1 Introduction

In electrical discharge machining (EDM), it is well-known that removal efficiency is defined as the ratio of the removal volume to the volume of metal molten by a single discharge. This value is usually not higher than several percent [1], which is the reason for the low material removal rate of EDM compared to conventional machining methods. The removal efficiency is low because only a small percent of the molten material can be ejected from the discharge crater and the remaining is resolidified. Since the low material removal rate of EDM is a serious problem restricting its applications in manufacturing, studies on increasing removal efficiency in EDM have been drawing considerable attention from researchers over the past decades. Many researchers have investigated the influences of the shape of discharge current pulses on the removal efficiency for increasing the removal efficiency. Kobayashi et al. [2] found that low tool wear ratios can be obtained from ramp up pulse shapes compared to ramp down and rectangle shapes of discharge current pulses. Ishikawa and Kunieda [3] and Shinohara and Kunieda [4] proposed five types of current pulse shapes and investigated their machining characteristics under long discharge durations of 50 to 200 μs and found that the pulse shape which shows the highest removal efficiency differs depending on the machining conditions. With respect to the improvement of machining performances in EDM, in recent decades, the development of higher quality switching devices is drawing more attention to the improved performance of switching circuits, and researchers are working on increasing the performance of pulse generators in EDM by developing different kinds of pulse generators using these switching circuits. Especially in micro-EDM, Chung et al. used an inductor as an electric storage part to realize a high-frequency bipolar pulse generator. Using this pulse generator with inductance, microholes without electrolytic corrosion were successfully fabricated, and positive pulse duration of several hundred nanoseconds with the repetition rates of MHz was provided to the machining gap [5].

On the other hand, to increase the removal efficiency, a new LC pulse generator was proposed to generate pulse with higher removal efficiency [6] by utilizing the principle of the traditional boost circuit [7], which can obtain significantly large output voltage from a low input voltage using induced electromotive force generated by inductance. The boost circuit is generally used for DC-to-DC converters with output voltage greater than the input voltage. The boost circuit is activated with switching frequencies sufficiently high to produce DC output voltage. Jiang and Kunieda [6] used lower switching frequencies to obtain pulse trains to be applied to the interelectrode gap of EDM. The shape of the current pulse generated by the LC pulse generator with higher rising speed showed superiority in machining with higher efficiency compared to the conventional RC generators. Moreover, the LC pulse generator could generate high open voltage for EDM gap and high discharge current pulse with short duration even with very low voltage input, such as 5 V [6].

However, the LC pulse generator has the following problem. With conventional generators for EDM, such as the RC generators or transistor generators, high open voltage applied to the EDM gap can be kept constant until discharge is ignited [8]. In the LC pulse generator, however, an inductor is used to store and release energy using a low-voltage power supply. The pulse open voltage is generated due to the induced electromotive force, which means that the open voltage is not kept constant, but generated within a significantly short time. Thus, the probability that discharge can occur during the short pulse duration is low, which is why the discharge frequency of the LC generator is lower than the conventional generators [6]. Low discharge frequency reduces the material removal rate in EDM although the removal volume per discharge is higher with the high rising speed discharge current pulse.

Hence, this paper is aimed at increasing the discharge frequency of the LC pulse generators to obtain material removal rates higher than the conventional LC pulse generators. The principle of the modified LC pulse generator is based on the use of an additional transistor pulse generator which is widely used in practical EDM machine tools [8]. In practical transistor pulse generators, an auxiliary transistor pulse generator is often connected to the EDM gap in parallel to the main transistor pulse generator. In sinking EDM, auxiliary transistor pulse generators which have a high-impedance with high-open voltage are often used to ignite discharges more easily, leading to higher stability in machining [9, 10]. In wire-EDM, especially when deionized water is used as the dielectric fluid, auxiliary transistor pulse generators which also have high-impedance but low open voltage are used to initiate a preceding discharge followed by a high current that rises with high speed due to the main transistor generator with high open voltage. Thereby, erosion of the workpiece in water due to electrolysis can be prevented during the discharge delay time [11]. Based on the above technologies used in traditional transistor pulse generators, the present work proposes a modified LC pulse generator in which a high impedance transistor pulse generator is used to apply the open voltage continuously to the gap until discharge is ignited, thereby the discharge probability can be increased to 100%, allowing to the discharge frequency to be increased to a high level. When discharge is ignited in the gap, the conventional LC generator supplies a high discharge current pulse with a short pulse duration and high rising speed. Hence, both the advantages of the transistor generator and conventional LC generator can be acquired at the same time.

