# Vibration and Stress Response of High-Speed Train Gearboxes under Different Excitations
## 1 Introduction  
As a critical component of a high-speed train mechanical traction drive system, the primary function of the gearbox is to transmit the power of the motor to the wheelset. With the increase in train operating speed, the mechanical performance of the train at high speed is affected by various sources of excitation, such as the frequency range of vibration, which is significantly higher than that of conventional trains. These sources of excitation were not evident in low-speed trains in the past. Gearboxes of high-speed trains have been working in very harsh conditions for a long time. The manufacturing of machinery and equipment is more focused on high reliability and long service life [1; 2; 3; 4]. Hence, it is of great engineering significance to study the dynamic response of the gearbox under the complicated internal and external excitation. The high-speed train gearbox has special working environment in comparison with gear transmission systems in machine tools, aviation, wind turbines, etc. [5; 6; 7; 8]. The gear wheel is fixed on the wheelset axle directly through interference fit, and the gearbox housing is hinged with the wheelset axle through bearing; due to this installation method, the vibration of the wheelset will be transferred to the gearbox directly. The wheelsets and tracks of trains are made of steel. Due to manufacturing errors, installation errors, and wear and tear, rigid shocks are generated between the wheels and tracks when the vehicle is running, which is the main source of excitation for high-speed train gearboxes. As themileage of high-speed trains increases, the uneven wear of the wheels in the circumferential direction makes the wheel-rail impact more and more serious, which leads to a sharp increase in the amplitude of the vibration of the gearbox. Figure 1 is a photograph of the uneven wear that occurs in the wheels of high-speed trains, a phenomenon known as wheel polygonal wear. Figure 2 shows the evolution trend of vibration acceleration of high-speed train gearboxes with operating mileage obtained from long-term tracking tests. Vibration fatigue and reliability problems of mechanical systems have received a great deal of attention from researchers [9; 10; 11; 12]. A great deal of work has been done in the field of railroad vehicles, which focuses on the effect of internal excitation sources on gearboxes [13; 14; 15; 16]. Previous studies [17; 18; 19] have shown that the wheel polygonization will lead to a surge in vibration response of various components of the vehicle. [PERSON] et al. [20; 21] used an intelligent algorithm to improve the accuracy of the gearbox model and studied the influence of harmonic traction torque on the vibration and stress of the gearbox. [PERSON] et al. [22] established a dynamic model of a high-speed train and a finite element model of the gearbox housing and analyzed the influence of internal excitation (the periodic variation of meshing stiffness) and external excitation (rail excitation, harmonic traction torque). [PERSON] et al. [23] established a multi-body dynamic model of a high-speed train with flexible gearbox housing to investigate the influence of the wheel polygonization on the dynamic response of the gearbox housing. Gearbox excitation sources in high-speed trains can be divided into external sources and internal sources. There are three external excitation sources according to the connection between the other components and the gearbox, which are the wheelset, the motor, and  
Figure 1: Wheel polygonal wear. Figure 2: The evolution trend of vibration acceleration of high-speed train gearboxes with operating mileage. the bogie frame [24; 25]. It should be mentioned that the excitation from the bogie frame is generated by another two excitation sources coupling. The internal excitation is caused by the time-varying stiffness of the gear meshing [13]. It can be seen from the above analysis that the gearbox on the railway vehicle is in a nonlinear system with multi-input and high-frequency coupling.