# A Study on the Effect of Gear Hobbing Process Parameters on the Residual Stress of the Tooth Root
## 4 Results and Discussion
### Orthogonal Test Analysis
Since the measurement of residual stress in the tooth root is conducted after machining, the influence of the interaction between the process parameters must be considered. Based on the test results presented in Table 7, the influence of the interaction of gear hobbing process parameters on the residual stress at the root of the tooth is obtained, as shown in Figure 8. In the figure, the horizontal coordinate is the two-way combination of three process parameters: hob speed, axial feed speed, and radial cutting depth, and the vertical coordinate is the residual stress value of the tooth root. If the residual tensile stress that is generated during gear machining exceeds 150 MPa, it may affect the performance. Therefore, the value of the residual stress is divided from 150 MPa in this study, so that the influence of the process parameters on the residual stress of the tooth root can be more clearly distinguished. Figure 8: \(Cont.\)  
Figure 7: Importance of gear hobbing machining parameters. According to the findings presented in Figure 8a, under the interaction effect of the hob speed and axial feed speed on the residual stress of tooth root, the residual tensile stress is lowest in the range of 2-2.75 axial feed speed when the hob speed is low. With the increase in hob speed and axial feed speed, the residual tensile stress will increase. The reason  
Figure 8: **(a)** The effect of interaction of gear hobbing process parameters on residual root stress (interaction diagram of hob speed and axial feed velocity). **(b)** The effect of interaction of gear hobbing process parameters on residual root stress (interaction diagram of hob speed and radial cutting depth). **(c)** The effect of interaction of gear hobbing process parameters on residual root stress (interaction diagram of axial feed speed and radial cutting depth). is that the increase in hob speed and axial feed speed will elevate the cutting force and the cutting temperature, resulting in the phenomenon of regional heating concentration, which together lead to the increase in residual tensile stress. Additionally, it is evident from the results that the influence of the hob speed on the residual stress of the tooth root is obviously greater compared to the axial feed speed. The reason is that the increase in hob speed results in a rapid rise in cutting temperature, and the speed of the temperature increase brought on by the hob speed is much higher than the temperature increase rate brought on by the axial feed speed rate, which is the main source of the increase in cutting temperature. Consequently, the hob speed plays a more prominent role in determining the residual stress at the root of the teeth, aligning with the findings from the simulation of a high-speed hobbing process mentioned in reference [36]. According to the findings presented in Figure 8b, the interaction effect between the hob speed and radial cutting depth on tooth root residual stress is similar to that in Figure 8a. Under the condition of low hob speed, the residual tensile stress decreases with the decrease in radial cutting depth. When the hob speed is 750 r-min\({}^{-1}\) and the radial cutting depth is maximum, the residual tensile stress is the highest. However, when the hob speed is 750 r-min\({}^{-1}\) and the radial cutting depth is the smallest, there is also a small residual tensile stress, clearly indicating that the interaction effect of process parameters on the residual stress of the tooth root is prominent. According to the findings presented in Figure 8c, under the interaction between the axial feed speed and the radial cutting depth on the residual stress at the root of the tooth, when the axial feed speed is slower than 3.5 mm/min, the residual tensile stress decreases with the decrease in radial cutting depth. The size of the axial feed speed is directly related to the cutting area and chip thickness, which will affect the cutting temperature and the machining quality of hobbing.