Design of VHF micro-EDM discharge state detection method based on energy coupling detection

Because the pulse frequency of VHF micro-EDM power supply (30–300 MHz) is higher than that of traditional EDM power supply and the pulse has two characteristics of positive and negative bipolar, it is impossible to use traditional discharge state detection technology to meet the requirements of VHF discharge state detection. And during the experiment, it was found that the resonant frequency of the VHF pulse would migrate with the change of circuit impedance, leading to the change of pulse voltage amplitude. In order to break through the limitations of traditional detection method, this paper combined the technology of EDM discharge state recognition and microwave detecting technology, based on the principle of electrode impedance change, put forward a discharge condition detection method of VHF pulse source based on energy principle of coupling detection, the method using a double-directional coupler and rf receiver device for detecting pulse energy. It can detect the inter-electrode power of a VHF pulse source with a frequency range from 30 to 300 MHz and a power range below 100 W and realize accurate discharge status identification of VHF micro-EDM.


Introduction
With the increasing demand for micro-scale structure manufacturing in the manufacturing field, micro-EDM, as a kind of wide application of non-contact manufacturing technology, has high machining accuracy, low cost, and controllability is strong, small to processing material hardness requirement, there is no macroscopical cutting force, etc., so it has great application prospects in the field of micron-scale threedimensional structure processing [1].
In the process of micro-EDM, discharge state detection is one of the key technologies in EDM pulse power supply, and it is the guarantee for realizing efficient and precise EDM [2]. The size of the discharge gap directly has a great influence on the cutting performance indicators such as the discharge efficiency, the electrode feed speed, and the surface roughness of the workpiece. Real-time and stable control of the discharge gap is realized to ensure that the discharge gap is within a suitable range, and high corrosion removal efficiency can ensure the stability and efficiency of processing. However, it is very difficult to directly measure the size and change of the discharge gap, but the gap size can be indirectly reflected by the voltage, current, and related electrical parameters of the discharge gap. The traditional EDM state recognition technology includes average voltage detection, breakdown delay detection, and high-frequency signal detection. In recent years, with the development of intelligent algorithms such as neural network recognition, fuzzy logic recognition and fuzzy neural recognition, many researchers have applied them to the detection of diacharge state. However, these methods are not suitable for the discharge state detection of micro-EDM pulse power supply with a narrow pulse width and a small duty cycle.
The gap average voltage detection method is the most commonly used state detection method used in EDM, which is to compare the measured average gap voltage with the set threshold voltage to judge the state of micro-EDM discharge. Pamidighantam et al. [3] proposed an inter-electrode pulse recognition system based on an average voltage detection method based on detecting peak voltage and breakdown delay.

