Data-Driven Model for the Dynamic Characteristics of O-Rings for Gas Bearing Supported Rotors

Abstract

The measurement results of various nitrile butadiene rubber (NBR) O-Ring sizes are presented, and reduced-order models are developed in order to predict the stiffness and damping coefficient as a function of O-Ring geometry, Shore hardness, squeeze, and excitation frequency. The results show that the curvature ratio d/D needs to be considered in the reduced-order models. The assessment of the model suggests a maximum deviation of 30% in predicted stiffness compared to the measurement data. However, taking into account the typical Shore hardness tolerance given by O-Ring manufacturers and other measurement uncertainties, the proposed model enables the prediction of various O-Rings with a good accuracy in the frequency range of 1.5–3.75 kHz, which corresponds to typical gas bearing supported rotor applications.

Flexible Support for Gas-Lubricated Bearing Bushings

“…The results suggest that the stiffness of the investigated O-Rings seems to increase with frequency, while the damping coefficient decreases with increasing frequency. This corroborates results obtained by Smalley et al [11], Tomioka et al [17], Green et al [18] and by Bättig and Schiffmann [19]. In the investigated frequency range of 1500-4500 Hz, the average radial stiffness for a single O-Ring is 5.5e+05 N/m, while the average damping coefficient is 6.16 Ns/m.…”

“…A model using 1D beam elements as well as a 3D model using tetrahedral elements has been set up to determine the radial and tilting stiffness k r and k t . O-Rings, whose dynamic characteristics are highly dependent on the excitation frequency [11,18,19,20,21], the membrane measurement results suggest that the radial stiffness k r is independent of the excitation frequency f , which makes their use as a flexible support for HGJB bushings significantly easier and more predictable.…”

Unbalance Response Analysis of a Spindle Supported on Gas Bearings: A Comparison between Different Approaches

“…Park and Kim [5] and Belforte et al [6,7] proposed new types of feeding systems that could increase the rotor bearing system performance. The integration of external dampers, e.g., O-rings [8,9], air rings [10,11] and bump foil [12,13], makes it possible to increase the dynamic stability of rotor bearing systems. In this regard, Liebich et al [14] presented a comprehensive analysis on the use of elastomeric rings by proposing a new approach to optimize their material properties.…”

“…In this regard, Liebich et al [14] presented a comprehensive analysis on the use of elastomeric rings by proposing a new approach to optimize their material properties. The dynamic performance and stability of journal bearings can be evaluated through nonlinear rotor bearing models, i.e., the orbit method, or models that are obtained by the linearization of the stiffness and damping coefficients of the bearings [8]. The orbit method includes the complete nonlinear equations of the rotor and the bearings, which are numerically integrated to obtain the shaft center orbits corresponding to any set of geometrical, running and initial conditions.…”