2 Principle of conventional LC generator

2.1 Advantages of conventional LC generator

Figure 1 shows a conventional LC generator [6]. In the circuit shown, Uin is a constant DC power source, C1 is a capacitor used to prevent leak current flowing through the gap, L is an inductor used to store energy and inductively boost the gap voltage, and S is a switching transistor for controlling the current direction. When the switch S is on, the inductance stores energy from the power supply and releases the energy to the gap for causing ignition when the switch S is off. In the ideal state, the current of inductance can be infinite when the switch S is kept on, but since the charging speed of inductance is finite, the inductance current can be limited by the charging time. The charging time of the inductance is determined by the on-time of the switch which can be controlled by the switching frequency and duty ratio. Conventional LC generators are able to boost the voltage to significantly high levels of 500 V or higher due to the electromotive force, up to the maximum limit of the Zener diode which is packaged in the switching transistor S in parallel connection with the gap and capacitance C1, using a low voltage power supply Uin of only 5 V. Since there is no obvious resistance in the circuit, the same inductance current that was reached during the switch-on period can be supplied to the interelectrode gap at the instant S which is switched-off, and dielectric breakdown occurs in the gap. This means that LC generators can generate high peak current pulses. Moreover, the discharge current pulse shows a high rising speed which can realize higher removal efficiency than conventional generators such as the RC generator with which the pulse shape is sinusoidal. For instance, when the pulse duration is 200 ns, the rising time of discharge current to 5 A is shorter than 50 ns [6].

Fig. 1
figure 1

Principle of conventional LC generator

Full size image

As shown in Fig. 2, when machining materials with high resistivity such as single crystal SiC of 0.2 Ω·cm in resistivity, the potential drop in the workpiece reached about 70 to 80 V with the discharge peak current of 3 A. Usually in practical uses, the power supply voltage of conventional generators is set to 100 V maximum for safety and to reduce costs. Thus, such a large potential drop inside the material results in decreased discharge current, which has been proved by many investigations [12,13,14,15]. However, in the case of the LC generator, the discharge current can be made equivalent to the inductance current independent of the resistivity of the workpiece material due to the electromotive force [6]. Thus, the LC generator has the advantage in the electrical discharge machining of high resistivity materials because a high voltage power source is not necessary.

Fig. 2
figure 2

Application of LC generator to high resistivity materials: a through-hole machined in SiC wafer; b discharge current and voltage used for SiC machining [6]

Full size image

2.2 Reasons for low discharge probability

Figure 3a shows the open voltage pulses generated by a conventional LC generator when no discharge occurs. Figure 3b shows the magnification of the open voltage pulse, and Fig. 3c shows the discharge voltage and current when discharge occurred. Since discharge usually occurs after a discharge delay time which can be changed stochastically depending on the dielectric strength of the interelectrode gap [16], such a short duration of the open voltage results in significantly low discharge frequency of EDM. In fact, when the switch is turned off, because the LC generator can serve as an LC resonant circuit, the duration can be estimated by \(\pi \sqrt{\mathrm{LC}}\) which is usually shorter than several μs where C is the serial combination of the capacitor C1 added in the circuit and the gap capacitance, and L is the value of the inductor added in the circuit. In the case that L = 50 μH and C = 10 nF, the duration is only 2.5 μs as shown in Fig. 3b. Furthermore, the current through L increases slowly while energy from the power source is stored in the inductor’s magnetic field. Inductance current iL can be roughly estimated by:

$${i}_{L}\approx \frac{{U}_{\mathrm{in}}}{L}\cdot {t}_{\mathrm{on}}$$
(1)

where ton is the open time of the switch. For example, it takes 30 μs to charge the inductor with 3 A with inductance current iL when L = 50 μH and Uin = 5 V. Hence, the interval between consecutive pulses is 30 μs at least. For this reason, the duty ratio of high open voltage pulse is only several percent as shown in Fig. 3a which is far lower than the conventional generators.

Fig. 3
figure 3

Gap voltage and current pulses in LC generator under no discharge and discharge conditions (Uin = 5 V, L = 50 μH, C = 10 nF)

Full size image

The duration of the open voltage pulse is significantly short in the order of several microseconds, and the discharge delay time in EDM is dissipated from sub-microseconds to hundreds of microseconds following the exponential distribution [16]. Hence, the conventional LC generator cannot realize high discharge frequency for EDM. The only method to solve this problem is to increase the duty ratio of the open voltage pulse to a high level. Thus, in this paper, a conventional transistor pulse generator is installed to apply a high open voltage to the gap continuously until discharge occurs. In the transistor pulse generator, the open voltage can be maintained in a long period which is controlled by the on-time of the switching transistor. Theoretically, the duty of open voltage in the transistor pulse generator can be very high, which results in much higher discharge frequency in EDM than the conventional LC pulse generator. Thus, the combination of the LC generator and the transistor generator can increase the discharge frequency of the LC generator. The cost of installing the auxiliary transistor pulse generator is insignificant because the main discharge energy is supplied by the LC pulse generator. Moreover, the current supplied from the transistor circuit may be negligibly low.

