# Development of gear transmission dynamics

### 1) Analytical theory

The theoretical basis of gear transmission dynamics research is mechanical linear dynamics theory and nonlinear dynamics theory, but the two theories develop with the development of gear transmission dynamics research.

Before the 1950s, gear transmission was usually studied as a single degree of freedom system, and meshing impact was used as excitation to analyze and study the vibration characteristics and vibration response of gear transmission, so as to express the working performance and dynamic behavior of gear transmission system. After the 1950s, gear transmission is usually simplified as a mechanical vibration system, considering the elasticity of parts and components, and taking nonlinear factors such as meshing stiffness as excitation analysis, the dynamic response of gear transmission system is obtained to understand the transmission dynamic characteristics and dynamic behavior of gear transmission system. The development of nonlinear gear dynamics theory promotes the research on the dynamic characteristics of gear transmission.

### 2) Analysis system and analysis method

The analysis system of gear transmission dynamics gradually develops from a single pair of gears to the whole gear transmission system composed of shaft, bearing and gear. The dynamic analysis of the whole gear transmission system can not only effectively understand the dynamic performance of the gear transmission system in the working process, but also understand the dynamic problems of other parts in the system and their influence on the dynamic behavior of gear meshing, so as to obtain the vibration response of gear transmission, the vibration characteristics of gear transmission and box, By analyzing the vibration, noise and impact of the complete gear transmission, the whole gear transmission system can work reliably and stably.

At present, the main methods to analyze the dynamic behavior of gear transmission are time domain method, frequency domain method, analytical method and numerical analysis method. These methods can accurately and comprehensively study the dynamic behavior of gear transmission system and solve the dynamic problem of gear transmission.

### 3) Analytical model

According to the different requirements for the dynamic performance of gear transmission system, the analytical model is also different. According to whether the nonlinear factors in the process of gear transmission are considered or not, it can be divided into linear time-varying models; Linear time invariant model; Nonlinear time invariant model; Nonlinear time-varying model. According to the degrees of freedom involved in the model and different research objects, it is divided into single degree of freedom system model of single pair gear transmission; Multi degree of freedom model of single pair gear pair; Multi degree of freedom analysis model of multi pair gear pair transmission and complete gear system.

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