## 4 Results
### Structural Analysis of Bearing Thrust Loads  
Figure 5 presents the structural analysis results of bearing thrust loads for 9 speed drives, and combinatorial cases of helix angle directions of planetary gear sets are in \(RRLR\) and \(LLRR\) directions. The scope of this study is to analyze the influence of thrust loads yielded by helix angle directions on bearing power losses. The input torque applied to the input shaft is a pure torque, hence no radial loads on bearings are found in the automatic transmission structure. We display the results of bearings supporting thrust loads, which cover bearing 1 to 12. Here, \(L\) and \(R\) represent left- and right-hand helix angles of a sun gear, respectively. In the sense of letter locations amongst 4 capital letters, the letter in the far left and the one in the far right denote the angle directions of the first and fourth (or last) planetary gear sets. Thus, \(RRLR\) in Figure 5 means that the first, second and last helix angles are in right-hand and the third has a left-hand angle. Figure 5: Bearing thrust loads resulting from (**a**) \(RRLR\) and (**b**) \(LLRR\) directions of helix angles. From the results in Figure 5, it is identified that different thrust loads act to respective bearingss at a speed drive and thrust loads on individual bearingss are varied by changing speeds. As actuating brakes and clutches in accordance with the actuation table, torques and rotational speeds of central members of a planetary gear train are changed in magnitude and direction. As parts which are connected to the central members are supported by bearings, variations of the magnitudes of thrust loads occur by changed power flows. In comparing the results of Figure 5a,b, it is found that the maximum magnitudes of thrust loads are applied to different bearings. In the \(RRLR\) case, the maximum thrust load is on bearing 4 at the reverse speed, meanwhile the maximum load is recognized on bearing 7 to 10 in the \(LLRR\) case. In addition, the maximum magnitudes of the cases have different values. This distinction is systematically yielded by applying the different helix angle directions to the planetary gear train. Figure 6 displays the results of the maximum values in bearing thrust loads derived from the first to reverse drives for the entire 16 combinations of helix angle directions of planetary gear sets, and it shows that every combination yields different maximum bearing load conditions. Generally, larger gear ratios are assigned for the first and reverse drives of a power transmission than other drives, and larger torques are accordingly produced in these drives. This means that the largest thrust loads on bearings are identified under the first or reverse drive, and the results shown in the figure consist of the maximum values on individual bearings, which are identified from the first or reverse drives. In Figure 6, for 8 cases (colored in red) in the total combinations, the values of bearing 1 to 3, 11 and 12 are from the first drive, and bearing 4 to 10 have the maximum thrust loads from the reverse. However, for the other cases (colored in blue), the maximum loads of bearing 4 to 10 are obtained from the first speed and the maximum values of the others are from the reverse drive. In designing a transmission, amongst diverse magnitudes of loads acting on a bearing, the maximum load is one of the critical factors to select a proper bearing in considering bearing load capacity, since the bearing must have enough mechanical strength to tolerate various spectrums of loads in playing a role. In order to investigate which maximum load is totally supported for all combinations, all maximum loads on bearings are added up for every combination, and the result is presented in Figure 7. Here, it is identified that  
Figure 6: Maximum bearing thrust loads of the entire combinations of helix angle directions. (**a**) \(RRRR\)/\(RRLR\)/\(RRLR\)/\(RRLL\) directions; (**b**) \(RLR\)/\(RLR\)/\(RLR\)/\(RLLR\)/\(RLLL\) directions; (**c**) \(LRR\)/\(LRR\)/\(LRLR\)/\(LRLLL\) directions.