SSME SEAL TEST PROGRAM: TEST RESULTS

FOR SAWTOOTH PATTERN DAMPER SEAL--INTERIM PROGRESS REPORT

NASA CONTRACT NAS8- 35824

Prepared by

Dara W. Childs, Ph.D., P.E.

Professor of Mechanical Engineering

February 1986

TRC-Seal-1-86

(NASA-CK-1788C1

III

) SSME SEAL TEST PROGRAM

TEST RESULTS FOE SAWTOOTH PATTEBN DAMPER

SEAL Interim Proqress Report JTexas A6M

Dniv. ) 101 p HC A06/MF A01 CSCL 11A

G3/37

N86-2394D

Unclas

16969

Turbomachinery Laboratories

Mechanical Engineering Department

stion, Tex.:
SSME SEAL TEST PROGRAM:

TEST RESULTS FOR SAWTOOTH-PATTERN DAMPER SEAL

INTERIM PROGRESS REPORT

NASA CONTRACT NAS8-358211

Prepared by

Dara W. Childs, Ph.D., P.E.

Professor of Mechanical Engineering

Turbomachinery Laboratories

Mechanical Engineering Department

Texas A&M University

College Station, Texas 77843

February 1986

TRC-Seal-1-86
TABLE OF CONTENTS

Page

ABSTRACT 1

LIST OF FIGURES 3

LIST OF TABLES 6

NOMENCLATURE 8

INTRODUCTION 10

TEST CONFIGURATIONS AND CAPABILITY

Test Configurations 15

Test and Data Capability 21

DYNAMIC TEST DATA 24

CONCLUSIONS: 52

REFERENCES 53

APPENDIX A. STATIC TEST RESULTS FOR SAWTOOTH PATTERN STATORS . . . 54

APPENDIX B. DYNAMIC TEST DATA FOR SAWTOOTH-PATTERN 77
ABSTRACT

Test results consisting of direct and transverse force coefficients are

presented for eleven, sawtooth-pattern, damper-seal configurations.

The designation "damper" seal refers to a seal which uses a

deliberately roughened stator and smooth rotor as suggested by von

Pragenau [1] to increase the net damping force developed by a seal.

The designation "sawtooth-pattern" refers to a stator roughness pattern

whose normal cross section to the axis of the seal resembles a saw

tooth with the teeth direction opposing fluid motion in the direction

of shaft rotation. The sawtooth pattern yields axial grooves in the

stator which are interrupted by spacer elements which act as flow

constrictions or "dams".

All seals tested use the same smooth rotor and have the same,

constant, minimum clearance. The stators which were tested examined

the consequences of changes in the following design parameters:

(a) axial-groove depth (tooth height),

(b) number of teeth,

(c) number of sawtooth sections,

(d) number of spacer elements (dams),

(e) dam width,

(f) Axially aligned sawtooth sections versus axially-staggered

sawtooth sections, and

(g) Groove geometry.

From a rotordynamics viewpoint, none of the sawtooth-pattern seals

performs as well as the best round-hole-pattern seal. The best

sawtooth-pattern stator yielded 18$ more net damping than a smooth seal

1
versus 38$ more net damping for the best round-hole-pattern damper

seal. Maximum damping configurations for the sawtooth and round-holepattern stators had comparable stiffness performance; however, the

maximum-damping saw-tooth-pattern stator leaked approximately 20$ more

than the maximum-damping round-hole pattern stator.

From a leakage viewpoint, several of the sawtooth pattern stators

outperformed the best (maximum-damping) round-hole pattern seal by

approximately 20$.
LIST OF FIGURES

page

1. Round-hole pattern stator number, insert number one .... 13

2. Axially-grooved, sawtooth-pattern stator insert with end

seals 14

3. High-Reynolds-Number seal test section 16

4. Cross-section of sawtooth-pattern stator 17

5. Schematic for sawtooth-pattern stators 1 through 4 18

6. Schematic for sawtooth-pattern stators 5 through 7 19

7. Schematic for sawtooth-pattern stators 8 through 11 .... 20

8. Radial and tangential force coefficients for sawtooth

stator 1 25

9. Radial and tangential force coefficients for sawtooth

stator 2 26

10. Radial and tangential force coefficients for sawtooth

stator 3 27

11. Radial and tangential force coefficients for sawtooth

stator 4 28

12. Radial and tangential force coefficients for sawtooth

stator 5 29

13. Radial and tangential force coefficients for sawtooth

stator 6 30

14. Radial and tangential force coefficients for sawtooth

stator 7 31

15. Radial and tangential force coefficients for sawtooth

stator 8 32
16. Radial and tangential force coefficient? for sawtooth

stator 9 33

17. Radial and tangential force coefficients for sawtooth

stator 10 34

18. Radial and tangential force coefficients for sawtooth

stator 11 35

19. Cef versus AP for sawtooth stators 1 through 4,

a smooth stator, and the optimum-damping round-holepattern stator 40

20. Kef versus AP for sawtooth stators 1 through 4,

a smooth stator, and the optimum-damping round-holepattern stator 41

21. CL versus AP for sawtooth stators 1 through 4,

a smooth stator, and the optimum-damping round-holepattern stator 42

22. Cef versus AP for sawtooth stators 5 through 7,

a smooth stator, and the optimum-damping round-holepattern stator. 43

23. Kef versus AP for sawtooth stators 5 through 7,

a smooth stator, and the optimum-damping round-holepattern stator 44

24. CL, versus AP for sawtooth stators 5 through 7,

a smooth stator, and the optimum-damping round-holepattern stator 45

25. Cef versus AP for sawtooth stators 8 through 11,

a smooth stator, and the optimum-damping round-holepattern stator 46
26. Kef versus AP for sawtooth stators 8 through 11,

a smooth stator, and the optimum-damping round-holepattern stator 147

27. CL, versus AP for sawtooth stators 8 through 11,

a smooth stator, and the optimum-damping round-holepattern stator H8
LIST OF TABLES

page

1. Dimension? of sawtooth-pattern stators 22

2(a). Measured values for Kef, Cef, and Mef for sawtooth

stators 1 through 4 37

2(b). Measured values for Kef, Cef, and Mef for sawtooth

stators 5 through 7 38

2(c). Measured values for Kef, Cef, and Mef for sawtooth

stators 8 through 11 39

A.1 Test Data: Operating Conditions and Parameters for stator 1 . 55

A.2 Test Data: Operating Conditions and Parameters for stator 2 . 57

A.3 Test Data: Operating Conditions and Parameters for stator 3 . 59

A.14 Test Data: Operating Conditions and Parameters for stator 4 . 61

A.5 Test Data: Operating Conditions and Parameters for stator 5 . 63

A.6 Test Data: Operating Conditions and Parameters for stator 6 . 65

A.7 Test Data: Operating Conditions and Parameters for stator 7 . 67

A.8 Test Data: Operating Conditions and Parameters for stator 8 . 69

A.9 Test Data: Operating Conditions and Parameters for stator 9 . 71

A.10 Test Data: Operating Conditions and Parameters for stator 10. 73

A.11 Test Data: Operating Conditions and Parameters for stator 11. 75

B.I Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 1 78

B.2 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 2 80
B.3 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 3 82

B.4 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 4 84

B.5 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 5 86

B.6 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 6 88

B.7 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 7 90

B.8 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 8 92

B.9 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 9 94

B.10 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 10 96

B.11 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 11 98
NOMENCLATURE

c: Cross-coupled damping coefficient, introduced in Eq. (1),

FT/L.

k: Cross-coupled stiffness coefficient, introduced in Eq. (1),

F/L.

mr, nr: Empirical turbulence coefficients to define the seal-rotor

friction factor.

ms, ns: Empirical turbulence coefficients to define the seal-stator

friction factor.

A: Dynamic seal eccentricity, introduced in Eq. (2).

C: Direct damping coefficient, introduced in Eq. (1), FT/L.

Cef: Net damping coefficient, introduced in Eq. (10), FT/L.

CD: Discharge coefficient, introduced in Eq. (11).

CL,: Leakage coefficient, introduced in Eq. (12).

Minimum radial seal clearance, L.

FX» FY: Cartesian components of the seal reaction force, introduced

in Eq. (1 ), F.

Fr, FQ: Radial and circumferential components of the seal reaction

force, F.

K: Direct seal stiffness coefficient, introduced in Eq. (1),

F/L.

M: Seal added mass coefficient, introduced in Eq. (1), M.

Mef: Effective seal added-mass coefficient, introduced in Eq.

(10), M.

AP; Seal pressure differential, F/L2.

R: Seal radius, L.

Ra • 2pVCr/u: Reynolds number.

V: Average axial fluid velocity in the seal L/T.

X, Y: Seal displacement components, introduced in Eq. (1), L.

Xr: Seal rotor friction factor, defined in Eq. (5).
o •= X(L/Cr): Axial pressure-gradient coefficient,

p: Seal density. M/L3.

u>: Seal rotational and precessional velocity, T"1

p: Seal viscosity, FT/L2.
INTRODUCTION

The test and analysis results which are reported here were obtained

under NASA Contract NAS8-3582i4. The present work continues research

activity which began in January of 1980 under NASA Contract NAS8-33716.

Earlier contract reports C3~7] provide detailed information covering

the following points:

(a) test-section and facility description,

(b) test-objectives and procedures, and

(c) data acquisition, analysis and procedures.

Most of this information is not repeated here, and interested readers

are referred to earlier reports.

From a rotordynamics viewpoint, seal analysis has the objective of

predicting the coefficients for the following motion/reaction-force

model

(1)

FX

FY

=

K k"

-k K

X

Y

+

C c"

_-c C_

X

.

