## 3 Results and Discussion  
### Structural Characteristics of the Revolving Cycloid Milling Cutter  
A revolving cycloid milling cutter was proposed to enhance the quality and efficiency of processing titanium alloy parts. A cycloid rotates around the center of the cutter to form the profile of the cutter end tooth of the revolving cycloid milling cutter. The intersection of the orthogonal helical surface and the tool profile surface is taken as the cutting edge curve. The structural characteristics of the revolving cycloid milling cutter and the ball end milling cutter are compared in Figure 3. The different structural characteristics of the two milling cutters make the difference in the tool angle and tool parameters, which affect the cutting force, tool wear, and surface quality of the workpiece. Therefore, it is necessary to identify the differences between the two tools through numerical simulation before discussing the results.  
It can be seen from the figure that the revolving cycloid milling cutter has short end teeth with a contour similar to a part of an ellipsoid. As a result, the helix angle of the cutting edge generated by the contour of the end tooth is increased rapidly.  
Equivalent cutting helix angles of the revolving cycloid milling cutter and the ball end milling cutter with the same radius are compared in Figure 4. Specifically, \(\psi\) in the figure represents the machining inclination angle, while point B\({}_{1}\) and point B\({}_{2}\) are the tool-workpiece contact points of the revolving cycloid milling cutter and the ball end milling cutter, respectively.  
\(\beta_{1}\) and \(\beta_{2}\) represent the tool helix angles at point B\({}_{1}\) and point B\({}_{2}\), respectively. With the machining inclination angle \(\psi\) as a parameter, \(\beta_{1}\) and \(\beta_{2}\) were simulated numerically. The result is shown in Figure 5. As can be seen from the figure, \(\beta_{1}\) is greater than \(\beta_{2}\) as the machining inclination angle changes from \(0^{\circ}\) to \(90^{\circ}\). Specifically, when the machining inclination angle is greater than \(5^{\circ}\) and less than \(60^{\circ}\), an apparent advantage can be found in \(\beta_{1}\), indicating that the actual cutting helix angle of the revolving cycloid milling cutter is larger than expected. Furthermore, the angles are interrelated and mutually  
Figure 4: Comparison of helix angles: (**a**) Revolving cycloid milling cutter; (**b**) Ball end milling cutter.  
Figure 3: Comparison of structural characteristics of the revolving cycloid milling cutter and ball end milling cutter (**a**) Revolving cycloid milling cutter; (**b**) Ball end milling cutter.  
affected in the design and cutting process of the milling cutter. According to the literature [24], when the helix angle is smaller than 45\({}^{\circ}\) and the cutting depth is less than 0.3 mm, the relationship between the working rake angle \(\gamma_{\alpha\epsilon}\) of the milling cutter, the helix angle \(\beta\), and the normal rake angle \(\gamma_{n}\) can be expressed by Equation (1):  
\[\sin\gamma_{\alpha\epsilon}=\sin\gamma_{n}\cos^{2}\beta+\sin^{2}\beta. \tag{1}\]  
The equation shows that when the normal rake angle is constant, the working rake angle increases with increasing helical angle. With the helix angle \(\beta\) as a parameter, the working rake angle \(\gamma_{\alpha\epsilon}\) was simulated numerically according to Equation (1). The result is shown in Figure 6.  
It can be observed from the figure that the working rake angle also increases with increasing helix angle. Also, an obvious increasing trend of the working rake angle with the helix angle can be witnessed when the helix angle is greater than 20\({}^{\circ}\).