Stability analysis of multi-leaf oil-lubricated foil bearings with back springs based on nonlinear oil film force model

Oil-lubricated foil bearings have become one of the preferred choices for supporting high-speed rotor systems due to their characteristics, such as low friction losses and excellent adaptability. This study presents an efficient and accurate solution for calculating the stability of multi-foil oil-lubricated foil bearings with back springs. Based on the static and dynamic characteristics solved by the finite difference method, a nonlinear oil film force model considering multiple parameters was established through polynomial fitting. The dynamic model of the bearing-rotor system was established using the finite element method, and the Newmark method was employed to solve the dynamic response for the analysis of bearing stability. The bearing test rig was designed and constructed to assess the vibration characteristics. The stability solution method proposed in this paper eliminates the calculation process of oil film force in traditional methods, significantly improving computational efficiency. The research demonstrates that increasing the bearing clearance and length results in a sharp decrease in the instability threshold speed. The experimental results confirm the validity of the theoretical model, and the instability phenomenon induced by the dominance of low-frequency components is observed at 125,358 r/min.