Y

+ M

* •

X

Y

where X, Y are components of the seal-rotor displacement relative to

its stator and FXI FY are components of the reaction force. The

diagonal and off-diagonal stiffness and damping coefficients are

referred to, respectively, as "direct" and "cross-coupled". The

cross-coupled coefficients arise due to fluid rotation within the seal.

The coefficient M accounts for the seal's added mass.

10
If a circular orbit of the form

X = A coswt, Y = A sinut (2)

is assumed, Eq. (1) yields the following definition of force

coefficients which are, respectively, parallel and perpendicular to the

rotating displacement vector

Fr/A = -K -coj + Mo)2

(3)

Fe/A = k - Co>

Observe that the cross-coupled-stiffness coefficient k yields a

"driving" tangential contribution in the direction of rotation, while

the direct damping coefficient develops a drag force opposing the

tangential velocity.

A prior investigation [6] examined five new "damper seal"

configurations which were largely inspired by von Pragenau's work [1].

Von Pragenau's analysis predicts that a smooth-rotor/rough-stator

combination will yield a reduced asymptotic fluid tangential velocity

within the seal, which will, in turn, yield a reduction in the

cross-coupled stiffness coefficient. A reduced cross-coupled stiffness

coefficient reduces the destabilizing tangential driving force on the

rotor, yields an increased net damping force, and generally enhances

rotor stability and response. A subsequent and more comprehensive

analysis by Childs and Kim [2], yields the same sort of encouraging

predictions.

The results of [6] confirmed that damper seals could yield

11
increased net damping coefficients and showed particularly encouraging

results for the round-hole pattern configuration of figure 1. The

report [7] provided test data for twelve additional round-hole-pattern

seal configurations.

The results of [6] also included test results for the sawtoothpattern, axially-grooved seal of figure 2. The teeth in the sawtoothpattern cross section are directed against fluid rotation, with the

intuitive expectation that this arrangement reduces the average

circumferential fluid velocity and thereby reduces the cross-coupledstiffness-coefficient, k. Test results for this seal showed a

substantial increase in net damping as compared to a smooth seal;

however, the leakage performance was only slightly better than a smooth

seal and substantially worse than the hole pattern seal. The present

report provides test data for eleven, sawtooth-pattern seals which are

"inspired" by the original axially-grooved seal of figure 2, but have

additional intermediate separators between the sawtooth pattern

sections to improve leakage performance. The hope and expectation of

this test program was that a sawtooth-pattern seal could be developed

which retained or improved upon the damping performance suggested by

the test results for the stator of figure 2, while sharply improving

the leakage performance.

12
Olmcnilont In Mllllm«t«r»

O O O O O

O O O O O

O O O O O

o o o o

279 Ola 10 0««p

97

s.»«

Surface RovglMMi* Octal)

Figure 1. Round-hole pattern stator number insert number one.

13
'J

v////

-4.7

*////>

b

[-7.9

— 49.9—

10

|

12

1.0

i:

7.0

0Olm«n«loni In

109 T««th

Surfeet 0«toN

Figure 2. Axially-grooved, sawtooth-pattern stator

insert with end seals.
TEST CONFIGURATIONS, CAPABILITY. AND RESULTS

Test Configurations

The seal test section Is illustrated in figure 3 and is designed to

accept candidate seal inserts. All seals tested use a smooth rotor and

have a constant minimum clearance, i.e., no taper. Figure H

illustrates the assembly procedure for the sawtooth-pattern seal. The

sawtooth-pattern sections are pressed into a stainless-steel housing

and separated by dams. A brass retaining ring at the seal entrance

holds the seal-ring/dam assembly together.

All stators tested had 1 inch ( 101.6 mm) internal diameters, were

2 inches (50 mm) long, and had .020 in (.508 mm) minimum radial

clearances.

Figure 5 illustrates the dimensions and arrangements for stators 1

through 4. Observe that the axial-grooves in the seal section are

aligned for seals 1 and 3 (straight), but are staggered for seals 2 and

i*. The groove-depth (tooth height) of 2.5^4 mm is characteristically

large for these four stators.

Figure 6 illustrates the dimensions for seals 5 through 7. By

comparison to figure 2, seal 5 has the same cross-section as the

original axial-grooved seal. The three, stator cross sections of

figure 6 differ only in the number of teeth or grooves. For these

stators, the groove-depth to minimum-clearance ratio, h/Cr, is two.

15
HOLLOW

ROLLER

BEARING

HIGH REYNOLDS NUMBER

SEAL TEST SECTION

PROXIMITY

PROBE

ITYPICALI

TEST

INLET INLET & OUTLET

•THERMOCOUPLE

ITYPICALI

•THRUST

BEARING

PRESSURE

TRANSDUCER

(TYPICAL)

-MECHANICAL

OUTLET-1 SEAL

INLET

Figure 3. High-Reynolds-Nuaber seal test section.

16
SEAL ASSEMBLY

St«lnle«8

Steel

Housing

Sc«l

Ring*

V/A A7/77

V

Brass

.RetatnlnR

Ring

Figure *l. Cross-section of sawtooth-pattern stator.

17
Sea In 1 Ttirnuch 4

2.54mm

SEALS 1 and 3 straight

3.81mm

Dan

Seal Ring

SEALS £ and ^ staggered

Figure 5. Schematic for sawtooth-pattern stators 1 through

18
ORIGINAL PAGE IS

OF POOR QUALfTY

Seals 5 Through

SEALS 5.6 and 7 straight

•7.7038B

2.54mm

SEAL .5

105 teeth

SEAL 6 80 teeth

2.54mm

SEAL 7 55 teeth

2.54ma

Figure 6. Schematic for sawtooth-pattern stators 5 through 7.

19
MJUS B TIIKOIICH I I

SEALS 9 AND 11 STACCERKD

0.4775m

3.335mm

60 TEETH

SEALS 8 AND 10 STAGGERED

1.9845BB-*-

•*- 3.3172nn

1.524

Figure 7. Schematic for sawtooth-pattern stators 8 through 11

20
Figure 7 illustrates the dimensions of seals 9 through 11. The

h/Cr ratios for this group of seals is 3-0.

The parameter,

hole area

total area

was easily calculated for the round-hole pattern seals. For the

present seals, the area of a single "hole" is defined to be An - BXE.

Table 1 provides, the dimensions, and h/Cr and Y ratios for all of the

sawtooth-pattern stators.

Test and Data Capability

The rotor segments of the test seal are mounted eccentrically on the

rotor of figure 2 with the eccentricity A. Hence, rotor rotation

generates a synchronously precessing pressure field. Axially spaced,

strain-gauge, pressure transducers are provided to measure the

transient pressure field, and the transient pressure measurements are

recorded and integrated to define Fr/A, Fg/A, and |F|. In any test,

five to ten cycles of data, containing on the order of 2,000 data

points, are analyzed. Each data point yields a calculated value for

Fp/A, FQ/A and |F|, and average and standard-deviation values are

calculated for the test case. Observe from Eq. (3) that the test

apparatus yields only the net radial and tangential force coefficients

and can not be used to separately identify the seal coefficients.

The analysis of von Pragenau [1] and Childs and Kim [2] indicates

that the seal rotor and stator roughness are important in defining the

cross-coupled stiffness coefficient k and net-damping-force coefficient

21
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22
Fg/A. For homogeneous roughness, estimate? for the relative roughness

parameters can be obtained from measured results for the axial pressure

gradient and leakage rate. The required data, consisting of the supply

and discharge pressures and pressure measurements at axial locations

throughout the seal, are sampled, averaged, and recorded immediately

before transient data are recorded. For homogeneous-roughness

stators, this data can be used as input data for predictions of seal

rotordynamic coefficients. However, no analytical model presently

exists for the inhomogeneous and discontinuous roughness pattern

presented by these sawtooth stators.

For a given seal configuration, a test matrix is carried out with

variations in the flowrate (axial Reynolds number) and shaft rotational

speed. The flowrate is varied from a minimum value, which Is

sufficient to yield adequate signal-to-noise ratios of the transient

pressure measurements, out to the maximum flow capability of the

circuit. Shaft rotation speed is incremented from approximately 1,000

rpm to 7,200 rpm. In a given test series, the axial Reynolds number is

held constant and the running speed incremented.

For a given test, the following two types of data are secured:

(a) steady-state "input" data consisting of the pressure

differential, average fluid density and viscosity, mass leakage

rate, and rotational speed, and

(b) "output" data consisting of Fr/A, F0/A, \F\ versus the axial

Reynolds number and shaft running speed.

The tables of Appendices B and C provide this type of data for each

test of each seal configuration.

23
DYNAMIC TEST RESULTS

Figure 8 through 18 illustrate measured result? for Fr/A and Fg/A

versus Ra and cj for the sawtooth-pattern seals. Each curve of these

figures corresponds to a fixed axial Reynolds number, Ra. Appendix B

contains the data presented in these figures.

The results of figures 8 through 18 generally follow the

predictions of Eq. (3). The radial force coefficients starts at a

negative valve for low running speeds and increases in an approximate

quadratic fashion as w increases. The tangential force coefficients is

an approximate linear function of 01.

