“…Studying the nonlinear characteristics of rotor-bearing systems, such as the rotor-bearing motion system, helps people understand system behavior and predict system performance, gaining a deeper understanding of the vibration behavior, stability, and motion trajectory of rotor systems, and thereby optimizing system structures.Huihui Miao et al [28] study of the dynamic characteristics of the spindle system in a CNC vertical milling machine under the action of unbalanced forces is carried out using the lumped mass method. A system of differential equations with eighteen degrees of freedom was developed for the overall system, and the effects of spindle speed and bearing parameters on the vibration characteristics and stability of the spindle were investigated, and the validity of the model was verified by experiments.Jin Hao et al [39] concluded that thermal-mechanical interaction may cause errors in the dynamic characteristics of high-speed spindles, therefore, a closed-loop iterative modeling method was proposed to improve the accuracy of the model.Zhao et al [29] A considered radial clearance and nonlinear Hertz contact, and introduced the time-varying bearing nonlinear support reaction force into the rotor concentrated mass model, and analyzed the effect of bearings on the nonlinear vibration of the rotor system under combined loads.Fang [ 30 ] established a multi-degree-of-freedom rotor model based on the method of restoring force coupling.The steady-state analysis of bearing stiffness fluctuations was conducted, and the mechanisms and varying patterns of typical resonance responses such as super-harmonics, sub-harmonics, Hopf bifurcation, and chaos in rotor parameter vibrations were discussed.Xie [31] studied the lubrication performance, dynamic characteristics and vibration characteristics of the water-lubricated bearing-rotor coupling system under different lubrication states, and verified the reliability of the theory through experiments.…”