Transform the dynamic governing equation with inner excitation and time-variable stiffness from non-linear differential equation into approximate linear equation. The exciting force caused by time-variable stiffness

gear error and meshing shock is treated as right term of this equation. The time-variable stiffness is acquired by 3D finite element contact procedure

while the exciting force caused by meshing shock is obtained by 3D dynamic contact finite element mixed formula. In this process

gear error exciting force is simulated according to the to the profile tolerance which is determined by the machining precision of gearing. The exciting force can be applied on 3D finite element model for whole gear system in order to solve the vibration response of gearbox.