## 2 Processing Principle and Experimental Details  
Figure 1 exhibits the machining principle of the proposed HEUM method. The HEUM process was divided into two stages. In the first stage, the hydrogen embrittlement treatment of a workpiece is carried out; then, in the second stage, the treated workpiece is taken for machining. The hydrogen embrittlement treatment is carried out for 0-40 min in a phosphoric acid solution of 98 g/L, with the voltage of the regulated power supply set to 0-20 V. The effect of hydrogen embrittlement on the organization of the Inconel 718 alloy is irreversible, and the maximum hydrogen diffusion depth can be calculated to be about 9.80 um according to [PERSON] et al. [22]. During the machining, a WC machining tool (Shenzhen KISONICS Technology Co., Ltd., Shenzhen, China) with a diameter of 0.5 mm underwent ultrasonic vibrations at a frequency of 40 kHz in its own axis. The experimental parameters are shown in Table 2, where the tool diameter was 0.5 mm, the amplitude was 2.28-9.3 um, the hydrogen embrittlement s time was 0-40 min, the hydrogen embrittlement voltage was 0-20 V, the feed rate was 20 um/min, the set depth of the observation pattern was 0.1 mm, and the set depth of the through-hole was 1.5 mm. A machine fluid nozzle was employed to supply the free abrasive particles into the machine zone with a given flow. The Inconel 718 specimen with dimensions of L40 \(\times\) W40 \(\times\) T1 mm was fixed on the workpiece fixture as a workpiece. As shown in Figure 2, the HEUM setup was established in this experiment by installing an ultrasonic tool on a three-axis moving platform. The physical drawing of the workpiece is shown in Figure 3, where the yellow-colored square area is the machining area, the size of which is 10 \(\times\) 10 mm. Figure 4 shows a schematic diagram of a through-hole machined in one pass taken by laser confocal microscopy. The ultrasonic amplitude was measured using laser multi-frequency interferometry (Polytec Co., Ltd., Waldbronn, Germany). The relationship between voltage and amplitude is shown in Figure 5. The ultrasonic transducer designed in this study was capable of achieving stable ultrasonic vibration, with the primary vibration direction along the z-axis. The ultrasonic amplitude in the other axis was negligible. The ultrasonic voltage and amplitude exhibit a linear relationship, with a maximum amplitude of 9.3 \(\upmu\)m.  
Figure 4: Through-hole schematic. Figure 3: Inconel 718 workpiece. Figure 2: Experimental setup. The tool wear and material removal depth were measured using a laser confocal microscope (Olympus Co., Ltd., Tokyo, Japan). In order to simulate the single abrasive machining of the sidewall, nanoscratch tests (Anton-Paar Co., Ltd., Graz, Austria) were carried out with HE samples. In the nanoscratch experiment, the indenter's load was incrementally raised to a specified value, while the diamond grain (B-T74) was advanced at a scratching rate of 5000 \(\upmu\)m/min with a peak load of 20 mN and a loading rate of 0.1 mN/s at a scratch length of 1000 \(\upmu\)m. This process resulted in the formation of a groove, the depth of which increased progressively. This behavior resembled the microcutting action exhibited by a single grain in HEUM. For comparative analysis, a non-treated workpiece was also subjected to testing. The morphological features were analyzed using a scanning electron microscope (SEM) manufactured by Zeiss Co., Ltd. in Oberkochen, Germany. Following this, the hardness was evaluated using a commercial nanoindenter (Shimadzu Co., Ltd., Kyoto, Japan) at a peak load of 10 mN and a loading speed of 0.2926 mN/s, employing a Vickers indenter.