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Liu et al. [4] established a numerical model of the relationship between the steady-state value of average voltage, circuit parameters, and pulse parameters and carried out a theoretical study on the gap average voltage detection method in micro-EDM. However, the selection of the threshold voltage of this method needs to be obtained through a lot of experiments and processing experience, and for high-frequency micro-EDM, this hysteretic control method is likely to cause instability in the processing process and affect the processing efficiency. Bhattacharyya et al. [5] proposed the high-frequency component detection method to distinguish the discharge state by detecting the change of high-frequency component in the gap voltage. When the micro-EDM is steadily processed, the number of high-frequency components is in a stable state, while when the arc discharge occurs, the voltage high-frequency component will be weakened. The basic principle of this method is to detect the high-frequency component of the discharge waveform, amplify it, and then judge the discharge state according to the threshold value. But the detection circuit of this method is complex and has poor stability [6]. Snoeys et al. [7] and Zhou et al. [8] identify the discharge state by using the different gap breakdown delay conditions in the discharge process of EDM. However, due to the instability and irregularity of breakdown delay problems in both normal discharge and arc discharge, the discharge state cannot be accurately judged, so it has not been widely used. Geng et al. [9] proposed a gap-averaged pulse width voltage detection method for the problem that the servo reference voltage needs to change constantly and then perform average voltage processing on this part of the waveform. Although this method eliminates the influence between pulses on the detection state, the introduction of the sampling switch will introduce highfrequency interference to the detection system. Although the above detection method can detect the discharge state of the discharge gap, its detection accuracy is low, and the effect is not ideal. From the perspective of realizing monopulse detection and formulating corresponding countermeasures, Jiang et al. [10,11] proposed a wavelet transform method, which can express local details of signals in both time domain and frequency domain. By analyzing the high-frequency coefficient or low-frequency coefficient of the electrical pulse signal after wavelet transformation, the details neglected in the average voltage detection method can be revealed. Tarng et al. [12] proposed a neural network recognition method with strong fault tolerance and better recognition of gap discharge state by taking advantage of neural network self-learning. Tarng et al. [13] and Kao et al. [14] developed a fuzzy logic detection method, which adopted a fuzzy discriminator to achieve fuzzy processing of gap voltage and current values by setting a fuzzy control algorithm, and then quickly and accurately identified the gap discharge state by feature rules.
The VHF pulse power supply is different from the traditional independent transistor type or RC charge-discharge type power supply. It belongs to a new type of EDM power supply; its discharge frequency can reach the level of very high frequency (30 ~ 300 MHz); the waveform is standard sine wave; the pulse width is compressed to several nanoseconds, with higher pulse frequency and narrower pulse width, so the surface quality of EDM can be greatly improved. The research of Wang et al. [15] proved that compared with traditional power sources, the machining surface quality of VHF power sources was significantly improved, and surface defects such as the recasting layer, heat-affected zone, and microcracks were significantly improved.
Realizing the detection of the discharge state of the VHF power supply is the primary requirement to further improve the controllability of this new type of power supply for VHF discharge removal processing. The existing detection methods can only be applied to the traditional low-frequency, unidirectional pulse discharge machining, and the maximum frequency does not exceed 10 MHz, which cannot be used for state detection in VHF micro-EDM. The main reason is that the traditional gap average voltage detection method cannot be used for AC bipolar pulses, and bipolar signals are directly processed by this method. After that, it becomes a zero-level signal, which cannot be used for state judgment, and the digital processing method based on high-speed signal sampling has too high requirements on the sampling system, which greatly increases the difficulty and cost of hardware and software development. Moreover, because the detection circuit of the traditional detection method and the electrode machining circuit are not isolated, the high-frequency pulse energy generated during the processing of the VHF pulse power supply directly connected to the detection line will damage the components on the circuit board. Therefore, in order to accurately detect the inter-electrode discharge state of the VHF pulse power supply, a stable and continuous judgment can be realized. In this paper, a new method for detecting discharge state of VHF micro-EDM based on energy coupling detection is proposed. This method has strong applicability and can realize the detection of discharge state of pulse power supply with a pulse frequency of 30 ~ 300 MHz and output power of less than 100 W, which solves the problem that the traditional detection circuit cannot detect bipolar pulse and high-frequency pulse. By establishing a circuit simulation model and conducting an EDM experiment, the application effect of this method in the VHF pulse power supply is analyzed, which provides a guarantee for the engineering application of the VHF micro-EDM method.

