## 2 Cutting Test
### Experimental Methods and Plans
#### 3.1.2 Surface Topography and Surface Roughness  
Figure 4 gives the ultrasonic elliptical vibration cutting (UEVC) and conventional cutting (CC) of nickel-based superalloys under the parameters of Table 3 regarding the workpiece surface morphology and surface roughness change rule. The parameters of cutting speed of 4 m/min, feed rate of 17 \(\upmu\)m/rev, depth of cut of 3 \(\upmu\)m, ultrasonic amplitudes of \(A_{y}\) = 4.5 \(\upmu\)m and \(A_{z}\) = 1.2 \(\upmu\)m, and a tool nose radius of 0.5 mm were selected. The Figure 4 shows the cutting depth and machining surface roughness in bar graph; as the cutting depth (\(a_{p}\)) increases, the surface roughness (\(Ra\)) also gradually increases. The reason for this phenomenon is that, with the increasing cutting depth, the contact area between the tool and the workpiece increases, and the contact area between the chip and the front face increases, which leads to an increase in the cutting force, which produces a large number of harmful vibrations, which worsens the surface morphology of the workpiece and increases the surface roughness. Comparing the two cutting methods, the increase in surface roughness is more significant for regular cutting than for ultrasonic elliptical vibratory cutting because regular cutting is more sensitive to changes in the depth of the cut. In contrast, ultrasonic elliptical vibratory cutting reduces average cutting forces and, at the same time, reduces tool wear and extends tool life. So, ultrasonic elliptical vibration has less effect on the variation of cutting depth, which is a significant advantage in surface roughness and provides better surface quality. By observing the surface of the workpiece using super depth of field, we can see the significant difference between ultrasonic elliptical vibratory cutting and regular cutting in Figure 5. As can be observed from Figure 5a, ultrasonic elliptical vibratory cutting formed a series of complex and uniform vibration traces on the surface of the workpiece, and  
Figure 4: Surface roughness change with cutting depth in UEVC and CC. Figure 3: Cutting mechanisms and material-removal mechanisms: (a) ultrasonic elliptical vibration cutting process; (b) conventional cutting process. these textures showed apparent regularity. Specifically, the unique interrupted cutting of ultrasonic elliptical vibratory cutting processes create a delicate texture, causing the machined surface to display a unique texture pattern. In contrast, the surface of conventional cutting is rougher, with irregular veins that leave visible pits and scratches from the cutting process. These irregular veins and pear grooves significantly reduce the overall aesthetics and functionality of the workpiece, as shown in Figure 5b. These undesirable phenomena have improved substantially after the adoption of ultrasonic elliptical vibratory cutting technology. This advanced machining technology reduces surface defects and effectively enhances overall quality of the machined surface, thus providing crucial technical support for high-precision machining. Using white-light interferograms to observe the surface morphology, it can be seen from Figure 6a that there is a significant difference between ultrasonic elliptical vibratory cutting and ordinary cutting. The surface after ultrasonic elliptical vibratory cutting shows a high degree of flatness, with the vibration traces on the surface being uniform and regular and the contrast between the peaks and valleys of the waveforms being prominent. These features indicate the remarkable effect of the ultrasonic elliptical vibration technique in improving the surface quality. On the other hand, from Figure 6b, we can observe that the surface of regular cutting has cut marks of different sizes with many burrs and pits on the surface, thus seriously affecting the roughness and overall appearance of the surface.