# Analysis and Optimization of Driveline Bushing for Lateral Ride Vibration under Shock Excitation
## 2 Model
### Model Validation  
A field measurement over a 20 mm obstacle (Figure 2) at 35 km/h was conducted, which represents a typical working condition when the vehicle passes over a speed bump. In the test, the vehicle passes over the obstacle with both wheels of each axle, i.e., the left and right wheels of one axle were exposed to the shock excitation simultaneously. All the other test conditions met the requirement of Chinese standard GB/T 4970-2009. The r.m.s acceleration of the driver seat rail that was applied in the ride comfort analysis was measured with a triaxial accelerometer (PCB 356A26), which had a sensitivity of approximately 50 mV/g with an operating range of \(\pm\)100 g. The accelerometer was mounted at the seat rail of the driver based on GB/T 4970-2009, which is shown in Figure 3. The test data was recorded with a sampling rate of 512 samples per second by Simcenter SCADAS Mobil. A duration of 1.4 s signal was employed to compute the running r.m.s. acceleration using Equation (1) [31].  
\[a(t_{0})=\left\{\frac{1}{\tau}\int\limits_{t_{0}-\tau}^{t_{0}}\ [a(t)]^{2}\mathrm{d}t \right\}^{\frac{1}{2}} \tag{1}\]  
where \(a(t)\) is the instantaneous acceleration, \(\tau\) is the integration time for running averaging, \(t\) is the time and \(t_{0}\) is the time of observation. The integration time was 0.02 s and the overlap were 50%. The running r.m.s. accelerations in the three translational directions computed with the simulation results were compared with those from the measured data, as shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Bushing**} & \multirow{2}{*}{**Geometry**} & \multicolumn{6}{c}{**Properties**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Dynamic Rate (\(\times\)10\({}^{5}\) N/m)**} & \multicolumn{2}{c}{**Loss Angle (Degree)**} \\ \cline{3-8}  & & x & y & z & x & y & z \\ \hline Left-Front & \(\Phi\) 0.08 m \(\times\) 0.05 m & 8.0 & 4.5 & 15 & 5 & 5 & 5 \\ Right-Front & \(\Phi\) 0.08 m \(\times\) 0.05 m & 18 & 4.6 & 20 & 5 & 5 & 5 \\ Rear & \(\Phi\) 0.04 m \(\times\) 0.075 m & 2.4 & 20 & 8.0 & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of the bushings.  
Figure 2: Speed bump used in the test.  
the lateral acceleration at the DR and the LR had considerable changes, which were 59.7% for DR and 63.3% for LR. Therefore, in the following analysis the vibration at the lateral direction was the main topic as that in the other two directions were still considered. It is found six bushing parameters, \(k_{\text{x\_FL}}\), \(k_{\text{y\_FL}}\), \(k_{\text{x\_FR}}\), \(k_{\text{y\_FR}}\), \(k_{\text{x\_RR}}\) and \(k_{\text{y\_RR}}\), had an important effect on ride vibration at the seat rails in the lateral direction. All these six parameters cause at least 10% change in the lateral VDV, as shown in Figure 6. A bar with a positive value means the VDV increased with increasing value of the corresponding parameter, and vice versa. It can be seen from Figure 6 that the effects of each influential parameter on the VDVs at the driver and the rear left passenger seat rails were very close. In the following work, only the ride vibration at the driver seat rail was considered.