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 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 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.