## 2 Cutting Test
### Analysis of the Effect of Cutting Parameters on Surface Roughness
#### 3.2.2 Effect of Feed Rate on Surface Roughness  
Figure 9 shows the bar graphs of the variation of surface roughness with feed rate for the parameters of Table 4. The parameters of cutting speed of 1 m/min, depth of cut of 3.5 \(\upmu\)m, ultrasonic amplitude 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 surface roughness of the workpiece shows a significant increase with the increase in feed. Specifically, the surface roughness value is 82 nm when the feed rate is 16 \(\upmu\)m/rev. When the feed rate is increased to 22 \(\upmu\)m/rev, the surface roughness rises sharply to 200 nm, indicating that the feed rate severely affects the surface roughness. The analysis shows that when the feed is small, the machining environment and low thermal conductivity of workpiece may lead to the degradation of the machined surface quality due to the long cutting time; moreover, too large a feed leads to an increase in the residual height of the tool in the feed direction, which directly affects the workpiece surface roughness.  
As shown in Figure 10 below, we set the feed rate to 16 \(\upmu\)m/rev, 18 \(\upmu\)m/rev, 20 \(\upmu\)m/rev, and 22 \(\upmu\)m/rev to study its effect on the surface roughness of the workpiece. The results  
Figure 8: Surface morphology at different cutting speed: (**a**) \(v\) = 1 m/min; (**b**) \(v\) = 2 m/min; (**c**) \(v\) = 3 m/min; (**d**) \(v\) = 4 m/min.  
Figure 9: Surface roughness change with feed rate in UEVC.  
clearly show that at a feed rate of 16 \(\upmu\)m/rev, the material-removal rate per unit time is low, which results in relatively low cutting forces and temperatures, and under these conditions, due to the gentler cutting action, the ultrasonic elliptical vibration produces a more detailed \"fish scale\"-shaped vibration pattern, which contributes to a smoother surface. However, with the progressive increase in feed, we observed an increasing residual height on the workpiece surface, which directly led to a significant increase in surface roughness. Specifically, higher feeds increase the cutting forces, making the cutting area rougher and deteriorating the surface quality.  
In the ultrasonic elliptical vibratory cutting process, the correct feed selection is critical to ensure the surface quality of the workpiece. When the feed increases, the thickness of the cutting layer and the width of the chips increases as well, leading to a rise in the contact area between the cutting edge of tool and the surface of workpiece. This change increases the friction and cutting force and the difficulty of chip discharge, leading to the buildup of chips between the front face of the tool and the workpiece. This can cause chattering, making the machining process stage unstable and thus reducing the surface quality of the workpiece. In addition, more comprehensive chips are not easy to break during the cutting process and tend to wrap around the tool, which may lead not only to scratches on the surface of the workpiece but also exacerbate the wear of the tool, further destroying the quality of the surface of the workpiece. However, ultrasonic elliptical vibratory cutting technology has the advantage of reducing the phenomena of chipping the built-up edge and burrs, which provides strong technical support to improve the quality of cutting machining. Therefore, in the actual cutting process, as far as possible, we recommend choosing a smaller feed, such as \(f=16\upmu\)m/rev, to balance the machining efficiency and workpiece surface quality.