G Model CIRPJ 439 No. of Pages 15 CIRP Journal of Manufacturing Science and Technology xxx (2017) xxx–xxx Contents lists available at ScienceDirect CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj Analysis of micro-EDM electric characteristics employing plasma property A.B.M.A. Asad, M. Tanjilul Islam, Takeshi Masaki, M. Rahman* , Y.S. Wong Department of Mechanical Engineering, National University of Singapore, 117575, Singapore A R T I C L E I N F O Article history: Available online xxx Keywords: Micro-EDM RLC network RC power supply Spark gap Discharge energy Plasma Stray capacitance A B S T R A C T Micro-electro discharge machining (micro-EDM) involves simultaneous complex processes associated with electrical characteristics and plasma properties, which lead to the removal of material from both electrode and workpiece. Unfortunately, existing micro-EDM models are simple electro-thermal based and not capable to connect the link between plasma and electrical circuit. This article presents a theoretical study to model the electric properties of micro-EDM plasma discharge for RC power supply with direct current (DC) source. Analysis presented in this study provides signiﬁcant insight for realizing changes in the current waveform due to changes in parameters like input voltage, capacitance, inductance and the charging resistance. This research bridges a crucial gap in the present theoretical understanding on the interaction of micro-EDM plasma with different circuit elements of micro-EDM power supply. Furthermore, by employing this proposed model, a novel stray capacitance measurement method has been presented to adjust pulse energy at minimum level for smallest machinable features. The robustness of the analytical model is substantiated by validating it on multiple experimental results of measured data as well as literature data. © 2017 CIRP. Introduction Owing to recent trends in the miniaturization of products in areas such as information technology, biotechnology, and the environmental, medical and optics industries, micro-EDM process is becoming a key supportive technology for micro machining. Major beneﬁts are the absence of cutting force, and ﬂexibility for machining irrespective of the material’s hardness. Material removal mechanism in EDM process is associated with plasma formation, which is generated by an electric breakdown in the electrode and workpiece gap space ﬁlled with dielectric under a condition when the electric ﬁeld strength exceeds the dielectric strength. Finally, this ignition process leads to a subsequent current ﬂow that generates an electric discharge, which lead to the removal of material from both electrode and workpiece. Through optimization of the process parameters, high-aspect-ratio micro features can be achieved using micro-EDM process. A proper analytical model is necessary to better interpret and predict results for micro-EDM process. The analytical modelling of the EDM process has been investigated by various researchers since 1971 [1]. Most of these existing models are based on electro-thermal * Corresponding author. E-mail address: mpemusta@nus.edu.sg (M. Rahman). properties of EDM process. In electro-thermal model, researchers considered various shapes of heat sources, e.g., disk heat source, point heat source etc. to obtain temperature/plasma distribution equations. Snoeys and Van Dijck [2] reported a study using a disk heat source while DiBitonto et al. [3] proposed model using a point heat source approximation. A comprehensive attempt to model the plasma channel was reported by Lhiaubet et al. [4]. The properties of diatomic plasma were taken as a constant and the ﬂuid dynamic equation was included in the model. Eubank et al. [5] reported variable mass cylindrical plasma which expands with time. Recent research efforts includes Gaussian distribution model as a heat source to numerically investigate MRR in EDM process [6]. Unlike the above mentioned models where the thermophysical properties of the material are considered to be constant or average, Weingärtner et al. [7] considered temperature varying thermophysical properties value over the whole temperature range from solid to liquid melt. Researchers have also used calorimetric model to investigate material removal rate (MRR) [8] and electromechanical model to estimate stress distribution inside the metal due to the electrostatic force [9]). However, these models lacked focus in linking between the plasma and electrical circuit. Due to the complex simultaneous processes associated with micro-EDM plasma, an analytical model based on micro-EDM plasma and electric network is necessary for optimization of machining https://doi.org/10.1016/j.cirpj.2017.09.005 1755-5817/© 2017 CIRP. Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 2 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx parameters. Proper understanding of the electrical characteristics and plasma properties in micro-EDM process can also help to minimize the spark energy released from each spark to achieve smaller unit removal, which will result in smaller machinable feature size and ﬁner surface roughness. Unfortunately, not much attempt has been made to investigate on the discharge itself and on the plasma created during the process. Descoeudres [10] has studied the EDM plasma with electrical measurements. However, current literature lacks the necessary modelling approach to bridge the gap between the power supply/electrical circuit and plasma generation. There are two major types of micro-EDM power supply, namely resistance-capacitance (RC) or relaxation type and transistor type power supply [11]. The relaxation type pulse generators are the popular choice for micro EDM because it is difﬁcult to obtain signiﬁcantly short pulse duration with constant pulse energy using the transistor type pulse generator [12]. So, the RC based power supply has found widespread applications in micro-EDM, and is somewhat a rebirth after being replaced by transistor type power supply for conventional EDM power supply. In an RC or relaxationtype circuit, discharge pulse duration is dominated by the capacitance of the capacitor and the inductance of the wire connecting the capacitor to the workpiece and the workpiece to the tool [13] and the discharge energy is determined by the used capacitance and applied voltage. In the case of typical RC type power supply, the repetition of the charging and discharging occurs in which capacitor C is charged through resistor R and discharged between the electrode and workpiece produces an extremely short width pulse discharge. For micro EDM in RC type power supply alongside main capacitor there is stray capacitance contributed by the electric feeder, the tool electrode holder and work table, and between the tool electrode and workpiece. Stray capacitance contributes in parallel to the installed capacitor and when the installed capacitance is negligible the discharge energy per pulse is determined by the stray capacitance. Thus, in micro-EDM in order to reduce the pulse energy, it is important to minimize stray capacitance between wire and workpiece. The existing method for estimation of stray capacitance requires a voltage and a current probe to be employed for simultaneous acquisition of voltage and current waveform [14,15]. Actual discharge energy is then computed as the product of the two waveforms obtained. While the acquisition of the current waveform can be performed using a contactless probe with negligible inductive loading on the EDM circuit; however, generally a voltage probe is required to be directly connected