Electrical Discharge Machining Processes · minimization of wear of electric power contacts. They...

Electrical Discharge Machining Processes

Masanori Kunieda*Department of Precision Engineering, School of Engineering, The University of Tokyo, Tokyo, Japan

Abstract

Electrical discharge machining (EDM) is a removal process which exploits melting and evaporatingof workpiece materials caused by pulse discharges which are ignited several thousands to tens ofthousands times per second in the small gap between the tool electrode and workpiece. Theadvantage is that electrically conductive materials can be machined very precisely into complicatedshapes independent of their hardness. Hence, EDM is preferably used in die and mold making,aeroengine manufacturing, and micro-hole drilling for ink jet and fuel nozzles, where complicatedshapes in hard materials and with high precision have to be machined. This chapter first describes theprinciple of EDM. Then, the removal mechanism due to single pulse discharge is explained in detailsfrom the thermophysical aspects, followed by the clarification of the gap phenomena in consecutivepulse discharges. Thus, the machining characteristics of EDM are understood theoretically based onthe fundamental insight into the phenomena.

Introduction

In the 1930s, the first attempts were made to machine metals with electrical discharge. The Americancompany ELOX developed “disintegrators” to remove broken taps from valuable workpiecematerials such as cemented carbide and high-speed steel (Schumacher et al. 2013). Erosion wascaused by intermittent arc discharges occurring in air between the tool electrode and workpiececonnected to a DC power supply. Arc discharges were initiated by mechanical contact between thetool electrode and workpiece and interrupted by separation due to vibration and rotation of the toolelectrode. This process was not precise because the discharge energy was not controlled by a pulsegenerator, leading to overheating of the machining area.

During World War II, physicists B. R. and N. I. Lazarenko in Moscow conducted studies on theminimization of wear of electric power contacts. They tested different materials with discharges ofdefined energy, generated by a capacitor. B. R. Lazarenko published the paper “To invert the effect ofwear on electric power contacts,” in 1943 (Lazarenko 1943a). This idea started the development ofEDM, using controlled discharge conditions, for achieving precision machining (Lazarenko 1943b).Since then, EDM technology has developed rapidly and become indispensable in manufacturingapplications such as die and mold making, micromachining, prototyping, etc., because electricallyconductive materials can be machined very precisely into complicated shapes independent of theirhardness.

*Email: [email protected]

Handbook of Manufacturing Engineering and TechnologyDOI 10.1007/978-1-4471-4976-7_71-1# Springer-Verlag London 2013

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Overview

PrincipleFigure 1 shows the principle of EDM. Pulsed arc discharges are generated with the interelectrodegap width of micrometer to tens of micrometer range in a bath of a dielectric liquid like oil ordeionized water. Discharge location is only one for each pulse because once dielectric breakdownoccurs at a location, temperature rises up to 7,000 K in the arc plasma. Since the ionization in theplasma channel is accelerated with increasing the temperature, the electrical conductivity is elevatedresulting in the concentration of electric current at the discharge spot. The heat fluxes from the arccolumn thus generated exceed 109 W/m2 (based on Eq. 6) on the anode and cathode spots,generating a minute discharge crater on both surfaces due to melting and evaporating of the electrodematerials. Removed materials are cooled and resolidified in the dielectric liquid, forming sphericaldebris particles which are flushed away from the gap with the dielectric liquid.

The next pulse voltage must not be applied to the gap until the temperature at the previousdischarge spot falls sufficiently to recover the dielectric strength, enabling the next discharge tooccur at different place. In this way, discharges are dispersed over the electrode surfaces; thereby theshape of the tool electrode is copied on the workpiece electrode.

Thus, to copy the tool electrode shape on the workpiece, it is essential to use pulse discharge torandomize the discharge location. If discharge is not intermittently ignited, the temperature at thedischarge location cannot decrease; thereby the plasma stays at the same location where thedischarge was first generated, resulting in serious thermal damage on the workpiece.

Sinking EDM and Wire EDMFigure 2 shows the configuration of a sinking electrical discharge machine. The workpiece can beformed either by the replication of a shaped tool electrode (Fig. 3) or by 3D movement of a simpleelectrode like in milling (Fig. 4) or a combination of the above. The electrode material is normallycopper or graphite. The numerical control monitors the gap conditions (voltage and current) andsynchronously controls the different axes and the pulse generator. The dielectric liquid is filtrated toremove debris particles and decomposition products.

Figure 5 outlines the wire electrical discharge machining (WEDM) method. Complicated shapescan be cut using a wire electrode of 0.02–0.33 mm in diameter like a wire sawing machine (Fig. 6).The wire electrode is usually a plain brass wire or coated wires, such as zinc coated brass or coatedsteel wires. Sometimes tungsten or molybdenum wires are used in case of thin wires. Since wire

Fig. 1 Concept of EDM


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orientation can be changed by controlling the horizontal position of the upper wire guide relative tothe lower guide, all types of ruled surfaces can be cut. Since discharge currents with a high peakvalue over a short duration are used, current is supplied through both the upper and lower feedingbrushes to obtain a quick rise in the discharge current by reducing the inductance and to avoid wirebreakage due to Joule heating. Tension is applied to the wire to reduce vibration and deflection,which deteriorates cutting accuracy.

In WEDM, water is most often used as the dielectric liquid, but its specific electrical conductivityshould be decreased using deionizing resins to avoid electrolysis and to keep high open voltage. Useof deionized water is preferable to hydrocarbon dielectrics considering higher material removal ratesand fire safety. However, finer surface finish can be obtained with hydrocarbon dielectrics under thesame discharge energy. In contrast, hydrocarbon dielectrics are normally used in sinking EDMbecause surface roughness is better and tool electrode wear is lower compared to deionized water.

