Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory

Different from the mainstream research, this study fully considers the anisotropic micro-topography of the tooth surface when studying the dynamic characteristics of gears. An anisotropic 3D fractal rough tooth surface model is proposed based on fractal geometry theory. The major advantage of the novel model is that it contains more surface micro details, especially on the tooth width, which are ignored in general studies. The backlash and time-varying meshing stiffness (TVMS) are then revised on the basis of this model. Finally, a 6-degree-of-freedom nonlinear dynamic model considering surface topography is established and the influence of fractal parameters on gear dynamics is investigated. The results show that the fractal parameters change the backlash and TVMS and have an obvious impact on the dynamics and vibration responses of the transmission system. The rough gear system enters chaos earlier and has better stability at high speeds in comparison with the smooth system. As the fractal dimension increases, the dynamic transmission error amplitude gradually decreases and the system tends to stable periodic motion. The characteristic scale coefficient yields a more moderate but opposite effect on the dynamic response of the system compared with the fractal dimension. The finding of this study can provide theoretical guidance for tooth surface machining from the perspective of tooth surface morphology.