References - DMU

References

REFERENCES

1.1 Willis, Rev. R. "On the Pressure Produced on a Flat Surface when Opposed to a Stream of Air Issuing from an Orifice in a Plane Surface'. Trans. Cambridge Phil. Soc. 3P1 pp 121-140,1828

1.2 Hirnt G. A. 'Study of the Principle Phenomena Shown by Friction and of Various Methods of Determining the Viscosity of Lubricants'. Bull. Soc. Industr. Mulhouse 26, No. 129, p 188-277,18-54 (in French)

1-3 Kingsbury, A. 'Ebcperiments with an Air Lubricated Bearing' . JASNE, 9, p 267-292,1897

1.4 Pink, E. G. and Stout, K. J. 'Applications of Air Bearings to

Manufacturing Engineering'. Paper B4,2nd Joint Polytechnic Symposium on Manufacturing Engineering, Ianchester Polytechnic,

June 1979

2.1 Pink, E. G. 'An Ebcperimental Investigation of Ebcternally Pressurised

Gas Journal Bearings and Comparison with Design Method Predictions'.

Paper G3, Gas Bearing Symposium, University of Cambridge, 1976

2.2 Pink, E. G. 'Experimental Investigations of Externally Pressurised

Gas Journal Bearings and Comparison with Design Methods'.

University of Southampton, Department of Mech. Eng. Report No.

ME/76/4, April 1976

2.3 Mori, H. 'A Theoretical Investigation of Pressure Depression in Externally Pressurised Gas Lubricated Circular Thrust Bearings.

Trans. of A. S. M. E., Journal of Basic Eng. p Vol. 83D9 1961, p 201-208

2.4 Mori, H. and Miyamatsu, Y. 'Theoretical Flow Models for Externally

Pressurised Gas Bearings'. Trans. of A. S. M. E., Journal of Lub. Tech,, Vol. 91, Series F. No. 2,1969t p 181-193

2.5 Mori, H. and Ezuka, H. 'A Psuedo-Shock Theory of the Prassure Depression in Externally Pressurised Circular Thrust Gas Bearings'. Proceedings

of J. S. L. E. - A. S. L. E. International Lubrication Conf., Tokyo,

June 1975, p 286-294

Refs. 1.1 to 2-5

2.6 Foupard, M. and Drouin, G. 'Theoretical and Ekperimental Pressure Distribution in Supersonic Domain for an Inherently Compensated Circular Thrust Bearing'. A. S. M. E. Paper No. 72-Lub-43,1972

2.7 Vohr, J. H. 'A Study of Inherent Restrictor Characteristics for Hydrostatic Gas Bearings'. Paper 30, Gas Bearing Symposium, University of Southampton, 1969

2.8 McCabe, J. T., Elrod, H. G., Carfagno, S. and Colsher, R. 'Summary of Investigations of Entrance Effects of Circular Thrust Bearings'. Paper 17, Gas Bearing Symposium, University of. Southampton, 1969

2.9 Hagerup, H. J. 'On the Fluid Mechanics of the Inherent Restrictorl,

Trans. of A. S. M. E., Journal of Fluid Engineering, Vol. 96, ge'ries 1, No. 4,1974, p 341-j47

2.10 Lowe, I. R. G. 'Study of Flow Phenomena in Rcternally Pressurised Gas

Thrust Bearings'. National Research Council of Canada, Mech. Eng.

Report No. MT-61,1970

2.11 Wilcock, D. F. (Editor) 'Design of Gas Bearings'. Mechanical Technology

Incorp., Iatham, New York, 1967

2.12 Elrod, H. G. -and Glanfield, G. A. . 'Computer Procedures for the Design

of Flexibly Mounted Externally Pressurised, Gas Lubricated

Journal Bearings'. Paper 22, Gas Bearing Symposium, University of

Southampton, 1971

2.13 Kreith, F. 'Reverse Transition in Radial Source Flow between Two

Parallel Planes'. Physics of Fluids, Vol. 8, No. 6,1965, pp 1189-90

2.14 Vohr, J. H. 'Analysis of the Pressure Loss Characteristics of the Gas

Feeding Regions of the NASA AB-. 5 Gyro Gimbal Bearing'. Mechanical

Technology Incorp., Iatham, New York, Report No. MTI-63TR 35,1963

2.15 Arnberg, B. T. 'Review of Critical Flowmeters for Gas Flow Measurements'.

Trans. A. S. M. E., Journal of Basic Eng., Dec. 1962, p 447-460

2.16 Grace, H. P. and Iapple, C. E. 'Discharge Coefficients of Small Diameter

Orifices and Flow Nozzles'. Trans. A. S. M. E. t July 1951, p 639-647

Refs. 2.6 to 2.16

2.17 Marsh, H., Bennet, J. and Hudson, B. C. 'The Flow Characteristics of Small Orifices Used in Externally Pressurised Bearings'. Paper E3,

Gas Bearing Symposium, University of Cambridge, 1976

2.18 Markho, P. H., Grewal, S. S. and Stowell, T. B. Discussion of Ref. 2.17

2.19 Markho, P. H., Grewal, S. S. and Stowell, T. B. 'An Experimental

Investigation of the Effect of Misalignment and Directionality of

an Externally Pressurised, Orifice Compensated Air Journal Bearing'.

Trans. A. S. M. E., Journal of Lub. Tech., Vol. 101, Jan. 1979, p 28-37

3.1 Tang, I. C. and Gross, W. A. 'Analysis and Design of Zcternally--

Pressurised Gas Bearings'. A. S. L. E. Trans., 5,1962, p 261-284

3.2 Holster, P. L. 'Reliable and Easy to Handle Design Formulae for

Externally Pressurised Gas Thrust and Journal Bearings'. Paper 2,

Gas Bearing Symposium, University of Southampton, 1967

4.1 Pao, R. H. F. 'Fluid Dynamics', Charles E. Merrill, 1967, Ohio

4.2 Streeter, V. L. 'Fluid Mechanics'. McGraw - Hill, 1966

4-3 Mori, H. and Yabe, H. 'Theoretical Analysis of Externally Pressurised

Thrust Collar Gas Bearings'. A. S. L. E. Trans., 6,1963, P 337-Y+5

4.4 Lund, J. W. 'A Theoretical Analysis of Whirl Instability and Pneumatic

Hammer for a Rigid Rotor in Pressurised Gas Journal Bearings'.

Trans. of A. S. M. E., Series F, Vol. 89, No. 2,1967, p 154-166

6.1 Castelli, V. and Pirvics, J.

Bearing Film Analysis'. Oct. 1968, P 777-792

'Review of Numerical Methods in Gas

Trans. A. S. M. E., Journal of Lub. Tech.,

6.2 Rowe, W. B. and Stout, X. J. 'Design of Externally Pressurised Cas Fed

Bearings Employing Slot Restrictors'. Tribology International,

Aug. 1973, p 140-144

Refs. 2.17 to 6.2

6-3 Peaceman, D. W. and Rachford, H. H. 'The Numerical Solution of Parabolic

and Elliptic Differential Equations'. Journal of Soo. Indust.

Appl. Math., Vol 3, No. 1,1955, p 28-41

6.4 Kazimierski, Z. and Jarzecki, K. 'Stability Threshold of Flexibility

Supported Hybrid Gas Journal Bearings'. Trans. A. S. M. E. ', Journal

of Lub. Tech., Vol. 101,1979, P 451-457

6.5 Kazimierski, Z. and Makowski, Z. 'Investigation of High Stiffness

Gas Lubricated Thrust Bearing'. Paper 2, Gas Bearing Symposium, Leicester Polytechnic, 1981

7.1 Shires, G. L- 0 'The Viscid, Flow of Air in a Narrow Slot'. National

Gas Turbine Establishment, Memo No. M46, Dec. 1948

7.2 Robinson, C. H. and Sterry, F. 'The Static Strength of Pressure Fed

Gas Journal Bearingst Jet Bearings'. A. E. R. E. Rep. R/R 2642

Sept. 1958

7.3 Shires, G. L. 'The Vented Pressure-Fed Gas Journal Bearing.

U. K. A. E. A., Winfrith, AEEW-R1110 March 1962

7.4 Grassam, N. S. and Powell, J. W. 'Gas Lubricated Bearings'. Butterworths,

1964

7.5 Powell, J. W. 'Design of Aerostatic Bearings'. Machinery Publishing

Co. Ltd. 1971

7.6 Dudgeon, E. H. and Lowe, I. R. G. 'A Theoretical Analysis of Hydrostatic

Gas Journal Bearings'. National Research Council of Canada,

Mech. Engineers' Report No. MT-54,196.5

7.7 Ausman, J. S. 'Theory and Design of Self-Acting Gas Lubricated Journal

Bearings Including Misalignment Effects'. Proceedings of lst

International Symposium on Gas Lubricated Bearings, Washington D. C.,

U. S. A., October 1959

7-8 Lundt J. W. 'The Hydrostatic Gas Journal Bearing with Journal Rotation

and Vibration'. Journal of Basic Engineering, Trans. A. S. M. E.,

Series D, Vol. 86,1964, P 328-336

Refs. 6.3 to 7-8

7.9 Constantinescu, V. N. 'An Approximate Method for the Analysis of Externally Pressurised Gas Journal Bearings'. Paper 1, Gas Bearing Symposium, University of Southampton, 1967

7-10 Pink, E. G. 'Investigations into Design Methods for Externally Pressurised Gas Journal Bearings' University of Southampton, Department of Mech Eng., Report No. ME/73/28, Dec. 1973

7-11 Pink, E. G. 'Investigations into Design Methods for Externally Pressurised Gas Journal Bearings'. Paper A3, Gas Bearing Symposium, University of Southampton, 1974 (Also published in Tribology International, Dec. 1974, p 265-269)

7.12 Pink, E. G. and Stout, K. J. 'Design Procedures for Orifice Compensated Gas Journal Bearings Based on Experimental Data'. Tribology

International, Feb. 1978, p 63-75

7.13 Pink, E. G. and Stout, K. J. 'Orifice Restrictor Losses in Journal Bearings' Proceedings of Instn. of Mech. Engrs. Vol. 193, No. 1, 1979, p 47-52

7.: L4 Stowell, T. B., Markho, P. H. and Grewal, S. S. 'An Experimental

Investigation of the Effect of Inter-Orifice Variations on the Performance of an Externally Pressurised, Orifice Compensated Air

Journal Bearing'. Trans. A. S. M. E., Journal of Lub. Tech., Vol. 102,

Oct. 1980, p . 505-510

7.25 Auburn, J. H. C. 'The Static Performance of Externally Pressurised

Journal Bearings'. University of Southampton, Department of Mech

Eng., Report No. ME/80/12, June 1980

7-16 Grewal, S. s. 'An Investigation of Externally Pressuristýd, Orifice Compensated Air Journal Bearings with Particular Reference to Misalignment and Inter-Orifice Variations'. Ph. D. Thesis, Liverpool Polytechnib, 1979

9.1 Pink, E. G. 'A Comparison of the Performance of Orifice Compensated and Slot Entry Gas Lubricated Journal Bearings'. M. Phil. Thesis, Leicester Polytechnic, 1978

Refs. 7.9 to 9.1

10.1 Pink, E. G. Unpublished work carried out at Leicester Polytechnic,

S. R. C. Grant No. GR/A/20927,1976-78

11.1 Pink, E. G. and Tawfik, M. 'The Effect of Errors in Manufacture on Aerostatic Bearing Performance'. Paper F2, lst Joint Polytechnic

Symposium on Manufacturing Engineering, June 1977, Leicester

Polytechnic

13.1 Ausman, J. S. 'Finite Gas Lubricated Journal Bearing'. Proceedings of Institute of Mechanical Engineers, Conference on Lubrication and Wear, London, 1957,1)1? -39-45

13.2 Ausman, J. S. 'An Improved Analytical Solution for Self-Acting, Gas

Lubricated Journal Bearings of Finite Length'. Trans. A. S. M. E.,

journal of Basic Engineering, June 1961, p 186-194

13.3 Gross, W. A. 'Numerical Analysis of Gas Lubricated Films'. Proceedings

of the First International Symposium on Gas Lubricated Bearings,

1959, Washington D. C.