Characteristics and ApplicationsSince EDM is a thermal process, even hard materials such as quenched steel, cemented carbide, andelectrically conductive ceramics can be machined. EDM also allows machining of complicated

Fig. 2 Sinking electrical discharge machine

Fig. 3 Sinking electrical discharge machining (Seibu Electric & Machinery)


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shapes. Since the tool electrode does not need to rotate for material removal like milling or grinding,holes with sharp corners (Fig. 3) and irregular contours (Fig. 6) can be machined without difficulty.Reaction forces generated in the EDM gap are insignificant, which also facilitates the machining ofthin and flexible parts, deep grooves and holes (Fig. 3), and micro parts (Masaki 1993; Fig. 7) whichare difficult to machine by milling.

Generally, machining accuracy of EDM is very high in the order of several micrometers, andachievable surface roughness is Rz 0.4 mm. On the other hand, the material removal rate of EDM islow compared to other machining processes. Hence, EDM is preferably used in die and moldmaking, fuel jet nozzles drilling, and aeroengine manufacturing, where complicated shapes in hardmaterials and with high precision have to be machined.

Fig. 4 Milling electrical discharge machining (Sodick)

Fig. 5 Wire electrical discharge machining (WEDM)


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Pulse Generators

Relaxation Pulse GeneratorEarly EDM equipment used relaxation pulse generators with capacitor discharges as shown in Fig. 8.The capacitance is charged according to the following equation:

u0 ¼ 1

C

ði tð Þdt þ i tð ÞR (1)

Here, u0 is the open voltage of the power source, and i(t) is the charge current. When the gapvoltage exceeds the dielectric breakdown strength, discharge is ignited in the gap as shown in Fig. 9.Discharge current ie(t) can be obtained from the following equation:

1

C

ðie tð Þdt þ L

die tð Þdt

þ ue ¼ 0 (2)

Here, ue is discharge voltage. Discharge duration is several microseconds or less, even shorterthan ten nanoseconds followed by recovery of dielectric strength of the gap. Thus, charging anddischarging of the capacitance can be repeated autonomously. This type of pulse generator has been

Fig. 6 Wire electrical discharge machining (Sodick)

Fig. 7 Micro electrical discharge machining (Masaki 1993)


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used, especially in WEDM until recent years because discharge current with high peak values andshort duration is needed in WEDM due to the reasons described in section “Influence of pulseconditions.” Disadvantage of the relaxation pulse generator is the difficulty of pulse control. Forexample, since the gap voltage starts rising immediately after each discharge, deionization of theplasma cannot be secured. Therefore, in the case that the plasma is not extinguished after discharge,the current from the power source leaks through the discharge gap, disabling the charge of thecapacitance. Thus, with the recent development of power transistors which can handle large currentswith high response, relaxation pulse generators have been replaced with transistor pulse generatorsshown in Fig. 10. However, the relaxation-type pulse generators are still being used in finishmachining and micromachining because it is difficult to obtain significantly short pulse durationwith constant pulse energy using the transistor pulse generator.

Transistor Pulse GeneratorWith the transistor pulse generator, a series of resistances and transistors are connected in parallelbetween the direct current power supply and the discharge gap as shown in Fig. 10. Here, considerthe case that the open voltage of the power supply is 100 Vand only one transistor is switched on. Itis known that in EDM, when discharge is ignited, the gap voltage drops to around 20 V independentof the discharge current. This is because larger current brings about higher degree of ionization andgreater diameter of the arc column resulting in increased electrical conductivity of the plasma.Hence, the discharge voltage ue is normally around 20 V. The discharge current obtained is therefore4 A using a single transistor circuit in this example. Thus, it is found that the discharge current can beraised by increasing the number of transistors which are switched on at the same time.

Figure 11 shows the waveforms of the gap voltage and current, which are typical in sinking EDMoperations. When the transistors are switched on, the open voltage uo, 100 V in the case of Fig. 10, isapplied between the tool electrode and workpiece. However, discharge does not occur immediately,

Fig. 8 Relaxation pulse generator

Fig. 9 Gap voltage and discharge current with relaxation pulse generator


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but its ignition is delayed by td. This is because dielectric breakdown needs a statistical time lag inwhich initial electrons should be generated by the collision of cosmic, radioactive, ultraviolet, andX-rays with the neutral species in the gap and the formative time lag in which the initial electrons areaccelerated to generate the electron avalanche (Meek and Craggs 1978). In EDM, since the dielectricliquid is contaminated with electrically conductive debris particles, the ignition delay time isdetermined not only by the gap width but also by the concentration of debris particles in the gap.

After the dielectric breakdown, a discharge current, ie, flows in the gap. The gate control circuitkeeps the transistors on for the preset discharge duration, te, after the dielectric breakdown, resultingin a uniform discharge crater size independent of the ignition delay time which can vary statisticallyfor each discharge. Then after the fixed discharge interval, to, the transistors are again switched onand open voltage is applied between the electrodes.

The discharge energy per single pulse q is expressed as

q ¼ ue � ie � te (3)

where ue is the discharge voltage, which is around 20 V. Hence, discharge current and dischargeduration are set by operators considering whether the process is for a roughing or a finishingoperation. To obtain stable machining, the discharge interval should be sufficiently long so thatthe plasma is extinguished and hence the dielectric breakdown strength is recovered during the

Fig. 10 Transistor type pulse generator

Fig. 11 Gap voltage and current waveforms


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interval. Duty factor, the ratio of discharge duration to the average discharge cycle time, can bedefined as

D:F: ¼ tete þ to þ tdh i (4)

where htdi is average ignition delay time measured. With increasing D.F., material removal rate canbe increased, while machining becomes unstable. Advanced electrical discharge machines cancontrol the discharge interval adaptively by monitoring the gap voltage waveforms.

