design charts for arbitrarity pivoted, liquid-lubricated, flat-sector-pad

A

lnil

S A TECHNICAL NOTE

8 DESIGN CHARTS FOR ARBITRARILY PIVOTED, LIQUID-LUBRICATED, FLAT-SECTOR-PAD THRUST BEARING

Izhuk Etsion

Lewis Reseurch Center Cleuehnd, Ohio 44135

N A T I O N A L AERONAUTICS A N D SPACE A D M I N I S T R A T I O N WASHINGTON, D. C. JULY 1977 p i?

@ - _- .-.I - -

https://ntrs.nasa.gov/search.jsp?R=19770020462 2018-02-01T14:58:57+00:00Z

-- ~- 1. Report No. 2. Government Accession No.

NASA TN D-8344 _._ - 4. Title and Subtitle

DESIGN CHARTS FOR ARBITRARILY PIVOTED, L UBRIC ATED, F LA T- S EC TOR- PAD THRUS T BEARING

LIQUID-

9. Security Classif. (of this report)

Unclassified

7. Author(s)

Izhak Ets ion

9. Performing Organization Name and Address

Lewis Research Center National Aeronautics and Space Administration Cleveland, Ohio 44135

20. Security Classif. (of this page)

Unclassified

2. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Washington, D. C. 20546

5. Supplementary Notes

TECH LIBRARY KAFB. NM

-- 5. Report Date

Ju ly 1977 6. Performing Organization Code

8. Performing Organilation Report No.

E-8899 10. Work Unit No.

505-04 11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Note 14. Sponsoring Agency Code

_ - 6. Abstract

A flat, sector-shaped geometry for a liquid-lubricated thrust bearing is analyzed considering bot1 the pitch and ro l l of the pad. Results are presented in design char t s that enable a d i rec t approac. to the design of point- and line-pivoted, tilting pad bearings. Michell bearing approximation and i t is found that this approximation always overest imates load

A comparison is made with the

capacity.

7. Key Words (Suggested by Authorb) )

Bearings Thrus t bear ings

~ ~~

18. Distribution Statement

Unclassified - unlimited STAR Category 37

DESIGN CHARTS FOR ARBITRARILY PIVOTED, LIQUID-LUBRICATED,

FLAT-SECTOR-PAD THRUST BEARING

b

Lew

f lzhak Etsion"

s Research Center

SUMMARY

A flat, sector-shaped geometry for a liquid-lubricated thrust bearing is analyzed considering both the pitch and roll of the pad. center- of-pressure location, unit load, friction 10s s coefficient, and lubricant flow are presented in design charts. These charts enable a direct approach to the design of both point- and line-pivoted pads and also provide the necessary procedures for the design of nontilting flat pads. The various features of point- and line-pivoted configurations a re discussed, and a comparison is made with the Michell bearing approximation.

Performance characteristics such as

It is found that this approximation always overestimates load capacity.

INTRODUCTION

Although during the last three decades the commonly used flat sector pad has been extensively analyzed, most of the investigators treated a simplified oil film shape (refs. 1 to 9). Either a linear film thickness variation was assumed in the circumferential direction, independent of the radius, o r some sort of an exponential oil film shape was used. In some works (e. g. , refs. 1 and 7) the sector shape is transformed into a rectangular configuration, which further distorts the actual geometry.

An actual tilting pad assumes both pitch and roll about some point and, for the flat surface, the clearance varies in both the radial and circumferential directions, with the circumferential variation being sinusoidal rather than linear. Therefore, all of the previously mentioned solutions are approximations and may lead to an overly optimistic

*National Research Council - National Aeronautics and Space Administration Re- search Associate.

design of a flat, sector- shaped tilting pad. When dealing with pivote&pad bearings it must be remembered that, in order to

satisfy ‘equilibrium of moments, the resultant of the hydrodynamic pressures must pass through the pivot. Thus, for a given pivot location, the solution of the Reynolds equation should result in a predetermined location for the center of pressure. Unfor- tunately, such a direct solution is impossible and the designer must presently use a tedious iteration approach (refs. 10 and 11) or select a certain pad orientation and place a point pivot at the resulting center of pressure (ref. 12). In both cases the solutions are limited to specific design points. That is, for given values of load, speed, and minimum film thickness there corresponds only one pivot location. In real applications the pivot is fixed within the pad area. Hence, when changing the operating candi- tions the pad must change its pitch and roll angles so that the center of pressure will always stay at the pivot location. A complete analysis of the tilting pad thrust bearing must therefore cover all the possible pitch and roll angles for possible pivot locations within the pad area. The objective of this work is to obtain such a solution to provide the necessary data for the design of flat, sector-shaped tilting pad thrust bearings. This will be presented for the incompressible case in the form of design charts that give the load capacity, friction loss, and lubricant flow for various pivot locations and pad tilt angles. p res s ibili ty numbers.

