# Analysis and Optimization of Driveline Bushing for Lateral Ride Vibration under Shock Excitation
## 5 Optimization of Rear Drive Unit Bushing Parameters
### Optimized Ride Vibration  
To find out the performance of the optimized differential bushings, the VDVs and the running r.m.s. acceleration at the driver seat rail in all three translational directions were calculated with the MBD model. The comparison between the VDV calculated with the baseline parameters and the optimized parameters at the driver seat rail (VDVR) and at the rear left passenger seat base (VDVLP) is listed in Table 3.  
It is shown that the optimized lateral VDV\({}_{\text{DR}}\) decreased by 47.5% compared with the baseline case. Improvements were also found in the fore-and-aft and vertical directions, although slight (about 1%). As discussed in the sensitivity analysis, the fore-and-aft and vertical vibrations at the driver seat rail were not sensitive to the change of the stiffness of differential bushings. As such, the improvement in ride quality in these two directions were limited through optimizing the differential bushing. For this reason, the overall VDV\({}_{\text{DR}}\) did not show apparent reduction after the optimization. Nevertheless, the reduction of the VDV\({}_{\text{DR}}\) reached 46.7% in the lateral direction after the optimization. The acceleration time histories at DR and LP before and after the optimization are shown in Figure 8. It can be seen the second peak of the lateral acceleration at DR when the rear axle crossed the obstacle was significantly reduced by 60% (from 0.28 to 0.11 m/s\({}^{2}\)) through the optimization of the differential bushings. Similarly, for the LP seat, the peak acceleration in the lateral direction was decreased by 55% from 0.55 m/s\({}^{2}\) to 0.25 m/s\({}^{2}\). In terms of the fore-and-aft and vertical directions, the bushing optimization did not show any adverse effects on the accelerations at the two seat positions. The running r.m.s. accelerations at the DR and LP are given in Figure 9. Same pattern can be found that the second peaks in the lateral direction were greatly reduced from 0.21 to 0.10 m/s\({}^{2}\) (for the DR) and from 0.38 to 0.15 m/s\({}^{2}\) (for the LP) respectively. While the differences of the running r.m.s. acceleration in the other two directions were hardly noticeable. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**VDV (m/s\({}^{-1.75}\))** & **Direction** & **Baseline** & **Optimized** \\ \hline \multirow{3}{*}{Driver} & Fore-and-aft & 0.79 & 0.78 \\  & Lateral & 0.13 & 0.07 \\  & Vertical & 0.55 & 0.55 \\ \hline \multirow{3}{*}{Left passenger} & Fore-and-aft & 0.79 & 0.79 \\  & Lateral & 0.23 & 0.10 \\ \cline{1-1}  & Vertical & 0.84 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of VDVs between the baseline and the optimized bushings. Figure 8: Comparison of accelerations at seat rails between the baseline and optimized models. The jerk (Figure 10), which is the rate of the change of acceleration and usually used for evaluating the impact response, indicates that the optimization of the differential bushings benefits more the vibration absorption on the second peak corresponding to the rear wheels hitting the bump. The running r.m.s. jerk also shows same trend (Figure 11). These results were consistent with the fact that the differential was situated right upon the rear axle. The relatively localized differential vibration was transmitted through the bushings to the rear subframe where the rear suspensions were attached. The comforts according to the ISO 2631-1: 1997 were calculated for the baseline and the optimized vehicle. In the lateral direction, as shown in Figure 12, the weighted acceleration peak of the baseline vehicle was eliminated by optimizing the differential bushing. Although there was a large variation between individuals in their perception of vibration. The vibration at the driver and the rear passenger seats were reduced below the median perception threshold (about 0.015 m/s\({}^{2}\)). It is, for the optimized vehicle, very likely that the driver or the passenger could not perceive any vibration in the lateral direction when the vehicle hit a bump at low speeds.