13.4 Raimondi, A. A. 'A Numerical Solution for the Gas Lubricated Full

Journal Bearing of Finite Length'. A. S. L. E., Trans., Vol. 4,1961,

131-155

13.5 Elrod, H. G. and Malanoski, S. B. 'Theory and Design Data for

Continuous Film Self Acting Journal Bearings'. A. S. L. E., Trans.,

Vol. 8,1965, P 323-338

13.6 Powell, J. W. 'Hydrodynamic Effects in Hydrostatic Gas Bearings'.

Engineer, July 27,1962, pp 148-150

13.7 Powell, J. W. 'Experiments on a Hybrid Air Journal Bearing'. A. S. M. F.

paper 64-WA/LUB-11,1964

X 13.8 Cunningham, R. E., Fleming, D. P. and Anderson, W. J. T periments on Rotating Externally Pressurised Journal Bearings - l. 'Load Capacity

and Stiffness'. NASA Tech. Note. NASA TN D-5191t 1969

Refs. 10.1 to 13.8

13-05 Majumdar, B. C. 'Analysis of Ebcternally Pressurised Gas Journal

Bearings with Journal Rotation'. Wear, Vol. 24 , 1973, p 15-22

13-10 McFarlane, C. W. R. and Reason, B. R. 'Experimental Studies in the operating Performance of a Hybrid Air Journal Bearing with Particular Reference to Pressure Profile Measurement'. Paper 20, Gas Bearing Symposium, Leicester Polytechnic, 1981

14.1 Gross, W. A. 'Investigation of Whirl in Externally Pressurised Air

Lubricated Journal Bearings'. Trans. A. S. M. E., Journal of Basic

Engineering, March 1962

14,2 Stout, K. J. 'Externally Pressurised Bearings'. Ph. D Thesis,

Ianchester Polytechnic, 1971

14.3 Tawfik, M. 'The Design of Fxternally Pressurised Bearings for Combined Axial and Radial Loading'. Ph. D Thesis, Leicester Polytechnic, 1981

16.1 Graeme, J. G. 'Designing with Operational Amplifiers - Application

Alternatives'. McGraw -Hill, 1977

16.2 Stout, K. J. and Rowe, W. B. 'Externally Pressurised Bearings - Design

for Manufacturep Part 3'. Tribology Internationall August 1974,

p 195-212

17.1 Sternlicht, B. and Elwell, R. C. 'Synchronous Whirl in Plain Journal

Bearings'. A. S. M. E. paper 62-LUBS-19,1962

17.2 McCann, R. A. 'Stability of Unloaded Gas Lubricated Bearings'.

Trans. A. S. M. E., Journal of Basic Engineering, December 1963,

p 513-518

Refs. 13.9 to 17.2

Appendices

APPENDIX A- RESTRICTOR LOSS EQUATIONS

Al Resistances in Series

Assumptions:

(a) Cd identical for all flow areas

(b) Incompressible flow i. e. low Mach Rumbers

Equating flow through orifice area Al, curtain area A2 and the combined

effective flow area Ae :

_17 rd.

where Ae = effective flow area of the overall resistance

Cancelling, squaring and rearranging:

f4e zIr

Therefore:

XL

XL- ease*

(Ael)

9o. os (A. 2)

A1

and:

(A-3)

Substituting Equation (A. 1) into (A. 2)

A, 7 [47fA -_

74

Rearranging gives:

4e- (A. 4) 2-

Using Ae in the isentropic flow equation:

2-

ý

for pocketed orifices

e ý--Z/

xz 0/1

for inherently compensated orifices

Note: As �L -> 0; Ae «> CdA,

As ýL :> -'> ; Ae -> CdA2

A-2

A2 Entrance Loss Effects

Assumptions:

(a) Incompressible flow i. e. low Mach No.

(b) Pressure loss in bearing film dependent upon Reynolds' Number

and dynamic pressure in the form obtained by previous studies.

Flow completely fills secondary flow area.

Equating mass flow through overall resistance:

Q 127 [? 0 -; ý. c 12

ce c 4, C)

4L

Cancelling, squaring and rearranging:

7

-7ý- r4zew Z- /,

/ ( From assumption (b):

ivWe -e (ee)

Rearranging Equation (A. 6)

'2 ('-'-) 1 k'4

(A. 6)

. oaoo (A-7)

A-3

From F4uations (A. 1) and (A. 4): -

(A. 8) 1

/00 / -, A F":. Z az 2-

Substituting Equation (A. 8) into (A-7):

,e -0

to rT

, . *eoe (A. 9)

Substituting Equation (A. 9) into (A. 5):

Using CORF in the isentropic flow equation:

77-

oe7'

A

APPENDIK B- EFFECT OF J. ' ON BEARING STIFFNESS

Equating mass flow rates through orifice with that through the bearing

clearance gives:

2-1

1, e 4s-5 o". v

7-

'low

Defining 0 as-.

/

r( !» Equation (B. 1) becomes:

/

For A -=

11- 7.

can be defined. as:

ele, /I- (B. 2)

B-i

Substituting for do . CZ14.

For S., i

into Equation (B. 2)-

____ "/

1r/

a')lý = // wloý.

(B

Substituting for into Equation (B. 2):

. @... (B. 4)

The concentric bearing stiffness is dependent on Thus the effect

of cP. on bearing stiffness is given by the ratio of Equation (B. 3) to (B. 4):

ý= >�e

(7 ;, 4

, eZ. e, 7a wz. 70ýc= 02-)

In a similar manner, it can be shown that:

Sbjjýieji (, F� = cv) J'h ? es s (f. 7- --0)

2-

2- CF

'L

= _____

/+_. J2 3

B-2

APPENDIK C- PROOF THAT /TZ ol

"t. r/

;rz can be written as

__ 7f ZZ 7 i'-' L 471L

? (4//

i((J 22 7 L

re-aiTanging gives:

a// (4 ý) 2-

//

Z: - T IT

60*

(' /«. 9 ('))

-01

-14 ..... I

eA

But:

IT I

A/I

-" 2r iZ: /7 42(/ -ei) -ý --Z (/

-'1- -2 -5.

/ 'I al

C-'

/46

r J/>)(/)7 2rL' ( 44. / / 41. J

-7-4 -2[ý

Substituting these identities :

k-1

- S- 2F7

which by definition equals

Therefore:

__

z 7= zf7 ct'JL/ 1e7J

L 'J 1e /

a-2

APPENDIX D

Listing of Computer Program Used for

Plotting the Flow Net of Single Admission Bearings

00100 $RESET-FREE 00200 $SET SUPRS 00300 $SET AUTOBIND 00400 $BIND=FROM (L)B00317/A, (L)B00317/B 00500 FILE l(KIND=DISK. TITLE="PLOT/IS01.11) 00600 FILE 5=INPUT, UNIT=REMOTE 00700 FILE 3=OUTPUT. UNIT=REMOTE 00800 FILE 6=OUTPUT. UNIT=PRINTER 00900 C EP BEARINGS - 01000 c 01100 c 01200 C 01300 01400 01500 01600 01700 01800 01900 02000 02100 02200 02300 02400 02500 C 02600 02700 02800 C 02900 03000 03100 03200 03300 03400 03500 C 03600 03700 03800 03900 04000 04100 04200 04300 04400 C 04500 04600 04700 04800 04900 05000 05100 05200 C 05300 05400 05500C

CALCULATES AND PLOTS ISOBARS AND STREAMLINES SINGLE PLANE COLLAR BEARING AND SINGLE ADM JOURNAL

COMMON X. Y. Pl, P2, Fl, PB, PD, ANG. XP(100). YP(100) CALL PLOTIN CALL DEVICE (1,0) CALL SHIFT2050,100) WRITE(3.5)

5 FORMAT(lHO, 12H NE, NPBR, PD? ) READ(5, /)Pl. P2, PD WRITE(6,20)Pl, P2, PD WRITE(3,20)Pl. P2, PD

20 FORMATOH 5HN*SW=, F7.2,7H N*PBR=, F8.5.4H PD=. F7.4) WRITE (3,21)

21 FORMAMH 42H SINGLE ADM JOURNAL = 1, COLLAR READ TYPE OF BEARING

READ(5, /)M IF (M EQ. 2) GO TO 22

TYPE 1- SINGLE ADM JOURNAL WRITE(3,23)

23 FORMAT(lH 9H L. N. L/D? ) READ(5, /)Bl, N-SW WRITE(3.24)Bl: N, SW

24 FORMAT(lH 3H L=, F6. l, 3H N=, 14,5H L/D=, F6.3) GO TO 28

TYPE 2- COLLAR THRUST 22 WRITE(3.25) 25 FORMAMH 11H RC, N, RORI? )

READ(5, /)RC, N, RORI WRITE(3,30)RC, N, RORI WRITE(6,30)RC, N, RORI

30 FORMAT(lH 4H RC=, F6.1,3H N=, 14,6H RORI=, F6.3) SW=(ALOG(RORI))/2

28 PI=3.142 CALCULATES AND PLOTS X AND Y FOR STREAMLINES

DO 180 K=1,6 ANG=(K-1)*PI/12 Y=(K-1)*PI/6 DO 190 I=1,39 X=(40-I)/39.0 CALL STR1 IF(M EQ. 1) GO TO 26

TYPE 2- COLLAR THRUST YP(I)=EXP(X*SW)*RC*Y/N XP(I)=(EXP(X*SW)*COS(Y/N)-l)*RC

MIRRORS STREAMLINES

THRUST = 2)

D-1

05600 YP(79-I)=-EXP(-X*SW)*RC*Y/N 05700 XP(79-I)=(EXP(-X*SW)*COS(Y/N)-l)*RC 05800 GO TO 27 05900 C TYPE 1- SINGLE ADM JOURNAL 06000 26 YP(I)=Y*Bl/(2*SW*N) 06100 XP(I)=X*Bl/2 06200C MIRRORS STREAMLINES 06300 YP(79-I)=-YP(I) 06400 - XP(79-I)=-XP(I) 06500 27 CONTINUE 06600 190 CONTINUE 06700 CALL MOVT02(XP(l), YP(l)) 06800 CALL POLTO2(XP, YP, 78) 06900 IF (K EQ. 1) GO TO 202 07000 C MIRRORS STREAMLINES 07100 DO 200 I=1,78 07200 YP(I)=-YP(I) 07300 200 XP(I)=XP(I) 07400 CALL MOVT02(XP(l), YP(l)) 07500 CALL POLT02. (XP, YP, 78) 07600 202 CONTINUE 07700 180 CONTINUE 07800 C CALCULATES AND PLOTS X AND Y FOR ISOBARS 07900 15 WRITE(3,6) 08000 6 FORMAT(lH0,9H PB, YMAX? ) 08100 READ(5. /) PB, YM 08200 IF(PB GT. 10) GO TO 161 08300 WRITE(3,50)PB, YM 08400 WRITE(6,50)PB, YM 08500 50 FORMAT(lHO, 4H PB=, F7.4,6H YMAX=, F7.4) 08600 X=(PD-PB)/(PD-1) 08700 DO 160 I=1,20 08800 IF(YM. LT. 1.0) GO TO 70 08900 C NOT OF CLOSED FORM AROUND INLET 09000 Y=YM*PI*(20-I)/19 09100 GO TO 71 09200 C CLOSED FORM AROUND INLET 09300 70 Y=YM*PI*COS((I)*PI/40) 09400 X=YM*PI*(SIN((I)*PI/40))/Pl 09500 71 CALL PRE2 09600 IF(M EQ. 1) GO TO 31 09700 C COLLAR THRUST 09800 YP(I)=EXP(X*SW)*RC*Y/N 09900 XP(I)=(EXP(X*SW)*COS(Y/N)-l)*RC 10000 C MIRRORS ISOBARS 10100 YP(40-I)=-YP(I) 10200 XP(40-I)=XP(I) 10300 YP(39+I)=-EXP(-X*SW)*RC*Y/N 10400 XP(39+I)=(EXP(-X*SW)*COS(Y/N)-l)*RC 10500 YP(79-I)=-YP(39+I) 10600 XP(79-I)=XP(39+I) 10700 GO TO 32 10800 C SINGLE ADM JOURNAL 10900 31 YP(I)=Y*Bl/(2*SW*N) 11000 XP(I)=X*Bl/2

