# Substructuring of a Petrol Engine: Dynamic Characterization and Experimental Validation
## 4 Frequency Response Results of the Full FEM Model  
Modal-based frequency response analyses were performed for the full FEM engine model, considering the real loads occurring during the operation of the engine. In particular, the wide open throttle (WOT) condition was simulated, thus the maximum intake of air-fuel mixture, occurring when the throttle is completely opened, was considered as the engine working condition. Moreover, vertical loads representing the pistons and roll loads (from crankshaft rotation) were considered. For the former, only loads corresponding to the second engine order were needed (being the remaining negligible), whereas the fourth and sixth order were also added for the latter. Such loads were applied on a RBE3 element that in turn distributed the load onto the elements of interest. The objective of these analyses was to simulate the impact of the aforementioned bracket on the vibrations measured at the mounts during the engine operation. Experimental measurements of the mount vibrations were also available and were used here for validation. Figure 6: Numerical/experimental comparison on the acceleration/force ratio measured at the engine mount for the vertical bending load case: (**a**) with and (**b**) without the crankcase–gearbox bracket shown in Figure 3.  
Figure 7 shows the magnitude of the numerical displacement evaluated at the engine and gear mounts, with and without consideration of the presence of the bracket. It is worth noting that the adoption of the bracket has a positive effect at the engine mount just inside the range 5000-5500 rpm, whereas it seems to be ineffective elsewhere. On the contrary, a sensible positive bracket impact on the gear mount total displacement is evident above 4500 rpm. Apparently, only the bracket turns out to increase the magnitude of gear mount vibrations in the 5500-6000 rpm range because, as shown in the following, the model prediction in such a range, with reference to the gear mount, is inaccurate. Considering the experimental outcomes, as expected, the impact of the bracket introduction is also positive in the range 5500-6000 rpm: it is therefore sufficient to compare the blue testing lines of Figure 8a,b to understand that the total displacement is always lower when considering the bracket addition. Figures 8 and 9 show the experimental/numerical comparisons in terms of the displacements at the gear and engine mounts respectively. The setup for the experimental modal analyses is shown in Figure 10, which also highlights the supporting structure adopted to hold the engine. As previously anticipated, an acceptable correlation was obtained between the data but not for the gear mounts without the bracket (Figure 8b). A possible explanation could be related to the approximations inherent in the modelling of interface connections between the engine parts, where nonlinear contact conditions are skipped in order to reduce the computational burden but with the consequence of possible unrealistic interpenetration between interface surfaces. This aspect can become critical at high frequency (or namely at high engine rpm) as shown in Figure 11, where it is possible to observe that the gear mount presented excessive relative motions with reference to the gearbox at 210 Hz (referring to the second order, this corresponds to engine rpm slightly higher than 6000). Some remaining discrepancies can be ascribed to the uncertain damping attributed to the structural elements and to the simplified modelling of the bolts that interconnect the different parts of the engine. In any case, the full FEM modelling was considered as validated. Figure 7: Displacement magnitude calculated at the (**a**) engine and (**b**) gear mounts considering the realistic operating loading condition.