Air flow and attitude angle compared with theory for rotating externally pressurized air journal bearing

Anderson, W. J.

Cunningham, R. E.

Fleming, D. P.

English

NASA Technical Reports Server

NASA TECHNICAL NOTE 
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EXPERIMENTS ON ROTATING EXTERNALLY 
PRESSURIZED AIR JOURNAL BEARINGS 
II - Attitude Angle and Air Flow 
by Robert E. Cunningham, David P. Fleming, 
and William J. Anderson 
Lewis Research Cenler 
Cleveland, Ohio 
NASA TN 0-5192 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • JUNE 1969 
https://ntrs.nasa.gov/search.jsp?R=19690018578 2020-03-23T21:09:43+00:00Z
EXPERIMENTS ON ROTATING EXTERNALLY 
PRESSURIZED AIR JOURNAL BEARINGS 
II - Attitude Angle and Air Flow 
By Robert E. Cunningham, David P. Fleming, 
and William J. Ander son 
Lewis Research Center 
Cleveland, Ohio 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
NASA TN D-5192 
For sale by the Clearinghouse for Federal Scientific and Technical Information 
Springfield, Virginia 22151 - CFSTI price $3.00 
AB STRACT 
Experimental attitude angles and airflow are compared with theory for a pair of 
2i-inch (6. 3- cm) diameter by 3~-inch (9. 5-cm) long externally pressurized air bearings. 
Attitude angles vary with shaft speed as predicted by small-eccentricity pressure per-
turbation theory but are generally larger in magnitude. The attitude-eccentricity locus 
of the journal center for a supply pressure ratio of 1. 7 is Similar to that of a plain self-
acting bearing. Measured airflows were in excellent agreement with calculated values. 
Shaft speeds varied from 0 to 25 000 rpm, and radial loads varied up to 20.2 psi (139 
kN/m~ . The supply pressure range covered was approximately 24 to 88 psia (169 to 
6 10 kN/m~ . 
ii 
EXPERIMENTS ON ROTATING EXTERNALLY PRESSURIZED AIR JOURNAL BEARINGS 
II - ATTITUDE ANGLE AND AIR FLOW 
by Robert E. Cunningham, David P. Fleming, 
and Will iam J. Anderson 
Lewis Research Center 
SUMMARY 
Experimental attitude angles and gas weight flows are measured and compared with 
theoretical values for a pair of ~-inch (6. 3-cm) diameter, 3!-inch (9. 5-cm) long ex-
ternally pressurized air lubricated bearings. Results show that attitude angles vary 
with shaft speed as predicted by the small-eccentricity perturbation theory but are gen-
erally larger in magnitude. The attitude eccentricity locus of the journal center for a 
supply pressure ratio of 1. 7 is similar to that of a plain self-acting bearing. 
Excellent agreement was obtait:led between measured values of airflow through the 
bearing and those determined analytically. The speed range covered in these experi-
ments was 0 to 25 000 rpm and radial loads were varied from 0 to 189 pounds (840 N) 
per bearing or 20.2 psi (139 kN/m2). Bearing supply pressures were varied from 
24 to 88 psia (169 to 610 kN/ m 2). 
INTRODUCTION 
Experimental results for load capacity and stiffness of an orifice compensated, ex-
ternally pressurized bearing are reported in part I of this investigation (ref. 1). These 
results are compared with the small eccentricity, linearized PH and the small-
eccentricity pressure perturbation theories (refs. 2 and 3). 
The effect of load and rotation on journal locus is well documented both experimen-
tally and analytically for the plain self-acting journal bearing (refs . 4 and 5). The 
analyses of references 2 and 3 may be used to determine attitude angles for rotating ex-
ternally pressured bearings. However, little experimental information of this kind is 
available. In addition, for this bearing design to be considered in machines operating in 
a closed-loop cycle, something of the flow requirements must be known. The flow rates 
and pressures required to support a given load will determine the power that has to be 
supplied by a compressor. Analytical flow rates are given by reference 7, which is sim-
ilar to the analyses of references 2 and 3. Because of the approximations made in the 