D-2

11100C MIRRORS ISOBARS 11200 YP(40-I)=-YP(I) 11300 XP(40-I)=XP(I) 11400 YP(39+I)=-YP(I) 11500 XP(39+I)=-XP(I) 11600 YP(79-I)=YP(I) 11700 XP(79-I)=-XP(I) 11800 32 CONTINUE 11900 160 CONTINUE 12000 YP(79)=YP(l) 12100 XP(79)=XP(l) 12200 CALL MOVT02(XP(l), YP(l)) 12300 CALL POLTO2(XP, YP, 79) 12400 GO TO 15 12500 C PLOTS CENTRELINES 12600 161 DO 60 I=1,39 12700 Y=1.2*PI*(39-I)/38 12800 IF (M EQ. 1) GOTO 61 12900 YP(I)=RC*Y/N 13000 YP(79-I)=-YP(I) 13100 XP(I)=(COS(Y/N)-l)*RC 13200 XP(79-I)=XP(I) 13300 GO TO 62 13400 61 XF(I)=O. O 13500 XP(79-I)=O. O 13600 YP(I)=Y*Bl/(SW*N*2) 13700 YP(79-I)=-YP(I) 13800 62 CONTINUE 13900 60 CONTINUE 14000 CALL MOVT02(XP(l), YP(l)) 14100 CALL POLT02(XP. YP. 78) 14200 IF(M EQ. 1) GO TO 65 14300 YP(1)=EXP(SW)*RC*PI/N 14400 XP(1)=(EXP(SW)*COS(PI/N)-l)*RC 14500 YP(2)=EXP(-SW)*RC*PI/N 14600 XP(2)=(EXP(-SW)*COS(PI/N)-l)*RC 14700 GO TO 66 14800- 65 YP(1)=PI*Bl/(2*SW*N) 14900 XP(1)=Bl/2 15000 YP(2)=YP(l) 15100 XP(2)=-XP(l) 15200 66 CALL MOVT02(XP(l), YP(l)) 15300 CALL POLT02(XP, YP, 2) 15400 YP(1)=-YP(l) 15500 YP(2)=-YP(2) 15600 CALL MOVT02(XP(l). YP(l)) 15700 CALL POLT02(XP, YP, 2) 15800 CALL DEVEND 15900 STOP 16000 END 16100 C 16200 C 16300C

D3

16400 SUBROUTINE STR1 16500C STREAMLINES - ITERATES Y FOR GIVEN X AND ANGLE 16600 COMMON X, Y, P1, P2. Fl, PB, PD, ANG, XP(100), YP(100) 16700 1300 BL=O. O 16800 DO 2000 J=1.13 16900 P3=Pl*(X+2*(J-7))/2 17000 A2=TANH(P3) 17100 Al=TAN(Y/2) 17200 TP=Al/A2 17300 GO TO 2002 17400 2001 TP=TAN(Y/2) 17500 2002 BL=BL+((-l)**(J-7))*ATAN(TP) 17600 2000 CONTINUE 17700 Dl=ANG-BL 17800 TP=O. O 17900 DO 2100 J=1.13 18000 Al=TAN(Y/2) 18100- A3=(l/COS(Y/2))**2 18200 P3=Pl*(X+2*(J-7))/2 18300 A2=TANH(P3) 18400 GO TO 2004 18500 2003 A2=1.0 18600 2004 A4=1+(Al/A2)**2 18700 D2=A3/(A4*A2*2) 18800 2100 TP=TP+((-l)**(J-7))*D2 18900 YNEW=Y+Dl/TP 19000 IF (ABS(YNEW-Y) LE. 0.0001) GO TO 2005 19100 Y=YNEW 19200 GO TO 1300 19300 2005 RETURN 19400 END 19500 C 19600 C 107tin r 19800 SUBROUTINE PRE2 19900 C PRESSURES - ITERATES X FOR GIVEN Y AND PRESSURE 20000 COMMON X, Y, P1, P2, Fl, PB, PD, ANG, XP(100), YP(100) 20100 1103 TP=0.0 20200 BL=0.0 20300 DO 1000 J=1,13 20400 P3=Pl*(1+2*(J-7)) 20500 IF(ABS(P3) GE. 50) GO TO 1001 20600 P4=COSH(P3) 20700 Al=ALOG(P4-1) 20800 GO TO 1002 20900 1001 Al=ABS(P3)-ALOG(2) 21000 1002 P5=Pl*(X+2*(J-7)) 21100 IF(ABS(P5) GE. 50) GO TO 1003 21200 P6=COSH(P5) 21300 A2=ALOG(P6-COS(Y)) 21400 GO TO 1004 21500 1003 A2=ABS(P5)-ALOG(2) 21600 1004 TP=TP+((-l)**(J-7))*(Al-A2) 21700 P7=Pl*(2*(J-7)) 21800 IF(ABS(P7) GE. 50) GO TO 1005

D-4

21900 22000 22100 22200 22300 22400 22500 22600 22700 22800 ý2900 23000 23100 23200 23300 23400 23500 23600 23700 23800 23900 24000 24100 29200 24300 24400 24500 24600 24700 24800 24900 25000 25100 25200 25300 25400 25500 25600

P8=COSH(P7) A3=ALOG(PB-COS(P2)) GO TO 1006

1005 A3=ABS(P7)-ALOG(2) 1006 CONTINUE 1000 BL=BL+((-l)**(J-7))*(Al-A3)

Fl=TP/BL Dl=(PB**2-1)/(PD**2-1)-Fl TP=0.0 DO 1100 J=1.13 P5=Pl*(X+2*(J-7)) IF(ABS(P5) GE. 50) GO TO 1101 Al=Pl*SINH(P5) A2=COSH(P5)-COS(Y) A3=Al/A2 GO TO 1102

1101 A3=Pl 1102 TPzTP+((-l)**(J-7))*A3 1100 CONTINUE

D2=TP/BL XNEW=X-Dl/D2

1105 IF (ABS(XNEW-X) LE. 0.0001) GO TO 1104 X=XNEW GO TO 1103

1104 RETURN END

c c c

SUBROUTINE PPT C PRINTS X AND Y

COMMON X, Y, P1, P2. Fl, PB, PD, ANG, XP(100), YP(100) DO 3000 J=1.78 WRITE(3.3001)J. XP(J), YP(J)

3001 FORMATOH . 3H I=, I4,3H X=, F8.2,3H Y=, F8.2) 3000 CONTINUE

RETURN END

D-5

Appendix E-

ýquations Describing Bearin Clearance

in

L

No Errors ho, x = h. +E Cos 8ý

Beari g_lap2. r h.,,, = h,, Cos 8-', 'ýob2Lapefr L-ýý 11

. (L-2x)

100 ýL ý

Beitmouthing

x- < L12

h. +E CosE) + %hbeltmouth. (L-4mý 100 2L 'J

12 <- x- <,

he, x = h,, 1+e Cos 8- %h. betimouth (3L- 4 1 100 2L

Barrelli g x- < L/2

he, x n- ho 11+E COS 8- 100 a 2L

I

12 <' "ý- L

he; x nf h. [i +ECose + L31 . (3L- 4 -x)

100 2L

E-1

9vality

he h. +eGos9+%h,, MZC Sin(2E)±A 02 )l

260-- 11

Beari g TO C::: y heyx = h. + ýý-Lt L-2x- Cos f

1-6 ý.

L

Local Burring at Pbckets

hp4xketsnf ho 11 +c Cos 9-b, -ý. -

I

Combined Tapff, Lvaliýy, Tilt and Burring

hc he, x =f h. +rý. -tt (L-2-4 -. 2 ýJCOS 8+ %h. MZ Sin 2e ± ff- - film ho hoý L /J 200 2) 100 2L hq h. 1+@

,. 6(L-2-x. Cos 0+ %h. MZC. Sin(2E)±n -tt (L -2 % Ntape

. (L-2x) pxkets

[h. L

)] - 200 2 100 2L

b h0

E -2

APPENDIX F- RELATED PUBLICATIONS

The papers listed below have been published by the Author during the

period of this study.

Pink, E. G. and Stout, K. J. 'Orifice Restrictor Losses in Journal

Bearings'. Proceedings of the Institution of Mechanical

Engineersp Vol. 193t No. 1,19799 p 47-52

2. Pink, E. G. and Stout, K. J. 'Applications of Air Bearings to

Manufacturing Engineering'. Paper B4,2nd Joint Polytechnic

Symposium on Manufacturing Engineering, Lanchester Polytechnic,

1979

Stout, K. J. and Pink, E. G. 'Orifice Compensated EP Gas Bearings:

The Significance of Errors of Manufacture'. Tribology

International, June 1980, p 105-111

Pink, E. G. and Stout, K. J. 'Characteristics of Orifice Compensated Hybrid Journal Bearings'. Paper 3,8th International Gas Bearing

Symposiumo April 1981

Pink, E. G. 'The Application of Complex Potential Theory to Externally

Pressurised Gas Lubricated Bearings'. Paper 19,8th International

Gas Bearing Symposium, April 1981

Figures

H -Pt

L 11W

CLEARANCE SICE

2 40 CONCENTAIC

P41,

HIGH CLEARANCE SIDE

Figure 1.1

RIL Axial Pressure Profile

Principles of Operation

II1 11 fII

II%xN. %NT

(a) Annular or Inherently Compensated

(b) Pocketed Compensated

Figure 1.2 Typical Orifice Designs

Figure 2.1 Pressure Losses Local to an Inherently, Compensated Restrictor,

PO 10

df

PO Pressure loss through orifice- area 7cdfh

F? --

-___

h

Inertia I oss es Theoreticat

viscous. pressure prof i te

Pressure recovery in bearing film

Figure 2.2, Pressure Distribution Local to an Inherently Compensated

Restrictor for Choked Flow Conditions.

1.0

1

0.8- (a) Supersonic pres

I sure prof ile [zero friction I

(b) Post-shock pressures [single-normal shock]

PO (c) Typical laminar

-pressure prof ile

0.6-1

, 0.2 H.

'I

shock wave

0III 1234.5 6 -8-, 9- 10 f low area

throat area

Figure 2.3 Comparison of Various Theoretical Pressure Profiles

with Ekperiment - Inherently Compensated Thrust Bearing.

S

pa

2W

2 (i 0

3

2

I.

1

2Rc)/df = 30 df =2 mm

Po I Pa 5

0x Experimental data by Mori ef. at; (Ref. 2.4)

-Various theories(see text)-

h= 29p m

2M

2 (ii)

2 Ov) h=90pm

00

0.

10 20 2-R 'li

30

Figure 2.4 Pressure Losses Local to a Pocketed Orifice

PO

4 CL

V

dR

PO Sýcondary Pressure Loss II at Edge of Pocket

Pressure Loss. Area 7(dth Though Orifice

Area 9d 4 Theoretical Viscous

P, 4- Pressure Profile p

F)

Pressure Recovery in Bearing Film

pllýý

tl% 0

0.8

'0.7

0.6

11-C d

do

0.1 0.2 0-3

Figure 2.5 Experimental Qý at Choked Conditions Against do Ruby Jewels

0.9

CL8

Q5 10.6 0.7 0.8 Q9 Figure 2.6 Correlation of Cd , ýith Pressure Ratio'Based, on

Recovered Conditions in Pocket

n-7

00 0 0 00 'Ou 00

CCL 0 1ýý "0 0ý 0 C(r 00 0

0

0 P. R- =347.8

d=0.09-), 0.30mm 0 b- = 0.15 --*0.41 mm

pl, i/

3

p

- "P00'a

I

Figure 2-7 Comparison of Various Theoretical Pressure Profiles

with Ebcperiment - Pocketed Compensated Thrust Bearing.

