Dynamic Analysis of Planetary Gear Transmission System Considering the Flexibility of Internal Ring Gear

A rigid-flexible coupled dynamic model of the planetary gear transmission system was developed considering the flexibility of the internal ring gear (flexible internal ring gear) and the sun shaft based on the shell theory and Timoshenko beam theory, respectively. For the dynamic modeling, the time-varying meshing stiffness and static transmission error excitations were considered and the Runge–Kutta numerical algorithm was applied to calculate the dynamic response. The results indicate that the flexibility of internal ring gear sharply decreases the dynamic factor between the internal ring gear and the planet gear, and it also shows significant positive influences on the system load-sharing performance. For the fixed internal ring gear, the maximum stress is located on the midpoint along the axial direction. The maximum dynamic deformations appear at the ends of the tooth surface along width direction, and the dynamic deformation shows a decremental trend from the tooth top edge to the tooth root edge. The load-sharing coefficient decreases rapidly with the increase in the thickness, as the support stiffness is small. The misalignment of one of the planet pins and various static transmission errors have a negative influence on the load-sharing coefficient of the planetary gear transmission system.