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FE Modeling for Single Spark in EDM Considering Plasma Flushing Efficiency
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Procedia Manufacturing 26 (2018) 617–628 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
FE Modeling for Single Spark in EDM Considering Plasma FE Modeling for Single SparkEfficiency in EDM Considering Plasma Flushing Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June Flushing Efficiency 2017, Vigo (Pontevedra), Spain S. Jithinaa, Ajinkya Rautaa, Upendra V. Bhandarkaraa, Suhas S. Joshia,a,* S. Jithin , Ajinkya Raut , Upendra V. Bhandarkar , Suhas S. Joshi *
Department of Mechanical Engineering, Indian Institute of Technology Mumbai – 400076, Costing models for capacity optimization inBombay, Industry 4.0:IndiaTrade-off Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai – 400076, India between used capacity and operational efficiency * Corresponding author. Tel.: +91-22-25767527 a a
E-mail address:author. [email protected] * Corresponding Tel.: +91-22-25767527 E-mail address: [email protected]
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Due to complex nature of single spark phenomenon in EDM, the removal mechanism needs better comprehension and clarity. In this thisnature work of presents finitephenomenon element simulation single spark during electrical discharge machining Due context, to complex single aspark in EDM,ofthea removal mechanism needs better comprehension andtaking clarity.into In consideration significant aspectsa such temperature dependency of material properties, Gaussian distribution heat flux, this context, this work presents finiteaselement simulation of a single spark during electrical discharge machiningoftaking into Abstract plasma channelsignificant radius varying withsuch current and discharge duration, and in factors such as cathode energy of fraction, and consideration aspects as temperature dependency of variability material properties, Gaussian distribution heat flux, flushingradius efficiency. Such a model can offer a better prediction of the crater profile obtained on the work surface which plasma channel varying with current and discharge duration, and variability in factors such as cathode energy fraction, and Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, enables it to beefficiency. extended Such to multi-spark scenarios for predicting texture EDMsurface process. FE plasma flushing a model can offer a better predictionthe of surface the crater profileobtained obtainedthrough on the work which information based that on athe real timeradius basis and, necessarily, much moreincreasing efficient.values In thisof context, capacity optimization simulations crater crater depth increases with the operating such FE as enables it toshowed be extended to multi-sparkand scenarios for predicting the surface texture obtained through parameters EDM process. goes beyondshowed the traditional aim of capacity maximization, contributing also forvalues profitability and such value. / d ), which is the ratio between crater discharge and pulse It isand alsocrater observed the crater ratio (rorganization’s simulationscurrent that the on-time. crater radius depththat increases withaspect increasing of the operating parameters as c c Indeed, improvement approaches suggest instead of radius andlean cratermanagement depth, showson-time. aand highcontinuous value at low values of discharge current andratio pulse Thisoptimization is due feeble penetration / capacity dc), which the to ratio between crater discharge current and pulse It is also observed that the crater aspect (rcon-time. maximization. study of costing modelsand is anvalidation important research topic deserves of heatand through the cathode body forvalue lowoptimization values the and operating parameters. The the is FEdue model isthat made against radius craterThe depth, shows acapacity high at low of values of discharge current pulse on-time.ofThis to feeble penetration contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical experiments and it was found that the model displays improved prediction at high values of the operating parameters. The in of heat through the cathode body for low values of the operating parameters. The validation of the FE model is made error against dcwas bymanagement the model fromon 9.1different to 13.4 %costing which represents ahigh good prediction crater profile by the The model. prediction rc / it model forofcapacity modelsat(ABC and TDABC). A generic model haserror been experiments and found thatvaries thebased model displays improved prediction values of theof operating parameters. in by the model varies from 9.1 to 13.4 % which represents a good prediction of crater profile by the model. prediction ofand rc /itdwas developed used to analyze idle capacity and to design strategies towards the maximization of organization’s c value. trade-offPublished capacitybymaximization © 2018The The Authors. Elsevier B.V. vs operational efficiency is highlighted and it is shown that capacity © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of thescientific scientific committeeofofthe NAMRI/SME. optimization might hide operational inefficiency. © 2018 The Authors. Published by Elsevier B.V.committee Peer-review under responsibility of the 46th SME North American Manufacturing Research Conference. © 2017 The Authors. Published by B.V. committee of NAMRI/SME. Peer-review under responsibility ofElsevier the scientific Keywords: FEM; EDM; Single-spark;ofCrater radius; Plasma flushing Peer-review under responsibility the scientific committee ofefficiency the Manufacturing Engineering Society International Conference Keywords: FEM; EDM; Single-spark; Crater radius; Plasma flushing efficiency 2017. a
1. Introduction energy generated Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity;thermal Operational Efficiency
by spark discharges for material The schematic of thedischarges EDM process 1. Introduction thermal removal. energy generated by spark for Electrical discharge machining (EDM) is a popular is given removal. in Fig. The 1. Workpiece (cathode) tool material schematic of the EDMand process 1.Electrical Introduction non-traditional machining method(EDM) which isutilizes the (anode) a small gap of an order 10 discharge machining a popular is givenare inseparated Fig. 1. by Workpiece (cathode) andoftool non-traditional machining method which utilizes the (anode) are separated by a small gap of an order of 10 The cost of idle capacity is a fundamental information for companies and their management of extreme importance 2351-9789 2018 The Authors. Published by Elsevier in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured Peer-review of the scientific committee of NAMRI/SME. 2351-9789 2018responsibility The Authors. Published by Elsevier B.V.hours in several©under ways: tons of production, available of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility the761; scientific committee NAMRI/SME. * Paulo Afonso. +351 253 of 510 fax: +351 253 604of741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.072
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to 100 microns known as spark gap. The spark gap is filled with a liquid dielectric. This liquid dielectric acts as an insulator initially, but under suitable electrical conditions it undergoes breakdown to form plasma channel comprising of positive ions and electrons. These ions and electrons are accelerated by the applied electric field and they impinge the electrodes at high velocities. This results in a localized heating of very small regions on both cathodic and anodic surfaces to very high temperatures which leads to material removal through melting and evaporation. However, molten material is not fully flushed away by the dielectric and this portion of molten material resolidifies to form recast layer on the electrode surfaces. The temperature gradient also results in heat affected zone (HAZ) below the recast layer in both the electrodes. Anode has a higher plasma channel radius than that of cathode due to the former emitting positive ions instead of electrons. This results in a decrease in heat flux intensity and leads to anodic crater being smaller in size than cathodic crater.
Fig. 1. Schematic of EDM process
During every spark discharge a large number of diverse phenomenon such as plasma formation, heat conduction, heat radiation, heat convection, implosion of plasma channel, shock wave formation, removal of molten metal by dielectric, resolidification, electrical phenomena, chemical phenomena, etc. and their interactions are occurring. Due to these complex phenomenon underlying, the mechanism of spark generation and material removal still needs better comprehension and clarity [1]. A number of
researchers have attempted to simulate the spark erosion mechanism utilizing both analytical and numerical methods. The most prominent work among the analytical models was by DiBitonto et al. [2], where they gave a cathode erosion model to predict the crater dimensions when the operating parameters are known. However, a number of numerical models proposed for the spark erosion process, which came later, have been found to give a better prediction of crater dimensions due to the possibility of adopting more realistic assumptions which are related to the actual EDM operation [3]. Among the numerical models, researchers have utilized a variety of methods which include finite element method (FEM), finite difference method (FDM), generalized minimal residual method (GMRES), etc. towards this goal. FEM is seen to be the most popular when it comes to simulations of EDM process. One of the initial applications of FEM in simulation of a spark discharge was attempted by Yadav et al. [4]. They evaluated the temperature distribution and thermal stresses caused on the work material due to the input heat flux during a spark discharge. They observed that significant values of compressive and tensile stresses are developed in a thin layer around the discharge region which could lead to damage on the work surface. In another work, Das et al. [5] used an FE simulation to evaluate crater dimensions, phase transformations and residual stresses resulted on the cathode surface after spark discharge. Joshi and Pande [6] suggested that adoption of more realistic assumptions such as temperature dependency of material properties, inclusion of latent heat of fusion, Gaussian distribution of heat flux, spark radius value dependent on current and discharge duration, etc. during FE simulation improves the prediction of crater dimensions and MRR. Kalajahi et al. [7] performed a FE study to analyze the effect of different operating parameters on temperature distribution on the cathode. They found that the temperature distribution, thereby crater dimensions, show a continuous increase with the increasing values of the operating parameters such as current, voltage and duty cycle. However, crater dimensions show an increase in value up to a high value of discharge duration. For further increase in discharge duration, the crater dimensions decrease. Shabgard et al. [8] gave a model to predict recast layer thickness (RLT) taking into consideration the plasma flushing efficiency (PFE) as a function of discharge current and pulse on-time.
