Dynamics of wheels and other rolling elements in machines are significantly affected by the friction phenomena between the surfaces. When modeling the transitions between rolling and slipping motion, the simplest choice is applying the Coulomb friction model or the similar but improved models like the Stribeck model. However, when the local deformations are not negligible, often the so-called creep force models are used, which contain a coupled nonsmooth effect of the kinematic variables. This study investigates the effects of the different contact models on the properties of the vibrations. The models are demonstrated on 2D test problems of rolling elements. Mathematical methods of nonsmooth dynamics and singular perturbation are utilized to explore the details of the phenomena.