discharge machining (EDM) is a widely used nontraditional machining process in the manufacture of complex shaped dies, molds and critical parts used in automobile, aerospace, surgical and other industrial applications. The process uses thermal energy of the spark to machine electrically conductive parts regardless of the hardness of the work material. This unique feature of EDM has a distinct advantage in the manufacture of complex shaped die and molds made up of hard materials which are difficult to machine by conventional machining processes [1]. The EDM process, however, has limitations such as longer lead times and lower productivity which restricts its application. Researchers worldwide are thus, focusing their attention on improving the productivity and finishing capability of the EDM process. Various aspects of EDM process have been studied in detail like types of EDM machines (Wire cut/Die-sinking), tooling, control circuits, process performance under chosen process conditions, online machine control, etc., [1–3]. In the present context, studies on the development of analytical process models of die-sinking EDM process are particularly relevant. Literature reports several attempts to develop such process models by analyzing the spark phenomenon and mechanism of material removal in EDM [4–18]. These thermo-physical models of

the EDM process, however, significantly over- predict the process performance (material removal rate (MRR), tool wear rate and crater size) possibly due to the simplifying assumptions such as constant spark radius, disc or uniform shaped heat flux source, constant thermal properties of work and tool material, etc., [4]. Attempts have also been directed on developing EDM process models from experimental results using design of experiments (DOE) techniques such as response surface methodology (RSM), factorial analysis, regression analysis, Taguchi technique, etc., [1]. These models are, however, specific to chosen tool/work materials, experimental conditions and limited experimental data generated. They thus, lack generality. A need, therefore, exists to develop a comprehensive thermo-physical process model for EDM for accurate prediction of the crater cavity and MRR. The present paper is an attempt in this direction. Rest of the paper is organized as follows. Section 2 presents review of relevant papers on the analytical modeling of EDM process. Thermo-physical model of EDM process using finite element method (FEM) is presented at length in Section 3. Section 4 presents the comparison of the results obtained by our thermo-physical (FEM) model with the reported analytical and experimental results and our own experimental results. Section 5 presents parametric studies carried out using thermo-physical model for a typical tool–work material pair. Section 6 summarizes the conclusions from this work. 2. Literature review

∗ Corresponding author. Tel.: +91 22 2576 7545; fax: +91 22 2572 6875, +91 22 2572 3480. E-mail address: [email protected] (S.S. Pande).

Since the early seventies, researchers worldwide have attempted to model the electric discharge phenomena (plasma channel) and the mechanism of cathode and anode erosion in the EDM

1526-6125/$ – see front matter © 2010 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jmapro.2010.02.001

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Nomenclature Cp Cpeff Cv t Di EDM FEM Fc I Kt LH MRR q Rpc r T Ta Tm t ton toff V x, y z

ρ

Specific heat (J/kg K). Effective specific heat (J/kg K). Crater volume (µm3 ). Elemental disc volume (µm3 ). Electric discharge machining. Finite element method. Fraction of power going to the cathode. Discharge current (A). Thermal conductivity (W/m K). Latent heat of melting (kJ/kg K). Material removal rate (mm3 /min). Heat flux at cathode surface (W/m2 ). Spark radius at cathode surface (µm). Radial coordinate. Temperature variable (K). Ambient temperature (K). Melting temperature (K). Time variable (s). Discharge on-time (µs). Discharge off-time (µs). Discharge voltage (V). Cartesian coordinates. Depth or axial coordinate. Density (kg/m2 ).

process. Two different mechanisms have been proposed to analyze the material removal viz., electro-mechanical analysis [5] for short discharge pulses (less than 5 µs) and electro-thermal analysis [6–17,19,18,20,21] for the normal EDM operation involving material removal due to the intense plasma energy generated between the cathode and anode. The electro-thermal analysis of EDM process is considered more relevant in the present context. Snoeys and Van Dijck [6,7] developed an electro-thermal model by utilizing a semi-infinite cylinder with a disk heat input. The work was developed further by Van Dijck and Dutre [8] using a two-dimensional heat flow model for both finite and infinite continuum. Beck [10,11] reported an alternative approach using a semiinfinite cylinder with a disk heat source considering constant thermal properties and heat flux. Jilani and Pandey [12,13] used a similar approach and assumed that the erosion will take place on the melting area of the electrodes. In the late eighties, DiBitonto and his coworkers [16] developed a Point Heat Source Model (PHSM) for cathode erosion of EDM process and compared it with their exhaustive experimental studies carried out in cooperation with AGIE Inc., USA. The results predicted by their model were closer to the experimental ones when compared with all the previous models [4]. This work was thus considered as a bench mark in the EDM process model development and was followed by further researchers [18,22,23] for thermal stress analysis, development of Powder Mixed EDM (PMEDM), etc. Further in 1993, Eubank et al. [19] have developed a comprehensive variable mass, cylindrical plasma model for the EDM spark based on fluid mechanics, thermodynamics and radiation theories. Important numerical data in terms of plasma pressure and temperature have been reported. They concluded that the superheating is the dominant mechanism for the spark erosion. Shankar et al. [20] proposed an FEM based approach to analyse the spark profiles at the inter electrode gap and at cathode and anode cross sections. They considered that the spark profile is non-cylindrical with the smallest cross section occurring at the middle of a discharge. The experimental studies [19,24,25] carried