to the circuit which introduces additional stray capacitance and therefore, may impact the accuracy of the measurement. To resolve the above mentioned issues, this paper aims to provide an analytical model of the electric properties of microEDM plasma for a RC power supply circuit by incorporating the electrical equivalent of plasma into an electrical network of RC power supply circuit having DC source. Detailed analysis is presented in this paper to provide signiﬁcant insight for the changes in the current waveform due to changes in parameters, and to introduce the measurement of stray capacitance technique based on non-linear least square ﬁtting method. Fig. 1. Parallel plate model of micro-EDM plasma. During the discharge process the electrons will have thermal energy of a few eV to bring atoms into excited states and from the collision process dielectric molecules gets dissociated which ﬁnally forms plasma to conduct current with very high current density. Even though the usual RC based micro-EDM circuit is powered by a constant DC power supply, the presence of the large series resistor limits the current ﬂowing into the channel. Most of the power dissipated in the plasma is supplied by the capacitor placed in parallel to the plasma and therefore micro-EDM discharge can be compared to the commonly used capacitive discharges in plasma engineering [17] as opposed to other type of discharge known as inductively coupled plasma discharge where the electric ﬁeld is generated by a time-varying magnetic ﬁeld of transformer action. In capacitive discharge, obviously, the electric ﬁeld results from surface charges on electrodes and charges in dielectric ﬁlling up the gap space. Fig. 1(b) shows the homogeneous model of plasma [16] where the plasma is divided into a central quasineutral bulk of thickness b and space charge sheaths of width s1 and s2. A current i ﬂows across the discharge plates and the plates are separated by a distance d = b+ s1 + s2 and having cross sectional area A. In response to the current ﬂow, a discharge plasma forms between the plates, accompanied by a voltage v across the plates and a power discharge P into the plasma. Assuming that the plasma is in a quasineutral state, it can be considered that almost everywhere the electron density and ion density are equal, i.e. ne n. In this given model it is also considered that the sheath regions are much smaller compared to the width of the bulk plasma; b (s1 + s2). According to this model the plasma impedance is deﬁned as the ratio of voltage and current for current ﬂow in a capacitor given by Eq. (1) [18]. zb ¼ ub 1 ¼ ivC b Ib ð1Þ where, Ub is the voltage across plasma, Ib is the current through the plasma, Cb is the capacitance of the plasma, Cb = ebC0; and C0 is the vacuum capacitance of a capacitor given by C0 = e0A/d. e0 is the dielectric constant of vacuum, eb is the plasma dielectric constant which is given by Eq. (2) [16]. v2pe vðv jvm Þ Electrical equivalent network of micro-EDM plasma eb ¼ 1 The two parallel electrode plates across which the EDM plasma forms is shown in Fig. 1 [16]. Where due to a very high electric ﬁeld strength initially a weakly-ionized channel forms which then rapidly grows from one electrode to the other and results in primary electron avalanche starting from the cathode. Subsequently this forms a streamer as the initiation of a discharge process as could be seen in Fig. 2. In Eq. (2),v is the angular frequency of the oscillation of plasma, vpe electron plasma frequency and nm is the effective electron–ion collision frequency for momentum transfer. Using the value of Cb and eb, ﬁnally the bulk plasma containing two parallel electrodes can be represented by a combination of an inductor (representing electron inertia) in series with a resistor (representing electron– neutral collisions), and a parallel capacitor (representing the ð2Þ Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx 3 Fig. 2. Breakdown mechanisms leading to a spark discharge. Propagation of: (a) the primary electron avalanche; (b) a positive streamer; (c) a negative streamer [29]. electric ﬁeld in the bulk plasma) and could be expressed by Eq. (3) [17]. 1 1 ¼ jvC 0 þ Zb Rb þ jvLb ð3Þ Where, C0 is the vacuum capacitance, Lb is the inductance of the bulk plasma given by Eq. (4) and Rb is the resistance of the bulk plasma given by Eq. (5). Lb ¼ 1 v2pe C 0 Rb ¼ vm Lb ð4Þ ð5Þ In Eq. (4), electron plasma frequency is denoted as vpe, which can be evaluated using Eq. (6); and vm is the effective electron–ion collision frequency for momentum transfer. sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ne e 2 ð6Þ vpe ¼ e0 me Where, me = mass of electron, ne = electron density in plasma, e0 = vacuum permittivity, and e = charge of electron. Now from the above discussion, the network shown in Fig. 3(a) can be considered as the electric circuit equivalent of plasma and can be replaced as the plasma in the electric network of power supply circuit shown in Fig. 3(b). In Fig. 3(b), Rd is the resistance of the discharge line including the resistance of the cable, L is the inductance of the discharge path, C is the capacitance of the installed capacitor including the stray capacitance and R is the resistance of the resistor installed after the DC source. Evaluation of electric components in plasma Evaluation of C0 C0 is the vacuum capacitance of a parallel plate capacitor with an Area of cross section A and a distance between the capacitor d, as shown in Eq. (7). C 0 ¼ e0 A d ð7Þ Table 1 shows values of experimentally obtained electrode gap at spark for Tungsten electrode and SUS-304 workpiece with a simple implementation of RC setup without any gap control and was performed on the universal multi-process machine tool proposed by Rahman et al. [19]. Since, the theoretical analysis and the experimental works of this research is focused on the context of micromachining in the lower dimensional range of micromachining domain, practically the maximum applied voltage can be 100V–110 V and capacitance is 470 pF and the electrodes will be between 20 mm–40 mm diameter. From Table 1 and above argument a fair assumption can be made that the value of d will be between 1.2 mm–6 mm and the range of cross section area A will be a theoretically bounded by the surface area of 20 mm–200 mm diameter plate for the range of voltage and capacitance settings. Fig. 4(a) shows plot of C0 at different gap distance d and ranging between surface area of 20 mm–200 mm electrode diameter. The maximum obtained value of plasma capacitance is only 0.2782 pF in the simulation range which is even 20–30 times smaller compared to stray capacitance of the system and electrode holder [14]. Practically, the value of C0 is even smaller as during the discharge the plasma only forms over a small portion of the electrode and not the common cross section on the electrodes facing each other. Descoeudres et al. [20] reported that the contact surface between the plasma and the electrodes can be estimated to be equal from measurements of crater diameter, which was 10 mm. Their experiments were conducted at a much higher power settings compared to the usual power settings for micro-EDM [14,15]. where the crater sizes ranges from 2.2 mm to 5 mm. Practically, since the plasma temperature in micro-EDM is extremely high and much higher than the boiling temperature of SUS-304, electrode plasma interface diameter can never be larger than the crater size as at the interface of plasma and electrode deﬁnitely erosion of metal will occur rendering the electrode plasma interface diameter to be slightly smaller