Servo Feed Control (Gap Control)Tool electrode feed is not constant, which is different from the conventional machining methodswhere cutting tools are fed at a constant feed speed. The servo feed control shown in Fig. 12 keepsthe working gap at a proper width. Larger gap widths cause longer ignition delays, resulting ina higher average gap voltage. When the average gap voltage measured is higher than the servoreference voltage preset by the operator, the feed speed is increased. On the contrary, the feed speedis reduced or the electrode is retracted when the average gap voltage is lower than the servo referencevoltage. Thus, short circuits can be avoided even when debris particles or humps of discharge cratersbridge the gap. Hence, the feed speed of the tool electrode is changed adaptively according to thevariation of the discharging surface area during the process.

For example, suppose the reference voltage is set by the operator at 25 V, with the dischargeduration of 100 ms and pulse interval of 40 ms. Since the servo feed is controlled so that the averagegap voltage equals 25 V, the following equation can be obtained:

100 V� tdh imsþ 20 V� 100 mstdh imsþ 100 msþ 40 ms

¼ 25 V (5)

From the above equation, the average ignition delay time htdi is found to be 20 ms. Then,D. F. canbe obtained from Eq. 4 as 0.625. Since the average discharge cycle time is htdi + te + to¼ 160 ms, thedischarge frequency can be calculated as 6.25 kHz. When the servo reference voltage is set high, the

Fig. 12 Principle of servo feed control


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gap width is enlarged; thereby removal of debris particles from the gap becomes easy. Lower D. F.leads to more stable machining. However, the accuracy of replicating the tool electrode shape intothe workpiece is lowered, and material removal rate decreases.

In some cases, the average ignition delay time is used in place of the average gap voltage tomonitor the gap width (Altpeter and Perez 2004).

Discharge Phenomena

Single Pulse DischargeInitial electrons, which are generated by the ultraviolet ray, X-ray, cosmic ray, and radiation from theearth crust, are accelerated by the electric field and ionize the neutral species due to collision,resulting in an electron avalanche. Thus, the electric field is distorted and streamers are developedtoward both the anode and cathode. The accelerated positive ions bombard the cathode surface;thereby secondary electrons are emitted (secondary emission). With increasing the current density,the surface temperature rises, activating the electrons to jump over the work function of the material(thermal emission). High electric field existing on the cathode extracts the electrons due to thetunneling effect (field emission). When both temperature and electrical field are high, the thermaland field emission processes strongly interfere with each other (T-F theory) (Lee 1959).

These emitted electrons are accelerated toward the anode and collide with the neutral atoms in thegap. Thus, great amount of positive ions are formed due to collision ionization, resulting in anestablished discharge (Meek and Craggs 1978). In EDM, the temperature at the discharge spot risesover the melting point and even higher than the boiling point of the electrode materials. Hence,thermal and field emissions of electrons from the cathode spot are dominant compared to secondaryemission; thereby the current density at the discharge spot reaches over 108–109 A/m2. Therefore,EDM discharge is an arc discharge. The arc plasma is highly ionized resulting in high currentdensities with the comparatively low discharge voltage of about 20 V. The discharge voltage iscomposed of an anode drop, cathode drop, and voltage drop in the positive column, and its value willslightly change depending on electrode materials, dielectric fluids, gap width, and pulse conditions.

Figure 13 shows the gap phenomena due to a single pulse discharge. The constituents of the arcplasma are vapors of the dielectric liquid, molecules, and atoms generated by the decomposition ofthe dielectric, atoms and ions of the anode and cathode materials, and electrons. The arc plasmatemperature in EDM was measured using spectroscopic analysis, and it was found that the temper-ature reaches 6,000–7,000 K (Natsu et al. 2004a).

Fig. 13 Single pulse discharge phenomena


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The diameter of the arc plasma expands with the passage of time because high-temperature regionis enlarged due to heat conduction and because high-energy particles are dispersed due to diffusionand convection. Figure 14 shows the side view of the plasma generated between copper electrodeswith discharge current of 36A (Kojima et al. 2008). It is found that the plasma expansion iscompleted within 90 ms, and the resultant crater diameter was 0.1 mm. Figure 15 shows the plasmaand discharge crater observed from the reverse side of a transparent plate electrode (Kitamuraet al. 2013). Ga2O3 single crystal was used as the cathode plate, and discharge current was 20 A. Thedark area at the center indicates the discharge crater formed on the Ga2O3 single crystal plate, and theviolet area surrounding the crater shows the plasma region. These images taken by high-speed videocameras show that the diameter of arc plasma is significantly larger than the gap width and that thegrowth rate of discharge crater is slower than that of the arc plasma.

Fig. 14 Temporal change in arc plasma diameter

Fig. 15 Expansion of arc plasma


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Due to the high temperature of the plasma, electrode materials and dielectric liquid evaporate,molecules are dissociated, and atoms ionized, resulting in a rapid expansion of a bubble. Figure 16shows side views of a bubble generated by a single discharge in deionized water and EDM oil. Thebubble and dielectric liquid are analogous to the spring and mass oscillation system, respectively(Eckman andWilliams 1960). Starting from the initial condition, where the bubble is compressed ina small volume, the dielectric liquid is accelerated radially. At the moment the pressure inside thebubble equals the atmospheric pressure, the kinetic energy peaks. Hence, the bubble continuesexpanding. The diameter of the bubble peaks when all the kinetic energy is transferred to thepotential energy of the bubble. The diameter of the bubble reaches several millimeters, several tensof times greater than the gap width. Thereafter the bubble starts contracting until it is compressed toits initial diameter. In reality, the viscosity of the liquid causes damping in the oscillation.

