# Characteristic Analysis of Bump Foil Gas Bearing Under Multi-Physical Field Coupling
## 1 Introduction  
Oil-free rotor-bearing systems are widely used in aerospace [1], new energy vehicles [2], and other industries. Gas bearings are one of the main oil-free rotor-bearing systems. Due to the compressibility of gas and the coupling of temperature fields with gas viscosity and density, the bearing characteristics of gas bearings are complex. Vibration instability often occurs in the design and development process of high-speed-rotor-gas-bearing systems. Analysis of the bearing characteristics of gas bearings is important for the design and development of high-speed-rotor-gas-bearing systems. The accuracy bottleneck of foil gas film support system performance prediction focuses on the nonlinear response modeling of the bump foil and flat foil. This research faces dual technical challenges: the nonlinear characteristics of the contact interface of foil-laminated materials such as dry friction damping and contact heterogeneity lead to deformation prediction errors, and the multi-scale coupling effect of gas film thickness and flexible structure deformation reduces the convergence stability of the fluid-solid coupling equation [3]. A shell element finite element analysis framework for foil gas film support was constructed by [PERSON] and [PERSON] and [PERSON] and [PERSON] (2018). The factors affecting the static characteristics of the bearing were studied. Among them, the stiffness of the flat foil mechanism had a great influence, and the use of a bump foil bearing with greater stiffness could reduce the deformation of the bump foil receiving the load, revealing that the stiffness of the flat foil plays a leading role in supporting static stiffness. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) deduced the calculation formula of maximum gas film pressure distribution by using an analytical method. By assuming some conditions, and when the angular velocity was large enough, it was found that the product of the pressure and the gas film thickness is a constant, which corresponds to the maximum gas film pressure of the bearing. Substituting the compressible Reynolds equation, the maximum gas film pressure can be obtained. [PERSON] and [PERSON] and [PERSON] (2018) used a shell element to carry out finite element modeling of the top foil and combined the elastic support of corrugated foil with fluid pressure load to establish a static and dynamic performance prediction model of the foil bearing. [PERSON] et al. [PERSON] et al. (2018) studied the influence of excitation frequency, nominal clearance, loading direction, and elastic structure on the performance of bump foil air bearings. [PERSON] et al. [PERSON] et al. (2018) presented a novel aerostatic bearing with back-flow channels, which were designed to connect the feed pocket and low-pressure region of the bearing clearance directly. The high-pressure zone of the aerostatic bearing in the return flow channel of the bearing can increase in size with the disappearance of the eddy current in the inlet, thus increasing the load capacity. [PERSON] et al. [PERSON] et al. (2018) established a foil air bearing model to solve the slip problem in air-wing interfaces and studied the changes in various performance parameters under the slip and non-slip states of air bearings. The heat accumulation of gas films is particularly significant in air bearings operating at high speeds and ultra-high speeds. Due to the low heat capacity of air, the temperature rise in air films can reach several times that of normal temperature, even under medium friction power consumption. This sharp temperature rise not only leads to the thermal softening of the supporting material but also changes the pressure distribution of the gas film [PERSON] et al. (2018). [PERSON] et al. [PERSON] et al. (2018) solved the compressible Reynolds equation by combining the simplified energy equation of the lattice Boltzmann equation and analyzing the thermal characteristics of the air bearing. The study found that 75-85% of the heat generated in the film is transferred through this cooling air.