An inspection of Eqs. (3) suggest that sufficient independent

equations could be obtained to calculate all the rotordynamic

coefficients by simply testing at three running speeds. However, the

fact that the coefficients depend on u> precludes this approach. While

K, C, and M are weak functions of u through their dependence on a, the

"cross-coupled" coefficients k and c are linear functions of tu. In

fact, if the fluid is prerotated prior to entering the seal such that

the inlet tangential velocity is UQO •= Rco/2, then theory predicts that

k = Cu)/2, c = Mco, and

Fp/A - -K, Fe/A = -Coo/2 (M)

The present test apparatus provides no intentional prerotation, and the

expected result is of the form

k - b-iCoj/2, b!<1

c - b2Mo>, b2<1 (5)

Fe/A • -Cef to • -C(1-b1/2)u)

Fr/A • -Kef + Mef u)2 • -K + M(1 -b2)u>2 (6)
z

-J

I<

o

-i

-3

-3

-4

-5

-6

-7

-8

-9

-10

X

z

X

a

cr

3

2.7

2. 4

2. 1

1.8

1.5

1.2

.9

.6

.3

0

'.6

.8

1.2

1.3

1.6

Z. 1

2.4

2. /

3

SAWTOOTH PATTERN #1

y -0. 40i h/Cr-5. 0

a RA- 90134

o RA- 129963

A RA- 160284

0 RA- 257800

o RA- 326400

80

160 320 480 640 800

240 400 560 720

ROTOR SPEED (RAD/SEC)

1BO 320 460 040 800

80 240 400 380 720

ROTOR SPEED (RAO/SEC)

Figure 8. Radial and tangential force coefficients for sawtooth

stator 1.

25
SAWTOOTH PATTERN *2

•y -0. 40, h/Cr-5. 0

D

o

RA- 69929

RA- 89929

RA- 154735

RA- 253100

RA- 327338

X

i

z

Ul

<

s.

Q

a

o

-i

-2

-3

-4

-3

-6

-7

-e

-e

-10

4

3.6

3.2

2.8

2. 4

2

1.6

.'e

.4

o

-.4

-.6

-1.2

-1.6

-2

-2.4

-2.6

-3.2

-3.6

-4

160 320 460 040 600

80 240 400 560 720

ROTOR SPEED (RAO/SEC)

60

160 320 460 640 800

240 400 SCO 720

ROTOR SPEED (RAO/SCO

Figure 9. Radial and tangential force coefficients for sawtooth

stator 2.

26
0

z -I

I -

2

w

 -3

~ -0

"• -io

z

N

Z

o

a:

4

3.6

3.2

2.8

2.4

2

1.6

1.2

.8

. 4

c

-. 4

-. e

-J.2

-i.e

SAWTOOTH PATTERN #3

-y -0. 78i h/Cr-5. 0

D RA- 90341

O RA- 90341

A RA- 160186

0 RA- 206700

O RA- 245110

80

1 00 320 480 840 800

240 400 SCO 720

ROTOR SPEED (RAO/SEC)

160 320 480 040 800

00 240 400 SBO 720

ROTOR SPEED (RAO/SEC)

Figure 10. Radial and tangential force coefficients for sawtooth

stator 3.

27
2

Z.

_l

•z.

UJ

o

z

2

<

o

a

4.5

4

3.5

3

2.5

2

1.5

I

.5

0

-.5

-J

-1.5

-2

SAWTOOTH PATTERN *4

•y -0. 74j h/Cr-5. 0

D RA- 90044

o RA- 129923

A RA- 160136

+ RA- 210021

RA- 262694

160

eo

320 460 640

2*0 400 560

600

720

ROTOR SPEED (RAD/SEC)

160 320 480 840 BOO

60 240 400 500 720

ROTOR SPEED (RAO/SEC)

Figure 11. Radial and tangential force coefficients for sawtooth

stator 4.

28
X

x

Z

z

UJ

O

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

X

5

ac.

4

3.6

3.2

2.8

2. 4

2

1.6

1.2

.8

. 4

0

. 4

.6

1.2

1.6

2

2.4

2.6

3.2

3.6

4

SAWTOOTH PATTERN <cs

y -0.64, h/Cr-2.0

Q RA- 89974

o RA- 130129

A RA- 130129

+ RA- 250335

0 RA- 344320

0 160 320 480 640 800

60 240 400 560 720

ROTOR SPEED (RAD/SEC)

160 320 480 640 800

80 240 400 560 720

ROTOR SPEED (RAD/SEC)

Figure 12. Radial and tangential force coefficients for sawtooth

.stator 5.

29
SAWTOOTH PATTERN #

•y -0. 49, h/Cr-2. 0

o

o

RA- 90125

RA- 130062

RA- 159877

RA- 250101

RA- 319763

z

X

2

Z

Z

LJ

O

2

Q

K

0

-I

-2

-3

-4

-*,

-6

-7

-e

-9

-10

4

3.6

3.2

2.8

2.4

2

1.6

1.2

.8

. 4

0

-. 4

-.6

-1.2

-1.6

-2

-2.4

-2.8

-3.2

-3.6

-4

0 160 320 460 640 800

80 240 400 560 720

ROTOR SPEED (RAO/SEC)

160 320 480 640 eoo

80 240 400 seo 720

ROTOR SPEED (RAO/SEC)

Figure 13. Radial and tangential force coefficients for sawtooth

stator 6.

30
z -

2

x

-4

-6

z

Ul

0

a

a:

-8

-10

-12

4

3 6

3.2

2 8

2. 4

2

1.6

1.2

.6

. 4

0

-. 4

-.8

-1.2

-1.6

-2

-2.4

-2.8

-3.2

-3.6

-4

SAWTOOTH PATTERN t

-y -0. 34, h/Cr-2.0

Q RA- 89898

O "A- 129912

A RA- 159929

+ RA- 249908

O RA- 362041

0 160 320 480 640 600

80 240 400 560 720

ROTOR SPEED (RAO/SEC)

160 320 480 640 800

80 240 400 S60 720

ROTOR SPEED (RAO/SEC)

Figure 1U. Radial and tangential force coefficients for sawtooth

stator 7.

31
I

•y

2

X

Z

LU

O

X

2

Q

a

-2

-4

-6

-e

-10

-12

4

3.6

3.2

2.8

2.4

2

1.6

1.2

.8

. 4

C

-. 4

-.8

-1.2

-1.6

-2

-2.4

-2.8

SAWTOOTH PATTERN #£

-y -0. 48, h/Cr-3. 0

Q RA- 90086

o RA- 129906

A RA- 159888

+ RA- 219990

rt RA- 282205

0 ICO 320 480 640 800

80 240 400 560 720

ROTOR SPEED <RAO/SEC>

0 160 320 480 640 BOO

80 240 400 900 720

ROTOR SPEED (RAD/SEC)

Figure 15. Radial and tangential force coefficients for sawtooth

stator 8.

32
SAWTOOTH PATTERN *

•y -0. 681 h/cr-3. 0

O RA- 900B9

o RA- 130063

A RA- 160274

+ RA- 219859

RA- 252237

z

o

0

-1

-3

-3

-4

-5

-e

-7

-e

-s

-10

0 100 320 460 040 BOO

80 240 400 560 720

ROTOR SPEED (RAO/SEC)

z

x

z

0

cr

5

4.5

4

3.5

3

2.5

Z

I. 5

1

.5

0

-.5

-1

-1.5

-2

60

100 320 460 640 600

240 400 SOO 720

ROTOR SPEED (RAD/SEC)

Figure 16. Radial and tangential force coefficients for sawtooth

stator 9.

33
SAWTOOTH PATTERN #10

•y -0. 33» h/Cr-3. 0

D RA- 90048

RA- 129810

RA- 180088

RA- 218819

RA- 318898

z

X

«*\ _J

z

LJ

U

-2

-4

-8

-9

-10

-12

*~ "'

o

a

4

3.8

3.2

2.8

2.4

2

1.8

1.2

.8

. 4

0

>. 4

.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

80

180 320 480 840 800

240 400 560 720

ROTOR SPEED (RAO/SEC)

160 320 480 640 800

80 240 400 560 720

ROTOR SPEED (RAD/SEC)

Figure 17. Radial and tangential force coefficients for sawtooth

stator 10.

34
•z.

•z.

Ul

o

7.

Z

-2

-6

-8

-10

-12

a

cr

u. -

SAWTOOTH PATTERN #

•y -0. 47j h/Cr-3. 0

Q RA- 89973

o RA- 130003

A RA- 159973

+ RA- 220132

o RA- 272141

0 160 330 460 640 600

80 240 400 560 720

ROTOR SPEED (RAO/SEC)

640 800

240 400 580 720

ROTOR SPEED (RAD/SEC)

Figure 18. Radial and tangential force coefficients for sawtooth

stator U.

35
The term Cef denotes the "net damping coefficient" resulting from the

drag force Cu>A and the forward whirl excitation force kA. Note

that the procedure of curvefitting the data with respect to co

eliminates the running-speed dependency. Further, Kef is the zerorunning speed intercept of the Fr/A versus w curve, and Cef is the

slope of the F0/A versus oi curve. Experimentally-determined values are

presented in tables 2(a), 2(b) and 2(c) for Kef, Cef, and Mef.

From a rotordynamics viewpoint, Kef and Cef can be used for direct

comparison of the performance of seal configurations at the same

pressure differential. For leakage comparison, the leakage coefficient

is defined using the conventional discharge-coefficient definition

pV2

AP = Cd (7)

2

which yields

,Cr. -1/2

Q - 2irRCrV - (—) Cd • 2irR2

v/2AP^ = CL • 2irR2v/ 2AP

R p p

Hence,

Cr -1/2

C

L - ( —) Cd - Q (2TiR2

 V/^2APJ (8)

R p

The coefficient CL is a nondimensional relative measure of the leakage

to be expected through seals having the same radius.

