## 4 Results and Discussions
### Displacement of DACBB  
When the DACBB is loaded by the external loads, the center of DACBB will deviate from its original position. Therefore, in this section, the influences of external loads and axial preload on the radial and axial displacements of DACBB are evaluated.  
Figure 7 shows the radial and axial displacements of DACBB under different external radial/axial loads and axial preloads. The angular misalignment of inner ring is ignored. As shown in Figure 7a,b, the influences of external radial load and axial preload on the radial and axial displacements of DACBB are illustrated. The external axial load is 3000 N, and the axial preload is changing from 100 N to 600 N. It can be observed that, with the increase of radial load, radial displacement of DACBB gradually increases, and the radial displacement is almost linearly related to the external radial load. However, with the growth of axial preload, the radial displacement of DACBB tends to be decreased. Meanwhile, it is also found that, under lower external radial load, the influence of axial preload on the radial displacement is not significant. However, as the external radial load gradually increases, the radial displacement obviously decreases with the increase of axial preload. Moreover, as described in Figure 7b, axial displacement of DACBB shows the opposite tendency compared to the result illustrated in the Figure 7a. Axial displacement significantly decreases when the external radial load increases. Similarly, the axial displacement of DACBB is also obviously dependent on the axial preload. With the increase of axial preload, axial displacement of DACBB shows the decreasing trend.  
\begin{table}
\begin{tabular}{c c} \hline
**Structure Parameters** & **Value** \\ \hline The diameter of ball (\(D_{iw}\)/mm) & 9 \\ The pitch diameter of ball center (\(d_{m}\)/mm) & 65 \\ Unloaded contact angle (\(\alpha_{0}\)/degree) & 25 \\ Axial distance between two rows (\(d_{c}\)/mm) & 16 \\ The groove curvature coefficient of inner ring (\(f_{i}\)) & 0.515 \\ The groove curvature coefficient of outer ring (\(f_{e}\)) & 0.525 \\ Rolling ball number of each row (\(Z\)) & 18 \\ Bearing clearance (\(\Delta_{i,e}\)/mm) & 0 \\ The Young’s modulus (\(E\)/MPa) & \(2.06\times 10^{5}\) \\ The Poisson’s ratio (\(v\)) & 0.3 \\ Rated static/dynamic load (KN) & 40.2/38.4 \\ \hline \end{tabular}
\end{table}
Table 2: Structural parameters of ACBB 7010 AC/DB.  
Figure 7c,d describes the dependence of radial and axial displacements of DACBB on the axial preload \(F_{0}\) and external axial load \(F_{a}\). The external radial load applied on the DACBB is 3000 N. As shown in Figure 7c, under different the axial loads and axial preloads, the variation of radial displacement of DACBB is different from that shown in Figure 7a. With the increase of external axial load, the radial displacement of DACBB gradually decreases. Meanwhile, it is also found that, under lower axial load, the radial displacement of DACBB is more sensitive to the axial preload than that under higher axial load. When the DACBB is loaded by lower axial load, radial displacement of DACBB significantly decreases with the increase of axial preload. However, as the axial load increases, the decreasing tendency of radial displacement tends to be reduced, and finally radial displacement becomes almost independent on the axial preload when the axial load exceeds 5000 N. In the same range of axial load, under lower axial preload, the radial displacement of DACBB is more sensitive to the applied axial load than that under higher axial preload. Furthermore, as shown in Figure 7d, with the increase of external axial load, the axial displacement of DACBB increases evidently. The influence of axial preload on the axial displacement of DACBB is the same as that shown in Figure 7b.