VHF discharge characteristics
In EDM, the electric pulse width has a great influence on the machining quality. The smaller the pulse width is, the smaller the single pulse energy is, and the smaller the erosion pits produced by a single discharge will be, the better the surface processing quality of the parts is. The traditional electric spark realizes the compression of the pulse width by continuously optimizing the switching performance of the transistor, but because the switching performance of the existing transistor has reached the limit, the pulse width of the traditional form of pulse power supply has been difficult to achieve a wide range of compression [16] and very high frequency. The pulse power supply adopts different forms, and the high-frequency (30 ~ 300 MHz) discharge pulse is obtained through the oscillating circuit, which not only greatly compresses the pulse width, but also ensures a high open-circuit voltage. Processing efficiency pulse power supply realizes the generation of very high-frequency pulses by pulse resonance amplification technology. The schematic diagram of the VHF pulse power supply circuit is shown in Fig. 1.
Different from the traditional pulse power supply, the output pulse generated by the VHF power supply is a sine wave. To apply it to micro-electrical machining, a stable and reliable detection method is required to control the machining process to ensure that the pulse gap is in a normal discharge state. The typical discharge state waveform of the VHF pulse power supply is shown in Fig. 2. The pulse is a typical bipolar sinusoidal waveform with a high pulse frequency.
The VHF pulse has the characteristics that the open-circuit pulse voltage changes correspondingly with the pulse frequency. The main reason is that the VHF signal will be affected by the impedance of the transmission line during the transmission process, resulting in the change of the energy transmission efficiency, which in turn leads to the interpolar pulse. Amplitude is the change of pulse energy between poles. For the same circuit hardware conditions, the pulse frequency will change significantly with the transmission impedance, so even if the circuit conditions remain stable, the pulse output effect will change significantly. In order to verify this feature, in a certain hardware circuit state, keep the output amplitude of the signal source unchanged and realize pulse output of different frequencies by adjusting the output frequency of the signal source. In this case, the opencircuit peak voltage at each frequency is shown in Fig. 3; according to Table 1, it can be seen that the open-circuit voltage increases first and then decreases with the increase of the pulse frequency, and reaches the maximum value at about 75 MHz, indicating that the pulse power system is the best in this processing condition. The resonant frequency is around 75 MHz.
In summary, the output waveform of the VHF pulse power supply has the characteristics of positive and negative bipolarity, the pulse period is short and the change is fast, the open-circuit voltage value changes significantly with the frequency, and the VHF pulse resonance frequency will migrate with the change of the system impedance, which affects the output pulse. The consistency of the voltage amplitude leads to uncontrollable processing efficiency, which is more difficult to detect than the traditional unipolar power supply with a stable voltage waveform. Therefore, it is necessary to propose a new detection method suitable for the VHF power supply.

Impedance change between electrodes
In the process of micro-EDM, the voltage amplitude between the positive and negative electrodes will change significantly with the change of the machining state, and the change of the machining discharge state is mainly the embodiment of the construction and disconnection of the discharge channel between the electrodes. It shows that after the discharge pulse breaks down the medium between the two stages, the impedance state between the electrodes changes rapidly. The equivalent circuit of the electrode impedance is shown in Fig. 4, including typical resistance, inductance, and capacitance. The value of the inter-electrode impedance can be represented by Eq. (1).
When the pulse frequency of the VHF power supply and the output peak value of the signal source remain unchanged, the peak-to-peak value of the pulse between the processing electrodes varies significantly with the impedance between the electrodes, and the peak-to-peak value of the voltage between the electrodes corresponds to the power between the electrodes. When the inter-pole state changes, the inter-pole impedance changes, and finally, the inter-pole power distribution changes. Therefore, in the process of processing, with the difference of the discharge state between the electrodes, the power distributed between the electrodes is also constantly changing. As long as the detection of the power change between the electrodes can be realized, the judgment of the discharge state can be realized.

Power distribution between poles
The energy of the inter-electrode discharge is all provided by the VHF pulse source, but not all the energy will be transmitted to the inter-electrode for EDM due to line loss and other reasons. According to the law of energy conservation, Eq. (2) can be obtained. (1) (2) P T = P D + P L + P R In the formula, P T is the total power output by the VHF pulse source. P D distributes energy between the poles. P L is the total loss of energy in the process of transmission to the inter-pole, mainly includes transmission line loss and reflection loss. P R is the space radiation loss.
Since the output pulse of the VHF pulse source has the characteristics of the radio frequency pulse, the transmission process of the pulse energy conforms to the radio frequency transmission theory, and the energy will change and reflect due to the change of the impedance between the electrodes during the transmission process. Among the three parts of energy, since the impedance state of the electrode and the workpiece does not meet the optimal impedance required by electromagnetic radiation, the space radiation loss PR only accounts for a small part of the total energy, and the influence of this part is ignored in the subsequent calculation. The energy transmission loss in PL is mainly caused by the transmission line and the device. Since the 50 Ω standard impedance line is selected for the transmission line, and the devices are all qualified products, the transmission loss is also less and can be ignored in the calculation; the reflection loss is the main part of the energy loss and is the part that must be considered in the calculation, and this loss can be directly measured in some way.
According to transmission line theory, the reflection coefficient is a parameter representing the proportion of electromagnetic wave reflected due to impedance problem in the transmission medium. Its size is the ratio of the voltage peak-to-peak value of the reflected pulse to the voltage peak-to-peak value of the incident pulse.
In the formula, Γ L is the reflection coefficient, U refl is the reflected wave voltage, U inc is the incident wave voltage, Z L is the inter-pole impedance, and Z 0 is the transmission line characteristic impedance. So the relationship between the reflection coefficient and the reflected power is as follows: In the formula, P r is the reflected power, and P f is the incident power.
The voltage standing wave ratio is the ratio of the voltage peak value to the voltage valley value of the traveling standing wave. This value can be calculated by the modulus value of the reflection coefficient: In the formula, VSWR is the voltage standing wave ratio. The ratio of incident wave energy to reflected wave energy is as follows: From the perspective of energy transfer, the mismatch between the signal source impedance and the load impedance determines the strength of the reflected signal from the load. The ideal standing wave ratio should be 1:1, at this time, the ratio λ of incident energy to reflected energy is infinite, and the pulse energy will maintain the traveling wave transmission state and meet the impedance matching, and the load power reached maximum. The worst standing wave ratio is infinite; in this state, it is a pure standing wave state, the pulse energy is completely reflected, λ is 1, and no energy is transmitted. That is, the larger the standing wave ratio, the larger the reflected power, the lower the energy transmission efficiency, and the lower the inter-electrode energy corresponding to the VHF micro-EDM.

