In this paper we investigate the nonlinear dynamic behavior of a rotor with an architecture targeting space turbopumps. Depending on the rotor speed of rotation, these pumps can be supported by ball bearings with a loose fit, i.e. having an outer-race housing clearance, and by annular seals providing 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 undergoing the lowest vibration levels to ensure pump safety. In this context, the aim of the paper is to analyze the case of an academic rotor test bench designed to present a dynamic bending behavior similar to that of space turbopumps. The investigation focuses on the test bench equipped with two hydrodynamic bearings and two ball bearings with loose fit. The rotor response when passing through its first critical speed and triggering nonlinear bearing-housing contact phenomena is assessed experimentally and numerically. The hydrodynamic bearings are located at the two shaft ends and the ball bearings at the middle of the shaft. The rotor finite element model is detailed first and the test bench presented. Then, the nonlinear dynamic response of the rotor subject to a mass unbalance and a permanent bow is obtained. The numerical results are computed using either a full transient step-bystep time integration technique or an arc-length continuation method. The main objective is to assess how the nonlinearity stemming from the loose fit of the ball bearings alters the original rotordynamics. Moreover, a parametric analysis based on mass unbalance and on outerrace housing clearance is conducted. Major nonlinear phenomena are highlighted such as the resonance peak flattening at the critical speed, and the numerous harmonics triggered by the hydrodynamic bearing and contact forces. The results obtained and the model proposed here are of considerable relevance for the design of space turbopumps and other pumps having a similar architecture.