analyses, the validity and range of applicability of the results must be checked experi-
mentally. 
The objectives of part II of this investigation are (1) to determine the effects of load 
and shaft speed on bearing attitude angles while varying the supply pressure, (2) to 
measure the mass flow rates through the bearing, and (3) to compare these results with 
those obtained from analysis. 
The results reported in this investigation were obtained with a pair of 2i-inch 
(6. 3-cm) diameter, 3~-inch (9. 5-cm) long orifice compensated, externally pressurized 
air lubricated bearings. The rotor was operated in the two bronze bearings at an aver-
age radial clearance of 0.00135 inch (0.034 mm). Rotor speeds were varied from 
o to 25 000 rpm which corresponds to a range of compressibility number A of 0 to 2.8. 
Externally applied unidirectional loading varied up to 189 pounds (840 N) per bearing or 
20 . 2 psi (139 kN/m1 of projected area. Air supply pressure ratios P siP a varied from 
1.7to6. 
APPARATUS AND PROCEDURE 
The experimental data for this investigation were obtained with the apparatus shown 
in the photograph of figure 1. A detailed description can be found in part I (ref. 1). 
One of the bronze test bearings and the rotor used in this study are shown in fig-
ure 2. Each of the bearings has 12 orifice plugs arranged in two circumferential rows 
of six. The manner in which the orifice plugs are mounted is shown schematically in the 
section view (fig. 3(a)) . The relation of the restrictor length to diameter ratio is shown 
in the enlarged detail of figure 3(b). 
The procedure used in obtaining the data reported herein is basically the same as 
that outlined in part I (ref. 1). In addition, the flow measurements for both upper and 
lower bearings were measured using a calibrated flowmeter and were recorded. Read-
ings were made at each change in the supply pressure to the bearings with the rotor in a 
concentric pOSition (unloaded). Eccentricity and attitude angle were determined from the 
capacitance probe readings. 
Photographs of the rotor attitude-eccentricity locus were also made by taking suc-
cessive exposure of the same film at each new load increment. 
2 
(a) Photograph 
Turbine drive f' 
.-- -Rotor 
.--
buckets -- _____ ~ . 
capacitance I -- -~~OO~;;;;~~ 
distance probes- __ 
;- Speed sensor 
I 
I 
Upper test bearing -_ 
Orifice restricters, .--'--
12 per bearing -.--/ 
" Lower test ,," 
bearing -" 
" .--
(b) Schematic. 
~ --- \ 
Bearing supply 
air inlet 
.... -.,..-Externally 
pressurized 
load shoe 
Bearing supply 
air inlet 
--Thrust bearing 
CD-10091-15 
Figure 1. - Externally pressurized air bearing test apparatus. 
3 
Figure 2. - Test bearing and rotor. 
(a) Method of orifice mounting. CD-9940-15 
Figure 3. - Section view of test bearing. 
4 
C-68-1924 
0.07 in . 
(1. 8 mm) 
(b) Orifice detail. 
RESULTS AND DISCUSSION 
Bearing attitude angle is defined as the angle in the direction of rotation, between 
the load vector and the bearing-journal line of centers (fig. 4) . The results of this in-
vestigation are plotted in figures 5 to 7. A comparison is made in figure 5 of attitude 
angle against eccentricity ratios at increasing supply pressures. These curves show 
that there is a decrease in bearing attitude angle with increasing supply pressures at a 
given eccentricity ratio and compressibility number. This illustrates the decreasing 
contribution of rotational or self-acting effects on the overall hybrid performance as 
supply pressure increases . It appears, however, that as long as there is any journal ro-
tation, the attitude angle will always be appreciably greater than for the zero-speed 
case (i. e., zero attitude angle at any eccentricity ratio). The small orbits seen in the 
photograph of figure 5(d) are due to rotor imbalance . The near circular orbits at low 
eccentricities flatten out at higher eccentricities because of the asymmetric film stiff-