Figures 19 through 27 illustrate Kef, Cef, and CL versus AP for

all of the sawtooth-pattern stators. For comparison purposes, results

are also given in these figures for a smooth stator and the holepattern stator with maximum net damping.

36
KEF(EXP) MEP(EXP)

SAWTOOTH PATTERN #1 h/Cr= 5.O

25 TEETH, TOOTH DEPTH= 2.540mm, GAMMA=O.4O

RA= .9013E 05

RA= . 1300E 06

RA= . 16O3E 06

RA= .2578E 06

RA= .3264E 06

.4126E O6

. 4918E 06

.60O2E O6

. 1971E 07

.3003E 07

SAWTOOTH PATTERN #2

25 TEETH, TOOTH

RA= .8993E 05

RA= . 1300E O6

RA= . 1598E 06

RA= .253 IE 06

RA= .3273E 06

DEPTH= 2.540mm,

. 1942E O6

.5279E 06

.8402E 06

.209QE 07

.3417E 07

SAWTOOTH PATTERN *3

25 TEETH, TOOTH

RA= .9O34E 05

RA= . 1300E 06

RA= . 1602E O6

RA= .2067E O6

RA= .245 IE 06

SAWTOOTH PATTERN

25 TEETH, TOOTH

RA= .9004E 05

RA= . 1299E O6

RA= . 1601E 06

RA= .2101E O6

RA= .2620E 06

DEPTH= 2.54Omm,

.235 IE 06

.62O2E O6

.9123E O6

. 1669E 07

. 1942E O7

#4

DEPTH= 2.540mm,

-.8431E 05

.3121E 06

.7688E 06

. 1082E 07

.2142E 07

2254.

4021.

4878.

8255.

. 1190E 05

h/Cr= 5.0

GAMMA=O.40

2712.

4362.

5166.

8746.

. 1 286E 05

h/rr= 5.0

GAMMA=0.74

2174.

6327.

8093.

. 1061E 05

. 13S7E 05

h/Cr= 5.0

GAMMA=O.74

3352.

5634.

7151.

9724.

. 1116E 05

2.542

4.592

6.008

5.444

6.O92

4.935

6.886

5.989

7. 178

7.S25

3.O6O

2. 124

1.765

2.016

5.865

6. 171

4.265

3.653

5.865

2.483

Table 2(a). Measured values for Kef. Cef, and Mef for sawtooth

stators 1 through H.

37
EF(EXP) MEF(EXP)

SAWTOOTH PATTERN *5 h/Cr = T.O

105 TEETH, TOOTH DEPTH= l.O16mm, GAMMA=O.64

RA= . 89-57E 05

RA= . 130 IE O6

RA= . 1600E 06

RA= . 2503E 06

RA= .3443E 06

SAWTOOTH PATTERN

80 TEETH, TOOTH

RA= .9O12E 05

RA= . 130 IE 06

RA= . 1599E O6

RA= .25O1E 06

RA= . 3198E O6

SAWTOOTH PATTERN

55 TEETH, TOOTH

RA= . 8<>90E 05

RA= . 1299E O6

RA= . 1599E 06

RA= .2499E O6

RA= .3620E 06

. 2567E

. 58-54E

.4427E

. 2352E

. 4O25E

#6

DEPTH= 1.

.27O3E

. 6323E

.8114E

. 2203E

.3-57 IE

#7

DEPTH= 1.

. 3352E

. 38O9E

. 6550E

. 1460E

. 3O07E

06

O6

06

O7

07

0 1 6mm ,

06

06

06

07

O7

O 1 6mm ,

05

O6

06

07

07

1-580.

O Tie=" ~

s

4687.

7^10.

. 3 1C'7E 05

h/Cr= 2.O

GAMMA=0. 49

2110.

3592.

4898.

^24 1 .

. 1 1 83E O5

h/Cr= 2.O

GAMMA=O. 34

1 69 1 .

3083.

4179.

8072.

. 1203E O5

5.726

6.118

8.840

4. 5 34

7.046

5.830

6.826

7.631

9.c'25

5.7-56

6.874

7.041

6.81-5

10.23

1 1. 36

Table 2(b) Measured values for

stators 5 through 7.

Cef. and Mef for sawtooth

38
^EF(EXP) CEF(EXP) MEF(EXP)

SAWTOOTH PATTERN 4*8 h/Cr = 3.0

60 TEETH, TOOTH DEPTH=1.524mrt,, GAMMA=0.48

RA= . 900*E 05

RA= . 1299E 06

RA= . 15^9E 06

RA= . 2200E O6

RA= . 2822E 06

SAWTOOTH PATTERN

60 TEETH, TOOTH

RA= . 9009E O5

RA= . 130 IE 06

RA= . 1603E 06

RA= . 21-^E 06

RA= . 2522E 06

SAWTOOTH PATTERN

60 TEETH, TOOTH

RA= . «005E 05

RA= . 1298E O6

RA= . 160 IE 06

RA= .2198E 06

RA= .3167E 06

-.2086E

. 5965E

. 7869E

. 1489E

. 1 804E

#9

DEPTH= 1.

.6691E

. 6953E

.9550E

. 1218E

. 1599E

#10

DEPTH= 1.

. 1809E

. 57O7E

. 1 1 28E

. 2292E

. 3600E

SAWTOOTH PATTERN 4*11

6O TEETH, TOOTH DEPTH= 1.

RA= .8997E 05

RA= . 1300E 06

RA= . 1600E 06

RA«= .2201E 06

RA= .272 IE O6

. 2242E

. 5037E

.1169E

. 1868E

. 2729E

O5

O6

06

O7

07

524rrifTi,

05

06

06

07

07

524fTicn ,

06

O6

07

07

07

524mm,

O6

06

07

O7

07

2554.

5342.

6954.

. 1018E

. 1449E

h/Cr= 3.0

GAMMA=0.68

309O.

5632.

7796.

. 1121E

. 1316E

h/Cr= 3.0

GAMMA=0.33

3110.

5061.

6865.

9164.

. 1477E

h/Cr= 3.0

GAMMA=0.47

3327.

5685.

8292.

. 1125E

. 1404E

O5

05

05

O5

O5

05

05

7. 92C'

3.759

5.777

7. 125

1 1.84

6.841

4.512

5.4'--'S

11. 46

11.18

7.3*7

7. 625

5.947

5. 2*O

12.37

9.012

8.991

7.561

9.716

13.50

Table 2(c). Measured values for Kef. Cef, and

stators 8 through 1 1 .

for sawtooth

39
D

O

A

DAMPER SEAL #3: h/CCr- 3.0 •

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #1

SAWTOOTH PATTERN #2

SAWTOOTH PATTERN 03

SAWTOOTH PATTERN #4

- 0 .34

• -y

« y

i y

i y

- 0

- 0

- 0

- 0

o

01

W

u

.02

.018

.016

.014

.012

.01

.008

.006

.004

.002

0

4

4

74

74

12 18 24 30

IS 21 27

(Po-Pb)ovg (Bars)

Figure 19. Cef versus AP for sawtooth stators 1 through 4,

a smooth stator, and the optinun-damping round-holepattern stator.
LL.

LU

5

4.5

4

3.5

3

2.5

2

1.5

1

.5

0

-.5

-1

D

O

A

DAMPER SEAL #3j h/ Cr- 3. 0 i

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #1 i -0

SAWTOOTH PATTERN #2 t

SAWTOOTH PATTERN #3 »

SAWTOOTH PATTERN #4 «

- 0 . 34

y

T

-0

- 0

- 0

4

4

74

74

6 12 18 24 30

3 9 15 21 27

CPa-Pb> ovg (Bars)

Figure 20. Kef versus AP for sawtooth stators 1 through 4,

a soooth stator, and the optlaur-damplng round-holepattern stator.

41
a

O

A

DAMPER SEAL #3: h/Cr- 3. 0 i -y - 0 . 34

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #1 : -y - 0 . 4

SAWTOOTH PATTERN #2 : -y - 0 . 4

SAWTOOTH PATTERN #3 i y - 0 . 74

SAWTOOTH PATTERN #4 » - 0 . 74

o

o

0

*

t—

UJ

I-H

U.

U_

UJ

0

u

UJ

o

U^J

_J

9

8. 1

7.2

6.3

5. 4

4.5 .

3.6 .

2.7

1.8

.9

0

-

o

^^^

o ^ ^"

0 6 1 2 1 8 2 4 3 0

3 9 15 21 27

(Pa-Pb)avg (Bars)

Figure 21. CL versus AP for sawtooth stators 1 through 4,

a smooth stator, and the optimuar-daoplng round-holepattern stator.

42
n

o

DAMPER SEAL #3: h/ Cr- 3. 0 « y

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #5 t -y - 0 . 64

SAWTOOTH PATTERN #6 : -y - 0

SAWTOOTH PATTERN #7 : y - 0

- 0 . 34

49

34

o

01

U)

u.

LU

(Po-Pb)avg (Bars)

Figure 22. Cef versus AP for sawtooth stators 5 through 7,

a smooth stator, and the optimum-damping round-holepattern stator.
u.

UJ

n

o

A

DAMPER SEAL #3: h/ Cr= 3.0 :

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #5 : -y - 0

SAWTOOTH PATTERN #6 : -y - 0

SAWTOOTH PATTERN #7 : -v - 0

y 0 .34

64

49

34

3 9

(Pa-Pb)avg (Bars)

Figure 23. Kef veroua AP for sawtooth atators 5 through 7*

a eaooth etator, and the optimum-damping round-holepattern stator.

44
LEAKAG

E COEFFICIEN

T * 100

0

C

c

L

<

9

8. 1

7.2

6.3

5.4

4.5 .

