The paper investigates numerically the nonlinear dynamic behavior of a rotor whose design is similar to spatial centrifugal turbopumps. Depending on the rotor speed of rotation, these pumps can be supported by ball bearings with loose fit (hereafter named hybrid bearing), i.e. having a clearance between their outer race and their fixed housing, and by annular seals which develop radial fluid forces thanks to the Lomakin effect. Moreover, such turbopumps often operate in supercritical regime, which means that they must pass through critical speeds while experiencing the lowest vibration levels to ensure the pump safety. In this context, the paper aims to analyze numerically the case of an academic rotor test bench designed so as to present a bending rotordynamics similar to that of the turbopump and built for experimental validation purposes. The investigation focuses only on the test bench equipped with hydrodynamic and ball bearings. Thus, two hydrodynamic bearings are located at the two shaft ends and one hybrid bearing is located at the middle of the shaft. The finite element model of this rotor is first detailed. Then numerical analysis, using either a full transient step-by-step time integration technique or an arc-length continuation method, is performed to compute the rotor unbalance response when passing through its first critical speed. The main objective is to evaluate how the contact nonlinearity from the ball-bearing loose fit alters the original rotordynamics. In particular, interesting nonlinear phenomena such as jumps, hysteretic behavior, quasi-periodic motions and hardening resonances are shown. Furthermore, some non-expected frequencies highlighted in the full spectrogram are identified as the complex nonlinear modes responding because of the rotor/stator contacts.