2 Ro/dR 7.5 AR B-Omm do 0.8 mm 00

.\41.0 mm

D Po / Pa 3 0

0 ox Experimental dafa by

Mori et. al. (Ref. 2-4) ==Various theories (see text)

0

0 h= 29pm

X2 X3

5U h9

2.5 s 2R

IS

-

'7

h

Figure 3.1 Flow Element

p P+ dP L. dy

0.01 0.1 1 As 10 Figure 3.2 Relationship of Feeding Parameter with Kgo

Pd PO

Figure 3.3 Pd/Po Against. Feeding Parameter

0

/is t;

Figure 3.4 IT Against Feeding Parameter

0.01 0.1 Asý 10

d Pd

dh Po - Fj

0.01

Figure 35

W Aý

Sensitivity of Orifice Pressure Pd with Changes

in Film Clearance.

10

-1i; -- -

dz

ov

ý(Pu) dx Tx-

Y, V X, U

Figure 4.1 Elemental Cube

Figure 4.9 Flow Net of Two Sources Close to Each Other

sources sinks sources sinks - sources

01 0- k=2-fb

_L/2

ýj

L

0.,

XD n

0. -. 1

.

r -2

0

k=l 0

- k=O

-

rz r

U101 U- 1,2 -0

(a) Source and Sink Arrangement

230 -3 (b) Flow Network

Figure 4.3 Single Admission Journal Bearing

y

Figure 4.4 Annular Thrust Bearing

v

, 69 n

4x n -,

27c n

x-y -21ane

Figure 4.5

0

In ýj - In I Ro R [R-c

u-v Plane Conformal Transformation

"0.

n holes equatty" spaced

boundary boundary

s rc in ou es s ks c; ources sinks sources

0- k=2-0

-kzl

2 7c

0- 11

--

ý4

-F k=0 -0

r=-2 r r=l


k=-l -0

0- k=-2 -0

I

Figure 4.6 Annular Thrust Bearing,.

c

sinks sinks sources

00 a

7* 7c 0 n

-01 -

0

0

sources sinks sinks

00k= 2--0


1. ZD

k: Ø-O

k=-l-. o

n, -- k=-2-0

-� �4

(b) Flow Network

Figure 4.7 Double Admission Journal Bearing

Qd 1 Pa nd/O 0.1

3

2

1

N; 10

K=5

Ný 2

0 t2 t4 ±6 tB ±10 range of summing terms

Figure 4.8 Effect of the Number of Summing Terms on Calculated

Film Pressures

., /read LAUD

read N5, nd/0, Pd/Pa

u o ournal or , jannular thrust,

I read Rc, N, RO/Ri

0ý I incre ent oc

increment X calculate y

0( 0-0912

Fmirror aboutaxes I

-plotstr amlines

/read P/P, syrr:. al: x: ý7

T increment V= 0-ly calculate 7 MU

mirror isobar

Zrp-lot

4isobar

-Plot centrelines,

end

Figure 4.9 Flow Diagram for the Computer Program Used for Plotting the Flow Net Of Single Admission Bearings

Pd

p L

4.

100

N5

10

P2 2 L -P a

P2_p2 d aý

Figure 5.1 Line Feed Correction Factor V; t-

0.01 0.1 nd

Figure 5.2 Determination of

1

I

p

PO

I

m

Figure 5.3

with, clispersion

decreasing

Ilk

PO Effect of on Orifice and Film Pressures

line feeding

U. V-I Asý 10

Figure 5.4 Orifice and Film Pressures Against Asý

ý, -W R Cd 0-8

1 4 4 ý ft ýf . - n T

0.6 1 1 1 1 ////

,

0 .6 - - 0. 0.. , I M

0.2

n I

. I M H

G

0.01 0.1 1 AS9 10

Figure 5-5 _U Against As 5 for Various YX

0.01 0.1 1 As-9 10 Figure j. 6 Sensitivity of Film Pressures with Changes in Clearance

for Various //X

i+J, j

ll 01 1-, 1

01 ---+

AY 1

i, j-i 11) ij-i

x

GA AY

AX cm

Figure 6.1 Elemental Area I

i+2, j-l x i+2, j x I i*2, j+l 1 x

i +1, j-2 X +lyj i+l, j+l

x i+l, j+2 X x IE <

x x x -E ix x

i, j-2 ij I, j+j 41+2

X x x x i-l, j-2 j-1 j J+2

x 1-2, j-1

x i-2, j

x i -2, j+l

Figure 6.2 Grid Network Used in Finite Difference Analysis

assign pressure values to pockets

set filmp ssures

relax film pressures sequentially downstream

of pockets

f ilm pressure convergence

test

calculate flow from each pocket to surrounding grid points and through the respective orifice

I

calculate new pocket pressure from Newton Raphson iteration to give

flow rate equality

pocket pressure L co

t Sul Onvergence

tt st est

I I

Figure 6.3 Routine for Evaluation of Film Pressures

d

Cý Pbcketed OHf ice

A Lýý df

Inherentty Compensated Orifice

Figure 7.1 Typical Journal Bearing Designs

0 L w

E, - eccentricity ratio at bearing centre ptane 6T - t; 't eccentricity ratio wrt ends F-I - F-2

2 - eccentricity ratios at ends

%filt- E- x 100

Figure 8.1 Geometry of Tilted Bearing

I =1 C,

j =J SPAN41

L -1

JDIV+'

w

Ti,

Figure 8.2 Axial and Ciroumferential Divisions

i

býaring

ILý 3. XE !0. (- -i ,- N-73k .0a *--

X

J. x -E ýb - <-----> , ---N -00yC0ý rc

x<

j=1 jJSP

L

IF

7ý D

Figure 8.3 Grid Network

central admission a/L =0.5

PO /Pa =5 Aj = 0.5

F. =0 pocketed prifices 6 =-0.5

0.3 w

(Pc7 Pa)

0.2

0.1

0

L/D

(a) Single Admission

Figure 9.1 Circumferential and Dispersion Losses

012

Q

OJ

w 11 LD (R-P, )

., 0. -.

aoubte admission a/L =0.25

PO I Pa S

S. =0 pocketed orifices E ='0.5

01 ý

0.1

VO

L/D (b) Double Admission

Fiý; ure 9.1 (con-b. )

1, - -, ..

0.5

0.4 w

LD (Ma)

0.3

0ý

- fl_c

0.4

0.2

0.1

o �: 0

L/D =1 double admission a/L = 0.25

PO /Pa =5 As; = O. S

F6 =0 pocketed orifices

0.5 F, 1

Figure 9.2 Effect of on Load/Deflection characteristics

0.6

0.5

w 1) M6-ý)

0.4

o. 3

0.2

0.1

ýdoubte admission

alL = 0.25 Po /Pa =5 Asý = 0.5

2. =0 po'cketed orifices

dt's

0

O. S E

Figure 9-3 Effect of L/D on load/Deflection Characteristics

double admission a/L = 0.2S

Po/Pa =S Aýý = O. S

S. =0 pocketedorifice 1/. X =1

r-

PL

f PH

L/D 0 -----L/O

L/b = 1.5 --L/D =2

PH'

PL

Pa

2

1.0

0.8

P,, P,, 0.6

0.4

0.2

(a)

0 0.5

Figure 9.4 Bearing Film Pressures

n

(b)

0.6

0.

0.1 w

0

0.2

0.1

4-- aol

L/O 1 clcýuble admission, ------A a /L = 0.25 S, =0 pocketed orifices

Cd 0.8 w

- - ----- ----- -

P-/P, =2

' 77 4 4 - 1 72ýý 7

_ P 9 1P, =2 8

5 - N H

As; 10

Figure 9.5 Load Capacity Against, MT,

^ If I

U. b

0.5

0.4 w

1) Ro-Pa)

0.3

0.2

0.1

A

I I

L/D=1 cloubte admission a /L =0.25 Po / Pa =5

fr. =0 pocketed orifices

Aiý=0.5

0.1

0.01

10

ý 0.5 E v 1

, As-ý Figure 9.6 Mad Capacity Against Various

o.

0.1

w Di rä,

Q

I

L/D=1 double admission aIL =0.25

::: P. / P" =5 =0 pocketed orifices

0.5 Cd 0.8

1 -ý=

-::: III __ -- II I

(II

!L ''I'

4- 0.01 0.1 A,

Figure 9.7 Loacl Capacity Again*st Asý - Various

10

a

0.5

0-ý w

LD (P,, -R)

0.3

0.2

0.1

L/D =1 double adrýiision a/L = 0.25 A,; = O. S

=0 pocketed orifices

R/R2 oa

0 0 0.5

Figure 9.8 Load Capacity Against E- Various Po/Pa

Q6

, 0.5

w

0.4

-0.3

-L/D =1 Po/Pa =5 AsF, = 0.5

9,, =0 pocketed orifices I /, x =1

a/L=0.25

0.5

0.2 -

0.1

0 0 0.5 1

Figure 9.9 Load-Capacity Against, F, -, Various a/L

0.6

0.5

0.4

w LD (e-Pa

0.3

0.2

I

L/D =1 double admission a /L = 0.25 P,, /P, 5 Asý 0.5

pocketed orifices Eý= 0

inherently compenvated orif ices Y.

01

O' 0 0.5 61

Figure 9.10 Load Capacity Against F- - Various Types of Compensation

13

O. b

0.6

0.4

L/0=1 double admission a/L =0.25

P,, / P,, =S '/-x =1 Cd = 0-8

pocketed orifices JL=O

irherentty compensated ori f ices k= 00

Asý=l

0. s 0.2

0 0 0.5

0.1

..; E

Figure 9.11 Mass Flow Rate-Against E

0.0

0.0 Tq

(Po7R)LD2

0.0

0.0,

0.0

0

(a) Single Admission

Figure 9.12 T. Against As5 - Various

0.01 0.1 1 A, T, 10

0.06

0.05

0.04 Tq

(Q, 7R)LD7 0.03

0.02

0.01

04-- 0.01

Double Admission

0

Figure 9.12 (cont. )

0-1 10

As

I

L/D=1 double admission a/L =0.25 Po /Pa =5


Asg

0.10

Tq

(Po-R)LD2

0.05

0.5

10

0.1

0

0 -- I

0 0.5 6T

Figure 9.13 -f,, Against ET- Various AS'ý

1

Po /pa =5 0.08 Asý = 0.5

I k- =1 5- W =0 ET = 0.5

0.06- a IL =0.25 Tq pocketed orifices . 9. =0,,

(P,, -Pa) L D2 -- inherently compensated

ori fices F6

0.04-

0.02

a /L =0.5 potketed or inherently compensated orif ices

0 012

Figure 9.14 Y'q Against L/D Ratio

0.10

I

L/D =1 double admission a/L = 0.2S N, ý = O. S


Tq (P. 7R)LD2

1

0.05

P,, /R,, = 2 s

0 0.5 ET 1

Figure 9- 15 Tc, Against CT - Various Po/Pa

0.01

Tq , TP-,

) - Pý) LD2

0.05

L/D =1 doub(e admission a IL = 0.25

Po /Pa =5 Asý = 0.5

pocketed orif ices

inherently compensated orif ices S. = 00

A 0.5

Figure 9.16 T. Against various Types of Compensation

0.5

-iw

Q4

Q3

a2

L /D =1 cloUble admission a/L = 0.2S

Po / Pa =S A, ý 0.5

1.0 pocketed orifices dR /D 0.03

corrected line' feed"Model finite difference solution

A

0.1

0 0.5 e, -1

Figure'9.17 Comparison Between Corrected Line Feed Model and Fini-ýe Difference SolAioii - Varying n

0.

7

O. Z

0.3

o.