The solutions are also valid for the tilting pad gas bearing at low com-

SYMBOLS

A

F

F -

H

h

K

P

P

Q

pad area, p (r: - rf)I2

friction 10s s

nondimensional friction loss, F/Kwrohg

nondimensional film thickness, h/h

film thickness

2

P

bearing parameter, 6pw(ro/h2) 2

dimensionless pressure, p/K

pressure

volumetric oil flow

2

2 Q nondimensional flow, Q/( 1/2)wh2ro

R nondimensional radial coordinate, r/ro

r radial coordinate

W pad load capacity

2 W nondimensional load, W/Kro

-

-

p angular extent of pad

E tilt parameter, y r /h

y tilt about pitch line

8 angular coordinate, measured from leading edge

p viscosity

7 shear stress

w shaft speed

Subscripts:

cp center of pressure

i inner radius

2 leading edge

0 outer radius

p pitch line

t trailing edge

1 maximum film thickness

2 minimum film thickness

O P

THEORETICAL BACKGROUND

The incompressible Reynolds equation in polar coordinates is

I1 IIll1111 IIIIIII llll111 1

In order to solve equation (1) for the pressure distribution, the oil film thickness h has to be expressed in terms of the independent variables r and 8. In an earlier report (ref. 13), it was shown that any pitch and roll of a sector- shaped pad about a certain point can be transformed to a corresponding pure pitch about a certain radial line. This radial line may o r may not be located between the leading and trailing edges of the pad. This can be understood from figure 1 by visualizing a plane parallel to the runner that goes through the origin of the sector (point 0 in fig. 1). The radial line (called the pitch line) about which the pad motion is purely pitch is the intersection between this parallel plane and the plane of the tilted sector, and it can be either inside or out- side the sector boundaries. By considering the clearance h along this radial pitch line as a reference, the film thickness at any point (r, 8) is given by

P

h = h + y r sin(8 - 8) (2) P P

where y is the amount of tilt about the pitch line. If we let p = KP, h = Hh and r = Rro, where K = 6,uw(ro/h2) , equations (1) and (2) can be transformed to the di- mens ionles s fbrm

2 P’

and

H = 1 + ER sin(0 - e) (4) P

where H2 in equation (3) is the dimensionless minimum film thickness h /h tilt parameter E is -y(ro/hp). The boundary conditions for equation ( 3 ) a re P = 0 along the pad boundaries.

Four parameters a re needed to determine a unique solution of equation (3): the radius ratio ri/ro, the pad angular extent p, the radial pitch line location 0 and the

P’ tilt parameter E. Equation ( 3 ) is expanded by finite differences and solved numerically by using the Gauss-Seidel iteration method (ref. 14). After the pressure distribution is known, the total load capacity is obtained from

and the 2 P

The pad area is given by

4

and the dimensionless unit load of the bearing is

The dimensionless radial and angular coordinates of the center of pressure a re given

by

R ‘P =‘sl W ri/ro J6’PR2df3dR

and

sin 0 =&- f 1 lp PR2 sin f3 de dR WR ri/ro

CP

The shear stress on the runner is

and the power loss is

Defining the dimensionless power loss

Kwrohg 2

gives

5

L

The circumferential volumetric flow is obtained from

dR (9)

When evaluating the integral at 8 = 0, equation (9) gives the inflow across the leading edge. At 6 = p the outflow across the trailing edge is obtained.

RESULTS AND DISCUSSION

In total, 12 different geometries were analyzed. Inner to outer radius ratios were 0.3, 0.5, and 0.7 at pad angles of 30°, 45O, 60°, and 90'. ous tilt parameters and pitch line locations. yro/h2 was used as the basis for calculations since the minimum film thickness h2 rather than h is of importance to the designer. The pitch line location 8 was re- stricted to the range p - 7r/2 < 8 < 7r/2. This assures a circumferentially converging film thickness all over the pad area (ref. 13) and eliminates the possibility of cavita- tion.

obtained at various pitch line locations. geometries there is a sharp maximum at 8 /p = 1. load capacity from a given pad, the pad should be tilted in a way that maintains a uniform minimum film thickness along its trailing edge.

A physical explanation for this is that the pressure buildup in the lubricating film is affected by the resistance to lubricant outflow. inner and outer circumferences oE the pad, but the larger portion leaks across the trailing edge. boundary. the highest pressure buildup can be achieved by maintaining uniform h2 along the trailing edge.

