The vibration and noise of gear transmission seriously affect its accuracy, bearing capacity and stability. The tooth side clearance reserved in the design to prevent the gear teeth from getting stuck determines the tooth surface meshing, gear tooth disengagement and tooth back contact during the transmission process. The coincidence degree of the gear pair is generally greater than 1.0, resulting in the time-varying number of meshing teeth of the gear. The result of the combined action of the two makes the gear mesh in a variety of conditions, such as single/double tooth surface meshing, gear tooth disengagement and single/double tooth back contact, which causes gear tooth impact and affects the transmission stability. Gou et al. considered the multi-state meshing characteristics of gear pair, established the nonlinear dynamic models of spur gear pair and face gear transmission system respectively, which laid a methodological foundation for revealing the dynamic characteristics of gear transmission system.
The structure of bevel gear tooth profile is complex, and its dynamics research results are few. Karray et al. established a single-stage bevel gear dynamics model and studied the influence of gear local damage on dynamics characteristics. Kiyono et al. established a two-degree-of-freedom dynamic model of bevel gear pair, and analyzed the dynamic characteristics of bevel gear, spur gear and helical gear. Wang et al. established the dynamic model of bevel gear transmission system including shaft and bearing based on the finite element method. Cheng et al. obtained the cone based on TCA method
An improved dynamic model of bevel gear transmission system is established. Yassine et al. analyzed the dynamic characteristics of the faulty bevel gear system and compared it with that of the fault-free bevel gear system. Fang Zongde et al. established the dynamic model of the multi-degree-of-freedom straight bevel gear transmission system including time-varying stiffness and error excitation. Wang Sanmin et al. established the dynamic model of the 8-DOF spiral bevel gear transmission system with various time-varying parameters. Wang Lihua has established a dynamic model of 12 degrees of freedom spiral bevel gear transmission system with various time-varying parameters, and studied its dynamic characteristics. Jiang Hancheng et al. established the dynamic model of the gear-rotor-case coupling system considering the flexibility of the shafting and the gearbox, and deduced the meshing relationship of various gear pairs. These studies mainly focus on the calculation of system parameters, dynamic modeling and the study of nonlinear dynamic characteristics, without considering the influence of coincidence degree on the meshing characteristics of the system.
Based on the meshing principle of bevel gear, the time-varying meshing stiffness and load distribution rate of bevel gear transmission system are calculated by using the finite element method; The multi-state meshing dynamics model of bevel gear transmission system including time-varying meshing stiffness, load distribution rate, comprehensive transmission error and bearing support is established. By defining different Poincar é sections, the influence of meshing frequency and comprehensive transmission error on the meshing state and dynamic characteristics of the system is studied, which provides a theoretical basis for the design and optimization of system parameters.