i. R. G. LOWE
Mechanical Engineering Division, National Research Council o f C a n a d a , O t t a w a , C a n a d a
Some Experimental Results From Compliant Air Lubricated Thrust Bearings
Experimental results are presented from a series of tests on axisymmetric, inherently compensated, air thrust bearings which had one compliant surface. The results demon- strate that in general compliant surface bearings have greater load capacities than equivalent rigid surface bearings. The dependence of load, flow, and stability on the nature of the compliant layer is also shown. Comparisons with the load capacities pre- dicted theoretically by Pirvics and Castelli show agreement in the rcmge of most practical interest, that is when the load advantage vis-a-vis rigid bearings is greatest.
Introduction
WE IEVERAL workers [ 1 - 5 ] ' have demonstrated, both theoretically and experimentally, t h e behavior with incompress- ible lubricants of thrust bearings one surface of which is a rela- tively compliant elastomer. Pirvics and Castelli [1] have ana- lyzed the problem of a gas-lubricated compliant surface bearing.
Reported herein are the results of an experimental study of this latter problem. An inherently compensated thrust bearing with a single central inlet and one compliant surface was tested over a range of air supply pressures, compliant layer thicknesses, and hardnesses.
Description of Experiment
The thrust bearing tested in this work was circular with a single central inlet operating as an inherent restriction, i.e., the annular orifice a t the entrance t o the clearance space was the control re- striction. The bearing geometry was chosen to correspond to
1 Numbers in brackets designate References at end of paper.
Contributed by the Lubrication Division of T H E AMERICAN SO-
CIETY OP MECHANICAL ENGINEERS and presented at the ASLE-
ASME Joint Lubrication Conference, Atlanta, Ga.t October 16-18, 1973. Manuscript received bv the Lubrication Division, March 2, 1973. Paper No. 73-Lub-41.
t h a t of Pirvics and Castelli. An outer diameter of 102 mm (4.0 in.) and an inlet diameter equal t o 6.35 mm (0.250 in.) gave a corresponding radius ratio of 0.0625. T h e bearing assembly, all parts of which were fabricated from mild steel, is shown in Fig. 1.
The vertical alignment of the thrust pads was achieved by an en- circling journal air bearing. The load was applied b y means of weights suspended from a loading platform as shown in Fig. 2.
Three capacitance probes were set into t h e upper, or moving, thrust pad t o insure t h a t the upper and lower pads were parallel.
Final adjustment could be effected readily by means of small balance weights. Air was fed into the bearing through the lower thrust p a d from a filtered laboratory air supply. A Moore Nullmatic pressure regulator was used and the flow was measured by a calibrated meter of t h e Rotameter type. Large diameter hose was used t o avoid any upstream restrictions which might have caused instability in the bearing. The bearing air supply pressure was measured from a tapping very close to the inlet.
As shown in Fig. 1 t h e capacitance probes indicated the dis- tance from three small pads outside of the actual bearing area.
(The height of these pads in relation t o the plane of the bearing was accurately known.) Consequently, the gap measured by the capacitance probes was an apparent value, i.e., the clearance be- tween the lower t h r u s t pad and the plane of the undeflected sur- face of the rubber.
•Nomenclature-
c = mean apparent clearance between undeflected elastomer and rigid surface
c' = cG/tpa = dimensionless clearance G = shear modulus of elasticity for rub-
ber
L = W/TrRfya = dimensionless load capacity
p = pressure (absolute) pa = atmospheric pressure pr = recess pressure (absolute) p, = supply pressure (absolute)
P = p/pa = dimensionless pressure PR = Pr/Pa = dimensionless recess pres-
sure
Ps = Ps/Pa = dimensionless supply pres- sure
r = radius A',- = inlet radius /?o = outside radius
{ = rubber thickness
T = t/Ro = dimensionless thickness
v = Poisson's ratio
rubber
Journal of Lubrication Technology Copyright © 1974 by ASME OCTOBER 1974 / 547
CAPACITANCE I PROBES 13
F i g . 1 Schematic r e p r e s e n t a t i o n of the e x p e r i m e n t a l c o m p l i a n t surface thrust b e a r i n g (R0 = 5 0 . 8 m m ( 2 . 0 i n . ) , R, = 3.18 m m ( 0 . 1 2 5 in.)
