# Numerical and Experimental Analysis of the Oil Flow in a Planetary Gearbox
## 2 Materials and Methods
### CFD Modeling of the Oil Flow
#### 2.4.2 Meshing Approach  
As the investigated planetary gearbox is composed of spur gears, it is possible to exploit an extruded mesh approach. Extruded meshes are preferable over tetrahedral meshes, since they exhibit higher quality, lower memory usage, and faster calculation times. In a first step, the domain was decomposed in three subdomains which were meshed separately. The introduction of AMIs (Arbitrary Mesh Interfaces) [30] enabled the connection of adjacent non-conformal mesh domains. In this way, AMIs ensure the continuity of the field variables across the mesh discontinuities. In Figure 2, the three subdomains and the assembled domain are shown.  
Figure 2: Domain decomposition: the AMIs enable the numerical connection among the 3 subdomains.  
The first and the third subdomains are composed of the external parts of the gearbox and include a portion of the housing, the planet carrier, and the planet shafts. Their geometry is relatively simple, and an extruded mesh can be obtained. On the other side, the second subdomain contains the planets, the ring gears, and the remaining parts of the housing and of the planet carrier. The geometry of this subdomain is much more complex and, to generate a swept mesh, it is necessary to create axial partitions in correspondence with each tooth flank. Additional partitions with the shape of the planets, the ring gears, and the planet carrier profiles were created. Once all the necessary partitions were implemented, an extruded mesh was obtained for the second subdomain. In Figure 3, the longitudinal and the cross views of the assembled mesh are reported.  
The final mesh is composed of about 0.65 M prismatic elements. A grid sensitivity analysis of the CFD model was performed. The element number was varied from 0.37 M to 0.78 M. The maximum deviation of the power loss was only about 4%, even if the oil flow could be resolved better with increasing the element number. The grid with 0.65 M elements was chosen as a good compromise between oil flow resolution and computing time. The element size in the computational domain was of 1 mm. The analysis performed by [PERSON] et al. [2] on the same system was composed of about 0.73 M tetrahedral elements, thus resulting in a comparable number of elements, but in a different cell type. The quality parameters of the initial and the displaced mesh at the end of the imposed motion are listed in Table 4. As can be seen, the max non-orthogonality (angle between the line connecting two cell centers and the normal of their common face) was kept below 70 and the maximum skewness (distance between the intersection of the line connecting two cell centers with their common face and the center of that face) was kept below 4. The geometry and the mesh computation phase was handled via Python [31] scripts and Salome [32].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Max Non-Orthogonality** [\({}^{\circ}\)] & **Max. Skewness [-] \\ \hline Initial mesh & Displaced mesh & Initial mesh & Displaced mesh \\
50.7 & 66.1 & 1.6 & 2.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quality parameters of the mesh.  
Figure 3: Longitudinal and cross views of the assembled mesh. A full extruded mesh is obtained.