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A theoretical and experimental study into the steady-state performance characteristics of industrial air lubricated thrust bearings D.A. Boffey*, M. Waddell** and J. K. Deardent

The effect of pocket length on the steady-state performance characteristics of a single orifice industrial aerostatic bearing has been studied experimentally. For a given air gap the pocket length is found to have an important influence on stiffness. A further theoretical and experimental study of the performance of the twin orifice version of the bearing has been made. Load capacity and film stiffness are found to improve at the expense of flowrate. There is considered to be satisfactory agreement between predicted and observed performance. Keywords: bearings + gas lubricants, pocket length, single orifice, twin orifice

This study completes a trio of investigations concerned with the steady-state performance characteristics of externally pressurized air lubricated thrust bearings in the x, y and z displacements of a Ferranti coordinate measuring machine (CMM).The first of the investigations I was concerned primarily with the effect of restrictor size on film stiffness in the y displacement and the second ~ , with the effect of pocket depth on film stiffness in the z displacement. The current paper deals with two topics:

and pockets as shown in Figs l(a) and (b). The single orifice bearing had a 250/am diameter orifice, feeding into a hole of diameter 4.5 mm and pocket 1 mm wide x 39/am deep. The overall length of the pocket was varied between 30 and 70 mm as indicated in Fig l(a). The twin orifice bearing had orifices each of 250/am diameter and the overall length of the pockets was fixed at 20 ram.

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(1) An experimental investigation of the effect of varying pocket length on the performance of a single orifice bearing (2) A theoretical and experimental investigation of the performance of a standard twin orifice bearing The single orifice bearing was originally employed as the standard in the x displacement of the CMM later to be superceded by the twin orifice design. The purpose of part 1 of the investigation was to see if the film stiffness of the single orifice bearing with extended pocket could match that of the present standard twin orifice bearing at the design air gap of 10/am and pressure of 4.5 bar (gauge). In the CMM the bearings operate in pairs, so that angular film stiffness is not important. Part 2 of the investigation was to see how closely the experimental performance of the standard twin orifice bearing could be predicted theoretically; close agreement would encourage future theoretical studies prior to manufacture and test. Ref 3 is recommended as a reference on fluid film bearings.

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Apparatu s Bearing geometry The two bearings tested were each 90'x 30 mm, one with a single orifice and pocket and the other with a twin orifice *Department of Mechanical Engineering, University of Edinburgh, Edinburgh EH8 9YL, UK **kbrrnerly of University of Edinburgh; now at Property Services Agency, Civil Service, Edinburgh, UK tFerranti Ltd., Dalkeith, Midlothian, UK

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Fig l (a) Single and," ( b ) twin orifice bearing geometries. All dimensions in m m

0301-679X/85/040229-05 $03.00 © 1985 Butterworth & Co (Publishers) Ltd

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Boffey, Waddell and Dearden - air lubricated thrust bearings

Test rig The test rig is very similar to that reported in Ref 2. A schematic of the arrangement is shown in Fig 2. The only differences are the probe mounts, which cater for the different test bearing dimensions, and a micrometer system which prevents rotation of the bearing spindle and probe plates. Variations in air gap were detected due to the probe plate (fixed to the test bearing) not being quite parallel to the base plate of the rig.

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Instrumentation The pressurized air supply to the test bearing and load spindle is controlled by precision regulators fitted with pressure gauges. The air-flow to the bearing is measured using a 'Gapmeter' flow measuring system. A Wayne Kerr TE 200 capacitance type measuring system is used to give a direct reading of air gap from probes mounted at two diagonally opposite corners of the test bearing. In this industrial application the bearings have a supply pressure of 4.48 bar (65 psig) and an air gap of 10/am (0.004 in).

Test procedure

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Fig 2 Schematic of test rig where p is the film pressure and x and y are perpendicular coordinates in the plane of the film. The volumetric flow (G) into the bearing through an orifice restrictor is governed by either the unchoked or choked equations respectively:

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Single orifice bearing The purpose of the tests was to obtain cures of load versus air gap and volumetric air flow versus air gap. Initially, they were carried out for the bearing with no pocket at supply pressures of 3, 4 and 5 bar gauge. The same bearing then had an overall pocket length of 30 mm inserted and was tested at the same three pressures. The procedure was repeated for overall pocket lengths of 50 and 70 ram. Load was increased by adding masses to the load pan. At each load the test bearing was first vented to atmosphere and the Wayne Kerr measuring system set to zero to ensure no warping of the test rig. At each load the air gap was taken to be the average of the two probe readings.

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The test procedure was identical to that for the single orifice bearing except that the bearing pocket remained fixed at 20 ram.

The volumetric flow/unit length from the pocket into the bearing film is governed by the Poiseuille equation:

The volumetric flow readings were taken at each of the above points and corrected to allow for the absolute supply pressure.

Supply pressure Pressure in pocket Ratio of specific heat capacities Universal gas constant Absolute temperature Orifice radius Orifice discharge coefficient (Pi/Ps)cr Critical pressure ratio

1 dp G/unit length = - h3 12/2 dx

Theory Stiffness curves

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To obtain a curve of film stiffness versus air gap it is necessary to differentiate the load versus air gap curve. This was achieved using the Edinburgh Regional Computing Centre program 'Curvefit'.4 The procedure adopted was identical to that outlined in Ref 2 and a polynomial of degree five was employed throughout.

The field equation and the flow equations are sufficient to predict the steady-state performance of an aerostatic bearing in the manner described below.

