## 3 Analysis and Optimization of Friction Flash Temperature of Gears Tooth Surface
### Micro-Geometry Modification Method to Reduce Tooth Surface Flash Temperature
Third, take the unit load of tooth surface at current contact position into Equations (9)-(17), and the tooth surface flash temperature at the current meshing position can be obtained. Fourth, after calculating \(N\) meshing positions in one meshing cycle, store the maximum flash temperature value of each node of each meshing position. Finally, the maximum flash  
Figure 6: Relative sliding speed and load distribution on the tooth surface of involute cylindrical gears. temperature of each node is integrated into a developed plane of tooth surface, and the flash temperature distribution of the entire tooth surface can be obtained. The changes of tooth surface flash temperature distribution with speed and torque before and after modification of G1735 gear pair are shown in Figure 8. It can be seen that the flash temperature distribution of the theory tooth surface is biased, and the maximum flash temperature appears at the tip and root of tooth right end, the maximum value at full load is 110.6 \({}^{\circ}\)C. After tooth modification, the maximum flash temperature is significantly reduced, and is mainly distributed in the middle of the double-tooth contact area symmetrical with the pitch line. The maximum flash temperature is 73.5 \({}^{\circ}\)C. When the speed is constant, as the torque increases, the maximum contact flash temperature position gradually transitions from the left to the middle of the tooth face, and the distribution area also expands to the entire tooth surface except the surface edge. When the torque is constant, as the rotational speed increases, the flash temperature distribution area almost does not expand, while the maximum flash temperature increases from 39 \({}^{\circ}\)C to 73.5 \({}^{\circ}\)C. It can be seen that because the relative sliding speed of the tooth surfaces near the pitch line is relatively low, the flash temperature on both sides near the pitch line is generally very low--only a few degrees Celsius. \begin{table}
\begin{tabular}{l l c c c} \hline  & **Item** & **Symbol** & **Pinion (G17)** & **Wheel (G35)** \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} Tooth \\ profile \\ \end{tabular} } & Barrelling/\(\upmu\)m & \(C_{A}\) & 10 & 0 \\  & Slope/\(\upmu\)m & \(F_{H\alpha}\) & 0 & 0 \\  & Tip relief start/mm & \(\mu_{T}\) & 43 & 70 \\  & Tip parabolic relief/\(\upmu\)m & \(F_{K\alpha}\) & 28 & 32 \\ \hline \multirow{4}{*}{
\begin{tabular}{l} Tooth \\ lead \\ \end{tabular} } & Lead crown/\(\upmu\)m & \(C_{\beta}\) & 9 & 0 \\  & Lead slope/\(\upmu\)m & \(F_{H\beta}\) & \(-11\) & 0 \\  & Bottom end relief length/mm & \(L_{\beta}\) & 10 & 10 \\  & Bottom parabolic end relief/\(\upmu\)m & \(\delta_{BP}\) & \(-22\) & 0 \\  & Top end relief length/\(\upmu\)m & \(L_{T}\) & 10 & 10 \\  & Top parabolic end relief/\(\upmu\)m & \(\delta_{TP}\) & \(-20\) & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Micro-geometry parameters of gearest-G1735 modification. Figure 7: The scheme and evaluation of tooth surface micro-geometry modification. (**a**) Theory tooth surface contact stress. (**b**) Modified tooth surface contact stress. (**c**) Tooth surface modification. Figure 8: _Cont_. The influence of tooth surface modification on the flash temperature of the gear pair is significant. It can be seen from Figure 9, the full-load maximum flash temperature of the 13 groups gear pairs after modification is lower than before, and the range of reduction is 7.9-37.1 \({}^{\circ}\)C, the reduction rate is 17.1-42.8%. This result shows that properly designed tooth surface modification can greatly improve the gear anti-scuffing capacity. Taking the G1735 gear pair as the research object, under the load spectrum, the maximum flash temperature distribution pattern before and after tooth modification is shown in Figure 10. It can be seen that the highest flash temperature point is located at the maximum power point (1500 r/min, 2000 Nm), and taking this load point as the center, it  
Figure 8: Colormap of tooth surface flash temperature distribution of gearset-G1735.