# Dynamic Behaviour of an Automotive Dual Clutch Transmission during Gear Shift Maneuvers
## 7 The Results of the Numerical Simulation
### Results comparison  
The best result, obtained according to this strategy of advancing the pre-selection phases to the next gears (case b), can be better evaluated by observing Figures 11 and 12, where the gear motion of the various gear pairs are reported. These figures compare the differences in terms of rattling behaviour referring to the above different strategies adopted in the case histories.  
These figures show, always for a time duration of 10 s, the angular relative motion between the teeth of the six gear pairs during the various shifting transients. As compared  
Figure 11: Angular relative motions of the various rattling gear pairs during a run-up transient: case (a).  
Figure 12: Angular relative motions of the various rattling gear pairs during a run-up transient: case (b).  
to the previous strategy (case a) an improvement about the rattling behaviour can be highlighted by observing, in the Figure 12, the time intervals where the synchronisation and the engagement and disengagement phases of the clutches occur.  
Furthermore, in concomitance with the phases of engagement and disengagement of the clutches, observed in the sequence 1 st-2 nd (time interval: 2.3-2.6 s in Figure 11); in the sequences 2 nd-3 rd (4.6 s-4.9 s); 3 rd-4 th (8.0 s-8.3 s in Figure 12), the relative motion of the gear teeth under load is free from strong deformations. If the teeth relative motion exceeds the circumferential backlash(from \(-40\times 10^{-6}\) m to \(+40\times 10^{-6}\) m) the interaction force is due to direct contact between the loaded teeth, expressed considering the meshing stiffness. This circumstance, evidenced from the comparisons of the results relative to the time histories of both cases of study, highlights better performances for the case b due to a significant reduction in the oscillations of the gear teeth motion. The adopted technique, simulated in the case b, where the gear rattle phenomenon is highly attenuated, represents the correct strategy that can be pursued to improve the vibro-acoustic behaviour of a gearbox equipped with a DCT system.  
The better rattling behaviour obtained with the proposed strategy is also confirmed by a frequency analysis. It is well known that for a non-stationary phenomenon the Fourier transform is not useful, but it is necessary to perform a time-frequency analysis. Therefore, the wavelet transform of the 2, 3, 4 gears' angular relative motion has been calculated. Figures 13-15 show diagrams in which the colour indicates the amplitude at a certain frequency and at a certain time instant. By comparison of the second and third gears' angular relative motions wavelet transforms between case (a) and (b) the reduction of vibrations induced is evident. The frequencies of rattle, the yellow lines in the figures, can be obtained multiplying the shaft speed for the gear number of teeth. As an example the rattle frequency of second gear between 2 s and 2.6 s is about 160 Hz (shaft angular speed 500 rpm (8.33 round/s), teeth number 19). For the 4 th the improvement is minor, almost negligible.