ness. 
The plot of figure 5(a) compares the experimental journal locus of the externally 
pressurized bearing to that of a plain self-acting bearing. The theoretical curve was 
produced from the data of reference 5 for a bearing with an LID of 1. 5. In addition to 
having a smaller attitude angle at smaller eccentricity ratios, attitude angle is more 
nearly constant in the externally pressurized bearing. The rather large attitude angles 
for the externally pressurized beari~g again illustrate the predominance of self-acting 
characteristics at low supply pressure. 
f--AttU""\ I angle, <{J 
Figure 4. - Representation of bearing 
attitude ang Ie. 
5 
6 
o 
6. 
Compressibi lity 
number, 
II 
o 
1.1 
Rotor 
speed, 
rpm 
o 
10000 
--- Theory for plain journal bearing 
70° of finite length (ref. 5) 
10° 20° ?JJ0 40° 
Bearing att itude angle, rp 
(a) Air supply pressure ratio, 1. 7. 
Compressibility Rotor 
number, speed, 
II rpm 
o 0 0 
6. 1.1 10000 
o 1.6 15000 
o 1.8 17400 
(b) Air supply pressu re ratio, 2. 3. 
Figure 5. - Attitude angle versus eccentricity ratio. Bearing average radial clearance, 0.00135 inch (0.0034 mm); 
rotor diameter, 2.5 inch (6.3 cm); bearing length, 3.75 inch (9.5 em); number of orifices, 12; orifice diameter, 
0.022 inch (0.56 mml. 
o 
10° 20° 30° 40° 
Bearing attitude angle, rp 
(c) Air supply pressure ratio, 2.9. 
10° 20° 30° 
Bearing attitude angle, rp 
(d) Air supply pressure ratio, 3. 6. 
Figure 5. - Continued. 
Compressibility Rotor 
number, speed, 
" rpm 
000 
6. 1.1 10000 
o 1. 6 15000 
o 2.2 20000 
~ 
--
iii 
.. I 
u ~ 
°if 
~ 
Rotor center locus at 10 000 rpm 
or compressibility number of 1.03. 
Compressibi lity Rotor 
number, speed, 
" rpm 
000 
6. 1.1 10000 
o 1. 6 15000 
o 2.2 20000 
o 2.8 25 000 
7 
Compressibility Rotor 
number, speed, 
A rpm 
o 0 0 
6. 1. 05 10 000 
o 1. 6 15000 
o 2.2 20000 
o 2.8 25000 
20° 30° 40° 
Bearing attitude angle, rp 
(e) Air supply pressure ratio, 4.8. 
Compressibility Rotor 
number, speed, 
A rpm 
000 
6. 1.1 10000 
o 1. 6 15000 
o 2.2 20000 
50° 
20° 30° 
Bearing attitude angle, rp 
(I) Air supply pressure ratio, 6. O. 
Figure 5. - Concluded. 
8 
Figure 6 shows the variation of experimental attitude angles with compressibility 
number at an eccentricity ratio E of O. 1. Also plotted are analytical predictions, ob-
tained from the computer program in reference 7. At all supply pressures investigated 
the measured attitude angles are greater than the small-eccentricity pressure pertur-
bation theory predicts. This is not surprising, however, since this bearing has only six 
orifices per row. A greater number of orifices, of course, would more closely approxi-
mate the line pressure source assumed by theory. 
The computer program of reference 7 was also used to calculate the airflow through 
the bearings. The orifice discharge coefficients used to calculate the theoretical flow 
were obtained from experimental data reported in reference 6. As shown in figure 7 
measured airflow (rotor concentric in bearing) was in excellent agreement with the cal-
culated values. This undoubtedly is due to using values of the discharge coefficient 
which vary with supply pressure. Values of airflow measured for the eccentric case 
(radial load applied to shaft) did not vary significantly from the concentric case . 
50 
40 
g> 
"C 
s-
",-
30 c;, 
c 
co 
'" "C 
.3 
B 20 co 
"" C 
L. 
to 
'" 
"" 10 
/ 
I 
I 
/ 
/ 
/-----
/ 
Air supply 
pressure ratio, 
Psi Pa 
L7 
2.3 
2.9 
3. 6 
4.8 
6.0 
Theoretical (ref. 6) 
Air supply 
pressure 
ratio, 
Ps/Pa 
_-------1.7 
_===-_-,2.3 
~--4.8 
=-_ -----6.0 
Compressibility number, 1\ = (6~wIPa)(R/C)2 
Figure 6. - Bearing attitude versus compressibility numbers at varying supply pressure 
ratios . Rotor eccentricity ratio, 0.1; bearing average radial clearance, 0.00135 inch 
(0. 034 mm); rotor diameter, 2.5 inches (6.3 em); bearing length, 3. 75 inches (9.5 em); 
