## 4 Application in Crankshaft Bearing Design  
### Interference Assembly Problem of Crankshaft Bearing  
The method proposed in this study is applied to the structural design of a new electronically controlled single-cylinder diesel engine. The crankshaft bearing support of this new designed engine adopts sliding mode, the support system of which is shown in Figure 10. At operating temperature, bearing sleeve, bearing block and cylinder expand freely. Interference fit is formed between the bearing sleeve and block, as well as between bearing block and cylinder bearing hole. Therefore, only appropriate assembly interference can ensure that the contact pair is able to resist certain friction torque without causing excessive assembly stress.  
The material property of the components of crankshaft bearing support system is shown in Table 3.  
The initial design at normal temperature (25 \({}^{\circ}\)C) indicates that the interference between bearing sleeve and the bearing block is 0.0825 mm, and the gap between bearing block and cylinder bearing bore is 0.025 mm. Iterative calculations around the initial design are needed to determine the allowable range of the interference, and then determine the tolerances of components. Minimum interference (_i.e._, the assembly interference between bearing sleeve and bearing block is minimum, and the gap between bearing block and cylinder bearing bore is maximum) corresponds to the minimum contact  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Mechanical Variables and Locations**} & \multicolumn{1}{c}{**FEM Solution (MPa)**} & \multicolumn{1}{c}{\begin{tabular}{c} **Analytical Solution** \\ **(MPa)** \\ \end{tabular} } & \multicolumn{1}{c}{\begin{tabular}{c} **Relative Error** \\ \end{tabular} } \\ \hline \multirow{4}{*}{\begin{tabular}{c} Contact \\ pressure \# \\ \end{tabular} } & Interior contact & 14.5879 & \begin{tabular}{c} 13.0753 (Sequence) \\ 14.5441 (Coupling) \\ \end{tabular} & \(-\)10.30\% (Coupling) \\ \cline{2-5}  & & & 10.9596 & \begin{tabular}{c} 8.5253 (Sequence) \\ 11.0214 (Coupling) \\ \end{tabular} & \
\begin{tabular}{c} \(-\)22.21\% (Sequence) \\ 0.56\% (Coupling) \\ \end{tabular} \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Stress \end{tabular} } & inner cylinder & \(\sigma_{r}\) & \(-\)14.88 \(\pm\) 0.64 & \(-\)14.5876 & 2.00\% \\ \cline{2-5}  & \(\sigma_{\theta}\) & \(-\)188.05 \(\pm\) 0.58 & \(-\)188.4664 & \(-\)0.22\% \\ \cline{2-5}  & \(\sigma_{r}\)(in) & \(-\)14.503 \(\pm\) 0.029 & \(-\)14.5879 & \(-\)0.58\% \\ \cline{2-5}  & \(\sigma_{\theta}\)(in) & \(-\)5.355 \(\pm\) 0.016 & \(-\)5.1756 & 3.47\% \\ \cline{2-5}  & \(\sigma_{r}\)(out) & \(-\)10.986 \(\pm\) 0.055 & \(-\)10.9596 & 0.24\% \\ \cline{2-5}  & \(\sigma_{\theta}\)(out) & \(-\)8.895 \(\pm\) 0.021 & \(-\)8.8039 & 1.03\% \\ \cline{2-5}  & \(\sigma_{r}\) & \(-\)10.965 \(\pm\) 0.055 & \(-\)10.9596 & 0.05\% \\ \cline{2-5}  & \(\sigma_{\theta}\) & 23.945 \(\pm\) 0.027 & 23.8610 & 0.35\% \\ \hline \multicolumn{2}{c}{\# “Sequence” and “Coupling” represent sequential analysis and holistic coupling analysis, respectively; \({}^{*}\) Statistical analysis of 20 nodes selected randomly on the contact surface was conducted, with the expression of mean \(\pm\)STD; only the stress component on contact surface was concerned; for medium cylinder, the “in” and “out” represent the interior and exterior contact pair, respectively.} \\ \end{tabular}
\end{table}
Table 2: Contact pressure and stress analysis for tri-layer thick-walled cylinders by FEM and analytical method.  
pressure, when it needs to be ensured that no relative rotation occurs between the contact components. Maximum interference (_i.e._, the assembly interference between bearing sleeve and bearing block is maximum, and the gap between bearing block and cylinder bearing bore is minimum) corresponds to the maximum contact pressure, when it needs to be ensured that no plastic yielding occurs for the contact components.