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They reported that PFE increases with increasing discharge current and it decreases with increasing pulse on-time. Different authors have tried to incorporate some realistic assumptions to bring their FE model closer to the actual EDM process. However, in addition to those assumptions, it is also essential for a singlespark model to consider the variable nature of factors such as cathode energy fraction (FC) and plasma flushing efficiency (PFE), with the operating parameters. Though Shabgard et al. [8] takes into consideration the variable nature of FC and PFE with discharge current and pulse on-time, they use PFE as a correction term after simulation to calculate crater dimensions. However, for crater shape/profile to be predicted taking into consideration the variable nature of PFE, it is necessary that PFE be included as a correction term during simulation. A proper prediction of the crater shape is essential for using this model for multiple spark scenarios for the surface texture prediction under different operating conditions. Hence, the goal of the current work is to develop an FE model for predicting the crater profile obtained during single discharge of EDM process, while taking into consideration the above mentioned important aspects. EDM have been traditionally used to machine electrically conductive and hard-tomachine materials such as Ti6Al4V, tungsten, etc., and these materials are finding innovative applications with technological advancements over last few decades. This has resulted in the tolerance requirements for different components made with these materials becoming more and more stringent. Thus an accurate prediction of crater dimensions formed during individual sparks at different parameter settings can contribute toward improving the accuracy of EDM process. Nomenclature T r z t Kt ρ Cp rg
temperature in Kelvin radial coordinate in metres height coordinate in metres time in seconds thermal conductivity in W/m.K work material density in kg/m3 specific heat capacity of work material in J/kg.K plasma channel radius in µm
I ton q(r) Fc U PFE hc LH Ts Tm rc dc
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discharge current in A pulse on-time in µs Gaussian heat flux in J/m3 cathode energy factor gap voltage in V plasma flushing efficiency convective heat transfer coefficient latent heat of fusion solidus temperature liquidus temperature crater radius crater depth
2. Finite Element Model A finite element model is proposed in this section to simulate an individual spark during the EDM process taking into consideration important aspects of the process such as temperature dependent material properties, Gaussian heat flux, and a variable plasma channel radius, cathode energy fraction and plasma flushing efficiency. Due to consideration of these important aspects, this model could give a more accurate prediction of crater profile. The authors have, in their previous work [9], extended an analytical model for prediction of crater profile on cathode during a single discharge to multiple-spark scenarios for simulation of surface texture generated during the EDM process. However, a finite element approach can give a better prediction for surface texture. This is because a numerical approach allows for a simulation of the complex heat flux input conditions which are resulted due to the occurrence of multiple sparks simultaneously during the EDM process. Hence, the authors aim to develop a FEM model for single spark simulation which gives an accurate prediction of crater shape. This single spark model will be extended to develop a multiple spark model for surface texture prediction as a future work by the authors. 2.1. Model Details The following assumptions are taken in the model: A Gaussian heat flux distribution with an expanding plasma channel radius. Work material is homogeneous and isotropic.
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Work material properties such as density, thermal conductivity and specific heat are temperature dependent. Fraction of energy going to cathode is a variable dependent on spark energy. Plasma flushing efficiency considered as a function of discharge current and pulse on-time. Dielectric material is assumed to influence cathode energy fraction (Fc), plasma flushing efficiency (PFE), and convective heat transfer coefficient (hc). The values of these parameters are computed to suit an assumption of hydrocarbon oil as dielectric. The governing equation for the single-spark problem is the Fourier heat conduction equation in cylindrical coordinates, which is as follows:
1 T Kt r r r r
T T (1) C p Kt z t z
where, r and z are cylindrical coordinates, T is the temperature, t is the time and Kt, ρ, and Cp are work material properties such as thermal conductivity, density and specific heat capacity, respectively. Since these material properties are dependent on temperature value, their variation with temperature needs to be considered for simulation of single spark conditions. Heat source in this scenario is the discharge column. The heat source is comprised of two aspects: heat source radius and heat flux distribution. The discharge column radius or plasma channel radius is found to be dependent on both pulse on-time and discharge current. Hence, we adopt the prominently used plasma channel radius equation provided by Ikai and Hashigushi [10]: 0.44 rg 2040 * I 0.43 * ton
(2)
where, rg is the plasma channel radius, I is the discharge current and ton is the pulse on-time. Different heat flux distributions such as point heat flux, uniform disk heat flux and Gaussian heat flux have been adopted by different authors. A number of authors have reported that an assumption of Gaussian heat flux distribution gives a better prediction for the model, in comparison to the other heat flux assumptions. We adopt the Gaussian heat flux
distribution equation given by Yadav et al. [4] for this model: 2 r q (r ) q0 exp 4.5 rg
(3)
and
q0
4.45FCUI rg2
(4)
where, Fc is the cathode energy fraction, U is the gap voltage, and r is the radial distance from the center of plasma channel. Cathode energy fraction (Fc) is the fraction of energy which goes to cathode from the total energy that is generated during individual spark discharge. It is taken as a constant value of 0.18 by most authors following the cathode erosion model proposed by DiBitonto et al. [2]. However, Harminder [11] have proved experimentally that FC varies with a variation in the operating parameters such as discharge current and pulse on-time. Based on his experimental data [11], the authors’ had suggested an adoption of FC values, considering a range of spark energy values, in their previous analytical model [9] which is as follows:
0.109 ( E 0 to 50 mJ ) FC 0.187 ( E 50 to 100 mJ ) 0.256 ( E 100 mJ ) as
(5)
where, E is the input spark energy and is evaluated
E UIton
(6)
Plasma flushing efficiency (PFE) is the ratio of the actual amount of material removed to the theoretical amount of material supposed to be removed during a spark discharge. Most of the single spark models available in the literature have assumed a PFE of 100% during simulation and later on evaluated PFE by comparing simulated results with experimental data. In the authors’ previous work [9], the improvement in crater dimension prediction with consideration of PFE in the model was emphasized. Hence, a variable PFE parameter needs to be incorporated for the simulation for a better prediction
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of crater dimensions and crater profile. Therefore, we adopt the following curve fit model [9] we developed previously based on works by DiBitonto et al. [2] and Shabgard et al. [8]: 2
PFE 0.1093 2.238 *10 * I
(7)
8.441*104 * ton 4.67 *105 * I * ton 2 4.912 *106 * ton
If the equation gives a value of PFE greater than 1, then PFE is assumed to have a value of 1. Such a curve fit model for PFE using data from more than one work in literature (in Refs. [2] and [8]) was used because the presence of more data points at different combinations of discharge current and pulse on-time improved the PFE prediction. This equation for PFE is used to modify the heat flux distribution equation (given in eq. (3)) as follows:
q0' PFE * q0
where, hc is the convective coefficient. And, on boundaries A2, A3 and A4
T 0 n
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heat
transfer
(13)
where n is direction normal to the boundary. This is because boundaries A2, and A3 are assumed to be insulated being very far away, and the boundary A4 lies along the axis of symmetry of the model. The axisymmetric thermal model of EDM with the initial and boundary conditions is represented in Fig 2.
