A translational- rotational- coupling dynamics model for a NGW double helical planetary gear train（ DHPGT） is developed to investigate the free vibration characteristics. Based on the established model,the differential equations of motion of the system are derived. Through the solution of the system eigenvalue problem,the natural frequency and vibration mode are acquired corresponding. According to the characteristics of transmission system,the vibration modes of a DHPGT can be classified into three categories,i. e.,the central components axial torsional vibration mode,the central components translational mode and the planet wheel vibration mode. Based on the loci veering / crossing principle,the influences of loci veering and loci crossing on the transmission characteristic are analyzed from the perspective of modal strain energy and vibration modes.The simulation results demonstrate that vibration modes and modal energy exchange abruptly when a loci crossing occurs,while vibration modes and modal energy change step- by- step but do not exchange when a loci veering occurs. The conclusions are then verified by numerical simulation of an example system. The present research can accurately forecast natural frequency and the point of modal and modal energy mutation,a fundamental theoretical basis for the parameter optimization,noise reduction and vibration suppression for the DHPGT is provided.