Select the type of coupler
Directional coupler is a commonly used energy distribution component in microwave systems, which mainly realizes transmission power distribution through internal microstrip, and the energy coupling is directional. Directional coupler can not only transfer the energy in the main transmission line to the secondary line, and has a good isolation function, so the directional coupler is mainly used for microwave system signal isolation measurement, to achieve microwave energy detection. The directional coupler mainly has a standard directional coupler with only a one-way coupling port and a dual directional coupler with both positive and negative coupling ports. The standard directional coupler shown in Fig. 5a has four ports, including the input end and the straight-through end on the main transmission line, through which the main energy flows. In addition, there is an isolation end and the secondary output port, between which there is a phase difference of 90°. The double-directional coupler shown in Fig. 5b has a pair of main ports (incident input and reflection input) and a pair of coupled output ports (incident coupling output and reflection coupling output), so there is no need to distinguish the access direction of the coupler specifically in the process of use. At the same time, the dual directional coupler can measure the input power and the reflected power of the transmission line at the same time. After removing the loss of the coupler itself, the incident and reflected energy can be effectively reflected. Because of the need to realize the detection of incident energy and reflected energy at the same time, the detection system needs to choose a double-directional coupler.

Power calculation of directional coupler
The RF pulse power enters from the incident input port, and a lower power signal is coupled out through the forward coupling end, and the signal magnitude is the magnitude of the incident power minus the coupling degree of the coupler. When the power enters from the reflection input port, the coupled signal of the reflected power will also be obtained by the reflection coupling end. The basic formula for coupled power calculation is as follows: where P C is the coupling power, P Ain is the main power, and η C is the coupling power ratio.
where L C is the coupling coefficient. Available

Analysis of the principle of detection
The output waveform of the coupling end of the directional coupler is still a bipolar VHF pulse, but the pulse energy has a huge attenuation compared with the pulse energy in the main transmission line, which can facilitate the later detection, and the coupled energy is very important to the main transmission line. Transmission line energy transfer does not cause significant energy attenuation. Therefore, it is necessary to introduce a detector to realize the detection of the coupled out energy.
The system uses a logarithmic detector to process the coupled signal and converts the high-frequency signal coupled by the coupler into a corresponding DC signal, which is convenient for acquisition. The detector is mainly used to detect some characteristic information in the radio frequency pulse signal. It is mainly used to identify the existence or change of the wave, oscillation, or signal. The output signal of the logarithmic detector has a corresponding relationship with the envelope of the input signal. The change of the input signal determines the change of the input signal.