3 Investigation on discharge probability of conventional LC generator

Before designing the modified LC generator, the highest discharge probability of the conventional LC generator was investigated. For every cycle of the switching on and off of the switching transistor S, the open voltage pulse shown in Fig. 3b is applied to the gap. Hence, the discharge probability of the LC generator can be defined as the discharge frequency divided by the switching frequency of the LC generator.

$$\mathrm{Discharge}\;\mathrm{probability}=\frac{\mathrm{Discharge}\;\mathrm{frequency}}{\mathrm{Switching}\;\mathrm{frequency}}\ast100\%$$
(2)

The discharge probability of the conventional LC generator was investigated under different open voltage values, different feed speeds, different tool materials, and different dielectric fluids to obtain a better combination of machining conditions for higher discharge probabilities using the conventional LC generator. Figure 4 shows the schematic of the experimental setup. The polarity of the workpiece is positive since higher removal volume can be realized under such a short discharge duration obtained from the conventional LC generator [17, 18], and the tool is fed at a constant speed without a servo feed system. Under a certain switching frequency, the discharge frequency was measured using a current sensor, and the discharge probability of LC pulse generator was obtained from Eq. (2).

Fig. 4
figure 4

Experimental setup to investigate discharge probability in LC generator

Full size image

3.1 Discharge probability of conventional LC generator under different open voltages

Figure 5 shows the relationships between the discharge probability and open voltage obtained from drilling experiments. The machining parameters are listed in Table 1. Different peak open voltages can be realized by using different Zener diodes in parallel connection with the switch. In fact, the diode integrated in different types of MOSFET can be used to control the peak open voltage. The tool electrode is a tungsten rod 300 μm in diameter, and the dielectric fluid is an EDM oil. In this figure, the horizontal axis shows the feed depth which increases in proportion to the machining time, because the tool is fed at a constant feed speed of 0.5 μm/s. The vertical axis shows the discharge probability calculated from the discharge numbers measured using a current sensor and pulse counter. Since discharge is normally unstable at the beginning of machining [19], the first two points in each curve show relatively lower discharge probability than other points with larger feed depths. It can be seen from Fig. 5 that with increasing open voltage, the discharge probability increases. However, the discharge probability decreases suddenly when the feed depth exceeds a certain limit because flushing of debris particles becomes difficult, resulting in a short circuit.

Fig. 5
figure 5

Influences of open voltage value on discharge probability

Full size image
Table 1 Machining parameters used to investigate influence of open voltage on discharge probability
Full size table

Thus, a higher open voltage realizes a higher discharge probability, but excessively high voltages are not acceptable due to safety reasons. Under the conditions used in this experiment, the discharge probability was 20.2% at highest.

3.2 Discharge probability of conventional LC generator using different tool materials

It is known that the dielectric breakdown strength is affected by the work function of the electrode material [20]. Furthermore, the wear of tool electrodes increases the number of debris particles suspended in the gap, which may result in a decrease of the dielectric breakdown strength of the gap [21]. Figure 6 shows the influence of tool materials on the discharge probability measured under the machining parameters shown in Table 2. EDM oil was used, but other parameters are the same as in Table 1. Different tool materials did not show significant difference in the discharge probability, but their machining stability was quite different. Copper showed the highest discharge probability and stability. Tungsten showed the second highest discharge probability and stability, while steel showed the worst discharge probability and stability. The work function of steel, tungsten, and copper was 4.5, 4.55, and 4.65 eV, respectively [22]. The work function of tungsten carbide was 4.32–4.82 eV [23]. As known, the work function determines the electron emission ability on the cathode surface. Lower material work function may result in higher electron emission capability. Nevertheless, the discharge probability was lowest with tool steel, which indicates that the work function is not the dominant factor to determine the discharge probability. This suggests that the maximum feed depth is rather closely related to the thermal conductivity of the material because higher conductivity results in quicker recovery of the dielectric strength of the gap during the discharge interval [8]. The thermal conductivity and work function are shown in Table 3. Since complicated physics are involved in the mechanism of the dielectric breakdown, further investigation is necessary. Still, the discharge probability was lower than 20% independent of the tool material.