3.6 .

2.7 .

1.8 .

.9

0

3 DAMPER SEAL #3: h/Cr- 3. 0 . -y - 0 .

3 SMOOTH SEAL - 20 mils clr

^ SAWTOOTH PATTERN #5 : T - 0 . 64

h SAWTOOTH PATTERN #6 » -y - 0 . 49

> SAWTOOTH PATTERN #7 : -y - 0 . 34

0-n° «- o-i u O u — O

/

<V , r, - •- * 0

A ^ "r, ----A— • • • A

I i 1 — I f

6 12 18 24 30

3 9 1 5 2 1 2 7

(Po-Pb)avg (Bars)

Figure 24. CL versus AP for sawtooth stators 5 through 7.

a smooth etator, and the optiBuo-daoping round-holepattern stator.

45
o

01

u.

LU

U

D

O

A

+

O

IS

DAMPER SEAL #3: h/ Cr- 3. 0

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #8 : T - 0

SAWTOOTH PATTERN #9 : -y = 0

SAWTOOTH PATTERN #10 : -y -

SAWTOOTH PATTERN #11 i

T - 0 . 34

48

68

.33

0 . 47

(Pa-Pb)avg (Bars)

Figure 25. Cef versus AP for sawtooth stators 8 through 11,

a aoooth otator, and the optlaum-daaping round-holepattern stator.
u.

UJ

5

4.5

4

3.5

3

2.5

2

1.5

1

.5

0

-.5

-1

D

O

A

+

O

El

DAMPER SEAL #3: h/ Cr= 3. 0 : -y =

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #8 : y - 0 . 48

SAWTOOTH PATTERN #9 : y - 0 . 68

SAWTOOTH PATTERN #10 t y - 0 . 33

SAWTOOTH PATTERN #11 : -y - 0 . 47

0 .34

12 18 24 30

15 21 27

(Pa-Pb)avg (Bars)

Figure 26. Kef versus AP for sawtooth stators 8 through 11.

a smooth etator, and the optlmun-daaplng round-holepattern stator.

47
a

o

A

DAMPER SEAL #3: h/Cr= 3. 0 : -y - 0 . 34

SMOOTH SEAL - 20 mils clr

SAWTOOTH PATTERN #8 : -y - 0 . 48

SAWTOOTH PATTERN #9 : -y - 0 . 68

SAWTOOTH PATTERN #10 : y - 0 . 33

SAWTOOTH PATTERN #11 : y - 0 .47

a

o

0

*— »

*

i—z

LU

•— i

U

*— i

U.

LL

LU

O

U

LU

0

iC

<

LU

_J

9 T

8. 1 .

7.2

6.3 .

5.4 .

4

e

• O

3.6

2.7

1.8

.9

0

f-. .- Q O

.f"

O

.

- 6 0 0 O

8 'P 'flg ^--M —ft

6 12 18 24 30

3 9 1 5 2 1 2 7

(Pa-Pb)avg (Bars)

Figure 27. CL versus AP for sawtooth stators 8 through 11,

a smooth stator, and the optimum-damping round-holepattern stator.

48
Test result? for stators 1 through H are presented in figures 19

through 21. Results for thee seals are grouped together, because they

have the same groove geometry and h/Cr - 5. From figure 19, the

damping performance of those seals is, at best, comparable to that of a

smooth seal and substantially inferior to the best damper seal. As

illustrated in figure 20, Kef for these seals is generally less than

comparable values for the damper seal and significantly less than

measured values for a smooth seal. Stators 1 and 2 have perceptibly

higher stiffness valves than stators 3 and

 14, presumably because of

differences in Y for the two stator groups. Test results for holepattern seals [7] showed a consistent drop in Kef as Y increases.

Figure 21 shows stators 1 through 4 to leak substantially less than a

smooth seal. Stators 1 and 2 leak worse than the damper seal; seals 3

and 4 leak less. The original vortex flowmeters used for leakage

measurements were replaced by turbine flowmeters between tests for

stators 3 and ^, because they yielded invalid data at higher Reynolds

numbers.

The results for sawtooth patterns 5 through 7 are grouped together

in figures 22 through 25, because these stators have the same groove

geometry, and all have h/Cr = 2. The sawtooth cross-section of stator

munber 5 coincides with the original axially-grooved seal of [6].

These seals differ only in the number of grooves used in the sawtooth

cross section with a consequent change in the hole-density parameter Y.

Figure 22 shows the damping performance of these stators to be

comparable to a smooth seal and substantially inferior to the best

hole-pattern damper seal. The stiffness results of figure 23 are

erratic but generally show stiffness values on a par with the damper
seal. The leakage result? of figure 25 show that all of these seals

leak worse than the hole-pattern damper seal but less than a smooth

seal.

The results for stators 8 through 11 are grouped together in

figures 25 through 27 because they have the same groove geometry and

all have h/Cr «• 3-0. The design for these seals was guided by results

for the hole-pattern seal which showed maximum damping to result for

h/Cr •= 3.0 and Y - 0.3^. Figure 25 shows that all of these stators

have better damping performance than a smooth seal and worse than the

hole-pattern damper seal. Figure 26 shows lower Kef values for stators

8, 9, and 11 than the damper seal, but higher or comparable values for

stator 10. Figure 27 shows superior leakage performance for stator 9

(Y=0.68), lesser but comparable performance for stators 11 (Y=0.147) and

8 (Y=0.'47), and the worst performance for stator 10 (Y°0.33). Stators

8 and 11 have about the same leakage performance as the hole-pattern

stator. All of the sawtooth-pattern stators have much better

performance than the smooth seal.

From an overall viewpoint the best leakage performance for a

sawtooth pattern seal is provided by stators #9 (Y-0.68, h/Cr=3) and #3

or #4 (Y-O.?^, h/Cr=5.0). The maximum effective damping performance is

turned in by seals #8 (Y-0.48, h/Cr-3), #10 (Y-0.33, h/Cr=3), and #11

(Y-O.JJ7, h/Cr-3); each of which provides a maximum at various AP values

in figure 21. The maximum Kef values are provided by seals #10

(Y-0.33, h/Cr-3) and #7 (Y-0.31*, h/Cr-2).

These results support the following general conclusions:

(a) Leakage performance is improved by increasing Y and h/Cr.

From table 1, the minimum-leakage stators used dams with thin

50
widths (0=0.4775 mm). A comparison of the results for stators 3

and 4 or 1 and 2 in figure 20 shows no particular advantage for

either straight or staggered assemblies.

(b) The clear superiority of the h/Cr = 3 ratio in maximizing

Cef is evident in the superior performances of stators 8, 10, and

11. The results do not seem to be particularly sensitive to Y.

(c) Stiffness is decreased by increasing h/Cr and Y.

From a rotordynamics viewpoint, stator number 10 has the best

combined attributes of maximizing Cef and Kef. Interestingly, the

parameters Y - 0.33 and h/Cr = 3 are almost exactly those obtained for

the hole-pattern seal with maximum damping (Y-0.3^, h/Cr=3). Note,

however, from figures 27 that stator number 10 leaks substantially

more than the hole-pattern damper seal.

51
CONCLUSIONS

The results of this test program support the following general

conclusions:

(a) A sawtooth-pattern damper seal can be developed which has

substantially better leakage and damping performance than a

corresponding smooth seal; however, the best sawtooth-pattern seal

tested in this program was substantially inferior to the best

round-hole-pattern seal developed earlier, in terms of both netdamping coefficients and leakage.

(b) Leakage performance is improved by increasing Y and h/Cr. No

advantage is demonstrated by using staggered versus inline

assembly of sawtooth-pattern seal segments. Leakage performance

is better with thin dams, which increases Y.

(c) For the h/Cr ratios tested (2, 3, 5), h/Cr - 3 is clearly

superior.

(d) Stiffness is decreased by increasing h/Cr and Y.

(e) In terms of Y and h/Cr, the sawtooth pattern seal with the

best rotordynamic performance in terms of the ordered criteria (i)

maximum damping and (ii) maximum stiffness had h/Cr - 3, Y - 0.33.

These are almost the same nondimensional parameters which were

obtained for the maximum-damping round-hole-pattern seal (h/Cr-3,

52
REFERENCES

1. von Pragenau, G. L., "Damping Seals for Turbomachinery," NASA

Technical Paper 1987, 1982.

2. Childs, D. W. and Kim, C-H., "Analysis and Testing of Turbulent

Annular Seals with Different, Directionally Homogeneous Surface

Roughness Treatments for Rotor and Stator Elements," ASMS Trans.

Journal of Trlbology Technology, July 1985t Vol. 107, pp. 296-306\

3- Childs, D. W., "SSME HPFTP Interstage Seals: Analysis and

Experiments for Leakage and Reaction-Force Coefficients," Progress

Report, NAS 8-33716, Texas A&M University-Turbomachinery Laboratories

Report, Seal-1-83, 15 February 1983.

H. Childs., D. W., "SSME HPFTP Interstage Seals: Analysis and

Experiments for Leakage and Reaction-Force Coefficients," Supplementary

Progress Report, NASA Contract NAS8-33716, Texas A&M

University-Turbomachinery Laboratories Report Seal-2-83, 15 July 1983.

5. Childs, D. W., "SSME Seal Program: Leakage Tests for

Helically-Grooved Seals," Progress Report NASA Contract NAS8-33716,

Texas A&M University, Turbomachinery Laboratories Report, Seal-3-83,

November 1983.

6. Childs, D. W., "SSME Interstage Seal Research" Progress Report

Contract NAS8-33716, Texas A&M University, Turbomachinery Laboratories

Report, Seal-1-84, January 1984.

