*4.3. Surface Machining Quality Analysis of UEVC*

The residual stress of UEVC machined surface with phase differences of 45◦ , 90◦ and 135◦ is extracted to obtain the evolution diagram of residual stress on the UEVC material surface, as shown in Figure 13.

Through the analysis of the machined surface topography under the two cutting trajectories in Figure 13, it can be obtained that different cutting trajectories will produce different morphologies on the material surface. For machining of different surface topographies, different cutting trajectories can be generated by adjusting the cutting parameters and ultrasonic parameters. It can be found from the curve that under the two cutting tracks, the residual stress on the machined surface is mainly compressive stress, but the tensile stress is also intermittently distributed. In addition, the tensile stress distribution range is wide when the phase difference is 135◦ . Compared with the surface residual stress diagram, it can be found that the tensile stress appears at the surface protrusion position, that is, the position where one effective cutting cycle (tool–workpiece contact) ends and another effective cutting cycle begins. The reason for this is that in the later stage of the effective cutting cycle, the tool begins to pull the material upward, resulting in tensile stress at the protrusion position [28]. In the next cutting cycle, the tool cuts the material using tensile stress, resulting in a small distribution range of tensile stress on the machined surface. Compared with the phase difference of 45◦ and 90◦ , the tensile stress distribution range of machined surface with 135◦ phase difference is wider. By analyzing the cutting path when the phase difference is 135◦ , it is found that the lifting stage of the tool is long.

Based on the above analysis, it can be concluded that the difference in cutting trajectory under phase difference control has a significant impact on the material removal

The residual stress of UEVC machined surface with phase differences of 45°, 90° and 135° is extracted to obtain the evolution diagram of residual stress on the UEVC material

mode. The influence of cutting speed on material removal is not obvious.

*4.3. Surface Machining Quality Analysis of UEVC* 

surface, as shown in Figure 13.

**Figure 13.** Evolution of surface residual stress of UEVC material. **Figure 13.** Evolution of surface residual stress of UEVC material.

Through the analysis of the machined surface topography under the two cutting trajectories in Figure 13, it can be obtained that different cutting trajectories will produce different morphologies on the material surface. For machining of different surface topographies, different cutting trajectories can be generated by adjusting the cutting parameters and ultrasonic parameters. It can be found from the curve that under the two cutting The plastic deformation value of the UEVC machined surface is extracted to obtain the evolution diagram of plastic deformation of the UEVC material surface, as shown in Figure 14. By analyzing the plastic deformation of the machined surface, it can be concluded that the degree of plastic deformation of the machined surface with phase difference of 45◦ and 90◦ is higher than that with a phase difference of 135◦ . In a cutting cycle under the two cutting trajectories, the plastic deformation value of the machined surface first decreases and then increases. At the same time, it can be found that the thickness of plastic deformation layer first increases and then decreases during a cutting cycle. The main reason for this is that there is compressive stress at the lowest point of the machined surface, and the stress transmission range is wider [29]. It leads to a wider range of plastic deformation along the depth direction. The reason the plastic deformation value is opposite to the thickness of the deformation layer is the different effect of stress [30]. At the beginning of a cutting cycle, the tool cuts downward, and the material surface bears the tensile stress in the cutting direction. Therefore, high plastic deformation occurs along the cutting direction, but the effect of compressive stress along the depth direction is weak. When the tool is near the lowest point, the material surface mainly bears the compressive stress along the

depth direction, which is mainly manifested in the greater depth of plastic deformation. The different performance of the two trends further shows that there is a "press–shear–pull" transformation in the removal process of UEVC material. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 16 of 18

**Figure 14.** Evolution of surface plastic deformation of UEVC materials. **Figure 14.** Evolution of surface plastic deformation of UEVC materials.

### **5. Conclusions 5. Conclusions**

In this paper, a UEVC finite element simulation model was established, and the UEVC cutting trajectory is planned. The cutting mechanism of the UEVC process is explored through simulation analysis. Through the analysis of cutting deformation, stress distribution, force heat change law and chip formation mechanism in each stage of the UEVC process, the mechanism of micro removal of materials in the UEVC process was obtained. The results show that: In this paper, a UEVC finite element simulation model was established, and the UEVC cutting trajectory is planned. The cutting mechanism of the UEVC process is explored through simulation analysis. Through the analysis of cutting deformation, stress distribution, force heat change law and chip formation mechanism in each stage of the UEVC process, the mechanism of micro removal of materials in the UEVC process was obtained. The results show that:

(1) The cutting temperature and cutting force in the UEVC process follow a law of periodic change. Different from traditional cutting, the cutting temperature in the UEVC process has a decreasing stage. The maximum point of cutting force in each cutting cycle is when the material removal is the greatest. The maximum point of cutting force is ahead of the maximum point of cutting temperature. (1) The cutting temperature and cutting force in the UEVC process follow a law of periodic change. Different from traditional cutting, the cutting temperature in the UEVC process has a decreasing stage. The maximum point of cutting force in each cutting cycle is when the material removal is the greatest. The maximum point of cutting force is ahead of the maximum point of cutting temperature.

(2) The removal process of UEVC material is a "press–shear–pull" composite cutting process. When the tool cuts into the material, the material is brittle. With increasing temperature, the material undergoes plastic deformation. The tool extrudes the material to form the chips, and the material is removed by adiabatic shear under the influence of high temperature. (2) The removal process of UEVC material is a "press–shear–pull" composite cutting process. When the tool cuts into the material, the material is brittle. With increasing temperature, the material undergoes plastic deformation. The tool extrudes the material to form the chips, and the material is removed by adiabatic shear under the influence of high temperature.

(3) Differences in UEVC trajectories affect the removal mode of materials and form different surface morphologies. In a cutting cycle, when the phase difference is 45° and

(3) Differences in UEVC trajectories affect the removal mode of materials and form different surface morphologies. In a cutting cycle, when the phase difference is 45◦ and 90◦ , there is secondary cutting in the cutting process. When the phase difference is 135◦ , the tool presses the location of chip separation following chip separation. Both methods make the machined surface more flat.

(4) For different cutting paths, compressive stress is distributed at the lowest point of the machining pit, and tensile stress is distributed at the protrusion position. The plastic deformation value of the surface layer of the machined surface first decreases and then increases, and the thickness of the surface plastic deformation layer first increases and then decreases. Compared with phase differences of 45◦ and 90◦ , the distribution range of compressive stress and plastic deformation of machined surface at 135◦ phase difference are smaller.

**Author Contributions:** Conceptualization, Z.W. and X.F.; methodology, Y.P.; software, X.M.; validation, Y.Z. and S.R.; formal analysis, Y.P.; investigation, Y.Z.; resources, X.M.; data curation, Z.W.; writing—original draft preparation, Z.W.; writing—review and editing, X.F.; visualization, X.F.; supervision, Y.P.; project administration, X.F.; funding acquisition, X.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by "the General program of National Natural Science Foundation of China (5217052208), Scientific research leader studio project of Jinan (2019GXRC054), General project of Shandong Natural Science Foundation (ZR202102280460) and Intelligent Bearing Manufacturing Innovation and Entrepreneurship Community Funded project of Shandong" and "The APC was funded by 5217052208".

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