out using high speed cameras and fiber optics have, however, shown that the spark profile is barrel shaped with the cathode arc root much smaller than the bulk plasma. The anode arc root is considerably larger in diameter than that of the cathode but smaller than the bulk plasma. The results by Shankar et al. [20] are thus, not found realistic. Panda and Bhoi [26] developed a threedimensional transient heat conduction model of EDM process considering the growth of the plasma channel. The model however, has limited applicability as it considered constant spark radius for all discharge conditions. Kansal et al. [18] developed an axi-symmetric thermal model for the PMEDM based on assumptions such as Gaussian distribution of heat source and constant spark radius for discharge conditions. Marafona and Chousal [23] developed an electro- thermal model based on Joule effect using FEM. The resulting melting volume per discharge pulse was compared with the experimental data reported by DiBitonto et al. [16]. Most of the above thermo-physical models of the EDM process are based on assumptions such as cylindrical spark plasma [6–14], uniform (disc) heat source [6,8,10–13], point heat source [9,16], constant [6,8,12,14] or expanding heat flux radius [7,13,15] and constant thermo-physical material properties [6,8,10–13, 16,17] over the temperature range. Many of these simplifying assumptions do not simulate the real life conditions and so severely limit the applicability of the results. In 2007, Yeo et al. [4] critically compared various reported EDM thermal models with the experimental results (AGIE SIT data) published by DiBitonto et al. [16] in terms of the predicted geometry of the crater due to single spark and the material removal at the cathode. They have conclusively reported that DiBitonto’s model predicts results closer to the experimental data when compared with all the other models. However, DiBitonto’s process model also over-predicts the results to a large extent when compared with the experimental results mainly due to the simplifying assumptions such as the approximation of heat source at cathode as a point and crater cavity of hemispherical shape, which are not realistic. In conclusion, the reported theoretical models based on thermal analysis have limited applicability, as they are based on the assumptions like the use of constant spark radius, approximation of heat source to a point or disc shaped (uniform) and constant thermal properties of work/tool materials. A need thus, exists to develop a more comprehensive and realistic numerical process model based on the thermal analysis of EDM to predict accurately the shape and size of crater cavity by modifying the above stated assumptions. This has been the primary focus of the present research work. 3. Thermo-physical model of the EDM process 3.1. EDM spark In EDM, the tool (anode) and the work piece (cathode) are immersed in a dielectric medium separated from each other by a small gap of the order of about 5–10 µm [2]. A controlled spark is generated between the two electrodes by applying a voltage (∼200 V) which breaks down the dielectric medium causing the voltage falls to about 25–30 V (discharge voltage) and the current to rise to a constant value set by the operator. During the ontime of EDM spark (of the order of microseconds), electrons start flowing from cathode to anode which ionizes the dielectric medium and form a plasma channel between the cathode and anode. The intense heat generated in the plasma channel melts and even vaporizes some of the work and tool material causing material removal. The molten metal is held back at its place due to the large plasma pressure [16,19] and as soon as the spark

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3.3. Assumptions

• Work piece and tool materials are homogeneous and isotropic in nature.

• The material properties of the workpiece and tool are temperature dependent.

• During the EDM operation, heat is transferred from plasma

• Fig. 1. Schematic representation of the domain considered for the numerical model.

• • •

to electrodes by conduction and radiation, while from plasma to dielectric by convection and radiation [19]. In the present work, the primary mode of heat transfer between plasma and electrodes is considered to be conduction. EDM spark channel is considered as a cylindrical column and the spark radius is assumed to be a function of discharge current and time [27]. Heat flux is assumed to be Gaussian distributed [17]. The zone of influence of the spark is assumed to be axi-symmetric in nature. Only a fraction of total spark energy is dissipated as heat into the work piece, the rest is lost into the dielectric convection and radiation. Flushing efficiency is considered to be 100%. There is no deposition of recast layer on the machined surfaces.

3.4. Governing equation For the transient, non-linear thermal analysis of EDM process, Fourier heat conduction equation is taken as the governing equation, 1 ∂

Fig. 2. Process continuum and boundary conditions.

on-time is over (the spark collapse) the dielectric gushes back to fill the void. This sudden removal of pressure results in a violent ejection of the molten metal from the work surface forming small craters at locations, where material has been removed. Controlled spark discharges between the tool and workpiece give the desired material removal and production of the cavities of desired shape on the work surface. Owing to the complex nature of the EDM process involving spark plasma, dielectric medium, flushing conditions, etc., it is very difficult to experimentally observe the spark and associated crater formation phenomenon. 3.2. Process continuum and boundary conditions The primary mechanism of material removal in EDM process is the thermal heating of work surface due to intense heat generated by the plasma, which raises the temperature of the electrodes (tool, work) beyond their melting point, sometimes even the boiling point. For the thermal analysis of the process, conduction is thus considered as the primary mode of heat transfer between the ions of plasma and the molecules of work/tool [4,6–17,19,18,21]. During the process, spark discharges may occur over work surface at locations where the inter electrode gap is minimum. All discharges can be considered to be identical. The present analysis is thus, carried out for a single spark operation and the results have been extended for multi-spark operation. A small cylindrical portion of the workpiece around the spark is chosen for analysis. Figs. 1 and 2 show the two-dimensional axi-symmetric process continuum and the associated boundary conditions taken for the analysis. Following assumptions have been made during the thermal analysis.