Basic equations

Solution

For a compressible isothermal film of constant thickness, Reynolds equation for an aerostatic bearing s reduces to:

The field equation was solved by the relaxation method. 6 Due to the symmetry of the twin orifice bearing it was only necessary to analyse one quarter of the bearing surface. The resulting 45 x 15 mm portion of the bearing was divided into a 30 x 10 mesh and, with the exception of the pocket, all grid points were initially set to zero pressure

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August 85 Vol 18 No 4

Boffey, Waddell and Dearden - air lubricated thrust bearings

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The derived family of stiffness versus air gap curves is presented in Fig 4, which shows that maximum stiffness increases with increase in pocket length. At the same time there is a distinct reduction in optimum air gap. The somewhat irregular behaviour in load capacity at the design air gap of 10 pm is not reflected in the stiffness results. For an overall pocket length of 50 mm the stiffness peaks at 33 MN/m, with an optimum air gap very close to the design value. At the same air gap the stiffness of the bearing with an overall pocket length of 70 mm is 35 MN/m.

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The corresponding curves of volumetric flowrate versus air gap are shown in Fig 5. At the design air gap of 10/Ira the bearing is operating in the unchoked region for all pocket 50 d

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Fig 3 Added mass versus air gap for various lengths; single orifice bearing; Ps = 4 bar (gauge) The relaxation procedure on the Apple microcomputer was performed for 500 iterations, at which point the pressure profile had effectively converged. When this situation was reached the pressure was integrated over the bearing surface to yield load capacity. The pressure profile also yielded the pressure gradients along the pocket/film interface (dp/dx). The fixing of the supply pressure determined which orifice equation to use and the corresponding air gap (h) was determined by equating flows from the supply into the bearing and from the pocket into the film. Stiffness curves were obtained in the manner previously referred to. In the derivation of the theoretical curves a discharge coefficient (Cd) of 0.625 was used. This was based on information provided in Ref 7. (It has subsequently been pointed out to the authors that for a compressible fluid Cd may be in the range 0.7-0.8).

Results and discussion Effect of varying pocket length in the single orifice bearing Fig 3 shows plots of load versus air gap without a pocket and for overall pocket lengths of 30, 50 and 70 mm at a supply pressure of 4 bar gauge. It shows that there is an increase in maximum load capacity as overall pocket length is increased, although at the design air gap of 10/~m, the load capacity with an overall pocket length of 50 mm is of the order of 50 per cent higher than that with an overall length of 70 mm.

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Conclusions Increasing pocket length in the single orifice bearing increases maximum load capacity, although there is some irregularity in load capacity at the design air gap. Maximum film stiffness also increases with increase in pocket length but the optimum air gap falls at the same time.

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Load capacity and film stiffness of the twin orifice bearing are some 25 per cent higher than those of the single orifice bearing at the design air gap and supply pressure. However, this superior performance is at the expense of a doubling in air flow rate.

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There is satisfactory agreement between the predicted and observed performance characteristics of the twin orifice bearing which would justify the use of theoretical studies in the future.

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Fig 6 A d d e d mass versus air gap," comparison o f theory and experiment," twin orifice bearing," Ps = 4 bar (gauge)

For supply pressures of 3 and 5 bar (gauge) the performance characteristics are qualitatively similar to those already described;maximum load capacity, film stiffness and flow rate all increase with increase in supply pressure.

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lengths and the effect of pocket length is to increase flowrate.

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At no time was the bearing found to exhibit pneumatic hammer instability.

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Comparison of theory and experiment in the twin orifice bearing In Fig 6 a comparison is made between theory and experiment of load versus air gap with the supply pressure set at 4 bar (gauge). A similar comparison of film stiffness versus air gap is made in Fig 7. Both results are considered to be satisfactory and to justify the use of theoretical studies prior to manufacture. The maximum experimental film stiffness of 41 MN/m is seen to occur very close to the design air gap of 10/am.

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Fig 7 Stiffness versus air gap," comparison o f theory and experiment; twin orifice bearing; Ps = 4 bar (gauge) 6000

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A comparison of the experimental load capacities in Figs 3 and 6 at the design air gap of 10 #m shows that the twin orifice bearing has a capacity 25 per cent greater than the single orifice bearing with an overall pocket length of 50 ram. This is accompanied by a similar increase in film stiffness at the same air gap as evidenced by a comparison of Figs 4 and 7. However, the superior load capacity and film stiffness of the twin orifice bearing is at the expense of a two-fold increase in volumetric flow at the design air gap (compare Figs 5 and 8).

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In Fig 8 a comparison of airflows to the bearing is made with the supply pressure set at 4 bar (gauge). The agreement here is within 15 per cent which is improved if a higher value of discharge coefficient is assigned. Comparison of single and twin orifice bearings

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Boffey, Waddell and Dearden - air lubricated thrust bearings

References

4. Mooljee N.K. Curvefit on EMAS 2900, User Note 11. Edinburgh Regional Computing Centre, January 1983

1. Boffey D.A., Duncan A.E. and Deaxden J.K. An experimental investigation of the effect of orifice restrictor size on the stiffness of an industrial air lubricated thrust bearing. Tribology International, 1981,14(5), 287.

5. Design of gas bearings vol. 1, Mechanical Technology Inc., Latham, New York, 1969

2. Boffey D.A., Barrow A.A. and Deaxden J.K. An experimental investigation into the performance of an aerostatic thrust bearing. Tribology International, 1985, 18(2)

6. Trumpler P.R. Design of film bearing. Collier Macmillan Ltd, London, 1966

3. Gross W.A. et al. Fluid film lubrication. Wiley-Interscience, 1980, New York & Chichester

7. Massey B.S. Mechanics of fluids. 4th Edn, Van Nostrand Reinhold, 1979

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