Due to the coupling of the damper journal with the elastic ring and oil film, the elastic ring squeeze film damper (ERSFD) shows better dynamic performance in comparison with the traditional squeeze film damper (SFD). Therefore, a novel rigid–elastic–oil coupled mathematical model was established. The elastic ring deformation, as the key point, is solved according to the planar bending theory. Then, based on the pressure governing equation of the oil film, using the central finite difference method, the oil film pressure was addressed. Meanwhile, the Simpson method was implemented to calculate the dynamic characteristic coefficients (equivalent stiffness $Ke$ and damping $Ce$) of ERSFD (DCCEs). Also, we analyzed the influence of journal eccentricity, oil film radius clearance, flexibility coefficient and damping hole diameter on the DCCEs, and the results were compared and verified with the existing literature. The sensitivity of each parameter to the DCCEs was analyzed by using the linear regression method. According to the results, the flexibility coefficient has the greatest effect on the DCCEs, followed by the oil film radius clearance. The eccentricity of the journal and damping hole diameter have the least impact. This work will provide a theoretical basis for reflecting on the bearing dynamic characteristics more truly and accurately.

(1) Background: To better understand the dynamic characteristics of a ball bearing with an elastic ring squeeze film damper (ERSFD) under sudden unbalance, a novel dynamic model was established by fully considering the coupling between the ERSFD, bearing outer ring (the journal), rotor, and disc (loading bearing); (2) Methods: An improved secant method was developed to determine the initial eccentricity values of the bearing’s outer ring and the disc. The dynamic response of the outer ring under different speed ratios, damping ratios, and mass ratios was solved using the variable-step Runge–Kutta method; (3) Results: In comparison, a low-speed ratio, high damping ratio, and low mass ratio were more conducive to suppressing the bearing vibration. When the imbalance was suddenly introduced, the displacement amplitude of the eccentricity, transmissibility, amplitude–frequency response, and the radius of the outer ring center locus increased; (4) Conclusions: This work provides a reference for further studying the nonlinear vibration of rolling bearings coupled with an ERSFD.

Capacitance-based methods are widely used to evaluate lubricant film thickness in machine elements where direct optical access is unavailable, especially in rolling bearings and other multi-contact components. This review examines the physical basis, historical development, and modern methodological routes of capacitance-based film thickness determination, with emphasis on four coupled interpretive layers: film geometry, dielectric response, electrical topology, and parasitic/background effects. The literature shows that the field has evolved from simple dielectric-gap conversion toward more strongly constrained interpretation using elastohydrodynamic lubrication priors, dielectric identification, network-aware reduction, and frequency-domain information, particularly under grease lubrication, starvation, and transient conditions. Across these studies, capacitance-derived film thickness is not a methodologically uniform quantity but an inferred result whose meaning depends on what is prescribed, what is estimated, and what ambiguity remains unresolved. The main unresolved challenges are geometry–dielectric non-uniqueness, parasitic and topology uncertainty, and limited validation under realistic operating conditions. Overall, capacitance-based film thickness determination in practical machine elements is best understood as a constrained electromechanical inference problem, and future progress will depend on stronger identifiability, more informative broadband measurements, and clearer reporting of assumptions, inference targets, and validation basis.