∂T = ρ Cp (1) r ∂r ∂t where r and z are the coordinates of cylindrical work domain; T is temperature; Kt is thermal conductivity; ρ is density and Cp is specific heat capacity of work piece material. Fig. 2 shows the associated boundary conditions applied. In EDM process, the work piece is immersed in dielectric medium; the temperature of the domain is thus assumed to be ambient temperature (Ta ) to start with. The top surface of the workpiece (boundary 2) is in contact with the dielectric medium. Heat flux (q) boundary condition is applied on this surface. 

Kt r

∂T ∂r



+

∂ ∂z



Kt

∂T ∂z



3.5. Heat input Important factors which contribute to the accurate calculation of the MRR in single spark EDM model include the amount of heat input, radius of plasma spark and the thermo-physical properties of material. Researchers have assumed two forms of heat input models viz., point source model with hemispherical crater cavity [16] or uniformly distributed heat flux model [6–13,26]. Both these models are simplistic as in actual practice neither is there a point heat source (like laser beam) nor is there any uniform (constant) application of heat on the work piece. A spark radius exists at the cathode electrode [2]. Consideration of average thermo-physical material properties and constant EDM spark radius make the reported models [6–13] simplistic and less accurate in predictions. In this present work, the Gaussian distribution of heat flux input [17] has been used to approximate the heat from the plasma. The heat q entering the workpiece due to EDM spark is given by,

( q(r ) = qo exp −4.5



r Rpc

2 )

.

(2)

Using this equation, the maximum heat flux qo can be calculated as under [18]. qo =

4.57Fc VI

π R2pc

(3)

where Fc is fraction of total EDM spark power going to the cathode; V is discharge voltage; I is discharge current and Rpc is spark radius at the work surface.

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3.6. Spark radius Spark radius is an important factor in the thermal modeling of EDM process. In practice, it is extremely difficult to experimentally measure spark radius due to very short pulse duration of the order of few microseconds [2]. Different approaches have been proposed by researchers in the literature. Notable among them being spark radius equation based on boiling point by Pandey and Jilani [15], relation based on underwater welding experiments by Patel et al. [17] and the empirical equation for specific tool/work material by Erden [28]. The equations proposed by these researchers are not realistic in nature as the EDM spark is controlled both by discharge energy and discharge on-time [2]. Ikai and Hashiguchi [27] have derived a semi-empirical equation of spark radius termed as ‘‘equivalent heat input radius’’ which is a function of discharge current, I (A) and discharge on-time, ton (µs) (Eq. (4)). It is more realistic when compared with the other approaches. Fig. 3. Temperature distribution obtained at the end of a spark.

0.44 Rpc = (2.04e − 3)I 0.43 ton (µm).

(4)

In the present work, this approach has been used to calculate the equivalent heat input at cathode using Eqs. (2)–(4). The heat flux equation derived and used for further analysis in this work is, q(t ) =

3.4878 × 105 FcVI 0.14 0.88 ton

( exp −4.5



t ton

0.88 ) (5)

where Fc is the fraction of total power going to the cathode; V is the discharge voltage; I is the discharge current; t is the time (µs) and ton is time (µs) at the end of electric discharge. Eq. (5) controls the amount of heat which is applied on the cathode which in turn, causes removal of material from cathode during operation. Energy distribution factor (Fc ) is an important factor in this equation as it governs the amount of energy going to cathode. Various values of Fc were proposed in the literature ranging 0.18–0.5 [4,19]. DiBitonto and co-workers [16] used the data that were gathered over a long period of time and for different operating conditions. Comparing the experimental and analytical results, they recommended that the energy distribution for cathode (Fc ) should be chosen as 0.183 for good correlation between the analytical and experimental results. In the present work, the value of Fc (0.183) has been chosen and studies have been carried out further to see its effect on the MRR.

Fig. 4. Predicted bowl shaped crater using the FEM analysis.

3.7. Solution methodology The governing equation (Eq. (1)) with boundary conditions outlined earlier was solved by FEM to predict the temperature distribution at the end of each transient heat transfer analysis cycle. ANSYSTM 10.0, a FEM solver was used. A two-dimensional continuum of size ten times the spark radius was considered for the analysis. Four-noded, axi-symmetric, thermal solid element (PLANE 55) was used for discretization of the continuum. Nonlinear material properties viz., temperature dependent thermal conductivity was employed. Convergence conditions were tested by increasing the number of elements in the mesh. The transient heat transfer problem was solved by applying the heat flux at the spark location (Eq. (5)) and using the discharge duration as the time step for the analysis. Fig. 3 shows the results for a typical problem showing the temperature contour plots. The results are for work material AISI P20 tool steel with machining conditions—discharge current 5 A, discharge voltage 40 V and discharge duration of 30 µs. The nodes showing temperature more than melting point were selected and eliminated from the complete mesh of the work domain for further analysis. A typical crater cavity ‘generated’ by this analysis is shown in Fig. 4.

Fig. 5. Calculation of crater volume.