(8)
Thus,
q0' PFE * by '
4.45FCUI rg2
(9)
Hence the updated Gaussian distribution is given
q (r )
PFE *
4.45 FCUI
rg2
2 r exp 4.5 rg
(10)
This modified equation of heat flux distribution will be used in the simulation of a single spark during EDM process. Finally, the initial and the boundary conditions for the FE simulation problem are as follows: Initial condition: o
T T 25 C 298K , t 0 i 0
(11)
Boundary conditions: On boundary A1
q ' (r ), r rg T Kt hc (T T0 ), r rg z 0, t ton
(12)
Fig. 2. Axisymmetric thermal model of EDM
2.2. Model implementation ABAQUS, an analytical software, was used for implementing the numerical model. The simulation is performed considering stainless steel grade 304 (SS 304) as cathode or work material. The variation in thermo-physical properties of SS 304 such as thermal conductivity, specific heat, and density with respect to temperature are given in Table 1. These values are computed using equations given by Valencia and Quested [12] which are as follows:
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10.33 15.4*103 T 7 *107 T 2 for 298K T 1633K 355.93 196.8*103 T Kt for 1644K T 1672K 6.6 12.14*103 T for T 1793K
(14)
C p 443 0.2T 8*107 T 2
(15)
Table 1. Thermo-physical properties of SS 304
Temperature (K)
for 298K T 1727 K
8020 50.1*102 T 298 for 298K T 1727 K 2 6900 80.0*10 T Tm for T 1727 K
(16)
Some additional properties of SS 304 related to latent heat of fusion are given in Table 2. These temperature dependent material property values are input to the model. An axisymmetric section is drawn to represent the cathode based on thermal model shown in Fig 2. The Gaussian heat flux distribution (obtained from eq. (10)) is applied for the length of plasma channel radius evaluated using eq. (2). An initial condition of ambient temperature (298 K) for the body is assumed. The boundary condition of convection on the top face is given with a surface film coefficient value of 8000 W/m2K. The whole section is meshed with a mesh size of 0.5 µm. The selection of such a small mesh size is to improve the accuracy in prediction of crater dimensions. After the FE simulation, the region with temperature above the melting temperature (1454 oC or 1727 K) of SS 304 is deleted to obtain the crater shape and dimensions. FE simulations for different operating parameter combinations can be performed after calculating the plasma channel radius and Gaussian heat flux distribution at those parameter values. The FE model is validated against the experimental data from the single spark experiments performed by Assarzadeh and Ghoreishi [13].
298 348 373 448 473 498 548 573 598 648 673 748 773 848 873 948 973 1003 1023 1048 1073 1273 1473 1573 1644 1672 1727 1773 1813 1963 2113 2163
Thermal conductivity (W/mK) 14.9 15.6 16.0 17.1 17.5 17.8 18.6 18.9 19.3 20.0 20.4 21.5 21.8 22.9 23.2 24.3 24.7 25.1 25.4 25.7 26.0 28.8 31.5 32.8 32.4 26.9
Specific heat (J/kgK)
Density (kg/m3)
502.5 512.5 517.5 532.4 537.4 542.4 552.4 557.3 562.3 572.3 577.2 592.2 597.1 612.0 617.0 631.9 636.8 642.8 646.8 651.7 656.7 696.3 735.9 755.6 769.6 775.2 786.0
8020 7995 7982 7945 7932 7920 7895 7882 7870 7845 7832 7795 7782 7744 7732 7694 7682 7667 7657 7644 7632 7532 7431 7381 7346 7332 7304 6860 6828 6708 6588 6548
Table 2. Additional properties of SS 304 [12] Latent heat (LH)
Solidus temperature (Ts)
Liquidus temperature (Tm)
247 kJ/kg
1400 oC
1454 oC
3. Results and Discussion 3.1. Parametric Analysis Parametric analysis is performed to study the effect of different operating parameters on the simulated crater dimensions. A number of FE simulations are performed according to the parameter combinations given in Table 3. It could be observed that Fc values are evaluated using eq. (5) which is in turn based on E value calculated from eq. (6). The other dependent variables such as rg, PFE, q0, and q’0 are calculated based on the eq.s (2), (7), (4), and (9), respectively. PFE values vary in the range of 0.25 to 1 for these parameter combinations. This indicates that the flushing efficiency is low for low current and
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high pulse on-time which means that the resolidification is high. In contrary, for high current and low pulse on-time combinations, the flushing efficiency is maximum, indicating very less amount of resolidification. The simulated craters at different operating parameter combinations are shown in Fig 3. After FE simulation, temperature distribution on the section is obtained. The craters are obtained in the model by deleting the elements of the section which are at a temperature value higher than the melting point. It could be observed that among the crater dimensions, crater radius tends to be higher in all simulations giving the craters an elliptical shape. This is resulted due to the Gaussian heat flux being applied to the top face which causes more heat dissipation in the radial direction. The temperature gradient below the crater surface results in a heat affected zone. The variation of crater radius and crater depth with the operating parameters such as discharge current and pulse on-time are shown in Fig 4. It could be observed from Fig 4(a) that crater radius and crater depth show continuous increase with discharge current. This is because as the discharge current increases, it causes the input pulse energy to increase. The increase in input pulse energy leads to a larger amount of material to be heated above the melting temperature and thus a crater with larger dimensions is formed. The variation of crater dimensions with pulse on-time is shown in Fig 4(b). It is understood that, similar to the case of discharge current, crater dimensions show a continuous increase with pulse on-time. The input discharge power is constant for all these simulations as discharge current and discharge voltage is kept constant. However, with an increase in pulse on-time, the duration for which the cathode is subjected to the discharge power increases, along with an increase in the plasma channel radius. This leads to a larger region to be heated above the melting temperature as the pulse on-time increases.
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(a) 10 A – 100 µs
(b) 20 A – 100 µs
(c) 30 A – 100 µs
(d) 40 A – 100 µs
(e) 50 A – 100 µs
(f) 50 A – 75 µs
(g) 50 A – 50 µs
(h) 50 A – 25 µs Temperature (in K)
(i) 50 A – 10 µs Fig. 3. FE simulations under different operating parameter combinations depicting crater dimensions and temperature distribution (units in Kelvin)
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results in low value of crater depth in comparison to that of crater radius. Thus, the end result is a high value of rc / dc at low pulse on-times. As pulse ontime increases, the heat flux is applied for a longer duration which allows the heat to better penetrate the cathode body.
