Exploration of nonlinear characteristics of gear-bearing systems with friction composite effects

Gear systems exhibit strong nonlinear and non-smooth dynamics caused by time-varying meshing stiffness (TVMS), tooth friction, and backlash. The alternating engagement of the single and double teeth and the change in the direction of the friction force at the position of the pitch circle caused discontinuity of stiffness. In this study, a TVMS calculation method that considers friction was discussed, and a mechanical model of gear transmission that considers friction and tooth-side clearance was established. The actual discontinuous stiffness was evaluated using Fourier transform, and the dynamic response of the system caused by the discontinuity was compared. Through phase and Poincaré diagrams, the influence of the discontinuity in the TVMS, considering friction, on the bifurcation characteristics and dynamic meshing force was discussed, and the disengagement characteristics of the system under various periodic-motion states were investigated. The results show that a shift in the friction vector resulted in a step phenomenon in the TVMS, which became more evident with an increasing friction coefficient. For low-speed gear systems, stiffness simulation employing Fourier transform can accurately replicate the system response; however, it can obscure the stiffness step phenomenon. The range of the four-period motion generated within the chaotic behavior of the continuous system expanded from 0.003 to 0.008. The periodic motion rapidly increased the disengagement rate of the system. The disengagement rate increased rapidly from 16.8 % in a single cycle to 58.5 % in two cycles. The results of this study provide a theoretical basis for gear design.