Debris particles removed from the crater proceed straight through the bubble as can be seen inFig. 15, and hit the opposite electrode surface, which is wetted with the dielectric liquid, or penetratethe bubble wall and as a result decelerate. They then solidify into a spherical shape under theinfluence of surface tension. Thus, the dielectric liquid is important for the cooling and flushing ofdebris particles. Without the liquid, the molten and evaporated debris particles are reattached to theopposite electrode surface.

After discharge, ions and electrons are recombined, and the dielectric strength of the gap isrecovered. The evaporated atoms and molecules are solidified or condensed to form debris particlesor dielectric liquid, but gases such as hydrogen and methane which are generated by the dissociationof the working oil are left to form a bubble. The resultant diameter of the bubble is smaller than themaximum diameter during oscillation, but even larger than one millimeter. Hence, in consecutivedischarges, the working gap is mostly occupied by bubbles although the discharge gap is submergedin dielectric liquid (Kitamura et al. 2013).

When discharge is ignited in a gas, the plasma is easy to expand because there exists no liquidwhich serves as an inertia to resist the quick expansion of the high-pressure plasma. Hence, theplasma completes expanding within 2 ms after dielectric breakdown, and thereafter, its diameterremains constant during discharge (Kojima et al. 2008). Since the discharge gap is mostly occupiedwith bubbles in actual EDM processes where pulse discharge occurs consecutively, the rate ofplasma expansion is more similar to the discharge in gas rather than that in liquid.

Fig. 16 Side view of bubble oscillation (ie: 20 A, te: 100 ms, gap width: 0.1 mm, anode: Cu f 5 mm, cathode: Cu f5 mm)


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Energy DistributionIt is very important to know the percentages by which energy is distributed to anode and cathodeamong the total discharge energy q given by Eq. 3 to discuss the material removal rate of workpieceand wear rate of tool electrode.

First, consider the heat transfer by heat conduction due to the thermal motions of plasmaconstituents. Assuming the plasma is in thermo-equilibrium, the energy inputs into anode andcathode would be equal because the temperature distribution in the plasma is more or less symmet-rical between the anode and cathode regions. Then, consider the kinetic energies of charged particlesaccelerated by the electric field. On the anode surface, all the discharge current is carried by electronswhich are bombarding the anode. In contrast, the cathode surface gains energy due to the kineticenergy of the impinging positive ions and loses energy equivalent to the work function of thecathode material due to the emission of electrons. Hence, the discharge current on the cathode is thesum of the charges of the impinging ions and departing electrons per unit time. Due to the continuityof current, the discharge current on both electrodes must be equal. Thus, increase in the electroncurrent results in decrease in the ion current on the cathode surface. Ion bombardment heats theelectrode, while electron emission cools the cathode surface because free electrons in the metal mustgain the energy equivalent to the work function of the metal to be emitted from the surface. Hence, itis considered the energy input to anode is greater than that into cathode. In reality however, physicsis more complicated because the drop of electric field on the cathode (in the cathode sheath) isgreater than that on the anode. Since analysis of EDM arc plasma is extremely difficult, the energydistribution must be obtained from experiments. The energy distribution in a single discharge wasmeasured by comparing the measured temperatures of foil electrodes with the calculated resultsobtained under the assumed ratio of the energy distributed to electrodes, using a finite differencemodel (Xia et al. 1996; Hayakawa et al. 2001; Zahiruddin and Kunieda 2010). When the calculatedand measured temperatures were in agreement, the energy distributed to the anode and cathode wasfound as shown in Fig. 17. The energy distribution into the anode is consistently greater than thatinto the cathode regardless of discharge duration. In micro EDM, where the discharge duration is inthe order of nanoseconds to sub-microseconds, energy distribution into the electrodes is lower thanthat in the macro (normal) EDM. This is because a large amount of energy is used for establishing thearc plasma. On the contrary, with the discharge duration extraordinarily long compared to that usedin normal EDM processes, most of the energy is distributed to electrodes, because the arc plasma isfully developed. In the normal EDM processes, the ratio of energy distributed to the anode andcathode to the total discharge energy � is about 40–48 % and 25–34 %, respectively. Thus, the heatflux on the electrode surface can be expressed as

Fig. 17 Energy distribution into anode and cathode


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q00 ¼ �ueie

p d tð Þ2

� �2 (6)

where d(t) is the arc plasma diameter.

Removal MechanismTemperature Rise in ElectrodeGiven the energy distribution ratio � and time-dependent diameter of the circular heat source d(t) asboundary conditions, the following heat diffusion equation can be solved to obtain the temperaturedistribution in the electrodes:

∂∂x

k∂T∂x

� �þ ∂∂y

k∂T∂y

� �þ ∂∂z

k∂T∂z

� �þ _q ¼ rcp

∂T∂t

(7)

Here, T is temperature, r is density of the electrode material, cp is specific heat, k is heatconductivity, and _q is the rate at which energy is generated per unit volume of the electrode due toJoule heating. Nowadays, with the development of powerful computers and numerical methods, it isno longer difficult to take into account the temperature dependence of thermophysical properties ofelectrode materials and latent heat of melting and vaporization. However, it should be emphasizedthat correct temperature distributions cannot be obtained unless correct boundary conditions areused, i.e., energy distribution ratio � and plasma diameter d(t).

