# Rotation Accuracy Analysis of Aerostatic Spindle Considering Shaft's Roundness and Cylindricity
## 4 Results and Discussions
### Comparison with Experimental Results  
The aerostatic spindle used in this paper to validate the simulation results is mainly used for precision milling. For ensuring the stability of continuous running, the spindle is water-cooled. The four shafts are fitted into the spindle in turn, and the bearing, motor and other parts are installed. The motor is a Kollmorgen KBMS-10X01 frameless motor with the rated speed of 18,600 r/min. The driver belongs to Sieb and Meyer's SD2S series. After two stages of drying and filtering, the gas supply pressure is set to 0.4 Mpa (same as the numerical calculation). This system is mounted on a natural granite cubic base with a side length of 200 mm. For the consistency of the measurement results, other parts and related configurations remain unchanged throughout the test, except for the replacement of the shaft.  
Using sensors to measure the standard gauge installed on the spindle, the rotation errors are usually measured without load, and the track of the ideal axis of the rotation of the spindle is fitted as the basis of the analysis. Due to the small size of the spindle, there is not enough space to install the standard gauge and there is a section of finish-machined cylinder in the front of the shaft as an alternative.  
The dynamic radial rotation errors were measured using the Lion Precision CPL290 spindle errors analysis instrument. The bandwidth of the sensor is 15 kHz and the resolution is 0.01 \(\upmu\)m. The spindle speed range is set to 500 to 10,000 r/min, and the data are collected every 500 r/min. Figure 9 is the test rig of the spindle rotation error measurement, and the results of shaft 1 at 1000 r/min are shown in Figure 10. Following measurement, the data of the four shafts are plotted in Figure 11.  
Figure 8: Gas film force of shaft: (**a**) gas film force of shaft 1 (5 revolutions) at 6000 r/min; (**b**) gas film force of shafts in different speeds.  
As can be seen from Figure 11, in the rotation speed range of [500, 10,000] r/min, the rotation radial errors of shaft 1, shaft 3 and shaft 4 are always close to each other, except for individual speeds. When the speed exceeds 2000 r/min, the errors of shaft 2 are obviously larger than those of the other three shafts, and the \"particularity\" of shaft 2 in Figure 11 is consistent with that in Figures 7 and 8b. In the analysis results of Figures 7 and 8, the original data are obtained from the measurement of the roundness and cylindricity errors of the shaft. It can be seen that there must be a correlation between the measurement results of the roundness and cylindricity errors of the shaft and the rotation errors.  
The roundness errors of all shaft sections measured using the cylindricity meter are plotted, as shown in Figure 12. It can be seen that the roundness error lines of the four shafts overlap with each other and the difference is not obvious. For example, the roundness error values of section 11 of shaft 1 and section 15 of shaft 2 are both 2.69 \(\upmu\)m, and the roundness error values of section 19 of shaft 2 and section 10 of shaft 4 are both 2.25 \(\upmu\)m. Figure 13 is a composite drawing of roundness errors for section 19 of shaft 2 and section 10 of shaft 4. It can be seen that although the roundness errors values are the same (2.25 \(\upmu\)m), their actual  
Figure 11: Spindle radial rotation errors of four shafts.  
Figure 9: Test rig of spindle rotation error measurement.  
shapes are quite different. Therefore, the roundness error values cannot reflect the shape of the shaft.