Abstract: The nonlinear dynamical model of the low pressure cylinder-generator system is established after considering the sub-synchronous resonances. The unbalanced mass can arouse bending-torsional coupling vibration of the rotor system and the balance more large the vibration more serious. The bifurcation equations of the rotor with bending-torsional coupling are obtained by using the average method. Transition sets and bifurcation diagrams are obtained according to the singularity theory. The parameter plane is divided into four regions. In different regions there are different bifurcation modals. The bifurcation characteristics are analyzed by analytical and numerical results. It is found that under the sub-synchronous resonance, only considering the torsional vibration of rotor system is incomplete and bending-torsion coupling vibration analysis is more reasonable. All these results presented here can provide a basis for the optimal design and fault diagnosis of rotor systems.