or equal to the crater diameter, r [20]. Therefore, it can be assumed that the interface diameter is 0.1 mm–0.2 mm smaller than the crater Table 1 Gap width at different voltage and capacitance. Fig. 3. (a) Electrical equivalent circuit of plasma, (b) electrical network of RC power supply with a DC source having micro-EDM plasma replaced by the equivalent circuit. Voltage (V) Capacitance (pF) Electrode gap (mm) 60 60 100 100 Stray (11 pF) 470 Stray (11 pF) 470 1.20 3.30 3.30 5.90 Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 4 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx diameter and can be estimated to be in between 2 mm–5 mm for this analysis, which was mentioned earlier. Fig. 5(a) shows the plot of plasma inductance at varying electrode diameter and electron density of plasma at 1.2 mm electrode gap and Fig. 5(b) shows the same at 6 mm electrode gap. The result shows that the plasma inductance value ranges from 0.65 pH–67.8 pH. Even with a power supply circuit conﬁguration with the minimum wire length of 10 cm, the inductance contributed by the wire is 0.1090 mH for tin plated copper stranded AWG20 wire [23] which is about 1600 times larger than the inductance of this micro-sized plasma and therefore, the inductance of the plasma can also be neglected. Evaluation of Rb Eq. (5) states the value of plasma resistance Rb, and combining Eqs. (4), (5) and (6), Eq. (9) can be obtained as follows Rb ¼ vm Lb ¼ vm v2pe C 0 ¼ me vm d ne e2 A ð9Þ Now, from the deﬁnition of resistivity, d me vm d R b ¼ rb ¼ A ne e2 A ð10Þ Therefore, the plasma resistivity (rb) can be stated as the following in Eq. (11) rb ¼ m e vm ne e2 ð11Þ Fig. 4. (a) Plot of plasma capacitance vs electrode area at different electrode gap; (b) the effective area contributing to the capacitance is taken as the electrode plasma interface diameter of 2 mm–5 mm. Where, vm is the effective electron–ion collision frequency in quasineutral plasma. The electron–ion collision, vm can be computed from Coulomb force and is given by Eq. (12) [17]. diameter. Fig. 4(b) shows the plot of C0 at different gap distance d and ranging between surface area equalling to the electrode plasma interface diameter of 2 mm–5 mm and this resulted in a capacitance value of 1.7385 1004 pF making at approximately 35,000 times smaller than the stray capacitance. Therefore, it can be concluded that C0 in micro-EDM plasma with the electrode dimension and electrode gap at spark mentioned above can be really small and in analyzing the electric interaction with the capacitance C0 can be ignored. vm ¼ Where, V is the characteristic velocity of a Maxwell–Botzmann distribution and can be considered as equal to the mean thermal velocity ðvth Þ given by Eq. (13) [30] Evaluation of Lb Where, T is the temperature of plasma in Kelvin and Botzmann’s constant is denoted by kB. Now, replacing Eq. (13) in Eq. (12) the following, Eq. (14), can be obtained. From the deﬁnition of inductor it is known that an inductor will try to resist any change in the ﬂow of current. Under an electric ﬁeld the electrons in plasma gains directional kinetic energy and any changes in the ﬂow of current will be resisted by the inertia of the particles; therefore, it can be said that the inductance of plasma is the ensemble of the inertia of particles and is related to the characteristic frequency at which the electrons oscillate among the heavier immobile ions. This electron plasma frequency is related to electron density ne and given by Eq. (6). From Eqs. (4), (6) and (7), Eq. (8) can be obtained. 1 dme Lb ¼ 2 ¼ vpe C0 Ae2 ne ð8Þ Descoeudres et al. [21] reported that electron density at the beginning of the discharge is 2 1018 cm3 and electron density reported by Nagahanumaiaha [22] is 3.5 1018 cm3. For the simulation of inductance value the electron density value can be considered to be bounded in a range of 1 1018 cm3 to 3.5 1018 cm3. Concerning the surface area contributing to the inductance of the plasma is also given by the electrode plasma interface ne e4 ð12Þ 16Pe20 m2e V 3 V ¼ vth ¼ 8kb T Pme 12 ð13Þ 1 vm ¼ ne e4 P2 1 2 ð14Þ 3 ð4e0 Þ2 me ð8kb T Þ2 Now, replacing vm in Eq. (11) the following plasma resistivity (rb) can be obtained: 1 rb ¼ 1 m e vm m2e e2 P2 ¼ 1 3 ne e2 ð4e0 Þ2 m2e ð8kb T Þ2 ð15Þ This estimation of Coulombic collision was based on the assumption that the deﬂection angle after collision is large; but a more detailed treatment leads to Spitzer resistivity given by Eq. (16) [17]. 1 rb ¼ 1 m e vm m2e e2 P2 ¼ ln A 3 2 ne e ð4e0 Þ2 ð8kb T Þ2 ð16Þ Where, the correction factor ln(L) ln(lD/bp/2) = ln(4pND), called the Coulomb logarithm that is related to the number of particles ND in a Debye sphere and from our assumption ND = 1, resulting in ln Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx 5 Fig. 5. (a) Plot of plasma inductance at various electron density and electrode plasma interface diameter at 1.2 mm electrode gap; (b) and at 6 mm electrode gap. (L) 2.531, which also shows good agreement to the value of ln (L) 2.2 obtained by Descoeudres et al. [20]. Descoeudres et al. [20] reported from their observation that the plasma temperature reaches 8110 K and remains constant throughout the discharge; and Nagahanumaiaha [22], reported that plasma temperature ranges from 5167 K to 7889 K with an average plasma temperature of 6170 K. Therefore, it was estimated that the plasma temperature remains in a range of 5167 K–8110 K to compute a possible range of plasma resistivity which is shown in Fig. 6. Now, again consider that the electrode plasma interface diameter is 2 mm–5 mm for this analysis, as has been mentioned earlier. Fig. 7(a) shows the computed resistance at different plasma temperature at 1.2 mm electrode gap and at 6 mm electrode gap shown in Fig. 7(b). It can also be assumed that crater diameter ranging around 2.2 mm can only be obtained at very small energy settings and at those settings the required electrode gap is in the range of 1.2– 1.5 mm. Therefore, in Fig. 7(a) the resistance value shown in higher electrode plasma interface diameter has been ignored and can only focus was between 2 mm–2.5 mm interface diameter based on the earlier assumption that the interface diameter is 0.1 mm–0.2 mm smaller than the observed crater diameter. In this range of electrode plasma interface diameter the plasma resistance Rb varies between 25 V–80 V (with mean around 50 V). Similar arguments can be placed for the case of a 5 mm crater size which can only be obtained at larger capacitance and voltage settings; and that will yield a larger electrode gap, like 6 mm for spark. At 5 mm electrode plasma interface diameter and 6 mm electrode gap it can be seen from Fig. 7(b) that the plasma resistance Rb also varies in the range between 30 V–76 V (mean 50 V). Therefore, it can be assumed that micro-EDM plasma resistance remains between 25 V–80 V, with a mean around 50 V for electrode gap within 1.2 mm–6 mm and for obtained crater diameter between 2.2 mm–5 mm. Analysis of the RC power supply electric network involving micro-EDM plasma Fig. 6. Plasma resistivity at different temperature. From the evaluation of the equivalent electric network of plasma, the inductive and capacitive load of micro-EDM plasma Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 6 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx Fig. 7. (a) Plot of plasma resistance at different temperature and electrode plasma interface diameter at 1.2 mm electrode gap; (b) and the same at 6 mm electrode gap. can be essentially ignored and consider only the resistive network. From the evaluation of plasma resistivity, rb