## 1 Introduction  
Aerostatic bearings are considered to have the advantages of low friction, high precision, and no pollution. Aerostatic bearings are highly valued in the machining and research of fine and precision surfaces [1]. Firstly, traditional mechanical bearings face issues such as high frictional losses, short service lives, and the need for frequent maintenance. With the increasing demand for better-performing mechanical equipment under extreme conditions like high speeds, heavy loads, and ultra-high temperatures in fields such as engineering machinery and aerospace, traditional lubrication methods are no longer sufficient. Aerostatic bearings, as a new type of support without contact or friction, can effectively address these problems experienced by traditional bearings under harsh conditions, enhancing the reliability and efficiency of mechanical systems. In addition, advances in micro- and nano-technology and computational fluid dynamics (CFD) have greatly accelerated the research of aerostatic bearings. Advancements in ultra-precision technology offer more possibilities for bearing structure design, leading to further optimization of bearing performance [2, 3]. CFD provides an essential means for studying gas flow patterns inside bearings, aiding with improving bearing design and enhancing bearing performance [4]. Through the application of ultra-precision technology and computational fluid dynamics, researchers can better understand the working principles of aerostatic bearings, thus driving continuous innovation and development of this technology. Additionally, research on aerostatic bearings has garnered attention and support from the international engineering community. The increasing demand in fields like aerospace, energy, etc., is setting higher requirements for mechanical equipment. In recent years, with the increasing complexity of equipment, the precision requirements for key components have become higher and higher. Aerostatic bearings, as one of the core components of precision equipment, have attracted widespread attention. Therefore, it is necessary to conduct a more in-depth study on the design, manufacturing, and characteristics of gas static-pressure thrust bearings [5; 6; 7; 8; 9; 10]. The throttle valve, an important component that affects the performance of aerostatic bearings, can be classified as a small-hole throttle valve, an annular throttle valve, a narrow-slot throttle valve, or a porous throttle valve [11; 12]. Among them, the orifice throttle valve has a simple structure, convenient processing, and relatively stable overall performance, making it the focus of research for many scholars [13]. Aerostatic bearings have garnered extensive attention from researchers worldwide. Initially, [PERSON] [14] introduced the concept of hydrostatic gas bearings. Subsequent studies, such as by [PERSON] et al. [15], leveraged computational fluid dynamics to investigate the performance of aerostatic thrust bearings with a six-hole design, focusing on how various operational parameters affect their efficacy. [PERSON] et al. [16] employed Reynolds numbers to gauge micro-vibration levels in gas hydrostatic circular thrust bearings, with the aim of improving stability through structural optimization and Reynolds number maximization. Furthermore, [PERSON] et al. [17] applied the finite difference method (FDM) and the flow balance principle in Cartesian coordinates to resolve the primary equation governing multi-hole integrated orifice restrictor aerostatic bearings, noting substantial changes in load capacity and stiffness based on orifice count and size. [PERSON] et al., [18] advanced the study by modeling and simulating the static properties of porous, orifice, and multi-orifice aerostatic rectangular thrust bearings, particularly examining how increased gas pressure affects load capacity and stiffness. [PERSON] [19] explored the effects of pad geometry and inlet conditions on the performance of externally pressurized rectangular gas bearings through experimental methods. [PERSON] et al.