Analysis of error motions of axial locking-prevention hydrostatic spindle

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.

Relationship between elliptical form error and rotation accuracy of hydrostatic journal bearing

Purpose The form error of shaft and hole parts is inevitable because of the machining error caused by rotation error of tool axis in machine tools where the elliptical form error is the most common in shaft and bearing bush. The purpose of this paper is to present the relationship between the elliptical form error and rotation accuracy for hydrostatic journal bearing in precision spindle and rotation table. Design/methodology/approach An error averaging effect model of hydrostatic journal bearing is established by using Reynolds equation, pressure boundary conditions, flux continuity equation of the land and kinetic equation of shaft in hydrostatic journal bearing. The effects of shaft and bearing bush on rotation accuracy were analyzed quantitatively. Findings The results reveal that the effect of shaft elliptical form error on rotation accuracy was six times larger than bearing bush. Therefore, to improve the rotation accuracy of hydrostatic journal bearing in spindle or rotation table, the machining error of shaft should be controlled carefully. Originality/value An error averaging model is proposed to evaluate the effect of an elliptical form error on rotation accuracy of hydrostatic journal bearings, which solves the Reynolds equation, the flux continuity equation and the kinetic equation. The determination of form error parameters of shaft and bearing bush can be yielded from finding results of this study for precision design of hydrostatic journal bearings.

Precision design of hydrostatic thrust bearing in rotary table and spindle

According to the increasing needs of rotary table and spindle to satisfy high-precision machining requirements, the accuracy of rotary table and spindle becomes an important issue due to the error averaging effect of hydrostatic thrust bearing. The objective of this study is to research a methodology to guide the precision design of hydrostatic thrust bearing in rotary table and spindle. A run-out error model based on error averaging effect is established using the Reynolds equation, pressure boundary conditions, flux continuity equations of pad and dynamic equations of shaft. The axial run-out error and angular error are calculated considering perpendicularity error and flatness error of the components. The simulation results show that the two perpendicularity errors between axis line and thrust bearing bushing surface have same direction, and the axial run-out error could reach to the maximum values. Also, the flatness error of thrust bearing bushing surface has a big influence on axial run-out error. Following the outcomes, the precision design of hydrostatic thrust bearing was conducted. The axial run-out errors of rotary table and spindle with hydrostatic thrust bearing were experimentally studied, and the results have good coherence to the simulation data. The run-out error model is demonstrated to be an effective approach to guide the precision design of hydrostatic thrust bearing in other rotary tables and spindles.