Fig. 6
figure 6

Influences of tool materials on discharge probability

Full size image
Table 2 Machining parameters used to investigate influence of tool materials on discharge probability
Full size table
Table 3 Machining parameters used to investigate influence of tool materials on discharge probability
Full size table

3.3 Discharge probability of conventional LC generator under different feed speeds

Increase in the feed speed leads to shorter gap width, which may realize discharge breakdown with shorter delay time. Figure 7 shows the effect of the feed speed on the discharge probability. The machining parameters used in the experiment are shown in Table 4. From the measurement of the inlet diameter of drilled holes, the constant feed speeds of 0.1 μm/s, 0.5 μm/s, and 1 μm/s were found to result in the side gap widths of 15 μm, 11 μm, and 9 μm, respectively. Since higher feed speed results in shorter frontal gap width, discharge ignition in the frontal gap is much easier than in the side gap, which may decrease the side gap width. Figure 7 shows that lower constant feed speed results in lower discharge probability but larger limit of the feed depth because of the larger frontal gap width. The discharge probability was highest at the highest feed speed of 1 μm/s. However, higher feed speed resulted in smaller depth due to easy occurrence of short circuit in the frontal gap.

Fig. 7
figure 7

Influences of constant feed speed on discharge probability

Full size image
Table 4 Machining parameters used to investigate influence of tool feed speeds on discharge probability
Full size table

The maximum discharge probability of the conventional LC generator was about 20% at highest under the conditions used in the present work.

4 Increasing discharge frequency using modified LC generator

4.1 Modified LC generator combined with high impedance transistor generator

Section 3 described that the highest discharge probability of the conventional LC generator is about 20%, which is not sufficiently high for industrial uses. Since the material removal rate is determined by the product between the discharge frequency and removal volume per discharge, the low discharge probability of the LC generator limits the material removal rate. Hence, to take advantage of larger removal volume per discharge pulse with a low voltage input, an auxiliary circuit should be attached to the LC pulse generator to increase the discharge probability. To realize higher discharge probability and higher removal rate, the conventional transistor pulse generator was combined with the conventional LC generator as shown in Fig. 8. The transistor pulse generator was controlled with the switching transistor S2, which determined the maximum discharging frequency of the modified LC pulse generator. This allows the discharge frequency of the modified LC pulse generator to reach a higher discharge frequency which is almost equivalent to conventional transistor generators. Figure 9 shows the experimental setup and example of workpiece.

Fig. 8
figure 8

Principles of modified LC generator

Full size image
Fig. 9
figure 9

The setup of drilling experiments and the example of drilling

Full size image

In the modified LC generator, Uin1 is a low-voltage DC power supply which is used to supply energy to the conventional LC generator; Uin2 is a high voltage DC power supply which is used to supply energy to the conventional transistor pulse generator; L is an inductor for storing energy; R is used to control the current supplied from the conventional transistor generator; C1 is a capacitor which prevents continuous current leak through the gap during the discharge interval. When the modified LC generator starts working, both switches S1 and S2 are on. High voltage Uin2 is applied to the gap, and the energy starts being stored in the inductor by the low voltage power supply Uin1. This condition is maintained during the discharge delay time. When discharge occurs, small current can flow in the gap, and the current sensor detects the rising edge of the current waveform. Immediately, the S1 is triggered to be switched off, and large current and energy are supplied to the gap.

Since the high open voltage is continuously applied to the gap until a discharge is ignited, the discharge frequency can increase to a high level equivalent to conventional transistor pulse generators. The auxiliary transistor circuit works as an igniter of discharge, but does not serve as a machining function. Since a large R is used, energy lost in the transistor circuit is negligibly small. The definition of discharge probability in Section. 3 does not make sense in transistor pulse generators, because the open voltage is maintained until the dielectric breakdown. Thus, the discharge frequency is a more suitable index for comparing the material removal rate of the conventional LC generator and the modified LC generator than the discharge probability. Figure 10 shows the discharge current and open voltage waveforms of the modified LC pulse generator. It was found that the constant high open voltage can be kept by the high impedance transistor pulse generator until the dielectric breakdown, followed by the high rising speed discharge current pulse obtained by the LC pulse generator. When the discharge occurred, a tiny discharge current supplied by the high impedance pulse generator flowed in the gap, and the gap voltage decreased. The interval time between ignition detection and the rising of the discharge current pulse is several hundred ns. During the interval time, after the response of the detection, the switch S1 turns off, and the high induced voltage is generated which is used to charge the stray capacitance of the switch and capacitance C1. High current was supplied from the LC pulse generator. After the discharge, the gap voltage was recovered to the high value which can ensure that the next ignition occurs as early as possible, thereby realizing high discharge frequency.

