A mathematical model to investigate the dynamics of a Jeffcott-rotor having intermittent contact with a stator is presented. The advantage of this model is found in the consistent sub-model of the stator which is implemented as an additional vibratory system, interacting with the rotor model via nonlinear contact forces. Such forces are generated by a contact model, consisting of contact stiffness, damping and friction. The contact model is activated during the contact phase which is defined by both geometrical and force-dependent conditions. As the rotor disk and the stator are connected by a high contact stiffness during the contact phase, an integration algorithm suitable for numerically stiff systems has to be employed. Begin and end of rotor-stator contact are defined as state events and localized by an iterative procedure. The model allows to study the effect of the visco-elastically suspended stator on the rotor motion when intermittent contact occurs. Numerical studies are carried out for parameter variations of the rotor speed and the mass ratio of the stator and the rotor. Results are presented as Poincaré-maps and bifurcation diagrams, exhibiting rich dynamical behavior. The numerical studies show and confirm that the damping parameter of the stator suspension has significant influence on the type of motion obtained for the rotor-stator system. As damping is decreased, periodic solutions with few contacts become less likely and non-periodic behavior of the system dominates.