Theoretical Verification on the Motion Error Analysis Method of Hydrostatic Bearing Tables Using a Transfer Function

A new method using a transfer function is introduced in the present paper for analyzing the motion errors of hydrostatic bearing tables. The relationship between film reaction force in a single-side hydrostatic pad and the form error of guide rail is derived at various spatial frequencies by finite element analysis, and it is expressed as a transfer function. This transfer function clarifies so called 'the averaging effect of an oil film' quantitively. It is found that the amplitude of film force is reduced as the spatial frequency increases or the relative width of the pocket is reduced. The motion errors of a multi pad type table are estimated using a transfer function, the form errors of a guide rail and the geometric relationship between the pads. The method is named as the Transfer Function Method (TFM). The motion errors calculated by the TFM show good agreement with the motion errors calculated by the Multi Pad Method considering the entire table as an analysis object. From the results, it is confirmed that the proposed TFM is very effective to analyze the motion errors of hydrostatic tables.