Fig. 10
figure 10

Pulse waveforms of modified LC pulse generator (R = 1 kΩ, L = 50 μH, C1 = 10 nF)

Full size image

4.2 Comparison of discharge frequency between modified LC pulse generator and conventional LC pulse generator

Since the material removal rate is proportional to the discharge frequency, the discharge frequency was compared between the conventional LC pulse generator and modified one. Figure 11 shows the discharge frequency under the constant feed speed of 0.5 μm/s and open voltage Uin2 of 200 V and 50 V. The dielectric fluid was an EDM oil. The discharge parameters are listed in Table 5. Figure 11 shows that the modified LC generator has a higher discharge frequency than the conventional one whether the open voltage is 200 V or 50 V. Therefore, under the same constant feed speed, larger feed depth which is 264 μm was obtained compared to the conventional LC generator where machining was stopped at the feed depth of 96 μm due to the occurrence of short circuit when open voltage was 50 V. If the open voltage increased to 200 V, the discharge frequency increased to 10 kHz when the modified LC pulse generator was used. The results shown in Fig. 11 can prove that the modified LC pulse generator improved the discharge frequency to 2 times or higher than that of conventional pulse generator and obtained larger feed depth resulted from the higher machining stability.

Fig. 11
figure 11

Comparison of discharge frequency between conventional LC pulse generator and modified LC pulse generator under different open voltage

Full size image
Table 5 Parameters of modified LC generator used in experiments
Full size table

Figure 12 shows the machining results under different constant feed speed. The experimental parameters are listed in Table 6. Under the constant feed speed of 1 μm/s, the discharge frequency can increase to 12 kHz when using the modified LC pulse generator. The value is almost 3 times higher than that of the conventional pulse generator. It can prove that the modified LC pulse generator shows higher discharge frequency than the conventional LC pulse generator. When the feed speed is 0.1 μm/s, the discharge frequency is lower than that of 1 μm/s. The reasons have been demonstrated in Section. 3.

Fig. 12
figure 12

Comparison of discharge frequency between conventional LC pulse generator and modified LC pulse generator under different feed speed

Full size image
Table 6 Parameters of modified LC generator used in experiments
Full size table

4.3 Comparison of material removal rate between modified LC generator and conventional LC generator

The previous section verified that discharge frequency can be increased using the modified LC pulse generator to increase the material removal rate and maximum feed depth.

Hence, dependence of the maximum feed depth on the tool feed speed and open voltage Uin2 were compared between the conventional LC generator and the modified LC generator as shown in Figs. 13 and 14, respectively. In the experiments, the constant feed speed was used to feed the electrode. Other discharge parameters were the same as Table 5. Maximum feed depth could be obtained by measuring the feed depth at which machining was interrupted due to the occurrence of short circuit in the drilling experiments. It is found that the same depth of hole can be machined with higher feed speed and lower open voltage using the modified LC generator. In other words, the modified LC generator can achieve larger feed depth than the conventional LC generator under the same constant feed speed and open voltage, thereby realizing higher material removal rate and higher aspect ratio.

Fig. 13
figure 13

Comparison of maximum feed depth between conventional LC pulse generator and modified LC pulse generator under different feed speeds (open voltage = 200 V)

Full size image
Fig. 14
figure 14

Comparison of maximum feed depth between conventional LC generator and modified LC generator under different open voltage (feed speed = 0.5 μm/s)

Full size image

Figure 15 shows the comparison of the tool wear ratio between the conventional LC generator and modified LC generator. It was found that the difference is insignificant because there is no difference in the discharge voltage and current between both generators. Therefore, the modified LC pulse generator can increase the discharge frequency, while it does not change other machining characteristics of the conventional LC pulse generator.

Fig. 15
figure 15

Comparison of tool wear between conventional LC generator and modified LC generator

Full size image

5 Conclusions

Using the LC generator, current pulses with short duration and high rising speed for high efficiency EDM machining can be obtained due to the induced electromotive force even with a low-voltage power source. However, discharge frequency is low because the open voltage duration is short. On the other hand, the conditions higher open voltage, shorter gap width, and use of copper as tool material can increase the discharge probability. However, under any machining conditions, the discharge probability of the LC generator cannot exceed 20%. Hence, the LC generator was modified by combining the transistor generator with the conventional LC generator circuit to increase the discharge frequency. The machining results showed that the discharge frequency of the modified LC generator is two to three times higher than the conventional LC generator, thus realizing higher material removal rate.