From the time-dependent plasma diameter shown in Fig. 14 and the influence of discharge currenton the plasma diameter obtained by the same authors (Kojima et al. 2008), the plasma diameter canbe expressed as

d tð Þ ¼ 1:7� 10�3 � t0:35 � ie0:48 (8)

Here, units of d(t), t, and ie are [m], [s], and [A], respectively. This equation is based on theempirical equation obtained by Saito and Kobayashi (1967) and Ikai et al. (1992) who assumed thatheat source diameters are equal to discharge crater diameters which were measured in experimentsas follows:

d tð Þ ¼ 2:4� 10�3 � t0:4 � ie0:4 (9)

As described in section “Single Pulse Discharge,” the plasma diameter is larger than that of thedischarge crater. Hence, d(t) in Eq. 8 is larger than that in Eq. 9. However, since the temperaturedistribution in the plasma is not uniform, the degree of ionization is not uniform. Therefore, thecurrent density may be more concentrated near the axis of the cylindrical plasma, resulting ineffective heat source diameter smaller than that of the plasma diameter. Hence, d(t) in Eq. 9 was usedin place of Eq. 8 as the heat source diameter.

Figure 18 shows the analysis model to calculate the temperature distribution inside the electrodedue to single pulse discharge. The heat transfer equation was solved using a simplified modelassuming an expanding circular heat source with a uniform heat flux and ignoring the metal removaland temperature dependence of thermophysical properties. Figure 19 shows the calculated resultswhen carbon steel is used as the electrode material, assuming the energy distribution ratio of 25 %.Given the boiling and melting points of carbon steel are 3,273 and 1,808 K, respectively, it is found


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that the melting region is expanding with the passage of time after dielectric breakdown. However,the peak temperature at r ¼ z ¼ 0 and boiling region decrease with time because the heat fluxdecreases due to plasma diameter increase with time. During the discharge interval, 20 ms after theend of discharge, temperature of the whole discharged spot falls below the melting point and all thematerial is resolidified.

Mechanism of RemovalCalculation of the temperature distribution in the electrode only is insufficient to obtain the volumeof removal due to a single discharge. Simulations of crater formation and eruption of molten pool areindispensable. There is no doubt that the material can be ejected when its temperature exceeds theboiling point. However, it is still difficult to calculate the removal amount because some of themolten material is removed, but not all the molten region is ejected (Zahiruddin and Kunieda 2010;Van Dijck 1973). It is the commonly accepted view that the metal removal occurs due to boiling ofthe superheated molten mass in the crater. However, the thermo-hydrodynamics calculations of thecrater formation and debris ejection due to boiling have been difficult. Hence, it has been believedthat most of the metal removal occurs due to boiling at the end of the discharge because boiling of thesuperheated metal is suppressed by the bubble pressure which is significantly high during discharge(Zolotykh 1959).

Van Dijck (1973) calculated the volume of the region inside the normal boiling point isothermalsurface, at the end of discharge when the bubble pressure was considered to be at normal atmo-spheric pressure. The calculated volume agreed well with the measured material removed per pulse.It was also found that the material removal efficiency, which was defined as the ratio of the ejected to

Fig. 19 Temperature distribution in steel workpiece (cathode) (ie: 30 A, te: 100 ms, energy distribution to cathode: 25%)

Fig. 18 Analysis model for temperature distribution in single pulse discharge


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melted volume, was only 1–10 %. However, high-speed camera images of flying debris scatteredfrom discharge points in Fig. 15 show that material removal occurs even during the discharge(Kitamura et al. 2013). Thus, the development of computation models which can simulate thematerial removal phenomena is eagerly awaited.

In some cases, molecular dynamics (MD) simulation can be very helpful to analyze the phenom-ena which are difficult to model using conventional thermo-hydrodynamics simulations. Figure 20shows the forming mechanism of a discharge crater analyzed by the MD simulation (Yanget al. 2010, 2013). Both the space and time domains which can be handled are unrealisticallysmall compared with those used in EDM. Nevertheless, Fig. 20 clearly demonstrates the evidence ofthe superheating theory. It is found that removal can occur at any time when the pressure inside themolten pool exceeds the pressure outside (Yang et al. 2013).

The superheating theory indicates that removal can occur without a liquid dielectric. In air,however, most of debris particles are reattached to the opposite electrode surfaces as described insection “Single Pulse Discharge.” Hence, the major role of dielectric liquid is cooling and flushingdebris particles but not material removal. However, the dielectric liquid affects the expansion rate ofthe arc plasma. The rate of increase in the plasma diameter d(t) given by Eq. 8 is significantly higherin gas. Hence, the heat flux from the plasma generated in liquid is higher than that in gas, resulting inlarger removal due to higher-temperature distribution in the discharge crater (Takeuchi and Kunieda2007).

Residual StressThe temperature rise due to discharge results in a compressive thermal stress on the electrode surfaceuntil the stress is released by material yielding at a high temperature. The stress becomes nearly zerowhen the material is molten. After discharge, due to the temperature decrease, the molten materialresolidifies and starts shrinking, generating a tensile residual stress on the surface (Yang andMukoyama 1996). Thus, a resolidified layer, called white layer, is formed on the surface. Sincethe white layer is a hard and brittle layer, the tensile stress causes micro cracks on the EDMedsurfaces. Since such a heat-affected layer is not acceptable for practical use of the workpiece, thethickness of the layer should be minimized in finish processes.