L /D =1 double ad mission a/L = 10.2S Po I Pa =S

Af = 0.5 i. =0 pocketed orifices n 0.06

0.03

d%= 0.01

/ff/

corrected line feed model v finite difference solution

,A 0.1

0 0.5 E. 11

Figure 9.18 Comparison Between Corrected Line Feed Model and

Finite Difference Solution - Varying dR/D

v

0.4

w o. 3

0.2

0.1

L/D =1 double admission -a/L = 0.2S

P/P 0a =S A, f = O. S

S. =0 pocketed orifices E = O. S

0.05 d, /D 0-10

Figure 9.19 Combined Effect of n and dR/D on Load Capacity

Po

LID = 0.5 alL = 0.5

n= 16 P', 1 P', = 3.04

d. = 0.09mm h, = 10.5jim Ck= 1.2mm

0.16 QD = 0.031 A't = 1.41

Pa

PO

experiment complex potential theory finite difference solution

P (a)

Figure 10.1 Experimental and Theoretical Pressure Profiles

Concentric Conditions

PO

L/D = 0.5 alL = 0.5

nz 16 ý/P, = 5.08

d. = 0.09mm I. I. = 10.5)jm dR = 1.2mm 5=0.16

dRJO = 0*031 Asg = 0.846

Pa

PO

77::::

t, -


Pa


PO


Ra

P, 0

pa


Ll ID =1 PO

alL = US

PO / P. = 1.68 do = 0.26mm

In =

h. z 30jum dR 2 1.8mm S=0.42

dRID = 0.047

I

Asý = 0.86

NJ p

PO

experiment -- complex potential tFewy finite difference solution,

Pa

(e) - .-


Po

x

LID =1 a/L = 0.2s

n=8 PC IR = 3.04

d, = 0.26 mm h. m 21.1, um dR z Umm 5Z0.53

41U 3 0.047 Age 2 1.30

x


Ra

PO ,

(r) Figure 10.1 (cOnt-)

pa

po

x

experiment complex potential theory finite difference sotution

(g)

Figure 10.1 (cont. )*

ý PO

pa

Po


Pa

(h)


1 5z- --

PO

PO

.

(i)

pa


. comptex potentiat theory finite difference solution

.3

P/r pa

2

1

3

21

11

.4

h�=31.5, um 4=0.75 A, ý=0.43 ho = 35.5)um g. = 0.72 Aj = 0.30

(j)


L /D = 1 double adm a/L = 0.25

n 8 pi, I P, 3.67

d. = 0.31mm dR= 2. Smm b 0.08mm

dR/D O. Os Cd 0.92

h. = 30. um dR = 1-8MM i= 0.42

dRID = 0.047 AZ = 0.86

e)Wiment finite diMpenc-e

solution

- corrected line feed

,m del -,,, ".

la

load capacity W Newtons

mass flow rate G xiTskgls

28.6 17.8'

29.7 15.8

30.7 15.0

(a)

Figure 10.2 Experimental and Theoretical Pressure Profiles

Eccentric Conditions

R 0

/

ho = 21.1, um dR ý 1-8MM 9=0.53

dRID = 0.047 = 1.30

m9miment finite difk*enc-e

solution corrected line feed

ffodel


mass flow rate G xlTskg/s

70 31.8

73.9 29.3

81.2 27,5

(b)


R 0

dR 1-8ýlm s 0.53

dRM 0.047 AZ 037

pa

e4wiment finite diffefenc-e


rnodel


mass flow rate GxlTskg/E

168 62.7

168.9 62.1

183.2 58.7

(c)


/

119-

"d R «=

9-1.4 &Jlfi

0 lAMM

,= 0.53 dpnl = 0.047 Aj = 0.51

e)qvriment finite diffefencte


model

9

R

a


mass flow rate Gx 1TS kg/s

286 107

28S. 9 108.2

330.2 101.2

(d)


PO

L/D 1 a/L 0.2S

n8 Po /Pa 5.08

1/1 . df = 0.66 mm

30jim 5.5

dRID = 0.017 Aj = 0.359

N

p

a

mperiment finite difference

solution correde6 tire feed

rwdel


mass flow rate 6.1TS kg/s

138 88.8

142.3 92.8

144.0 93.6

(e)

Figure IO. Z (cont. )

3

%a

2

1

3

P/P a

2

ol

hH

j

L/O = 1 double adm a/L = 0.25

n 8 R, I Pa 3.67

d,, 0.31mm dR= 2.5mm b= 0.08 mm

dRA3 = 0.05 Cd = 0.92 e= 1 B. 9, U m

po

000 0 hL

00 00

0

0

00

00 0 CD OD 0

o experiment

finite difference Pa h,, 3 1.5, um 4=0.75 A, ý 0.43 0.6 h, 35.5pm 8. = 0.72 As; 0.30 0. S3

hH I


L/D = 1 double admission a/L = 0.25

n 8 P,, I P, 3.67

d. 0.31 mm dR= 2.5mm b= 0.08mm

dR/D = 0,05 Cd = 0.92 e= 1 8.9, U m

PO

3

Ra

0 0

0 0

o experiment

finite difference Pa ho=31.5, um 5. =0.75 A, ý=0.43 8=0-6 h, =35.5, um *. =0.72 A&=a30 F-=0.53

(g)


(a) Pocketed Compensated Orifices

Figure 10.3 Experimental and Theoretical LOad/Deflection Curves

12 e pm

0.4

w LID =1 double admission a/L = 0.25

n8 PC /R S. 08

df 0.66 mm ho 30jim (air gauge) 2=5.5 Z_-N,

CiRAI = 0.017 AST = 0.359

0.3

experiment finite difference solution corrected line feed model

0.2

0.1

0 10 20 e pm

30

(b) Inherently Compensated Orifices


0.5

0.4

. -f +2S, 37 ro- -(pi--pl)

3

0.3

0.2

0.1

0

0.1 1

10 0.031

+

+ clý,

0.,, ý . -ýj 1 '0 - 4)

X00 X

theory X experiment Po /R=1 . 7--b-7.8

x F-=0.25 0 F-=O. t

+ 8=

0.1 0.2 0.4 0.6 O. B 1 Asý


11

Figure 10.4 Load Capacity Against Asý

- Experimental and Theoretical Values

(L4

0.3

w LD (Po- Pa)

0.2

0.1

0

0.1 1

"1

LJL-JLJ

LM=l. n=B ýN=0-008,

UV ++ Pr--lrj +

+

XX I

theory X experiment P,, /P,, --3.0-7.8

xE=0.25 oE=0.5 +E=0.8 XX

0.1 0.7 0.14 0.6 0.8 1 Asý

(b) Inherently Compensated Orifices


23

L /D = 1 double admission a/L = 0.2S

O. S R, I Pa = 3.67 d. = 0.31 mm dR= 2.5mm

0.4 - b 0.08MM 0 dR /D 0.05 0

Cd 0.92 0 0.3

0.2 - o-experiment

finite difference

0.1 ------ h,, =31.5, um Z=0.75 A, ý=0.43 ho=35.5pm k=0.72 A&=0-30

1

10 20 30 e )uM

Figure 10.5 Load Capacity Against Deflection

- Experimental and Theoretical Values

0

G g/s

0.8

0.6 10 20 30

e ju m

Figure 10.6 Mass Flow Rate Against Deflection

- Experimental and Theoretical-Values

20-- L/D =1 double admission a/L = 0.25

n8 Po I Pa 3.67

d. 0.31 mm dR= 2.5mm Kb=0.08mm

N/jum 00 dR /D = 0. OS Cd 0.92

0

0 0 10 20 30

eum

o experiment

finite difference ho=31.5, um Z=0.75 Ar. ý=0.43 ho = 35.5. um Er = 0.72 Asý = 0.30

Figure 10.7 Radial Stiffness Against Deflection

- Fxperimental, and Theoretical Values

0.10

Tq

P. ) L02

0.05

LID =1 a/L = 0.2S

n=8 Po /Pa =4/

/0-

do= 0.26mm .0 ho= 30, um dR = 1-8mm

0 9=0.42 dRID = 0.047 0 Aj = 0.42

0

X .0

0

0

0 experiment finite difference solution corrected line feed model

0. 0.5 ., ET

Double Admission

Figure 10-P Torque Against Tilt

- Pink's Experimental Data and Theoretical Values

400

300

KA

Nm radian

200

100

0

L/O = 0.5 a/L = 0.5

n =16 df = 0.33 mm ho = 19.7pm 9=4.2

df /D = 0.0087 Vx= 0.68 W=O

Po / Pa Asý

3.04 0.71 5.08 0.42 7.80 0.28

a -experimnt KT. 1. (Ref corrected line fýpd model

234567 RO / Pa

(b) Single Admission


0.10

q (P- p

0 a)L2 0

L/D = double_ admission a/L = 0.25

n 8 R, I R, 3.67

d. 0.31 mm dR= 2.5mm b= 0.08mm

dR/O = 0-05

Cd = 0.92

0.05

a 10

0

/0

20 30 el pm

o experiment

finite difference ho=31.5, um k=0.75 Asý=0.43

- ho =35.5, u m P. = 0.72 A,; = 0.30

Figure 10.9 Torque 1, gainst Tilt

- Grewal'B Experimental Data and Theoretical Values

w

PL L/O = 1.5 doutge admission a/L = 0.25

Po / Pa =4 n= 12 slots/ raw

PH ho= 24.5. um K96= 0.49

7p P. a PH

0 N

. oe

100, 3-

oe 5 10 15 20 25 S. N, e jum

PL

2-- -experiment line feed model (Ref, 6.2)

(a) Film Pressures

Figure 10-10 Film Pressure Characteristics (Slot Bearing) Against

Deflection - Ebcperimental and Theoretical Values

0.5

0.4

Po- Pa

03

02

0.1

0

e um

(b) Pressure Differential

I


w

LID Z1 PL alL m 0.2s nz8

P. /pa = 5.08 do= 0.26mm h. = 30. um dR = 1.8(ntn PH 5=0.42

dRID = 0.047 Aj Z 0.28

AK PH

7Ra

3--

10 io 30 eUM

experiment finite differeme solution

2-- corrected line feed model

(a) Film Pressures

Figure 3.0-11 Film Pre: ýsure Characteristics (Orifice Bearing) Against

Deflection - Experimental and Theoretical Values

a

0.

PM-PL

Po- Pa

0.

solution !d model

0.1

ov 0 10 20

e um 30

(b) Pressure Differential

Figure 10-11 (cont. )

L/D =1 double admission aft = 0.2S

n8 Po I Pa 3.67

d,, = 0.31mm dR= 2. Smm b=0.08mm

dRID = 0. OS Cd = 0.92

os

0

//Th �I

0.1 0.2 0.3 0.4

-ý7

o experiment

finite difference ho=31.5, um 9. =0.75 Aýt=0.43 ho=35.5, um *. =0.72 As; =0.30

1.5

pm- pa

1.0

Figure 10.12 Pressure Differential Against Load Capacity

Experimental and Theoretical Values

Figure 11-1 Variation of Load Capacity Due to the Departure of ho from Optimum

0 0.2 0.4 0.6 O. b 1.0 12

0.4

w

0.3

0.2

0.1

00

UD=l a/L=0.25

Asý(Opt) 0.42 P. / R. 5

S. a25 dK/D=0.03

n=B \ 1.0

do 1.2 djopt)

OY pi cat,

w

e/ ho 0.2 0.4 0.6 OB 1

Figure 11.2 Variation of Load Capacity Due to the Departure of do from Optimum

A

I

L/D=1 top orif ices Ot = 0.8 do a/L = CL25 bottom orifices Obý 1-2 do

Asý = 0.42 P. ý P, =5 Ot = 0.9 d.,

9. =CL25 Ob = 1.1 do

DA 4/D=0-03 n=8

all orifices 1.04

0t1.1 d. Ot = 1.2 d,, 0b 0-9 4 Obý 0.8 d,,

Top

Qý

w

Li -

deflection from nut[ positioD hc)

II nv 02 0.4 0.6 0.8 1.0 1.2

(a) Variation of Load Capacity

Figure 11.3 Effect of Mismatched Orifices

Top

0.2

e h,,

ol

0

I - 01

-0.2

top OrifiEes oversized bottom orifices undersized

total % variation in orif ice sizes from winat 10 20 30 40

top orifices undersized 'bottom orifices oversi7ed

(b) Variation of Eccentricity at Null Position


0.5

0.4

w

0.3

01

LID=l a/L =0.25 As'ý = 0.42

Barre(Lod P. / P, = 5 ý, =0.25

40%h.

dk/D=0.03 20% h. ertgrs n=8

Fý

-

w

20%h, 40%h,

Bellmouthed

% ol w

0.2

Tapered 40%h. L

w

e/ho

0.2 0.4 0.6 0.8

Figure li. 4 Effect of Non-Parallelism on Load Capacity

Figure 11.5 Effect Of Out-Of-Roundness on Load Capacity

0 0.2 0.4 0.6 0.8 1.0

w

0. '.