7. Childs, D. W., "SSME Seal Test Program: Test Results for HolePattern Damper Seals" Interim Progress Report Contract NAS8-3582^,

Texas A&M University, Turbomachinery Laboratories Report,

July 1985.

53
APPENDIX A.

STATIC TEST RESULTS FOR SAWTOOTH

PATTERN STATORS
A.I Test Data: Operating Conditions and Parameters for stator 1,

SAWTOOTH PATTERN ttl

25 TEETH, TOOTH DEPTH= 2.540mm, GAMMA=0.40

DR. D. CHILDS TEXAS A?/M .JIJN 85

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

1.771

1 . 328

1 . 927

2. 113

2.562

3.111

4. 171

4.312

4.462

4.353

4.47O

5.6O4

6.245

6.235

6.391

6.376

6.603

7.200

15.662

15.638

15.660

15.675

RHO

O'g/M )

1562.614

1567. 144

1567.426

1574.624

1574.333

1553.664

1568.656

1578.434

1583. 100

1572.572

1564.637

1554.211

1554.485

1555.251

1560.830

1558.448

1556.750

1549.492

1565.627

1564.261

1561.005

1566.O64

MIJ

(N sec/M )

. 149E-03

. 1 50E-O3

. 150E-03

. 152E-03

. 152E-03

. 146E-03

. 151E-03

. 153E-03

. 154E-03

. 152E-03

. 14*E-03

. 146E-03

. 147E-03

. 1 47E-03

. 148E-03

. 1 48E-03

. 147E-03

. 145E-03

. 149E-03

. 149E-03

. 148E-03

. 1 49E-O3

MOOT

U g/sec)

2. 117

2. 143

2. 142

2. 172

2. 160

2. 105

3. 11 1

3. 140

3. 183

3. 117

3.07"

3 . 000

3.719

3.702

3.765

3.754

3.743

3.699

6. 115*

6. 108*

6. 105*

6. 118*

CPM

( Cyc/mi n )

1083.

1791.

2691.

3614.

5310.

7136.

1O7<5.

1818.

2740.

3614.

5310.

7186.

1O40.

1765.

2661.

3529.

5310.

7186.

1079.

1780.

2661.

3571.

55
23. 15.632 1568.528 . 150E-03 6.315* 5310.

24. 16.015 1550.847 . 145E-O 3 6.154* 7186.

25. 24.511 1533.-301 .142E-03 7.436 1020.

26. 24.606 153c'.6'-'4 . 142E-O3 7.429 1724.

27. 24.575 1541.781 .142E-03 7.4*2 2586.

28. 24.773 1545.763 .143E-03 7.482 3468.

2"r'. 24.048 1546.371 . 144E-03 7.459 5310.

30. 25.074 1555.547 .146E-O3 7.070 7186.

* ESTIMATED

56
A.2 Test Data: Operating Conditions and Parameters for stator 2

SAWTOOTH PATTERN #2

25 TEETH, TOOTH DEPTH= 2.540mm, O.AMMA=0. 40

DR. D. CHILDS TEXAS A?/M

Case

1.

2.

3.

4.

5.

6.

7.

8.

*.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

1 . 852

1 . 872

1.915

1 . *92

2.517

3.208

4 . 067

4.058

4. 136

4. 157

4 . 33*

5.571

5.852

6.O97

6. 169

3.944

6.284

7.281

15.301

15.295

15.292

15.327

RHO

0 q/M )

1572.581

1568. 366

1 567 . 302

1564. 127

1560.O65

155*. 566

1570.826

1 56* . 9*6

1571. 408

1571. *66

155*. 46*

156O.343

155*. 464

1566.893

1564.223

1555.661

1556.726

1554.951

1563.062

1562.493

1559.358

1557.727

MU

<N sec/M )

. 151E-03

. 150E-O3

. 150E-03

. 1 49E-03

. 148E-03

. 1 48E-O3

. 151E-03

. 151E-03

. 151E-03

. 151E-O3

. 148E-03

. 148E-03

. 148E-03

. 1 50E-03

. 149E-03

. 147E-O3

. 147E-03

. 147E-03

. 149E-03

. 148E-03

. 148E-03

. 147E-03

57

MOOT

(Kg/sec)

2. 148

2. 141

2. 135

2. 132

2. 104

2. 123

3. 123

3 . 0*8

3. 109

3.111

3 . 048

3.059

3.749

3.785

3.773

3.017

3.721

3.711

• 6.039*

6.036*

6.030*

6.O34*

CPM

( Cyc /mi n )

1083.

1796.

2685.

3561.

5333.

7186.

1083.

17*6.

2697.

35*3 .

5333.

7186.

1071.

1791.

2673.

3529.

5333.

7229.

1068.

178O.

2661.

3529.
2 5 .

24.

-~icr

26.

27.

28.

29.

30.

15.

15.

24.

24.

24.

24.

24.

24.

314

276

453

550

553

610

768

8^6

1555.

154'-'.

1 546 .

1554.

1554.

154S.

1 55 1 .

1548.

=>88

171

736

38'?

342

028

430

561

. 147E-O3

, 145E-03

. 144E-03

. 146E-O3

. 146E-03

. 144E-03

. 145E-03

. 144E-03

6.

6.

7.

7.

7.

7.

7.

7.

027*

OO7*

6 1 2

640

6O5

522

542

063

5333

7 1 86

1038

1749

2626

3458

5333

7186

* ESTIMATED

58
A.3 Test Data: Operating Conditions and Parameters for stator 3-

SAWTOOTH PATTERN #3

25 TEETH, TOOTH DEPTH= 2.540mm, G,AMhA=.74

PR. D. CHILD'S TEXAS A?/M JIJL 85

Case

1.

2.

3.

4.

c-

_' .

6.

7.

y .

•3.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

3 . 302

3.272

3.347

3.534

3.8 2O

3.'r'05

7.21 '-•>

7 . 27*

7 . 365

7

-S --i •-•

• ^_^_O

7 . 680

8. SO 3

10.618

10.665

10.088

10.427

10.659

1 1 . 234

18.378

18.389

18.395

18.385

RHO

(Kq/M )

1571.601

1564.658

1563.036

1571.633

1571.^61

1548.476

1581.941

1581.071

1582.264

1570.718

1573.583

1559.061

1575.780

1577.425

1563.663

1565. 158

1564.231

1551.642

1564.530

1564.043

1571.861

1563.803

MU

(N sec/M )

. 151E-03

. 149E-O3

. 149E-03

. 151E-03

. 151E-03

. 145E-03

. 154E-03

. 154E-03

. 154E-03

. 151E-03

. 152E-03

. 148E-03

. 152E-03

. 153E-03

. 1 49E-03

. 149E-03

. 149E-O3

. 146E-03

. 149E-03

. 149E-03

. 151E-03

. 149E-03

59

MOOT

Cfg/sec)

2. 168

2. 143

2. 135

2. 155

2. 161

2.084

3. 182

3. 162

3. 171

3. 128

3.11 6

3.047

3.861

3.880

3.768

3.788

3.782

3.710

5.044*

5.044*

5.056*

5.043*

CFM

(Cyc/mi n )

1083.

1 786 .

267-5.

3604.

5333.

7186.

107C>.

1818.

«TM« "7 «~i """i 2/3 J.

3593.

5333.

7186.

1071 .

1802.

2673.

3571.

5333.

7186.

1064.

177O.

2691.

3550.
23.

-.4.

25.

26.

27.

23.

29.

30.

18.

IS.

26.

26.

27.

27.

27.

27.

353

3

c/6

753

CK/ 3

012

080

24<>

062

1557.

1554.

1542.

1552.

1555.

1553.

1555.

1541.

1

-»er

...O

4

C

'8

«5*>0

170

346

727

145

7S6

. 147E-03

. 146E-03

. 143E-03

. 145E-03

. 14&E-03

. 1 45E-03

. 146E-03

.142E-03

5.

CJ

6.

6.

6.

6.

6.

6.

02S*

n ~;o«

043*

08S*

Q'3'5#

101*

123*

075*

5333

7/ A IS '„*A >ff

1031

174-5

o/. o^> <co ;>»_

350'5

5310

7186

# ESTIMATED

60
A.1

! Test Data: Operating Conditions and Parameters for stator i\.

SAWTOOTH PATTERN tt4

25 TEETH, TOOTH DEPTH= 2.54Omrri, GAMMA=.74

DR. D. CHILDS TEXAS AS/M AUG 1985

Case

1.

-£—i. m

3.

4.

5.

6.

7.

•T' •

*.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

2.647

2.752

2.810

2 . 352

3.053

3.614

6.21 3

6 . 276

6. 313

6.4-5-4

6.714

6.339

10.369

10.433

1O.067

10.275

10.093

10.240

16.940

17.247

17.250

17.710

RHO

O'q/M )

155C'.595

1558.975

1561.488

1559.89C'

1563.428

1572.O61

156^.641

1566.237

1562.40I=>

1563.464

1566.c'80

1577. 190

1558.714

1559.318

1572.338

1570.426

1563.946

1571.519

1564.816

1568.887

1569.980

1575.003

MU

(N sec/M )

. 148E-03

. 148E-O3

. 149E-03

. 148E-O3

. 14«E-03

. 151E-O3

. 151E-03

. 150E-O3

. 14*E-03

. 1 49E-O3

. 150E-O3

. 153E-03

. 148E-O3

. 148E-O3

. 151E-03

. 151E-03

. 149E-03

. 151E-O3

. 149E-03

. 150E-03

. 150E-03

. 152E-O3

61

MDOT

(Kq/sec)

2. 125

2. 121

2. 1 14

2. 106

2. 124

2. 148

3. 105

3 . O97

3 . 049

3.088

3.035

3. 133

3.754

3.760

3.830

3.826

3.782

3.817

4.947

4.997

4.991

5.045

CPM

(Cyc/mi n )

) 060 .

