An improved meshing stiffness calculation algorithm for gear pair involving fractal contact stiffness based on dynamic contact force

The contact stiffness, which is under effects of topography at tooth meshing surface, is determined by the dynamic contact force from the holistic meshing behavior of gears. However, in previous literature, the comprehensive effect of contact force on contact stiffness is often replaced by meshing force, which results in the mismatch between contact stiffness and meshing force. To precisely model contact stiffness and meshing stiffness of gear pair, in this paper, fractal contact stiffness model is first established based on the length scale of microscopic asperities, by which the inherent nonlinear relationship between contact force and contact stiffness is revealed. Subsequently, the improved convergence algorithm based on static and dynamic deformation is applied to calculate the actual contact force. Then the contact stiffness and dynamic response of the system are solved. Based on the proposed method involving fractal contact stiffness, the influences of surface roughness are investigated. The calculation results are also compared with those of traditional method, which reveal that dynamic contact force is irreplaceable in the stiffness modeling.