O
CAPACITANCE PROBE OUTPUTAIR FLOW METERING
£.
"I rjMANOMETERS or PRESSURE T'DUCER FOR PRESSURE DISTRIBUTION
LOADING PLATFORM
F i g . 2 Schematic d i a g r a m of the e x p e r i m e n t a l a r r a n g e m e n t
the desired nominal rubber thickness. Chalk dust was used on the rubber during grinding with good results.
T h e thickness of the rubber sample was then measured using gauge blocks and an indicator gauge as mentioned previously.
(A gauge block was also used on top of the rubber surface to spread the load of the indicator gauge spring.) Sample thickness mea- surement accuracy, including repeatability of any one measure- ment, was estimated as ±0.0025 mm (0.0001 in.).
Poisson's ratio and the shear modulus of elasticity for the rub- ber were estimated from the measurements of Rightmire [4].
Fig. 3 shows the results of Rightmire (neglecting Neoprene and Urethane) and the curves drawn by this author to estimate v and G from Shore A hardness measurements. For example, v for the 50 Durometer sample was 0.4998 and the shear modulus, G, was estimated as 1030 k N / m2 (150 psi).
Test Procedure
The testing procedure used, identical for each rubber hardness, was as follows. A given rubber sample was bonded to the mild steel thrust pad and then ground to the maximum desired thick- ness. T h e thicknesses were chosen to closely correspond to the thickness ratios (thickness/bearing radius) treated by Pirvics and Castelli [1]. In the t h r u s t bearing test rig (Fig. 2) load- clearance curves were established for several supply pressures.
At the same time the pressure distributions near the inlet were recorded. Stability maps were also constructed by increasing the supply pressure at a given load until pneumatic hammer could be detected audibly (or until the maximum lab supply pressure of 655 k N / m2 (95 psig) was reached without evidence of instability).
I t was found necessary to counterbalance some of the tare loading to complete some of the stability curves.
Because of the deflection of the elastomer, negative apparent clearances for the bearing were possible under high loading con- ditions and the capacitance probes had to have an initial "set- back" from the plane of the undeflected rubber surface. The initial setting of the capacitance probes could not be accomplished merely by resting the upper bearing pad on the lower as the r u b - ber deformation was significant in some of the more compliant cases. I t was necessary to measure the height of the rubber pad using gauge blocks and an indicator gauge (1 division = 0.00005 in.) and then set the capacitance probes for an adequate set-back.
As explained later, pressure taps close to the inlet hole were needed to establish the pressure immediately after the entrance to the clearance space in these inherently compensated bearings.
Six pressure t a p holes of diameter equal to 0.051 m m (0.002 in.) were drilled into the surface of the lower thrust plate. T h e taps had an angular separation of 60 deg, and their mean dis- tances from the edge of the inlet hole were as follows 0.089, 0.191, 0.305, 0.432, 0.610, 0.991 mm (0.0035, 0.0075, 0.012, 0.017, 0.024, 0.039 in.). Pressures at these taps were measured either by mercury manometers or by resistance strain gauge pressure transducers.
Natural rubber was the elastomer chosen for these tests.2 One sample had a Shore A hardness of 50 while the other measured 30.
A standard Durometer was used for the hardness measurements and the specimens were found to be of very uniform hardness, varying by not more than ± 1 over their area. (The rubber diameter was 117 m m (4.60 in.) so t h a t it extended well beyond the outside diameter of the bearing.)
Bonding of the rubber to the cleaned and ground mild steel surface was found to be quick and effective using a quick-set ad- hesive (Type 404 from Locktite Corporation). When immersed in hot water the rubber sample could be removed from the mild steel plate with only slight difficulty. Inspection of the sepa- rated surfaces revealed t h a t the bond had uniformly covered the entire area of the rubber surface.
