# Multibody Simulation for the Vibration Analysis of a Turbocharged Diesel Engine
## 1 Introduction  
Structural and acoustic modeling methods [1], used to predict the vibroacoustics and aeroacoustics performance of aerospace [2] and automotive systems, have become a key tool in the design process. Car engine dynamics are explored especially in the low frequency range and at low engine speeds, where the direct vibration transmission by the engine mounts is a critical excitation mechanism, but raising the maximum analyzed frequency constitutes an important industrial challenge for automotive and aerospace industry. There are several examples in the literature describing a combination of multi-body simulation, including flexible FE subsystems, to perform dynamics and acoustic simulation of mechanical components. In [3], a multibody model of a valve train system for a car engine was developed in order to analyze its resonant vibrational behavior. The dynamics of the valve train system were analyzed, applying a ramp to the crankshaft with a variable engine speed and considering the motion unsmoothness deriving from the inertia and combustion pressure loads. In [4] the development of a numerical model to predict the noise radiating from manual gearboxes due to gear rattle is provided. The measured data are used to identify and reproduce the input excitation that is primarily generated from engine combustion forces. The dynamic interaction of the gearbox components, including flywheel, input/output shafts, contacting gear-pairs, bearings, and flexible housing is modeled using flexible multibody techniques. The acoustic response to the vibration of the gearbox housing is then predicted using vibroacoustic techniques. In [5; 6] the numerical modeling of noise radiated by an engine and by a car body, respectively, using the so-called Acoustic Transfer Vectors and Modal Acoustic Transfer Vectors concepts is presented. The dynamics of the engine are described using a finite element model loaded with an RPM-dependent excitation. In [7], a technique to compute the noise radiated by a large truck engine is presented: the vibration is computed using a commercial FEM code, whose results are subsequently used in an acoustic radiation computation. In [8], a vibroacoustic numerical and experimental analysis was carried out for the chain cover of a low powered four-cylinder four-stroke diesel engine. A Boundary Element (BE) model of the chain cover was realized to determine the chain cover noise emission, starting from the previously calculated structural vibrations. The numerical vibroacoustic outcomes were compared with those observed experimentally, obtaining a good correlation. In [9; 10], a novel and effective mathematical model and advanced analytical approaches to achieve a more accurate prediction of the spiral level gear dynamic response were developed to investigate the underlying physics affecting gear mesh and gear dynamic response generation and transmissibility. In [11], an in-depth investigation of the dynamical load sharing behaviors of a four-planetary gear system with multi-floating components was provided. In [12], the impact of coupling engine structure with rotating components on the engine noise and vibrations across all rpm and frequency range is illustrated. The need for accurate models forms a major obstacle to the implementation of cylinder balancing methods for engines with a high number of cylinders [13]. This is due to closely spaced cylinder firings and the fact that the crankshaft dynamics cannot be ignored, partly due to the increased length of the crankshaft, and partly because analysis of higher frequency components is required to obtain sufficient information for balancing the cylinder-wise torque contributions. This deformation can assume significant values depending on the engine-load configuration (load change, crankshaft stiffness, kind of aspiration of the engine), and as such it is of great importance for safe engine operation.