Relationship between roundness errors of shaft and radial error motions of hydrostatic journal bearings under quasi-static condition

A new approximate model is established in this paper to predict the radial error motions of hydrostatic journal bearings with different number of recesses under quasi-static condition. The formulas are based on the equivalent third power of film thickness. Definitions of averaging coefficients are made which directly illustrate the relationship among the radial error motions, the roundness errors of shaft and the structural parameters of bearing. It is found that the hydrostatic journal bearings with six recesses have advantage over the bearings with three, four and five recesses in the view of rotation accuracy when the shafts have same roundness errors. Experiments are done to give a proof to support the opinion that the trilobal roundness errors of shaft mainly affect the radial rotation accuracy for hydrostatic journal bearings with four recesses compared with the elliptical roundness errors of shaft, using a hydrostatic rotary table with an outer diameter of 320 mm. The novelty of this paper is that the theoretical approximate solution of averaging coefficients for hydrostatic journal bearings with different recesses are obtained and the main working harmonic components in roundness errors which have main influence on rotation accuracy are pointed out.