# Multibody Simulation for the Vibration Analysis of a Turbocharged Diesel Engine
## 2 Problem Description and Modeling Approach  
The analyzed problem concerns a numerical study of the vibrations of an in-line 4-cylinder, 4-strokes, internal combustion turbocharged diesel engine, to be used as a first step for future vibroacoustic analyses. Instead of a complex numerical analysis of the system through a direct FEM, which could involve prohibitive number of degrees of freedom, the authors present a modeling approach exhibiting a gradually increasing complexity. Starting from rigid body analysis and introducing progressively the elastic behavior of the various subsystems, using then a modal FEM analysis, the impact on accuracy of such modeling refinements comes out. The originality of the overall approach is related to the combination of various numerical approaches with an experimental analysis, for a very complex system. The analyses are focused on the 2 nd, 4 th, 6 th, and 8 th order of motion irregularities that are analyzed at the flywheel and pulley. In addition, the time-dependent simulation results at the engine support brackets (engine bracket, gearbox bracket and differential bracket) are evaluated, condensed to a vibration index and finally compared with the experimental results. A Multi-Body Dynamic Simulation (MBDS) of the crank train was used to characterize its dynamic behavior, starting from engine geometrical data and the available combustion loads, with both mechanical and combustion forces acting simultaneously on the crankshaft. In order to examine the vibration behavior of the considered internal combustion engine, the behavior of the crankshaft was specifically analyzed with a focus on its torsional vibrations, namely calculating the motion irregularities of the crankshaft itself. For the issue at hand, the modeled components were: crankshaft, pistons, connecting rods, main and connecting rod bearings, engine mounts (also named \"support brackets\"), contact stiffness between piston and cylinder. The first realized model assumed rigid bodies, allowing assessing the course of the motion irregularities of the crankshaft at low frequencies. With a maximum regime for the engine established at 4500 rpm, we considered 0-300 Hz a low frequency range: component resonances in this range can be activated by the 2 nd and 4 th engine order. The considered mid-frequency range was 300-700 Hz: resonances in this range can mainly be activated by the 6 th and 8 th engine order. High frequencies, higher than 700 Hz, can only be activated by aeroacoustics phenomena. The next step was the introduction of a crankshaft flexible model, leveraging on a FEM approach, in order to evaluate more accurately its dynamic behavior at higher frequencies. The frequency range of interest was anyway limited to the low-medium frequencies because the whole engine was modeled as rigid with the only exception of the crankshaft. Focusing on the low-medium frequency range, it was reasonable to assume a negligible influence from the modal behavior of other components than the crankshaft. Subsequently, the crankshaft FE model was further refined taking into consideration the presence of another component, the clutch: this allowed obtaining more accurate support brackets vibrations. Finally, a numerical-experimental correlation for the validation of the numerical model was carried out. Hypermesh and Abaqus [23] codes were respectively used for the FE modeling and modal analysis, whereas the realization of the multibody (MB) model and the forced vibrations analysis was demanded to AVL/Excite code [24]. The MB code considered the behavior of individual bodies as linear elastic; such bodies can be subject to both large rigid body motions and small deformations. The applied external forces come from the pressure cycle of the combustion gases [25]: from Figure 1 it is possible to appreciate the cycle variations at different regimes. All the forces of an inertial nature are calculated internally by the code according to the actual speeds and accelerations of the bodies.