# Dynamic Characteristics of Urban Rail Train in Multivehicle Marshaling under Traction Conditions
## 4 Analysis and Discussion
### Vibration and Comfort Analysis of Urban Rail Trains  
#### 4.2.1 Vibration Response Analysis  
Figure 10a,b show the vertical acceleration and lateral acceleration of each carriage body, respectively. The vertical acceleration and lateral acceleration of the six-carriage car increase monotonically. In terms of vertical acceleration, the motor car is larger than the trailer, but the difference is not obvious. The variation range of M1 is the largest, in the range of 0.018-0.385 m/s\({}^{2}\). T1 is the smallest, with a variation range of 0.011-0.365 m/s\({}^{2}\). In terms of lateral acceleration, there is no obvious difference between the carriages, and the overall variation range is 0.022-0.472 m/s\({}^{2}\). Figure 10c,d show the vertical and lateral accelerations of the bogie frames of each car, respectively. The vertical and lateral accelerations of the six carriages monotonically increase. The vibration accelerations of M1 and M4 are relatively large, the vertical acceleration ranges are 0.262-1.523 m/s\({}^{2}\) and 0.239-1.512 m/s\({}^{2}\), respectively, and the lateral acceleration ranges are 0.083-1.062 m/s\({}^{2}\) and 0.086-1.042 m/s\({}^{2}\), respectively. The vibration acceleration of the four motor cars is greater than that of the two trailers because the traction motor will generate large vibration during operation, and the gear mechanism adopts a helical gear which will generate large vertical vibration and lateral vibration during operation. The vertical vibration acceleration has a significant effect. Figure 10e,f show the vertical and lateral accelerations of the wheelsets of each carriage, respectively. The vertical and lateral accelerations of the six carriages monotonically increase. The vertical and lateral accelerations of the four motor cars are both greater than those of the two trailers, indicating that the traction transmission system has an obvious influence on the vibration acceleration of the train wheels. The ranges of the vertical and lateral accelerations of the motor car are 0.26-13.86 m/s\({}^{2}\) and 0.15-11.84 m/s\({}^{2}\), respectively, and the ranges of the vertical and lateral accelerations of the trailer are 0.13-3.47 m/s\({}^{2}\) and 0.11-3.01 m/s\({}^{2}\), respectively. The vibration acceleration of the axle box is significantly greater than that of the bogie frame, and the vibration acceleration of the bogie frame is significantly greater than that of the car body, indicating that the primary suspension and the secondary suspension suppress most of the vibration. Figure 9: Nonlinear critical speed of each car of the marshaling urban rail train. Each curve represents the convergence rate of transverse movement of each carriage respectively. The traction transmission system will generate a large vertical vibration during operation, which will affect the vibration response of each component of the train. Therefore, it is also important to compare and study the vibration frequency of each component of the motor car and the trailer. A short-time Fourier transform is performed on the vibration signals of the car body, bogie frame and axle box of the two adjacent carriages M2 and T1, and the time-frequency diagrams are obtained [36; 37], as shown in Figures 11 and 12. Figure 10: Vibration acceleration of each component of the marshaling urban rail train: (**a**) vertical acceleration of car body; (**b**) lateral acceleration of car body; (**c**) vertical acceleration of bogie frame; (**d**) lateral acceleration of bogie frame; (**e**) vertical acceleration of wheelset; and (**f**) lateral acceleration of wheelset. Figure 11: Time–frequency diagram of the vertical vibration acceleration of the motor car and trailer: (**a**) car body of the motor car; (**b**) car body of the trailer; (**c**) bogie frame of the motor car; (**d**) bogie frame of the trailer; (**e**) wheelset of the motor car; and (**f**) wheelset of the trailer.