Design of energy coupling detection system
Based on the variation law of impedance between electrodes and the principle of the directional coupler, an indirect state detection method based on energy coupling is established as shown in Fig. 6. The detection method is to characterize the difference in the magnitude of the open-circuit voltage between the electrodes and the discharge state between the electrodes by detecting the changes of the incident power and the reflected power in the energy transmission line.
By coupling the energy from the transmission line in a certain proportion through the directional coupler, the detection circuit can avoid the interference of the impedance state between the poles, which will affect the energy distribution between poles. The double-directional coupler can simultaneously couple the incident energy and reflected energy in the transmission line, and the incident energy and reflected energy can be accurately obtained by detecting the energy equivalent signal coupled. Firstly, the coupling energy is monitored and collected by a spectrum analyzer to preliminarily verify the feasibility of the method. A VHF discharge status detection system with the dual directional coupler is built, as shown in Fig. 6. In the figure, the isolator at the output of the VHF pulse source is used to absorb the reflected energy in the transmission line, prevent the reflected energy from interfering with the incident signal, and protect the front-end pulse source. In order to detect the power level of the coupling signal, the output signal of the directional coupler is detected by the RF power detector, and the signal power is converted into the corresponding voltage. The voltage signal output by the power detector can be collected and read by the ADC (digital-to-analog converter) module. The digital signal converted by ADC is processed by MCU (single-chip microcomputer) to determine the interpolar state.

Experiment method and state judgment method
The VHF micro-EDM discharge state detection experiment was carried out on the single-station three-axis EDM motion platform developed by the China Academy of Engineering Physics. The tool electrode is supported on the Z-axis, and the workpiece is fixed on the X-Y motion platform through the fixture tooling to keep the oil-based EDM medium continuously flushed. The tool electrode is a 0.1-mm tungsten electrode, and the processed specimen is a 0.1-mm-thick brass sheet. By controlling the Z-axis movement and with the observation assistance of the microscopic imaging device, the contact and disengagement control between the tool electrode and the workpiece is realized to change the discharge state. Electric pulse outputs with different frequencies and different power amplitudes are generated by adjusting the VHF pulse power supply. The table shows the setting parameters of the VHF pulse power supply in the experiment. The RF transmission line in the detection system adopts 50 Ω impedance, which realizes impedance matching with the VHF power supply and the coupler detector, so as to prevent the working performance of the components from being affected. First, use the spectrum analyzer to record and collect the incident power and reflected power coupled by the coupler for pulses of different frequencies and different powers, analyze the relationship between incident power and reflected power with frequency and total pulse power, also analyze variation of reflected power under different discharge states by changing the electrode state. Then, add a detector module to detect and process the coupled signal, and observe and record the voltage data through an oscilloscope. According to the schematic diagram, the VHF energy coupling detection method discharge state detection system is built as shown in Fig. 7. The red curve in the figure illustrates the voltage signal transmission path. The output signal of the coupler is detected by the spectrum analyzer, and the detector is detected by the oscilloscope. The output signal is detected.

Coupling experiment of coupler
The schematic diagram of the coupler coupling test experiment is shown in Fig. 8. The coupler directly records and collects the equivalent signals of the incident power and reflected power coupled by the dual directional coupler through the spectrum analyzer. The basic performance parameters of the coupler are shown in Table 2

Inter-pole open-circuit power detection
It mainly detects the power level of the open circuit between the poles and detects and collects the output of the coupler and the detector, respectively, to obtain the power level between the poles. First, the energy at the output end of the dual directional coupler is collected, and the energy at the coupling end is obtained through the spectrum analyzer. According to Fig. 9, it can be preliminarily concluded that when the pulse frequency changes, the incident energy and reflected energy change, and the energy difference (the energy distributed between the poles) also changes accordingly. When the open and short state changes between the poles, the reflected energy also changes, so when the frequency is stable, the current discharge state can be judged by the change of the reflected energy. The incident and reflected power in the frequency range of 50-75 MHz are collected and calculated, respectively, and the variation trend of the incident power and reflected power with the pulse frequency    Fig. 10. It can be found that the incident power is basically maintained at 40 W. It fluctuates up and down from left to right, but the reflected power changes obviously with the pulse frequency, showing a trend of decreasing first, then increasing, then decreasing, and then increasing. It shows that with the change of the pulse frequency, the impedance state between the electrodes also changes obviously, which leads to different reflection coefficients between the electrodes, resulting in the change of the reflected power.
From Eq. (2), it can be obtained that the distribution power between the electrodes is mainly the difference between the incident power and the reflected power between the electrodes, so the variation trend of the distribution power between the electrodes with the pulse frequency can be obtained as shown in Fig. 11. The reflected power is just the opposite; when the inter-pole state is an opencircuit state, the inter-pole power fluctuates with the pulse frequency. The maximum value appears at 55 MHz and 70 MHz, and the minimum value appears at 60 MHz, and the power varies with frequency. The amplitude reaches about 15 W.
The energy coupling detection and collection are performed on the power pulses with the pulse frequency of 50-75 MHz and the output amplitude of the signal source of 50-250 mV, respectively. According to the collected data, the variation law of the pulse power between the poles with the pulse frequency and the output amplitude of the signal source can be obtained as shown in Fig. 12. It can be found that when the pulse frequency is constant, with the increase of the output amplitude of the signal source, the power between the open-circuit electrodes increases gradually; when the output amplitude of the signal source is constant, with the increase of the pulse frequency, the power between the open-circuit electrodes increases first and then the trend of falling and rising and falling. And under different signal source output amplitudes, the change trend of the open-circuit inter-pole power with the pulse frequency is basically the same and is not affected by the change of the signal source output amplitude.

