## 4 Results and Discussion
### Predictions of Different Wheels  
As described above, both the dimension analysis method by [PERSON] et al. [35] and the fluid flow method considering the dynamic depth integrating the air-oil ratio can make a good predictor of churning power losses for a typical disc. These approaches are then applied to other wheels including the spur gear, straight level gear, and orthogonal face gear. Figures 10-12 show the total no-load power losses using these two analytical approaches against rotational speed for the spur, bevel, and face gears. The experimental results are also superimposed in Figures 10-12. To sum up, acceptable agreements between the theoretical calculations and experimentations are shown, except in the case of an oil depth \(h/R_{0}\) of 0.3 and rotational speed of approximately 6000 rpm caused by experimental measuring errors.  
Figure 8: Comparison between the calculations determined by various methods and disc measurements (\(h/R_{0}=0.5\)) [35; 54; 55].  
Figure 9: Comparison between the calculations determined by various methods and disc measurements (\(h/R_{0}=0.3\)) [35].  
Some observations can be made:  
* There is no doubt that the rotational speed and oil-immersed depth are the most important parameters in energy dissipation. The higher the rotational speed of the gears is, the stronger the windage effect of the gear teeth becomes. The greater the oil depth of the wheels is, the more obvious is the chuming effect of the cylinders. These two aspects balance and lead to these complex phenomena of various wheels under splash lubrication. It is also found that for spur, bevel, and face gears, the oil-churning characteristics are similar to that of the disc, and the influence of windage behavior can be neglected at low speeds.
* Broadly speaking, the calculations for these gears are in accordance with experiments. The accuracy of predictions for the oil depth of 0.5 is higher than that of 0.3. For the depth of 0.5, the average relative errors between the calculations based on [PERSON] et al. [35] and the experiments are about 21.39%, 14.04%, and 12.02% for the spur, bevel, and face gears, respectively, while the average relative errors between the calculations based on the fluid flow method and experiments are about 16.89%, 10.09%, and 17.23%, respectively, as listed in Table 3. For the depth of 0.3, the average relative errors between the calculations based on [PERSON] et al. [35] and experiments are about 27.58%, 48.71%, and 10.23% for the spur, bevel and face gears, respectively, while the average relative errors between the calculations based on the fluid flow method and experiments are about 28.75%, 16.29%, and 35.70%, respectively, as listed in Table 4. Both of these approaches have their merits, but the latter method loses to the experimental data, as the applicability and accuracy of the physical analytical method are better.
* Furthermore, different kinds of gears have different windage effects. The windage power losses of discs can be ignored as shown above. However, the windage losses of spatial crossed gears (bevel and face gears) are much higher than those of spur cylindrical gears, and this ultimately affects their total no-load power losses under the condition of splash lubrication.