number of orifices, 12; orifice diameter, 0.022 inch (0.56 mm). 
9 
3.0xlO-3 
2.5 
u 
u 2.0 ~ 
'" :e '" 0, 
-'>< 0 
0 :;;; 
:;;; ~-
~- 1.5 0 ;;:: 
;;:: 
'" 
'" 
'" '" 
'" 
E 
'" E ~ 
~ <t: 
:.;: 1.0 
.5 
o 
7x10-3 
6 
5 
4 
3 
2 
o 
Q 
/, 
o 
!:::. 
I 
/, 
/, 
/, 
/, 
I 
j, 
;, 
!J 
Ii 
!J 
Bearing 
U
L 
pper }EXPerimental 
ower 
U
Lower } calcu lated pper 
Supply pressure, Ps' psig 
3 4 5 
Supply pressu re, Ps' N/m2 
Figu re 7. - Compar ison of calcu lated and experimental 
va lues of air mass flow. Atmospher ic pressure, 
14.4 pSia (99 kN/m2); rotor diameter, 2.5 inches 
(6.3 cm); bearing length, 3.75 inches (9.5 cm); 
number of orifices per bear ing, 12; orifice diameter, 
0. 022 inch (0. 56 mml. Radial clearances: upper 
beari ng, 0.00132 inch (0.0335 mm); lower bear ing, 
0. 00138 inch (0. 035 m ml. 
SUMMARY OF RESULTS 
The following results were obtained from experiments conducted with a pair of 
2~ inch (6. 3-cm) diameter by 3~-inch (9. 5-cm) long externally pressurized air bearings. 
An 18-inch (46-cm) long rotor was operated vertically in the two bearings at a radial 
clearance of 0.0013 inch (0 . 033 mm). Speeds were varied from 0 to 25 000 rpm and 
radial loads up to 189 pounds per bearing or 20.2 psi (840 Nor 139 kN/m1 . Air supply 
pr essure ratios P si p a varied from 1. 7 to 6. 
1. Attitude angles at small eccentricity ratios vary with shaft speed in the same 
manner as predicted by small-eccentricity perturbation theory. 
2. Attitude angles are , in general, lar ger than the theory predicts . 
10 
I 
I 
3. The journal locus of an externally pressurized bearing at an air supply pressure 
ratio of 1. 7 is similar to that of a plain self-acting journal bearing. 
4. Excellent agreement was obtained between measured and calculated weight flows 
of air. 
Lewis Research Center, 
National Aeronautics and Space Administration, 
Cleveland, Ohio, February 25, 1969, 
129-03-13-05-22. 
11 
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APPENDIX - SYMBOLS 
bearing radial clearance, 
in.; mm 
rotor diameter, in.; cm 
orifice diameter, in.; mm 
rotor eccentricity, in.; mm 
bearing length, in.; cm 
number of orifices 
lubricant mass flow, lb/sec; 
kg/sec 
rotor angular speed, rpm 
atmospheric pressure, psi; 
N/m2 
R 
W 
E 
A 
W 
bearing supply pressure, psi; 
N/m2 
rotor radius, in; cm 
applied radial load, lb; N 
rotor eccentricity ratio, e/C 
bearing compressibility number, 
(6/lw/P a)/(R/C) 2 
absolute viscosity, (lb) (sec)/in. 2; 
(N) (sec) /m 2 
rotor angular speed, rad/sec 
bearing attitude angle, deg 
,--~.----
I 
! 
REFERENCES 
1. Cunningham, Robert E.; Fleming, David P . ; and Anderson, William J.: Experi-
ments on Rotating Externally Pressurized Journal Bearings. I - Load Capacity and 
Stiffness. NASA TN D-5191, 1969. 
2. Lund, J. W.: A Theoretical Analysis of Whirl Instability and Pneumatic Hammer for 
a Rigid Rotor in Pressurized Gas Journal Bearings. J. Lubr. Tech., vol. 89, 
no. 2, Apr. 1967, pp. 154-166. 
3. Lund, J. W.: The Hydrostatic Gas Journal Bearing with Journal Rotation and Vibra-
tion. J. Basic Eng., vol. 86, no. 2, June 1964, pp. 328-336. 
4. Sternlicht, B.; and Elwell, R. C.: Theoretical and Experimental Analysis of Hydro-
dynamic Gas-Lubricated Journal Bearings. Trans. ASME, vol. 80, no. 4, 
1fay 1958, pp. 865-878. 
5. Sternlicht, B.: Gas-Lubricated Cylindrical Journal Bearings of the Finite Length-
Static Loading. J. Appl. Mech., vol. 28, no. 4, Dec. 1961, pp. 535-543. 
6. Anon.: Design of Gas Bearings. Vol I: Design Notes. Mechanical Technology, Inc., 
1966. 
7. Fleming, David P.; Cunningham, Robert E.; and Anderson, William J.: Stability 
Analysis for Unloaded Externally Pressurized Gas-Lubricated Bearings with Journal 
Rotation. NASA TN D-4934, 1968. 
NASA- Langley, 1969 - 15 E -4607 13 



Experiments on rotating externally pressurized air journal bearings. Part 2 - Attitude angle and air flow

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