Influence of shape errors and inertia effects on the error motion of the aerostatic spindle

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.