Tooth surface friction is a force formed by the relative sliding between the two contact tooth surfaces of a gear meshing pair, which changes periodically in size and direction.On the one hand, tooth friction produces tooth wear, heat generation and energy loss; on the other hand, it is also an internal exciting force, which excites vibration perpendicular to the direction of engagement line (OLOA), and is strongly coupled with non-linear factors such as tooth side clearance, time-varying stiffness and engagement impact, so that the dynamic characteristics of gear transmission system show complex non-linear characteristics.For the research of tooth surface friction force, more attention has been paid to heat generation and energy consumption caused by friction. Vibration excited by friction has not been paid enough attention. In earlier gear dynamics studies, tooth surface friction and its periodic characteristics are often neglected or equivalent to viscous damping.

Houser and Vaishya eliminate the dynamic influence by digital filtering technology and measure the quasi-static friction more accurately. The experimental research proves that the friction force perpendicular to the meshing line has an important influence on the dynamic load and system vibration, which is more pronounced under high torque and low speed conditions.Kim studied the air noise caused by tooth surface roughness through experiment, pointed out the important influence of tooth surface micro-morphology on gear noise, and firstly correlated tooth surface micro-morphology, friction excitation and gear noise.Iida et al. studied the influence of gear-tooth friction on the dynamic characteristics of the system by using a simple gear vibration model with only the degree of freedom of the sliding direction of the tooth surface. It was found that the time-varying friction on the tooth surface would increase the damping of the system and excite the vibration.The influence of meshing force fluctuation caused by time-varying meshing stiffness on the meshing action line was not considered in the study.

Similarly, Hochmann focuses on the periodic excitation of friction and assumes that the meshing stiffness of the gears is constant.Singh et al. summarized the average load distribution between pre-set contact teeth pairs, treated meshing stiffness as square wave, and solved the dynamic transmission error of single-degree-of-freedom dynamic equation by Floquet theory and harmonic balance method (HBM).Simplified equation and analytical solution are obtained due to the assumption of equal load between teeth, but the influence of actual meshing stiffness can not be reflected and the accuracy of the solution is not enough.Velex and Cahout used the iteration method to study the friction force, profile modification and time-varying stiffness of spur and helical gears, and compared the measured and simulated bearing forces.It is found that there is a noticeable fluctuation in the bearing force at low speed, which is caused by the reciprocating variation of the friction direction on the tooth surface.In subsequent studies, Velex and Seansott analysis found that Coulomb friction is an important excitation source in the translation vibration of spur and helical gears, especially for gears with high overlap.Lundvall et al. considered tooth profile modification and manufacturing errors in establishing a multi-degree-of-freedom model to analyze the influence of friction on rotational vibration.

The numerical method is used to study the effect of tooth profile modification on the excitation of dynamic transmission error (DTE) when the friction force is taken into account.However, these studies do not consider time-varying friction forces and actual meshing stiffness, and their interaction.LiuThe translation-rotation dynamic model considering the changes of friction and meshing stiffness of gear teeth was established, and the influence of friction on the bending strength of gear roots was mainly analyzed. The parameter non-stability and dynamic response were analyzed by using the iteration integration method. The research indicated that the time-varying friction coefficient and the bending of gear teeth caused by friction were important factors affecting the dynamic response of gear.He established a more accurate dynamic model of spur gear and helical gear, taking into account the actual time-varying stiffness, and compared the influence of time-varying friction coefficient obtained by multiple tooth surface lubrication models on the analysis results under different lubrication interface conditions.The research results show that different lubrication models have little influence on the dynamic transmission error, while the profile modification has no effect on the friction direction vibration; the friction force on the tooth surface has a greater influence on the second order amplitude of the dynamic transmission error in the meshing line direction.