To calculate the material removal due to single spark discharge, the cavity volume was divided into number of cylindrical discs (Fig. 5). The x–y coordinates of the node boundary generated by the ANSYSTM 10.0 are used for the calculation of crater volume. Total crater volume Cv t (µm3 ) is given by, Cv t =

n−1 X

Di

(6)

i=0

where volume of a disc, Di is given by, Di = π



xi + xi+1 2

2

(yi+1 − yi )

(7)

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where x and y are the coordinates of nodes and n is the number of nodes. Eqs. (6) and (7) were used to calculate the crater volume generated by a single spark discharge. In practice, the actual material removal during EDM process will be governed by factors such as ignition delays, high frequency of sparks, flushing efficiency, phase change of electrodes, random behavior of debris particles, etc., [4,22]. It is very difficult to incorporate these factors into the numerical process models. As a result, in the present work, ideal MRR was computed for chosen process conditions considering that all sparks are equally effective with 100% dielectric flushing efficiency. The MRR (mm3 /min) is computed by, MRR =

60 × Cv t ton + toff

(8)

where Cv t is the material removed per discharge pulse; ton is discharge duration and toff is the discharge off-time. During the EDM process, material is removed predominantly by melting than evaporation. Latent heat of melting is thus, an important factor in the thermal modeling as it signifies the consumption of a considerable amount of supplied heat (generated in the spark plasma) for the phase change of the work/tool material during melting [20]. The DiBitonto’s model has ignored the effect of latent heat of melting in their analysis. In our work, it was decided to study the effect of the latent heat during melting in the analysis. The latent heat of melting was considered to be distributed over the temperature zone from room temperature to the melting point temperature of the work/tool material and was incorporated by enhancing the specific heat of work material. The effective heat capacity Cpeff is computed by using Eq. (9) and applied. Cpeff = Cp +

LH

1T

(9)

where Cp is the specific heat of work material; LH is the latent heat of the work material and 1T is the temperature difference between melting point temperature of work material and room temperature. The above thermo-physical FEM based model was run in both modes viz., by considering as well as ignoring the latent heat of melting. 4. Results and discussion The results predicted by our thermo-physical model viz., MRR, crater cavity shape and size were compared with the published experimental results and our own experimental results. These results are reported in the sections to follow. 4.1. Model validation using published results In 2007, Yeo et al. [4] critically compared the prediction accuracies of five well-referred thermal models reported by Snoyes and Van Dijck [6,7], Van Dijck and Dutre [8], Beck [10,11], Jilani and Pandey [12,13] and DiBitonto et al. [16] with the experimental data of DiBitonto et al. [16] in terms of the predicted geometry of the crater due to single spark and material removal at the cathode. It has been conclusively reported that DiBitonto’s model predicted results closer to the experimental data when compared with all the other models which over-predict significantly. To compare the accuracy of prediction of our model (Section 4) it was, therefore, decided to compare the results predicted by our model with the above theoretical and experimental results (AGIE SIT data) reported by Yeo et al. [4] (in particular, the DiBitonto’s model). The machining conditions adopted for carrying

Fig. 6. Comparison of computed and experimental results: cathode erosion.

out our analysis were exactly the same reported by Yeo et al. [4]. Table 1 shows the comparison of the reported experimental results (AGIE SIT), reported theoretical model results [4] and the results predicted by both of our numerical models (considering as well as ignoring the latent heat of melting). Fig. 6 shows the comparison of the MRR predicted by our model, Yeo’s recommended model [16] and the AGIE SIT experimental data [16]. It is seen that the values of the MRR predicted by our model are further closer to the experimental results when compared with those by DiBitonto et al. [16] for a wide range of discharge energy levels up to 650 mJ. Our model has gone a step further than DiBitonto’s model [16] to the experimental results possibly due to the incorporation of real life conditions in the analysis such as Gaussian distribution of heat flux, discharge current and discharge on-time dependent spark radius equation, use of temperature dependent thermal properties and consideration of latent heat of melting. Our model considers the transient analysis of single spark with the expanding radius, which also may have added more accuracy to the predicted results. DiBitonto’s model, in comparison, has approximated the spark as a point heat source on cathode which created hemispherical crater cavity (Fig. 8). This is quite simplified when compared with the reality. Fig. 6 shows that, for higher values of discharge energy (>650 mJ), our model under-predicts the MRR when compared with the experimental results. This could possibly be because we have used the equivalent spark radius equation given by Ikai and Hashiguchi [27] in the present work which is not valid for the discharge energy levels greater than 670 mJ. Therefore, in the present work, comparison between the results predicted by our model in the high energy zone (above 650 mJ) and the experimental results has not been attempted. Table 1 and Fig. 6 also show the results from our model considering the latent heat of melting (Table 1). It can be noted that the predicted values of the MRR (considering latent heat) are further closer to the real experimental results for medium to higher energy spark domain (from 80 mJ onwards). A significant portion of the supplied discharge energy in this domain seems to be utilized in the phase change of the work material showing reduction in the MRR. As the discharge energy increases, the gap between our models (with and without latent heat) increases indicating that the effect of latent heat is more significant in the higher energy zones. Fig. 6 shows that three distinct energy zones exist viz., low energy zone (less than 100 mJ), medium energy zone (100–650 mJ) and high energy zone (more than 650 mJ). In the medium energy zone, our model under-predicts the MRR in comparison with the

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Table 1 Comparison of the predicted results: cathode erosion. Expt. no.

