Fractal-based dynamic response of a pair of spur gears considering microscopic surface morphology

The meshing surfaces of a gear pair are rough from a microscopic perspective and the surface topography will affect the dynamic response. To study the influence of real surface topography on the gear system dynamic performance, this paper establishes a 3-degree of freedom transverse-torsional dynamic model with regard to the morphology of the interface. By fractal theory, the expression of backlash between gears is modified based on the height of asperities. The time-varying stiffness is calculated according to the fractal method rather than assuming a constant, which is more realistic. The dimensionless dynamic differential equations are established and solved with surface topography affected backlash function and time-varying stiffness. The dynamic response of the gear system with respect to fractal dimension and fractal roughness is analyzed.