After bonding, a surface-grinding operation was used to attain
Results and Discussion
T h e experimental load-clearance and flow-clearance curves are presented in Figs. 4 to 9. In several cases load and flow curves for a geometrically similar rigid surface bearing are shown for comparison. These rigid-bearing curves were determined before the rubber sample was bonded to the steel thrust pad and were confirmed by calculations using the method of reference [7].
Complete load-clearance curves for all thicknesses could not be determined for the softer rubber because of the onset of pneu- matic hammer instability.
I t is to be noted that the rubber thicknesses quoted in these figures are nominal with deviations of ±0.0025 mm (0.0001 in.) as mentioned earlier. Because the determination of the mean apparent clearance depended upon the rubber thickness measure- ments the same deviation applies to the clearance measurements.
Fig. 8 is an example of flow-clearance curves for the two rubber hardnesses at a nominal thickness of 3.2 mm (0.127 in.) while Fig.
9 illustrates the effect of sample thickness at a constant supply pressure.
Several general observations can be made from Figs. 4 to 9:
A -500 o
Z '499 O
-I—.,
T\
50 100 HARDNESS
SHEAR MODULUS G x l o ' 12 P*' J kN/m3
'- See Acknowledgments.
Fig. 3 Results of R i g h t m i r e [4] plotted to a l l o w the d e t e r m i n a t i o n of Poisson's r a t i o a n d the shear m o d u l u s o f e l a s t i c i t y f r o m Shore A hardness measurements
In every case tested the maximum load capacity of the com- pliant bearing was greater than t h a t of the rigid bearing at the same supply pressure ratio. This is in accord with the results of references [2 to 6] and with the predictions of reference [1].
For the harder 50 durometer rubber, load capacities increased with rubber thickness u p to 6.35 mm (0.250 in.), Fig. 4. A further increase in thickness to 8.67 mm (0,3415 in.) did not appear to have a significant effect. An inverse load-thiekness re- lationship seemed to app'y to the softer 30 Durometer rubber at least at lower apparent clearances, Fig. 6.
The compliant, bearings in general had stiffnesses equivalent to that of the rigid bearing and the stiffness increased with supply pressure. The harder rubber bearing stiffnesses were somewhat
greater than those for the softer rubber. What is more im- portant is that the compliant bearing stiffness was nearly constant in the region of small apparent clearances and did not exhibit the rapid loss of stiffness which is characteristic of rigid bearings as they approach their maximum load capacity.
These curves also illustrate the negative clearance which is possible with compliant surface bearings. T h e more compliant rubber, Fig. 6, exhibited higher negative values of clearance t h a n the harder sample, Fig. 4. Maximum negative clearance values also increase with sample thickness, e.g., Fig. 6.
By comparison to rigid bearings the compliant bearing flow rates are higher at any given apparent clearance and supply pres- sure ratio, Fig. 9. The flow-clearance curves in general indicated
LOAD N lSQOr-
Ibs 3 0 0
Shore A h a r d n e s s = 5 0 t h i c k n e s s i n / m m
-3415/8-674 -2503/6-358 1268/3-521
s } Ps- 4
- • 0 4 —02 6 ^ H ^04 ^06 ^08 0 0 m m MEAN APPARENT CLEARANCE
Fig. 4 Experimental load-clearance curves. Compliant surface of natural rubber with a Shore A hardness of 50.
LOAD N 1 5 0 0r
lbs 3 0 0
lqpo
Shore A hardness =30 thickness i n / m m . 2 5 4 8 / 6 - 4 7 2 .1895/4-813 . 1 2 6 9 / 3 - 2 2 3
- 0 2 0 -02 -04 -06 MEAN APPARENT CLEARANCE
Fig. 6 Experimental load-clearance curves. Compliant surface of natural rubber with a Shore A hardness of 30.
N 1500
1000
500
~
lbs 3 0 0
_
2 0 0
100
- 0
Ps- 6(
Shore A hardness = 50 COMPLIANT SOLID
- 0 4 - 0 2 0 -02 04 -06 -08 10 m m MEAN APPARENT CLEARANCE
Fig. 5 Comparison of rigid and compliant surface bearings. Compliant layer of natural rubber, thickness = 3.221 mm (0.1268 in.), T = 0.0634.
