Abstract: In the field of diesel, petrol and aero engines design, exhaust gas turbocharging has become a critical technique for enhancing its air intake and power while reducing fuel consumption and emissions. The core component in a turbocharger is the rotor-bearing system at ultra-high speed. The rotor of small size and light weight supported by floating-ring bearing (FRB) has been extensively used in automotive turbocharger to reach the speeds between 100 000 and 300 000 r/min, but complicated nonlinear dynamics phenomena including oil whirl/whip, jumping, bifurcation and chaos probably appear in the response of unsteady fluid-film force and self-excited unbalance force, which have a great significance for the healthy operation of the high-speed turbocharger. By applying the finite difference method to calculate the transient pressure distribution of double fluid film based on Reynolds lubrication theory, this paper developed a nonlinear oil-film force model for the floating-ring bearing through Simpson integration. On this foundation, D’Alembert’s principle and the transfer matrix method were adopted to establish the dynamical differential equations for the turbocharger rotor considering the gyroscopic effect induced by impellers. Consequently, this work described a coupling model of dynamics and tribology for the turbocharger bearing-rotor system. The numerical methods in nonlinear dynamics, e.g. phase portrait, Poincare mapping, bifurcation diagram and frequency-response spectrum, were then adopted to analyze the rotor unbalance vibration response and bearing oil-film instability characteristics of this system, providing theoretical support for the design of turbocharger bearing-rotor. The results showed that at a small impeller unbalance (unbalance offset distance e=4 μm), the 0.49×/0.13× sub-synchronous inner/outer oil whirl suppresses the 1× synchronous unbalance effect and the system was unstable throughout a wide range of ascending rotor speeds. While the unbalance was relatively large (e=14 μm), the generated 1× synchronous unbalance vibration with small amplitude can maintain this system security at the rotor speeds less than the threshold of approx. 120 000 r/min. If the rotor speed kept on rising, the oil-film instabilities successively dominated by the 0.35× and 0.24× sub-synchronous responses occurred. Only at the appropriate unbalance offset (e=9 μm), a stable “interval region” of medium-high speeds (approx. 80 000 to 170 000 r/min) characterized by the synchronous small-amplitude vibration emerges. During the “interval region”, the interactive nonlinear stiffness and damping effects between the inner and outer oil-films kept the rotor orbiting in the form of stable single periodic motion, which also effectively prevented the 1× synchronous unbalance vibration from reaching excessive amplitude with ascending rotor speed. The emergences of “interval region”, bifurcation, and chaos strongly depended on the design parameters of rotor and bearing. An increase in unbalance can effectively suppress the sub-synchronous oil whirl at relatively low rotor speeds. At high speeds, the effect can also prevent the rotor from entering chaos by the path of quasi-periodic bifurcation, but an excessive unbalance induced oil whip accompanied by frequency locking. By offsetting the rotor unbalance appropriately, the “interval region” can transfer to a range of higher rotor speeds, which can enable a turbocharger to avoid fluid-induced instability and to run healthily under the requirement of some high speeds.