1 2 3 4 5 6 7 8 9 10 11 12 13

MRR (mm3 /min)

Machining conditions Current (A)

Pulse on-time (µs)

Pulse off-time (µs)

Discharge power (mJ)

Expt. results [16]

Theoretical analysis DiBitonto et al. [16]

Our numerical model (without latent heat)

Our numerical model (with latent heat)

2.34 2.83 3.67 5.3 8.5 10 12.8 20 25 36 44 58 68

5.6 7.5 13 18 24 32 42 56 100 180 240 420 560

1 1.3 2.4 2.4 2.4 2.4 3.2 3.2 4.2 4.2 5.6 7.5 10

0.33 0.53 1.19 2.39 5.1 8 13.44 28 62.5 162 264 609 952

0.3 1.6 3.1 8.4 23.2 32 50.5 89.7 125 226 246 346 559

13.82 17.26 21.78 35.58 63.79 77.18 100.33 164.65 207.2 304.56 373.09 494.03 579.47

12.13 16.36 20.37 34.49 62.86 76.37 96.68 152.81 197.92 262.28 302.6 356.6 364.82

12.13 14.88 16.45 27.14 53.5 64.43 80.75 135.29 157.19 210.61 242.59 261.05 270.12

Work material—steel (iron), tool material—copper, discharge voltage = 25 V, thermal conductivity (Kt ) = 56.1 W/m K, Heat capacity (Cp ) = 575 J/kg K, density (ρ) = 7545 kg/m3 , latent heat = 247 kJ/kg, melting point temperature (Tm ) = 1808 K [4].

Fig. 8. Comparison of predicted crater shapes (Expt. no. 7 Table 1). Fig. 7. Effect of energy distribution factor on the MRR.

experimental results. This is unrealistic as the experimentally observed MRR cannot be more than what is predicted by the theoretical model, which assumes 100% Plasma Flushing Efficiency (PFE). This discrepancy may be due to the fact that during the medium energy, spark discharges with higher discharge durations, the contact area of plasma with the work surface is larger which might lead to the lower energy densities and indicate lower MRR. To correct this discrepancy, it was decided to try out higher energy distribution factors Fc used in our numerical model. Eubank et al. [19] reported that the energy distribution factor for cathode and anode increases with increase in the applied discharge energy. This is due to the fact that the higher energy plasma produces large temperatures, which further dissipate more heat to the electrodes. To test out, we tried the energy distribution factors Fc of 0.2, 0.25 and 0.3 in the present work. Table 2 and Fig. 7 show the variations of the MRR with respect to discharge energy for different values of Fc . It can be seen that in the low energy zone (less than 100 mJ), with Fc = 0.183, our model predicts the MRR closer to the experimental results in comparison with DiBitonto’s model. Using higher energy distribution factors (0.2, 0.25 and 0.3) in this energy range, the prediction accuracy of the model considerably suffers due to the over-prediction of the MRR. In the medium energy zone (100–650 mJ), our model with Fc = 0.2 corrects the above mentioned discrepancy by predicting

the MRR above the experimental results. Though the model overpredicts the MRR, it is found closer to the experimental results in comparison with DiBitonto’s model. The model considerably overpredicted the MRR with Fc = 0.25 and 0.3. Looking at various results, it can be concluded that the Fc value between 0.183 and 0.2 can be used for the medium energy zone to make the model realistic and more accurate during prediction. Based on these studies, it can be recommended that the energy distribution factor Fc of 0.183 for lower energy level (less than 100 mJ) and 0.183–0.2 for the medium energy level (100–650 mJ) should be used to obtain the realistic and accurate erosion rates (MRR). However, detailed investigation needs to be carried out on this aspect for the medium and high energy zones. Yeo’s recommended model predicts the shape of the crater cavity to be hemispherical. In comparison, our model predicts the shape of the crater cavity as shallow bowl shaped (Figs. 5 and 8). Similar shaped (bowl) crater cavities have been experimentally observed by Das et al. [22] and Schulze et al. [29] under different EDM process conditions. Our process model is thus seen to predict the process performance parameters (MRR, shape of crater) better and closer to the experimental results. To gain further confidence, it was thought appropriate to carry out a set of our own experiments to validate the developed thermophysical model of EDM process. Details are presented in the next sections.

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Table 2 Effect of energy distribution factor on the MRR. Expt. no.

1 2 3 4 5 6 7 8 9 10 11 12 13

MRR (mm3 /min)

Machining conditions Current (A)

Pulse on-time (µs)

Pulse offtime (µs)

Discharge power (mJ)

Expt. results [16]

Theoretical analysis DiBitonto et al. [16]

Our numerical model Fc = 0.183

Our numerical model Fc = 0.2

Our numerical model Fc = 0.25

Our numerical model Fc = 0.3

2.34 2.83 3.67 5.3 8.5 10 12.8 20 25 36 44 58 68

5.6 7.5 13 18 24 32 42 56 100 180 240 420 560

1 1.3 2.4 2.4 2.4 2.4 3.2 3.2 4.2 4.2 5.6 7.5 10

0.33 0.53 1.19 2.39 5.1 8 13.44 28 62.5 162 264 609 952

0.3 1.6 3.1 8.4 23.2 32 50.5 89.7 125 226 246 346 559

13.82 17.26 21.78 35.58 63.79 77.18 100.33 164.65 207.2 304.56 373.09 494.03 579.47

12.13 14.88 16.45 27.14 53.5 64.43 80.75 135.29 157.19 210.61 242.59 261.05 270.12

15.19 18.42 22.91 36.51 68.64 84.30 110.42 178.55 220.24 274.75 319.37 378.16 346.33

21.68 25.96 32.52 54.27 98.67 115.17 162.41 191.90 294.59 443.06 508.24 610.25 563.01

26.59 32.58 41.96 66.84 119.23 143.07 184.53 250.90 393.94 561.11 745.21 951.16 865.56

(a) Tool and workpiece specimen.

