A newly treated boundary conditions to enhance accuracy of finite element analysis for orifice-type aerostatic bearings

Abstract

Although numerical approaches have been extensively employed for solving the Reynolds equation in order to predict the performance of air bearings, we found inappropriate boundary settings can cause significant numerical errors if the grid-dependent condition is ignored. The current scrutiny is focused on crucial procedures for adopting the finite element method to assess the performance of orifice-type aerostatic bearings. To this end, numerical models for a single orifice-type are established and then checked by varying mesh sizes, mesh types, and boundary conditions (BCs). The obtained results reveal that those numerical models with a single-source node are grid-dependent, and the relative error is so large that the results are not credible compared with the analytical solution and becomes worse with denser meshes. This peculiar phenomenon can be mathematically interpreted by a one-dimension finite difference model calculated manually and auxiliary sources have proved to be an effective technique to reduce single-source numerical error to an acceptable level. Additionally, a physical explanation is given based on engineering systems modeling. By this view, rules of setting high pressure on the edge of recess are proposed and three types of grid-independent BC settings are proposed. Stiffness test experiments based on manufacturing a rotary table adopting multi-orifice aerostatic thrust bearings are further carried out to validate these numerical models, and the discrepancy between measured and calculated stiffness is reported to be lower than 5%.