# Experimental Study of See-Saw Mode Nano-Vibration on Orifice-Type Restrictors
## 1 Introduction  
Aerostatic bearings are widely employed in ultra-precision machine tools, owing to their low friction and high accuracy. When in use, the aerostatic bearings are supplied with external compressed air, which enters through restrictor orifices to form a layer of gas film that floats the slide. Many efforts are taken to properly align the air-supply pressure, restrictor parameters and gas clearance to ensure the optimal static performance of load capacity and stiffness [1; 2; 3]. For nanometer and sub-nanometer moving and positioning demands, absolute stability of the slide is required. Hence, the dynamic performance of the slide garners the most research attention. However, the air-supply pressure, restrictor parameters and gas clearance determine the flow-field characteristics (e.g., pressure distribution, temperature transmit, mass flow rate and charge coefficient), which are related to the gas-flow pattern. The Reynolds-number kinetic parameter is used to judge laminar or turbulent gas-flow patterns. [PERSON] et al. [4] showed that when the fluid Reynolds number exceeds a certain value, the pressure of the gas film will be greatly changed, affecting bearing stability. [PERSON] et al. [5] verified that the Reynolds number represented the degree of bearing micro-vibration; that is, when the Reynolds number increases, the gas film becomes turbulent and the vortex is enhanced to enlarge the vibration. In large Reynolds-number cases, self-excited vibrations (i.e., pneumatic hammering [6]) occurs at a low specific stiffness, often causing shock waves [7]. Hence, some researchers have regarded the micro-vibration as a vortex excitation. [PERSON] et al. [8] established a relationship between gas vortices and nano-vibrations, demonstrating that the vibration energy of the aerostatic bearing increases with the strength of the air vortices. [PERSON] [9; 10; 11] confirmed the vibration's macroscopic factors of gas-source fluctuation, guideway noise, environment features, etc., further illuminating the relationship of the three micro-scalefactors (i.e., first-order velocity slip, flow factor and effective viscosity) of the vibration. He showed that with the increase in film thickness, the micro-scale factors have little effect on the frequency at the maximum amplitude. However, they can be used to correct the vibration equations. Most research has focused on the gas film itself. Nonetheless, the fluid-structure interaction (FSI) phenomenon should be further considered with respect to vibration. Practically, the FSI is a two-way problem. That is, the structural deformation of the slide or the restrictor and the air-gas pressure fluctuation mutually interact. [PERSON] et al. [12] created a two-way fluid structure interaction model with conjugate heat transfer was created to study a spiral groove thrust bearing at various operating conditions, and they claimed that it is possible to use fluid-structure interaction to predict the load capacity for high-speed spiral groove thrust bearing. [PERSON] et al. [13] presented a novel fluid-structure interaction-thermal coupled model for the lateral lubricating gaps between gears and lateral bushes in external gear machines (EGMs), and proposed a novel relative lubricant film thickness measurement method in gear machines using capacitive sensors presented to validate the spatial film thickness predictions. [PERSON] et al. [14] studied the multi-physics coupling phenomenon of a high-speed aerostatic spindle. [PERSON] et al. [15] clarified the impact of structural deformation on a bearing using an FSI simulation model. [PERSON] et al. [16] established a theoretical model of fluid-structure interactions using a numerical simulation to resolve the mechanical properties of aerostatic guideways with porous restrictors. [PERSON] et al. [17] used the CFD-FSI technique to analyze a three-lobe journal bearing based on ANSYS Workbench software to estimate the structural deformations, fluid pressure forces and displacements. [PERSON] et al.