(a)
(a)
(b) Fig. 4. Variation of crater dimensions with (a) discharge current, and (b) pulse on-time
Crater aspect ratio (rc / dc) could be defined as the ratio of crater radius to crater depth. The variation of crater aspect ratio with discharge current and pulse on-time is shown in Fig 5. It is observed from Fig 5(a) that rc / dc has a maximum value of 1.7 at low discharge current of 10 A. This is because at low currents, sufficiently large pulse power is not generated for enough heat to penetrate the cathode body. This leads to a very low value of crater depth in comparison to that of crater radius and thereby results in a high rc / dc value. For higher values of discharge current, the rc / dc remains constant around the value of 1.35. The variation of rc / dc with pulse on-time is shown in Fig 5(b). It could be seen that rc / dc shows a maximum value at a pulse on-time value of 20 µs. For pulse on-time values higher than 20 µs, rc / dc shows a decrease. This is because at low pulse on-time, the crater radii values are nearer to the spark radii values and the time for heat to dissipate through the cathode body is very less. Hence, a small region around the spark radius is melted by the spark and it
(b) Fig 5. Variation of crater aspect ratio with (a) discharge current, and (b) pulse on-time
3.2. Model validation The FE model is validated against experiments performed by Assarzadeh and Ghoreishi [13]. FE simulations are performed according to the operating parameters given in Table 4. Two comparisons were made. The first one refers to the prediction error between the results predicted by our model and the experimental results in Ref [13]. Refer comparison 1 in Table 4. This was done to evaluate the efficiency of our model in predicting the crater dimensions. The second comparison is between the model results and the experimental results in Ref [13]. Refer comparison 2 in Table 4. This was done to compare
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the prediction error of our model (evaluated in comparison 1) with the prediction error of the model in Ref [13]. It could be understood from Comparison 1 in Table 4 that the prediction error in crater dimensions are lesser at high parametric combinations of discharge current and pulse on-time. The prediction errors in crater radius and crater depth vary from 11% to 29.6% and 1.8% to 18.5%, respectively. These error ranges are within acceptable limits. The prediction error in crater aspect ratio (rc / dc) was also taken into consideration as it represents the error in prediction of crater shape by the model. An accurate prediction of crater shape is of importance for the prediction of surface texture obtained through EDM process. It could be observed that the prediction error in rc / dc varies from 9.1% to 13.5%. This shows that the model gives a good prediction for crater shape at different parameter settings. It could be observed from Comparison 2 that the prediction errors in rc , dc, and rc / dc for the model by Assarzadeh and Ghoreishi [13] varies in the ranges 9.3% to 18.1%, 10.5% to 14.1%, and 18.3% to 27.9%, respectively. Hence, the model in Ref. [13] gives a better prediction than our model for crater radius at all parametric combinations and for crater depth at a low parametric combination. However, our model gives a much better prediction for crater aspect ratio (rc / dc) as compared to Ref. [13]. This means that our model gives a better prediction of crater shape and hence more suitable for adoption in multispark simulations of EDM process for the purpose of surface texture prediction. The simulated and experimental crater dimensions are compared in Fig 6. The area of the section for simulations of experiment numbers 1, 2, and 3 were selected as 100 µm x 100 µm, 200 µm x 200 µm, and 250 µm x 250 µm, respectively due to increase in plasma channel radius with increasing values of operating parameters. FE simulation at discharge current and pulse on-time values of 40A and 22 µs is shown in Fig 6(a). The crater radius and crater depth values calculated by the model are 33.5 µm and 22.5 µm, respectively. The experimentally obtained crater radius and depth values are 47.6 µm and 27.6 µm, respectively. The difference between the simulated and experimental crater dimensions might due to using a low Fc value of 0.109 for simulation. In actual experimental condition, the fraction of energy going to the cathode could be higher. Thus it there is a
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requirement for extensive experimental studies to evaluate variation of Fc at different parametric levels of discharge current and pulse on-time for generating an improved model for Fc. FE simulation at current and pulse on-time values of 50A and 125 µs is shown in Fig 6(b). The crater radius and crater depth calculated by the model are 81 µm and 56.5 µm, respectively. The experimentally obtained crater radius and depth values are 94.2 µm and 58.4 µm, respectively. It could be seen that in this case simulated and experimental crater depths are in more agreement with a prediction error of 3.3 % as compared to simulated and experimental crater radii with a prediction error of 14 %. FE simulation at current and pulse on-time values of 60A and 200 µs is shown in Fig 6(c). The crater radius and crater depth calculated by the model are 103.5 µm and 69.5 µm, respectively. The experimentally obtained crater radius and depth values are 116.3 µm and 70.8 µm, respectively. The predicted and experimental crater depths are in good agreement in this case too with a low prediction error of 1.8%. Thus it could be said that the crater dimensions predicted by the FE model are in good agreement with those measured from experiments. The deviation of the model results from the experimental results were due to considering rg, FC, and PFE as functions of controlled parameters such as discharge current, discharge energy and pulse ontime. However, in actual scenario, rg, FC, and PFE are also influenced by noise variables such as presence of debris particles and gas bubbles in the dielectric medium, and variation in spark gap, gap pressure, and discharge energy gradient with time. Hence a number of repetitions of single spark experiments need to be done to reduce the effect of these noise parameters on the experimental data.
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4. Conclusions A finite element model for single spark simulation in EDM is proposed. The salient features of the model includes consideration of realistic assumptions such as Gaussian heat flux distribution, plasma channel radius dependent on pulse on-time and current, temperature dependent material properties, latent heat of fusion, and variable cathode energy factor and plasma flushing efficiency. The following are the conclusions of this work:
Temperature (in K)
(a)
Temperature (in K)
(b)
Temperature (in K)
(c) Fig 6. Comparison of FE simulation results with experimental results at operating parameters (a) 40A – 22 µs, (b) 50A – 125 µs, and (c) 60A – 200 µs
Crater radius and crater depth are seen to increase with the increasing values of operating parameters such as discharge current and pulse on-time. This is due to increase in input pulse energy and duration of input heat flux. Crater aspect ratio shows a high value at low values of discharge current and pulse on-time. This is due to significantly larger radial heat distribution at low operating parameter values. An adoption of more realistic assumptions has led to a good prediction of crater profile by the model. FE model gives an error range of 9.1 to 13.4 % for the prediction of crater aspect ratio. This single spark model could be used in a multiple spark scenario for surface texture simulation due to its improved prediction of crater profile.
S. Jithin et al. / Procedia Manufacturing 00 (2018) 000–000
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S. Jithin et al. / Procedia Manufacturing 26 (2018) 617–628
Table 3. Parametric analysis Ex. No. Operating parameters
1 2 3 4 5 6 7 8 9
I (A)
ton (µs)
10 20 30 40 50 50 50 50 50
100 100 100 100 100 75 50 25 10
627
Spark energy, Cathode E (mJ) energy fraction, Fc
Spark radius, rg (µm)
Plasma flushing efficiency, PFE
Heat flux, q0 (1010 J/m3)
Modified heat Crater dimensions flux, q0’ (1010 J/m3) rc (µm) dc (µm)
30 60 90 120 150 112.5 75 37.5 15
34.6 46.7 55.6 62.9 69.2 61.0 51.0 37.6 25.1
0.25 0.43 0.61 0.78 0.96 1 1 1 1
3.86 7.30 7.73 11.0 11.4 14.6 15.3 16.4 36.7
0.97 3.13 4.68 8.61 10.9 14.6 15.3 16.4 36.7
0.109 0.187 0.187 0.256 0.256 0.256 0.187 0.109 0.109
23 46 58.5 72 79.5 72 58 40.5 28
13.5 34.5 43 53.5 58 52.5 41.5 28 19.5
(Gap voltage, U = 30V) Table 4. Model validation Ex. Operating No. parameters
1 2 3
I (A) 40 50 60
ton (µs) 22 125 200
Experiments [13]
rc (µm) 47.6 94.2 116.3
dc (µm) 27.6 58.4 70.8
Our model prediction
rc / dc rc (µm) 1.72 33.5 1.61 81 1.64 103.5
dc (µm) 22.5 56.5 69.5
rc / dc 1.49 1.43 1.49
(Gap voltage, U = 20V)
Comparison 1: Prediction error (%) between our model and experiments in Ref [13] error in error in error in rc dc rc / dc 29.6 18.5 13.4 14.0 3.3 11.2 11.0 1.8 9.1 [7]
References [1]
[2]
[3]
[4]
[5]
[6]
Schumacher BM. After 60 years of EDM the discharge process remains still disputed. J Mater Process Technol 2004;149:376–81. doi:10.1016/j.jmatprotec.2003.11.060. DiBitonto D, Eubank P, Patel MR, Barrufet M a. Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model. J Appl Phys 1989;66:4095–103. doi:10.1063/1.343994. Tlili A, Ghanem F, Salah N Ben. A contribution in EDM simulation field. Int J Adv Manuf Technol 2015;79:921– 35. doi:10.1007/s00170-015-6880-1. Yadav V, Jain VK, Dixit PM. Thermal stresses due to electrical discharge machining. Int J Mach Tools Manuf 2002;42:877–88. doi:10.1016/S0890-6955(02)00029-9. Das S, Klotz M, Klocke F. EDM simulation: finite element-based calculation of deformation, microstructure and residual stresses. J Mater Process Technol 2003;142:434–51. doi:10.1016/S0924-0136(03)00624-1. Joshi SN, Pande SS. Thermo-physical modeling of diesinking EDM process. J Manuf Process 2010;12:45–56. doi:10.1016/j.jmapro.2010.02.001.
