# Optimization Design of RV Reducer Crankshaft Bearing
## 4 Optimization Example
### Optimization Design of Crankshaft Bearing of RV-110E  
The convergence history of the bearing fatigue life of RV-110E is shown in Figure 11. After approximately 4 h of running time, optimization results satisfying all the design constraints are obtained. The fatigue life increases to 4840.1 million revolutions after 76 cycles. After this, there are small increases in the fatigue life, which increases to 5064.8 million revolutions after 196 cycles.  
Figure 10: Contact stress between raceway and roller of crankshaft bearings of RV-20E: (**a**) Contact stress before optimization; (**b**) Contact stress after optimization.  
Figure 9: Crown drops of crankshaft bearing rollers of RV-20E.  
A comparison of the parameters of RV-110E before and after optimization is presented in Table 3. By substituting the optimization variables into the above constraints, it can be known that all optimization variables can satisfy the constraints. Before optimization, the fatigue life of the crankshaft bearing was 1912.2 million revolutions. After optimization, the bearing life is increased to 5125.3 million revolutions. The fatigue life after optimization is increased by 168% compared with that before optimization.  
Figure 12 shows the structure of the crankshaft bearing of RV-110E before and after optimization. For RV-110E, the change in the structure of the crankshaft bearings is similar to that of RV-20E. The outer raceway diameter and roller diameter are also increased. The inner raceway diameter is decreased, and the number of rollers is reduced. The radius of the crankshaft bearing distribution circle is also increased. Although these dimensions have been changed, due to the constraints, the amount of change is within a limited range. Therefore, the change will not weaken the cyclo  
Figure 11: Convergence characteristic of fatigue life of crankshaft bearing of RV-110E.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Before Optimization** & **After Optimization** & **Rounded Values** \\ \hline \(r_{o}\) (mm) & 46.875 & 48.75 & 48.75 \\ \(D_{ue}\) (mm) & 6 & 9.3109 & 9.3 \\ \(D_{m}\) (mm) & 36 & 37.189 & 37.2 \\ \(z\) & 18 & 12 & 12 \\ \(L_{ue}\) (mm) & 10 & 10 & 10 \\ \(P_{d}\) (\(\mu\)m) & 0 & \(-\)6.4545 & \(-\)6 \\ \(K_{1}\) & 0 & 1.118 & 1.12 \\ \(K_{2}\) & 0 & 0.6317 & 0.63 \\ \(Z_{m}\) (\(\mu\)m) & 0 & 12.1601 & 12 \\ \(L_{10r}\) (\(10^{6}\)Rev) & 1912.2 & 5183.26 & 5125.3 \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of the design variables and fatigue life of RV-110E.  
Figure 13 shows the crown drops of crankshaft bearing rollers of RV-110E. The crown drop at the end of the roller is 12 \(\upmu\)m. The ratio of the crowning length to the effective contact length is 0.63. The roller diameter is increased after optimization, which helps to reduce the contact stress between the raceway and the roller.  
The contact stress on the roller that bears the maximum load is shown in Figure 14. Before optimization, the flat profile of the roller resulted in edge stress concentrations at the roller ends. The stress in the middle of the roller was approximately 1500 MPa. The maximum stress was 2660 MPa at the end of the roller. After optimization, the edge stress concentration is effectively eliminated. The maximum stress on the roller is reduced to 1380 MPa. The stress in the middle of the roller is reduced to 1300 MPa. The distribution of the contact stress over the length of the roller is much more uniform. This is beneficial for increasing the bearing life.  
Figure 12: Diagram of crankshaft bearing of RV-110E: (**a**) Structure of the crankshaft bearing before optimization; (**b**) Structure of the crankshaft bearing after optimization.  
Figure 13: Crown drops of crankshaft bearing rollers of RV-110E.