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.

Applying graphene (Gr) coatings to high-entropy alloys (HEA) is anticipated to enhance their tribological characteristics. The current understanding of the mechanism by which the Gr/HEA is enhanced at the atomic level is still limited. Molecular dynamics simulations revealed the mechanical behavior and strengthening mechanism of the Gr/AlCoCrFeNi HEA during nanoindentation and nanoscratch. The results demonstrate a substantial increase in the indentation hardness of the Gr/AlCoCrFeNi HEA by about 2.4 times. When Gr changed from a single layer to three layers, it further improved (3.2 times for a double layer and 3.9 times for three layers). At the same time, the friction coefficient is effectively reduced. Furthermore, the elevated in-plane stiffness of the Gr coating leads to an expansion of the effective loading area, resulting in increased Shockley dislocation and stair-rod dislocation density within the Gr/AlCoCrFeNi HEA, thereby amplifying the strain hardening effect and reducing subsurface damage. Qualitative experiments confirmed the excellent wear resistance of the Gr/HEA, and coating Gr increased the width of scratches, effectively confirming our simulation results. These findings provide valuable insights for the development and design of Gr/HEA composite coatings with enhanced mechanical properties.

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 this study, an extended Reynolds equation incorporating the shape errors and the inertia effects of compressible fluid was formulated. The pressure-solving equation for the gas film was constructed using a second-order finite difference method. By combining the measurement data from the cylindricity of multiple shafts obtained from a cylindricity measuring instrument, the variation of the aerostatic bearing load capacity with the rotation of the shaft was calculated, both with and without considering the inertia effect. An experimental rig was also constructed to measure the error motion data of the corresponding shaft. The results of numerical analysis and experimental validation demonstrated that shafts with larger cylindricity error values exhibit greater deviations in the calculated bearing load capacity, which correspondingly leads to larger radial error motion values measured in the experiment. When the roundness error value of the shaft is small or the shaft speed is low, the influence of inertial effects on the calculation results of the load capacity deviation is minimal and can generally be disregarded.

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.