[8]
[9]
[10]
[11]
[12]
Model in Ref [13]
rc (µm) 39 83.5 105.5
dc (µm) 31.5 64.5 79
rc / dc 1.24 1.29 1.34
Comparison 2: Prediction error (%) between the model and experiments in Ref [13] error in error in error in rc dc rc/dc 18.1 14.1 27.9 11.4 10.5 19.9 9.3 11.6 18.3
Hosseini Kalajahi M, Rash Ahmadi S, Nadimi Bavil Oliaei S. Experimental and finite element analysis of EDM process and investigation of material removal rate by response surface methodology. Int J Adv Manuf Technol 2013;69:687–704. doi:10.1007/s00170-0135059-x. Shabgard M, Ahmadi R, Seyedzavvar M, Nadimi S, Oliaei B. Mathematical and numerical modeling of the effect of input-parameters on the flushing efficiency of plasma channel in EDM process. Int J Mach Tools Manuf 2013;65:79–87. Jithin S, Bhandarkar U, Joshi SS. Analytical Simulation of Random Textures Generated in Electrical Discharge Texturing. J Manuf Sci Eng 2017;139:111002 (1-12). doi:10.1115/1.4037322. Ikai T, Hashigushi K. Heat input for crater formation in EDM. Proc. Int. Symp. Electro-Machining-ISEM XI, EPFL, 1995, p. 163–170. Singh H. Experimental study of distribution of energy during EDM process for utilization in thermal models. Int J Heat Mass Transf 2012;55:5053–64. doi:10.1016/j.ijheatmasstransfer.2012.05.004. Valencia JJ, Quested P.N. Thermophysical properties. ASM Handb Cast 2008;15:468–81.
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doi:10.1361/asmhba0005240. Assarzadeh S, Ghoreishi M. Electro-thermal-based finite element simulation and experimental validation of material removal in static gap single- machining process. Proc Inst Mech Eng Part B J Eng Manuf 2017;231:28– 47. doi:10.1177/0954405415572661.
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46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
FE Modeling for Single Spark in EDM Considering Plasma FE Modeling for Single SparkEfficiency in EDM Considering Plasma Flushing Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June Flushing Efficiency 2017, Vigo (Pontevedra), Spain S. Jithinaa, Ajinkya Rautaa, Upendra V. Bhandarkaraa, Suhas S. Joshia,a,* S. Jithin , Ajinkya Raut , Upendra V. Bhandarkar , Suhas S. Joshi *
Department of Mechanical Engineering, Indian Institute of Technology Mumbai – 400076, Costing models for capacity optimization inBombay, Industry 4.0:IndiaTrade-off Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai – 400076, India between used capacity and operational efficiency * Corresponding author. Tel.: +91-22-25767527 a a
E-mail address:author. [email protected] * Corresponding Tel.: +91-22-25767527 E-mail address: [email protected]
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Due to complex nature of single spark phenomenon in EDM, the removal mechanism needs better comprehension and clarity. In this thisnature work of presents finitephenomenon element simulation single spark during electrical discharge machining Due context, to complex single aspark in EDM,ofthea removal mechanism needs better comprehension andtaking clarity.into In consideration significant aspectsa such temperature dependency of material properties, Gaussian distribution heat flux, this context, this work presents finiteaselement simulation of a single spark during electrical discharge machiningoftaking into Abstract plasma channelsignificant radius varying withsuch current and discharge duration, and in factors such as cathode energy of fraction, and consideration aspects as temperature dependency of variability material properties, Gaussian distribution heat flux, flushingradius efficiency. Such a model can offer a better prediction of the crater profile obtained on the work surface which plasma channel varying with current and discharge duration, and variability in factors such as cathode energy fraction, and Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, enables it to beefficiency. extended Such to multi-spark scenarios for predicting texture EDMsurface process. FE plasma flushing a model can offer a better predictionthe of surface the crater profileobtained obtainedthrough on the work which information based that on athe real timeradius basis and, necessarily, much moreincreasing efficient.values In thisof context, capacity optimization simulations crater crater depth increases with the operating such FE as enables it toshowed be extended to multi-sparkand scenarios for predicting the surface texture obtained through parameters EDM process. goes beyondshowed the traditional aim of capacity maximization, contributing also forvalues profitability and such value. / d ), which is the ratio between crater discharge and pulse It isand alsocrater observed the crater ratio (rorganization’s simulationscurrent that the on-time. crater radius depththat increases withaspect increasing of the operating parameters as c c Indeed, improvement approaches suggest instead of radius andlean cratermanagement depth, showson-time. aand highcontinuous value at low values of discharge current andratio pulse Thisoptimization is due feeble penetration / capacity dc), which the to ratio between crater discharge current and pulse It is also observed that the crater aspect (rcon-time. maximization. study of costing modelsand is anvalidation important research topic deserves of heatand through the cathode body forvalue lowoptimization values the and operating parameters. The the is FEdue model isthat made against radius craterThe depth, shows acapacity high at low of values of discharge current pulse on-time.ofThis to feeble penetration contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical experiments and it was found that the model displays improved prediction at high values of the operating parameters. The in of heat through the cathode body for low values of the operating parameters. The validation of the FE model is made error against dcwas bymanagement the model fromon 9.1different to 13.4 %costing which represents ahigh good prediction crater profile by the The model. prediction rc / it model forofcapacity modelsat(ABC and TDABC). A generic model haserror been experiments and found thatvaries thebased model displays improved prediction values of theof operating parameters. in by the model varies from 9.1 to 13.4 % which represents a good prediction of crater profile by the model. prediction ofand rc /itdwas developed used to analyze idle capacity and to design strategies towards the maximization of organization’s c value. trade-offPublished capacitybymaximization © 2018The The Authors. Elsevier B.V. vs operational efficiency is highlighted and it is shown that capacity © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of thescientific scientific committeeofofthe NAMRI/SME. optimization might hide operational inefficiency. © 2018 The Authors. Published by Elsevier B.V.committee Peer-review under responsibility of the 46th SME North American Manufacturing Research Conference. © 2017 The Authors. Published by B.V. committee of NAMRI/SME. Peer-review under responsibility ofElsevier the scientific Keywords: FEM; EDM; Single-spark;ofCrater radius; Plasma flushing Peer-review under responsibility the scientific committee ofefficiency the Manufacturing Engineering Society International Conference Keywords: FEM; EDM; Single-spark; Crater radius; Plasma flushing efficiency 2017. a
1. Introduction energy generated Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity;thermal Operational Efficiency
by spark discharges for material The schematic of thedischarges EDM process 1. Introduction thermal removal. energy generated by spark for Electrical discharge machining (EDM) is a popular is given removal. in Fig. The 1. Workpiece (cathode) tool material schematic of the EDMand process 1.Electrical Introduction non-traditional machining method(EDM) which isutilizes the (anode) a small gap of an order 10 discharge machining a popular is givenare inseparated Fig. 1. by Workpiece (cathode) andoftool non-traditional machining method which utilizes the (anode) are separated by a small gap of an order of 10 The cost of idle capacity is a fundamental information for companies and their management of extreme importance 2351-9789 2018 The Authors. Published by Elsevier in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured Peer-review of the scientific committee of NAMRI/SME. 2351-9789 2018responsibility The Authors. Published by Elsevier B.V.hours in several©under ways: tons of production, available of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility the761; scientific committee NAMRI/SME. * Paulo Afonso. +351 253 of 510 fax: +351 253 604of741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.072
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S. Jithin et al. / Procedia Manufacturing 26 (2018) 617–628 S. Jithin et al. / Procedia Manufacturing 00 (2018) 000–000
to 100 microns known as spark gap. The spark gap is filled with a liquid dielectric. This liquid dielectric acts as an insulator initially, but under suitable electrical conditions it undergoes breakdown to form plasma channel comprising of positive ions and electrons. These ions and electrons are accelerated by the applied electric field and they impinge the electrodes at high velocities. This results in a localized heating of very small regions on both cathodic and anodic surfaces to very high temperatures which leads to material removal through melting and evaporation. However, molten material is not fully flushed away by the dielectric and this portion of molten material resolidifies to form recast layer on the electrode surfaces. The temperature gradient also results in heat affected zone (HAZ) below the recast layer in both the electrodes. Anode has a higher plasma channel radius than that of cathode due to the former emitting positive ions instead of electrons. This results in a decrease in heat flux intensity and leads to anodic crater being smaller in size than cathodic crater.
