# Modeling and NVH Analysis of a Full Engine Dynamic Model with Valve Train System
## 1 Introduction  
The valve train system is one of the important sources of vibration and noise in an internal combustion engine. For an ideal valve train system, on the one hand, the valve should be opened and closed as quickly as possible to improve the ventilation efficiency; on the other hand, each component should be operated smoothly to avoid the occurrence of jump, bounce, and overload, causing failures or noise vibration harshness (NVH) problems. The valve train dynamic model is used to simulate the motions and forces of the valve, spring, rocker, camshaft, hydraulic lash adjuster (HLA), and other parts during the actual operation of the engine. Therefore, the establishment of a comprehensive and accurate dynamic model is of great significance for studying dynamic problems and predicting the vibration and noise.  
The earliest valve train dynamic model is a single degree of freedom (DoF) model proposed by [PERSON] [1]. All the valve train parts, including the valve, washer, lock, and part of the spring, are simplified as an equivalent mass. The model is too simple to predict the valve motion accurately. [PERSON] established a valve train dynamic model with two DoFs, and demonstrated how the parameters of the model were selected to give the minimum vibration amplitude [2]. Since the 1980s, it has become easier to solve complex multivariate dynamic equations with the assistance of the modern computer. Models with distributed masses take elastic deformations into consideration, and more factors can be studied. [PERSON] formulated a 6-DoF dynamic model to predict the forces and the motions of the end-pivot rocker-arm cam system components [3]. [PERSON] built a valve traindynamic model with 21 DoFs to simulate the single valve train system of an overhead valve (OHV) engine [4]. [PERSON] studied the jump and bounce phenomena of a driven valve system based on a multiple-DoF dynamic model [5]. [PERSON] and [PERSON] considered the valve spring as a continuous flexible body. The valve spring was modeled as a distributed parameter system governed by the damped wave equation [6]. [PERSON] et al. investigated the nonlinear dynamic behavior of a cam mechanism with an oscillating roller follower in the presence of defects by a multiple-DoF lumped-mass model with two nonlinear hertzian contacts [7]. [PERSON] et al. proposed a mode matching method (MMM) for valve train components in a multiple-DoF dynamic model. The amount of lumped masses for each flexible component was determined based on its natural frequencies and the considered frequency range [8]. [PERSON] et al. proposed an enhanced flexible dynamic model for a valve train with clearance and multi-directional deformations and verified the model with experiments. They investigated the effects of valve clearance and cam rotation speed on the contact force, acceleration, and dynamic transmission error [9].  
Based on various multiple-DoF valve train dynamic models, each body and joint in the system has been modeled and analyzed in detail. However, all the above approaches just consider the valve train system as an independent system, ignoring the interaction between the valve train system and other parts of the engine, which will affect the accuracy of the dynamic modelling. In this paper, the dynamic models of the valve train system and other parts of the engine are combined into one model, forming a completed coupled engine dynamic model with the valve train system. In this coupled approach, not only the internal interactions of the valve train system, but also the external interactions between the valve train system and other parts of the engine are taken into consideration. For a valve train system in the form of end-pivot rocker arm with roller finger follower, the external interactions act not only on valves, springs, and bearings, but also on HLAs. Based on the full engine model coupled with valve train system, the dynamic simulation is performed, and the vibration and noise characteristics are predicted.