The rotation accuracy of the aerostatic spindle can easily be affected by shaft shape errors due to the small gas film clearance. Thus, the main shaft shape errors with the largest scale—that is, the roundness and cylindricity errors—are studied in this paper, and a dynamic mathematical model is established with the consideration of the roundness, cylindricity errors, and spindle speed. In order to construct the shaft model, the discrete coefficient index of the shaft radius based on roundness measurement data are proposed. Then, the simulation calculations are conducted based on the measured cylindricity data and the constructed shaft model. The calculation results are compared with the spindle rotation accuracy measured using the spindle error analyzer. The results show that the shaft with a low discrete coefficient is subjected to less unbalanced force and smaller rotation errors, as obtained by the experiment.

In the working process of the gas bearings, the unbalanced force of the rotor will increase nonlinearly with the increase in the rotating speed, resulting in an increase in the rotor’s vibration amplitude. On the other hand, with the increase in the rotating speed, the hydrodynamic effect will increase, and the nonlinear increase in the gas film force and stiffness will inhibit the increase in the vibration amplitude. In order to deeply study the influence of the unbalanced force and nonlinear gas film force on the vibration amplitude of the ultra-precision aerostatic motorized spindle, taking the double slit throttling gas bearing as an example, according to the equilibrium equation of the rotor under the combined action of gravity, the gas film force, and the unbalanced force, a calculation program based on the finite difference method for solving the rotor’s equilibrium position is completed. The calculation results show that: the hydrodynamic effect can significantly increase the bearing capacity and cause the change of the static equilibrium position of the rotor, but the offset amplitude of the static equilibrium position of the rotor gradually slows down with the increase in the rotating speed. The hydrodynamic effect improves the stiffness near the static equilibrium position of the rotor, making the rotor vibration track tend to be more “round”. Although the unbalanced force of the rotor increases nonlinearly as the rotating speed increases, the maximum offset between the dynamic equilibrium position and the static equilibrium position of the rotor under the action of the rotating unbalanced force is approximately linear with the rotating speed. Compared with the air supply pressure, the rotor unbalance and rotating speed are the main factors affecting the rotor dynamic equilibrium position offset. This study has a reference role in the in-depth study of the influence of rotating speed and rotor unbalance on the rotor static equilibrium position and dynamic equilibrium position offset, as well as in the design of gas bearings and the prediction of rotor vibration amplitude.

Micro-hole aerostatic bearings are important components in micro-low-gravity simulation of aerospace equipment, and the accuracy of micro-low-gravity simulation tests is affected by them. In order to eliminate the influence of air resistance on the attitude control accuracy of remote sensing satellites and achieve high fidelity of micro-low-gravity simulation tests, in this study, a design and parameter optimization method was proposed for micro-hole aerostatic bearings for a vacuum environment. Firstly, the theoretical analysis was conducted to investigate the impact of various bearing parameters and external conditions on the bearing load capacity and mass flow. Subsequently, a function model describing the variation in bearing load capacity and mass flow with bearing parameters was obtained utilizing a BP neural network. The parameters of aerostatic bearings in a vacuum environment were optimized using the non-dominated sorting genetic algorithm (NSGA-II) with the objectives of maximizing the load capacity and minimizing the mass flow. Subsequently, experimental tests were conducted on the optimized bearings in both atmospheric and vacuum conditions to evaluate their load capacity and mass flow. The results show that in a vacuum environment, the load capacity and mass flow of aerostatic bearings are increased compared to those in standard atmospheric conditions. Furthermore, it has been determined that the optimal solution for the bearing’s load capacity and mass flow occurs when the bearing has an orifice aperture of 0.1 mm, 36 holes, and an orifice distribution diameter of 38.83 mm. The corresponding load capacity and mass flow are 460.644 N and 11.816 L/min, respectively. The experimental and simulated errors are within 10%; thus, the accuracy of the simulation is verified.

In the research on the aerostatic spindle, for quantifying the influence of shaft shape errors on its rotation accuracy, the calculation models of unbalanced air film force (UAFF) and centrifugal inertia force (CIF) are established. Based on the typical shape of the shaft, three composite cylinder models are constructed. The data sources are selected from the cylindricity measurement results of the shaft and substituted into the model for calculation. The results show that, for the shaft in this paper, when the roundness deviation is ≤1.25 μm and the cylindricity deviation is ≤2 μm, the influence of shape errors on the rotation accuracy of the shaft is small enough. The harmonic analysis of the data source shows that the magnitude and stability of the UAFF on the shaft are determined by the actual shape of the shaft’s cylindrical surface, and cannot be inferred only by the value of shape errors.

In the working process of ultra-precision aerostatic motorized spindles, the journal and the rotor must have a certain eccentricity to have a certain bearing capacity and stiffness, which will induce the unbalanced magnetic pull (UMP). The intercoupling of the UMP and the gas film force will affect the motion state of the rotor and the accuracy of spindles. In order to deeply study the influence of the UMP caused by the rotor eccentricity on the equilibrium position of aerostatic spindles, a physical model of an aerostatic spindle based on slit throttling gas bearing is established and the coupling effect between the rotor and the motor rotor is studied and analyzed as a whole. The equilibrium position of the rotor under the combined action of gravity, the gas film force and the UMP is deduced, and a gas–magnetic field coupling calculation program based on the finite difference method is proposed. The calculation results show that with the increase in rotational speed, the equilibrium position of the rotor will move to the center of the journal in the micron scale, and the moving amplitude will gradually slow down. The UMP caused by rotor eccentricity can offset the rotor equilibrium position in nanometer scale, and the influence degree decreases sharply as the rotor moves to the journal center. With the increase in rotational speed, the direct stiffness and the cross stiffness will increase, and the amplitude of the cross stiffness is greater than the direct stiffness. This study is of great significance for further studying the influence of the rotor eccentricity on the equilibrium position and the accuracy of the rotor.

The solution of equilibrium positions is a critical component in the calculation of the dynamic characteristic coefficients of aerostatic bearings. The movement of the rotor in one direction leads to bidirectional variations in the air film force, resulting in low efficiency when using conventional calculation methods. It can even lead to iterative divergence if the initial value is improperly selected. This study concentrates on the orifice throttling aerostatic bearings and proposes a novel method called the bivariate interpolation method (BIM) to calculate the equilibrium position. The equilibrium equation for the rotor under the combined influence of air film forces, gravity, and external loads is established. A calculation program based on the finite difference method is developed to determine the equilibrium position. The process of solving the equilibrium position and the convergence is compared with the secant method and the search method. Furthermore, the variation trend of the equilibrium position and stiffness when the external loads changes are studied based on the BIM. Finally, the correctness of the BIM to solve the equilibrium position is proved by comparing it with the experiment results. The calculation results indicate that the BIM successfully resolves the problem of initial value selection and exhibits superior computational efficiency and accuracy. The equilibrium position initially moves away from the direction of the external load as the load increases, and then this gradually approaches the load direction. The main stiffness increases with increases in the external load, while the variation in cross stiffness depends on the direction of the external load.