# Vibration and Stress Response of High-Speed Train Gearboxes under Different Excitations
## 2 Modeling of High-Speed Train with Gear Transmission
### Model Verification with Measured Data  
A line test was conducted on a high-speed train gearbox in China to study the vibration characteristics of the gearbox of the high-speed train. The B&K vibration transducers were used to measure the vibration acceleration of the gearbox and the axle box on the wheelset. The signals of each measurement point were continuously collected by the eDAQ data recording system as shown in Figure 6, which can ensure the authenticity of the sampled data; the test system has high accuracy, fast dynamic response, and can achieve continuous sampling throughout the test, thus ensuring the completeness of the test data. The data sampling frequency in the test is 10 kHz. Points 1 and 2, respectively, measured the vertical and the lateral vibration acceleration of the gearbox. Point 3 measured the vertical vibration acceleration of the axle box on the wheelset. Figure 4: Gearbox modality. Figure 5: Wheel set modality. The above system was used to measure the vibration acceleration in both directions of the gearbox and the axle box on the wheelset during the whole operation of the traction-uniform-braking of the high-speed train. The vertical vibration acceleration of the axle box and gearbox at the speed of 300 km/h is as shown in Figure 7. The vibration acceleration amplitude reaches a maximum of 600 m/s\({}^{2}\), and the RMS value is 63.6 m/s\({}^{2}\). We performed a fast Fourier transformation (FFT) on the vibration acceleration signal to obtain the frequency spectrum characteristics of the vibration acceleration of gearbox and axle box, as shown in Figure 8. It can be seen from the spectrum diagram that there are multiple main frequency vibrations in the axle box and gearbox. Since the wheel radius is 0.434 m, it is calculated that 30.6 Hz is the wheelset rotation frequency when the train is running at the speed of 300 km/h; this was to more intuitively express the main frequency of the vibration in the frequency spectrum chart, so that the frequency of the wheelset is presented as f, so another main frequency can be expressed as multiples of f. According to the spectrum diagram, it can be analyzed that there are obvious 1 st order polygonal wear and 17 th-19 th order polygonal wears of the wheelset. Figure 8: Spectrum of gearbox and axle box. Figure 6: Measuring points of gearbox and axle box. Figure 7: Vibration of gearbox and axle box. Comparing the vibration components of the axle box and gearbox at each main frequency in the frequency domain, it can be seen that the vibration of the axle box is greater than that of the gearbox at f and 17-19 f, while the vibration of the gear box is greater than that of the axle box at the gear meshing frequency. This is because the gear mesh is the internal excitation of the gearbox, the vibration energy at this frequency is generated by the gearbox and transferred to the axle box through the wheelset, while the vibration energy at the other vibration main frequencies is generated by the wheel-rail contact and transferred to the gearbox through the wheelset. The short-time Fourier transform (STFT) was performed on the vertical vibration acceleration of the gearbox to verify the above analysis. It can be seen from Figure 9 that during the traction condition of the train, the main vibration frequency of the gearbox increases with the increase in speed. At the constant speed of 300 km/h, the main frequency of the vibration of the gearbox remains unchanged, and then in the braking condition, the main frequency of vibration decreases with speed. At the constant speed of 300 km/h, the interval between the main frequencies of each vibration is 30.6 Hz, which indicates that these main frequencies are caused by the polygonal wear of wheels. In addition, even if the vehicle operates speed changes, which means the excitation frequency also changes, the amplitudes of the vibration acceleration of the gearbox in the frequency range of 300-400 Hz, 400-500 Hz, around 600 Hz, and 800-900 Hz are still obvious in the whole traction-constant speed-braking operation.