0.

r

L/D= 1 a/L=0.25

Asý 0.42 P. I pa 5

56 0-2 5

-, dit /D = 0.03 n8 !1=o

h,,

0.1

0.2

0.5

et ec

w

eV L 0

0 0.2- 0.4 0.6 O. B

Figure 11.6 Effect of Bearing Tilt on Load Capacity

L/D=l a/L=a25

0.4- Asý =0.42

ditiD =0.03 n

0.05 0.3 0.10

, a= 0.15 h. ý10

02

0.1V " '4,

w

e 0v -1 1

Yho I

0 0.2 0.4 0.6 os

Figure 11-7 Effect of Local Burring at Edge of Pocket on Load Capacity

.

w .

0. -

�� U, 4

(ý w

r

L/D =1 double admission a/L = 0.25

n Ma'= 7.8.

d,, = 0.11 mm h, = 11.9jum (airgauge) dR = 1.2mm 5=0.21

RID = 0*031 Asý = 0.55

P

:1 v04ae

)um 12


Figure 11.8 Comparison Between Experimental and Theoretical

T. naA Cananitv ITnnIndir-a- rffPt, +.. -z evp

10 experiment theory

6% Bell -Mouthed ; 6%Ovality; 3% Error in Straightness

Burr Bearing Ge*n-*try- Absolute Error he

I

Loading Orientation Error in h. in Straightness Ovality (air gauge

accuracy) d.

4L No Burr .

H 0 6% all

L 0 (4) all *S%

H oL With Bkffr

H "0' 1ý . 6%

all L 0.05

0.4

w

0.3

0.2

0-01

0

L/O =1 doubte admission a/L = 0.25

n8 PO/Pa 5.08

. df = 0.66mm 110= 30, um (air gauge) S=5.5

dRAI = 0.017 Aj = 0.359

experiment

theory 2% Beil. -mouthed; 2%ovaidy; I%Error in Straightness

Bearing Geoffwtry - Absolute Error Loading orientation Error in tU in

Straightness Ovality (aff gauge df accuracy)

Pressure Recajerv

ftessw lecovery

all -2%

all L

2% 42%

-

-�I'

0 10 zu

e ji m

(b) Inherently compensated Orifices


I

x

:. -Ilex ýe

y vx ýe2 2 eres + eif tari'[ eY

ex

A

Figure 13-1 Typical. BearingIGeometry

w

I

w

LDP.,

u

-(a) Load Capacity

degrees

10 Cn 2

67 &) r, 100

P. hi

1 10

(b) -Attitude Angle

Cn 67w rl hj

100

Figure 14-1 Effect of Cn on Aerodynamic Performance

4

II SIU1

Q 3

D

1

II 1ý / Cný6]

w

fi ni te dif terence solution Ausman (Ref. 13.2)

x- Raimondi (Ref. 13.4) o- Elrod Malanoski (Ret. 13.5)

016 0 Q2 0.4 Q6 Eu1

Figure 14.2 Load Capacity Against Aerodynamic Bearings L/D =1

5

w

D2 Pa,

4

L/D 2 C, = 6

w

3

2

1

finiteditterence solution Ausman (Ref. 13.2)

x Ra i mond i (Ref. 13.4) 0- Elrod & Matanaski (Ref. 13-5)

Q5

ON 0 ul 0.4 0.6 E 0.8 1

Figure 14-3 Load CaPacitY Against Aerodynamic Bearings L/D =2

System

tan

Suff ices A- aerodynýmit cont6bubon s- aerostatic -a res - resultant

ws rI ad

/ýres

force Diagram

WA rad

/-tý

w Ares

WAtan

Wres

Figure 14.4 Vector Addition of Aerodynamic and Aerostatic Loads

rnri

0

Dz

r*

Cri= 6 /4

inn)

ýo ol lo, 1 . 10 -/U. "3

. 00,

N

'0"

erodynamic- -A

Eý -- 71,

ri rl 1 7 2

4 -1.0 1w W

LID= 2 a IL = 0.25

Pa d ID = 0.03 =8

C --6 1 . n

Aemstatic t Hybrid ý0.8 Asý = 0.7 5

3- P. /P3ý= 5 4

Hybrid

-0.6 w 2

[)z (2- P, ) 2-

Ae-rostatic L Hybrid Only

0.4 -Aerostatic

1 1

02

0 0.2 0.4 0.6 ERes O. B 1

(a) Load Capacity

Figure 15 -1 Theoretical Predictions for Hybrid Bearings

- Various Cn

Ey 0.8 0.6 0.4 0.2

0

CD

(b) Attitude Angle/Shaft Locus

(A-)

0.2

0.4

EX

0.6

0-8


Aerodynamic 100 Oll

- Hybrid

w O2I

3

2

1

0

'

alL = 0.25 d /D= 0.03

n =8 Aerostatic I Hybri

P, / P, ý= 5 L/0=0.5; As'ý=0.5 L /11 =1; A, ý = 0.42 L/D=2; A6zO. 7

L/D=2

w 02 (po- Pa. ) Aerostatic & Hyb rid Cnz 2 Hybrid Only

F0.6

-Aerostat

0.4

--- Aerodyna m ic Cn=2 \\\,,

FO. 2

1 /

/0.5

O. L FA nP Res

Figure 15.2 Theoretical Predictions for Hybrid Bearings

- Various L/D

F'

5

4 w

D2 pa

3

2

1

CRes ,

1ý Figure 15.3 Theoretical Predictions for Hybrid Bearings

- Various Po/Pa

1.

w D'(Po-Ri

0.

a

0

0

LID= 2 P, IR= S

d ID= 0.03 n8

A, 5 0.7

a/L=0.25 hybrid

a5

. 6- 0.25

0.5

.2 aerostatic

n 0.5

6Rec,


- Various a/L

D2

'6Res


- Various As'ý

v 0.5

w,

D'(Rc- Pa

ERes


- Pocketed and Inherently Compensated orifices

v 0.5 1

A

w

LID=2

AerosiatiE L Hykbdid

a IL = 0.25 P, / P, = 5

Dri f ice Slot + 1.0 As'ý = 0.7 Kg. =O. S

S. = 0.25 n =12 3 dIt 10 = 0.03 ,

n=8

0.8 w jjykLid I: h--2 R-P. -Orifice

Slot

-0.6

Aerostatic 2- 0 rif ice

Slot

0.4

0.2

0.2 0.4 0.6 E 0.8 1


- Pocketed Orifices and Slot Entry Bearings

1.2

1.0 w

02 (p p .1 a

0.8

0.6

1 f,

2

Hybrid Cnz 2

0.4-

0.2-

0 0.5 1 ýRes

Aerostatic

LID=? aft = 0.25

P. M. =5 d 10 = 0.03

n8 Asl 0.7

tire of m in/max h through oritice

2 between orifices/,

FiVre 15.8 Theoretical Predictions for Aerostatic and Hybrid Bearings

- Effect of Orifice Orientation with Respect to Load

S

4

a3

2

1

1

P/r Pa

Low Clearance

(a) Axial

Figure 15-9 Typical Pressure Profiles for Hybrid Bearings

Aerodynah .c min/max hA

Hybrid min /max h

I. S

Aerodynamic Cn= 2 Aerostatic [Cn': Ol

---Hybrid Cn=2

A Aemdynamic min/max h

w

min/max hT w

i- /I �I

E=07

(b) Circumferential

at the plane of orifices

(c) Circumferential

at the bearing

centreline

I

LID= 2 alL z 0.25 POIR= 5 d 10 = 0.03

0.7

w O2F

ll-ýio H*id Csr- 2 Finite Difference

w supe -..

on D2 (R-ý) A

OLB

1-0.6

2-1

AKmtatic

ljý

i kcl

0.6

0.4

OL5 ERes

(a)

Figure 15-10 Hybrid Bearings - Comparison Between Finite Difference

Solution and Powell's Su-perposition Method

w

D21

(b)


0.5 LCRes

1

L

w 02P

L/D= 1 a /L = 0.2S P. / P. = S d ID 0.03

n Ac 0.42

4-1

w

D C) a) 0.0 2 (R- R

Q8 OA

3- Hybrid Cfv-- 2 0.4

Finite Difference SupeWition

-0.6 WS+ IVA

2-

-0.4

-0.2 Aems ta tic

0.5 ORes

(0)

1


I',

UD= 2 a/L= O. S 0.6 e/R=5 0.6 d /D = 0.03

n=8 Aj = 0.7

Hybrid In=2

Finite Difference Superposition

Aemstatic

0.5 ERes

1

(d)

1.4

1.0

0.8

0.4

0.2

0

Figure 15.10 (corit. )

I

*

L/0=2 a/L= (L25 R/P. = 2 d 10 0.03

n A, c 0.7

4-1

Hybrid Crf: 2

Finite Difference Stporposition 0.4

Aemstatic

0 O-S -. ERes

(e)

4

w D2, Pa

3

2

1

0


w

[)2 Fa

(r)


Q5 ERes 1

I

kýl LID= 2 a/ L 0.25 P, I P, S

d /D = 0.03 OL8 n=B

A55 = 0.7

inherentty cmVensated orifices

Hybrid Cn: --2 Finite Difference Super? os i tion

WS+ kVA

erostatic

w 0.5

(g)

I. 4

l. C

-- ý W,

- D2 -(Po - Pa)

0.1

0.1

0.

C'


1

0%

w

I

ERes.

Figure 15.11 Hybrid and Aerostatic Bearings - Comparison Between

Finite Difference Solution and Results from M. T. I.

os 1

02

0

L/D=2 a/L = 0.25 d-/D ý 0.03

n8 Asý 0.7

4-1.0

.w [)2 (p p

0.8 Hybrid

-0.6

'0.2

n

Cn= 6

Cn=2

C Crý'

'Aerostatic

--, Modified Superposition Finite difference

0.2 0.4 0.6 0.8 1

(a)

Figure 3.5-12 Hybrid Bearings - Comparison Between Finite Difference Solution and Modified Superposition Method

w

D2 F

Hybrid Cnz 2

0.6 L/UýZ /! -, I

1/ . 7/ //"

I. *- LIM

1- O2

0.5 ERes

aiL= 0.2S* polp, Z5

d 10 z 0.03

ý--JD LID=l ; Aj; =0.42 LID r-2; A95 z 0.7

w

DI (p_ p7)

(b)

1

riligure 15.12 (cont. )

D2

0.5

(C) ,

ERes


r

w

D2* Hybrid

Aerostatic

P. /P, = 2

I

0.2 U-4 U-6 4es 0; 6

(d)


w

C)2 (p -F ,, I 0i

0.5 ERes

(e)


KEY

1- Test Shaft 2- Sleeves 3- Hydrostatic Stave Bearings 4- Test Bearing 5- Pneumatic Load Cylinder 6- Load Adjusting Mechanism 7- Pressure Transducer 8- Capacitance Probes- 9- Pultey

Figure 16.1 Schematic Diagram of Test Rig

w

Figure 16.2 Test Bearing Mounting Arrangement

9 240v pressure

a amp,, f, 4 ac Nnsducer traisducer

P S. U.

mplifier ýearing Load

S. U.

ranWumr pressure t sd transducer amplifier

Bearing Sup* Presswe

P. S. U. D-V-M.

tacho a- ral glenerator

=±T1

_

Qq

X-Y Shaft-, *e& 4==d

plotter

capacitance probes

transd"r VVVV

n*ter P S. U. ýIVýM

C- D

c A+B C+D

oscilloscope

y analogue computer

Film Thickness/ Journal Locus

Figure 16-3 Test Rig Instrumentation

transducer amplifier output

. ..... . ... .... ...... .......... ...

