Hydrostatic spindles are widely used in precision optical grinder and lathe. Their high precision comes from the error averaging effect of oil film. The purpose of this paper is to give the quantitative analysis of the error averaging effect for a newly developed axial locking-prevention hydrostatic spindle. An approximate error motion model of the hydrostatic spindle is established to analyze the internal relationship between the geometric errors of the shaft and the error motions of the spindle including radial, tilt and axial error motions. The theoretical analysis shows that, the roundness errors of the two journals have a major impact on error motions while the coaxiality errors of two journals, the perpendicularity errors of front thrust plate and the coaxiality errors of the land of back thrust bearing, have no significant influences on error motions. The elliptical component of roundness errors of the two journals has significant influence on the axial error motion but no influence on the pure radial and tilt error motions, resulting into the fourth harmonic component of axial error motion. The trilobal component of roundness errors of the two journals has significant influence on the pure radial and tilt error motions but no influence on the axial error motion, resulting in the third harmonic component of pure radial and tilt error motions. The changes of recess pressures are not necessary condition for the error motions. Additionally, the experiment analysis shows that, the third harmonic component is the main part of the measured radial error motion and the third, fourth harmonic components are the main parts of the measured face error motion, which can be reasonably explained by the theory. The model proposed in this paper can be used to guide the precision design and optimization of hydrostatic spindle.
Comparison of spherical and aspherical intraocular lenses with decentration and tilt error using a physical model of human contrast vision and an image quality metric