Each pad was run at vari- A modified tilt parameter in the form

P P P

Figure 2 is a summary of results for the maximum available unit load that can be It is clear that for the whole range of pad

Hence, to obtain the maximum P

Some of this flow occurs along the

Hence, it would be advantageous to decrease the escape area along this For a given minimum film thickness h2, the least escape area and hence

As can be seen from figure 2, the load capacity drops sharply as 8 exceeds p. P

6

Therefore, it was found reasonable to limit the range of 0 the minimum film thickness, for any 7r/2 - p < 8 < p, is at the point (ro, p), and its dimensionless value is given by

to e / p = 1. h that case P P

P

H = 1 + E sin(@ - p) (10) 2 P

The modified tilt parameter given by

is therefore related to E through

yrO - E -- h2 I , + E sin(8 - p)

P

The design data for nine of the configurations are presented in figures 3 to 11 in groups of five charts for each pad geometry. pressure location for various constant values of yro/h2 and Op/p. Parts (b), (c), (d), and (e) give the unit load, power loss coefficient, inflow, and outflow, respectively, as functions of yro/h2 for various constant values of @ /p .

In each figure, part (a) gives the center-of-

P

Use of Design Charts

Pivoted-pad bearinzs. - The design charts can be used for both point-pivoted and line-pivoted tilting pads. They can be used either to determine minimum film thickness for a specified load, speed, and pivot location o r to find the pivot location for a given load, speed, and optimum minimum film thickness. The first approach is useful when designing for a special purpose, like a centrally pivoted pad, or when the operating conditions, like speed o r load, are changed after a pivot location has been se- lected for a certain design point. specified operating conditions or for optimization purposes. pad geometry, the designer selects the optimum value he wants from either part (b), (c), (d), o r (e). By this selection a set of the parameters yro/h2 and 0 / p is obtained, which, by part (a), determines the center of pressure that is identical to the pivot location. ply reversed. rameters yro/h2 and ep/p.

The second approach is used when designing for In this case, for a given

P

On the other hand, if the pivot location is known, the procedure is sim- From part (a) for each pivot location there corresponds a set of the pa-

For this set of parameters the dimensionless unit load

7

2 is found from part (b) in the form Wh2/6pur:A. Now for any given load and speed the minimum film thickness hg is obtained and then the tilt y can be found from the known tilt parameter yro/h2. The friction loss F, inflow Q1, and outflow &c can be found by using parts (c), (d), and (e).

With point-pivoted pads the design is straightforward. Once the pivot point is fixed, the pad alines itself by pitching and rolling, about the pivot, to obtain the necessary tilt y about the radial line at the proper angle 8 /p . However, when line- pivoted pads a re designed, the line pivot must,go through the center of pressure and be parallel to the pitch line at the angle 8 This assures equal performance of the line- and point-pivoted pads. capacity and lowest friction loss the line pivot should be parallel to the trailing edge ( 8 / p = 1). With nonradial line pivots this is not a problem at all, but with a radial line pivot the design is limited to those cases where lines of constant 8 / p in part (a) intersect lines of constant angular center-of-pressure coordinate, 8 / p = 8 / p . This assures equilibrium of moments about the radial line pivot. From the various parts (a) of figures 3 to 11 it can be seen that this demand makes the radial line-pivoted pad in- fe*ior to the point-pivoted one. A radial line pivot design eliminates one degree of freedom (pad roll) and fixes the radial location of the center of pressure (parts (a)). Thus the design for maximum unit load, where the desired 8 / p is 1 and 8 / p is always less than 1, is impossible with a radial line-pivoted pad.

Another special design is that of a centrally pivoted pad. Again from parts (a) it is seen that a flat, sector pad tilted about its mid-angular line cannot produce any load capacity. The fact that such a bearing does carry load in a real application is attrib uted to thermal and mechanical distortions, but the efficiency of such a design is still questionable when compared with the centrally point-pivoted pad. it can be seen from parts (a) and (b) that an angular location of 8 design for a flat sector pad. choose the optimum radial coordinate of the pivot that will maximize the unit load. This, in turn, results in the largest minimum film thickness for a given speed and load.

pared with a design for maximum unit load is quite high. A s an example, for a pad radius ratio ri/ro of 0 .5 and angular extent p of 45' the loss in unit load is almost 60 percent. compared with an optimum design for the same load and speed.

Tapered-land bearings. - The information that is contained in figures 3 to 11 is also useful for nonpivoting (fixed), flat, sector-shaped pads. For any desired operating condition, one can select a set of pitch line location 8 / p and tilt parameter

P

P

measured from the leading edge. P

For the highest load

P P

CP P

P CP

With the point pivot, / p = 0. 5 is a viable

More than that, for this angular location the designer can cp.