Inter-pole state change detection
In the previous article, the power detection between the open-circuit electrodes has been preliminarily verified, which shows that the energy coupling detection method can realize the detection of the energy between the electrodes. When the inter-electrode discharge state is detected and changed, the inter-electrode impedance will also change, which will cause the inter-electrode reflected energy to change significantly. Therefore, only the inter-electrode reflected energy needs to be monitored to determine the inter-electrode state change. When the output amplitude of the signal source is 250 mV, the coupled reflected energy of the coupler is detected by the spectrum analyzer, and the obtained data is calculated and processed to obtain the variation trend of the open and short circuit reflected energy with the pulse frequency as shown in Fig. 13. The ratio of open-short-circuit reflected power under different pulse frequencies is obtained as shown in Fig. 14. It can be concluded that under the same pulse frequency, the reflected power in the open-circuit state is always smaller than the pulse power in the reflected state, so the inter-electrode discharge state can be judged by judging the magnitude of the reflected power between the electrodes. The picture shows the variation trend of the reflected power between the electrodes with the pulse frequency under different discharge states when the output amplitude of the signal source is 250 mV. According to the figure, it can be concluded that under the same pulse frequency, the reflected power in the open-circuit state is always smaller than that in the reflected state. Therefore, the discharge state between the electrodes can be judged by judging the magnitude of the reflected power between the electrodes.

Detection test
The above results can preliminarily verify the applicability of the energy coupling detection method in VHF EDM detection by analyzing the coupled output signal of the dual directional coupler. To read the signal state, it is necessary to convert the coupled signal into a DC-level signal that can be read by AD to realize the final application of this method. Referring to the RF signal processing method, an RF detection module is introduced. RF detectors can accurately detect and measure the amplitude and power of RF signals and are widely used in wireless systems. A general RF detector detects a radio frequency input signal and outputs a voltage value. This voltage value has a certain numerical relationship with the power of the input signal, and according to the output voltage value, it can correspond to the input power value.
Using a logarithmic detector, the detection output is proportional to the root mean square of the input voltage V out ∝ V rms , and the square of the detection output is proportional to the input power V2 out ∝ W, so the relationship between the inter-pole power and the detection acquisition value is W ∝ (V2 inc-V2 refl), which can directly determine the inter-pole open-circuit power. The log detector model features the AD8361, an average response power detector for high-frequency receiver and transmitter signal chains up to 2.5 GHz. In most applications, it only requires a DC power supply between 2.7 and 5.5 V.

Inter-pole open-circuit power detection
After completing the energy detection of the coupler, connect the detector to conduct the experiment, and detect the pulses with the pulse frequency of 50-75 MHz and the output amplitude of the signal source of 50-250 mV. The trend of change with pulse frequency is shown in Fig. 15. It can be concluded that when the output of the signal source is unchanged, the floating range of the detector at the incident end is small, and the variation trend with the pulse frequency under the output of different signal sources is consistent. However, the change of the detection value of the reflection end with the pulse frequency is more obvious, showing a trend of first decreasing, then increasing, then decreasing, and then increasing, and the change trend with the pulse frequency under different signal sources is consistent. And it is consistent with the change trend of the coupling energy of the coupler above. It shows that the collected value of the detector can effectively reflect the change level of the reflected power between the poles. According to the change of the input reflection obtained above, the pulse frequency of 50-75 MHz and the output amplitude of the signal source of 50-250 mV of the pulse equivalent power between the poles of the power supply with the pulse frequency and the output amplitude of the signal source are shown in Fig. 16. It can be found that when the pulse frequency is constant, with the increase of the output amplitude of the signal source, the power between the open-circuit electrodes increases gradually; when the output amplitude of the signal source is constant, with the increase of the pulse frequency, the power between the open-circuit electrodes increases first and then the trend of falling and rising and falling. And under different signal source output amplitudes, the change trend of the open-circuit inter-pole power with the pulse frequency is basically the same and is not affected by the change of the signal source output amplitude. And it is consistent with the change law of the coupling energy of the coupler above.

