## 2 Experimental Setup  
The general experimental plan and procedure are shown in Figure 1. In terms of constructing the WEDM process observation system, a NAC MEMRECAM x-3 high-speed video camera (Nac Image Technology, Tokyo, Japan) with a NIKON Ai Micro-NIKKOR 55 mm F2.8 lens (Nikon, Tokyo, Japan) was selected. The SUMITA metal halide lighting system LS-M250 (Sumita Headquarters, Saitama, Japan) was used for illumination, and the experimental observation setup is shown in Figure 2. A steel SKD 11 tool (FUSHUN special steel, Fushun, China) (widely used in industry) with a thickness of 10 mm was chosen as the workpiece, the chemical composition of which is shown in Table 1. In addition, a brass wire (Cu63%/Zn37%) with 0.2 mm of diameter was used for machining. First, the workpiece surface was prepared by a Sodick AP200 L WEDM machine (Sodick, Inc., Schaumburg, IL, USA) with a roughing cut and twice trim cut. The machining parameters are shown in Table 2. Subsequently, the mean surface roughness (\(R_{a}\)) and the maximum surface roughness (\(R_{z}\)) were measured with a Mitutoyo C-3200 (Mitutoyo, Kanagawa, Japan). The resulting \(R_{a}\) and \(R_{z}\) were 0.41 \(\upmu\)m and 2.91 \(\upmu\)m, respectively. The workpiece was then fixed at a central position between the upper and lower nozzle, with a distance between the two nozzles of 30 mm. In the WEDM process, the wire moves into the workpiece to perform the cutting. However, it is difficult to observe the gap phenomenon when the wire is in the kerf due to the illumination. Therefore, an observation experiment was designed to ensure that the observed result was consistent with the real cutting process. As shown in Figure 3a, the wire was first made to touch the surface prepared through WEDM and then made to move back to the initial position. Additionally, due to water's light-absorbing and -scattering properties, which can darken the surrounding environment and diminish visibility, a smooth workpiece was placed behind the main workpiece to reflect light and enhance the brightness of the observation area. From the initial wire position shown in Figure 3b, cutting was carried out along the prepared surface of the workpiece using the same parameters in Table 3. To guarantee that the observation of the gap phenomenon was made under a stable machining state, observation did not begin until the wire advanced 5 mm along the cutting direction. Then, the observation was made during the next 1 mm of cutting. Finally, the gap width between the wire and the workpiece at the final wire position was measured as 11.3 um by making the wire touch the workpiece. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**WEDM Parameters** & **Roughing Cut** & **1 st Trim Cut** & **2 nd Trim Cut** \\ \hline Open voltage (V) & 80 & 80 & 80 \\ Servo voltage (V) & 35 & 53 & 30 \\ Wire winding speed (m/min) & 10 & 10 & 10 \\ Discharge off time (\(t_{\mathit{eff}}\)) (\(\upmu\)s) & 15 & 23 & 1 \\ Wire tension (N) & 12 & 12 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Machining parameters for preparing the workpiece surface. Figure 2: Experimental observation setup. The schematic diagram of the observation system is shown in Figure 4. For this observation system, the high-speed video camera was connected to a personal computer (PC) to save the image data. A Tektronix MDO3024 oscilloscope (Tektronix, Beaverton, OR, USA) was used with a sampling rate of 10 MS/s. The current was measured by a Pearson current sensor, and the voltage was measured by a Tektronix TPP200 voltage probe. Moreover, a current value of 100 A was set as the trigger threshold to activate the high-speed video camera to start recording. During the observation, the camera's framing signal was also saved using the oscilloscope for later synchronization of the image and the discharge signal.