# Rotation Accuracy Analysis of Aerostatic Spindle Considering Shaft's Roundness and Cylindricity
## 1 Introduction  
In contrast with traditional spindles, an aerostatic spindle uses compressed gas to form a gas film, which has the characteristics of high precision, high speed, and low noise. The film thickness of an aerostatic spindle is usually about 10 micrometers, which meets the high requirements regarding manufacturing errors relating to the shaft [1]. Manufacturing errors can be classified as dimensional errors and shape errors, which include roundness, cylindricity, waviness, and roughness. Shape errors of the shaft will cause the uneven distribution of the gas film in the bearing. When the shaft rotates, the thickness of the gas film in the bearing will change continuously, which will cause pressure fluctuation, and then produce an unbalanced force on the shaft. The unbalanced force will affect the stability and rotation accuracy of the spindle. [PERSON] et al. [2] pointed out that the shape errors of journal bearings can generally reduce the load-carrying ability and increase the flow rate. [PERSON] et al. [3] calculated the half frequency whirl phenomena and the instability threshold speeds for the bearings with shape errors. They found that the precision of the shaft is much more important than that of the bearing. [PERSON] et al. [4] studied the effects of shape errors of a shaft-bearing system on dynamic characteristics, and results show that the rotating speed at which the fluid whip occurs increased when shape errors existed. In order to reduce the radial error motion, [PERSON] et al. [5] analyzed the influence of several manufacturing errors, bearing parameters and feeding geometries of an aerostatic journal bearing and suggested that the radial error motion is mainly influenced by the shape errors of the shaft. [PERSON] et al. [6] presented research on the manufacturing errors of aerostatic porous journal bearings, and found that the circumferential waviness errors caused the obvious inhomogeneity of the flow field and the transformation of the morphology of the high-pressure region. [PERSON] et al. [7] established a new approximate model to predict the radial error motion ofhydrostatic journal bearings, and pointed out that the main working harmonic components in roundness errors had a major influence over rotation accuracy. [PERSON] et al. [8] proposed a numerical model using linear perturbation theory for the research on the influence of journal rotation and bearing surface waviness on the dynamic performance of aerostatic journal bearings. [PERSON] et al. [9] examined the influence of the waviness errors of a hydrostatic journal bearing by considering the rotational and bearing installation angles, and revealed that the load-carrying capacity varied according to the amplitude and phase angle of the waviness functions. [PERSON] et al. [10] investigated the effects of different forms of surface waviness on the stability of the hydrodynamic journal bearing system by using non-linear dynamic analysis and calculation method, and the results show that the existence of the surface waviness causes the oil film of the system to wave and increases the energy loss of the system. In order to study the surface roughness effects in hydrodynamic bearings, [PERSON] et al. [11] developed an analytical solution method based on the Reynolds equation using perturbation techniques under the assumption of waviness coupled with linear superposition that can be used in wide exponential land slider bearings. [PERSON] [12] analyzed the effect of surface roughness on the dynamic stiffness and damping characteristics of hydrostatic thrust bearings; according to the results, the mean stiffness and damping behaviours are significantly affected by the roughness pattern and the height of the roughness. [PERSON] et al. [13] studied the effect of stochastic roughness on performance of a Rayleigh step bearing operating under thermo-elastohydrodynamic lubrication. The results show that the directional orientation of the surface roughness could affect the performance of a bearing significantly.