(Note: The experimental curve for Ps = 6 was limited by the loading capacity of the apparatus.)
N 1500
lbs 3 0 0
ire A h a r d n e s s =30 - C O M P L I A N T
SOLID
M E A N APPARENT CLEARANCE
Fig. 7 Comparison of rigid and compliant surface bearings. Rubber hardness = 30 and thickness = 3.223 mm (0.1269 in.); T = 0.0634.
Journal of Lubrication Technology OCTOBER 1974 / 54S
FLOW
*10°
3r 3 0 D u r o m e t e r ; t=I269in i3-223mm
" I1" S O D u r o m e f e r ; t=1268in ; 3-321mm 9 "4
/ / * / / / /,*
/ / / /
// / /
>'/ - / /
•002 • 0 0 4 in
0 -OS -10mm M E A N APPARENT CLEARANCE
F i g . 8 Examples of f l o w - c l e a r a n c e curves f o r c o m p l i a n t surface thrust bearings
30 Durometer 50 Durometer
P.-3
thicker rubber layers). As well, the harder rubber bearings were somewhat stiffer and less prone to instability.
Instability Problems
Some difficulty was encountered with pneumatic hammer in- stability even though the bearing was inherently compensated.
Fig. 10 shows several stability maps determined for those oases where instability was present. The region to the right of any one of the curves is the region of instability; t h a t to the left, the stable operating region. I t can be seen that stability increases with the hardness of the rubber, and increases as the rubber thickness decreases. This would indicate t h a t the pocket or puddle formed in the rubber by the high pressure and which causes the increased load capacity also can act to induce insta- bility in the same manner as does a recess under an orifice.
Harder and thinner rubbers, being more difficult to deform, i.e., less compliant, are more stable.
Before carrying out this experimental work with inherently compensated bearings an orifice had been inserted in the inlet in such a way t h a t a 6.35 mm (0.250 in.) diameter recess with a 1.27 mm (0.050 in.) height was provided below the orifice. The compliant layer in this case was 50 Durometer Neoprene with a nominal thickness of 2.5 mm (0.1 in.). T h e use of an orifice provided a means whereby the recess pressure could be accu- rately calculated for comparison with the theory of reference [1].
I t was found however even with this thin, relatively hard elas- tomer t h a t the region of instability was very large. Reducing the recess height to 0.203 mm (0.008 in.) did very little to enlarge the stable region of operation. In order to be able to cover a range of elastomer thicknesses and hardnesses a change to in- herent compensation was made.
Comparison of Experiment and Theory
To compare the experimental results with the theory of Pirvics and Castelli [1] pressure profiles were measured near the inlet as described earlier. Thus the clearance space static pressure im- mediately downstream of the inherent restrictor could be found.
This pressure is equivalent to the theoretical recess pressure of reference [1] where it was assumed that the entrance pressure loss
was negligible.
For comparison with the predictions of reference [1] at a given normalized clearance (c' = 0.2, for example) it is necessary to de- termine c, the mean apparent clearance, for the particular rubber thickness t and shear modulus G under consideration. Thus for c' = 0.2, with G = 1030 k N / m2 (150 psi) for the 50 Durometer rubber from Fig. 3, and with the rubber thickness equal t o 3.221
- 0 5 0 -05 -lOrnm MEAN APPARENT CLEARANCE
F i g . 9 C o m p a r i s o n of flow~clearance curves f o r c o m p l i a n t layers of various thicknesses a n d hardnesses
a higher flow requirement for the softer rubber with the difference increasing with supply pressure and rubber thickness, Figs. 8 and 9. Softer and thicker rubber layers mean larger deformation under t h e loading, consequently actual clearances are larger.
However, the compliant bearing does not suffer a flow disad- vantage compared to the rigid bearing as long as the loading is kept sufficiently high. The compliant bearings can be run at low values of mean apparent clearances because of the deformation of the rubber surface.
