# Research status of dynamic characteristics of helical gears in China and abroad

The dynamic response characteristics of gear system refer to the dynamic behavior of gear system in the working process, mainly including the dynamic meshing force of gear teeth, the inherent characteristics of gear system and gear structure, and the dynamic response characteristics of gear system in time domain and frequency domain. The research on the dynamic response characteristics of gear transmission system is an important part of the dynamic design of gear transmission device.

The analysis theory of gear transmission is gradually developed from impact theory to vibration theory. Within the framework of vibration theory, gear dynamics has experienced the development from linear vibration theory to nonlinear vibration theory. In the aspect of analysis system, the dynamics of gear system is the transition from single pair of gears or single shaft rotor system to the whole complex structural system including gears, rotating shafts, bearings and shells; In the analysis and calculation methods of gear transmission system, from the basic time-domain method and frequency-domain method to the current numerical analysis method, numerical calculation method and experimental test method, we can study the transient response and stability of gear transmission system in an all-round way. At present, for the research on gear dynamic characteristics, domestic and foreign scholars have done a lot of research on the causes and influencing factors of vibration and noise in gear transmission system from the aspects of internal and external dynamic excitation, system response and dynamic characteristics of gear, and obtained many valuable and practical results.

Neriy et al. Established the dynamic analysis model of eight degree of freedom bending torsion axial swing vibration coupling of helical gear system transmission pair considering the stiffness of shaft and bearing, and solved the dynamic response of the system under the action of static transmission error. Considering the same problems as neriy, Kahraman established a linear dynamic model of helical gear system, emphatically analyzed the influence of axial vibration on the dynamic response characteristics of gear pair, and P. velex proposed a dynamic model of gear system including tooth surface geometric error and installation error to directly solve the instantaneous contact state of tooth surface; Later, Pasternak elastic foundation model is used to simulate the contact between gear teeth, two node beam element is used to simulate the shaft, and solid element is used to simulate the spur and helical gear system model of gear body. The software complex shaft program developed by the gear Laboratory of Ohio State University for calculating the dynamic response characteristics of complex shafting summarizes the internal excitation of gear meshing as transmission error, friction and reciprocating torque, introduces beam element to simulate gear and shaft, and constant stiffness element to simulate gear meshing stiffness, and the software can be used to calculate the inherent characteristics, dynamic response Predict the noise of gearbox. Palermo et al. Considered the spring damping element with time-varying stiffness to simulate the tooth interaction, established the multi-body dynamics model of helical gear meshing based on the accurately calculated three-dimensional geometric model of helical gear, and studied the static transmission error and dynamic transmission error at different speeds. Andersson et al. Proposed a method to calculate the stiffness and tooth load distribution of helical gear by finite element method, determine the gear deformation by real geometry and actual position, and establish a two degree of freedom model to determine the dynamic load of rotating elastic helical gear. The effects of different rotating speeds of helical gear on dynamic load and contact pressure are studied, and gear modification can be considered in this method. Jiang et al. Proposed the calculation method of time-varying contact line length, time-varying friction and time-varying friction torque considering time-varying meshing force and time-varying friction coefficient, established the dynamic model of helical gear system coupled with gear spalling fault and friction excitation, and studied the influence of tooth surface spalling fault coupled with friction excitation on the dynamic response characteristics of helical gear system.

To sum up, at present, there is little research on the dynamic modeling of helical gear system and the dynamic response characteristics of helical gear system. The tooth surface friction is an important excitation that can not be ignored in the study of gear dynamics. At the same time, due to the coupling of multiple nonlinear time-varying characteristics such as time-varying meshing stiffness, time-varying contact line and the change of tooth surface characteristics, the dynamic excitation mechanism becomes complex. The influence of this on the dynamic characteristics of helical gear system needs to be further studied.

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