it can be observed that the plasma resistivity is only dependent on plasma temperature and not on electron/ion density of the plasma. Observation from Descoeudres et al. [20] and detailed theoretical analysis of microEDM plasma by Dhanik and Joshi [24] indicated that the plasma temperature can be considered to remain constant throughout the discharge process — and therefore, the resistivity can be considered to remain constant. The electrode plasma interface diameter was reported to grow slightly during the discharge by Descoeudres et al. [20] but for very ﬁne short pulse ranging between 20 ns–100 ns — it can be considered that the electrode plasma interface diameter remains constant; and from this assumption the plasma can be simpliﬁed to a resistive network with constant resistance during the discharge. This will allow simplifying the electric network shown in Fig. 3(b) to the network shown in Fig. 8. Let’s, consider that the voltage across the capacitor is v, and the current ﬂowing to node marked A is i0 and the current ﬂowing out from node A to the plasma is i. Now, applying Kirchhoff’s voltage law (KVL) in loop 2 Eq. (17) can be obtained, applying KVL in loop 1 Eq. (18) can be obtained and applying Kirchhoff’s current law (KCL) in node A Eq. (19) can be obtained. di v ¼ Rd i þ L þ Rb i dt E v Ri0 ¼ 0 i ¼ i0 C dv dt ð18Þ ð19Þ Now, combining Eqs. (18) and (19) to replace i0 Eq. (20) can be obtained i¼ Ev dv C R dt ð20Þ ð17Þ Fig. 8. Simpliﬁed electrical network of plasma with the power supply network (RC circuit with a DC source). Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx Differentiating Eq. (20), Eq. (21) can be found 2 di d v 1dv ¼ C 2 dt R dt dt Now, replacing i and di/dt in Eq. (17) ! 2 Ev dv d v 1dv Ev dv C C þL 2 þ Rb v ¼ Rd R dt R dt R dt dt ð21Þ s1;2 ¼ Rb L 1 þ RC 2 ﬃ vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u( ) 1u Rb 1 2 1 Rb t þ þ 4 2 RC LC RLC L ð24Þ ð26Þ Now, the 3 cases of the solution exists, namely overdamped for real distinct roots, critically damped for real repeated roots and underdamped for complex conjugate roots. Investigating the discriminant will allow to analyze the type of solution that is required to be computed for some practical values of the circuit element. Let, R = 1 kV, L = 0.1090 mH; and C = 53 pF for this investigation which are some of the values reported by Masaki and Kuriyagawa (2010a). By taking the 1st and 2nd derivative of the discriminant with respect to Rb given by Eq. (26), Eqs. (27) and (28) could be obtained dD 2 2 ¼ R dRb L2 b RLC ð30Þ Solution of underdamped case The characteristic equation of the 2nd order differential equation given by Eq. (24) is given by the equation in (25) and the solutions are given by Eq. (26). Rb 1 1 R þ b ¼0 þ ð25Þ sþ s2 þ RC LC RLC L s ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 R þ b P2 Q¼ LC RLC ð23Þ Now, in Eq. (23) it can be observed that both Rd and Rb come as a summed term. The resistance of AWG20 tin plated copper stranded wire is about 34 mV/m and the resistance contributed by tungsten electrode system is around another 20 mV. Therefore, even for a 1 m long wire with a 32 mm electrode in the discharge path will make Rd = 54 mV; and thus it can be considered that Rd + Rb Rb to obtain the following: 2 d v Rb 1 dv 1 R R þ þ b v¼ b E þ þ 2 RC dt LC RLC L RLC dt underdamped, overdamped and critically damped cases of the differential equation given by Eq. (26) the following equation for voltage v and current i could be obtained (where, P and Q are given by Eqs. (29) and (30)). 1 Rb 1 þ ð29Þ P¼ 2 L RC ð22Þ Rearranging Eq. (22) and dividing both the sides of the equation by LC following equation can be obtained: 2 d v Rd þ Rb 1 dv 1 R þ Rb R þ Rb þ þ d þ E þ v¼ d 2 RC dt LC L RLC RLC dt 7 ð27Þ v¼E 1 Rb P Rb E ePt cosQt þ sinQt þ Q R þ Rb R þ Rb ! 2 Rb Ev Pt P þ Q sinQt þ i ¼ CE 1 e R R þ Rb Q ð31Þ ð32Þ Solution of overdamped case v¼ Rb E 1 1 ðP Q Þ þ 1 eðPþQ Þt þ ðP Q ÞeðPQ Þt þ 1 R þ Rb 2Q 2Q ð33Þ 2 3 P2 Q 2 Rb E 4 1 ðPþQ Þt ðPQ Þt 5 e ðP Q Þ þ 1 ðP Q Þe i ¼ C R þ Rb 2Q 2Q þ Ev R ð34Þ Solution of critically damped case v¼ Rb E 1 ePt PePt R þ Rb i ¼ C Rb E Ev PePt ð1 þ PÞ þ R þ Rb R ð35Þ ð36Þ Model validation Validation of the model by varying l 2 d D dR2b ¼ 2 L2 ð28Þ By setting Eq. (27) equal to 0 and since Eq. (28) is always positive, the minima of the discriminant of Eq. (26) is when Rb = 2 V and at that value Eq. (26) results in complex conjugate solution 1.8608 1007 j4.1605 1008 and demonstrates to be an underdamped case. Similarly, for values of Rb computed in section Evaluation of Rb to be between 25 V–80 V the solution yields a complex conjugate root. On the other hand, when the value of Rb changes to 93 V the solution turns to and overdamped having real distinct root. Moreover, for sweeping the equation between wide range of R and L values it is required to obtain all of the 3 solutions of the differential equation given by Eq. (24). Solving the Masaki and Kuriyagawa [14,15], added varying length of wire in the discharge loop to experimentally evaluate the effect of varying wire length (and essentially the effect of inductance, L) on discharge current waveform. In their experiment, the authors varied the wire length from 0.1 m (which is the minimum length required to connect the spindle head (tool electrode) to the capacitor) to 15 m and experiments were conducted at two different capacitance values: stray capacitance and 53pF. In this section, the proposed model of micro-EDM electric network deﬁned by the Eqs. (31)–(36) (which are the solutions of the differential Eq. (24)) involving the plasma impedance will be validated using experimental results reported by Masaki and Kuriyagawa [14,15]. Table 2 shows the condition used for easy Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 8 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx Table 2 Conditions and setting values for obtaining current waveform of varying L (adapted from Masaki and Kuriyagawa [14,15], except the equivalent inductance value which was not computed in the original report). Item Conditions and value Voltage [V] Capacitor capacitance [pF] Resistance [kV] Cable length [m] Equivalent inductance [mH] Machined depth [mm] Dielectric Tool electrode Workpiece material 60 6,47 + 6 1 0.1, 0.5, 1.1, 2, 3.9, 7.6, 15 0.1090, 0.7059, 1.7265, 3.3782, 7.1084, 14.8663, 31.3811 10 EDM oil (CASTY-LUBE EDS) Tungsten 32 mm diameter Stainless steel SUS304 referral. Masaki and Kuriyagawa [14,15] only reported the length of the wire used in the experiment and the experimentally obtained current waveform. For the computation of the model deﬁned by Eqs. (31)–(36), the inductance value of the wire length is required to be computed using Eq. (37) [23]. The computed inductance value is also shown in Table 2 [23]. 