The influence of time-varying meshing stiffness on the gear bearing considering the fractal characteristics of the tooth surface is studied. Firstly

the profile of gear is described by the fractal theory

and the Weber-Banaschek formula is used to calculate and analyze the influence of different fractal dimension D on the time-varying mesh stiffness

and the stiffness of different fractal dimension D is taken into the gear bearing system with the factors such as the nonlinear oil film force of the sliding bearing

the comprehensive transmission error and the backlash

etc. The influence of stiffness of different fractal dimension D on the dynamic characteristics of the system is analyzed. The dynamic differential equation is solved by Runge-Kutta method. The phase diagrams

the Poincaré diagrams

the time domain diagrams

the bifurcation diagrams and the three-dimensional spectrum diagrams of the response of the system are obtained. The results show that with the increase of fractal dimension D

the fluctuation of time-varying meshing stiffness decreases

and the system tends to more stable periodic motion; Compared with the stiffness of random disturbance

the gear bearing system is more sensitive to the change of gear meshing stiffness considering the fractal characteristics of the tooth surface

and it can better show the change of system response due to the change of tooth profile; With the increase of damping ratio

the system will tend to relatively stable single cycle motion.