## 2 Structural Characteristics and Dynamic Behaviors of Cylinder Liners
### Excitation Configurations
#### 2.2.2 Piston Side Thrust
The zone has a height of 15 mm, allowing it to simulate the effective contacting areas at the moment when the combustion shock occurs. Prior to the formal dynamic simulation, the correctness and accuracy of the established FE model is verified based on an experimental modal analysis. The modal test was conducted to obtain the free-free modal responses of the studied liner. Subsequently, the accuracy of the established FE model is confirmed by comparing modal frequencies from the modal test with that of the FEA. Table 2 shows a good agreement between simulated and measured modal frequencies, with an error (except for the first mode) of less than 3%. The material parameter configuration and the simplified geometric shape are thus shown to be appropriate to represent the cylinder liner's dynamic response features below 10 kHz. It should be noted that during the modelling process, certain geometric details such as the grooves of sealing surfaces on the outer surface of the studied liner are neglected, which leads to slight decrease of the first mode frequency in simulation. Numerical analysis for understanding vibration responses to the two main excitations is based on the established model when the input is either the force of in-cylinder combustion or the piston slap force. Figure 6 shows two representative responses with respect to the combustion shock and piston slap at a 370\({}^{\circ}\) crank angle under identical operating condition: 1800 rpm and 40 Nm. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Simulated** & **Measured** & \multirow{2}{*}{**Error (\%)**} & \multirow{2}{*}{**No.**} & **Simulated** & **Measured** & \multirow{2}{*}{**Error (\%)**} \\  & **Frequencies** & & & & **(Hz)** & & **(Hz)** & \\ \hline
1 & 929.0 & 974.7 & 4.62 & 9 & 6673.2 & 6569.7 & 1.58 \\
2 & 1229.7 & 1217.5 & 1.04 & 10 & 6979.5 & 6896.1 & 1.21 \\
3 & 2567.3 & 2584.8 & 0.68 & 11 & 7926.9 & 7872.2 & 0.69 \\
4 & 3128.7 & 3195.2 & 2.08 & 12 & 8732.6 & 8559.4 & 2.02 \\
5 & 4191.4 & 4117.7 & 1.78 & 13 & 9011.1 & 8956.7 & 0.61 \\
6 & 4301.5 & 4324.5 & 0.53 & 14 & 9321.0 & 9177.1 & 1.57 \\
7 & 4847.0 & 4711.5 & 2.88 & 15 & 9879.4 & 9760.0 & 1.22 \\
8 & 5832.1 & 5785.3 & 0.81 & 16 & 9939.9 & 10,012.5 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulated and measured mode frequency of cylinder liner. Figure 6: Total deformation of cylinder liner (mm); (**a**) Response to combustion shock; (**b**) Response to piston slap. As Figure 6a shows, most of the deformation caused by the combustion shock is in the liner's top portion. The piston slap response, on the other hand, extended throughout the entire liner structure, as seen in Figure 6b. Removing translation movement and deformations resembling static deformations, allows extraction of information concerning the magnitude of local high-frequency deformations. The amplitude of combustion shock-induced response is predicted to be about 0.02 microns, which, being a lot less than the roughness of the lubricated surfaces, may be regarded as negligible for predicting lubrications between piston rings and liners, however, deformation caused by piston slaps can reach 0.1 micron, or roughly one fifth of the amplitude of roughness. To further verify the rationality of the established model, the simulated and measured radial acceleration responses of a typical node on the anti-thrust side of the liner, corresponding to the measuring point in the following actual test, were examined. Figure 7 shows that the amplitude of simulated acceleration spectrum is close to the measured one in terms of significant peaks and frequency ranges. It is further shown that the established model can properly characterize the cylinder liner's dynamic response features.