## 4 Results and Discussion  
The results and discussion of cutting performances such as surface roughness, cutting force, cutting tool wear and machined surface morphology are also divided into two parts in accordance with the two experimental phases arranged in this study. They are illustrated in sequence, Phases 1 and 2, as follows:  
Figures 6 and 7 show the comparisons of surface roughness, Ra, of the HEAs with different elemental ratios using the Set 1 and 2 process parameters, respectively, in the first phase experiment subjected to different ultrasonic-assisted milling techniques. The surface roughness under lower cutting conditions (Set 1) is better than that of the higher ones (Set 2) for almost all the depicted cases. Among the ultrasonic-assisted milling techniques, the single-axis ultrasonic assistance induces a better result, while milling without assistance shows the worst cutting performance. The results obtained from the dual-axis and triple-axis ultrasonic assistances just fall between these above two extremes. This can be attributed to the fact that single-axis ultrasonic assistance provides the vibration along the z-direction accompanied by rotary action, which helps to stabilize the cutting process. This stable vibration pattern may effectively reduce the surface roughness and the quality of the machined surface is thus improved. On the other hand, HEAs may respond less effectively to multi-axis vibrations than to single-axis vibration, since multi-axis vibrations may complicate the internal stress distributions within the workpiece material, affecting the cutting performance ultimately. In comparison to the non-assisted technique, the surface roughness for single-axis could be reduced by approximately 12.5%, 25.9%, and 17.86% for a Mn elemental ratio varying from 0.1 to 1.0, respectively, using the  
Figure 4: Schematic diagram of side milling experiment setup. Figure 5: Photograph of the machine-tool, the ultrasonic systems, and measurement devices. Set 1 process parameters, while reductions of 22%, 23.2%, and 34.4% are found using the Set 2 process parameters. Figures 8 and 9 show the comparisons of cutting force of the HEAs with different elemental ratios using the Set 1 and 2 process parameters, respectively, in the first phase experiment subjected to different ultrasonic-assisted milling techniques. When milling with single-axis ultrasonic assistance, the cutting force exhibited a slight increase. This may be because, although ultrasonic vibrations may reduce the tool--workpiece frictional constraint, their high-frequency contact intensifies the interaction between the tool and workpiece, preventing the overall cutting force from decreasing. The cutting force was considerably increased with dual-axis ultrasonic assistance, possibly because the ultrasonic vibrations acted simultaneously in two axial directions, leading to non-uniform material removal behavior and cutting resistance was thus increased. The cutting force was also increased with triple-axis ultrasonic assistance, which was contrary to expectations. This could be attributed to the triple-axis vibrations causing more interference to the cutting tool in various axial directions, but rotary ultrasonic assistance (single-axis) was included, which induces the cutting forces to be slightly less than those of dual-axis. Overall, these results indicate that the cutting force may be reduced by ultrasonic assistance theoretically but complex multi-axis vibration dynamics may irregularly disrupt the workpiece material removal mechanism in practical applications. Moreover, as the Mn elemental ratio varied from 0.1 to 1.0, the cutting force was shown to be positively decreasing. The lower Mn  
Figure 6: Comparisons of surface roughness of the HEAs with different elemental ratios using the Set 1 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques.