## 1 Introduction  
The use of multibody dynamic analysis has become a crucial aspect in the design and development of heavy-duty diesel engines. This is mainly because it enables accurate simulation and prediction of the dynamic behavior of engine components, such as the valvetrain, which plays a decisive role in engine operation, ensuring precise valve timing and, consequently, optimal combustion and power output [1, 2]. The opening and closing of engine valves, synchronized with the crankshaft's rotation, require precise coordination. However, this synchronized motion can cause problematic phenomena such as valve bounce, discrepancies between actual and theoretical valve lifts, delayed valve openings, and advanced valve closing times [3].  
[PERSON] et al. investigated the influence of cam speed and valve clearance on jump and bounce phenomena, concluding that both factors significantly affect the occurrence of these problems [4]. Similarly, [PERSON] and [PERSON] analyzed inertial forces and found that reducing valve lift could mitigate the risk of valve jump [5].  
[PERSON] et al. studied the effects of valvetrain misalignment on valve and guide interactions in automotive engines, focusing on intentional misalignments [6]. Their findings emphasized the asymmetric load distribution influenced by damping interactions between the valve tip and the roller finger follower. Contact losses in valvetrain systems, especially at high engine speeds, have significant consequences, including disrupted valve timing and reduced engine performance. [PERSON] and [PERSON] underscored the importance of dynamic analysis to predict contact losses and optimize valvetrain design [7].  
[PERSON] highlighted how the interaction between camshaft speed and system stability affects oscillatory behavior [8]. Oscillations in valvetrain systems arise from the inherent dynamics of the components and their interactions. Even minor disturbances can cause the finger follower to deviate from its intended position. Due to limited lateral clearance, this deviation leads to the follower striking clearance boundaries, causing large misalignment angles. These misalignments result in significant variations in the contact forces between the cam and the roller, which contribute to oscillatory behavior. At low camshaft speeds, the system exhibits instability similar to that of an inverted pendulum, making it highly susceptible to perturbations.  
[PERSON] and [PERSON] addressed the issue of valve float by investigating the effect of increasing the rocker arm ratio to achieve larger valve lifts with smaller cam lifts [9]. This adjustment reduced cam velocities and accelerations, effectively mitigating valve float. They also experimented with increasing spring stiffness, which resulted in higher Hertz stress. The stiffer spring required a greater force from the cam to overcome resistance, leading to elevated contact forces at the cam and roller interface. Consequently, this increased Hertz stress posed challenges for the durability of the components.  
This study presents a comprehensive methodology for valvetrain system analysis by integrating kinematic and dynamic modeling approaches. While previous studies in the literature often focus on either kinematic or dynamic modeling separately, this study combines both approaches to achieve a more holistic analysis. Kinematic modeling is used to determine fundamental motion characteristics, whereas dynamic modeling provides a detailed examination of system vibrations, contact forces, and interactions between components. Additionally, the validation process in this study is conducted through engine vibration measurements, allowing for a direct comparison between experimental data and model predictions. This approach not only contributes to valvetrain design optimization but also offers a valuable framework for validating dynamic analyses through engine vibration data.