## 2 Materials and Methods
### Model Correlation  
The valvetrain system, a complex assembly of interacting components, is a significant source of vibration within an internal combustion engine [14; 15; 16; 17]. Rapid and repetitive movements of the camshaft, followers, pushrods, rocker arms, valves, and springs generate a complex interplay of inertial, impact, frictional, and torsional forces that directly contribute to engine vibration. Impact forces, primarily resulting from valve closing events and potential tappet/follower impacts, transmit impulsive vibrations through the cylinder head and engine block. Simultaneously, inertia forces arising from accelerating and decelerating valvetrain components induce oscillations, while friction within sliding contacts creates irregular vibrations. Torsional vibrations within the camshaft and timing drive system further exacerbate the problem, causing valve timing variations and structural stress. These vibrations are transmitted through the engine structure, which causes increased noise. Precise modeling of the valvetrain is critical to simulating the impact of its behavior on the engine structure and validating experimental data. The engine test is performed by measuring the vibration acceleration. The validation of the simulation results for the dynamic model in diesel engines was carried out through a structured comparison with the experimental test data on the Horiba test bench shown in Figure 4. The simulation framework was developed using the FEV Virtual Engine software suite, which allowed a detailed finite element model (FEM) of the engine to be constructed in Figure 5. This model incorporated accurate geometric representations of the engine components, such as the cylinder block, crankshaft, camshaft, and mounting points, along with material properties, including stiffness and damping characteristics obtained from the data sheets. In order to calculate the vibration in the system, the modal characteristics of the components at their operating speeds and corresponding frequencies, the directions and magnitudes of the forces depending on time and rpm are defined in the model. In the crank subsystem, connecting rods, pistons, and all bolts and fasteners are modeled with one-dimensional elements. The crankshaft, Torsional Vibration Damper (TVD), and flywheel are modeled with three-dimensional second-order tetrahedral elements. Second-order tetrahedral elements were used to create the finite element model of the engine block. Liners and flywheel housing parts are modeled with second-order tetrahedral elements, and they are connected to each other and to the engine block using one-dimensional and rigid elements. The main bearing caps are connected to the engine block at the respective positions. The simulations generated outputs including vibration acceleration distributions on flywheel housing and crankcase surfaces. Experimental validation was carried out on a prototype eight-cylinder diesel engine under test bench conditions that matched the simulation setup. The engine was instrumented with accelerometers to measure surface vibration accelerations. A synchronized data acquisition system recorded the signals at high resolution to ensure an accurate representation of transient behavior. The tests were performed under motored engine operation, with engine speeds ranging from 650 rpm to 1600 rpm. The engine was operated at constant speed by the dynamometer during the measured rpm. Horiba dynamometer is used for test specifications listed in Table 2.  
Figure 4: Engine test bench. Figure 5: Vibration measurement points on engine and dynamic model: (**a**) FEM model vibration request points. (**b**) Flywheel housing measurement point. (**c**) Crankcase vibration measurement point. To validate the simulation, multiple comparison surfaces were used. Crankcase and flywheel housing are one of the critical components for noise energy [18]. For this reason, measurements were taken from the points of these parts that were closest to the engine mounts.