Dynamic model of power four embranchments gear transmission system has been provided

and vibration equation of a single axis has also been established based on axis-element method. With the gear mashing matrix

coupling between equations of every axis can be achieved

which helped to establish dynamic equation of the whole power transmission system. Solving that equation

natural frequency and natural vibration of system were obtained

and the conclusion that the system needs damping design to make sure it work stably at the normal working speed has been conferred. Meanwhile

difference between dynamic load coefficients of different transmission errors has been analyzed

and results show that transmission error has an obvious effect on dynamic load coefficient of the power four embranchments gear transmission system.With the increase of the transmission error

the dynamic load coefficient is also increasing

especially in high speed stage gears the performance even more significant.The research methods and conclusions lay foundation for dynamic optimization design of power four embranchments gear transmission system.