## 4 Results and Discussions
### Theoretical Fatigue Life of DACBB  
Figure 16 shows the impacts of external radial load and angular misalignment on the theoretical fatigue life of DACBB. The external axial load and axial preload are 2000 N and 800 N, respectively. As shown in the Figure 16, the results suggest the nonlinear dependence of DACBB fatigue life on both radial load and angular misalignment. With the increase of external radial load or angular misalignment of inner ring, the fatigue life of DACBB will be significantly decreased. Moreover, it is also found that, under a lower radial load, the fatigue life of DACBB is more sensitive to the angular misalignment than that under higher radial load. Under lower external radial load, the fatigue life of DACBB rapidly decreases with the increase of angular misalignment. However, as the external radial load increases, such downward trend of fatigue life tends to be reduced. Moreover, in the same range of external radial load, the fatigue life of DACBB significantly decreases at lower angular misalignment, especially in the range of 0-0.2 mrad, whilst the change of fatigue life becomes more moderate when the angular misalignment is increased. Furthermore, as shown in the contour map of fatigue life described in Figure 16b, the variation pattern of DACBB fatigue life is almost independent on the direction of angular misalignment. The influence of negative misalignment angle on the fatigue life of DACBB is the same as that of the positive misalignment angle. Although the positive and negative angular misalignments are considered in this part, the figure of fatigue life is asymmetry with respect to 0 mrad. As a matter of fact, as shown in Figures 11 and 12, under positive angular misalignment, the contact load between rolling ball and raceway is not equal to that of negative angular misalignment. Figure 15: Influence of angular misalignment on the contact angle of DACBB: (**a,b**) contact angle of the left and the right rows under positive angular misalignment; (**c,d**) contact angle of the left and the right rows under negative angular misalignment. Meanwhile, it is also observed that the fatigue life of DACBB does not reach the maximum value at zero angular misalignment, and the value is a little bit greater than zero. Further, the corresponding size of angular misalignment slightly increases with the radial load. This means that the ring angular misalignment of a small size can improve the fatigue life of DACBB under combined loads. Figure 17 illustrates the influence of axial preload and angular misalignment on the fatigue life of DACBB. The external radial and axial loads are both 1500 N. As described in Figure 17, as the axial preload gradually increases, the fatigue life of DACBB shows a decreasing tendency. Meanwhile, the fatigue life of DACBB under smaller angular misalignment is more sensitive to the applied axial preload than that under higher angular misalignment. Under lower axial preload, the fatigue life of DACBB significantly decreases with the growth of angular misalignment. From the aforementioned analysis and discussion, it is seen that fatigue life of DACBB is closely dependent on the external load and axial preload. Particularly, angular misalignment is also an important factor that greatly affects the fatigue life of DACBB. In fact, as discussed in Figures 11 and 12, angular misalignment significantly influences the contact load distribution of DACBB. It leads to the fluctuation of contact load distribution, thus causes uneven load distribution in the bearing. With the increase of angular misalignment, the fluctuation is more sever. This leads to the fluctuation of contact  
Figure 16: Influence of angular misalignment and external radial load on the fatigue life of DACBB: (**a**) fatigue life of DACBB under different radial loads and misalignment angles; (**b**) contour map of fatigue life.