From the range of tests reported here it appears t h a t there are advantages in selecting the harder rubber over the softer. At low values of mean apparent clearance, where the load advantage over the rigid bearing is distinct, the load capacity of the 50 Durometer bearing was comparable to t h a t of the 30 Durometer bearing for rubber thicknesses of at least 6.35 mm (0.250 in.), see for example Figs. 4 and 6 (conversely, there was no advantage in
SUPPLY PRESSURE
70 80 90psi 500 kN/m2
Fig. 10 Stability m a p s f o r v a r i o u s thicknesses a n d hardnesses of the n a t u r a l rubber c o m p l i a n t layer
3 clearance xio
® n mm
o0-14 3-55
I
1-8
0 4 in
0 0-5 1 m m RADIAL DISTANCE
F i g . 11 Pressure d i s t r i b u t i o n s near t h e b e a r i n g i n l e t . S u p p l y pressure r a t i o = 5 . 0 ; n a t u r a l r u b b e r , SO D u r o m e t e r ; thickness = 3 . 2 2 1 m m ( 0 . 1 2 6 8 in.)
0 0 2 •003 i n
•025 -050 CLEARANCE
•075 mm
F i g . 12 D e t e r m i n a t i o n of t h e inlet pressure r a t i o , PR, f o r t h e t h e o r e t i c a l c l e a r a n c e v a i u e s
mm (0.1268 in.), the mean apparent clearance for comparison to the theory was found to be
c'tVa 0.2 X 3.221 X 101
G 1030 = 0.0630 mm (0.00248 in.) Experimental pressure profiles for this particular rubber sample are shown in Fig. 11 for a supply pressure ratio of 5. Note in this figure that the pressure ratio at the edge of the inlet i.e., with the radial distance equal to zero, was estimated simply by an extrapolation of the pressvire readings from the outer tappings where there were no pressure depressions. There was no attempt to make allowance for the differences in load capacity represented by the extrapolated (dashed) line and the actual pressure dis- tribution.
It is interesting to note in passing the form of the pressure dis- tribution curves. Pressure profiles near the inlet of rigid in- herently compensated thrust bearings have been studied by many workers (see reference [8] for a recent list.) The entrance re- gion static pressure distribution is complicated by pressure depres- sions due to supersonic flow and shock waves in some cases and due to subsonic flows with large kinetic heads in others. These pressure depressions tend to become deeper as clearance and, hence, flow increase. Although the use of only five (effective) pressure tappings did not allow adequate resolution of the pres- sure profiles, it is evident that the initial pressure drop and pressure depression associated with rigid bearings is present, perhaps to a lesser degree, in the compliant bearing.
In addition, the pressure recovery after a pressure depression is different to that noted in rigid bearings presumably due to the compliant nature of the surface. There must be a very local de-
NATURAL RUBBER 50 DUROMETER
t = -1268in;3-221mm; T - 0 6 3 4 G= 150 p s i ; 1030 k N / m2
C*" CG/tp 9 . 0 5 a
CM
• •2
PR = " / " a
F i g . 13 C o m p a r i s o n of e x p e r i m e n t a l results w i t h a n a l y s i s of Pirvics a n d Castelli [1] ( t h e o r y f o r T = 0 . 0 6 2 5 , v = 0 . 5 ) .
pression in the compliant layer immediately beneath the inlet due to the high supply pressure there. As well, the depression of the static pressure as the gas is accelerated into the clearance space -must cause a "ripple" in the surface of the rubber. The local rubber shape would also be much different in the finite elastomer case [5] where the air is let in through the compliant layer and where the air pressure must radius the inlet edge.
