Influence of geometric errors of guide rails and table on motion errors of hydrostatic guideways under quasi-static condition

Motion errors of hydrostatic guideways are mainly influenced by the geometric errors of guide rails and table which can be decomposed into harmonic waves of different frequencies based on Fourier transform. In this paper, a new approximate model is established to study the influence of geometric errors of guide rails and table on the motion errors of hydrostatic guideways using the equivalent third power of oil film thickness. It is found that, the motion errors are mainly affected by the geometric errors of guide rails rather than the geometric errors of table. The harmonic waves with wave numbers 0.5, 1.5, 2.5, 3.5, …, on the guide rails have no influence on the center displacement of table, and the harmonic waves with wave numbers 1, 2, 3, 4, …, have no influence on the yaw angle of table. The increment of land width and decrement of distance of two adjacent pads will result in enhancement of comprehensive averaging effect in consideration of center displacement and yaw angle. The approximate formulas have sufficient calculation accuracy compared with FEM when the ratio between amplitude of harmonic wave and initial film thickness is small. Using a deformed guide rail with wave numbers 0.5 and 1, the results of experiments agree well with the results calculated by approximate formulas and FEM. In the experiments, a novel method is proposed to manufacture the single harmonic wave of guide rail in the scale of micron meters, through which the amplitude and wavelength of the harmonic wave on guide rail can be controlled.