The governing vibration differential equation of a plus planetary gear set has derived from the Lagrange method. Its three often neglected components are considered: [1] the meshing damping, [2] the elastic bearing support of the sun wheel, [3] and the angles between the movement direction of the planet carrier and the gear meshing line. A simulation model for a plus planetary gear set is built. The influence that the key components have on vibration characteristics is analyzed. Model validation is performed by comparing the theoretical, simulated and measured natural frequencies. In order to reduce vibration and noise, a comprehensive finite element model of a plus planetary gear set is built. It provides useful information on dynamic transmission errors of the plus planetary gear set. The tooth profile modification is optimized by using the genetic algorithm. The optimal tooth profile modification is validated by the results of the experiment
