Gas foil bearing is lubricated by gas and belongs to sliding bearing. Gas foil bearing has the advantages of high applicable speed, no need of auxiliary equipment, high temperature resistance, simple structure, high reliability and maintenance-free, and is selected by high-speed and low-power rotating machinery. At present, it has been widely used in oil-free high-speed rotating machinery such as air cycle machine (ACM), fuel cell air compressor, blower, micro gas turbine and turbine generator. First, the principle of gas foil bearing The common gas foil bearing is shown in figure 1, which is mainly composed of bearing sleeve, wave foil and top foil. The principle is shown in Figure 2. Due to the eccentricity between the rotating shaft and the bearing, there is a wedge-shaped space between the rotating shaft and the surface of the foil at the top of the bearing. During the rotating motion of the rotating shaft, the surface of the rotating shaft continuously drives the gas in the surrounding environment into the wedge-shaped groove, thus forming a dynamic gas film with a certain pressure in the wedge-shaped groove. When the gas film pressure is large enough to support the load, the rotating shaft will be suspended and the friction will disappear. Picture 1 picture 2 II. Development of gas foil bearing The origin of gas foil bearing can be traced back to 1906, Sundberg. The theoretical research of foil bearing first started in 1953. Blok and Van Rossum[4] published a paper on oil-lubricated foil bearing, and put forward the term "foil bearing" for the first time. Subsequently, Patel, Cameron[5] and Ma[6] published papers to make a preliminary theoretical study on gas foil bearings, and Licht[7-9] made a lot of experimental studies on gas foil bearings between 1966 and 1969. Garrett El Cecil has made an important contribution to the research of gas foil bearings. In 1960s, a gas foil bearing test-bed was established, and a prototype of rotating machinery supported by gas bearing was made. 1969, gas foil bearing was first applied to air cycle machine. With the application environment of gas foil bearing becoming more and more complex and harsh, its elastic support structure is also developing continuously. The development course and main forms of the gas foil radial bearing structure are as follows: (1) Tension type gas foil bearing A.A.Pollock put forward the tension type bearing in the late 1920s, and then Jones and others improved the bearing structure as shown in Figure 3. [1 1] The main components of the bearing are tension pin, guide pin, foil, bearing sleeve and adjusting bolt. The foil is tensioned by a guide pin and a tensioning pin. When the rotating shaft rotates, there will be a dynamic pressure effect between the rotating shaft and the foil due to eccentricity, so that the rotating shaft is suspended. At that time, this type of bearing was widely used in tape recorders. However, the foil of the stretched radial bearing is in a stretched state for a long time, and the foil is prone to fatigue failure, which leads to short bearing life, unsatisfactory bearing capacity and great difficulty in manufacturing. Later, it was gradually replaced by other kinds of foil bearings [12]. Photo Figure 3 Schematic Diagram of Stretched Radial Bearing [1 1] (2) Flat Foil Gas Foil Bearing 1987 This kind of foil bearing was put forward by osaka sangyo university. The flat foil radial bearing has multiple layers of flat foil in the bearing sleeve and a closed bearing inner surface [13]. Many copper wires are placed between flat foils to provide support rigidity for bearings. The experimental results show that the rotor system supported by this bearing can run stably at 89000 r/min [14]. (3) Multi-leaf gas foil bearing With the support of NASA, the multi-leaf bearing was developed, as shown in Figure 4. The multi-leaf bearing has many leaf-shaped foils, one end of which is fixed on the bearing sleeve and the other end is hung on the adjacent foils. When the rotating shaft rotates, due to the existence of the wedge, the airfoil foil will expand radially under the action of air pressure, thus forming a stable air film between the inner surface of the bearing and the rotating shaft [15]. Fig. 4 Multi-leaf gas foil bearing (4) Wave foil gas foil bearing This kind of gas foil bearing is the most researched and successfully applied bearing at present. Wave foil radial bearing is mainly divided into three parts: bearing sleeve, wave foil and top foil. The top foil and corrugated foil provide rigidity and damping. This kind of bearing has the advantages of simple processing technology, long service life, good stability and large bearing capacity, and is widely used in modern high-speed light-load rotating machinery. According to the stiffness distribution of bearing corrugated foil, it can be divided into three generations [16- 18]. In 1960s, the United States developed the first-stage corrugated foil gas foil bearing [3]. The top foil of this corrugated foil gas foil bearing is a complete foil, and there are many circular ripples on the corrugated foil to provide elastic support for the bearing, as shown in Figure 5. Gray et al. [19] optimized the first-stage corrugated foil radial gas foil bearing, and proposed the second-stage foil radial bearing in 198 1. The corrugated foil of this generation of bearings is composed of three kinds of corrugated foil strips along the axial direction, as shown in Figure 6. By changing the structure of these three foils, the stiffness of different parts of the bearing is different, so that the gas film distribution of the bearing is more reasonable. On this basis, Heshmat[20] put forward the third generation corrugated foil radial bearing, and the foil of this corrugated foil bearing changes in all directions, as shown in Figure 7. The third-stage corrugated foil radial bearing is composed of various corrugated foils in the axial direction and the axial direction, and the stiffness distribution of the bearing is more reasonable, which significantly improves the performance of the bearing [2 1]. Picture Figure 5 Schematic Diagram of the First Generation Corrugated Foil Radial Bearing Picture Figure 6 Schematic Diagram of the Second Generation Corrugated Foil Radial Bearing Picture Figure 7 Schematic Diagram of the Third Generation Corrugated Foil Radial Bearing (5) Wire mesh gas foil bearing Lee[22] at the beginning of 2 1 century, a wire mesh gas bearing was disclosed, as shown in Figure 8. There is an annular wire mesh between the top foil and the bearing sleeve of this foil bearing, which brings rigidity and damping to the bearing. SanAndres and Chirathadam [23] optimized this kind of bearing. The later experiments show that the wire mesh gas foil bearing has good damping, which can absorb the vibration energy of the bearing rotor system and significantly