Inter-pole state change detection
After completing the preliminary verification of the coupler coupling experiment, the RF detection module is added to detect the coupled energy, and the reflected energy waveform and the reflected waveform under different inter-pole states are obtained. Figure 17 shows the comparison of the incident and reflected energy and the open-short-circuit reflected energy changes at 65 MHz and 70 MHz, respectively.
According to the above figure, it can be found that when the state between the poles does not change, the output waveform of the detector is stable, which is convenient for monitoring. Collect the output value of the reflector detector when the output amplitude of the signal source is 150 mV and 250 mV under different pulse frequencies, and obtain the curve of the detector output value changing with the pulse frequency as shown in Fig. 18.
According to the Fig. 18, the curve of the ratio of the detection output value with the pulse frequency under different inter-pole states is shown in Fig. 19. It can be found that the output value in the open-short state has changed

Experimental verification
The discharge state detection method based on energy coupling detection has been analyzed and demonstrated in the previous article, and the feasibility and applicability of this method have been verified. The state detection system is designed, and the corresponding processing experiments are carried out to verify the feasibility of the detection and control function of the system. Fig. 20, the detection system mainly involves the front-end processing of interpolar pulse, signal conversion, digital-analog isolation, AD acquisition, state judgment, control output, and other parts. The difference between the front-end processing of the interpolar pulse has been introduced and designed in the previous paper, so this section mainly analyzes the design of the MCU board system and the control and detection strategies of the two detection methods.

Energy coupling detection system
According to the system topology shown in Fig. 21, the overall framework of energy coupling detection is built. The VHF EDM discharge state detection system mainly  includes cascaded VHF pulse sources, energy coupling modules, radio frequency detection modules, isolation op amp module, data acquisition module, and status judgment unit. Except for the energy coupling module and the radio frequency detection module, other modules are the same as the inter-pole voltage division detection system. The energy coupling module is used to couple out the reflected energy in the VHF transmission line to achieve step-down without affecting the transmission line. The output signal is still a high-frequency bipolar signal, but the peak-to-peak value of the pulse is greatly reduced. In the RF detection module, the VHF pulse signal coupled by the coupler is converted into a smooth DC signal for subsequent acquisition and processing. The isolation op amp module is used to isolate the RF analog terminal from the data acquisition terminal to reduce interference to improve the sampling accuracy, and to isolate and convert the DC signal and input it to the data acquisition module. The data acquisition module is used to convert the smooth analog signal into digital quantity and transmit   Fig. 20 Schematic diagram of VHF discharge detection system module it to the state judgment module; the state judgment module is used to read the analog-to-digital conversion value and, according to the discharge state judgment method, to judge the open circuit, the normal discharge state, and the shortcircuit state, and at the same time, the discharge interval is subdivided and quantified.