When a centrally pivoted, flat, sector pad is used, the penalty in unit load a s com-

That means a reduction of about 35 percent in minimum film thickness as

8

I

yro/h2. Hence, the necessary taper y can be obtained which, together with the location 8 / p , completely defines the sector pad shape. Determining the minimum film

P thickness h2 for a nonpivoting pad at off-design points involves some cross plotting. In contrast to the tilting pad, the slope y of the nontilting pad is fixed while the center of pressure is free to change. Hence, since the parameter 8 / p is fixed too, for any given load and speed there corresponds a different value of yro/h2. A design curve can be constructed from part (b) for any line of constant 8 / p by multiplying values of Wh2/6pwroA by their corresponding values of (yro/h2)2. This enables one to plot the curve of Wy /6pwA against the parameter yro/h2 for the line of constant 8 /p . Now since y is known for the fixed pad, one can find from that curve the value of yro/h2 that corresponds to any given load and speed and therefore obtain the corresponding value of h2.

P

2 2 P

2 P

Comparison with Michell Bearing Approximation

As was mentioned in the INTRODUCTION, a common practice in tilting pad design is to approximate the oil film shape by a uniform taper in the circumferential direction. This type of bearing, where h is independent of r and varies linearly with 8, is known as the Michell bearing. approximation, the results of reference 6 were transformed to the same dimensionless form and compared with the results of the present work. sionless unit load W/KA for various maximum to minimum film thickness ratios. Two extreme configurations were chosen for the comparison. low radius ratio of 1/3 and large angle of 80°, while- the second sector has a radius ratio of 2 / 3 and an angle of 30'. From table I it is clear that the Michell bearing a p proximation overestimates significantly the load of an actual flat configuration. overestimation ranges from 13 percent at hl/h2 = 2, ri/ro = 2/3, p = 30°, and 8 / p = 1 to 170 percent at hl/h2 = 9, ri/ro = 1/3, p = 80°, and 8 / p = 0.5.

In order to check the accuracy of the Michell bearing

Table I presents the dimen-

The first sector has a

The

P P

CONCLUDING REMARKS

The pitch and roll of a sector pad about any point can be transformed to a pure pitch about some radial line. presented as a function of only two dimensionless parameters, namely, the tilt parameter and the radial line location. This in turn provides a direct approach to the design of flat, sector- shpaed, tilting pad bearings by eliminating the need of tedious iterations.

Numerical solutions for nine different sector pads having radius ratios of 0.3, 0 .5 ,

This transformation enables bearing performance to be

9

and 0.7 and sector angles of 30°, 45O, and 60' were obtained. Their performances are presented in design charts that enable the design of both point- and line-pivoted tilting pad bearings.

Point-pivoted pads a re superior to radial-line-pivoted ones since they have an ad- ditional degree of freedom. that of a centrally pivoted pad, can be accomplished with a point-pivoted flat configuration but not with a radial-line-pivoted one.

The Michell bearing approximation, commonly used for design purposes, is unsafe since it always overestimates the load-carrying capacity of an actual flat sector pad.

Special designs, like the one for maximum unit load or

Lewis Research Center, National Aeronautics and Space Administration,

Cleveland, Ohio, September 7, 1976, 50 5- 04.

REFERENCES

1. Brand, R. S. : The Hydrodynamic Lubrication of Sector-Shaped Pads. Trans. ASME, vol. 73, no. 11, Nov. 1951, pp. 1061-1063.

2. Charnes, A. ; Saibel, E. ; and Ying, A. S. C. : On the Solution of the Reynolds Equation for Slider-Bearing Lubrication. ASME, vol. 75, no. 8, Aug. 1953, pp. 1125-1132.

V - The Sector Thrust Bearing. Trans.

3. Kettleborough, C. F. ; Dudley, B. R. ; and Baildon, E. : Michell Bearing Lubrica- tion, Parts 1 and 2. Proc. Inst. Mech. Eng., vol. 169, 1955, pp. 746-765.

4. Sternlicht, B. ; and Sneck, H. J. : Numerical Solution of Reynolds Equation for Sector Thrust Bearings. Lubr. Eng., vol. 13, no. 8, Aug. 1957, pp. 459-463.

5. Kunin, I. A. : On the Hydrodynamic Theory of Lubrication of Pad Type Bearings. Wear, vol. 2, 1958, pp. 9-20.

6. Pinkus, 0.: Solution of the Tapered Land Sector Thrust Bearing. Trans. ASME, vol. 80, no. 10, Oct. 1958, pp. 1510-1516.

7 . Bosma, R. ; and Moes, H. : Design Charts for Optimum Bearing Configuration: 2 - The Pivoted-Pad Thrust Bearing. J. Lubr. Technol., Trams. ASME, ser. F, vol. 92, no. 4, Oct. 1970, pp. 572-577.