improve the stability of the system [24-26]. Photo 8 Wire mesh radial gas foil bearing (6) Bubble gas foil bearing Bubble bearing has fewer parts, and its elastic support structure is a foil with bubble protrusions, as shown in Figure 9. Kaneko[27] made some experimental research on bubble bearing. Feng and Kaneko et al. [28-29] made a systematic static and dynamic analysis of this bearing by establishing a simulation model. Fig. 9 Bubble-type gas foil bearing (7) Spring-type gas foil bearing Ju-hoSong[30] proposed a foil bearing with spiral spring as flexible support structure in 2006. By changing the wire diameter, pitch and number of circumferential distribution of the spring, the structural stiffness of the bearing can be changed conveniently. Jin Hu [3 1] increased the number of bearing circumferential springs by embedding the springs into each other. The experimental and theoretical results show that the embedded spring foil bearing has good structural stiffness and damping characteristics. Fig. 10 spring-type gas foil bearing (8) multi-cantilever gas foil bearing Feng He Zhao et al. [32] put forward a multi-cantilever wave foil gas foil bearing in 20 14, and its structure is shown in fig. 1 1. Through static and dynamic analysis, it is concluded that the deformation zone stiffness of corrugated foil is small in the starting stage, which reduces the starting friction torque of bearing; However, under heavy load, the deformed area of the foil is hard, which increases the bearing capacity. Fig. 1 1 Schematic diagram of multi-cantilever radial gas foil bearing 1995 Bosley[33] The cantilever foil bearing is widely used in micro gas turbine equipment by Capstone Company. In 20 17, Hu Xiaoqiang et al. [34] studied the static and dynamic characteristics of apex cantilever foil bearing, as shown in figure 12, which shows that the bearing has good stiffness and damping characteristics. Photo 12 cantilever foil bearing III. The gas foil bearing technology constructs a compressible fluid-elastic structure and a full-dimensional fluid-solid-thermal coupling model, reveals the wet-gas-liquid two-phase mixed lubrication mechanism of foil hydrodynamic bearing under the condition of elastic structure deformation, and puts forward a dynamic matching method of foil hydrodynamic bearing-rotor system with time-varying coupling of host performance and state, thus forming a foil hydrodynamic bearing and its rotor matching technology under complex multiphase working fluid lubrication. See the schematic diagram below for details: Picture 13 Picture 14 Picture 15 (1) Rotor dynamics calculation and analysis of gas floating bearing and high-speed rotor system. Gas foil bearing belongs to dynamic pressure bearing, and its stiffness and damping distribution play an important role in the performance of bearing rotor system. By optimizing the supporting structure of foil bearing, providing suitable stiffness and damping distribution for the bearing, establishing the dynamic theoretical model of air-floating foil bearing and calculating the dynamic stiffness and damping characteristics of the bearing are the basis of bearing-rotor dynamic characteristics analysis. Bearings with different stiffness and damping characteristics are suitable for different bearing-rotor systems. Combined with the structural characteristics of various products, the dynamic model of bearing-rotor is established by using transfer matrix method and finite element method, and the following analysis is made: critical speed of rotor: when the rotor with eccentric mass runs at critical speed, it will produce severe vibration. Generally, when the rotating speed of the generator set rises to a certain value in the process of starting and accelerating, it will cause strong vibration of the generator set, which is called critical rotating speed, that is, the natural vibration frequency of the rotor and its supporting system and the excitation frequency of the rotating speed at this time. In order to make the rotor run stably and safely, the critical speed of the rotor should be far away from the working speed 15%~20%. Unbalanced response: the analysis of steady-state unbalanced response can also be used to determine the critical speed of the system, but its more important task is to solve the steady-state unbalanced response of the rotor-support system when there may be imbalance in the rotor system, and to analyze and study how to take measures to limit the maximum unbalanced response and reduce the unbalanced response. Transient response: transient response analysis mainly refers to the sudden change of the unbalance of the rotor system, the sudden change of the external load acting on the rotor system, or the response analysis of the rotor system when the rotor system works at variable speed, including the displacement and deformation of the rotor system and the load transmitted by the supporting structure. Starting acceleration is the most common transient process. Modal analysis: calculate the forward and backward precession modes of the rotor system at different critical speeds, evaluate the logarithmic dissipation of the rotor under different forward and backward precession modes and different aerodynamic cross stiffness, and ensure the stability of the system operation. Stability analysis: draw critical velocity diagram, Campbell diagram, etc. The gyro effect of rotor system and the influence of aerodynamic cross stiffness of turbomachinery are introduced, and the stability analysis is carried out according to API requirements to determine the operating stability of air bearing-rotor system. (2) Operation durability and service life control technology of air-floating pressure bearing The durability and service life of air-floating pressure foil bearing determine whether the bearing can be stably applied to high-speed rotating equipment, and bearing structure design and manufacturing technology are the key means. Through a series of bearing structure design optimization, the effective matching of rotor bearing system under thermal balance is ensured, and the consistency and repeatability of machine rotor system after repeated disassembly are realized. Through the improvement of manufacturing technology, including the selection of bearing materials and heat treatment, foil stamping, foil laser cutting, surface wear resistance and optimization of lubricating coating, the consistency and repeatability of bearing stiffness and damping are ensured, and the durability and life of gas bearing are improved. At present, gas dynamic bearings (including radial bearings and thrust bearings) have completed 120000 repeated start-stop life tests on refrigeration centrifugal compressor equipment, simulating the worst working conditions. The theoretical uninterrupted working life of gas dynamic bearing can reach more than 20 years. draw