# Kinetics of Friction Excitation on Gear Face

In domestic research, Wang Sanmin et al. established a sub-non-linear dynamic model. By means of numerical calculation, the influence of friction on the periodic response and chaos response of gear system was studied. It was found that friction increased the components of super-harmonic and sub-harmonic response of the system and led the system to enter chaos state beforehand, but the degree of chaos was reduced.Sun Yuehai and others established a pair of mathematical models for the vibration of the involute gear drive system by using Lagrange equation. The influence of mass eccentricity of the gear and meshing friction of the gear teeth on the vibration of the system was considered and the numerical calculation results of dynamic response were given under specific driving conditions.Tang Jinyuan and others took friction coefficient as fixed value to compare the dynamic transmission error response. The result shows that the influence of friction on transmission error is not clear.Feng Zhiheng et al. analyzed the influence of time-varying friction coefficient on the dynamic characteristics of gear system when studying the multi-degree-of-freedom nonlinear dynamics of spiral bevel gears.A hybrid lubrication model for gear meshing was proposed and used to calculate the instantaneous friction coefficient at each mesh point in the meshing area of the tooth surface.It is considered that time-varying friction coefficient has an important influence on the dynamic characteristics of spiral bevel gears.

In most of the above literature and research reports, the time-varying sliding friction of tooth surface is simply treated as a Coulomb force with a given coefficient of friction for the purpose of establishing a model.Throughout the engagement cycle, the friction conditions such as dynamic load on the tooth surface, relative slip speed and oil film thickness on the tooth surface all change continuously. Therefore, as the position of the gear engagement space changes, the friction coefficient changes with time, while the friction force changes with the friction coefficient and engagement force, and its direction changes at the joint position.

Different lubrication theories such as Elasto-hydrodynamic lubrication (EHL), boundary lubrication theory and mixed lubrication are used to explain the sliding friction characteristics under different conditions.Benedict and Kelley obtained empirical values of the dynamic friction coefficient in the mixed friction region based on the roll tester experiment.Xu et al. recently proposed a new friction equation based on a non-Newtonian, thermoelastohydrodynamic lubrication model.Duan and Singh put forward a smooth Coulomb model for dry friction, which can smoothen the gear meshing joint.Hamrock and Dawson presented the formula for estimating the minimum oil film thickness under the linear contact condition of two disks. The calculated oil film parameters can be used in the mixed lubrication model of gears.

In conclusion, the tooth surface friction is an important excitation that can not be ignored in gear dynamics research and is directly related to gear noise.But unlike other interfacial friction, the dynamic excitation mechanism of tooth surface friction becomes complicated due to the influence of several non-linear time-varying characteristics of gear engagement.For example, the time-varying meshing stiffness, the change of relative slip speed, the change of lubrication conditions between teeth and the change of micro-characteristics of teeth will change the friction characteristics of teeth.Based on the existing research, this paper will further analyze the friction excitation characteristics and dynamic characteristics of tooth surface. 