Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes
Introduction
Because of their low friction and high accuracy of motion, aerostatic bearings have been applied successfully to various precision devices such as precision machine tools, precision measuring equipment and lithography associated production equipment. There are many types of restrictors used in aerostatic bearings, such as orifice-type, surface-compensated, compound, slot and porous. Among these, the orifice-type restrictor has been often used in actual devices because of its simplicity. There are two types of orifice-type restrictors: one is an orifice restrictor with a feed pocket and the other is an inherently compensated restrictor formed only by the feed hole. The mass flow rate of an orifice restrictor with a feed pocket is mainly affected by the diameter of the orifice, , whereas that of the inherently compensated restrictor is related to both the diameter of the orifice and the bearing clearance, πdsh. As Kazimierski and Trojnarski [1] show numerically and experimentally, an aerostatic bearing with orifices with a feed pocket could have static stiffness values 20–30% larger than those for bearings with inherently compensated restrictors. In addition, to obtain the bearing performance numerically, the discharge coefficients of the orifice have to be determined. However, the airflow around these orifice-type restrictors is very complicated and, therefore, the discharge coefficients are usually assumed based on experimental results. Accordingly, many researchers have studied the discharge coefficients of an orifice-type restrictor and the static and dynamic characteristics of aerostatic bearings with orifice-type restrictors associated with discharge coefficients.
Belforte et al. [2] investigated experimentally discharge coefficients of these orifice-type restrictors. They reported that, for an orifice restrictor with a deep pocket, the flow characteristics could be described by using two discharge coefficients for the orifice and the pocket edge. Renn and Hsiao [3] studied the mass flow rate of aerostatic bearings with pocketed orifice-type restrictors experimentally and numerically by using computational fluid dynamics (CFD). They found that CFD simulation results show good agreement with experimental data. Li and Ding [4] also studied the bearing performance by using CFD to solve numerically airflow within an orifice and the bearing clearance. They reported that the simulations could predict the experimental load capacity of orifice-type aerostatic bearings very well.
Recently, it has become easy to drill small feed holes of less than 0.1 mm diameter using laser beam machining and micro drills. If the diameter of an orifice becomes smaller than 1/4 of the bearing clearance, it is expected that higher stiffness can be obtained without forming a feed pocket, because the restricted area is not dependent on the bearing clearance. Accordingly, aerostatic bearings with orifice-type restrictors using these small feed holes have become commercially available. This type of aerostatic bearing usually has numerous small feed holes of less than 0.05 mm diameter without a feed pocket, which makes the restrictor easier to manufacture than the pocketed orifice-type restrictor. However, to our knowledge, there are few reports on aerostatic bearings with such small feed holes.
The objectives of this paper were to clarify the discharge coefficients of a small feed hole of less than 0.05 mm diameter without a feed pocket by using CFD and to investigate the static and dynamic characteristics of this type of aerostatic bearings by using the finite difference method (FDM), which adopts the discharge coefficients obtained by CFD. In addition, by comparing aerostatic bearings with typical compound restrictors, the usefulness of aerostatic bearings with small feed holes was confirmed.
Section snippets
Aerostatic thrust bearings with small feed holes
Recently, aerostatic bearings with small feed restrictors of less than 0.1 mm diameter became commercially available. These bearings are considered to have relatively higher stiffness and damping coefficient because they can be operated at small bearing clearances, of less than 10 μm and no feed hole has a pocket. Fig. 1(a) shows the geometrical configuration of the aerostatic thrust bearing with small feed holes. Generally, this bearing has numerous feed holes on the bearing surface to avoid a
Discharge coefficients of aerostatic thrust bearings with small feed holes
To numerically obtain the static and dynamic characteristics, discharge coefficients in a small feed hole must be determined. As Renn and Hsiao reported, CFD simulations can predict well experimental discharge coefficients. Therefore, CFD simulations were adopted to determine the discharge coefficients in this paper.
In Fig. 1(a), the simulation model of the bearing with a small feed hole for CFD is shown as a hatched area. This model is three dimensional as shown in Fig. 1(c) and a part of the
Static and dynamic characteristics of aerostatic bearings with small feed holes
The static and dynamic characteristics of the aerostatic annular thrust bearings with small feed holes were investigated using FDM. In calculations of the dynamic characteristics, the ordinary perturbation method was adopted as described elsewhere [10].
Fig. 6 shows the relationship between bearing clearances and load capacities for the bearings with small feed holes of 0.03 and 0.05 mm diameter. As seen in this figure, the load capacity increased with the number of feed holes. The maximum load
Comparison with aerostatic bearings with typical compound restrictors
Fig. 9 shows the dynamic characteristics of an aerostatic thrust bearing with typical compound restrictors (see Fig. 1(b)). It was assumed that the number of feed holes in the bearings with compound restrictors was n=8, the feed holes were 0.1 and 0.15 mm in diameter and the depth of the shallow groove was 15 μm. In the calculations, the FDM described elsewhere [8], [9] was used and the discharge coefficient CD was assumed to be 0.8. As seen in this figure, the aerostatic thrust bearings with
Conclusions
In this paper, the static and dynamic characteristics of aerostatic annular thrust bearings with small feed holes of less than 0.05 mm diameter were investigated numerically. CFD was used to determine the discharge coefficients of a small feed hole and the finite difference method was used to clarify the static and dynamic characteristics of aerostatic thrust bearings with small feed holes. As a result, the following conclusions might be drawn.
- 1.
In aerostatic bearings with small feed holes,
Notation
b damping coefficient CD1, CD2 discharge coefficients at two positions in a small feed hole ds diameter of a small feed hole gd depth of a circular groove gw width of a circular groove h0 average bearing clearance h bearing clearance ks static stiffness Ks dimensionless static stiffness= kd dynamic stiffness n number of feed holes p pressure pa ambient pressure ps0 supply pressure ps1 pressure in a small feed hole ps2 pressure at the boundary between the bearing clearance and a small feed hole P dimensionless
References (10)
- et al.
Discharge coefficients of orifice-type restrictor for aerostatic bearings
Tribology Int
(2007) - et al.
Experimental CFD study on the mass flow-rate characteristics of gas through orifice-type restrictor in aerostatic bearings
Tribology Int
(2004) - et al.
Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice-type restrictor on its performance
Tribology Int
(2007) - et al.
Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors
Tribology Int
(1996) - et al.
Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method
Tribology Int
(2002)
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