# Optimization Design of RV Reducer Crankshaft Bearing
## 4 Optimization Example
### Optimization Design of Crankshaft Bearing of RV-20E  
The convergence history of the fatigue life of crankshaft bearing of RV-20E is shown in Figure 7. After approximately 4 h of running time, optimization results satisfying all design constraints are obtained without any difficulty in convergence. The fatigue life increases to 11,896.1 million revolutions after 58 cycles. After this, there are small increases in the fatigue life, and it increases to 13,774.3 million revolutions after 216 cycles. Table 2 shows the comparison of the parameters before and after optimization. Before optimization, the profile of the roller was flat. Therefore, the values of \(k_{1}\), \(k_{2}\), and \(Z_{m}\) are set to 0. In practical situations, the optimization results must be rounded. The rounded parameters and life are also listed in the table. 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 4475.4 million revolutions. After optimization, the bearing life is increased to 13,254.2 million revolutions. The fatigue life after optimization is increased by 196% compared with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **20E** & **110E** \\ \hline Number of teeth & \(Z_{\text{g}}\) & 39 & 39 \\ Eccentric distance of crankshaft (mm) & \(e\) & 0.9 & 1.5 \\ Radius of pin tooth distribution circle (mm) & \(R_{z}\) & 52 & 82.5 \\ Radius of pin tooth (mm) & \(r_{z}\) & 2 & 3.5 \\ Width of cycloidal gear (mm) & \(B\) & 8 & 10 \\ Planet gear module (mm) & \(m\) & 1 & 1.25 \\ Diameter of crankshaft bearing (mm) & \(D_{L}\) & 12 & 20 \\ diameter of center hole (mm) & \(D_{h}\) & 24 & 43 \\ Torque (N-m) & \(T_{v}\) & 167 & 1078 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RV reducer design parameters. Figure 7: Convergence characteristic of fatigue life of crankshaft bearing of RV-20E. the life before optimization. After optimization, the value of the clearance is negative. This is because a proper negative clearance increases the bearing life. The structure of the crankshaft bearing of RV-20E before and after optimization is shown in Figure 8. The space of the cycloid gear is better used after optimization. The structural parameters of the cycloidal gear have not changed during the design optimization. The diameter of outer raceway is increased, while the diameter of the inner raceway is decreased. The roller diameter is increased, but the number of rollers is reduced. This makes the internal structure of the crankshaft bearing more reasonable. In addition, the radius of the crankshaft bearing distribution circle is increased. This is because the load of the crankshaft bearing from the cycloidal gear decreases as the radius of the bearing distribution circle increases. When the minimum thickness of cycloidal gear is too small, the structure strength of the cycloidal gear may be weakened. However, the constraint on the thickness of the cycloidal gear is considered in Section 3.3.8. Therefore, the thickness of the cycloidal gear after optimization will not be too thin. When the inner raceway diameter is too small, the contact stress between the inner raceway and bearings may exceed the strain limit. The constraints on contact strength have been proposed in Section 3.3.6, too. Therefore, the strength of the cycloidal gear and crankshaft bearing is not reduced after optimization. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Before Optimization** & **After Optimization** & **Rounded Values** \\ \hline \(r_{0}\) (mm) & 27.5 & 30 & 30 \\ \(D_{uv}\) (mm) & 3 & 5.2196 & 5.2 \\ \(D_{m}\) (mm) & 23.5 & 22.7802 & 22.8 \\ \(z\) & 23 & 13 & 13 \\ \(L_{uv}\) (mm) & 8 & 8 & 8 \\ \(P_{d}\) (\(\upmu\)m) & 0 & \(-\)2.4238 & \(-\)2 \\ \(K_{1}\) & 0 & 0.9627 & 0.96 \\ \(K_{2}\) & 0 & 0.7271 & 0.7 \\ \(Z_{m}\) (\(\upmu\)m) & 0 & 0.0096 & 10 \\ \(L_{10r}\) (\(10^{6}\)Rev) & 4475.4 & 13774.3 & 13254.2 \\ \hline \hline \end{tabular}
\end{table}