Turbochargers are widely used in high-performance internal combustion engine systems such as automobiles, aerospace, and marine applications. The operational stability of their core component, the floating ring bearing-rotor system, directly impacts overall performance and lifespan. Due to the unique dual oil film structure of floating ring bearings, while enhancing vibration damping capabilities, they also introduce significant nonlinear dynamic behaviors such as oil film vortex, sub-synchronous vibration, and bifurcation phenomena. This paper establishes a lubrication model for the floating ring bearing based on the Reynolds equation and JFO cavitation boundary conditions, and combines it with a rotor finite element model to construct a nonlinear dynamic model of the turbocharger floating ring bearing-rotor system. Based on this, speed-up simulations were conducted for the system under balanced conditions and under different unbalanced conditions, systematically analyzing oil film instability behavior. The research results indicate that unbalanced excitation has a significant regulatory effect on oil film vortex shedding, and the system may enter a chaotic state under specific operating conditions. Additionally, through methods such as waterfall plots, Poincare maps, and bifurcation analysis, the evolutionary of the system's nonlinear response was revealed. This study contributes to a deeper understanding of the physical mechanisms underlying oil film instability in turbochargers, providing theoretical support for system design optimization and vibration fault diagnosis.