Fig. 1. Schematic of EDM process
During every spark discharge a large number of diverse phenomenon such as plasma formation, heat conduction, heat radiation, heat convection, implosion of plasma channel, shock wave formation, removal of molten metal by dielectric, resolidification, electrical phenomena, chemical phenomena, etc. and their interactions are occurring. Due to these complex phenomenon underlying, the mechanism of spark generation and material removal still needs better comprehension and clarity [1]. A number of
researchers have attempted to simulate the spark erosion mechanism utilizing both analytical and numerical methods. The most prominent work among the analytical models was by DiBitonto et al. [2], where they gave a cathode erosion model to predict the crater dimensions when the operating parameters are known. However, a number of numerical models proposed for the spark erosion process, which came later, have been found to give a better prediction of crater dimensions due to the possibility of adopting more realistic assumptions which are related to the actual EDM operation [3]. Among the numerical models, researchers have utilized a variety of methods which include finite element method (FEM), finite difference method (FDM), generalized minimal residual method (GMRES), etc. towards this goal. FEM is seen to be the most popular when it comes to simulations of EDM process. One of the initial applications of FEM in simulation of a spark discharge was attempted by Yadav et al. [4]. They evaluated the temperature distribution and thermal stresses caused on the work material due to the input heat flux during a spark discharge. They observed that significant values of compressive and tensile stresses are developed in a thin layer around the discharge region which could lead to damage on the work surface. In another work, Das et al. [5] used an FE simulation to evaluate crater dimensions, phase transformations and residual stresses resulted on the cathode surface after spark discharge. Joshi and Pande [6] suggested that adoption of more realistic assumptions such as temperature dependency of material properties, inclusion of latent heat of fusion, Gaussian distribution of heat flux, spark radius value dependent on current and discharge duration, etc. during FE simulation improves the prediction of crater dimensions and MRR. Kalajahi et al. [7] performed a FE study to analyze the effect of different operating parameters on temperature distribution on the cathode. They found that the temperature distribution, thereby crater dimensions, show a continuous increase with the increasing values of the operating parameters such as current, voltage and duty cycle. However, crater dimensions show an increase in value up to a high value of discharge duration. For further increase in discharge duration, the crater dimensions decrease. Shabgard et al. [8] gave a model to predict recast layer thickness (RLT) taking into consideration the plasma flushing efficiency (PFE) as a function of discharge current and pulse on-time.
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They reported that PFE increases with increasing discharge current and it decreases with increasing pulse on-time. Different authors have tried to incorporate some realistic assumptions to bring their FE model closer to the actual EDM process. However, in addition to those assumptions, it is also essential for a singlespark model to consider the variable nature of factors such as cathode energy fraction (FC) and plasma flushing efficiency (PFE), with the operating parameters. Though Shabgard et al. [8] takes into consideration the variable nature of FC and PFE with discharge current and pulse on-time, they use PFE as a correction term after simulation to calculate crater dimensions. However, for crater shape/profile to be predicted taking into consideration the variable nature of PFE, it is necessary that PFE be included as a correction term during simulation. A proper prediction of the crater shape is essential for using this model for multiple spark scenarios for the surface texture prediction under different operating conditions. Hence, the goal of the current work is to develop an FE model for predicting the crater profile obtained during single discharge of EDM process, while taking into consideration the above mentioned important aspects. EDM have been traditionally used to machine electrically conductive and hard-tomachine materials such as Ti6Al4V, tungsten, etc., and these materials are finding innovative applications with technological advancements over last few decades. This has resulted in the tolerance requirements for different components made with these materials becoming more and more stringent. Thus an accurate prediction of crater dimensions formed during individual sparks at different parameter settings can contribute toward improving the accuracy of EDM process. Nomenclature T r z t Kt ρ Cp rg
temperature in Kelvin radial coordinate in metres height coordinate in metres time in seconds thermal conductivity in W/m.K work material density in kg/m3 specific heat capacity of work material in J/kg.K plasma channel radius in µm
I ton q(r) Fc U PFE hc LH Ts Tm rc dc
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discharge current in A pulse on-time in µs Gaussian heat flux in J/m3 cathode energy factor gap voltage in V plasma flushing efficiency convective heat transfer coefficient latent heat of fusion solidus temperature liquidus temperature crater radius crater depth
2. Finite Element Model A finite element model is proposed in this section to simulate an individual spark during the EDM process taking into consideration important aspects of the process such as temperature dependent material properties, Gaussian heat flux, and a variable plasma channel radius, cathode energy fraction and plasma flushing efficiency. Due to consideration of these important aspects, this model could give a more accurate prediction of crater profile. The authors have, in their previous work [9], extended an analytical model for prediction of crater profile on cathode during a single discharge to multiple-spark scenarios for simulation of surface texture generated during the EDM process. However, a finite element approach can give a better prediction for surface texture. This is because a numerical approach allows for a simulation of the complex heat flux input conditions which are resulted due to the occurrence of multiple sparks simultaneously during the EDM process. Hence, the authors aim to develop a FEM model for single spark simulation which gives an accurate prediction of crater shape. This single spark model will be extended to develop a multiple spark model for surface texture prediction as a future work by the authors. 2.1. Model Details The following assumptions are taken in the model: A Gaussian heat flux distribution with an expanding plasma channel radius. Work material is homogeneous and isotropic.
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Work material properties such as density, thermal conductivity and specific heat are temperature dependent. Fraction of energy going to cathode is a variable dependent on spark energy. Plasma flushing efficiency considered as a function of discharge current and pulse on-time. Dielectric material is assumed to influence cathode energy fraction (Fc), plasma flushing efficiency (PFE), and convective heat transfer coefficient (hc). The values of these parameters are computed to suit an assumption of hydrocarbon oil as dielectric. The governing equation for the single-spark problem is the Fourier heat conduction equation in cylindrical coordinates, which is as follows:
1 T Kt r r r r
T T (1) C p Kt z t z
where, r and z are cylindrical coordinates, T is the temperature, t is the time and Kt, ρ, and Cp are work material properties such as thermal conductivity, density and specific heat capacity, respectively. Since these material properties are dependent on temperature value, their variation with temperature needs to be considered for simulation of single spark conditions. Heat source in this scenario is the discharge column. The heat source is comprised of two aspects: heat source radius and heat flux distribution. The discharge column radius or plasma channel radius is found to be dependent on both pulse on-time and discharge current. Hence, we adopt the prominently used plasma channel radius equation provided by Ikai and Hashigushi [10]: 0.44 rg 2040 * I 0.43 * ton
(2)
where, rg is the plasma channel radius, I is the discharge current and ton is the pulse on-time. Different heat flux distributions such as point heat flux, uniform disk heat flux and Gaussian heat flux have been adopted by different authors. A number of authors have reported that an assumption of Gaussian heat flux distribution gives a better prediction for the model, in comparison to the other heat flux assumptions. We adopt the Gaussian heat flux
distribution equation given by Yadav et al. [4] for this model: 2 r q (r ) q0 exp 4.5 rg
(3)
and
q0
4.45FCUI rg2
(4)
where, Fc is the cathode energy fraction, U is the gap voltage, and r is the radial distance from the center of plasma channel. Cathode energy fraction (Fc) is the fraction of energy which goes to cathode from the total energy that is generated during individual spark discharge. It is taken as a constant value of 0.18 by most authors following the cathode erosion model proposed by DiBitonto et al. [2]. However, Harminder [11] have proved experimentally that FC varies with a variation in the operating parameters such as discharge current and pulse on-time. Based on his experimental data [11], the authors’ had suggested an adoption of FC values, considering a range of spark energy values, in their previous analytical model [9] which is as follows:
0.109 ( E 0 to 50 mJ ) FC 0.187 ( E 50 to 100 mJ ) 0.256 ( E 100 mJ ) as
(5)
where, E is the input spark energy and is evaluated
E UIton
(6)
Plasma flushing efficiency (PFE) is the ratio of the actual amount of material removed to the theoretical amount of material supposed to be removed during a spark discharge. Most of the single spark models available in the literature have assumed a PFE of 100% during simulation and later on evaluated PFE by comparing simulated results with experimental data. In the authors’ previous work [9], the improvement in crater dimension prediction with consideration of PFE in the model was emphasized. Hence, a variable PFE parameter needs to be incorporated for the simulation for a better prediction
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of crater dimensions and crater profile. Therefore, we adopt the following curve fit model [9] we developed previously based on works by DiBitonto et al. [2] and Shabgard et al. [8]: 2
PFE 0.1093 2.238 *10 * I
(7)
8.441*104 * ton 4.67 *105 * I * ton 2 4.912 *106 * ton
If the equation gives a value of PFE greater than 1, then PFE is assumed to have a value of 1. Such a curve fit model for PFE using data from more than one work in literature (in Refs. [2] and [8]) was used because the presence of more data points at different combinations of discharge current and pulse on-time improved the PFE prediction. This equation for PFE is used to modify the heat flux distribution equation (given in eq. (3)) as follows:
q0' PFE * q0
where, hc is the convective coefficient. And, on boundaries A2, A3 and A4
T 0 n
621 5
heat
transfer
(13)
where n is direction normal to the boundary. This is because boundaries A2, and A3 are assumed to be insulated being very far away, and the boundary A4 lies along the axis of symmetry of the model. The axisymmetric thermal model of EDM with the initial and boundary conditions is represented in Fig 2.