8. D'yackhov, A. K. : Optimum Relationship for the Dimensions of Thrust Bearing Pads. Russ. Eng. J., vol. 54, no. 3, Mar. 1974, pp. 9-12.

10

I '

9. Tieu, A. K. : A Numerical Simulation of Finite- Width Thrust Bearings, Taking into Account Viscosity Variation with Temperature and Pressure. J. Mech. Eng. Sci., vol. 17, no. 1, Feb. 1975, pp. 1-10.

10. Sternlicht, B.; Reid, J. C., Jr.; and Arwas, E. B. : Performance of Elastic, Centrally Pivoted Sector, Thrust Bearing Pads - Part I. J. Basic Eng., Trans. ASME, ser. D, vol. 83, no. 2, pp. 169-178.

11. Sternlicht, B. ; Carter, G. K. ; and Arwas, E. B. : Adiabatic Analysis of Elastic, Centrally Pivoted, Sector, Thrust-Bearing Pads. J. Appl. Mech., Trans. ASME, ser. E, no. 2, June 1961, pp. 179-187.

12. Floberg, L. : On the Optimum Design of Sector-Shaped Tilting Pad Thrust Bear- ings. Acta Polytech. Scand. Mech. Eng. Ser., 45, 1969.

13. Etsion, Izhak. Analysis of the Gas- Lubricated, Flat-Sector- Pad Thrust Bearing. NASA TN D-8220, 1976.

14. Presler, Alden F. ; and Etsion, Izhak: Computer Program for Flat Sector Thrust Bearing Performance. NASA TM X-73595, 1977.

11

7

Clearance ratio,

h d h 2

TABLE I. - COMPARISON BETWEEN UNIT LOAD OF FLAT SECTOR-

SHAPED PADS AND THEIR CORRESPONDING MICHELL BEARING PADS

Radius ratio, ri/ro, 1/3; angular extent of pad, p, 80'

Pitch line M3chell location, bearing

OP/P approximation

0.525

. 548

.456

.305

1 0.255 0.298

.242 .312

. 172 .255

.093 . 164

ratio, ri/ro, 2/3; angular extent of pad, p, 30'

1

Pitch line location,

Unit load, ( W / K A ) X ~ O ~

Michell bearing

approximation

0.336

.346

.298

.190

12

Figure 1. - Geometry of sector pad. \I .@I10 I

0 . 2 . 4 .6 . a 1.0 1.2 Pitch line location, e,/p

Figure 2. - Maximum available unit load as function of pivot location for various geometries.

.85-

.80-

- .- L

I Lo .75- - x .- L

CL u - 6 .70- 0

m 0

m -cj

.- +

- - .- .65-

L

3 .n m ar L a L

? .60- c c ar 0

.55-

.40

rilro=0.3 p = 300

. 5 0 -

Tilt parameter, Pitch line location,

Y'olh2 e,m

.1.00

1 1 1 I I 1 - - L _I . I .45 .50 .55 .@I .65 .70 .75 .80 .85

Center-of-pressure angular location, 0 CP lp

l a ) Center of pressure.

Figure 3. - Design charts for flat, sector-shaped pad with ratio of inner to outer radius rilro of 0.3 and angular extent p of 330.

14

r i h 0 = 0.5 p = 300

Pitch line

I I 1 1 1 1 1 1 1 1

Tilt parameter, yro/h2

(b) Load capacity.

Figure 3. - Continued.

15

16

r i l ro = 0.3 p = x P

I I I I I I I I I . I 0 2 4 6 8 10 12 14 16 18 20

Tilt parameter. yr,lh2

(c) Friction loss.

F i g u r e 3. - C o n t i n u e d .

rilro = 0.3 p-300


edp -1.007, -1.25- \

.05

I I I 8 . 10 12

Tilt parameter. yro lhp

( d ) Lubricant inflow.


I I II 14 16 18 20

17

.4l

.3!

.3

N O L N

5 .25 5 3- 0 - =, .2c 0 v) !A al

c 0

!A c

- .- 2 . 1 5 .- n

.IO

.05

0

ri/r, = 0.3 p-300 Pitch l ine

location,

-1.50

ep IB

_. .- -

1.00

I I I I 1 I I I I I 2 4 6 8 10 12 14 16 18 20

Tilt parameter, yr,/ h2

(e) Lubricant outflow at trail ing edge.

Figure 3. - Concluded.

18

r i l ro = 0.3 p - 4 9

I I L I I I I I I .50 .55 .60 .65 .70 .75 . a0 . a5 .43 .45

Center-of-pressure angular location, 0 lp CP

( a ) Center of pressure.

Figure 4. - Design charts for flat, sector-shaped pad with ratio of inner to outer radius rilr, of 0.3and angular extent of pad p of 450.

