# CFD Analysis on the Heat Dissipation of a Dry-Lubricated Gear Stage
## 3 Results
### Analysis of the Isothermal Flow Field  
Figure 5 visualizes the steady-state flow fields for the circumferential speeds v\({}_{\mathrm{t}}\) = {2.0; 5.0; 10.0} m/s by vectors that are colored based on the local flow velocity. Figure 5 shows the results for gear-C (a) and for gear-LL (b). It can be seen that the rotating gears drag air in the circumferential direction, especially by the teeth. The air flow around the gears also has a component in the radial direction. The results feature clear similarities to the fluid flow in a dip-lubricated gearbox investigated by [PERSON] et al. [3] and [PERSON] et al. [22], showing oil flowing in the circumferential as well as radial direction due to inertia forces. In the gear meshing zone, the individual air flows of the pinion and wheel encounter each other, which results in an axial deflection and flow.  
For gear-C, the flow field in the axial direction (z-direction) is symmetrical to the median plane. Air flows away from the gears in the radial direction. Consequently, air is drawn from the front- and rear side of the gearbox to the rotating gears, thus flowing back to the teeth. This leads to a distinct air flow in the middle of the gear width where the encounter and accumulation of axial air flow and its radial outflow can be observed.  
The flow fields for the gear-LL show a distinct radial and axial circulation of the air. Due to the \"conveying\" effect of the helical gear, air is drawn from the front side of the gearbox and moved to the rear side. From there, the air flows back along the side walls to the front wall of the housing. In the process, turbulence forms in the outer areas of the gearbox housing.  
Figure 4: Simulation methodology for the thermal CFD simulations of the gearbox.  
Figure 5: Isothermal flow fields in 3D view and top view for \(\rm{v_{t}}\) = {2.0; 5.0; 10.0} m/s based on a steady-state calculation for gear-C (**a**) and gear-LL (**b**).  
The results show higher flow velocities with increasing circumferential speed. High flow velocity is predominant especially near the gears. In the outer regions of the housing, a comparable low velocity can be stated. The comparison of gear-C and gear-LL shows that, for each configuration, the rotating wheel generates a more distinct flow field compared to the pinion. A much stronger multidirectional air flow in the gearbox is predominant for gear-LL compared to gear-C. The results suggest that, for the geometries studied, the tooth width and helix angle have a greater influence on the interaction of the gears with the air than the tip diameter and tooth module.  
Figure 6 visualizes the flow velocities \(v_{x}\) in the x-direction and \(v_{z}\) in the z-direction below the wheel of gear-C and gear-LL for \(v_{t}\) = [2.0; 5.0; 10.0] m/s. The velocities are evaluated on an evaluation line that is shown on the left exemplarily for gear-C. The vertical position on the evaluation line is represented by \(y^{\prime}\). The flow velocity \(v_{x}\) is zero at the gearbox housing bottom and equal to the circumferential speed of the wheels at the tip circle. For both gears, \(v_{x}\) decreases strongly in proximity of the tip circle. Then, \(v_{x}\) is relatively constant. At \(v_{t}\) = 10 m/s, \(v_{x}\) shows a higher value for gear-C compared to gear-LL. Hence, gear-C generates a stronger flow field in the radial direction. The flow velocity \(v_{z}\) is negative in proximity of the tip circle, which means a flow toward the rear of the gearbox. Near the gearbox bottom, \(v_{z}\) is positive, meaning a flow toward the front of the gearbox. The flow velocity \(v_{z}\) is, over wide ranges, higher for gear-LL compared to gear-C, which indicates a more pronounced conveying effect of the helical gear.  
It can be summarized that the steady-state flow fields show a physically plausible behavior and enable a differentiation between the investigated gears. The steady-state flow fields serve as a valid starting point for the transient and thermal analysis.