Nonlinear vibration and superharmonic resonance analysis of wind power planetary gear system

The nonlinear dynamic model of the NW (planetary gear structure with internal and external meshing and without planet carrier) planetary gear bearing was established in this study, taking into account factors such as random wind speed, time-varying support stiffness, bearing clearance, transmission error, tooth backlash, flexible ring gear, time-varying meshing stiffness, and tooth surface friction. The system's nonlinear behavior was described using phase trajectory plane, time–frequency analysis, time history, 3D frequency spectrum, FFT spectrum, phase diagram, and Poincaré map, as well as bifurcation diagram. Additionally, the superharmonic resonance characteristics of the system were analyzed using a multi-scale method, and the stability conditions for superharmonic resonance were determined through numerical analysis. Furthermore, the effects of meshing damping, displacement control parameters, and speed control parameters on the amplitude–frequency characteristics of the NW planetary gear-bearing system were examined. The conclusions indicate that the NW planetary gear-bearing system exhibits various nonlinear characteristics, and the system's stability can be improved by increasing damping and selecting appropriate time delay parameters.