2l 3 ð37Þ L ¼ 0:002l ln dw 4 Where, dw is radius of the wire in cm and l is the length of the wire in cm and the obtained value of L is in mH. In addition to the minimum wire length of 10 cm to conﬁgure the discharge circuit, as reported by Masaki and Kuriyagawa [14,15], there is also dead length of wire which has to be added in the return path of the current after discharge which contributes to additional inductance. Considering the structure of the equipment used by Masaki and Kuriyagawa [14,15] (the distance between the connections on the mandrel and XY table is approximately 20 cm) and travel length of both X and Y axes are 5 cm it can be considered that a minimum of additional 25 cm of wire is required to conﬁgure the return path of the current (this required minimum length was also conﬁrmed from personal communication with Masaki and Kuriyagawa [14,15]). Inductance is also contributed by the electrode, feeding system and workpiece. Considering a 3 cm long 0.300 mm diameter tool electrode — the contributed inductance should be around 0.0314 mH (this is about 35% of the contribution by 10 cm wire). Therefore, it can be assumed that the system had additional inductance equivalent to a total of 30 cm wire length (0.3929 mH) in the return path of the discharge current contributed by the wire in the return path, the tool electrode and other component of the feeding system. In order to validate the proposed model, computer simulation was performed using Matlab using the Eqs. (31)–(36). The program was written to compute the determinant equation based on the input R, L and C value to identify the appropriate solution case (underdamped, overdamped and critically damped). Simulation was performed at 3 different plasma resistance values — taking Rb = 40 V, 50 V and 60 V, keeping 50 V as the mean. The current waveform obtained from the simulation and the experimental waveforms of Masaki and Kuriyagawa [14,15] are compared in Fig. 9. Two important parameters of current waveform are the pulse width and peak current, which are compared between experimental and simulation results (Fig. 9). Pulse width is deﬁned by the time between the beginning of a discharge to the ﬁrst zero crossing of the current waveform and peak current is deﬁned by the peak value of the current over the discharge duration. The experimental current waveform for 0.1 m shows smaller peak current (300 mA) compared to the value obtained from the model (415 mA), but considering micro-EDM as a stochastic process and the presence of a debris particle in gap space might change the conductivity of plasma which may result in quite a signiﬁcant difference in peak current as well as in waveform. Comparing Figs. 6 (a) and 10 (a) of Masaki and Kuriyagawa [14,15], the same can be concluded as at the same setting one proﬁle shows a peak at 300 mA and the second one shows a peak at 400 mA. Moreover, usually the peak of the current proﬁle shows a well formed peak as could be seen in Fig. 10(a) of Masaki and Kuriyagawa [14,15] as opposed to the valley shaped peak that could be seen in Fig. 6(a) which indicates that the peak value of proﬁle in Fig. 10(a) is more appropriate. Another factor that might have contributed to the little difference is due to the fact that the current probe used for performing these experiments was band limited between 1.2 kHz to 200 MHz (Tektronix Current Probe — Model CT2) which signiﬁes that a very sharp movement happening in less than 5 ns will display an averaged response in the oscilloscope. Therefore, some variation with experimental data is expected but the congruency between the overall waveform and the changes observed due to varying L demonstrates excellent ﬁt of the theoretical value to the experimental data. Masaki and Kuriyagawa [14,15] reported that the current waveform generated at 15 m wire length was not showing clear waveform to measure pulse width and peak current. This phenomenon could be explained well using this model if it is assumed that given the experimental settings and inter-electrode gap if the steady state current drops below 30–40 mA the discharge stops and Rb becomes an extremely large resistor until the next breakdown, whereas if the steady state current remains above 50 mA then continuous arc discharge takes place — then. This makes a fair assumption based on the fact that in plasmas energy is dissipated in inelastic collisions, including the ionization events which maintain the plasma, and excitation collisions which lead to photon emission that makes the plasma visible; and electron energy is also dissipated in elastic collisions with the background neutral dielectric which causes the heat to get transferred to the ambience formed by dielectric and electrodes, thus continuous power to the plasma is needed to maintain it. Fig. 11 shows the simulated waveform at 15 m wire length and it can be observed that the slowly varying waveform did not cross below 30–40 mA at steady state and this caused a continuous power ﬂow to the plasma to keep it at arcing condition thus the peak and the pulse width were not identiﬁable. Validation of the model from discharge energy In the case of RC type power supply shown in Fig. 8, the repetition of the charging and discharging occurs in which capacitor C is charged through resistor R and discharged between the electrode and workpiece and therefore, the energy deposited in the gap from the spark is commonly computed by the energy that can be stored in the capacitor which is given by 1/2CV2 [25]. But, this Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx 9 Fig. 9. Showing experimentally obtained (left column) [14,15] and simulated current waveform at 3 different Rb values (40 V, 50 V, 60 V). Observed peak current and pulse width values are plotted in Fig. 10. Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 10 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx Fig. 12. Comparison between discharge energy computation methods. Fig. 10. Comparison between experimental and theoretical values for 53 pF and 6 pF capacitance of (a) discharge peak current at varying wire length and (b) discharge current pulse width at varying wire length. The model shows excellent agreement to both the data validating the model. The theoretical model deviates between 4%–7% from the 1/2CV2 method of computation, which is due to the fact that the model accounts for the power imparted to the plasma directly from the DC source during the discharge. Comparing to the experimental values, both the values obtained from 1/2CV2 method and values obtained using this proposed model ﬁt nicely at smaller discharge energy; but at higher energy both the values are overestimated from the experimentally obtained result. This could potentially indicate that the particular discharge captured was not from a fully charged capacitor, or it could even deviate from the assumption that the electrode plasma interface diameter remains same throughout the discharge — which may not be the case for larger pulse width; meaning that the plasma resistance was reducing gradually due to the slow expansion of interface diameter and thus less heat was deposited in the gap. But, this argument requires further investigation. assumption may not hold true always as the discharge can be from a partially charged capacitor and as well as for a small power would be supplied by the main DC source through the charging resistor R to the plasma during the discharge. Masaki and Kuriyagawa [14,15] proposed that discharge energy can be also measured by obtaining both the voltage waveform and current waveform and then multiplying the area under both the curves (since, power P(t) = V (t) I(t)). The proposed model given by Eqs. (31)–(36) has been used to compute the discharge energy in a single discharge from the theoretically computed voltage and current waveforms. Fig. 12 compares between the discharge energy obtained from the theoretical computation, experimental data of Masaki and Kuriyagawa [14,15] and the discharge energy obtained by computing 1/2CV2. Masaki and Kuriyagawa [14,15] performed experiments to observe the effect of supply voltages at 40 V and below on peak discharge current. The theoretically computed value by using this proposed model at 60 V or below did not show good ﬁt to the experimental results for values of voltage below 60 V as could be seen Fig. 13 (red line). This evaluation was done using Rb = 50 V which has been