Energy coupling state detection program
The energy coupling detection mainly judges the change of the state between the electrodes by the change of the reflected energy between the electrodes. When the electrode state is open circuit, the reflected energy is small, and when the electrode state is short circuit, the reflected energy is large, so when the detection value is large, it's short circuit, and when the detection value is small, it's open circuit. After the power pulse is stabilized, first collect the current voltage and calculate the open-circuit threshold, that is, the lower threshold of voltage setting C, and set the short-circuit threshold, that is, the upper threshold of voltage setting D, according to the processing requirements and daily experience. Interpolar state detection can be started. The current voltage value V now is collected in real time. When V now is less than the open-circuit threshold C, the inter-pole state is open-circuit, the control differential signal output is positive, and the machining axis can maintain the full feed state; when V now is greater than the open-circuit threshold C and less than the short-circuit threshold D, the state between the poles is the machining state, and the control differential signal output is positive, but the value is related to the on-site machining state, and the machining axis can maintain the state of slow feed; when V now is greater than the short-circuit threshold D, the state between the poles is a short-circuit state, and the control differential signal output is negative, and the machining axis is in the full-speed retract state. The specific judgment process is shown in Fig. 22.
According to the above judgment method, the corresponding program for energy coupling detection is written, an experimental test module is built, and the discharge state detection control test is carried out. The specific control signal waveform changing with the inter-electrode discharge state was obtained as shown in Fig. 23. The purple waveform in the figure is the interpolar discharge pulse signal waveform, which is a bipolar pulse. The blue waveform is the control differential output pulse, the maximum value is + 10 V, and the minimum value is − 10 V; the green waveform is the detection signal output by the energy coupling detection module of the interpolar pulse. In the open-circuit state, the peak-to-peak value of the pulse waveform of the inter-electrode discharge is large, the output value of the detection signal is small, and the differential output is positive; in the processing state, the peak-to-peak value of the pulse waveform of the interelectrode discharge is jittered, and the output value of the detection signal is also jittered synchronously. The differential output value is also constantly changing; in the short-circuit state, the peak-to-peak value of the pulse waveform of the inter-electrode discharge is small, and the output value of the detection signal also increases accordingly. The differential output is − 10 V, which ensures that the machining axis can quickly retreat and change the current short-circuit state as soon as possible.
In this section, based on the design of the discharge state detection system based on the energy coupling detection method, the overall design architecture scheme is proposed, and the discharge state detection system with STM32F103 as the control core is built, and the program design is carried out for the discharge state detection between the electrodes, and it is verified that the detection method can be realized. It can effectively detect the pulse energy between the poles of the VHF pulse in the morning, and complete the state detection during the machining process, which provides an important foundation for the application of the VHF EDM technology.
In order to further verify the validity of the device based on the energy coupling principle, an experiment was carried out on a self-developed EDM machine. The variation trend of the differential output and the spindle speed in the machining process is shown in Fig. 24. Whenever the differential output pulse changes, the detection system will quickly feedback and adjust the spindle speed. The SEM image of the discharge etching surface of Inconel718 is shown in Fig. 25. The Inconel718 has been successfully eroded, and there is almost no recast layer at the machining edge when the power is 50 W. The machined surface roughness is 235.54 nm and 266.70 nm at 50 W and 100 W power, respectively, while the conventional EDM method has a surface roughness greater than 300 nm with a high removal rate, and a thick casting layer will inevitably appear [17,18].

Conclusion
In this work, by studying the discharge state of the VHF micro-EDM process, the following research results are obtained: (1) Aiming at the detection requirements of VHF EDM discharge state, a method for detecting the discharge state of VHF pulse source based on the principle of energy coupling detection is proposed. The method combines electric spark discharge state identification technology and microwave detection technology and utilizes dual directional couplers and radio frequency detectors to realize pulse energy detection, which can realize accurate judgment of the discharge state of the VHF pulse source. (2) In view of the characteristics that the discharge characteristics of the VHF power supply are greatly affected by the inter-electrode impedance, this detection method is an indirect access detection method, which greatly reduces the impact on the inter-electrode impedance compared to directly connecting the detection circuit between the electrodes.
(3) The method can also detect the power between opencircuit poles and determine the optimal resonant frequency corresponding to the maximum power. In the processing system of this paper, the power between poles increases with the increase of the output amplitude of the signal source, and with the pulse frequency, it first increases, then decreases, then increases, and finally decreases again. Through the method, the open-circuit power of the control pulse can be maximized, and the processing efficiency can be improved under the energy output state of the signal source. Finally, the energy coupling detection method is used to detect the discharge state of the pulse power supply with a pulse frequency of 30 ~ 300 MHz and output power within 100 W, which fills the gap in the detection of the discharge state of the high frequency and high-power pulse supply. The machining experiment results show that the VHF pulse power supply can reduce the thickness of the recast layer and reduce the surface roughness, which plays an important role in improving the machining surface quality.