The torsional vibration model of the spur gear system with time- variant mesh stiffness,nonlinear clearance and the mass eccentricity caused by tooth breakage is established. The primary resonance and combined resonance of the model with tooth breakage are analyzed by multi- scale method. Then the different mass eccentricity causes the different bifurcation mode of the gear system by the singularity analysis,which comprehensively shows the dynamics mechanism of the tooth breakage fault. The results obtained herein can provide a theoretical basis for broken fault diagnosis of gearbox.