computed with the assumption that the value of electrode plasma interface diameter is 2 mm–2.5 mm (Section Evaluation of Rb). But, practically for voltages lower than 60 V the assumptions on diameter of electrode plasma interface needs to be corrected as the crater size changes Fig. 11. Shows that the theoretical pulse waveform remains above 50 mA which may cause a continuous arc discharge. Fig. 13. Plasma resistance for electrode plasma interface diameter 1 mm (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.). Validation of the model at lower DC supply voltage and at higher discharge energy Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx 11 Fig. 14. Comparison between experimental and theoretical value of peak current at different voltage settings. signiﬁcantly at such low voltage settings. Masaki and Kuriyagawa [14,15] observed that the crater size became 1.22 mm for 30 V input voltage. Therefore, the electrode plasma interface diameter can be considered as 1.0 mm (as it has been assumed that the electrode plasma interface diameter is slightly smaller than the crater size). Using plasma electrode interface diameter as 1.0 mm, plasma resistance was recomputed to be 165 V–325 V (with mean around 250 V) for the model (Fig. 13). With this corrected assumption, the model yielded good agreement with experimental ﬁndings at lower voltages (Fig. 14). Using plasma resistance value 250 V shows better agreement than the computation at 50 V which is shown in Fig. 14 as well. At the same time, this also needs to be observed that the model predicts a linear relationship at different voltages and peak current while the experiment indicates a sort of exponential relationship. Furthermore, while the calculation based on corrected assumption obtained better ﬁt with the experimental observation for lower voltages it deviated from the peak current that was observed at 60 V. This actually further establishes and validates the theoretical analysis that the model is based on the plasma resistance. In the mode value of plasma electrode interface diameter is required as an input to the model and is estimated from the crater size. Therefore, the value of inter-electrode gap and plasma electrode interface diameter (given by the crater diameter) plays a very important role in the understanding of micro-EDM energy discharge characteristics and interaction with plasma. The capability of the proposed model was further explored by comparing the theoretical result to experimental results published by Mahardika and Mitsui [26] which was done at higher voltage and larger capacitance settings. Their experimental conditions were: Supply voltage V = 110 V, C = 3300 pF, R = 1000 V and during their experiments they used another additional voltage probe (Tektronix P6109B) for taking voltage reading which added additional inductance of approximately 0.288 mH (L = 25 cm, dw = 0.075 cm). From the experimental results of Han et al. [27] it can be observed that the crater size obtained from this voltage and capacitor settings is about 12 mm on tungsten and tungsten carbide workpiece. Using this assumption the plasma resistance was recomputed to be between 5 V–10 V. Fig. 15(a) shows the experimentally obtained pulse proﬁle and the simulated pulse proﬁle is shown in Fig. 15(b) where good agreement between the pulse width (175 ns experimental value; simulated 165 ns–171 ns, mean 168 ns) and the pulse peak (experimental value 4.9 A; simulated 4.7 A–5.6 A, mean 5.1 A) can be observed. Observation on the current waveform generated by the proposed model As the proposed model investigates into the interaction between the micro-EDM power supply and micro-EDM plasma it can be used for elucidating the theoretical relationship of different circuit parameters and how that may change the energy discharged on the workpiece by a spark. In this section the effect of varying R on the pulse waveform will be analyzed which will lead to the selection of an appropriate value of R for micro-EDM power supply circuit to be developed. Effect of varying voltage V, Fig. 15. Current waveform (left Figure: a) [26] and simulated value at C = 3300 pF, V = 110 V (right Figure: b). Excellent match of pulse width (175 ns experimental value; simulated 165 ns–171 ns, mean 168 ns) and the pulse peak (experimental value 4.9 A; simulated 4.7 A–5.6 A, mean 5.1 A) can be observed. Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 12 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx inductance L and capacitance C on current waveform will also be observed from the model which will provide sufﬁcient background understanding for selection of these parameters during an experiment for desired output. This model can also be used for obtaining stray capacitance and inductance of the power supply circuit contributed by obtaining a current waveform and then using non-linear curve ﬁtting of the current waveform to the mathematical model. Effect of varying resistor R and selection of R for micro-EDM power supply Resistor R, shown in Fig. 8, plays a very critical role in designing the micro-EDM RC power supply. The main role of R is to limit the supply of current to the capacitor as well as to the plasma contained in the gap immediately after a discharge such that after the spark the discharge stops due to the lack of necessary ﬂow of current required to maintain the plasma. This energy is needed to maintain the plasma as there is loss from inelastic collisions, ionization events which maintain the plasma, energy dissipated in the form electromagnetic radiation loss ranging from visible light to other frequencies of electromagnetic waves including X-rays, and heat transferred to the background. Therefore, a large R is preferred from this concern to minimize arcing current. On the other hand after one discharge, as soon as the plasma is switched off, the best condition is to have the capacitor fully charged for the next discharge. But the charging time of the capacitor will be based on the time constant formed by the capacitor and the resistor. For a practical settings of micro-EDM experiment, C = 100 pF capacitor, V = 60 V and R = 400 V, 1 kV, 2 kV will have time constant t = 10 ns, 100 ns and 200 ns respectively. Essentially this will result in charging 63% of the capacitor and in most part of this period the capacitor is not charged enough to make the spark happen. From this perspective smaller settings of R will allow the capacitor to get quickly charged. Therefore, due to this contradictory relationship the value of R needs to be optimized such that it provides a balance between minimizing charging time and reducing the chance of arc. This is usually done by performing experiments as the fastest machining time resembles the optimal setting. In arcing condition the machine requires to perform back and forth motion repeatedly to stop the short condition which extends the machining time whereas, in slow charging case the machine takes longer time simply because of the reduction in spark per second. Experiments were conducted on the universal multi-process machine tool using the machining conditions shown in Table 3 and the machining time is shown in Fig. 16. The machining time indicates 1 kV gave the best machining time whereas 400 V took signiﬁcantly longer machining time and at 2 kV the machining time was slightly longer than for 1 kV, even though statistically the difference was not signiﬁcant (the same experiment was performed 3 times to obtain experimental testretest repeatability). Fig. 16. Machining time of 1 mm slot by WEDM using R = 400 V, 1 kV and 2 kV. The error bars