## 4 Results and Discussions
### Contact Angle of DACBB  
Figure 13 demonstrates the dependence of contact angle of DACBB on the axial preload. The external radial and axial loads are 550 N and 500 N, respectively. The misalignment angle of inner ring is 0.2 mrad. From the results depicted in Figure 13, it is seen that the contact angle is closely dependent on to the axial preload. Under lower axial preload, whether the left or the right row, the curves of contact angle exist the blank, which denotes the area where the contact angle is inexistent because of no direct contact between rolling ball and raceway. Under higher axial preload, the contact angle of the left and the right rows significantly increases with the increase of axial preload. As shown in Figure 13a, contact angles in the upper half part of the left row of DACBB are higher than those of lower half part. However, for the right row, the contact angles in the upper half part is smaller than those of lower half part. Figure 14 illustrates the influences of external radial and axial loads on the contact angle of the left and the right rows of DACBB. The axial preload and the external axial load are 500 N and 1000 N, respectively, angular misalignment is 0.5 mrad. As shown in Figure 14a,b, the closely dependence of contact angle of each row of DACBB on the external radial load can be clearly observed. As described in Figure 14a, rolling balls in the lower half part of the left row of DACBB do not direct contact with raceway, thus the contact angle in such a region does not exist. However, in the upper half part, contact angle decreases with the increase of external radial load. For the right row of DACBB, contact angle in the upper half part is inexistent when the external radial load is 1500 N. When the radial load exceeds 1500 N, the contact angle between rolling ball and raceway is existed because all the rolling balls are in contact with the raceway and participate in the load transfer. Meanwhile, contact angle increases with the increase of external radial load. Figure 13: Contact angle of each row of DACBB under various axial preload: (**a**) contact angle of the left row; (**b**) contact angle of the right row. Figure 14c,d describes the effect of external axial load on the contact angle of the left and the right rows DACBB. The external radial load is 1500 N. As shown in Figure 14c, the contact angle increases with the increase of external axial load. Meanwhile, in the lower half part, the contact angle of the left row does not exist when the axial load is smaller than 2000 N. Once the axial load exceeds 2000 N, the contact angle at each ball position does not exist because all the rolling balls are in contact with raceway. As for the right row of DACBB illustrated in Figure 14d, the contact angle decreases with the increase of axial load. When the DACBB is loaded by the axial load of 500 N, all the rolling balls are in contact with raceway. However, with the increase of external axial load, some rolling balls are no longer contact with raceway. Therefore, the contact angle is inexistent, and the inactive number of rolling balls will be increased. Figure 15 denotes the effect of angular misalignment on the contact angle of the left and the right rows of DACBB under combined external loads. The axial preload is 800 N, and the external radial and axial loads are 1500 N and 500 N, respectively. As illustrated in Figure 15, it can be observed that angular misalignment of inner ring significantly influences the contact angle of DACBB. Meanwhile, owing to the symmetrical structure of DACBB, contact angle also shows the symmetry similar to that of the contact load described in the figures of Section 4.3. As shown in Figure 15a,b, the influence of positive angular misalignment on the contact angle of the left and right rows of DACBB is described. For the left row of DACBB, it is found that, under lower angular misalignment, the contact angle in the lower half part tends to be decreased.