Fig. 20 Molecular dynamics simulation of material removal (Yang et al. 2010)


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Process StabilityProbability of DischargeTo ignite an electric discharge in clean oil at an open voltage of 100 V, the gap width must be lessthan several microns. In actual EDM processes however, since the dielectric liquid is contaminatedwith electrically conductive debris particles, whose average diameter is even more than one third ofthe gap width (Yoshida and Kunieda 1998), discharge can occur at gap widths of tens of micrometersor more (Bommeli et al. 1979; Schumacher 1990). This fact sometimes reduces the replicatingaccuracy due to the uneven distribution of the debris particles. On the other hand, the extended gapwidth is favorable for easy gap control because it is difficult to keep the gap width constant at severalmicrons.

In order to study the influence of debris particles, a debris particle with a diameter of 5 mm wasplaced in a gap of 20 mm as shown in Fig. 21 (Kunieda and Nakashima 1998). If it were true that thedischarge occurs at a point where the gap is shortest, then the discharge should occur at the pointwhere the debris particle is placed. However, experimental results showed that in most cases, thedischarge crater was not generated at the point where the debris particle was placed. This is becausethe probability of discharge in a certain area is obtained from the product of the probability ofdischarge per unit area and its surface area (area effect). Since the projected area of the debris particlein the direction normal to the electrode surface is negligible compared with the area of the electrodes(50 � 50 mm), the probability that discharge does not occur on the debris is greater than theprobability that the discharge occurs on the debris. This result indicates that the discharge location isdetermined in a probabilistic way and not deterministic.

Another example which indicates the probabilistic nature of discharge location is shown inFig. 22. In sinking EDM, when the tool electrode is fed by a distance during a certain time, theremoval volume per unit area on the tool electrode is greater at a curved surface than that at a flatsurface. The removal volume on an inclined surface is smaller than that on a horizontal surface.Therefore, the discharge frequency per unit area must be higher on a convex surface and lower on aninclined surface compared with that on flat and horizontal surfaces, respectively. To satisfy theserequirements, the gap width must be smaller on a convex surface and greater on an inclined surfacethan the gap on flat and horizontal surfaces, respectively. In wire EDM, the gap width distributionaround the wire is not uniform as shown in Fig. 22b, which never happens if discharge is locateddeterministically based on the gap width distribution.

Discharge Delay TimeThe discharge delay time depends upon the local values of the gap width and concentration of debrisparticles at the discharge location. Hence, the tool electrode feed is controlled based on the discharge

Fig. 21 Probabilistic nature of discharge location


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delay time as described in section “Servo Feed Control.” The average discharge delay time td,ave [ms]was quantified empirically as a function of the gap width, gap [mm]; concentration of debrisparticles, conc [mm3/mm3]; machining area, area [mm2]; and debris diameter, r [mm], under thefollowing machining conditions: copper anode, carbon steel cathode, discharge current of 3 A,discharge duration of 300 ms, and open circuit voltage of 120 V (Morimoto and Kunieda 2009).

td, ave ¼ 8:2� 1012gap8:8 � r2:9

area1:2 � conc1:6

� �(10)

The machining area is a factor because the probability of discharge within a specific area isproportional to the ratio of its surface area to the whole discharge area as described in the previoussection. td,ave was obtained experimentally based on the fact that the discharge delay time tdconforms to the exponential distribution obtained from the Laue plot method (Bommeliet al. 1979; Araie et al. 2008). The Laue plot shows the percentage of electric insulation that doesnot break down until time t after the supply of a pulse voltage (Institute of Electrical Engineers ofJapan 1998). Suppose a single pulse discharge was generated N times and the number of dischargeswhich did not occur until time t was n; then n as a percentage of N can be expressed by

n

N¼ exp � t

td, ave

� �(11)

where td,ave the average value of td is given theoretically (Mood et al. 1974) by

td, ave ¼X

td

N(12)

The Laue plot enables easy evaluation of the discharge delay time, which normally has a largescatter, from the slope td,ave as shown in Figure 23.

Discharge LocationTo obtain stable conditions in EDM, it is essential for the discharge locations to be dispersed over theworking surface. Figure 24 shows the equivalent circuit to detect discharge locations (Kunieda andKojima 1990). The electric feeder is intentionally divided, and each divided feeder is connected tothe tool electrode at each end. While the resistance of the feeder, ro, and contact resistance at thefeeding point, rc, are constant, the resistance in the tool electrode from each end of the tool electrode

Fig. 22 Non-uniform load removal and gap width due to probabilistic nature of discharge


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to the discharge location, R1 and R2, respectively, varies depending on the discharge location.Consequently, by measuring the ratio between currents i1 and i2 through each divided feeder, thedischarge location can be obtained in process.

Figure 25 shows the distribution of discharge locations measured with the extension of the depthof erosion. The working area of the tool electrode was a rectangle of 14 mm by 105 mm. Theabscissa shows the number of discharges sampled every 50 pulse discharges, and the ordinate showsthe discharge location along the longitudinal direction of the working surface. The dots indicate thelocation of each discharge. It was observed that when the depth of erosion was shallow, the processwas stable. The distribution of discharge location was uniform, and no relationship betweenconsecutive discharges was visible. The tool electrode feed rate was constant, and the distributionof gap width was uniform. With the increase of the eroded depth however, discharge becamelocalized. The area of localized discharges moved periodically with a period of several minutes.When the machining depth increased further, the localization became prominent, and the area oflocalization narrowed. The movement of the localized area was mostly periodical. In this phase, thetool electrode feed was not smooth, and the distribution of gap width was not uniform. Ultimately,discharge was concentrated at a certain location. In this hazardous situation, it was no longerpossible to continue the process, and thermal damage was left on the workpiece surface.