The inlet pressure ratios from Fig. 11 are replotted against clearance in Fig. 12. From this figure the inlet pressure ratio corresponding to the desired mean apparent clearance was de- termined. In the foregoing example c = 0.0630 mm (0.00248 in.) and PR — 3.38. Once this equivalent recess pressure was de- termined the load was obtained from the load-clearance diagrams, Fig. 5, and thus a point could be plotted in comparison to the curves of Pirvics and. Castelli. Fig. 13 shows the comparison made with theory for the rubber sample outlined previously at the five supply pressures tested and for three values of normalized clearance. The theoretical curves were drawn from Fig. 4 of reference [1] which was a load-clearance diagram for an elastomer thickness ratio T of 0.0625 and for an elastomer Poisson's ratio of 0.5, conditions only slightly different from those of this experi- ment. At the lowest value of normalized clearance, c' = 0.05, there is quite reasonable agreement considering the assumption made, for example in the determination of the rubber shear modulus. Theory and experiment diverge however as. c' and PR increase. In the low pressure, low clearance cases the fluctua- tions in the pressure profiles are negligible and the bearing is operating under conditions approaching those assumed in the analysis, that is steady viscous flow in the clearance space from a recess at uniform pressure. This is the region of most interest, the region where the bearing is carrying a significantly greater load than a corresponding rigid bearing. As the clearance and suppfy pressure increase, depressions in the pressure profile be- come more severe and probably turbulent flow occurs in the clearance space. (For example, if we consider c' = 0.05, at PR = 2.0, the entrance Reynolds number was 300 while for PR
= 5.5 at the upper end of the curve the entrance Reynolds num- ber was nearly 3000.)
Journal of Lubrication Technology OCTOBER 1974 / 551
Conclusions
T h e following general conclusions may be drawn from t h e ex- perimental work described:
Inherently compensated t h r u s t bearings can operate quite successfully when one of t h e pads is a compliant elastomer. Some consideration does need to be given to the possibility of pneumatic hammer instability.
Compliant surface air lubricated bearings show an increased load capacity over equivalent rigid surface bearings a t the same supply pressure. In some cases this increase was as much as 100 percent.
There is a corresponding increase in flow rate as compared to a rigid bearing so that compliant bearings should be designed to r u n near their maximum load capacity where the clearance is small and the flows are much reduced.
I t is possible to r u n the compliant bearings near this load limit because their stiffness is virtually constant. There is no rapid decrease in stiffness as the load limit is approached analogous to the rigid bearing case.
Stiffness of the compliant bearings (at least for the inherently compensated type) is n o t much different from that of their rigid bearing equivalents. Extremely soft elastomers would probably show some reduction in relative stiffness.
Bonding and machining of natural rubber is readily accom- plished.
Acknowledgments
The author would like to acknowledge the following contribu- tions which in fact made this work possible. M r . H. L. Nash of the Defence Research Establishment Ottawa, D e p a r t m e n t of National Defence, who supplied the rubber samples. Mr. C M . Barker and Mr. G. It. Barker of the Chemistry Division of the National Research Council of Canada who made the Durometer
— D I S C U S S I O N — — — — Vittorio Castelli
3I view with satisfaction the fact that the compliant surface bearing is receiving more attention every day, and furthermore that some experimental work is also being performed. The pres- ent paper does not provide a design manual for the single-feed ax- isymmetric thrust bearing, b u t it does add some important infor- mation to the field: (a) some load displacement curves; (b) some stability diagrams; (c) some comparison with theoretical data.
This writer also agrees with the general positive comment made by the author on the value of this type of bearing.
Two points must be raised: (1) From the paper it might be in- ferred that, at least for each material, there exists a relation be- tween shear modulus and Poisson's ratio (or bulk modulus). This has not been shown by anyone, b u t it might be an interesting point to investigate. However, until proven otherwise, the bulk modulus must be measured independently in order to design practical bearings from theoretical data. (2) The discrepancy be- tween theoretical curves and experimental ones a t high pressure ratios and large clearances might be due more to inertial effects than to turbulence. However, I would like to hear t h e author's ex- planation of t h e apparent negative stiffness demonstrated at high clearance and low pressure ratios.
The author exercised care in performing a series of measure- ments with elastomer-lined, nonrotating thrust bearings of simple geometry. The apparent objective was a comparison with theoret-
3 Professor, Department of Mechanical Engineering, Columbia Universi- ty, New York, N. Y.
4 San Mateo, Calif.
measurements of bonded and unbonded samples. Mr. W. C.
Michie for his skill in constructing the apparatus with the 0.050 mm (0.002 in.) pressure tappings. Mr. E. H . Dudgeon for his continued assistance and interest, and to Mr. P . Iludon of L'Uni- versite Laval who did much of the experimental work.
