This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada
Modeling and design of Ultra-Precision aerostatic bearings are challenging due to the many factors that influence their performance. One key factor is accurately modeling air bearing gaps and change in load capacity due to tilted pad or wedge-type air gaps. Ametek-Precitech has been using an efficient simulation strategy, making use of a thermal FEA model as an analogy to air bearing film flow. This approach allows to solve the Reynolds equation of classical lubrication for simple uniform gap conditions. However, this approach becomes limited when trying to assess tilted pads and damping. On the other hand, 3D CFD simulation 1) shows increased accuracy in film flow predictions, 2) accounts for entrance effects at orifice restrictors, and 3) can model the upstream flow through the orifices. This paper focuses on the migration from the 2D FEA thermal analogy model to a 3D CFD model of the air film to leverage the higher physical representation and potentially study the dynamic behavior of an opposed flat pads linear air bearing. Precitech air bearing pads use a combination of orifice restrictors and recess grooves for optimal performance, achieving both high load capacity and stiffness. The migration is achieved through a series of validation cases, starting with a one-inch square air gap for which an analytical solution is derived, and then with a ¼ symmetry model of the flat pad bearing which is compared with the 2D FEA thermal analogy result. These tests allowed us to establish a proper methodology to obtain high fidelity pressure distributions and mass flow rates for a barotropic fluid in laminar regime. It was observed that the pressure distribution was very well resolved with a minimal number of cells across the 0.0003-in gap. However, for accurate estimates of the mass flow rates, a minimum of 16 cells were required across the gap. The in-plane mesh density was not shown to be critical for accurate predictions. Moreover, this methodology allowed the modeling of cases reachable only with 3D CFD models. In this paper, we elaborate on the case of a tilted pad configuration, with a focus on asymmetrical flow rate distribution at the exit edges. Iterating from known models of inlet restrictor flows and pressure ratios, a solution was obtained for pressure centroid shift associated with a load at one end of the bearing. This is an indication of the air bearing tilt stiffness. Preliminary tests were also performed on the dynamic behavior with the 3D CFD model. The starting point was a test case for transient simulation of an instantaneous clearance change using a morphing mesh. The results showed potential use of this model for dynamic response prediction, allowing for design with increased damping. The migration from a 2D FEA model to a 3D CFD model has been successfully validated, allowing for further 3D and transient modeling and a wider qualification of bearing performance.
|Date||18th June 2019|