## 3 Results and Discussion
### The Effects of Tooth Number and Module on Scaffing Load Capacity
#### 3.1.3. Tooth Flash Temperature and Scaffing Safety Assessment  
The distribution of flash temperature on the tooth surface is a critical indicator for the assessment of gear scuffing load capacity. Table 6 illustrates the distribution of flash temperature on the tooth surfaces of five sets of control gears, which were designed with an increased number of teeth and a reduced module. The aim of this study is to investigate the influence of different parameters on the TSFT.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Gearest** & **Tooth Surface Load Distribution** & **Tooth Surface Load Distribution** \\  & **Peak Speed Load Case: 99 Nm, 25,000 rpm** & **Peak Torque Load Case: 450 Nm, 5000 rpm** \\ \hline G2263 & 13.6 & 13.6 \\ G2263 & 13.2 & 12.8 \\ G2266 & 13.2 & 12.9 \\ G2267 & 13.2 & 13  
The left column of Table 6 enumerates the conditions at the maximum rotational speed, while the right column enumerates the conditions at the maximum torque. At the maximum rotational speed, the maximum flash temperature on the tooth surface is observed to decrease with a decreasing module, with a reduction rate of 33.7%. The maximum flash temperature observed at this condition was 54.3 \({}^{\circ}\)C, while the minimum was 36 \({}^{\circ}\)C. Similarly, under the maximum torque condition, the maximum flash temperature on the tooth surface decreases as the module decreases, with values ranging from a maximum of 217.7 \({}^{\circ}\)C to a minimum of 153 \({}^{\circ}\)C, indicating a reduction rate of 29.7%. Moreover, the position and shape of the maximum flash temperature on the tooth surface remain largely unaltered. It is evident that the strategy of Denser Teeth Design significantly reduces the frictional flash temperature on the tooth surface under extreme conditions, thereby offering a substantial advantage for gear performance.  
Figure 7 illustrates that both the flash temperature value and the scuffing safety factor demonstrate a tendency to enhance the gear scuffing load capacity with the increase of tooth number following the dense tooth design. The minimum scuffing safety factor for the pinion with 22 teeth is 1.071. An increase in the number of teeth on the pinion to 30 would result in a safety factor of 1.399, representing a 30.6% improvement. It can thus be concluded that,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Gearest** & **Load Case: Peak Speed** & **Load Case: Peak Torque** \\  & **99 Nm @ 25,000 rpm** & **450 Nm @ 5000 rpm** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Flash temperature distribution on tooth surface of variable module gearsets.  
provided that the tooth root bending load capacity and the speed ratio remain unaltered, an increase in the number of teeth will result in a reduction in the likelihood of gear scuffing failure. Furthermore, it can be observed that the flash temperature under the peak rotational speed condition is significantly lower than that under the peak torque condition, with the corresponding scuffing safety factor approximately twice as large. This suggests that the peak torque condition represents a critical point with regard to scuffing in the high-speed reducer of electric vehicles.