(b) Schematic representation of tool and workpiece specimen. Fig. 9. Tool and workpiece specimen.

4.2. Experimental studies for model validation Two objectives were set up for carrying out the experimental studies viz., the study of the MRR for various spark energy levels and the study of crater shapes for the single spark EDM operation. 4.2.1. Experimental conditions Experiments have been conducted on the die-sinking EDM machine PS-50 ZNC, Electronica (Pune, India) available at Godrej and Boyce Manufacturing Co. Ltd., Mumbai. The discharge (spark) energy levels during machining were varied between 4.5 and 900 mJ by setting appropriate process parameters (current, discharge duration, discharge voltage and duty cycle) on the machine. AISI P20 mold steel and copper were chosen as the work material and tool material, respectively. Fig. 9 shows the workpiece and tool electrode specimens used in the experimental studies. Special EDM oil with 20–40 kPa pressure was used as the dielectric medium. Table 3 lists the different machining conditions set up during the experimentation. The discharge voltage of 30 V and a duty cycle of 50% were kept constant throughout. Totally, 18 experiments were conducted by repeating each of the machining condition (Table 3). Before the actual cutting on the EDM machine, all the specimens (workpiece and tool electrode) were washed and dried. Each specimen was weighed on an accurate weighing machine PRECISA XB 220 A (Swiss made, least count of 0.0001 g). After carrying out the experiments (Table 3), the machined workpiece

Fig. 10. Comparison of results: MRR.

and tool electrode specimens were weighed again to record the material removal. 4.2.2. Experimental results Table 3 shows the results of these experiments and their comparison with the results predicted by our thermo-physical model (Section 4).

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Table 3 Comparison of theoretical and experimental results. MRR (mm3 /min): expt. results

Experimental conditions Expt no.

Current (A)

Discharge duration (µs)

1 2 3 4 5 6 7 8 9

5 9 12 15 20 25 30 35 40

30 50 75 100 200 300 400 500 750

2.83 15.44 35.22 47.41 73.9 97.03 176.28 207.23 192.6

MRR (mm3 /min) predicted by our thermo-physical model With latent heat

Without latent heat

39.45 76.18 97.02 124.94 158.36 201.29 242.47 276.85 282

52.35 96.35 115.23 156.32 183.69 235.36 275.58 318.54 339.25

Discharge voltage 30 V, duty cycle 50%.

Fig. 10 shows the comparison of the MRR observed during the experiments and the values predicted by our thermo-physical model. The results predicted by the thermo-physical model overpredict, but follow a trend quite similar to the experimental results. Numerical results considering the latent heat are closer to the experimental results when compared with the results obtained by ignoring the latent heat indicating that a significant amount of heat is absorbed in the phase change of work material during the crater formation phenomenon. The consideration of latent heat in the thermo-physical (numerical) analysis is thus, significant and important. In effect, it reinforces our approach of considering latent heat in the development of the thermo-physical process model. Fig. 10 shows that the analytical results over-predict the MRR when compared with the experimental results by almost a uniform margin for all the energy levels. This could possibly be attributed to some simplifying assumptions in our numerical model such as ideal flushing conditions (100% flushing efficiency), 100% spark efficiency, no ignition delays, no deposition of recast layer, etc. In practice, such ideal conditions are not realized due to improper flushing of debris and arcing into the inter electrode gap during the machining with high energy discharges (with high currents and long discharge durations) thus, reducing the actual MRR. However, it is very difficult to model and incorporate such effects in the analytical model. The results reported above encouragingly show that the trends of the theoretical results predicted by our model match quite closely with the experimental results for all the spark energies ranging from roughing to finishing process conditions by almost a uniform margin. 4.3. Single spark experiments In the second part of the experimental studies, few single (limited) spark(s) experiments have been carried out. The aim was to study the crater shapes generated due to single spark discharges and to compare them with the ones predicted by our numerical model. Literature documents very scant experimental studies on the crater shapes generated due to single spark, as it is extremely difficult to create and control the conditions for the occurrence of single spark. No commercial setup is available to produce and control the single spark discharges. It was, therefore, decided to simulate single spark operation (limited sparks) by designing the tool electrodes on the available experimental facility. Fig. 11 shows the tool electrodes and workpiece specimen used for the experiments. Pointed tip copper tool electrodes were designed and ground to generate single (limited) spark discharges. The top surfaces of the workpieces were ground to mirror finish by using CNC Grinding Machine. From the tryouts using different EDM machining conditions, it was seen that it was possible to produce limited spark discharges (10–12) which were reasonably separated on the workpiece. After

