## 1 Introduction
The results of the analyses showed the existence of couplings between the radial and thrust bearings, particularly in their aerodynamic variant, and demonstrated the feasibility of using the analyzed bearing types in a gas microturbine. The linear rotodynamics analysis of the entire rotor with gas bearings was presented in the paper [7]. The gas bearings analyzed were externally pressurized and designed for oil-free turbomachinery. The results of the analysis of the dynamic response to rotor unbalance agreed well with those obtained from the experimental measurements. It was observed that the damping in the bearings decreased as the supply pressure increased, and the computationally obtained value of this parameter was approximately 30% lower than that determined experimentally. Unstable rotor operation was manifested by subsynchronous vibration with a frequency close to 50% of the rotor speed, occurring at higher speeds than predicted by calculations. A model of spherical aerodynamic bearings with a spiral groove is presented in the publication [8]. The three-dimensional analysis, which investigated the effects of selected bearing parameters on the steady-state characteristics of the bearing, was conducted using CFD (computational fluid dynamics) Fluent software. The commercial software used was found to accurately represent the complex flow phenomena occurring in gas bearings and predict their characteristics. Computational methods that account for fluid-structure interactions are increasingly being used to analyze gas bearings. An example of dynamic analysis considering such interactions was presented in the paper [9], focusing on a high-speed machine tool spindle supported by aerostatic radial and thrust bearings. Some authors propose analyzing the phenomena occurring in gas bearings while taking fluid-thermal-structural interactions into account. An example of such an analysis concerning gas foil bearings is presented in the paper [10]. A three-dimensional thermo-elastic-hydrodynamic model of a gas foil thrust bearing allowed the authors to determine the heat flux transfer path and the temperature distribution within the bearing. Some commercially available universal engineering programs have elements in their libraries dedicated to bearing analysis. Finite elements prepared in the Ansys program for the analysis of hydrodynamic (liquid-lubricated) bearings were used by the authorsof [11] to analyze aerodynamic gas bearings. Although the compressibility of the lubricant was neglected in this model, it allowed satisfactory results (e.g., stiffness and damping coefficients) to be obtained for gas bearings operating under specified conditions. This was explained by the similarity of phenomena occurring in aerodynamic and hydrodynamic radial bearings, especially when they operate with a small lubrication gap. However, the authors acknowledge that the proposed method of modeling gas bearings has yet to be fully experimentally verified. The authors of a subsequent publication [4] showed that advanced gas seals, where aerodynamic phenomena occur, can also have a significant impact on the dynamic stability of high-speed rotor systems. In their research, they used CFD software to analyze and optimize the gas seals, and the model used underwent experimental verification [4]. It was noted that the selection of an appropriate numerical grid had a major impact on the calculation results. Issues related to the development, modeling, and analysis of gas-bearing systems are also discussed in review articles. The authors of [12] presented various solutions for oil-free bearing systems that can be used in the rotors of automotive turbochargers, including gas foil bearings. In contrast, the review article [5] presented various fluid-lubricated bearings that operated under extreme working conditions. Among other things, attention was drawn to the possibility of improving the characteristics of classical aerodynamic gas bearings by using suitably designed shallow-depth grooves on the sliding surfaces.