19

Pitch l ine location,

r i l r o=0 .3 p = 450

I I I 0 2 4

I I I I 6 8 10 12

Tilt parameter, y ro lh2

(b) Load capacity.


I I 1 I 14 16 18 20

20

-I

rilro=0.3 p - 4 9

18 I I I I I I I I 2 4 6 8 10 12 14 16

Tilt parameter, y ro l h2

(c) Friction loss.


21

.50

.45

.40

.35

Y O N J= .?o s 5 - 2 E .25 .- “7 “7 a,

c 0 v) c

- .-

E .20 .- n

.15

. lo

.05

0

r i / r o = 0.3 p.49

Pitch line location.

e,ia

I I I L I 1 4 6 8 10 12 14

2 2

Tilt parameter, yrolh2

(d) Lubricant inflow.


1.00

1 L I 16 18 20

22

.40r

. 33

.25

.20

.15

-

-

-

-

.05 .lop

ri/ro = 0.3 p = 450

Pitch l ine location. e,ip

-0.75 and -0.50-,

- - - 1.00

! I I I I I I I I u 0 2 4 6 8 10 12 14 16 18 20

Tilt parameter, yro lhg

(e) Lubricant outflow at t ra i l ing edge.


23

.a+

.ao-

.75-

.70-

.65-

.@-

.55-

rilro = 0.3 p = @

Ti l t parameter.

Yrofhp

Pitch line locat ion,

aP1e

.M I I I I I I I I 1 .40 -45 .M .55 .a .65 .70 .75 .ao .85

Center-of-pressure angular location, 8,Ip

(a) Center of pressure.

Figure 5. - D sign charts for flat, sector-shaped p a l with ratio of inner to outer radius rifro of 0.3 and angular extent of pal €5 o f &

24

rib, = 0.3

P-600

0 1. 1 2 1 4

I 6

i 12

I 10

1 8

Tilt parameter, yr,,Jh2

i i 18 20 i

16 i 14

(b) Load capaciw.


25

lo5I 90 ri/ro = 0.5 0=600

. I 1 I 1. . .I 10 12 14 16 18 20 0 2 4 6 8


(c) Friction loss.


26

.50

.45

.40

.35

N O L

P .x) s

0

3-

"E .25 0 - .- Y) * a, r 0 VI c

- .-

.20 .- n

.15

.10

.05

-

-

-

-

Pitch l ine location.

e,lp

I

rilr, = 0.3 p = 600

I I I I I 4 6 8 10 12

Tilt parameter, yro lh2

(d) Lubricant inflow.'


I I I I 14 16 18 20

27

rilro - 0.3

P - d

- I 20

1 18

1 i I I . _ - 2 4 6 .-I 8 _-AI- 10 12 14 L 16 0


(e) Lubricant outflow at trai l ing edge.


28

I

I

.8!

.8C

- .- L

0 k .75 - - .- L

n. s" c' .70 0 .- c - 8 - m n .-

.65 E 2 YI m L n

L .60 c 0

c c m u

.55

.!% .4

nit Pitch l ine parameter, location,

yrolh2 eplp

rilro =0.5 p = 300

1.00

I I 1 1 I 1 I .65 .70 .15 .80 .45 .M .55 .60

Center-of-pressure angular location, €I,-,@

(a) Center of pressure. Figure 6. - Design charts for fiat, sector-shaped pad with ratio of inner to outer radius rilro of 0.5 and angular extent

p of 300.

29

1 .- L 1 1 1 I I 2 4 6 8 10 12 14 16 18 20

I I L - 0

Tilt parameter, yr,l h2

r i / r , = 0.5 p = 30


epip

(b) Load capacity.


30

b

I 0

I 2

I 4

I 6

r i / r o = 0.5 p = @

I I I I 8 10 12 14


(c) Friction loss.


I I I 16 18 20

31

.50

.45

.40

.35

.a

.25

.20

.15

.10

. 0:

32

rilro = 0.5 p=e

Pitch l ine l o a tion,

ep 'P -0.50 and -0.75 -

-1.00 -',

I I I 6

I 114 16

L 12

I I 8 10




I 18

I 20

.41

.3:

.x

N," N 5 .2:

d g .20 0

v1 VI a

.= 0

v1 .=

- .- E .15 n .-

.10

.05

0

ri/ro = 0.5

P - @


eP'P -

-1.25 and -1 .50h

-

.25

-/ .50

.75

1.00 ___. .

