# The Simulation Analysis of Cutting Characteristics and Chip Formation Mechanism in Gear Skiving
## 5 Simulation Results Analysis  
The stress states of the workpiece, chips, and tool at five different rotation positions during the gear skiving process, from tool entry to exit, are shown in Figure 7.  
* **Figure 8a:** In the initial stage of cutting, the cutting zone is divided into two segments. The approaching edge cuts into the workpiece from the root, while the intersection of the recessing edge and the top edge also engages the workpiece. * **Figure 8b:** As the tool and workpiece rotate relative to each other, the cutting width gradually increases, and the two cutting zones merge at the intersection of the approaching edge and the top edge, forming a V-shaped chip. * **Figure 8c,d:** As the tool continues to rotate relative to the workpiece, the thickness of the V-shaped chip increases. Due to the large cutting thickness of the skiving cutter, the shear zone connecting the chip to the workpiece material experiences significant stress, with the maximum stress occurring at the intersection of the approaching edge and the top edge. The chip is prone to fracture in this region. * **Figure 8e:** As the tool continues to rotate relative to the workpiece, the chip gradually separates from the workpiece material. The stress at the intersection of the approaching edge and the top edge decreases, indicating the formation of cracks in the chip in this region. Actual cutting processes also show that the chip is prone to fracture in this region [13], leading to fluctuations in cutting force and affecting the quality of the machined tooth surface. Figure 8e-j show the stress states at the five different rotation positions in the process from the tool entry to exit. During this process, the cutting stress on the cutting edge near the tool tip is the highest, indicating that the tool tip is the most susceptible to wear. The simulation results indicate that the maximum values of the equivalent stress of the tool are higher compared to the normal value. There are several possible reasons for this phenomenon:  
1. Due to the issue of simulation computation, the particle distance between SPH balls cannot be too small, which is selected as 0.1 mm, and it has sufficient calculation accuracy. Therefore, in order to better reveal the deformation law of skiving chips, the feed rate per revolution of the workpiece is increased to 1 mm, which is very large compared with the 0.2 mm in reality. 2. Actually, the tool edge radius is about 5 microns, but in simulation, the blade is sharp, which may result in the concentration of stress. 3. In the practice of gear skiving, the radial feed of the cutting tool is divided into multiple times, while in simulation, only one radial feed is implemented, so the material removal rate is very large. 4. The rake angle of the skiving tool is zero, which is another reason for the high cutting stress. Figure 7: Addition of gear skiving constraints addition. Figure 9 illustrates the contour plot of equivalent stress extracted from the cutting edge during the tool entry to exit process. As shown in the figure, the stress on the cutting edge near the tool tip peaks at a rotation angle of 25\({}^{\circ}\). At this rotation position, the cutting thickness is not the best, and the cutting conditions are not the worst, but due to the longer length of the cutting edge involved in the cutting, the cutting load is high, leading to high stress values on the cutting edge. Subsequently, as the cutting edge exits the cut, the stress values gradually decrease. Figure 8: _Cont._  
Figure 10 shows the maximum equivalent stress \(\sigma_{\max}\) at the points on the cutting edge during the tool entry to exit process. The maximum equivalent stress \(\sigma_{\max}\) can be expressed as:  
\[\sigma_{\max}(\psi)=\max[\sigma(\psi,\varphi_{\text{c}})] \tag{9}\]  
where \(\sigma\) is the equivalent stress extracted from the cutting edge during the tool entry to exit process.