## 4 Results and Discussion
Figure 7: Comparisons of surface roughness of the HEAs with different elemental ratios using the Set 2 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. content was insufficient to enhance the alloy's toughness and wear resistance effectively, resulting in a greater compression force acting on the cutting tool during the cutting process. Figures 10-13 show the cutting tool wear, V\({}_{\text{B}}\), of the HEAs with Mn elemental ratios of x = 0.1 and x = 1.0, respectively, using the Set 1 and 2 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. It can be observed that the lower cutting tool wear appeared in milling without assistance or subjected to single-axis ultrasonic assistance. This is likely due to the smaller tool-workpiece frictional constraint and heat accumulation. In contrast, cutting tool wear is more obvious in milling subjected to dual-axis or triple-axis ultrasonic assistance, particularly in the dual-axis situation in which cutting tool wear is more severe as indicated by the red boxes in Figures 10c, 11c, 12c and 13c. This reveals that multi-axis ultrasonic assistance may increase the complexity of cutting forces, and greater cutting tool wear is inferred due to heat accumulation and the resulting thermal stresses. Further analysis also indicates noticeable changes in cutting edge chipping in dual-axis or triple-axis situations, which may be correlated with thermal stress concentration caused by high-frequency vibrations. Additionally, the presence of a built-up edge on the cutting tool face indicates that with high-frequency ultrasonic assistance, irregular chip removal behavior during the multi-axis ultrasonic machining process may lead to chip adhesion on the cutting tool face, further accelerating cutting tool wear. Figure 8: Comparisons of cutting force 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. Figure 9: Comparisons of cutting force of the HEAs with different elemental ratios using the Set 2 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. Figure 11: Cutting tool wear of the HEA for x = 0.1 using the Set 2 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. (**a**) Without assistance. (**b**) Single-axis ultrasonic. (**c**) Dual-axis ultrasonic. (**d**) Triple-axis ultrasonic. Figure 10: Cutting tool wear of the HEA for x = 0.1 using the Set 1 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. (**a**) Without assistance. (**b**) Single-axis ultrasonic. (**c**) Dual-axis ultrasonic. (**d**) Triple-axis ultrasonic. Figure 12: Cutting tool wear of the HEA for x = 1.0 using the Set 1 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. (**a**) Without assistance. (**b**) Single-axis ultrasonic. (**c**) Dual-axis ultrasonic. (**d**) Triple-axis ultrasonic. Figure 13: Cutting tool wear of the HEA for x = 1.0 using the Set 2 process parameters in the first phase experiment subjected to different ultrasonic-assisted milling techniques. (**a**) Without assistance. (**b**) Single-axis ultrasonic. (**c**) Dual-axis ultrasonic. (**d**) Triple-axis ultrasonic. Figures 14 and 15 show the comparisons of cutting tool wear 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. In comparison to milling without assistance, the cutting tool wear for single-axis under lower cutting conditions (Set 1) was increased with the Mn elemental ratio varying from 0.1 to 0.5 but it was decreased for the Mn ratio of 1.0.