# Effect of the Anti-Yaw Damper on Carbody Vertical Vibration and Ride Comfort of Railway Vehicle
## 6 Results of Numerical Simulationsand Discussion  
This section examines the effect of the anti-yaw damper upon the carbody vertical vibrations and the ride comfort of the railway vehicles, by using to this purpose the results from numerical simulations. The characteristics of the vertical vibration behavior of the vehicle carbody are looked at based on the power spectral density of the vertical acceleration in the carbody reference points. To evaluate the ride comfort at the vertical vibrations, the ride comfort index calculated in the carbody reference points is being used. The reference parameters of the vehicle model are featured in Table 2. It is considered that the vehicle is traveling on a low-quality track, described by the coefficient \(A=1.080\cdot 10^{-6}\) radm. \begin{table}
\begin{tabular}{l l} \hline \(m_{c}=34,000\) kg & \(2k_{zc}=1.2\) MN/m \\ \hline \(m_{b}=3200\) kg & \(2c_{zc}=34.28\) kNs/m \\ \hline \(J_{c}=1,963,840\) kg\(\cdot\)m\({}^{2}\) & \(4k_{zb}=4.4\) MN/m \\ \hline \(J_{b}=2048\) kg\(\cdot\)m\({}^{2}\) & \(4c_{zb}=52.21\) kNs/m \\ \hline \(EI=3.158\)\(\cdot\)10\({}^{9}\) Nm\({}^{2}\) & \(L_{c}=26.4\) m \\ \hline \(m_{mc}=35,224\) kg & \(2a_{c}=19\) m; \(2a_{b}=2.56\) m \\ \hline \(k_{mc}=88.998\) MN/m & \(h=1.6\) m \\ \hline \(c_{mc}=53.117\) kNm/s & \(b=1\) m \\ \hline \end{tabular}
\end{table} 
Table 2: Reference parameters of the vehicle model. The eigenfrequencies of the vertical vibration modes of the carbody, corresponding to the reference parameters of the model without anti-yaw damper are the following: bounce eigenfrequency--1.17 Hz; pitch eigenfrequency--1.46 Hz; bending eigenfrequency--8 Hz. Figures 3-5 show the influence of the damping and stiffness of the anti-yaw damper upon the power spectral density of the acceleration in the carbody reference points at the velocity of 300 km/h. The mounting angle of the anti-yaw damper is 10 degrees. One observation concerns the increase of the eigenfrequencies of the carbody vibration modes. The increased eigenfrequencies areall the more pronounced the higher the anti-yaw damping, as seen  
Figure 4: Influence of the damping and the anti-yaw damper stiffness upon the power spectral density of the carbodyaccelerationagainst the front bogie. Figure 5: Influence of the damping and the anti-yaw damper stiffness upon the power spectral density of the carbodyaccelerationagainst the rear bogie. Figure 3: Influence of the damping and the anti-yaw damper stiffness upon the power spectral density of the carbody acceleration at the carbody center. in Figure 6. As for the influence of the anti-yaw damper stiffness, this manifests differently at the three carbody eigenfrequencies and is linked to the value of the anti-yaw damping. For \(c=1\cdot 10^{5}\)Ns/m, the increase in the anti-yaw damper stiffness does not affect the carbody bounce and pitch eigenfrequencies, yet triggers the reduction in the bending eigenfrequency (see Figure 6). For higher values of the anti-yaw damping, the following situations are encountered--the carbody bounce frequency decreases and the carbody pitch frequency increases along with the rise in the anti-yaw damper stiffness; the carbody bending frequency rises with the increase in the anti-yaw damper stiffness from \(5\cdot 10^{6}\) N/m to \(1\cdot 10^{7}\) N/m and then decreases down for further growth at \(5\cdot 10^{7}\) N/m. Another observation based on the results in Figures 3-5 refers to the fact that the anti-yaw damper results in the reduction of the carbody vibrations at the eigenfrequencies of the three vibration modes. This reduction is all the more effective as the stiffness of the anti-yaw damper is higher, which is also highlighted in the diagrams in Figure 7. These are obtained for \(c=5\cdot 10^{5}\)Ns/m,\(\alpha=10\) degrees, and various values of the anti-yaw damper stiffness ranging from \(10^{6}\) N/m to \(10^{8}\) N/m, proving the fact that the power spectral density of the acceleration continually decreases along with the increase in the anti-yaw damper stiffness.