77-

........ ........ ...... .

........... .... ----the6reticol " o mea sura

......... ..... . ............... ..........

....... ..... . ....... .... 7'ý -7'

pressure Bars

Figure 16.4 Pneumatic Load Cell Transducer Calibration Curve

* pm

. .t..

I

?I 'A' . ... ..... ...

output from Wayne Kerr amplifier TE 600B

Channel 'A'

Figure 16-5 Calibration Curves for the Outputs of the Wayne Kerr Amplifier and the Analogue Computer

(a) VX: ýýY z circuit

tan- I Circuit

pigu're 16.6 Circuit ýIagram for Analogue Computer

fjTj-'-+-ITY

circuit Y'. 1.0 . 111.

. Xf

volts

Circuit

tan-lDfl cir(uit LX'J volts

x of

, Ott&

Figure : L6.7 Output Curves from Analogue Computer

-1.0 0 4I. V

(b) tan -1 Circuit

Frequency Meter

I-.,. II Pick-up

Gear Wheel

Figure 16.8 Set-Up fOr Calibrating the Tacho-Generator

AIR IN

(9 on /of f

transducer (2)

Figure 16.9 Air Supply Circuit

CL

Figure 16.10 Oil Supply Circuit

)

-t

Figure 16.11 Diathragm Valves

Figure 16.12 Typical Test Bearing

Jewel placed over hole. '77 Rolled Flush with Bore.

0-08mm thick spacer pUced over jewel 4 sellotaped in

ition. Rotted Flush with Bore.

Spacer, of thickness equal io the required pocket depth, placed over jewel 4 sellotaped in position. Rotted Flush with Bore.

v

Sellotape ý spacer removed. I

Figure 16-13 Procedure for Mounting Jewels in Pockets

£i

'0000(

N177 I I-td

tam ,L 10 "o

Figure 1 16.14 Roundness Traces for L/D. = 1 Bearing

. 1,

_.

(... /

___ ___

11pm

00

�I

Figure 16-15 Axial Profile, Traces for L/D I Bearing

leutwou 0 WW os

WI

Figure 16.16 Test Shaft Assembly

1.0

0.8

w Ra

0.6

0.4

0.2

L/0=1

w h, 12.3 Pm

-experiment --. finite difference solution

speed C rpm n 1 1320 0.61 2 2000 0.93 3 3000 1.39 4 4000 1.86

0.5 Res

0.

(a) Load Against Deflection

1

Figure 17 -1 Aerodynamic Performance (Without Holes) for

L/D =1- Theory and Ekperiment

1

%M , CD 0

Co- 9


cJ

0.2

0.4

E

0.6

0.8

v


0.8 0.6 E 0.4 0-2

3 0

9 w

h. = 12.7 ju m

w

02R a

experiment finite difference sotution

speed rpm Cn

3 1 1320 0.57 2 2000 0.87 3 3000 1.30

_4 4000 1.74

2

2

1

0.5 ERes


00

Figure 17.2 Aerodynamic Performance (Without Holes) for L/D =2- Theory and Experiment

1 %0 ý CD

0

C-P

0.8 0.6 E 0.4

0.2

0.4

E

0.6

0.8

v

Attitude Angle/Shaft Locus

" (1

'*11 0.2 -

Lo


10

1

W=300N

200

100

1000 2000 3000 4000 r

EROS

0.5

95 degrees

sow spmd I rpm

I 0- 0 2 Cm

(c) Deflection Against Speed

90

80-

70-

60-

50- W. - 100 N

40- 300

30[

IV 1000 2000 3000

01- speed rem

(d) Attitude Angle Against Speed


0.4

0.3

w 2 D 2p a

0.2

0.1

L/D =1 (?

ww

a/L = O. 2S h, = 12.3jum

df/D --; 0.036 n=8

e xperiment -finite difL-rence solution

4 speed c rpm n

1 1320 0.61 2 2000 0.93 3 3000 1.39 2.

/

4 4000 1.96

0d 0.5 E Res


1

Figure 17.3 Aerodynamic Performance (With Holes) for L/D

- Theory and Experiment

c:: > 0

CP-

Z>(

A0 ý E A k Al

.2

.4

E

.6

.8


U-)


V

2

w w

D2 Pa

1

9.

--- w

4 a/L ='0.25 h, = 12.7pm

dt/D = 0.036 n

experiment 3

-finite difference solution

speed rpm Cn

1 1320 0.57 2 2000 0.87 3 3000 1.30 4 '4000 1.74

Øi 0

1,9, .5 6 Res


1

Figure 17.4 Aerodynamic Performance (With Holes) for L/D ho = 12.7 Pm - Theory and Experiment

%D C=>

0

CP- e->o

0.8 0.6 e 0.4


ell,


0.2

0.2

0.4

E

0.6

0.8

v

4

ý-: Res

de4es

ISO W 5,01\N

1000 2000 3000 4000 5000 rpm

CO

Deflection Against Speed

80-

70-

-W= 50 N 60-

50- 100

150

30-

20-

10 1 DOO 2000 3000 4wo 5000

01 111 -- -18. -

pm

0 C'm

(d) Attitude Angle Against, Speed


1.0

0.8

w Pa

0.6

0.4

0.2

A

ww

L/Di 2

all. = O. 2S h, = 17.9jum 2

df /D = 0.036 n=8

, experiment -finite difference solution

speed rpm Cn

1 1320 0.29 2 5000 1.10

0.5


Figure 17.5 Aerodynamic Performance (With Holes) for L/D - 2,

ho = 17.9 )m - Theory and Ebcperiment

1 0.8 0.6 E 0.4 0

CP

a2

0.4

E

0.6

0.8



0.2

0.

w

olee)

0.

0. '

ww

L/D--

a/L = 0.25 h, = 12.3jum

P. /P. 2 Asý 1.24 df/D 0.036 6-

n8 /3

-experirmnt ---finite difference solution - -moJified superposition

speed Cn rpm /2 1 aerostatic 0 2 2000 0.93 3 5000 2.

0 0 0.5

4eý

(a) Load Against DefleCtion

Figure 17.6 Hybrid Performance for L/D

Theory and Experiment

1

0.8 CD

0

CP

coll

I

a2

D-6

D. 8

Attitude Angle/Shaft Locus

0.6 0.4 0.2

Figure 17.6 (cont.

2.5

2. C

-w 01(po-R)

1.5

1.0

0.5

LID= 2

all. = O. 2S h, = 123jum

P. I P. 2 Asý 2.41 df/D 0.036

n8

-experiment -finite difference solution 3 modified superposition

speed rpm Cn

aerostatic 0 2 1320 0.57 3 '3000 1.30 4 5000 2.17

4. 0

0 0.5 ENS


'C.

I

Figure 17.7 Hybrid Performance for L/D - 2, ho - 12.7 um, Po/P& -2 - Theory and Experiment

1 0.8 0.6 E 0.4 0.2

CP

530 50

(b) Attitude Arqllo/Shaft Locuo

t4. )

/1000--7%

0

0.2

-0.4

0.6

0.8

il 0


1

300

200

1000 2000 3000 4M lo?, rpm oi 02 co

(c) Deflection Again3t Speed

degrees

90

80-

70-

60-

so-

40- W 100 N--

30-

20-

10- / lopo 2ý0 30ýO 40? 0

0 rpm

012

(d) Attitudo AnglO lealnut Spotxl


1.0

ng 0.8

w -62(R-4RI

0.6

aA. a 0.25 ho = 12.7 um

P. / P. mm 5 Agj 0.96 dfID 0.036

001- 00

4

experimnt f«wre Inktnft

idJ7fjwto uLt inn

0.4

mod, 644 lupwpooifion

spotd rpm cn

amstatic 0 2 1320 0.57 3 3000 1.30 4 sooo 2.17

02

0.5 1 o 0"

(a) I-Oad /Zainat Dafloction

Figure 17.8 Hybrid Parformanco for L/D ho - 12-7pto PO/V& -3 - 7boory and Fkporimant

Q

I

04

(b) Attitudo Anglo/Shart Locut)

12

14

E

D-6

0.8


1

ER.,

0.5

0

600

400

'W420ON

%pmd 1000 2m 3DOD 40M rpm

-j I 2

(c) Deflection Againat Speed

0

lor

50 -

40 -

30[

20

ot A

W&SON

OVA 2000 4000

(d) Attitudo Anclo Al; aInat SrnW

F19tav 17.8 (cont. )

0.8

0.6

w

D2 ( Ror Pa. )

0.4

0.2

A

L/Oz 2 I

W1

a /L c ý-2S

h, = 12.7; un Pala -a Ajj c 0.60 dt/D a 0.036

nzG

f iri to, dif forms ckMon modifad upwPoOm

Wood rpm Cn

aerest-Atic 0 2 1320 O. S7 3 SOCO 2J7

v 0.5 EROS

(a) izad Agaimt Dafloction

Figure 17-9 Hybrid Perfor=nco for qD - 2s ho

- Theory and tKporlzont

1 Q. 8 0.6 0.4 0.2 0

cr-, >, o

(b) Attitudo Anglo/Shaft Locus

(4)

V

'0.4

E

-0.6

0.8

il 0


6pas

800

W=400 N

1000 2000 3DOO 4000 5000 speed

Of III --L III rpm 0 Cn

Deflection-Against Speed

0 degrees

90

80-

70-

60-

50-

40-

30-

20- Wz SOON

10- 3DDO 4000

01 012 Cn

(d) Attitude Angle against Speed


2

w

0 D2(p-. R)

ww

L/D= 2

w

a/L = 0.25 ho = 17.9m

PIIR =2 AA = 0.86 df/D = 0.036

n=8 -experirrent

finite difference solution 1 c /sprposi n moamea Wrposinon S,

/ /

/ /

ell

speed rpm Cn

I aerostatic 0 2 1320 0.29 31 SOOO 1 1.10

06 0 0.5

6Res,


Figure 17-10 Hybrid Performance for L/D - 2, ho - 17-9 Um - Theory and Experiment

0.8 0.6 0.4

0

CP : 30 0.2

0.4

E

0.6

0.8

'I



0.2

600

7/ Soo

400 w

Newtons

300

200

100

Hybrid W =785 rad /s Cn = 2-28

x

L/D= 2 a/L = 0.5 P. /P, = 4.4 A, 'ý = 1.58 dR/Oz 0.078

n=8 ha = 15.2, um d. = 0.15 mm dR = 3.9mm 0= SOMM

pocketed orifices

Aerostatic zo X 00 experiment (Powell, Ref. 13.7)

/. //0 finite differerce solution

I'll, modified superposition

0

Figure 17-11

0.2 U. 4 U. b U-tj

Res

Comparison Between Theoretical Results and Experimental

Data by Powell

0.7-

0.6-

0.5-

D2 (Po-Pa)

0.4-

0.3 -

0.2 -

0.1 -

0ý 0

L/D = 1.5 a/L =0.25 P. IP, 3.6

Hybrid n6

23,800 rpm ho z 33.0jum

Cný 2.61 D= 615mm-

pocketed orifices

0

X/0 -I-, - ýO 0

X0

//00 Aerastatic

X.. 0

x experiment (Cunningham et at 0 Ref. 13.8)

--- finite difference solution

0.5


1

6

Figure 17-12 Comparison Between Theoretical Results and Experimental

Data by Cunningham et. al.

