# Modeling and NVH Analysis of a Full Engine Dynamic Model with Valve Train System
## 5 Results and Discussion  
### Valve Train Dynamic Analysis  
It is a common approach to consider the forces from the valve train to the engine body as external loads, which can be called an uncoupled approach. Based on the uncoupled approaches, previous researchers performed dynamic simulations [9; 22]. In this section, the dynamic analysis results using the coupled approach are compared with those in the uncoupled approach under the 2500 r/min WOT condition. The crank angles of 0 degree in the results are the moments of TDC on the compression stroke. Figure 20 shows the exhaust valve displacement and velocity comparisons between the two approaches. It can be found from Figure 20a that the moments of valve opening, maximum lift, and closing are basically the same in the two approaches. Due to the vibration of the cylinder head, the displacement should fluctuate slightly after the closure of the exhaust valve. In the uncoupled approach, the valve is completely stationary when the valve is closed, since the valve train dynamic model is independent of the cylinder head, while the slight displacement fluctuation can be captured accurately in the coupled approach. A slight fluctuation in the valve velocity curves in the coupled approach in Figure 20b can also be observed. The zooming in views at the opening and closing sections of the exhaust valve velocity are shown in Figure 20c,d. Since the rotation speed fluctuation and the disturbance from the cylinder head are not taken into consideration in the uncoupled approach, the valve velocity curve is relatively smooth and idealized except for the moment of opening. In the coupled approach, there are some fluctuations throughout the valve opening section. In the valve closing section, the velocity curve in the coupled approach is also not as smooth as that in the uncoupled approach. Figure 19: The positions of the acceleration sensors in the vibration experiments. As shown in Figure 21, compared with the uncoupled approach, the acceleration curve of the coupled approach has a more obvious fluctuation, especially in the positive acceleration section. When the valve is seating, there is an acceleration peak of 4474 m/s\({}^{2}\) in the coupled approach and 5050 m/s\({}^{2}\) in the uncoupled approach. The impact force from the engine valve is an important source of excitation from the valve train system. The exhaust valve seating force comparison is shown in Figure 22. When the valve is  
Figure 21: The exhaust valve acceleration comparison between the two approaches. Figure 20: The exhaust valve displacement and velocity comparisons between the two approaches: (a) exhaust valve displacement; (b) exhaust valve velocity; (c) exhaust valve velocity (opening section); (d) exhaust valve velocity (closing section). closed, the valve seat force is positively related to the in-cylinder pressure; therefore, the seat force curves of the two approaches are basically the same. When the valve is seated at the crank angle of 385 degrees, the peak force of the uncoupled approach is 412 N, while that of the coupled approach is 292 N. This shows that the flexible cylinder head model in the proposed approach may reduce the overestimated results of the valve seating force in the uncoupled approach. The camshaft bearing force is another important source of excitation to the engine. The comparison of the camshaft bearing force in the Z-direction is shown in Figure 23. When the valve is opening, the peak force of the uncoupled approach is 2586 N, while that of the coupled approach is 3385 N. In the coupled approach, the camshaft bearing not only bears the force of the cam to open the valve, but also reflects the impact of the cylinder head vibration. Therefore, in the coupled approach, there are more fluctuations in the bearing force curve even when the valve is closed, compared with those in the uncoupled approach. When the valve is opening, the HLA as a pivot bears the force of the valve opening.