## 4 Results
### Bearing Power Loss Analysis  
Bearing power losses of the transmission model, consisting of mechanical and spin power losses, are calculated by employing the power loss model described earlier, and the results are shown in Figure 8. The results present the total amounts of bearing power loss \(P_{b}\) for 1 to 8 forward drives, since the portion of the reverse drive is significantly low in driving cycles. For calculating spin power losses, the type of lubrication is set as oil bath and \(v_{o}=7.1\) is used for lubricant kinematic viscosity. Figure 9 presents the results of spin power losses of bearings for each forward drives and the total amounts of spin power losses of the entire forward drives. In the figure, it is noted that bearing 1, 2, 4 and 5 yield larger spin power losses than other bearings at certain drives since these bearings have higher relative rotational speeds at the drives. As described in the previous section, spin power loss is independent on thrust loads. Spin power loss analysis is carried out by calculating bearing rotation speeds with the kinematic analysis results, and the result is added to the results of mechanical power losses for the entire combinations of the helix angle directions. From the results in Figures 8 and 9, it is identified that mechanical power losses resulted by the helix angle directions are dominant in total power losses of bearings supporting thrust loads.  
Figure 8: Bearing power losses of the entire combinations of helix angle directions. (**a**) \(RRRR\)/\(RRRL\)/\(RRLL\) directions; (**b**) \(RLRR\)/\(RLRL\)/\(RLLR\)/\(RLLL\) directions; (**c**) \(LRRR\)/\(LRRL\)/\(LRLR\)/\(LRLL\) directions; (**d**) \(LLRR\)/\(LLRL\)/\(LLLR\)/\(LLLL\) directions.  
Figure 7: Total maximum thrust loads of the entire combinations of helix angle directions.  
In Figure 8, it is found that bearingss 4 to 10 have smaller power losses in the cases colored in red than the other cases highlighted in blue. Conversely, bearings 1 to 3, 11 and 12 produce smaller losses in the other cases highlighted in blue. This distinction is related to whether the maximum bearing loads are made in the first or reverse drive, and it implies that bearings having the maximum thrust loads in the reverse yield less total power losses since the reverse driving is not included in the power loss analysis. In order to investigate the total bearing power losses depending on the helix angle directions, all bearing power losses for every combination are added up and presented in Figure 10. Amongst the results for the entire combinations, it is identified that the case of _LLRR_ direction has the smallest total bearing power loss, whereas this case produces the largest bearing thrust load as recognized in Figure 7. However, _RRLR_ direction resulting in the smallest load has a large value in total bearing power loss. In designing a transmission, size and power efficiency are important factors for improving quality of a transmission. Based on the structural and power loss results and the assumption that as size of a bearing becomes larger, bearing load capacity increases, it is identified that _LRRL_, _LRLL_, _LLRL_ and _LLLL_ directions providing balanced performances in the aspects of load capacity and power efficiency would be the best options for the helix angle directions of planetary gear sets.