1 9.8 0.6 E

0.4 02 C>

0

CP

experiment (Cunninqýam et. al. Ref. 13.8) 0 10 000 rpm En 2 1-1 X 2SOOOrPm Cn22-8

finite difterence solution

(b) Shaft Locus

CA)

0.2

0.4

E

0.6

0.8

V


L/D =2 a/L = 0.25

n8 h. 20.3. um D -= 25.4 mm

pocketed orifices

pa

0 vul z AT,

Ox experimental for reversed direchons (McFarlaAe and Reason Pet. 13.10)

- finite differenc-p solution

0(a IISX

999

axial pressure profiles

04 jw

---I Po

P

(a) Pressure Profiles

Figure . 17.13 Comparison Between Theoretical Results and Ebcperiment,

L/D =2 alL = 0.25

n8 he 20.3; jm D 25.4mm

pocketed orifices

I

P0

Pa 0 901, Mr

Ox experimental for reversed directions (McFarlaAe and Reason Ret. 13.10)

- finitediffertrica sdution

0( & 19 SPO.

990

0(

x 0

axial pressure pmfiles

04 Wr

--I PC

(a) Pressure Profiles

Figure 17-13 Comparison Between Theoretical Results and Experimental Data bY McFarlane and Reason

0.6 0 60

Avg 51

- 500

E 0ý a --=-- -0 7= o. 4- - -- 0 40" Ro/Pa =3.04 00

0.3 Asý 0.50 30'* W 66N

0.2- 20"

0.1 101, 0.5 1.0 Cn 1.5

of I I 1 0 0 5 10 15 20 25

speed rpmxlo3

0.6

0.56

0.4

0.3-

0.2-

0.1 -

0 0 5 10 is 20 25 30 - 35

speed rpMX103 e

experiment (Mc Fariane and Reason Ref. 13.10)

. -. -. finite difference solution

Eccentricity and Attitude Angle

a

Po / Pa ý 5.0 A, ý = 0.30 W= 115N

01.0 Cn

6011

--: 500

4011

30"

C201,

101,

0


Tables

Table 2.1 Values of Experimental for Inherently

Compensated Restrictors (Choked Flow Conditions

Pink _(Ref.

2.2 )

df

mm

h Po/Pa cvm

0.26_5 22-7 7.8 o. 84

0.26.5 31.6 . 5.1. 0.79

0.26.5 31.6 7-8 0.80

0.310 21.1 5.1 0.80

0-310 21.1 7.8 0.80

0-310 30-0 . 5.1 0.78

0.335 19.7 7.8 0-79

tu 28.6 . 5.1 0.74

ei tu 7.8 0-71

0.3.50 24.1 7-8 0.80

le 33.0 7.8 0-73

o. 660 30-0 5.1 0-79

0.660 30.4 7.8 0.81

o. 66o 31.6 7.8 0-79

c I* Cl Min Value 0.67 w Cd Max Value 0.84_

C*cj Mean Value - 0-788

Table 2.1 (cont. )

(b) Mori and Miyamatsu (Ref. 2.4 )

dfý

-I mm

h

Pm

PO/pa

I

Cd 14

1.0 54 3.0 o. 84

62 3.0 0.8? - 68 3-0 0.86

80 3-0 0-83

91 3.0 0.8o

lo4 3.0 0-78

129 3.0 0.76

54 2.5 0.8.5

62 2.5 0-83

68 2.5 0-85

80 2.. 5 0-83

91 2.5 0.81

104 2.5 0-79

129 3-0 0.76

2.0 54 3-0 0.80

61 3.0 0.81

69 3-0 o. 86

80 3.0 0.83

104 3.0 o. 84

54 2.5 0.80

61 2.5 0-83

69 2.5 0.81

80 2.5 0.84

go 2.5 0.83

w Cýd Min - 0,76 CA* Max - 0.86

c )r d Mean - 0.788

0

-zle C., c C! 0 C,

c; 0 1 a

Cý 1 N CO

Cý 0-4 ý. 4

clý C*ý cr 0 0 6, :9 0 0 0 0 c 0 0 0,

r, L

Iý \0 C C) C-\ 1

14 C-N 9 'r p

IW ý 8 1 0 0 1 Cý 1% clý 0ý

11 2

I 1

-t N

\0 ý

*10 ý4 0 0 rý cc, 0

L j ;;; be C

ai tý %0 . .

42, - d \ý

is 0 (\J

-t

: 00 C14 ; ýl 1-4

%0

1% CY Clt 1: 1 C, C; C;

14 c5k W v Cý

Co.

0 . Wl

1, % 11 -ý, ý ": - llý %0 z VN ; Ci t %

CR 'A 1 4 "0 CNI c r-I I), + + I + + + C),

co

co l

(), cn

V -4 rl\

-4 C-I\

g 0ý C',

i ý 1 1 I

W 0 0 0 0 0 0 a

Ca. cli cm l

I x

CIO - I I I C; I 0 . ,6.

Cýl I O r= C;: C; : C;

0% ell%! R CCO-

C; - C; L- 11 . -ý I C'ý I c! I It e: l -:! 71-7

" 1-4 1 rý CID

of 7 co ri :

C) 2 ae E 0 0 CwN -0ý4 I

. Ie ; '

ý41 w -+ +++ + zi; Cli

w :F C; i c) 00 0: 0.001 C; aII CR C,

6c ig C,

to (10 0 C, 0

CY ct "ý N9 cl -I 0 cz 14 ýO " 10 r-

+

r, %

I

Cý I Ol "

;;; %) + + + + I I +

11 - '0 w

- CD

%, -, 14 C% ! 'I ! (71 'ý "1

7-T.

E E CY C - C; 0

1ý 1 00 31 0 C;: C; -4 I: x

- CL

i co %, % 1 cli cli -1 .1 co r- Cý

-0 If co cli

- ý -gl x

I CV r4 CY CY c"A j 41) 4 C; I

I

C; C; C;

0 L. 1 ý4 clý 0' C"

CY Ct

r4 LrN pq c; 0 0

+ + + + +

8

. 6ý ev

0, C8, w C;

Cl\ 16

i "i 0

\q 0 C; C; C; r

0 cv r4

(P - I

l l C) 0 C)

0

C; C; cc) ýt co .3 -. 0 ýt Cc, )

, or; r-: -

T-able 1,0,. 1, Comparisonof Ebcperimental and Theoretical Load Capacity Pocketed Compensated Orifices

Cý

4 r-4 C, C%j + 4 +

+ + +

CIO

CA r-4

(Ij

Cý

CY

C; C; C; C;

W' 8 8 8 %0 C) % N cq ri .

N

C C; CR C>

11 0 10 I I

10 L ) g; be (V Oll

Ol (\, +

" co +

0 en + I C\j

14 +

rq I

C; + I I +

0 I + +

.

C, M kll\ vs \0 . llý a- " rN Uý a %fN

cli - 'A -6 to C) r4 c 8 10

r-f

I I ulý 1.4

1 C; C; 0 a

11 C;

E P: 11 1. m 1

N 11" 0 1-4

CY

1 '41

C) 1 %0

x C> - cy . Cý l

-! ; (LO 0 . C; I C; C; c) I 0 o 0 0 C I 0 %0 Wý

eý 1 CO 1 r-,

1

ýo r,! - C4 co c 4

C-

- ý 1 + + + + 1 +

C), 0

f, rz l

w C; C; 0 C; o C; C; C; c. CL , It 1 4

1

Vý 3 x 8,8ý; 8 C;, 0 C; ý

C; I C; C; . C;

- C'j ; co I ()% I 1 01 .qiN r-

0 - i8 5ý I

"o ;m a 1 -A C Cý% -t 9, i. . 1- cl cl C, 1 -1 , ! S C * C;

i P

N f I- CY "i -, ( .. ) , ; - L- o 11 . 9. (ý -! 1 11 : C, ý! V-% I Vý a, ! ý" : g- I I c) N co

"I - ! d I rN z. ýA .. r4 C; i+ (1) .1+ + -+

cl @ Z8; ý Ok, ý N ; '

a C; C; 01c; C; 10 C

C2 -4 r- N .

GO 00C; 0000

1) L- 0

Ii l9 g -1

it,

1 " -ý I cl tv C! I" q. .2 Cý

4D 0 cg C%4 VI M -ý .2 It ui cu r ; % rl

;I o 1

C; a _ _ 0. C; . o C oo c C I

r-4 -- %0 , , 0 C%

Cý -

v x 16 N cc; 10 d It ;i

rl pl. Fý CLI

oll C;; C; C; C; 0 ol 0

I

o d

be N Cý A

01 "

"' r4

IAJ P 4t 4t Ct

. -ct !; ; I Co. 01 000, C) C

I Ol CL r,

S " l

ý ý !

x It li I I ! I

I C) O C>

i I) m

VA "' 8 I 4r :1 W"

4t ; VZ W N P4

1 C; 0 0 0 0 'o c; Q C31

- ýt C=O

CK) c=p

l C), all, d !s -t CO

Cp I

CO - :2

9 z; r.

CL-N I -il fril vi r ý: . m. Ti rn vi C4

Table 10.2 Comparison of Experimental and Theoretical Load Capacity

- Inherently Compensated Orifices

do = o. limm 11 do m 0.26MM

Xpl f Asg

Ut Ez 0) Aj

exp Ftheol

r16r, erro r

(E=o) -T-zdz-

OB exp Itheo

ertor

0.212

h, = 11.9 jim

1.68 3.04, l. 44 0.446 0.485 + 8.7

5.08. 0.861 0.362 0.380 + 5.0

7.80 0.561 0.271 10.283 + 4.4

1.68 0.474

ho m 21.1 UM

S. = o. 119 C. = 0.

0.195 0.1951 0 2.22 1

0.51610.440 1 7

-14.7 3.04 0.262 0., 132 1.23 o. 49i 1

0.477 2.9 5.08' 0.157 0.081 0.08 + 4.9 0.733 0.389ý 0.376 3.3

7.80- 0.102 0.0531 0.055 + 3.1 78 0.288 0.277 3.8

1.68 11 0.166

h. =3o. o ji

0*084

0.072 0.0811412.5 0.1340

m

-- 0.469

7.5 0-33510-310 - 3.04, 0.921 O. M 0.04 +40.0 0.464 0.269 0.237

- .j -4

5.08 0.278 0.170 0.197 . _

+l0.0 7.80 0.181 0.110 0.121 1 410.0 1

Table 10.3 Comparison of Experimental and Theoretical Masis Flow Ratos

- Pocketed Compensated Orifices

df =O. 31 mm df = 0.66mm px

P U (F-= 0) (JE=0)

, Asg exp

AS exp 1 theo % l'errot

1

6.51

h, =li. 9 NM

13.9

1

1.68

3.04 11.79' 0.586 0.471 -19.6

5.08 11.07 0-533 0.420 -21.2

7.80 - p 0.442 0.335 -24.2 1.49 0.542 0.527 -2.8

1.68 0.994

h0= 21*. l UM '

3.68 . 82

0.295 10.3001+ 1.7 12'.

20 10.3891

0.405 1 +4.1

3.04 0.550 0.286 0.2681 - 6.3 1.21 0.4861 0.4501 -7-4

5.08 0.329 0.181 0.179 - 11-1 0.727 0.357' 0. )54! -0.8

7.80 0.214 0.116 0.7 + 0-9

1

0.473 44.5

1.68 0.1-"J'

30. OMM

2-58 5.5

0.266 0.192 - 27. f 1.09 0. Yý6 0.116 -12.9

3.04 0.245 0 0 . 157 0 (). i)ls -14.6

1

0.600 0.3: 1 0.2fP() - 8.1

5.08 0.147 0-090

[

0-081 -10-0 0.159 0.184 0-195 + 6-0

7.80 0.096 0 . 059 0.053 -10.2

Table 10.4 Comparison of Experimental and Theoretical Mans Flow Rates

Inherently Compensated Orifices

Plates

f

Plate 1 The Exp. ýýPimental Test Rig and Instrumentation

Pla te 2 Test Bearing Assemb y

---

Rate 3 Instrumentation Panel

Plate 4 Cailbration Rig for C pacitance Probes

. A4L. $

Plate S Compensati g Valves

¶

Plate 6 Slave Bearing

Plate 7 Test Bearing. ý

Rate 8 LappLng__ýquipmenf

Plate 9 Air Gaugin __Lquipaent

Plate 10 Test Shaf t

-t

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