## 3 Results and Discussion
### The Effects of Helix Angle on Scaffling Load Capacity
#### 3.3.2 Comparison of Contact Ratio, Specific Sliding, and Load-Carrying Capacity  
Figure 11 illustrates the contact ratios and bending safety factors for the five gear sets previously discussed. It is evident that the total overlap ratio increases in a linear fashion with the helix angle, rising from 3.105 to 5.493, which corresponds to a 76.9% increase. The most notable enhancement is observed in the overlap ratio \(\varepsilon_{\beta}\), while the transverse contact ratio exhibits a minor fluctuation of approximately 7.4%. A correlation exists between larger helix angles and higher overlap ratios, which contribute to enhanced gear motion and improved NVH performance. However, a larger helix angle also results in \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Gearset** & **Symbol** & **B10** & **B15** & **B20** & **B25** & **B30** & \\ \hline \hline \begin{tabular}{c} Gear \\ Tooth number \\ \(m_{\text{n}}/\text{mm}\) \\ \end{tabular} & \begin{tabular}{c} Z26 \\ 26 \\ \end{tabular} & \begin{tabular}{c} Z75 \\ 75 \\ \end{tabular} & \begin{tabular}{c} Z26 \\ 26 \\ \end{tabular} & \begin{tabular}{c} Z75 \\ 75 \\ \end{tabular} & \begin{tabular}{c} Z26 \\ \end{tabular} & \begin{tabular}{c} Z75 \\ 75 \\ \end{tabular} & \begin{tabular}{c} Z26 \\ 26 \\ \end{tabular} & \begin{tabular}{c} Z75 \\ 75 \\ \end{tabular} \\ \hline \begin{tabular}{c} Gear ratio \\ Pressure angle \\ \(\delta_{\text{n}}\) \\ \end{tabular} & \(10^{\circ}\) & \(15^{\circ}\) & \(20^{\circ}\) & \(25^{\circ}\) & \(30^{\circ}\) \\ \begin{tabular}{c} Face width \\ \end{tabular} & \(b\) & \(40\) mm & \(87\) mm & \(90.2\) mm & \(94.4\) mm \\ \begin{tabular}{c} Center distance \\ Profile shift \\ coefficient \\ \end{tabular} & \(x\) & \(0.239\) & \(-0.283\) & \(0.375\) & \(-0.185\) & \(0.208\) & \(-0.245\) & \(0.316\) & \(-0.357\) & \(0.196\) & \(-0.237\) \\ \
\begin{tabular}{c} Tip diameter \\ Root diameter \\ \end{tabular} & \(d_{\text{n}}/\text{mm}\) & \(47.5\) & \(126.25\) & \(48.7\) & \(129.5\) & \(49.6\) & \(132.7\) & \(51.5\) & \(137.2\) & \(53.5\) & \(143.9\) \\
\begin{tabular}{c} Root diameter \\ \end{tabular} & \(d_{\text{f}}/\text{mm}\) & \(38.61\) & \(117.65\) & \(39.576\) & \(120.484\) & \(40.287\) & \(123.498\) & \(42.25\) & \(128.03\) & \(44.025\) & \(134.47\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Gearset parameters of variable helical angle. Figure 10: The tooth contact flash temperature and scuffing safety factors. (**a**) Contact flash temperature; (**b**) scuffing safety factors. greater axial forces during meshing, which can negatively impact the life of the supporting bearings. Consequently, for power transmission gears, a helix angle exceeding 30\({}^{\circ}\) is typically not advisable. Figure 11b depicts the correlation between the helix angle and the root bending safety factor for the G2675 gear pair, with all other variables maintained at their respective constant values. The bending safety factor under peak load conditions demonstrates a nonlinear increase from 1.44 to 1.51 as the helix angle is increased from 10\({}^{\circ}\) to 30\({}^{\circ}\). Gear pairs with helix angles of 25\({}^{\circ}\) or less exhibit relatively similar safety factors. While a 30\({}^{\circ}\) helix angle enhances the overlap ratio and the bending safety factor, it also increases the axial force on the gear, thereby increasing the load on the bearings and potentially affecting their fatigue life. Therefore, the helix angle for high-speed gears is typically maintained below 30\({}^{\circ}\). Figure 12 illustrates the variation in sliding velocity and specific sliding as a function of the helix angle. The pitch circles of the gears exhibit variation due to different helix angles, resulting in the sliding velocity and specific sliding curves for the five gear sets being distributed approximately as normal equidistant lines. While the highest sliding velocities remain essentially equal, the maximum specific sliding decreases with an increase in the helix angle.