Design/methodology/approach This study develops a novel approach for analyzing the nonlinear characteristics of floating ring bearings by utilizing second-order nonlinear stiffness and damping coefficients. The proposed method replaces traditional analytical solution models with a nonlinear stiffness and damping coefficient model, enhancing both computational efficiency and accuracy. The model is validated through extensive simulations that account for varying clearance ratios and load conditions. The results are compared with those obtained from conventional methods, demonstrating the effectiveness of the proposed approach in accurately capturing the nonlinear behavior of turbocharger floating ring bearings. Findings The study finds that the proposed nonlinear stiffness and damping coefficient model significantly enhances computational efficiency while accurately representing the nonlinear characteristics of floating ring bearings. The model not only reduces computation time but also provides a more precise analysis compared to traditional methods. Moreover, the research reveals that the clearance ratio and load conditions of the floating ring bearings have a substantial impact on the nonlinear stiffness and damping coefficients. These findings suggest that the proposed model and method could be highly beneficial for advancing the design and research of floating ring bearings in turbochargers. Originality/value With this statement, the authors hereby certify that the manuscript “Investigation on the nonlinear behaviors of floating ring bearings based on nonlinear stiffness and damping coefficient models” submitted to the journal Industrial Lubrication and Tribology is the results of their own effort and ability. They hereby confirm that this manuscript is their original work and has not been published nor has it been submitted simultaneously elsewhere. They further confirm that they have checked the manuscript and have agreed to the submission. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2024-0324/