# A Study on the Effect of Gear Hobbing Process Parameters on the Residual Stress of the Tooth Root
## 3 Experimental Process and Method of Gear Hobbing
### Residual Stress Measurement  
According to the analysis, when the load acts on the highest point of the meshing zone of a single pair of teeth, the bending stress generated by the tooth root is the largest. The dangerous cross-section of the bending stress of the tooth root can be determined by the 30\({}^{\circ}\) tangent method [25]. The dangerous cross-section of the bending stress of the tooth root is shown in Figure 4. The residual stress on the tooth root has a significant impact on the bending fatigue performance of the tooth root. When the gear is meshing, the superposition of the residual stress at the tooth root and the contact stress is more likely to produce bending fatigue [26]. Therefore, the residual stresses of the gear root were characterized by measuring the residual stresses of the contact point position on the gear with a 30\({}^{\circ}\) tangent. Residual stress measurement methods usually include drilling method (destroying the workpiece), strain gauge method, X-ray method, and other technologies, among which X-ray diffraction method is the most convenient and reliable, and it does not undermine the workpiece residual stress measurement method. The measurement method used in this study is the isotropic fixed \(\psi\) method [28]. Figure 4: Dangerous cross-section of tooth root bending stress ((a) schematic diagram; (b) actual picture) [25; 26; 27]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Number** & \begin{tabular}{c} **Hob Speed/** \\ **(r-min\({}^{-1}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Axial Feed Velocity/** \\ **(mm/min)** \\ \end{tabular} &
\begin{tabular}{c} **Radial Cutting Depth/** \\ **(mm)** \\ \end{tabular} \\ \hline
1 & 450 & & \\
2 & 600 & & \\
3 & 750 & 3.5 & 1.125 \\
4 & 900 & & \\ \hline
5 & & 2 & \\
6 & 900 & 2.75 & 1.125 \\
7 & & 3.5 & 1.125 \\
8 & & 4 & \\ \hline
9 & & & 0.84375 \\
10 & 900 & 3.5 & 1.125 \\
11 & & & 1.6875 \\
12 & & & 3.375 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Single-factor experiment scheme. In the study, DS-21L laboratory high-power X-ray residual stress tester was used to measure the residual stress at the root of the gear hobbing machining. The measuring instrument has automatic peak searching and positioning functions, which only need to fix the gear to prevent the gear from rolling during the measurement process. The measuring device and measuring scheme for residual stress at the root of gear are shown in Figure 5. The settings of important parameters for measuring residual stress at the root of the tooth are shown in Table 6. It should be noted that all gears in the machining test have undergone error detection and meet the machining accuracy requirements. Since the surface of the root of the gear after hobbing is not smooth and flat, there are numerous hobbing marks [29; 30], which make the measurement position inevitably affected by the machining tool marks. Therefore, in order to ensure the accuracy of the results, three positions of A, B, and C were selected for measurement along the outer circle of each gear at a distance of 120\({}^{\circ}\), and the average value as the root residual stress of this gear was taken; considering the phenomenon of stress release, the middle position of each measurement position is selected as the measurement point. Reflection or absorption may occur during the measurement process, which may affect the measurement result. Therefore, absorbing materials were used at the measurement position to block the reflection, thereby eliminating the influence of reflection on the measurement result [31].