In order to reveal the vibration mechanism under the working state of the polishing grinding head,the two teeth difference external compound planet gear transmission system for the new polishing grinding head is studied.The structure characteristics and the planet wheel assembly condition are analyzed,and the 3D model of the system structure is built up by using Solid Works software.The Simulation module is utilized for modal analysis of the transmission system by using finite element method.The natural frequency and corresponding vibration mode are obtained.The analysis results provided a useful reference for the study of free vibration,dynamic response and vibration suppression in polishing grinding of the two teeth difference external compound planet gear transmission system.