## 3 Experimental Methodology
### Experimental Results  
The windage drag torque of the disc is negligible as calculated by Equations (10) and (11). Figure 4 depicts the change laws of disc drag torque values as the sum of the torque of the no-gearing system and the windage torque of the disc in the gearbox housing against the rotational speed. It is observed that the drag torque of the disc is less sensitive to the rotational speed. Hence it can be inferred that the windage drag torque of the disc is negligible, as theoretically analyzed by Equations (10) and (11). Therefore, these experimental measurements are the baseline test to obtain the net no-load power loss of all types of wheels. The standard deviations of the total no-load resisting torque from 1000 rpm to 6000 rpm are 0.0812, 0.0080, 0.0055, 0.0066, 0.0058, and 0.0027, respectively. Figure 2: Schematic diagram of the ad hoc test bench for splash-lubrication tests: (**a**) three-dimensional model; (**b**) experimental set-up. Figure 3: Typical geometric structure: (**a**) disc; (**b**) face gear; (**c**) level gear; (**d**) spur gear. Furthermore, the net no-load resisting torque was obtained at different oil-immersion depths and rotational speeds (Figure 5). As presented, the total no-load torque consisting of windage and churning drag torques showed a positive correlation with the rotational speed and oil depth. However, the changing trends between the resisting torque and the speed do not dovetail neatly with the parabolic rate law (\(T_{all}\propto\omega^{\lambda},\lambda\
eq 2\)). The two main reasons resulting in this changing law may be the strong windage effects and the non-constant churning torque coefficient \(C_{ch}\). For example, at the immersion depth \(\overline{h}\) of 0.5, the resisting torque evolves as the rotational speed power of nearly 0.76 for the spur gear (speed power of 0.79 in ref. [13] and 0.84 in ref. [12]), while windage torque evolves as the rotational speed power 2 as concluded by [PERSON] et al. [27]. This suggests that both the windage and churning phenomenon are remarkable and co-exist as stated by [PERSON] et al. [12] and [PERSON] et al. [13]. Other gears have similar situations as shown in Figure 5. The standard deviations of the total no-load resisting torque for the immersion depth of 0.3 and 0.5 are listed in Tables 1 and 2, respectively. Figure 4: Evolution of the baseline drag torque of the disc against the rotational speed. Figure 5: Evolution of the total no-load resisting torque against rotational speed: (**a**) \(\overline{h}=0.3\); (**b**) \(\overline{h}=0.5\). Although these wheels are fairly comparable in size and form, they are diverse in power losses and fluid flow patterns due to the gear teeth. Different wheels have a greater or lesser degree of windage effect, while the windage effect of the disc is the smallest. For straight level gears and orthogonal face gears, the churning behavior was investigated by [PERSON] et al. (2016) and [PERSON] et al. (2017). Their studies found that due to the air-pumping effect around these cross gears, the dynamic oil depth appears instead of the static oil depth. Corresponding qualitative analysis was carried based on churning behavior images captured by a high-speed camera, as depicted in Figures 6 and 7. As observed, a great amount of oil is stirred up along the rotational direction of the wheel, and most of it then hits the right wall of the housing and works in unison to flow back to the pool. Meanwhile, a higher rotational speed or oil depth contributes to more violent waves. The oil-free surface is very close to calm at a lower rotational speed and oil depth (\(h/R_{o}=0.2\), \(n_{g}\approx 1000\) rpm), especially for the disc. The light windage effect of the gear teeth disturbs the surface of the oil pool in the gearbox for the spur, bevel, and face gears. At a higher rotational speed and oil depth (\(h/R_{o}=0.3\), \(n_{g}\approx 6000\) rpm), the front and right walls of the housing are filled with an enormous quantity of liquid droplets and ligaments, especially for these gears.