Fig. 11. Tool and workpiece specimen: single spark experiments.

the generation of such single (limited) spark discharges, the specimen were cleaned and scanned by using a three-dimensional topography measurement instrument (Taylor and Hobson’s Talysurf with a touch probe of 2 nm). 4.3.1. Shape and size characterization of craters For a typical machining condition (viz., current 5 A, discharge duration 30 µs, discharge voltage 40 V, work material – AISI P20 mold steel, tool material—copper), single spark discharge studies were carried out. After producing a few single (limited) spark craters on the workpiece specimen, a visual inspection was carried out and suitable craters were chosen for three-dimensional scanning by using Talysurf. A typical rectangular area of about 1 mm2 was chosen around the craters for carrying out the scanning. Fig. 12(a) and (b) shows two-dimensional and three-dimensional images of the crater cavities produced by single (limited) spark on the workpiece specimen. It can be seen that there are overlapping craters produced due to the generation of limited sparks. Out of all, crater cavity-A can be perceived to have been produced due to a single spark and was thus, chosen for further studies. Fig. 13 shows the three-dimensional zoomed-in view of the crater-A. It can be observed that the shape of the crater is obround

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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

µm

(a) Two-dimensional view.

(b) Three-dimensional view. Fig. 12. Scanned craters.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Table 4 Results of limited discharge experiments. Parameter

Experimental results

Numerical simulation

Crater depth (µm) Crater radius (µm)

14.7 41

18.44 32.56

µm

Fig. 13. Three-dimensional zoomed-in view of crater-A. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 15. Crater shape comparison.

Fig. 14. Crater shape at section Y–Y: experimental results.

showing a depression in the middle in blue color. The yellow color indicates the datum or the reference level of the image, while the red colored portion of the image shows the ridge formed around the crater cavity. The shape of the crater was studied at various cross sections. Fig. 14 shows the crater shape at a section Y–Y. It can be noted that the crater is of bowl shaped.

In literature, researchers proposed/predicted a variety of crater shapes from their analysis such hemispherical, cuboidal, shallow disc shaped, etc., [4]. To compare the experimental results with our numerical (FEM) model, numerical simulation was carried out at the same machining conditions. Fig. 5 shows the bowl shaped crater predicted by our numerical model for the similar machining conditions used for single spark experimental studies. The crater volume was computed by using Talysurf by approximating the boundary around the crater. Table 4 shows the comparative study of the results obtained by our numerical model simulation and those from the single (limited) discharge experiment for the typical machining condition. It can be seen that the numerical results viz., crater depth and crater radius predicted by our model are generally in good agreement with the experimental results. Fig. 15 shows the comparison of the shape and size of the crater predicted by our numerical model and our experimental studies. The bowl shaped crater obtained in the experimental results is quite similar to the one predicted by the numerical model. From Table 4 and Fig. 15, it can be observed that the experimental crater is shallower than the numerically predicted, possibly due to the deposition of recast layer over the crater.

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Fig. 16. Variation of the MRR with discharge current for discharge duration of 100 µs.

Fig. 17. Variation of crater depth with discharge current.

In conclusion, it can be said that the shape of the crater predicted by our model is realistic and is quite similar to the experimental results. 5. Parametric studies on EDM process After validating the numerical EDM model developed, it was decided to carry out parametric studies to understand the influence of input process parameters (discharge current, discharge duration, discharge voltage and duty cycle) on the process performance measures such as MRR and crater depth. ANSYS Parametric Design Language (APDL) [30] was used to build the single spark FEM model and automate the numerical simulation process for different input process parameters. The following ranges of the input process parameters identified from the published research [1,2] and machining handbook [31] were chosen for our study.

• • • • • •

Discharge current 5–10–20–30–40 A. Discharge duration (on-time) 25–50–100–300–500–700 µs. Duty factor 50%–65%–80%. Break down voltage 30–40–50 V. Work material AISI P20 mold steel. Tool material, copper.

Ninety numerical simulations were carried out in all the ranges of input process parameters outlined above. Based on the temperature distribution resulting due to the single spark, MRR and crater sizes were computed. Temperature dependent material properties of AISI P20 tool steel [32] and copper [17,32] were used. Important results are discussed in the next section. 5.1. Effect of discharge current Discharge current is one of the important process parameters in EDM as it directly governs the spark energy. Fig. 16 shows that the MRR increases monotonically with an increase in discharge current and duty cycle. These trends match with the experimental results reported by Chen and Mahdivian [33]. Higher values of discharge current and duty cycle are recommended for rough machining, while lower values are recommended for finishing operations. Fig. 17 shows that the crater depth (surface roughness) increases with the discharge current and voltage. It is observed that in the low discharge current range, the crater depth increases rapidly with current but tapers off further, indicating the production of

Fig. 18. Variation of the MRR with discharge duration for discharge voltage of 30 V.

