In the complex gear-rotor system with unparallel axes and multiple branches

based on sub-structure theory

each simple rotor was regarded as an axis element

and the gear meshing forces were considered as exciting forces of the element

then the vibration equations of all axes were established with lumped mass method in local coordinate system.In global coordinate system

all these vibration equations were synthesized to the lateral-torsional coupling vibration equation of the complex gear-rotor system.Through numerical calculation

the natural frequency and dynamic response of the system can be obtained.At last

the mode and lateral-torsional passive vibration of an aero-engine starting transmission system was analyzed with the axis element method proposed in this paper.