Fig. 24 Principle of measuring discharge locations

Fig. 23 Evaluation of discharge delay time using Laue plot


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The mechanism of the periodical movement of localized discharge is shown in Fig. 26. If theflushing of debris is difficult, local distribution of discharge spots cannot be eliminated once it iscreated at some area, even if the gap width of the other regions is narrower, since the dielectricstrength is considerably decreased due to contamination and temperature rise in the localized area.Meanwhile, the localized area moves to other regions, where the gap width is sufficiently short. Atthis moment, the position of the tool electrode is retracted resulting in the fluctuation of the feedspeed.

Relation Between Distribution of Discharge Location and Process InstabilityLocalization and concentration of discharges result from locally weakened dielectric breakdownstrength in the gap. There seems to be two causes for the decrease of the dielectric breakdownstrength. One of the causes is thermal. It was found both analytically and experimentally that it takes5 ms or less for the temperature at the center of the plasma generated by the preceding discharge todrop under 5,000 K, which is the temperature where the dielectric strength of the gap is considered torecover sufficiently (Hayakawa et al. 1996; Natsu et al. 2004a). When deionization is insufficientduring the discharge interval, subsequent discharges occur at the same location, resulting in thefurther increase in the temperature at the discharge spot, which accelerates the concentration.Formation of debris particles in the gap can be another reason. If flushing of the debris particles is

Fig. 26 Mechanism of movement of localized discharge

Fig. 25 Mechanism of movement of localized discharge


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insufficient, localization of discharge causes increased concentration of debris particles locally,leading to the acceleration of discharge localization.

FlushingTo maintain stable machining, it is critical to flush debris particles and cool the working gap in orderto prevent the localization and concentration of discharge locations. Normally, the tool electrode islifted periodically to replace the contaminated dielectric fluid in the gap with fresh one (Fig. 27a).Linear motor equipped sinking EDM machines realized increased removal rate, especially in themachining of narrow and deep grooves due to the high-speed jump flushing operation of toolelectrode which can prevent short circuiting. Machining accuracy was also improved because thelateral gaps of the groove became narrower and more uniform. The working gap can be flushed bya fresh dielectric fluid jetted from nozzles placed adjacent to the discharge gap (Fig. 27b). However,jetting of dielectric fluid merely from one direction causes increased density of debris particles in thedownstream, resulting in uneven distribution of gap width deteriorating the machining accuracy.Pressure or suction flushing through holes in the electrode or workpiece remains one of the mostefficient flushing methods at least if those holes have to be provided anyway or do not harm theworkpiece (Fig. 27c). Both in pressure and suction flushing, one can observe lower electrode wearand larger gap width at the outlet point in comparison with the inlet point (Koenig et al. 1977).

Machining Characteristics

Influence of Pulse ConditionsFigure 28 shows three machining characteristics which are most important in EDM practice:material removal rate, surface roughness, and tool electrode wear ratio. Here the tool electrodewear ratio is defined as the ratio of volume of tool electrode wear to the volume of workpieceremoval. Requirements for any two of the characteristics can be satisfied if the remaining one issacrificed using the discharge current waveforms indicated in Fig. 28. However, there is no currentwaveform which can satisfy all the requirements.

Current waveforms with higher peak current and longer discharge duration result in highermaterial removal rates. At the same time, low tool electrode wear can also be satisfied because thecarbon layer deposited on the anode tool electrode is thicker when longer discharge durations are

Fig. 27 Flushing methods


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used as described later (Xia et al. 1996; Natsu et al. 2004b; Kunieda and Kobayashi 2004). However,surface roughness is not good because the crater generated by each pulse discharge is large. Thus,this pulse condition is normally used in rough machining.

On the other hand, the pulse condition with longer discharge duration and lower peak currentbrings about both lower tool electrode wear ratio and better surface roughness. However, the lowerheat flux due to the lower current density at the discharge spot results in lower energy efficiency ofmaterial removal compared with the pulse condition with shorter discharge duration and higher peakcurrent even though the same pulse energy is applied. In this situation, the melted and evaporatedregions in the workpiece are small, and most of the energy distributed to the workpiece is dissipatedinside the workpiece due to heat conduction. Obviously, the material removal per pulse is small. Inaddition, longer discharge duration results in lower discharge frequency per unit time. Thus, thispulse condition is suitable for finishing.

Finally, pulse conditions with shorter discharge duration and higher peak current provide bettersurface roughness due to smaller discharge crater. Moreover, although material removal per pulse isnot large, it is large enough compared with the pulse condition with longer discharge duration andlower peak current under the same discharge energy per pulse because energy efficiency is higherdue to larger heat flux. Higher repetition rate of discharge per unit time due to shorter dischargeduration further increases the material removal rate. However, the tool electrode wear ratio is highbecause the carbon layer deposited on the tool electrode is thin. This is why extremely shortdischarge duration and high peak current compared with the case of sinking EDM, for example,1 ms and 100 A, are used in WEDM, where the problem of tool electrode wear is insignificant.

Influence of PolarityAs shown in Fig. 17, the energy dissipation into the anode is greater than into the cathode.Nevertheless, in sinking EDM, polarity of the tool electrode is normally positive except whenvery short discharge duration is used. This is because the carbon layer which is deposited on theanode surface due to thermal dissociation of the hydrocarbon oil (see Fig. 3) protects the anodesurface from wear (Xia et al. 1996; Natsu et al. 2004b; Kunieda and Kobayashi 2004). Since thecarbon layer is thick when the discharge duration is long, the tool electrode wear ratio is low with thepolarity of positive tool electrode under the pulse condition of longer discharge durations. On thecontrary, a negative tool electrode is used considering the energy distribution in the cases of finishmachining and micromachining where deposition of carbon layer is scarce and also in WEDMwhere deionized water is normally used as dielectric liquid.

