# Modeling and NVH Analysis of a Full Engine Dynamic Model with Valve Train System
## 5 Results and Discussion
### Vibration and Noise Results Analysis  
In the experiment, the engine rotational speed is 2500 r/min, thus the fundamental frequency is 41.7 Hz. There are obvious peaks at the second (83.3 Hz), fourth (166.7 Hz), and sixth order (250.0 Hz) frequencies in both the vibration and sound spectrums. As shown in Figure 26, the 1/3 octaves of the measuring point 2 acceleration on the cylinder head vertical to the surface in two simulation approaches are compared with the measured value in the experiment. In the uncoupled approach, the amplitude of the 80 Hz center frequency band is 4.68 m/s\({}^{2}\), which is much larger than the experimental value 1.43 m/s\({}^{2}\). The amplitude at the second-order frequency of 83.3 Hz is significantly overestimated using the uncoupled approach. In the other frequency bands, the amplitude difference between the uncoupled approach and the coupled approach is relatively small, and there is not much difference with the experimental value. The amplitudes of the low frequency bands have a great influence on the overall value; therefore, the vibration acceleration is severely overestimated in the uncoupled approach. Figure 24: The HLA seat force comparison between the two approaches. Figure 25: The spring force comparison between the two approaches. The vibration normal velocity level comparison colormaps between the two simulation approaches at the second order frequency of 83.3 Hz and the fourth order frequency of 166.7 Hz are shown in Figures 27 and 28, respectively. In order to show the velocity results of the cylinder head and the block more clearly, the intake manifold and the exhaust system are hidden in the colormaps, while in fact they are also involved in the calculation of vibration and noise. The velocity levels at the second order frequency of 83.3 Hz are where the two approaches differ most. As shown in Figure 27, the normal velocity levels of the upper parts of the engine including the cylinder head and the cylinder head cover in the uncoupled approach are larger than those in the coupled approach. This is consistent with the previous conclusion that the uncoupled approach overestimates the second-order vibration. The velocity levels at the fourth order frequency of 166.7 Hz are relatively close between the two approaches, as shown in Figure 28. In the coupled approach, the vibration velocities of the cylinder head and the block are slightly higher than those in the uncoupled approach, which is consistent with the previous 1/3 octave acceleration results on the cylinder head. The comparison of the acoustic results shows similar trends, as shown in Figure 29. The sound pressure level at the top measuring point at the second order frequency is 63.6 dB(A) in the uncoupled approach, which it is significantly overestimated compared with the experimental value 52.1 dB(A). The coupled approach value is 56.6 dB(A), which is much closer to the experimental value. The coupled approach has a higher accuracy at the fourth order frequency. The coupled approach value is 59.5 dB(A),  
Figure 27: The colormaps of the vibration normal velocity level comparison between the two approaches at the frequency of 83.3 Hz. Figure 26: The 1/3 octave of measuring point 2 acceleration comparison between two approaches. and the difference from the experimental value 60.4 dB(A) is only 0.9 dB(A). The uncoupled approach value is 54.8 dB(A), and the difference from the experimental value is 5.6 dB(A). At the sixth order frequency of 250 Hz, the coupled approach value also has a better precision. The measured value is 52.4 dB(A), and the value of the coupled approach is 57.7 dB(A), while the value of the uncoupled approach is 61.1 dB(A). The coupled approach shows a better accuracy on noise prediction in the lower frequency bands, which has a great impact on the overall sound pressure level value.