As a high speed rotating device, the modern turbocharger rotor is commonly supported by floating ring bearings (FRBs). The high nonlinearity there can always lead to quite complex and interesting phenomena rarely observed in other rotating applications. Using the run-up and run-down simulation method, this paper originally and systematically discusses the effect of bearing outer clearance on the rotordynamic characteristics of a realistic turbocharger rotor over the speed range up to 3000 Hz. The rotor is discretized by the Finite Element Method and supported by analytically calculated bearing forces. The linear analysis is proved to be effective in predicting the first two nonlinear jumps but inadequate to study the rotordynamic characteristics at higher rotor speeds. The nonlinearly simulated results show the appearances of distinct and interesting phenomena within the considered range of FRB outer clearance, which can be further divided into four groups. Within the same group, the simulation results are qualitatively similar to each other but quite dissimilar from the results from different groups. Moreover, the unwelcome Critical Limit Cycle Oscillation can be avoided by increasing the outer clearance size. Additionally, in some cases, the run-down simulations reveal distinct frequency maps as compared to the corresponding run-ups. Furthermore, it is seen that ring speed ratios can be considerably affected by the nonlinear jumps. Therefore, FRB outer clearance should be thoroughly examined to achieve the best rotordynamic performance.