# CFD Analysis on the Heat Dissipation of a Dry-Lubricated Gear Stage
## 2 Methods and Materials
### Numerical Modeling and Calculation
#### 2.3.1 Geometry and Mesh Models  
Geometry and mesh models of the considered gearbox and gears are generally based on previous studies by the authors ([PERSON] et al. [3; 31; 32] and [PERSON] et al. [22]). The modeling of the gear rotation requires a dynamic mesh handling technique, for which the sliding mesh method is used in this study. Therefore, each gear is surrounded by a cylindrical zone rotating with the gear. As the real gear dimensions are investigated, the center distance has to be increased from 91.5 mm to 96.5 mm (+5.5%). Hence, the gear meshing is not explicitly considered. Although this will influence the fluid flow in proximity of the gear meshing, it does not significantly influence the main fluid flow in the gearbox. As the considered gearbox with spur gear-C is symmetrical to the median plane (XY-plane, see Figure 1a), a half model with the symmetry boundary condition is used. For the helical gear-LL, a full model is required. Each model consists of the gear zones (1), the cylindrical zones (2), the transition zone (3), and the outer zone (4). Figure 2 shows the modular structure of the geometry models for gear-C (a) and gear-LL (b). Mesh models are developed based on the presented geometry models. The gear zones (1) of gear-C are discretized with prismatic and hexahedral elements, whereas the gear zones (1) of gear-LL are discretized with tetrahedral elements. For both investigated gears, the cylindrical zones (2) are discretized with prismatic and hexahedral elements. The transition zone (3) and the outer zone (4) are discretized with hexahedral elements. The transition zone (3) between the gear zones and the outer zone allows a suitable control of the meshing process. Each cylindrical mesh zone (2) is connected with the transition zone (3) via numerical interfaces that enable a consistent calculation of the flow field. The mesh models visualized in Figure 3 are named based on the underlying gear as Mesh\({}_{\text{gear-C}}\) (a) and Mesh\({}_{\text{gear-LL}}\) (b). Mesh\({}_{\text{gear-C}}\) has an element number of approx. 1.9 M due to the predominant discretization with hexahedral and prismatic cells. Mesh\({}_{\text{gear-LL}}\) has an element number of approx. 5.2 M due to tetrahedral elements in the gear zones and full model approach. Detailed information on the mesh models is given in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**v\({}_{\text{t}}\) in m/s** & \(T_{oil}\) **in K** & \(T_{MI}\) **in K** & \(T_{M2}\) **in K** \\ \hline
2.0 & 303.25 & 304.75 & 304.85 \\
5.0 & 306.35 & 309.05 & 308.85 \\
10.0 & 313.55 & 318.15 & 317.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured oil and component temperatures for different speeds at no-load [21]. The numerical modeling approach is described in the following Sections 2.3.2-2.3.4. The descriptions are partly based on [22], but reutilized to improve overall comprehension. Figure 3: Front view on the mesh model \(\text{Mesh}_{\text{gear-C}}\) (**a**) and \(\text{Mesh}_{\text{gear-LL}}\) (**b**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mesh Model** & **Zones** & **Element Size in mm** & **Element Number in M** & **Density in Elements per mm\({}^{3}\)** \\ \hline \multirow{4}{*}{\(\text{Mesh}_{\text{gear-C}}\)} & (1) Gear zones & 0.75 (prism./hex.) & 222,373 & 1.47 \\  & (2) Cylindrical zones & 1.00 (prism./hex.) & 784,795 & 2.56 \\  & (3) Transition zones & 1.00 (hex.) & 79,016 & 1.52 \\  & (4) Outer zone & 1.00 (hex.) & 810,488 & 1.01 \\  & Overall Model & 0.92 & 1.89 & 1.33 \\ \hline \multirow{4}{*}{\(\text{Mesh}_{\text{gear-LL}}\)} & (1) Gear zones & 0.75 (tet.) & 1,078,204 & 6.17 \\  & (2) Cylindrical zones & 1.00 (prism./hex.) & 2,291,204 & 2.42 \\ \cline{1-1}  & (3) Transition zones & 1.00 (hex.) & 102,866 & 1.52 \\ \cline{1-1}  & (4) Outer zone & 1.00 (hex.) & 1,744,630 & 1.01 \\ \cline{1-1}  & Overall Model & 0.92 & 5.21 & 2.45 \\ \hline \hline \end{tabular}
\end{table}