1775.

2673.

3550.

5333.

7186.

1071.

17^1.

2673.

3571.

5333.

7186.

1O75.

1775.

27O3.

3593.

5333.

7229.

1O68.

1791.

2691.

3604.
23. 17.652 1566. 121

=> . 14C'E-O3 4.c'56 5310.

24. 18.203 1575. 36C' . 152E-03 5.053 7186.

25. 26.834 1566.028 . 14'-'E-O3 6.202 1068.

26. 26.8^7 1570.ir'47 . 150E-03 6.237 1786.

27. 26.806 1567.587 . 14'r'E-O3 6.244 2661.

28. 27.063 1572.22^ .150E-03 6.266 3571.

2'=>. 27.171 1568.518 . 14OE-O3 6.190 5310.

30. 26.955 1563.5^0 .148E-03 6.106 7186.

62
A.5 Test Data: Operating Conditions and Parameters for stator 5.

SAWTOOTH PATTERN 85

105 TEETH, TOOTH DEPTH= 1.016mm, C-AMMA=0. 64

DR. D. CHILDS TEXAS AS/M SEPT. 1935

Case

1.

•*-. •

3.

4.

5.

6.

7.

8.

*•

1O.

11.

12.

13.

14.

15.

16.

17.

IS.

19.

20.

21.

22.

Pa-Pb

(Bars)

1.413

1.483

1.530

1.785

1 . 982

2. 2*5

3.360

3.401

3.478

3.642

4.161

4.044

5.213

5.280

5.451

5.215

6.002

6. 144

12.713

12.698

12.597

12.764

RHO

(h'g/M )

1562.525

1563.524

1560.395

1563.322

1568.470

156O.477

1566. 388

1565. 177

1567.863

1567. 167

1571.505

1561.680

1569.004

1569.590

1572.859

1561.992

1576.996

1562.043

1561. 198

156O.O15

1558.494

1556.633

MU

(N sec/M )

. 1 49E-03

. 149E-03

. 3 48E-03

. 149E-03

. 150E-03

. 148E-03

. 150E-03

. 150E-03

. 150E-03

. 150E-O3

. 151E-03

. 149E-03

. 151E-03

. 151E-03

. 152E-03

. 149E-03

. 153E-03

. 149E-03

. 148E-O3

. 148E-03

. 147E-03

. 147E-03

63

MOOT

(Kg/sec)

2. 116

2. 118

2. 103

2. 140

2. 145

2 . 1 26

3.0*1

3.O88

3 . 082

3.O94

3. 124

3.O58

3.801

3.816

3.839

3.771

3.862

3.776

5.862

5.861

5.848

5.836

CPM

( Cyc/mi n )

1O75.

1786.

2661.

3571.

5333.

7186.

1068.

1786.

2691.

3571.

5333.

7186.

1083.

1796.

2709.

3561.

5310.

7186.

1060.

1760.

2661.

3529.
23.

24.

25.

26.

27.

28.

29.

30.

13.

12.

24.

24.

24.

24.

24.

24.

267

8 1*

447

433

467

357

520

40'-"'

1565.

1546.

1 56C' .

157O.

1570.

1558.

1564.

1556.

484

424

OQg

538

264

141

331

987

. 14'r'E-03

. 144E-O3

. 150E-03

. 150E-03

. 1 50E-0 3

. 147E-O3

. 148E-03

. 146E-O3

5.

e=j

y .

y .

8.

8.

8.

8.

•

r'12

720

107

110

103

087

103

023

5310

7 1 86

JOS 3

1 780

267^

350*

52S6

7186

64
A.6 Test Data: Operating Conditions and Parameters for stator 6.

SAWTOOTH PATTERN #6

SO TEETH, TOOTH DEPTH= 1.016mm, GAMMA=0.49

DR. D. CHILDS TEXAS A?vM SEPT. 1985

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

IS.

19.

20.

21.

22.

Pa-Pb

(Bars )

1 . 823

1 . 904

2.035

2.226

2.424

2.748

4. l^-s

4 . 388

4.604

4.721

5. 155

5.057

6.6C'

<5

6.275

6.459

6.559

6.884

7.68O

15.864

16.389

15.808

15.981

RHO

<Kg/M )

1570.768

1567. O19

1567.3O6

1562.222

1561.609

1577. 118

1568. IS*

1576.474

1582.8O2

1585.451

1581.084

1558.649

1584. SOS

1568.556

1566.266

1565.866

1560.934

1568.370

1566. 193

1579.019

1568. 177

1571.689

MU

(N sec/M )

. 151E-O3

. 150E-O3

. 150E-03

. 149E-O3

. 1 49E-03

. 153E-O3

. 150E-03

. 152E-03

. 154E-03

. 155E-03

. 154E-03

. 148E-03

. 155E-O3

. 15OE-03

. 150E-03

. 150E-O3

. 148E-03

. 150E-03

. 149E-03

. 153E-03

. 150E-O3

. 151E-O3

65

MOOT

(Kg /sec)

2. 151

2. 129

2. 139

2. 131

2. 128

2. 189

3.08^

3. 130

3. 177

3. 195

3. 176

3.039

3.927

3.799

3.788

3.786

3.750

3.801

5.912

6.037

5.937

5.961

CPM

( Cy c / m i n )

1075.

1780.

2667 .

3561.

5310.

7186.

1060.

1 802 .

2740.

365^ .

5310.

7186.

10^5.

1796.

2685.

3571.

52S6.

7186.

1064.

1813.

2685.

3582.
23.

24.

~ier

j- -' •

26.

2.7.

28.

20.

30.

1

1

•— ,

-

2

6.

6.

5.

5.

5.

25.

25.

25.

3

C'6

71S

387

380

376

491

591

2-54

1 57 3 .

1568.

1565.

1564.

1563.

1568.

1567.

1544.

QV1

•^68

117

744

568

974

884

496

. 151E-03

. 150E-O3

. 148E-03

. 148E-03

. 148E-03

. 149E-O3

. 149E-03

. 143E-03

5.

5.

7.

7.

7.

7.

7.

7.

•3Q4

'

r'50

503

481

461

524

507

392

5286

7186

1075

1765

2661

3561

5286

7186

66
A.7 Test Data: Operating Conditions and Parameters for stator 7

SAWTOOTH PATTERN #7

55 TEETH, TOOTH DEPTH= 1.016mm, GAMMA=O.34

DR. D. CHILD'S TEXAS A?/M SEPT 1985

Case Pa-Pb

(Bars)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

1.

1.

1.

1.

1.

-.

3.

3.

3.

3.

3.

3.

4.

4.

4.

5.

5.

5.

10.

11.

11.

11.

163

191

264

656

858

124

156

197

263

472

841

914

914

893

864

027

231

630

857

429

564

624

RHO

O'g/M )

1552.

1556.

1556.

1577.

1567.

1577.

1580.

157*.

1574.

1582.

1 578 .

1572.

1579.

1578.

1572.

1575.

1567.

1567.

1560.

1572.

1575.

1574.

776

328

421

213

«52

490

274

89 1

740

988

365

686

846

396

490

250

119

713

114

582

129

787

MU

(N sec/M )

. 146E-03

. 147E-O3

. 147E-03

. 153E-O3

. 150E-03

. 153E-03

. 154E-03

. 153E-03

. 152E-03

. 1 54E-03

. 153E-03

. 151E-03

. 153E-03

. 153E-O3

. 151E-03

. 152E-03

. 150E-03

. 150E-03

. 148E-03

. 151E-03

. 152E-O3

. 152E-03

67

MOOT

(Kg/sec)

2.

2.

2.

-•

2.

J— m

3.

3.

3.

3.

O •

3.

3.

3.

3.

3.

3.

3.

5.

5.

5.

5.

089

O96

093

185

1 38

166

158

156

121

162

163

122

897

874

837

847

793

799

850

98O

993

995

CPM

(Cyc/min )

1040.

1760.

2655.

3614.

5310.

7186.

1103.

1818.

2703.

3647.

5310.

7186.

107-5.

1807.

2697.

3604.

5333.

7186.

1068.

1786.

2697.

3604.
23. 11. 74<r' 1 565.512 .14'-'E-0 3 5. *<:>•=> 5 310.

24. 12.184 1563.852 . 14>r'E-O3 5.c'00 7186.

25. 24.O50 1570.502 .150E-03 8.549 1O60.

26. 24.081 1572.648 .150E-03 8.571 1796.

27. 23.74<=- 1553.462 .145E-03 8.487 2614.

28. 23.7'=>6 1568.311 . 14C'E-03 8.526 3550.

2*. 24.117 1567.635 .149E-03 8.523 5333.

30. 24.150 1566.071 . 149E-03 8.4>:>7 7186.

