# Analysis of Train Car-Body Comfort Zonal Distribution by Random Vibration Method
## 4 Case Study
### Analysis of the Zonal Distribution Characteristics of Train Comfort  
In the simulation, a vehicle element was selected to traverse a track with Grade-6 track irregularities for 5 s at a speed of 350 km/h. MCM was applied 100 times to calculate the vibration acceleration of the car-body center of each vehicle element and then calculate the preliminary average of the zonal distribution of the Sperling index shown in Figure 6 according to Section 3.1 and compare it with the theoretical values calculated using the PEM according to the linearity of PSDs given in Section 3.2. To simplify the representation in the figure, the coordinate (_x,y_) was replaced by a length of the car body of 25 m and a width of the car body of 4 m. The mesh of the plane in which the car body was located was divided into 10 \(\times\) 10. In Figure 6, it can be seen that:  
1. The mean network of the zonal distribution of the Sperling index calculated using MCM-N\(\emptyset\)M was almost identical to the theoretical network calculated using PEM-FRF for both the horizontal and vertical components;
2. In Figure 6, the zonal distribution of the horizontal Sperling index is symmetric with respect to the pitch and roll axis of the car-body center. It has the cylindrical shape of the letter \"V\" and reaches the highest line at the rear and front edges of the car-body, respectively, while it reaches the lowest line on the pitch axis of the car-body;  
Figure 5: Car-body center Sperling index as the function of the order of vehicle element using MCM and PEM: (**a**) horizontal Sperling index; (**b**) vertical Sperling index. Figure 6: Zonal distribution of car-body Sperling index using MCM and PEM: (**a**) horizontal Sperling index; (**b**) vertical Sperling index. In Figure 6b, the zonal distribution of the vertical Sperling index is a symmetrically curved surface with respect to the roll axis of the Car-Body center. It reaches the highest points at the four vertices of the X\(-\)Y plane, where the center of the car body is located, while the lowest point is slightly in front of the center of the car body in the direction of travel;
4. Compared to Figure 5 in Section 4.3, the Sperling index of the center of the car body is smaller for both the horizontal and vertical components for Grade-6 track irregularities than for Grade-4 track irregularities;
5. In general, a small track irregularity had a negative effect on train comfort, and the zonal distribution of train comfort was not strictly symmetrical with respect to the center of the car body. The most comfortable area for the vertical component was near the front of the center of the car body, while the most comfortable area for the horizontal component was on the pitching axis of the center of the car body. The realistic evaluation of train comfort could be roughly characterized by the average value of the Sperling index during train operation, while the theoretical design of train comfort could be accurately determined by the PEM. Analysis of Influence of the Quality of Track Irregularity on the Zonal Distribution Characteristics of Train Comfort  
A vehicle element was simulated using the PEM to respectively cross a distance of track irregularity of Grade-1, Grade-3, and Grade-5 at a speed of 350 km/h to compare the different qualities of the track irregularities' influences on the zonal distribution of the Car-Body Sperling index, as shown in Figure 7. It can be seen in Figure 7 that:  
1. The symmetrical characteristic of the zonal distribution of the car-body Sperling index of the car body for the horizontal and vertical components was identical to that in Section 4.4;
2. With the deterioration in the quality of the track irregularities, the values of the Sperling index for the entire network increased significantly for both the horizontal and vertical components;
3. In general, train comfort deteriorated with the deterioration of the quality of track irregularities, so regular track maintenance is of great importance.