# Characteristic Analysis of Bump Foil Gas Bearing Under Multi-Physical Field Coupling
## 1 Introduction
By solving the Reynolds equation, the three-dimensional energy equation, and the heat balance equation of the rotor-bearing subsystem, [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) established a detailed thermohydrodynamic model considering the temperature of a gas film, the top foil, the corrugated foil, the bearing sleeve, and the rotor. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) proposed a coupled thermal-structural flow model for gas-lubricated foil bearings considering the bending and film effects of the top foil, as well as the thermal expansion of the journal, the bottom foil, and the bearing seat. The importance of the temperature effect and thermal deformation of foil structure was found. The modeling method of [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) is based on the basic theoretical framework of Heshmat elasticity, and the thermodynamic analysis of the flat foil was simplified by introducing a thermal resistance assumption. In this model, the flat foil is regarded as the main load-bearing unit of the viscous dissipation heat of the film, and the heat load that can be taken away by the air flow in the bottom cooling channel is assumed. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) proposed a multi-physical field coupling prediction framework for bump foil bearings based on thermohydrodynamics. By introducing a temperature-dependent material constitutive equation, the model successfully reproduces the attenuation law of foil stiffness under high-temperature conditions, and the prediction error of its dynamic characteristics is lower than that of the traditional isothermal model, making it a high-precision simulation tool for bearing design under extreme working conditions. [PERSON] and [PERSON] [16] presented analytical models for three-dimensional energy transfer, the axisymmetric heat conduction of the shaft, the thermal resistance of the corrugated plate arc, and gas flow mixing in gas foil bearing housings. The mixing of inlet air flow and thermal energy at the leading edge of the top foil was numerically studied. [PERSON] and [PERSON] [17] developed a thermo-elastohydrodynamic multi-field coupling numerical framework for bump foil bearings, revealing the speed-temperature influence mechanism. [PERSON] et al. [18] studied the thermo-elastic deformation behavior of a bump foil journal gas foil bearing during continuous loading at a specific stable speed. A three-dimensional numerical simulation method combining the finite volume method and the finite element method was used to obtain the coupling effect between thermal effect, elastic deformation, and fluid lubrication. [PERSON] et al. [19] constructed a three-dimensional thermal analysis model for the study of the thermal characteristics of dynamic pressure air bearings. By coupling the physical parameters affected by temperature, the model comprehensively considers the influence mechanisms of multiple factors on the temperature field, such as the heat dissipation boundary conditions, rotor speed, applied load, and oil film thickness. It was found that the increase in load mainly led to a temperature rise and range expansion in the original high-temperature region, but had little effect on the temperature distribution in the low-temperature region. [PERSON] et al. [20] proposed a fully coupled thermo-elastic-aerodynamic bearing model. The model includes the description of the deflection of the bump foil and the flat foil, the calculation of the pressure and temperature distribution in the gas film, and the temperature distribution in the surrounding structure (the rotor, the bearing sleeve, the flat foil and the bump foil). Based on a commercial simulation platform, [PERSON] et al. [21] developed a three-dimensional thermal elastohydrodynamic numerical framework for a bump foil bearing integrated with multi-component coupling. The model innovatively incorporates two pressurized chambers, bearing sleeves, and rotor-exposed sections into the solution domain.