- I I I I 1 I I I 2 4 6 8 10 12 14 16




+ 20

33

I I 1 I 11111lll11l111111llI I l 1 l l 1 1 1 l I II Ill lIIlll1lll111111lllll

rilro = 0.5 p . 4 9

Tilt parameter , Pitch l ine

location, Op'P

Yrolh2

I L I I L I I I I .40 .45 .50 .55 .@I .65 .70 .75 .80 .85

Center-of-pressure angular location, 0 /p


Figure 7. - Design charts for flat, sector-shaped pad with ratio of inner to outer radius ri/ro of 0.5and angular wtent p

CP

of 49.

34

.oo%

.W!

. Ml4(

.W3f

. oox

9 - 3

5 - .oo25 c .- c 3

.oo20

. a l l5

. oo10

. wo5

0

b

I

ri/ro = 0.5 p=4P

- Pitch l ine location,

- I I I I I I I I I I 2 4 6 8 10 12 14 16 18 20

Tilt parameter, yr0/h2

(b) Load capacity.


35

1%

135

120

105

N

= 9 0 s - Y

i c 0)

u .- E 75 8 VI VI - c 0 .-

60 t

45

30

1:

rilro = 0.5 p = 4 P

I I I I 16 14

I 12

I 2 4 6 8 10

I 1 Tilt parameter, yr,lh2

0 .L.. . - . I 18 20

36

(c) Friction loss.


.5(

.4!

.4t

.35

-Lo N c 3 .x 5 3%

2 .- .25 0 -

VI VI a,

c 0 VI c aJ

- .- E .20 .- n

.15

.IO

.05

0

rilro 0.5 B - 4 9


0 ,

ep IB

I I I - I I I I I I I 2 4 6 8 10 12 14 16 18 20

Tilt parameter. yro/h2



37

.40

.35

.a

N O L N

5 .25

5 - d r .20 1 0

VI VI a,

c 0

VI c

- .- E .15 n .-

.la

.05

0

r i /ro = 0.5 p.49

Pitch l ine location, -

-

-

._

1.00

I I I I I I I I I I 2 4 6 8 10 12 14 16 18 20


(el Lubricant outflow at trai l ing edge.


38

.85-

.80-

.- L

- 2 .75-

sv

.-.. I .- L

a. Tilt parameter,

Yrolh2

r$r0 = 0.5 a m 6 0 0


I .I - 1 I 1 I I- -2 .60 .65 .70 .75 .80 .85 .40 .45 .50 .55

Center-of-pressure angular location, e /p CP

(a) Center of pressure. Figure 8. - Design charts for flat. sector-shaped pad with ratio of inner toouter radius ri/ro of 0.5and angular extent

D of6@.

39


rilro = 0.5 l3=600

n 2 I I

4 6 I I I I. I . I. I 8 10 12 14 16 18 20


(b) Load capacity.


40

rilro = 0.5 8=600


1 1 I I I L I 1 I I 2 4 6 8 10 12 14 16 18 20


(c) Friction loss.


41

I

I

I l l 1111 II I I I IIIIIII11111111.1111111 111 11111 111111.11 I 1 1 1

I 0 L 2 4 L - . I L L - 6 8 10 .-1 12 - 14 1 16




rilro = 0.5

P = @

42

.40

.35

.?€I

-Lo N c 3 .25 5 - d Y= 3 .20 0

m VI m

c 0

VI c

- .- E .15 .- a

.IO

.05

0

r i l ro-0.5

P = @


/

I I I I I 1 I I I I 2 4 6 8 10 12 14 16 18 20

Tilt parameter, yr,,lh2

(e) Lubricant outflow at trailing edge.


43

I .- L

rilr, - 0.7

P = 300

- m U m .-

.65. L

2 h Y) W

L f .60- W

c W 0

c

.55 -

1 '%I

Tilt parameter, Pitch l ine

location,

-

-

. 2

1.00

enter-of-pressure angular location, e Ip CP

I .80

I ,85

(a) Center of pressure. Figure 9. - Design charts for flat. sector-shaped pad with ratio of inner to outer radius rilro of 0.7 and angular extent

P of@.

44

I

rilro = 0.7 8=300


. 0010

I I I I I I I I I I I 0 2 4 6 a 10 12 14 16 18 20

Tilt parameter, yrolhp

(b) Load capacity.


45

I I 111111111111 1.11111 1111111 I1

1%

135

12c

105

N r c S X Y -- c m

U .- .- = 7: 8 v) VI 0

c 0

- .- .- I3 60 t

45

XI

15

0

rilro = 0.7

8.300

I I I . I 1 I I I 2 4 6 8 10 12 14 16 18 20

I . - L


(c) Friction loss.