(8)
Thus,
q0' PFE * by '
4.45FCUI rg2
(9)
Hence the updated Gaussian distribution is given
q (r )
PFE *
4.45 FCUI
rg2
2 r exp 4.5 rg
(10)
This modified equation of heat flux distribution will be used in the simulation of a single spark during EDM process. Finally, the initial and the boundary conditions for the FE simulation problem are as follows: Initial condition: o
T T 25 C 298K , t 0 i 0
(11)
Boundary conditions: On boundary A1
q ' (r ), r rg T Kt hc (T T0 ), r rg z 0, t ton
(12)
Fig. 2. Axisymmetric thermal model of EDM
2.2. Model implementation ABAQUS, an analytical software, was used for implementing the numerical model. The simulation is performed considering stainless steel grade 304 (SS 304) as cathode or work material. The variation in thermo-physical properties of SS 304 such as thermal conductivity, specific heat, and density with respect to temperature are given in Table 1. These values are computed using equations given by Valencia and Quested [12] which are as follows:
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10.33 15.4*103 T 7 *107 T 2 for 298K T 1633K 355.93 196.8*103 T Kt for 1644K T 1672K 6.6 12.14*103 T for T 1793K
(14)
C p 443 0.2T 8*107 T 2
(15)
Table 1. Thermo-physical properties of SS 304
Temperature (K)
for 298K T 1727 K
8020 50.1*102 T 298 for 298K T 1727 K 2 6900 80.0*10 T Tm for T 1727 K
(16)
Some additional properties of SS 304 related to latent heat of fusion are given in Table 2. These temperature dependent material property values are input to the model. An axisymmetric section is drawn to represent the cathode based on thermal model shown in Fig 2. The Gaussian heat flux distribution (obtained from eq. (10)) is applied for the length of plasma channel radius evaluated using eq. (2). An initial condition of ambient temperature (298 K) for the body is assumed. The boundary condition of convection on the top face is given with a surface film coefficient value of 8000 W/m2K. The whole section is meshed with a mesh size of 0.5 µm. The selection of such a small mesh size is to improve the accuracy in prediction of crater dimensions. After the FE simulation, the region with temperature above the melting temperature (1454 oC or 1727 K) of SS 304 is deleted to obtain the crater shape and dimensions. FE simulations for different operating parameter combinations can be performed after calculating the plasma channel radius and Gaussian heat flux distribution at those parameter values. The FE model is validated against the experimental data from the single spark experiments performed by Assarzadeh and Ghoreishi [13].
298 348 373 448 473 498 548 573 598 648 673 748 773 848 873 948 973 1003 1023 1048 1073 1273 1473 1573 1644 1672 1727 1773 1813 1963 2113 2163
Thermal conductivity (W/mK) 14.9 15.6 16.0 17.1 17.5 17.8 18.6 18.9 19.3 20.0 20.4 21.5 21.8 22.9 23.2 24.3 24.7 25.1 25.4 25.7 26.0 28.8 31.5 32.8 32.4 26.9
Specific heat (J/kgK)
Density (kg/m3)
502.5 512.5 517.5 532.4 537.4 542.4 552.4 557.3 562.3 572.3 577.2 592.2 597.1 612.0 617.0 631.9 636.8 642.8 646.8 651.7 656.7 696.3 735.9 755.6 769.6 775.2 786.0
8020 7995 7982 7945 7932 7920 7895 7882 7870 7845 7832 7795 7782 7744 7732 7694 7682 7667 7657 7644 7632 7532 7431 7381 7346 7332 7304 6860 6828 6708 6588 6548
Table 2. Additional properties of SS 304 [12] Latent heat (LH)
Solidus temperature (Ts)
Liquidus temperature (Tm)
247 kJ/kg
1400 oC
1454 oC
3. Results and Discussion 3.1. Parametric Analysis Parametric analysis is performed to study the effect of different operating parameters on the simulated crater dimensions. A number of FE simulations are performed according to the parameter combinations given in Table 3. It could be observed that Fc values are evaluated using eq. (5) which is in turn based on E value calculated from eq. (6). The other dependent variables such as rg, PFE, q0, and q’0 are calculated based on the eq.s (2), (7), (4), and (9), respectively. PFE values vary in the range of 0.25 to 1 for these parameter combinations. This indicates that the flushing efficiency is low for low current and
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high pulse on-time which means that the resolidification is high. In contrary, for high current and low pulse on-time combinations, the flushing efficiency is maximum, indicating very less amount of resolidification. The simulated craters at different operating parameter combinations are shown in Fig 3. After FE simulation, temperature distribution on the section is obtained. The craters are obtained in the model by deleting the elements of the section which are at a temperature value higher than the melting point. It could be observed that among the crater dimensions, crater radius tends to be higher in all simulations giving the craters an elliptical shape. This is resulted due to the Gaussian heat flux being applied to the top face which causes more heat dissipation in the radial direction. The temperature gradient below the crater surface results in a heat affected zone. The variation of crater radius and crater depth with the operating parameters such as discharge current and pulse on-time are shown in Fig 4. It could be observed from Fig 4(a) that crater radius and crater depth show continuous increase with discharge current. This is because as the discharge current increases, it causes the input pulse energy to increase. The increase in input pulse energy leads to a larger amount of material to be heated above the melting temperature and thus a crater with larger dimensions is formed. The variation of crater dimensions with pulse on-time is shown in Fig 4(b). It is understood that, similar to the case of discharge current, crater dimensions show a continuous increase with pulse on-time. The input discharge power is constant for all these simulations as discharge current and discharge voltage is kept constant. However, with an increase in pulse on-time, the duration for which the cathode is subjected to the discharge power increases, along with an increase in the plasma channel radius. This leads to a larger region to be heated above the melting temperature as the pulse on-time increases.
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(a) 10 A – 100 µs
(b) 20 A – 100 µs
(c) 30 A – 100 µs
(d) 40 A – 100 µs
(e) 50 A – 100 µs
(f) 50 A – 75 µs
(g) 50 A – 50 µs
(h) 50 A – 25 µs Temperature (in K)
(i) 50 A – 10 µs Fig. 3. FE simulations under different operating parameter combinations depicting crater dimensions and temperature distribution (units in Kelvin)
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results in low value of crater depth in comparison to that of crater radius. Thus, the end result is a high value of rc / dc at low pulse on-times. As pulse ontime increases, the heat flux is applied for a longer duration which allows the heat to better penetrate the cathode body.
