## 3 Experimental Results and Discussion  
The Effect of Ultrasonic Processing Parameters on Specific Material Removal Rate and Surface Roughness  
In HEUM, the primary method for material removal relied on the ultrasonic vibrations of the tool driving the abrasive particles. During the machining process, the abrasive particles not only removed material through impact but also caused wear on the machining tool. Therefore, when discussing the material removal rate, it was necessary to consider tool wear to reflect changes in machining efficiency accurately. This work used the specific material removal rate to characterize the impact of HE on machining efficiency. Specific material removal rates were defined as  
\[\eta=\frac{l_{r}\Delta}{l\Delta_{r}}\times 100\% \tag{2}\]  
Figure 5: The effect of ultrasonic power on ultrasound amplitude.  
where \(\Delta_{r}\) was the actual removal depth, \(\Delta\) was the setting depth, \(l_{r}\) was the tool length after machining, and \(l\) was the tool's original length.  
The specific material removal rate under different ultrasonic amplitudes is shown in Figure 6. Regardless of the presence of HE, the specific material removal rate increased with the increase in ultrasonic amplitude. Compared with ultrasonic machining for the original workpiece, the introduction of HE could increase the specific material removal rate by up to 30%. The main reason is related to the quasi-cleavage flat facets that appeared in secondary cracks aligned with the feed direction instead of in the main crack [14]. Meanwhile, compared with the original workpiece, the HE workpiece shows low ductility, which is beneficial for improving machining efficiency [26].  
During machining through-holes, the effects of ultrasonic amplitude on the surface roughness of the sidewalls are shown in Figure 7. The changes in surface roughness of the sidewalls were not significant for both machining methods. Compared with the original workpiece, the surface roughness after HE was consistently lower, which was reduced from 0.34 \(\upmu\)m to 0.318 \(\upmu\)m, which was a relatively smooth surface for the application [27].  
Figure 6: The effect of ultrasonic amplitudes on specific material removal rate.  
Figure 7: The effect of ultrasonic amplitudes on surface roughness of the hole sidewall.  
Scratching grooves were observed by SEM; the result is shown in Figure 8. There is obviously material piling up on both sides of the groove in the original samples (Figure 8a-c), while in the HE samples (Figure 8d-f) comparation, there is none or little material piling up. As illustrated in Figure 8d-f, the surface quality remained high in the initial section of the groove. In the middle section, while there were minimal signs of burrs and material brittleness removal, the surface quality was still satisfactory, although a few micro honeycomb structures (Figure 8e) were noted within the groove. At the end of the groove, the removal of brittle material was clearly evident (Figure 8f), contrasting with the burrs that covered the end (Figure 8c). Overall, the surface quality throughout the rest of the groove was good. During the ultrasonic machining process, HE effectively minimized burr formation in the samples, ensuring consistently good surface quality.