46

.40

.35

.%

-Lo N 2 .25

3 - d z .- .20 VI VI 0)

c - .- VI c

.15 .- n

.10

.05

0

ri/ro = 0.7 8 = % 0


e,m

I I 2 4

I 1 - I I I L I I 6 8 10 12 14 16 18 20

Tilt parameter, yrofh2



47

.30

.25

NLO N z 3 .20 5 - d = 2 .I5 VI VI W

c

VI c W

- .-

.- E .10 n

.05

0

rilr, = 0.7 8=300


e,ip -1.25and -1.50 -, -1.00 and -1.75 7'1

-0.5, -0.75 and -2.00 ,\\I\\\\

-. 25 7;, '\ \\ 07\\\ \\ \

I- ~ 1 - 1- ~ I 10 12 14 16 18 20

1 . . ~ - 1 - .- -1- I 2 4 6 8

A Tilt parameter, yrolh2

(e) Lubricant outflow at trail ing edge.


48

.85

.80

.75

.70

.65

* @

.55

.%

Silt parameter,

Y@2

20-,-1.00

rilro = 0.7 B=4P


BP'B

.45 . % .55 .60 .65 .70 .75 . ao .a5 Center-of-pressure angular location, ecpip

(a) Center of pressure. Figure 10. - Design charts for flat, sector-shaped pad with ratio of inner to outer radius rilro of 0.7 and angular extent

p of4P.

49

, , ......-.-

. 001

. 00:

.002

- 5 .002 3 d 0 - 5

5 .001

.001

f000

ri/r, = 0.7 p = 450


epfp

1 1 I 6

I 1 I I I 1 I 8 10 12 14 16 18 20

Tilt parameter. yrolh2

(b) Load capacity.


50

135

120

105

N

s90 . L L

i c 0)

V .- E 15 8 VI VI 0

c 0 - .-

60 t

45

30

15

0

,

ri/ro = 0.7 p - 4 9

I Pitch line

I I 2 4

1 I I I , I I 6 8 10 12 14 16 18 20


(c) Friction loss.


51

.%

.45

.40

.35

NLo 2 .a 3 3 d 5 .25 .- VI VI al E 0

I=

- .- VI

g .20 .- n

rilro - 0.7 p . 4 9


ep'b 0.257,

.15

.10

.05

+$O _. .-I __ I._ - - I - L - L - . - 8 10 12 14 16 2 4 6 Tilt parameter, yrol h2

0



52


-0.25and -1.00 7,

%%and -0.75:!

epIp

__c==____ 0 .25

1.00

(e) Lubricant outflow at trailing edge.


E

53

.85

.80

- ._ I

LO .75 - I i- I

P V L - $ .70 .- - m V 0

m v

- - .- ' .65 z z v1 v1 aJ

a L

P .60 c c d

.55

.50

rilro = 0.7 B = 68

Tilt para meter, Pi tch l i ne

Y ro lh2 location, ep IP 20,. -0.50

.45 .50 .55 .60 .65 .70 .75 .80 .85 .40 Center-of-pressure angular location, OcplP


Figure 11. - Design charts for flat, sector-shaped pad with ratio of i nne r to outer radius rilr, of 0.7 and angular extent P o f 6 8 .

54


eP@

rilro = 0.7 e = 600

.m20 - 1.00

-======\- I c I 1 I 1 I 1 I I

0 2 4 6 8 10 12 14 16 18 Tilt parameter, y r o / h 2

( b ) Load capacity.


55

111l11llI 1111

rilro = 0.7 8 = @

/ Pitch line location,

c

" E

u VI VI 0

.- - 15

I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20


(c) Friction loss.


56

.m

.4:

.40

.35

NLO N

‘3 .?€I

-2- d

-IN

c .- c .25 VI VI al

c 0

VI

- .- s .- E .20 n

.15

.10

.05

0

ri/ro = 0.7 P-600

Pitch line

r 0.50 // //

1 I 2 4

I 1 I I I I 6 8 10 12 14 16

Tilt parameter, yro/hp



I 2 18 20

57

.20

+IN

.15 - s L c

2 0

VI VI a

0

VI c 0,

- .10 .-

E n .-

.05

rilro = 0.7 p -600

Pitch l ine

I I I I I I I I 20 i a

I 16

I 0 2 4 6 a 10 12 14

Tilt parameter, yr,/h2



58 NASA-Langley, 1977 E- 8899

N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N . D.C. 20546

P O S T A G E A N D F E E S P A I D NATIONAL AERONAUTICS A N D

S P A C E ADMINISTRATION

U S M A I L I 451

U

256 C C l C 1 U c 77f’325 SQiS963DS CEPT O F THE A f E F C h C E A T WEWPOLS L E E C F W T O B Y ATTN: TECHNICBL L l E I j A E Y (SUL) K I I i T L B N D A F B hM 87117

TMASTIR : If Undelivernble (Section 158 Postiil Mnnnnl) Do Not Return

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design charts for arbitrarity pivoted, liquid-lubricated, flat-sector-pad

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