# Brief introduction of dynamic theory of gear transmission system

The dynamic characteristics of gear system mainly include the natural frequency, dynamic response, dynamic stability, the influence of system parameters on the dynamic characteristics of gear system and gear fault diagnosis. Its dynamic behavior and working performance have an important impact on the whole machine. Therefore, the dynamics of gear transmission system has been widely concerned by people. Therefore, a lot of in-depth research has been carried out and a complete theoretical system has been formed.

In the dynamic analysis theory of gear transmission system, the impact theory was initially used as the research basis, and the tooth meshing impact was used to describe and explain the dynamic excitation and response of gear transmission. The gear transmission system is simplified into a single degree of freedom system, and the dynamic response behavior of the gear transmission system is expressed by the impact theory. Later, based on the vibration theory, the gear transmission system is transformed into an elastic vibration system to analyze the dynamic response behavior of the gear transmission system under the action of transmission error, meshing stiffness and meshing impact. It lays a foundation for the dynamics of modern gear transmission system.

In the research system of vibration theory, the dynamics of gear transmission system has developed from linear vibration theory to nonlinear vibration theory. Within the research scope of linear vibration theory, researchers often replace the time-varying tooth meshing stiffness with the average meshing stiffness, calculate the natural frequency and vibration mode of the gear transmission system from the average meshing stiffness, and use the numerical integration method to calculate the dynamic response of the gear transmission system. In the study of linear vibration theory, the stability of gear transmission system caused by time-varying meshing stiffness is not considered, and the nonlinear problem caused by tooth side clearance during tooth meshing is avoided. The influence of multiple pairs of gear pairs participating in meshing and the interaction between gear pair and gear shaft support bearing on the dynamic characteristics of gear transmission system is ignored. Compared with the linear vibration theory, when using the nonlinear vibration theory, various nonlinearities existing in the gear transmission system are considered, such as time-varying meshing stiffness, tooth side clearance, meshing error and so on. When using vibration theory to study the dynamics of gear transmission system, the meshing of gear teeth is simulated as an elastic element with time-varying stiffness. Because this elastic element with time-varying stiffness is an integral part of the whole gear transmission system, the interaction between excitation and system and response can be studied in the whole gear transmission dynamic system, so as to complete the parameter selection and structural optimization of the gear transmission system.

In the analysis of gear transmission system, it has experienced the transition from a simple system considering only one pair of gear pairs to a complex system including multiple pairs of gears, bearings, transmission shafts and gearbox. In this way, the dynamic characteristics of gear transmission system, the influence of parameters and parts of the system on the dynamic excitation of gear meshing process can be studied comprehensively. And the transmission route and transmission characteristics of these dynamic excitations in the gear system can be obtained. It can also study the dynamic meshing force of gears, the bearing reaction force, the vibration characteristics of gears, transmission shafts and boxes, as well as the generation of system noise, the embodiment and propagation of noise in the system.

There are both time-domain method and frequency-domain method, and both analytical method and experimental method can be used. Therefore, a variety of means and methods can be used to comprehensively study the transient characteristics, steady-state characteristics and chaotic characteristics of gear system.

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