An Improved Dynamic Modeling Approach of Aerostatic Thrust Bearing Considering Frequency-Varying Stiffness and Damping of Air Film

Abstract The damped mass-spring model is often used for the dynamic modeling and vibration analysis of aerostatic bearing systems by taking the air film as equivalent springs, especially when the bearing is used as a key component in mechanical equipment. However, the stiffness and damping of the air film are frequency-dependent, making the commonly used approach of taking static stiffness or fixed value as the spring coefficient no longer applicable for a bearing subject to a complex external force containing different frequencies. To address this issue, this paper develops the damped mass-spring model for the aerostatic thrust bearing considering the frequency-varying stiffness and damping by means of the linear superposition method. It indicates that the air bearing is still a linear system under a micro disturbance despite the frequency-dependent character of dynamic coefficients because the bearing vibration satisfies the superposition principle. The improved dynamic modeling approach is able to accurately and efficiently predict the overall dynamic response of the thrust plate with both axial and tilting motion when the plate is subjected to a multi-frequency vibration. In solving the overall dynamic response, the stiffness and damping associated with the responses of the transient part and steady part correspond to the natural vibration frequency and external disturbance frequencies, respectively. The feasibility and accuracy of the improved modeling approach are partly or completely verified by the direct trajectory calculation method, the computational fluid dynamics, dynamic mesh simulation, and a modal test. The proposed modeling method provides an effective way for the vibration analysis of air bearings, and in the meantime avoids the possible numerical errors caused by the traditional modeling approach.