# Modeling and NVH Analysis of a Full Engine Dynamic Model with Valve Train System
## 3 Modeling and Analysis
### FEM Models  
Based on three-dimensional digital models of the engine main components provided by the manufacturer, the FEM models of crankshaft, block, cylinder head, cylinder head cover, timing cover, oil pan, intake manifold, and exhaust system are established, as shown in Figure 3. Given the fact that the crankshaft has a regular and symmetrical structure, the first order hexahedral elements are adopted in the FEM model of the crankshaft. However, other components with many fillets, bolt holes, and oil channels are complex; therefore, second order tetrahedral elements are adopted in the FEM models of the rest components. The parameters of the FEM models are shown in Table 2.  
The natural frequencies and mode shapes of the main components are measured by the experimental free modal analysis through the Lanczos algorithm and the multi-input single-output (MISO) hammering method [15]. As shown in Figure 4, the components are hung on flexible ropes, a hammer of type PCB 086C03 is used to excite the structures, and an acceleration sensor of type PCB 356A16 is glued to the structures to acquire the vibration signals. The hammer and acceleration sensor are connected to the LMS SCADAS data acquisition front-end, and the signal acquisition and analysis software is LMS Test.Lab.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Elements** & **Material** & \begin{tabular}{c} **Density** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Young’s Modulus** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Poisson’s Ratio** \\ \end{tabular} \\ \hline Crankshaft & 93,196 & & 7.85 & 210,000 & 0.30 \\ Oil pan & 9043 & Steel & 7.85 & 210,000 & 0.30 \\ Block & 269,359 & Cast iron & 7.30 & 110,000 & 0.30 \\ Cylinder head & 139,218 & Aluminum alloy & 2.73 & 76,550 & 0.34 \\ Timing cover & 91,996 & & Polypropylene & 1.40 & 3150 & 0.35 \\ Cylinder head cover & 64,609 & & Polyamide & 1.50 & 1800 & 0.30 \\ Intake manifold & 166,391 & & Polyamide & 1.50 & 1800 & 0.30 \\ Exhaust system & 98,330 & Cast iron & 7.80 & 191,000 & 0.30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Specification of the engine components.  
Figure 3: Finite element method (FEM) models of the components.  
The first five modal frequencies of the simulations and measurements are listed in Table 3. Comparing with the experimental results of the components, the errors of the simulation results are within plus or minus 6%, and the mode shape of each component is consistent with the corresponding experimental results. The accuracies of the FEM models of main components are verified, and the FEM models can be used in the following simulations.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Components** & **Order** & **Simulation/Hz** & **Measurement/Hz** & **Error** \\ \hline \multirow{5}{*}{Engine block (up) and cylinder head} & 1 & 545.5 & 543.6 & 0.3\% \\  & 2 & 987.3 & 1042.0 & \(-\)5.2\% \\  & 3 & 1368.2 & 1435.9 & \(-\)4.7\% \\  & 4 & 1455.3 & 1488.6 & \(-\)2.2\% \\  & 5 & 1635.9 & 1673.8 & \(-\)2.3\% \\  & 1 & 327.5 & 309.8 & 5.7\% \\  & 2 & 793.3 & 790.9 & 0.3\% \\ Engine block (low) & 3 & 940.5 & 969.9 & \(-\)3.0\% \\  & 4 & 1182.8 & 1145.3 & 3.3\% \\  & 5 & 1461.8 & 1385.9 & 5.5\% \\  & 1 & 406.5 & 309.6 & 4.1\% \\  & 2 & 553.5 & 529.8 & 4.4\% \\ Crankshaft & 3 & 907.9 & 881.0 & 3.1\% \\  & 4 & 950.9 & 920.9 & 3.3\% \\  & 5 & 961.6 & 923.3 & 4.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Modal frequencies of components: comparison of the results from the simulation and measurement.  
Figure 4: Modal experiments of components.