## 4 Analysis of the Consecutive Discharge Occurrence
From Figure 13, it is clear that in both groups, most discharges occurred with a discharge delay time between 200 us and 400 us, and this percentage reaches around 65% due to the servo feed control. Moreover, it is clear that the discharge percentage in Group 1 was higher than that in Group 2 when the discharge delay time was less than 200 us, coinciding with the first bubble oscillation cycle. In contrast, when the discharge delay time was greater than 500 us, the percentage in Group 1 was lower than in Group 2, which coincides with the collapse of the bubble. In Group 1, the percentage of discharges \(d_{i}\) with a discharge delay time shorter than 200 us was 26.9%, whereas this decreased to 12.9% in Group 2. This means that during the first oscillation of the bubble, further discharges occurred under its influence. Concerning those discharges with a delay time greater than 500 us, the difference between Group 1 and Group 2 was 13.7%. Thus, when the discharge delay time was greater than 500 us, the discharge occurred mostly at a distance greater than 0.5 mm from \(d_{i-1}\). This finding suggests that after 500 us, with the disappearance of the bubble generated by \(d_{i-1}\), its influence on \(d_{i}\) was also diminished. Figure 11: Distance between discharge location of \(d_{i}\) and the center of the bubble generated by \(d_{i-1}\). Figure 12: Comparison of bubble radius and \(l_{i}\). In addition, the relationship between the discharge delay time and the undischarged probability was plotted and is shown in Figure 14. In this figure, the entire curve is divided into four zones. In Zone 1, the undischarged rate decreased very rapidly in the first 100 \(\upmu\)s, which corresponds to bubble expansion. The bubble expansion process caused more debris to be emitted from the working gap, and during this process, the discharge probability increased. When the bubble shrank to around 100 \(\upmu\)s to 200 \(\upmu\)s, as shown in Zone 2, the influence of the bubble on discharge occurrence decreased. Most discharges subsequently occurred in Zone 3, with a delay time of around 200 \(\upmu\)s to 400 \(\upmu\)s due to the servo feed control. After that, with the dissipation of the bubble, the influence of the bubble on discharge occurrence also diminished, resulting in a slower decline in the undischarged rate in Zone 4. To further explore the influence of bubble expansion on discharge occurrence, the same experiment was conducted under peak discharge currents of 50 A and 100 A. Following image processing, the bubble oscillation process was plotted in Figure 15, including the data obtained at a peak discharge of 150 A for comparison purposes. It can be observed that with a lower peak discharge current, the first bubble oscillation cycle is shorter, and the bubble size is smaller. In addition, under the peak discharge currents of 50 A, 100 A, and 150 A, the end times of the first bubble expansion are 50 \(\upmu\)s, 75 \(\upmu\)s, and 100 \(\upmu\)s, respectively. Figure 14: Relationship between the undischarged rate and discharge delay time. Figure 13: Comparison of discharge delay time. The relationship between the discharge delay time and the undischarged rate under each type of peak discharge current was then plotted and is displayed in Figure 16. This figure also shows the end time of the first bubble expansion. It can be observed that, under all conditions, in the period of the first bubble expansion, the undischarged rate decreased very rapidly. In other words, more discharges occurred during the process of bubble expansion. This result again confirms the influence of bubble expansion on discharge occurrence, which can be explained by the impact of the debris particles concentrated at the bubble boundary.