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In this paper, fault characteristics of a single span rotor system with two discs are investigated when the rubbing between a disc and an elastic rod (a fixed limiter) occurs. First, a finite element (FE) model of the rotor system is developed, a point–point contact model is established to simulate the rotor–stator rubbing by simplifying the disc and the rod as two contact points, and then the two models are coupled by contact force. In addition, the augmented Lagrangian method is applied to deal with contact constraint conditions and the coulomb friction model is used to simulate rotor–stator frictional characteristics. The vibration features of the rotor system with rubbing are analyzed with respect to the effects of the gaps between the disc and the rod, the contact stiffnesses under three typical cases with different rotating speeds. The simulation results show that different rotor motions appear, such as period-one motion (P1 …