After a quick literature review of rotordynamics, bearing dynamics and rotor vibrations during acceleration, the rotor of a slotless permanent magnet synchronous motor is being studied through simulations. In a first modal analysis, the critical speeds of the rotor are computed. There appear to be only two critical speeds around 40’000 [(rad)=s] which correspond to the first bending mode. The results are consistent but demand a lot of computational resources for simulation. Transient simulations are therefore performed on a simple 3D model after the failure to simulate the system correctly with an axisymmetric finite element formulation. These transient simulations converged with great difficulty and did not yield the expected results. Further investigation is required to continue the simulations.