are one SD (n = 3). The above experimental results could be similarly observed for optimizing R for micro-EDM RC circuit by computing the waveform proﬁle at R = 400 V–2 kV using this proposed model, as could be seen in Fig. 17. The current waveform up to R = 600 V had no zero crossing and remained above 100 mA at 60 V supply voltage beyond the ﬁrst 90 ns which can be considered as large enough current to maintain the plasma. From R = 700 V to R = 2 kV it had zero crossing within the ﬁrst 60 ns which may indicate that the power from the plasma was cutoff within this time and thus arcing was minimized. Therefore, practically the power supply circuit for micro-EDM should be designed with resistance R > 700 V. At resistance values above 900 V it can also be observed that the negative dip was below 50 mA compared to those at 700 V and 800 V. Given that micro-EDM is a stochastic process with signiﬁcant amount of process noise and presence of debris in the gap space changes the waveform — it can be concluded that a value of above 900 V will provide sufﬁcient safety margin in avoiding continuous arcing in the circuit. Effect of inductance on the current waveform In Section Validation of the model by varying l, as part of the validation of the model, current waveforms at different wire length in order to vary the inductance were generated using this model and was compared with the experimental data shown in Fig. 9. In this section, changes in current waveform with varying inductance will be further discussed. It can be observed in Fig. 18 that the peak current changes signiﬁcantly from 660 mA to 530 mA and the pulse becomes broader from 20 ns to 30 ns (ﬁrst zero crossing of current after the beginning of a discharge) for a change of inductance from Table 3 Machining conditions for WEDM experiments varying R. Item Conditions and value Setup used Feedrate Voltage [V] Capacitor installed [pF] Resistance [V] Estimated inductance L [mH] Machined slot size [mm] Dielectric Tool electrode Workpiece material WEDM 2.0 mm/s 60 100 pF 400, 1000, 2000 1.9043 1.0 Total EDM 3 oil Tungsten wire (AgieCharmilles) Stainless steel SUS304 Fig. 17. Current waveform computed theoretically at R = 400 V–2kV (C = 100 pF, L = 1.9043 mH, V = 60 V, plasma resistance Rb = 50 V). Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx Fig. 18. Current waveform at varying inductance value at 0.2457 mH, 0.5469 mH and 1.9043 mH (C = 100 pF, R = 1 kV, V = 60 V, plasma resistance Rb = 50 V) for equal energy discharged in all 3 proﬁles around 190 nJ. 0.2457 mH (l = 0.20 m; AWG20 wire) to 0.5469 mH (l = 0.40 m; AWG20 wire). At L = 1.9043 mH (l = 1.20m; AWG20 wire) the pulse becomes much broader having a width of around 50 ns and the pulse peak changes to 360 mA. But the computed energy under all these three waveforms remains the same at around 190 nJ. The similar effects of varying inductance by varying the length of the wire can also be observed in Fig. 9. Masaki and Kuriyagawa [14,15], observed that by increasing the wire length, the craters on the surface became larger, shallower and ﬂat; and therefore, this can be applied to improve the properties of the machined surface. One possible explanation to this can be provided assuming that the disk heat source based electro-thermal model is more appropriate at very small energy spark compared to the point source head model [3] and therefore, over longer spark duration but with the same amount of energy delivered — there is sufﬁcient time for the heat to get conducted and material removal by melting action is higher. On the other hand with very short pulse — there is rather less time for conduction and due to higher energy density removal by evaporation is increased where the heat is lost to the dielectric rather quickly. However, this argument requires further investigation. But, this can be stressed from the experimental observation that variation in L can be instrumental in changing surface properties of machined workpiece. Larger L increases machining time as the pulse gets larger but switching L can be an option where the initial machining is done with smaller L value and the ﬁnishing can be obtained by larger L value. 13 Fig. 19. Current waveform at varying capacitance (C = 50 pF, 100 pF, 200 pF) (V = 60 V, R = 1 kV, L = 1.9043 mH, plasma resistance Rb = 50 V). shown in Fig. 15 obtained at 110 V but a much higher capacitance value which signiﬁcantly changed the pulse width to 165 ns–171 ns and the pulse peak to 4.7 A–5.6 A indicating a change in both pulse width and peak. On the contrary, changing the supply voltage V (60 V, 80 V and 100 V) did not change the value of pulse width (remained at 50 ns) but signiﬁcant change in the pulse peak was observed (345 mA, 460 mA, 575 mA respectively) as could be seen in Fig. 20. This is also to be noted that the energy to be discharged in a pulse changes proportionally to the square of the input voltage. Therefore, it can be inferred from the earlier discussions in this chapter that higher input voltage will create a deep crater and will have increased proportion of removal by vaporization. Therefore, for rough machining higher supply voltage value around 110V– 120 V is preferred and for ﬁnal ﬁnishing cut the voltage needs to be reduced to 60 V. Non-linear curve ﬁtting for estimation of stray capacitance and inductance Stray capacitance determines the amount of minimum energy spark size that a circuit is able to provide and therefore it is desired to have the equipment and power supply to be designed with minimum stray capacitance. Depending on the length of the cable stray capacitance will eventually not be negligible [28]. Existing methods for estimation of stray capacitance depend on the fact that the discharge current pulse width depends on the capacitance which is a rather indirect and inaccurate inference for Effect of capacitance C and supply voltage V on the waveform Varying capacitance C and V increases the amount of energy stored in the power supply (as Ed = 1/2CV2). The effect of C can be observed from the simulation of pulse waveform shown in Fig. 19 with 3 capacitance values of C = 50 pF, C = 100 pF and C = 200 pF. Pulse peaks were at 265 mA, 345 mA and 440 mA; and pulse width was found to be 37 ns, 50 ns and 70 ns respectively (which are given by the ﬁrst zero crossing of current after the beginning of a discharge). It can be observed from the current waveform that both the peak and pulse width changed due to the change in capacitance which is similar to the change in inductance L. This is due to the fact the C actually changes the impedance and thus modulates the frequency of the waveform and at the same time there is higher energy stored which forces the pulse peak to be higher. Experimentally this was also observed in the pulse waveform Fig. 20. Current waveform at varying supply voltage (V = 60 V, 80 V, 100 V) (C = 100 pF, R = 1kV, L = 1.9043 mH, plasma resistance Rb = 50 V). Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 14 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx measurement of stray capacitance. Masaki and Kuriyagawa [14,15] proposed that the measurement of stray capacitance can be performed from actual discharge energy by observing the current and voltage waveform and computing their product. This requires a voltage probe to be connected to the circuit for simultaneous acquisition of a voltage and a current waveform which introduces additional stray capacitance and therefore, incurring inaccuracy in its measurement. During the computation of stray capacitance, Masaki and Kuriyagawa [14,15], computed the total discharge energy to be 31 pF and the system was installed with a 10 pF capacitor. During the measurement they used a voltage probe with 13–17 pF capacitance and from this they concluded that the system had a stray capacitance between 4–8 pF with a mean value of 6 pF. This clearly indicates the inaccuracy in the measurement of stray capacitance. Another alternative solution for stray capacitance measurement is to obtain the current waveform alone (without installing a voltage probe) from inductively coupled current probe (inductively couple probe does not have any loading or minimal loading effect on the power supply network) and then performing non-linear curve ﬁtting of the waveform with this model (given by Eqs. (31) and (32)). The green proﬁle in Fig. 21 shows one such plot obtained from the system using only a current probe. As there is sinusoidal oscillation in the current waveform, the underdamped case was taken as the solution for ﬁtting. Non-linear curve ﬁtting was done to obtain the value of C in the equation and the input values were R = 1000 V; L = 0.5019 mH (total 10 cm wire for the capacitor to tool electrode and 30 cm for workpiece to capacitor in the return path; explained in Section Validation of the model by varying l); Rb = 50 V, V = 60 V. The experimentally obtained current waveform provided inputvalue for the current at stray capacitance. The ﬁtting was performed using custom written Matlab program and the non-linear ﬁtting was done using Matlab routine lsqcurveﬁt (lsqcurveﬁt, R2012a). This routine performs non-linear ﬁtting to obtain least square error and ﬁnds coefﬁcients x that best ﬁt the equation of the model (Eq. (32)) and the optimization is done by computing the following equation: m 1X min 1 2 k F ðx; xdataÞ ydata k22 ¼ ðF ðx; xdatai Þ ydatai Þ x 2 2 ð38Þ 1 Where, input data isxdata, and the observed output is ydata; and xdata and ydata are vectors of length m and F (x, xdata) is a vectorvalued function (Eq. (31) in this case). Large scale optimization was used as the ﬁtting option with an initial guess of C = 50 pF. The ﬁtting program returned the value of stray capacitance based on the best ﬁtted curve. Fig. 21. Non-linear curve ﬁtting of the current waveform for computing stray capacitance. For ﬁtting input to the model was R = 1000 V; L = 0.5019 mH; Rb = 50 V, V = 60 V and initial guess of C = 50 pF (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.). Fig. 22. Non-linear curve ﬁtting of the current waveform for computing the value of inductance. R = 1000 V, C = 39 pF, Rb = 50 V, V = 60 V actual L = 0.5776 mH. With an initial guess of L = 5 mH, the model computed the value of L = 0.58936 mH. The red proﬁle in Fig. 21 has been obtained from the model of Eq. (32) computed using the value of stray capacitance, C, obtained from curve ﬁtting. After 18 iterations of computation the model estimated the stray capacitance to be 6.58 pF which matches well with the experimentally reported value of 6 pF by Masaki and Kuriyagawa [14,15]. Similar ﬁtting can also be performed for obtaining any other parameters of the proposed model. Non-linear curve ﬁtting was performed with another current waveform (Fig. 22) for computing the value of inductance. With an initial guess of L = 5 mH and input values of R = 1000 V, C = 39 pF, Rb = 50 V and V = 60 V the model computed the value of L = 0.58936 mH (actual L = 0.5776 mH). Limitations Although this work has generated many interesting and new ﬁndings, it has also opened new questions where further investigations are necessary to enhance our understanding of micro-EDM plasma and process. Firstly, this proposed analytical model is only applicable to micro-EDM process with electrode diameter between 20 mm–40 mm and maximum voltage settings are 100–110 V. Assumptions that plasma capacitance and inductance can be considered as negligible are limited within this scope and for single pulse discharge. Beyond the condition of single pulse discharge, this model is also not capable of explaining simultaneous multiple discharges, the impact from the presence of large debris within the electrode plasma interface, arcing and short circuit conditions, etc. Secondly, one distinct observation from this proposed model employing micro-EDM plasma properties is that the assumption of electrode plasma interface diameter is a critical parameter and requires re-computation for various discharge energy ranges. These can be considered as major limitations of this model leading to considerable simpliﬁcation of a complex problem which may then ﬁnally impact the outcome of the model rendering it to be unrealistic, specially if applied beyond the micro-EDM ranges deﬁned. Further development of the proposed model integrating the electrode plasma interface diameter will allow the model to factor in the changes in electrode plasma interface diameter based on discharge energy settings. Besides, the inclusion of plasma capacitance and plasma inductance as parameters, instead of considering them negligible within a speciﬁc range, will serve towards developing a generalized model of EDM process employing plasma properties. Finally, the physical properties of plasma are quite fascinating. Plasma physics is a complex phenomenon that spans across various sub-disciplines of physics (e.g., material, thermal, and electrical properties) and are topics of ongoing active Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005 G Model CIRPJ 439 No. of Pages 15 A.B.M.A. Asad et al. / NULL xxx (2017) xxx–xxx research. The advancement in our understanding of plasma physics will provide us with better characterization of plasma properties and can be employed in the context of micro-EDM to elucidate properties and critical parameters for improved micromachining. Conclusion This paper presented a theoretical analysis of the electric properties of micro-EDM plasma for an RC power supply circuit with a DC source. The following conclusions, which summarize the signiﬁcance of this study, can be drawn from the analysis It is analytically established in this paper that for capacitive plasma discharge the plasma can be resolved into capacitive, resistive and inductive components. In case of micro-EDM capacitive and inductive component of the plasma can be ignored and the model is proposed using the resistive component of the plasma. Presented analysis provides signiﬁcant insight for realizing changes in the current waveform due to changes in parameters like input voltage, capacitance, inductance and the charging resistance, which can be utilized for process parameter optimization. It has been demonstrated that the inductance and stray capacitance in micro-EDM power supply can be estimated using non-linear least square ﬁtting of experimentally obtained current waveform to the analytical model. Presence of inductance in the power supply network has been observed to minimize the peak height and increase pulse width of the current waveform which results in shallower and ﬂatter craters and improves surface roughness. The analysis and understanding developed through this study will considerably leverage the design of a power supply ﬁtting the appropriate role of all of the three components Resistance (R), Inductance (L) and Capacitance (C). 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Principles 1995, 1. Institute of Physics Pub, Bristol and Philadelphia. Please cite this article in press as: A.B.M.A. Asad, et al., Analysis of micro-EDM electric characteristics employing plasma property, NULL (2017), https://doi.org/10.1016/j.cirpj.2017.09.005

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