Sliding Friction Contact Stiffness Model of Involute Arc Cylindrical Gear Based on Fractal Theory

Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz theory. The contact surface coefficient is an exponential function of the load, radius of curvature and tooth line radius. The simulation results validate the reasonability of the contact surface coefficient and correctness of the fractal model. The contact surfaced coefficient increases with the increase of the load, radius of curvature and tooth line radius; the normal contact stiffness increases with the increase of material properties parameters, radius of the gear, load and fractal dimension (when fractal dimension is greater than 1.85, the normal contact stiffness decreases). Meanwhile, the normal contact stiffness increases with the decrease of roughness and decreases exponentially or linearly with the increase of friction coefficient. Research results are the foundation of the further analysis of arc gear contact problems.