## 4 Numerical Setup
### Boundary Conditions  
Gears generate significant amounts of frictional heat due to the relative sliding and rolling during the meshing process, including the sliding power loss and the rolling power loss. The formula proposed by [PERSON] [28] was used to calculate the gear frictional heat in the intermediate gearbox. The sliding power loss is:  
\[P_{s}=10^{-3}f\cdot F_{n}\cdot v_{s} \tag{9}\]  
where \(P_{s}\) is the sliding power loss, \(f\) is the friction coefficient, \(F_{n}\) is the average normal load, and \(v_{s}\) is the average sliding speed. The rolling power loss is:  
\[P_{r}=\frac{9\times 10^{4}v_{r}\cdot h\cdot b\cdot\varepsilon_{\alpha}}{\cos \beta_{b}} \tag{10}\]  
where \(P_{r}\) is the rolling power loss, \(v_{r}\) is the average rolling speed, \(h\) is the thickness of the elastohydrodynamic lubrication (EHL) oil film, \(b\) is the tooth width, \(\varepsilon_{\alpha}\) is the gear end face coincidence degree, and \(\beta_{b}\) is the helix angle of the gear base circle. Gear churning power loss cannot be ignored for the splash lubrication method. The calculation formula for gear churning power loss proposed in the British Standard ISO/TR14179-1-2001 [29] was used herein. The influence factors considered in the formula are the lubricating oil viscosity, component diameter, gear wetting coefficient, and arrangement coefficient. The calculation accuracy is relatively high. \[P_{ch}=\frac{7.37f_{g}\cdot v\cdot{n_{s}}^{3}\cdot D^{4.7}\cdot b\cdot\left( \frac{R_{f}}{\sqrt{\tan(\beta)}}\right)}{A_{g}\cdot 10^{26}} \tag{11}\]  
where \(P_{ch}\) is the churning power loss, \(f_{g}\) is the gear infiltration factor, \(v\) is the kinematic viscosity of the lubricating oil at the operating temperature, \(n_{s}\) is the gear rotational speed, \(D\) is the component diameter, \(b\) is the tooth width, \(R_{f}\) is the tooth surface roughness factor, \(\beta\) is the spiral angle, and \(A_{g}\) is the arrangement coefficient. The overall heat source \(Q\) is:  
\[Q=P_{s}+P_{r}+P_{ch} \tag{12}\]  
Considering the differences in the material characteristics and the tangential speed at the meshing points of the driving and driven gears, the heat source input to the two gears is different. Consequently, the heat distribution coefficient \(\gamma\)[30] is introduced:  
\[\gamma=\frac{\sqrt{\lambda_{1}\rho_{1}c_{1}v_{1}}}{\sqrt{\lambda_{1}\rho_{1}c_ {1}v_{1}}+\sqrt{\lambda_{2}\rho_{2}c_{2}v_{2}}} \tag{13}\]  
where \(\lambda\) is the gear thermal conductivity, \(\rho\) is the gear density, \(c\) is the specific heat capacity, \(\
u\) is the tangential velocity at the meshing point, and the subscripts 1 and 2 represent the driving gear and driven gear, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Number of Mesh Elements** & **Air Flow Rate of the Air Vent (kg/s)** \\ \hline Mesh 1 & 3,361,947 & 0.1334 \\ Mesh 2 & 6,432,064 & 0.1106 \\ Mesh 3 & 10,589,597 & 0.1052 \\ Mesh 4 & 15,206,765 & 0.1031 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mesh independence analysis. The heat source inputs to the driving gear and driven gear, \(Q_{1}\) and \(Q_{2}\), respectively, are:  
\[\left\{ \begin{array}{l}Q_{1}=\gamma Q\\ Q_{2}=(1-\gamma)Q\end{array} \right. \tag{14}\]  
[PERSON]'s method [31] was used to calculate the heat source of the bearing. [PERSON] divided the friction torque of the bearing into the friction torque generated by the load and the friction torque generated by the viscosity of the lubricating oil. To simplify the calculation, this paper applies the bearing heat source calculated by [PERSON]'s method to the inner ring raceway, the roller wall surface, and the outer ring raceway, according to the ratio of 1:2:1. In this study, all heat sources were applied to the corresponding contact zones in the form of volumetric heat sources, as boundary conditions [13]. The coupled thermal condition was adopted at the fluid-solid interface to simultaneously calculate heat convection and heat conduction.