(a)
(a)
(b) Fig. 4. Variation of crater dimensions with (a) discharge current, and (b) pulse on-time
Crater aspect ratio (rc / dc) could be defined as the ratio of crater radius to crater depth. The variation of crater aspect ratio with discharge current and pulse on-time is shown in Fig 5. It is observed from Fig 5(a) that rc / dc has a maximum value of 1.7 at low discharge current of 10 A. This is because at low currents, sufficiently large pulse power is not generated for enough heat to penetrate the cathode body. This leads to a very low value of crater depth in comparison to that of crater radius and thereby results in a high rc / dc value. For higher values of discharge current, the rc / dc remains constant around the value of 1.35. The variation of rc / dc with pulse on-time is shown in Fig 5(b). It could be seen that rc / dc shows a maximum value at a pulse on-time value of 20 µs. For pulse on-time values higher than 20 µs, rc / dc shows a decrease. This is because at low pulse on-time, the crater radii values are nearer to the spark radii values and the time for heat to dissipate through the cathode body is very less. Hence, a small region around the spark radius is melted by the spark and it
(b) Fig 5. Variation of crater aspect ratio with (a) discharge current, and (b) pulse on-time
3.2. Model validation The FE model is validated against experiments performed by Assarzadeh and Ghoreishi [13]. FE simulations are performed according to the operating parameters given in Table 4. Two comparisons were made. The first one refers to the prediction error between the results predicted by our model and the experimental results in Ref [13]. Refer comparison 1 in Table 4. This was done to evaluate the efficiency of our model in predicting the crater dimensions. The second comparison is between the model results and the experimental results in Ref [13]. Refer comparison 2 in Table 4. This was done to compare
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the prediction error of our model (evaluated in comparison 1) with the prediction error of the model in Ref [13]. It could be understood from Comparison 1 in Table 4 that the prediction error in crater dimensions are lesser at high parametric combinations of discharge current and pulse on-time. The prediction errors in crater radius and crater depth vary from 11% to 29.6% and 1.8% to 18.5%, respectively. These error ranges are within acceptable limits. The prediction error in crater aspect ratio (rc / dc) was also taken into consideration as it represents the error in prediction of crater shape by the model. An accurate prediction of crater shape is of importance for the prediction of surface texture obtained through EDM process. It could be observed that the prediction error in rc / dc varies from 9.1% to 13.5%. This shows that the model gives a good prediction for crater shape at different parameter settings. It could be observed from Comparison 2 that the prediction errors in rc , dc, and rc / dc for the model by Assarzadeh and Ghoreishi [13] varies in the ranges 9.3% to 18.1%, 10.5% to 14.1%, and 18.3% to 27.9%, respectively. Hence, the model in Ref. [13] gives a better prediction than our model for crater radius at all parametric combinations and for crater depth at a low parametric combination. However, our model gives a much better prediction for crater aspect ratio (rc / dc) as compared to Ref. [13]. This means that our model gives a better prediction of crater shape and hence more suitable for adoption in multispark simulations of EDM process for the purpose of surface texture prediction. The simulated and experimental crater dimensions are compared in Fig 6. The area of the section for simulations of experiment numbers 1, 2, and 3 were selected as 100 µm x 100 µm, 200 µm x 200 µm, and 250 µm x 250 µm, respectively due to increase in plasma channel radius with increasing values of operating parameters. FE simulation at discharge current and pulse on-time values of 40A and 22 µs is shown in Fig 6(a). The crater radius and crater depth values calculated by the model are 33.5 µm and 22.5 µm, respectively. The experimentally obtained crater radius and depth values are 47.6 µm and 27.6 µm, respectively. The difference between the simulated and experimental crater dimensions might due to using a low Fc value of 0.109 for simulation. In actual experimental condition, the fraction of energy going to the cathode could be higher. Thus it there is a
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requirement for extensive experimental studies to evaluate variation of Fc at different parametric levels of discharge current and pulse on-time for generating an improved model for Fc. FE simulation at current and pulse on-time values of 50A and 125 µs is shown in Fig 6(b). The crater radius and crater depth calculated by the model are 81 µm and 56.5 µm, respectively. The experimentally obtained crater radius and depth values are 94.2 µm and 58.4 µm, respectively. It could be seen that in this case simulated and experimental crater depths are in more agreement with a prediction error of 3.3 % as compared to simulated and experimental crater radii with a prediction error of 14 %. FE simulation at current and pulse on-time values of 60A and 200 µs is shown in Fig 6(c). The crater radius and crater depth calculated by the model are 103.5 µm and 69.5 µm, respectively. The experimentally obtained crater radius and depth values are 116.3 µm and 70.8 µm, respectively. The predicted and experimental crater depths are in good agreement in this case too with a low prediction error of 1.8%. Thus it could be said that the crater dimensions predicted by the FE model are in good agreement with those measured from experiments. The deviation of the model results from the experimental results were due to considering rg, FC, and PFE as functions of controlled parameters such as discharge current, discharge energy and pulse ontime. However, in actual scenario, rg, FC, and PFE are also influenced by noise variables such as presence of debris particles and gas bubbles in the dielectric medium, and variation in spark gap, gap pressure, and discharge energy gradient with time. Hence a number of repetitions of single spark experiments need to be done to reduce the effect of these noise parameters on the experimental data.
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4. Conclusions A finite element model for single spark simulation in EDM is proposed. The salient features of the model includes consideration of realistic assumptions such as Gaussian heat flux distribution, plasma channel radius dependent on pulse on-time and current, temperature dependent material properties, latent heat of fusion, and variable cathode energy factor and plasma flushing efficiency. The following are the conclusions of this work:
Temperature (in K)
(a)
Temperature (in K)
(b)
Temperature (in K)
(c) Fig 6. Comparison of FE simulation results with experimental results at operating parameters (a) 40A – 22 µs, (b) 50A – 125 µs, and (c) 60A – 200 µs
Crater radius and crater depth are seen to increase with the increasing values of operating parameters such as discharge current and pulse on-time. This is due to increase in input pulse energy and duration of input heat flux. Crater aspect ratio shows a high value at low values of discharge current and pulse on-time. This is due to significantly larger radial heat distribution at low operating parameter values. An adoption of more realistic assumptions has led to a good prediction of crater profile by the model. FE model gives an error range of 9.1 to 13.4 % for the prediction of crater aspect ratio. This single spark model could be used in a multiple spark scenario for surface texture simulation due to its improved prediction of crater profile.
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Table 3. Parametric analysis Ex. No. Operating parameters
1 2 3 4 5 6 7 8 9
I (A)
ton (µs)
10 20 30 40 50 50 50 50 50
100 100 100 100 100 75 50 25 10
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Spark energy, Cathode E (mJ) energy fraction, Fc
Spark radius, rg (µm)
Plasma flushing efficiency, PFE
Heat flux, q0 (1010 J/m3)
Modified heat Crater dimensions flux, q0’ (1010 J/m3) rc (µm) dc (µm)
30 60 90 120 150 112.5 75 37.5 15
34.6 46.7 55.6 62.9 69.2 61.0 51.0 37.6 25.1
0.25 0.43 0.61 0.78 0.96 1 1 1 1
3.86 7.30 7.73 11.0 11.4 14.6 15.3 16.4 36.7
0.97 3.13 4.68 8.61 10.9 14.6 15.3 16.4 36.7
0.109 0.187 0.187 0.256 0.256 0.256 0.187 0.109 0.109
23 46 58.5 72 79.5 72 58 40.5 28
13.5 34.5 43 53.5 58 52.5 41.5 28 19.5
(Gap voltage, U = 30V) Table 4. Model validation Ex. Operating No. parameters
1 2 3
I (A) 40 50 60
ton (µs) 22 125 200
Experiments [13]
rc (µm) 47.6 94.2 116.3
dc (µm) 27.6 58.4 70.8
Our model prediction
rc / dc rc (µm) 1.72 33.5 1.61 81 1.64 103.5
dc (µm) 22.5 56.5 69.5
rc / dc 1.49 1.43 1.49
(Gap voltage, U = 20V)
Comparison 1: Prediction error (%) between our model and experiments in Ref [13] error in error in error in rc dc rc / dc 29.6 18.5 13.4 14.0 3.3 11.2 11.0 1.8 9.1 [7]
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rc (µm) 39 83.5 105.5
dc (µm) 31.5 64.5 79
rc / dc 1.24 1.29 1.34
Comparison 2: Prediction error (%) between the model and experiments in Ref [13] error in error in error in rc dc rc/dc 18.1 14.1 27.9 11.4 10.5 19.9 9.3 11.6 18.3
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