Research on nonlinear characteristics of multi-clearance gear system based on fractal theory

The presence of factors such as tooth side clearance, bearing clearance, and time-varying meshing stiffness introduces strong nonlinearity into mechanical system, significantly impacting the reliability and safety of mechanical equipment. When analyzing the dynamic characteristics of gear systems, the clearance factor can not be ignored. Few studies have considered the coupling effect of bearing clearance and tooth side clearance on the nonlinear characteristics of gear system, and the influence mechanism remain unclear. In this paper, a nonlinear dynamic model of a single-stage gear system with six degrees of freedom (6-DOF) was established, incorporating the coupling effects of tooth side clearance and bearing clearance. Using the control variable method, the tooth side clearance and bearing clearance were regarded as constant or dynamic clearance, respectively. The dynamic characteristics of the gear system were analyzed through time history chart, phase diagram, Poincare section diagrams, and fast Fourier transform (FFT) spectrum. When studying dynamic clearance, the influence of surface micromorphology on the clearance was considered based on fractal theory. The results showed that when tooth side clearance and bearing clearance were regarded as constants, the periodicity of the gear system remained essentially unchanged despite variations in clearance values. When tooth side clearance was considering as a fractal clearance and bearing clearance as a constant, the system's periodicity changed with variations in the fractal dimension D. When tooth side clearance and bearing clearance were treated as fractal clearances, the system transitioned from a chaotic state to a periodic state with increasing fractal dimension D. This paper provides a theoretical foundation for the design and manufacturing of gear and bearing surfaces in the future. © 2024 Elsevier Ltd