References
1 Pirvics, J., and Castelli, V., "Characteristics of the Elastohy- drostatic Gas Lubricated Axisymmetric Thrust Bearing," Report No.
8, Lubrication Research Laboratory, Department of Mechanical En- gineering, School of Engineering and Applied Science, Columbia University, New York, Nov. 1900.
2 Dowson, D., and Taylor, C. M., "Elastohydrostatic Lubrica- tion of Circular Plate Thrust Bearings," JOURNAL OP LUBRICATION TECHNOLOGY, TRANS. ASME, Series F, Vol. 89, No. 3, July 1967, pp.
237-242.
3 Castelli, V., Uightmire, G. K., and Fuller, D. D., "On the Analytical and Experimental Investigation of a Hydrostatic, Axisym- metric, Compliant-Surface Thrust Bearing," JOURNAL OF LUBRICA-
TION TECHNOLOGY, TRANS. ASME, Series F , Vol. 89, No. 4, Oct. 1967,
pp. 510-520.
4 Rightmire, G. K., "An Experimental Method for Determining Poisson's Ratio of Elastomers," JOURNAL OP LUBRICATION TECH- NOLOGY, TRANS. ASME, Series F, Vol. 92, No. 3, July 1970, pp. 381- 388.
5 Benjamin, M. K., Rightmire, G. K., and Castelli, V., "Compli- ant-Surface, Fluid Film Bearings: Theory and Experiment for the Circular-Face Thrust Bearing, and Theory for the Journal Bearing,"
Rev. Roum. Sci. Techn.—Mech. AppL, Vol. 16, 1971, pp. 427-458.
G Benjamin, M. K., and Castelli, V., "A Theoretical Investiga- tion of Compliant Surface Journal Bearings," JOURNAL OP LUBRICA-
TION TECHNOLOGY, TRANS. ASME, Series F, Vol. 93, No. 1, Jan.
1971, pp. 191-201.
7 Dudgeon, E. H., and Lowe, I. R. G., "An Investigation of Centrally-Fed, Circular, Inherently-Compensated, Aerostatic Thrust Bearings," Paper No. 5, Gas Bearing Symposium, University of Southampton, Southampton, Mar. 1971.
8 Lowe, I. R. G., "A Study of Flow Phenomena in Externally Pressurized Gas Thrust Bearings," National Research Council of Canada, Mechanical Engineering Report MT-61, Dec. 1970.
ical results of Pirvies and Castelli [1], so that a simple, if not the most practical, configuration was used to facilitate comparisons.
For the limited data points presented herewith, agreement ap- pears to improve with decreasing PR = — and c' = c G / t pa.
Pa
Unlike the excellent characteristics of oil-lubricated elastomeric pads under heavy loads and at very small or negative apparent clearances, the gas-lubricated thrust pad may act as a dangerous brake and arresting device under similar conditions. It is certain- ly difficult to visualize applications to high-speed turbomachines, and the advantages as a "levitating p a d " in warehouses, aircraft hangars, and machine shops are not apparent.
Perhaps the most serious disadvantage, in comparison with rigid thrust pads, is the unstabilizing effect of the pressure-induced storage volume between the thrust surfaces, which is unavoid- able. For this and other reasons, it may be more profitable to mount a rigid thrust plate on rubber endowed with good damping properties, rather than to line it with the elastomer.
Incidentally, it is customary t o present data points, and it is hoped that the latter will be furnished in Figs. 4 through 9 in the
JOURNAL OF LUBRICATION TECHNOLOGY. The author may also like to comment on the loads carried by the rigid thrust bear- ings at what appears to be zero clearance.
It is not intended, of course, to discourage the author from probing the validity of the theoretical results [1] in the light of his own, and vice versa, even if practical applications do not loom on the horizon. Better understanding is certainly a worthy pursuit in itself. In connection with the latter, I notice in Fig. 11 what ap- pears to be a pressure undulation in the entrance zone (recovery zone), and it would be of interest to examine the corresponding distribution of the displacement wave (i.e., the "phase"). It is realized that the apparatus was not intended (nor is it probably
