The present paper focuses on the numerical investigation of the transient response of a rotorshaft affected by unilateral contact occurrences with friction mechanisms. Rotor-stator contact is initiated radially at the shaft level. The components are modeled under the rigid bodies assumption and the rotor dynamical response is investigated in the time domain. The turbomachine is assumed to be driven by two torques: the first one is prescribed while the second one is induced by friction using Coulomb's model. Particular attention is paid to the accurate prediction of the unknown rotational speed transient. The proposed methodologies are grounded on the Carpenter and Moreau-Jean time-marching algorithms, implying the use of Lagrange multipliers to solve the frictional and unilateral contact conditions. The simplest procedure considers only sliding friction while the most sophisticated one involves convex analysis in order to deal with normal and friction forces independently is case of stiction. The solutions predicted by the algorithms are compared and show good agreement. The sensitivity study on the stator properties and friction coefficient allows the identification of the conditions affecting the rotational speed limitation. Based on the response post-processing in the time and frequency domains, it is found that a higher friction coefficient, a stiffer stator support or a lighter stator leads to a decrease of the rotational speed maximum value.