shallow and wider craters at high currents. This trend of variation of crater depth with current is also seen in the reported experimental results [34]. Lesser values of discharge currents and voltages are recommended for finishing applications of EDM process to limit the depth of the craters. 5.2. Effect of duty cycle Duty cycle is defined as the ratio of discharge duration to the total spark time. It governs the generation of number of sparks per unit time; higher duty cycle indicates more number of sparks per unit time. Fig. 16 shows that an increase in duty cycle monotonically increases the MRR. Higher values of duty cycle can be used for roughing application. 5.3. Effect of discharge duration Spark discharge duration is another important process parameter in EDM, which decides the time for the discharge energy to be applied on the work surface during the total spark time (on + off). The spark off-time is generally decided by the ‘‘duty cycle’’. Fig. 18 shows the variation of the MRR with discharge duration for a typical machining condition. The MRR initially increases with discharge duration, attains maximum value and shows a

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Fig. 19. Variation of crater depth with discharge duration for discharge voltage 30 V.

decreasing trend further, possibly due to the constant duty cycle and decrease in flux density. A similar trend is also shown in the experimental results reported by Amorim et al. [35] and Panda and Bhoi [36]. As the current increases, the peak of the curves shifts towards right side indicating an increase in the MRR with current and discharge duration simultaneously. This trend of variation, in effect, justifies the use of equivalent spark radius proposed in our model (see Section 3.6, Eq. (5)), which is a function of both discharge current as well as the discharge duration. Fig. 19 shows that the crater depth increases with discharge duration, the rate of increase, however, tapers off subsequently. This might be due to the fact that higher discharge durations generate lower flux densities leading to the less heat conduction along the axial z-direction. 5.4. Effect of discharge voltage Discharge voltage is an important process parameter, which governs the heat flux applied on the cathode surface. Fig. 20 shows the variation of the MRR with discharge voltage for various values of discharge current and constant discharge duration. The MRR is found to increase with the discharge voltage. Higher values of discharge voltage increase the flux density producing larger material removal as well as the tool wear. Higher values of discharge voltages are recommended for roughing application. Results indicate that the performance measures of EDM process are influenced by four interacting process parameters viz., discharge current, discharge duration, discharge voltage and duty cycle. Discharge current and discharge voltage were found to be affecting significantly the crater depth, while discharge duration and discharge current were the main influencing process parameters for the MRR. Results predicted by the model have trends similar to the experimental results. 6. Conclusions A non-linear, transient, thermo-physical model of die-sinking EDM process has been developed using the FEM. Comprehensive thermal analysis of the process was carried out and the results obtained from our numerical model were compared with earlier analytical models, published experimental data and our own experimental results. It was found that the MRR values predicted by our model are closer to the experimental results when compared with all the earlier reported analytical models. Similarly,

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Fig. 20. Variation of the MRR with discharge current and discharge voltage.

the crater cavity shapes predicted by our model were found to be more realistic and closer to the experimental results when compared with those reported earlier by the analytical studies. Incorporation of factors such as the Gaussian distribution of heat flux, EDM spark radius as a function of discharge current and discharge duration, and consideration of latent heat of melting, etc., have possibly made our model closer to actual process conditions, thus improving its prediction accuracy. It was noted that it is essential to apply higher energy distribution factor for higher energy zones. The energy distribution factors 0.183 for lower energy zone (up to 100 mJ), while 0.183–0.2 for medium energy zone (100–650 mJ) were recommended. Typical parametric studies were carried out to study the effect of input process conditions on the process performance. The trends of variation of results were found matching with the published experimental results. The developed thermo-physical model can be used to carry out extensive parametric studies to understand the EDM process performance without going for actual experiments. The model can be used in conjunction with artificial intelligence (AI) tools and optimization techniques to obtain process conditions for optimum EDM performance. This will be the focus of our future work. References [1] Ho KH, Newman ST. State of the art in electrical discharge machining (EDM). Int J Mach Tools Manuf 2003;43(13):1287–300. [2] Kunieda M, Lauwers B, Rajurkar KP, Schumacher BM. Advancing EDM through fundamental insight into the process. CIRP Ann Manuf Technol 2005;54: 599–622. [3] Abbas NM, Solomon DG, Bahari MdF. A review on current research trends in electrical discharge machining (EDM). Int J Mach Tools Manuf 2007;47: 1214–28. [4] Yeo SH, Kurnia W, Tan PC. Critical assessment and numerical comparison of electro-thermal models in EDM. J Mater Process Technol 2007;203:241–51. [5] Singh A, Ghosh A. Thermo-electric model of material removal during electric discharge machining. Int J Mach Tools Manuf 1999;39(4):669–82. [6] Snoeys R, Van Dijck FS. Investigation of electro discharge machining operations by means of thermo-mathematical model. CIRP Ann 1971;20(1): 35–7. [7] Snoeys R, Van Dijck FS, Peters J. Plasma channel diameter growth affects stock removal in EDM. CIRP Ann 1972;21(1):39–40. [8] Van Dijck FS, Dutre WL. Heat conduction model for the calculation of the volume of molten metal in electric discharges [discharge machining]. J Phys D Appl Phys 1974;7(6):899–910. [9] Erden A, Kaftanoglu B. Heat transfer modeling of electric discharge machining. In: Proceedings of the 21st international machine tool design and research conference. London (UK): Swansea Wales Univ. Coll. of Swansea, Dept. of Mech. Eng., Wales in Assoc. with Macmillan Press, Ltd. 1981. p. 351–8. [10] Beck JV. Transient temperatures in a semi-infinite cylinder heated by a disk heat source. Int J Heat Mass Transfer 1981;24(10):1631–40.

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