Modelling and nonlinear dynamic behavior of a geared rotor-bearing system using tooth surface microscopic features based on fractal theory

This paper investigates the influence of microscopic features on the tooth surface of a geared rotor-bearing system on the system’s dynamic behavior. First, by upgrading the Weierstrass–Mandelbrot function to redefine the gear backlash equation and combining this with a nonlinear dynamic model of a geared system, an improved nonlinear dynamic model is established. Second, the effects of four crucial model parameters on the gear dynamics are examined through a series of numerical simulations, allowing us to explore the corresponding dynamic response and the model’s feasibility. The results show that surface roughness plays a significant role in the dynamic behavior of the gears, with lower surface roughness corresponding to better dynamic performance. The fractal dimension is found to be a non-negligible factor with respect to gear dynamics, and decreasing the fractal dimension proves advantageous to the dynamic response. As the stiffness coefficient decreases and the gear meshing damping increases, the stability of the system improves. Finally, the model is validated through a comparison of our theory with experimental data and another certified model. Our theory constructs a mathematical relationship between the gear dynamics and tooth surface micro-characteristics, forming a basis for future tooth surface topographies as well as a reference for the dynamic analysis of other highly paired systems.