This research paper formulates dynamic differential equations that take into account the performance of every component within the planetary gear transmission system comprehensively. It also develops calculation methods for stiffness and damping. Finite – element analysis is utilized to compute the particular meshing force among gear components during the system’s operation. It also serves to examine the dynamic response traits under the effect of this force. At the same time, we evaluate the effects of different parameter changes on the system’s amplitude response to determine the path for optimizing the system’s dynamic features.The results of the finite – element analysis show that when an external force is applied to the system, the displacements of the sun gear and other gear elements in the x and y directions fall within the range of -1 to 1 unit. Additionally, the dimensionless meshing force response between the gears can reach up to 1.337 units. The variation of three parameters such as eccentricity error, tooth frequency and shaft frequency error, and damping ratio can lead to a maximum vibration amplitude of 5.625 when the system is stressed, which should be optimized.
