A new approach to the critical speed calculation of general multi-mesh gear chain system included bevel gear is presented. A transfer matrix model based on Hibner's branch method is developed and the natural properties of the branched rotor system are calculated with using the λ-matrix formulation. A Campbell diagram, in which the excitation sources caused by the mass unbalance of the rotors, misalignment and the transmitted errors of the gearing are considered, shows that, at the neighborhood of the operating speed, there are the two critical speeds amplifying the first mode and the eighth mode.
