## 2 Semi-Analytical Calculation Model for Gear Surface Flash Temperature
### Calculation Model for Tooth Surface Load and Flash Temperature  
Due to the elastic deformation that occurs after the mechanical transmission system is loaded, a pair of conjugate involute helicoid surfaces will not mesh at the theoretical position after being loaded but will exhibit uneven load distribution, stress concentration, or edge contact, as shown in Figure 3a. This can lead to early tooth surface pitting, scuffing, wear, or gear tooth flank fracture, and can also cause whine noise and meshing impact problems in the gear system. Gear surfaces without micro-modification often experience edge contact, particularly near the tooth tips, roots, or at the ends of the tooth face. This occurs due to elastic deformation, leading to high contact stress and, consequently, larger friction heat. This consumption of input energy can generate high flash temperatures, which can lead to  
Figure 2: Sliding speed on the tooth surface of helical gearset. scuffing failures. The advent of gear modification technology addresses these issues by making minor adjustments at the micron level to the gear surface geometry. This results in a deviation from the theoretical gear surface, as illustrated in Figure 3c. This modified surface no longer conforms to the theoretical involute helix. Gear micro-modification enhances transmission accuracy, improves the stability of gear operation, mitigates phenomena like load bias and stress concentration, and thereby extends the service life and enhances the load-bearing capacity of gears. The flash temperature distribution across the gear surface correlates positively with local load and relative sliding velocity. This is tied to the gear's rotation speed and macro-geometry and thus cannot be altered through minor modifications. However, micro-modifications can reduce contact loads in areas with high relative sliding velocities, thereby minimizing flash temperatures on the gear surface. For electric vehicle high-speed reducers, gear tooth modification can lower the flash temperature of gear meshing surfaces, effectively enhancing their anti-scuffing capacity. Additionally, it can decrease power loss during meshing, improve drive efficiency, and extend the vehicle's driving range. During the meshing process of gears, flash temperatures can be caused by friction on the tooth surfaces. When the contact temperature exceeds the allowable scuffing temperature, it can lead to scuffing on the tooth surfaces. Scuffing is different from fatigue; it can occur almost instantaneously. There are typically two methods of calculation TSFT: the Block flash temperature and the integral temperature method. The integral temperature is an average value of TSFT. It is based on the flash temperature at the pinion tip and incorporates the load-sharing coefficient into influencing factors. The integral temperature value closely approximates the maximum flash temperature, making the risk analysis for scuffing similar to that obtained from the flash temperature method. In instances where local temperature peaks are present, such as in gears with low contact ratios, edge contact at the tip and root, or contact at geometrically sensitive areas, the integral temperature exhibits reduced sensitivity and is unable to reflect the distribution of flash temperatures on the tooth surfaces. To investigate the state of TSFT distribution in gear pairs following elastic deformation and under conditions of uneven loads, an enhanced flash temperature method is more suitable for analysis. The equation for calculating the TSFT at the instantaneous contact position of the gearset is as follows [7]:  
\[\Theta_{fl}=1.11\cdot\frac{\mu\cdot X_{\Gamma}\cdot X_{j}\cdot w_{n}}{\sqrt{2 \cdot b_{H}}}\cdot\frac{abs\big{(}v_{g1}-v_{g2}\big{)}}{B_{M1}\cdot\sqrt{v_{g1 }+B_{M2}\cdot\sqrt{v_{g2}}}} \tag{6}\]  
Figure 3: The strategy and evaluation of tooth micro-modification. (**a**) Theory tooth surface contact stress. (**b**) Modified tooth surface contact stress. (**c**) Tooth surface modification topography.