Influence of Thermal Properties of Electrode MaterialsSince EDM is a thermal process, the influence of thermal properties of electrode materials on theremoval volume is significant. When the heat flux from the arc column is equal, higher heat

Fig. 28 Relation between discharge current waveforms and machining characteristics


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conductivity results in lower temperature on the electrode surface. Hence, materials with higher heatconductivity are suitable as tool electrodes. On the other hand, under the same temperaturedistribution inside the electrode, when the surface temperature is not over the boiling point ormelting point, removal does not occur. Hence, materials with higher melting point and boiling pointare also suitable as tool electrodes. The results of heat conduction analysis shown in Figs. 19 and 29indicate that although both melting point and boiling point of copper are lower than those of steel,copper is more suitable as a tool electrode because copper has much higher heat conductivity thansteel. With the expansion of the plasma radius, the melted zone is even resolidified during thedischarge duration in the case of copper. During the discharge interval to, since the surfacetemperature at the discharge spot drops rapidly in copper, the time needed for the plasma to beextinguished is short, leading to stable machining.

Thus, considering the higher energy distribution to the anode, carbon layer deposition on theanode, and the thermal properties of electrode materials, it should be possible to select appropriatedischarge current waveforms, polarity, and tool electrode materials to obtain minimum tool electrodewear ratio even lower than several percentage.

Influence of Electric Conductivity of Electrode MaterialsIn the electric circuit shown in Fig. 10, the resistances in copper tool electrode and steel workpieceare negligible. In the machining of electrically conductive ceramics and semiconductors, however,discharge current obtained is lower than metallic workpiece because of significant voltage drop inthe workpiece electrode. Hence, power supplies with higher open voltage should be used, and theelectric feeder should be connected to the workpiece at the point closer to the discharging area.

The voltage drop is especially large adjacent to the discharge spot because the current density isextremely high in the order of ie/p (d(t)/2)

2. Zingerman (1956) states that Joule heating does not playa substantial role in the machining of metallic materials, because electrical potential drops in metallicworkpieces are negligibly small. According to the calculated results of Rich (1961), however, theJoule heating is extremely concentrated in a hemispherical volume directly under the discharge spot,and for high-resistivity metals, e.g., Hg, Sb, Fe, and Bi, the Joule heating is comparable to the energyinput from the arc plasma. Saeki et al. (1996) calculated the workpiece temperature distributionconsidering the Joule heating as well as the heat flux from the arc column and found that the removalof high-electric-resistivity material (Si3N4 –30wt%SiC) in a single discharge is greater than that ofsteel due to Joule heating under the same discharge current. However, it was found that a longer

Fig. 29 Temperature distribution in copper workpiece (cathode) (ie: 30 A, te: 100 ms, energy distribution to cathode:25 %)


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discharge interval is necessary to deionize the arc plasma and recover the insulation of the gap aftereach pulse, which results in a lower material removal rate of high-resistivity materials in a practicalEDM. In the case of ceramics and semiconductors, which are normally hard and brittle materials,debris particles are generated not only by melting and boiling but also by fracture due to thermalstress.

Summary

EDM processes involve transient phenomena occurring in a narrow space and in a short period oftime. These EDM phenomena are not in thermal equilibrium, but include transitions between solid,liquid, gas, and plasma. Chemical reactions, mass transfer, and displacement of boundaries occur atthe same time. Hence, compared to other discharge phenomena such as glow discharge in dryetching processes and arc discharge in welding processes, physics involved in EDM processes areobviously most complicated, rendering observation and theoretical analysis extremely difficult.Although it is a long way to fully understand the EDM phenomena, thanks to the advancements ofvarious surface analyzing equipments, microscopes, high-speed imaging devices, and software toolsfor numerical analysis, fundamental studies are progressing step by step, and some of the commonEDM knowledge which has been accepted for a long time is being modified. Given that numerousdischarge gap phenomena have yet to be fully understood, the potentials of EDM technology maynot be fully realized. For example, based on the fact that hydrocarbon dielectric is decomposed todeposit pyrolytic carbon on the electrode surface, a method to machine completely nonconductiveceramics was developed (Mohri et al. 2002). Furthermore, considering that removal can occurwithout a liquid dielectric, the dry EDM method was developed (Kunieda and Yoshida 1997).Undoubtedly, continuous efforts are expected to lead to further developments of the EDM technol-ogy in the future.

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Index Terms:

Arc discharge 1, 9Arc plasma 9–10Bubble 11Debris 11, 16, 19Dielectric liquid 3, 11, 15Discharge crater 15Discharge current 5–6, 12Discharge delay time 16Discharge duration 5Discharge energy 7, 12Discharge gap 6, 20Discharge interval 7Discharge location 2, 16–17, 19Discharge voltage 5, 9Electrical discharge machining (EDM) 2–3Heat flux 2, 12Material removal rate 4, 20Micromachining 21Plasma 12Polarity 21Pulse discharge 9Pulse generators 5Residual stress 15Servo feed control 8Sinking EDM 2, 16Surface roughness 4, 20Temperature distribution 13Tool electrode wear 20–21Tool electrode 1, 22Wire EDM (WEDM) 2, 16Workpiece 6


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