# Research on Double-Arc Cutting Tool Design and Cutting Performance
## 3 Fabrications and Detection of DACT
### Experimental Results and Conclusions  
#### 4.2.1 Milling of the Inclined Plane  
The surface roughness of the inclined plane is shown in Figure 18. The surface roughness value machined by the DACT is _Ra_3.270, while the surface roughness value processed by the BEM is _Ra_3.421. When comparing the experimental results, the surface roughness value machined by the DACT is smaller, and the processing quality is better.  
Figure 16: Machine tool and cutting tools: (**a**) inclined plane; (**b**) concave–convex ruled surface.  
Figure 17: Cutting force test layout.  
The surface topography of the inclined plane machined by DACT and BEM are shown in Figures 19 and 20, respectively. The cross-section profile curve data of the inclined plane machined by the DACT and BEM were collected and drawn using MATLAB, as shown in Figure 21.  
Figure 19: Workpiece surface topography machined by DACT.  
Figure 20: Workpiece surface topography machined by BEM.  
Through numerical analysis, the variance, the standard deviation, and the range of the cross-section profile curve data of the inclined plane machined by the DACT is 29.8403, 5.4626, and 22.3438, respectively. Meanwhile, the variance, the standard deviation, and the range of the cross-section profile curve data of the inclined plane machined by the BEM is 47.1185, 6.8643, and 30.2734, respectively.  
It is obvious that the variance, the standard deviation, and the range of the cross-section profile curve data of the inclined plane machined by DACT are always smaller than by BEM; thus, better processing quality can be obtained when machining with the DACT.  
The cutting force component \(F_{x}\), \(F_{y}\), and \(F_{z}\) in the direction of the X-axis, Y-axis, and Z-axis, respectively, of the DACT and BEM are shown in Figure 22, while the radial force \(F_{rnd}\) and the resultant force \(F_{rns}\) of the DACT and BEM are shown in Figure 23.  
Figure 21: Comparison of workpiece cross section profile curve between DACT and BEM.  
Figure 22: Cutting force: (**a**) \(F_{x}\) of DACT; (**b**) \(F_{y}\) of DACT; (**c**) \(F_{z}\) of DACT; (**d**) \(F_{x}\) of BEM; (**e**) \(F_{y}\) of BEM; (**f**) \(F_{z}\) of BEM.  
The averages of \(F_{x}\), \(F_{y}\), \(F_{z}\), \(F_{rad}\), and \(F_{res}\) of the DACT and BEM are analyzed comprehensively. The experimental data show that the axial force \(F_{z}\) and the resultant force \(F_{res}\) of the DACT are larger than those of the BEM in this experiment. As mentioned in Section 2.2, the effective cutting width of the DACT is larger than that of the BEM by selecting an appropriate feed direction angle \(\gamma\) so that more materials can be removed. It is obvious that the feed direction angle \(\gamma\) is 0 in this experiment, and the cutting width of the DACT is the largest. Thus, more materials were removed and the resultant force \(F_{res}\) of the DACT is larger. Due to the tool cutting edge angle \(Kr\) of the DACT being smaller than the BEM, the axial force \(F_{z}\) of the DACT is larger than that of the BEM. At the same time, the radial force \(F_{rad}\) of the DACT is smaller than that of the BEM.  
When analyzing the average of the axial force \(F_{z}\) and the radial force \(F_{rad}\) of the DACT and BEM, the ratios of \(F_{z}\) and \(F_{rad}\) are 0.6823 and 0.4794, respectively. The larger the ratio of \(F_{z}\) and \(F_{rad}\), the better the process stability of the cutting tool. Therefore, the process stability of the DACT is better than the BEM in this experiment.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cutting Force** & **DACT** & **BEM** \\ \hline The averages of \(F_{x}\) (N) & 6.5273 & 5.3025 \\ The averages of \(F_{y}\) (N) & 5.8546 & 7.3486 \\ The averages of \(F_{z}\) (N) & 6.3999 & 4.7959 \\ The averages of \(F_{md}\)