# Multibody Simulation for the Vibration Analysis of a Turbocharged Diesel Engine
## 2 Problem Description and Modeling Approach
### Models of Increasing Complexity
#### 2.2.1 Model SOL1  
For model SOL1, some components were schematized by an appropriate rigid body, such as a crankshaft, pulley, flywheel, clutch, connecting rods, pistons, piston pins and rings, or power unit (base, head, oil pan, distribution components, and accessories). In these cases, the specifications of geometric characteristics, values of inertia, mass, and position of the centers of gravity were sufficient. Moreover, the chassis was schematized by means of a \"Generic Body\" that represents the car chassis and can be considered as a constraint on the ground to which the powertrain must be clamped by three brackets: the engine, gearbox, and differential brackets (Figure 2a,b). In particular, \"Generic Body\" is a tool of EXCITE customized for the specific application by introducing the proper parameter settings. In order to represent the constraints between adjacent bodies, appropriate joints were used (Figure 2a,b). In the case of bearings, they were modeled by a revolution joint, with a given spring stiffness (related to the bearing stiffness) and damping value (related to the oil film characteristics). The stiffness values of the bearings were available from AVL database and selected for this specific engine version based on the following default values:  
* Stiffness at zero displacement 1e + 008 N/m
* Damping at zero displacement 10,000 Ns/m
* Stiffness at radial clearance 1e + 008 N/m
* Damping at radial clearance 20,000 Ns/m
* Radial clearance 0.0001 m.  
The joint force in radial direction is determined in the plane perpendicular to the main rotational axis as a function of the previously described parameters. The crankshaft was connected to the crankshaft using means of \"Revolute Joints\" that simulate the presence of the main bearings; this type of constraint allows us to recreate a linear contact between the  
Figure 5: (a) Powertrain with highlight of support positions: (b) engine bracket; (c) gearbox bracket; (d) differential bracket. Figure 6: Highlight of added point N.2, geometrically coincident with the N.1 but rigidly connected to the seismic mass. two bodies connected by a spring-damper modeling. In particular, the value of the clearance between shaft and crankcase and the stiffness and damping of the spring-damper system were inserted: these values depend on the maximum pressure in the combustion chamber, the bore, and the maximum force discharged on the single main bearings. No modeling of the oil film was provided, namely, hydrodynamics of the fluid in the main bearings (e.g., between piston and cylinder liner and the connecting rod) was not considered. Actually, in the literature it is proposed to take into account even the elastohydrodynamic interactions for some applications, because, for vibroacoustic analysis, some local modes, like those in correspondence of the bearings, can play an important role especially when considering the crankshaft bending behavior. Anyway, the focus of this work was solely on the shaft torsional behavior. In fact, the elastohydrodynamic interactions generally do not influence the torsional behavior because, due to a sufficiently high crankshaft stiffness, there is no coupling between the bending modes affected by elastohydrodynamic interactions and the torsional modes. Moreover, elastohydrodynamic allowance would cause a huge increment (three times) of run times. The bearings used in the engines to counteract the axial thrusts generated during motion were schematized with the constraint \"Axial Thrust Bearing\"; also for this case, clearance, stiffness, and damping values were provided. However, axial thrusts are considerably lower than those deriving from the vertical thrust, generated in the combustion chamber and acting on the main bearings (with this constraint, it was possible to connect a node of the shaft to more nodes of the crankcase).