68
A.8 Test Data: Operating Conditions and Parameters for stator 8.

SAWTOOTH PATTERN #8

6O TEETH, TOOTH DEPTH= 1.524mm, GAMMA=0.48

DR. D. CHILDS TAMU NOV 1985

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

3.020

2.534

2. Ill

2.513

2.637

2.676

5 . 650

5.843

5. 132

4.757

5.056

5.243

8.870

8.567

8.008

8. 170

7.744

8. 178

16.907

16.964

16.475

15. 197

RHO

U q/M )

15*9. 186

1583.923

1568.212

1585. 350

1584.438

1571.742

1569. 324

159O.*8O

1572.798

1567.061

157O.674

1564. 195

1575.438

1572.338

1569. 128

1588.052

1584.869

1574.O30

1565.687

1576.956

1575.028

1562.464

ML)

(N sec/M )

. 159E-03

. 155E-03

. 150E-03

. 155E-03

. 155E-03

. 151E-03

. 151E-03

. 156E-03

. 152E-03

. 150E-03

. 151E-03

. 14*E-03

. 152E-03

. 151E-03

. 150E-03

. 155E-03

. 155E-03

. 152E-03

. 149E-03

. 152E-03

. 152E-03

. 148E-03

69

MDOT

(Kg /sec)

2.270

2.208

2. 134

2.215

2.1«4

2. 163

3 . 0*5

3.215

3. 124

3.089

3.094

3.O72

3.847

3.833

3.817

3.929

3.904

3.837

5. 193

5.294

5.292

5. 159

CPM

( Cyc /mi n )

109*.

1835.

2685.

3670.

5310.

7186.

1064.

1840.

26*7 .

3571.

5310.

722*.

1071.

1802.

2685.

3659.

5310.

7186.

1075.

1796.

2697.

3540.
2 3 .

24.

jjfi •

26.

27.

28.

2*.

Or~i ;•'-' .

14.

1 3.

26.

26.

26.

26.

26.

26.

4

C'0

661

674

685

532

474

434

453

1 562 .

155C'.

1568.

1578.

1 572 .

1 57 1 .

1572.

1572.

672

015

874

748

455

205

SQ4

719

. 148E-03

. 147E-O3

. 14i:>E-O3

. 152E-O3

. 150E-O3

. 150E-O3

. 150E-03

. 150E-O3

5.

5.

6.

6.

6.

6.

6.

7.

131

123

512

598

634

723

855

O2 3

5 3 1 0

7186

107*

1807

2691

3582

5310,

7186,

70
A.9 Test Data: Operating Conditions and Parameters for stator 9.

SAWTOOTH PATTERN #*

60 TEETH, TOOTH DEPTH= 1.524mm, GAMI*1A=0.63

DR. D. CHILD'S TAMU NOV l'"'S5

Case

1.

-v

3.

4.

c6.

7.

8.

*.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

3.457

3.470

3. 177

3.215

3.410

3 . 5SS

7.311

7 . 440

6.942

6.863

6.643

7. Oil

10.873

10.773

10.909

10.355

9.754

9.726

20. 453

21.021

20.341

19.875

RHO

(Kq/M )

1577.0^9

1582.873

1572.945

1581.445

1575. O05

157<:>.434

1568.534

1583. 33O

1570. 156

1573.601

1574.706

1586.c'52

1572.766

1573.605

1584.866

1575.000

1574.462

1567.747

1567.058

1574.662

1570.219

1566.976

MU

(N sec/M )

. 153E-03

. 154E-03

. 152E-03

. 154E-03

. 152E-03

. 153E-03

. 150E-03

. 154E-03

. 151E-03

. 152E-03

. 152E-03

. 155E-03

. 151E-03

. 151E-O3

. 154E-03

. 152E-03

. 152E-03

. 150E-O3

. 150E-03

. 151E-03

. 150E-03

. 149E-O3

71

MOOT

U g/sec)

2. 177

2.207

2. 156

2. 197

2. 181

2. 173

3 . Oc'

<:>

3. 166

3.092

3. 130

3. 133

3.201

3.844

3.847

3.912

3.851

3.839

3.813

5.204

5.282

5.232

5.207

CPM

(Cyc/mi n )

1O75.

1813.

2697.

3636.

5286 .

7186.

1 064 .

1813.

2691.

3604.

5286.

7186.

1087.

1796.

2721.

3604.

5310.

7186.

1068.

1796.

2679.

3571.
jj o -

24.

25.

26.

27.

23.

20.

30.

10.

10.

27.

27.

27.

27.

27.

27.

406

376

362

236

357

321

167

195

1567.

1577.

1581.

15SO.

1532.

1579.

1571.

1573.

761

144

335

554

275

437

607

400

. 1

. 1

. 1

50E-03

5

5

. 15

. 1

. 1

5

5

2E-03

3E-03

3E-03

3E-03

2E-03

. 150E-03

. 151E-O3

5 .

5.

5.

6.

6.

6.

6.

6.

206

29O

005

007

031

050

111

200

5 3 1 0

7 1 86

1 0**

1796

27C>o

3604

5310

7186

72
A. 10 Test Data: Operating Conditions and Parameters for stator 10.

SAWTOOTH PATTERN

60 TEETH, TOOTH DEPTH= 1.524(T,ir,, GAMMA=0.33

DR. D. CHILDS TAMU DEC 1985

Case Pa-Pb

(Bars )

1.

2.

O •

4.

5.

6.

7.

8.

«•

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

1.

1.

1.

1.

2.

2.

4.

4.

— i

3.

4.

4.

6.

6.

6.

5.

6.

6.

12.

12.

12.

11.

795

586

602

621

204

711

146

OOO

700

803

319

84*

831

120

253

830

032

663

789

766

476

979

RHO

(Kq/M )

1577.

1574.

1575.

1566.

1 578 .

1 580 .

1577.

1577.

1572.

1584.

1 58 1 .

1576.

1587.

1571.

1587.

1571.

1584.

1569.

1576.

1582.

1584.

1578.

146

867

862

832

751

O05

064

241

719

394

356

759

446

350

240

014

656

947

233

442

178

669

MU

(N sec/M )

. 153E-03

. 152E-03

. 152E-03

. 150E-03

. 153E-03

. 153E-03

. 153E-03

. 153E-03

. 151E-03

. 1 55E-03

. 154E-03

. 153E-03

. 155E-03

. 151E-03

. 155E-03

. 151E-03

. 155E-03

. 151E-03

. 152E-03

. 154E-03

. 154E-03

. 153E-O3

73

MDOT

( k q / s e c )

2.

2.

2.

2.

2.

•—i

3.

3.

3.

3.

3.

3.

3.

3.

3.

3.

3.

3.

5.

5.

5.

5.

187

175

168

138

175

187

141

136

111

173

161

14O

*42

826

929

829

914

828

288

348

367

317

CPM

(Cyc/fTii n )

1079.

1 807 .

2721.

3571.

5333.

7186.

1 087 .

17*6.

2691.

3636.

5333.

7186.

1095.

1802.

2752.

3593.

5310.

7186.

1071.

1813.

2727.

3614.
23.

24.

25.

26.

27.

2;-!

29.

30.

11.

10.

25.

25.

25.

25.

25.

25.

135

682

42*

1*5

240

2*7

21*

163

1

1

1

1

570.

562.

575.

56*.

1577.

1576.

1574.

1575.

151

551

180

815

85*

074

225

861

. 1

. 1

. 1

. 1

. 1

. 1

. 1

. 1

51E-03 5.

4

5

8E-03

1E-03

50E-03

52E-03

51E-03

5

5

1E-03

1E-03

5.

7.

7.

7.

7.

7.

7.

238

1 66

446

424

530

566

656

808

5310

7186

] 0*5

1775

270*

3593 ,

531O

7186,

74
A.11 Test Data: Operating Conditions and Parameters for stator 11

SAWTOOTH PATTERN 811

60 TEETH, TOOTH OEPTH= 1.524mm, GAMMA=0.47

DR. D. CHILDS TAMU JAN 1C'S6

Cast

1.

2.

7»

4.

5.

6.

7.

8.

«.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Pa-Pb

(Bars)

2.451

2.521

2.26*

2.569

2.894

3. 137

5.082

5.778

5.587

5.074

5.448

6. 110

9. 321

9.383

9. 153

8.594

7.989

8.319

17.675

17.422

17.594

16.438

RHO

O'g/M )

1563.701

1576.753

1571.782

1575.264

1562.3**

1555.878

1574.743

1570.615

1578.406

1572.226

1566.074

1568.835

1572.8Q3

1581.614

1581. 115

1575.563

1569.818

1557.770

1567.672

1568.097

1576.4*2

1562.883 .

MU

(N sec/M )

.14*E-03

. 153E-03

. 151E-03

. 152E-03

. 149E-03

. 147E-03

. 152E-03

. 151E-03

. 153E-03

. 151E-03

. 150E-03

. 1 50E-03

. 151E-03

. 154E-03

. 1 53E-03

. 152E-03

. 151E-03

.147E-03

. 150E-03

. 150E-03

.152E-03

. 1 48E-03

75

MOOT

(Ka/sec)

2. 128

2. 172

2. 147

2. 175

2. 124

2.002

3. 117

3. 117

3. 156

3. Ill

3.081

3.092

3.824

3.899

3.887

3,849

3.827

3.722

5.206

5.227

5.296

5. 184

CPM

(Cyc/min )

1060.

1706.

2685.

3604.

5357.

7186.

1001.

1791.

2721.

35*3.

5333.

722*.

1083.

1807.

2721.

3604.

5333.

7186.

1071.

1770.

2709.

3561.
23.

24.

25.

26.

27.

28.

2

i:>.

30.

15.

14.

26.

26.

26.

26.

26.

26.

64O

422

743

857

503

•332

!-i24

446

1566.

1557.

1567.

1574.

1571.

1575.

1574.

1573.

6 ---'3

345

444

755

* 6 9

040

372

030

. 14C>E-03

. 147E-03

. 14C'E-03

. 151E-03

. 150E-03

. 151E-03

. 151E-03

. 151E-03

5.

5.

6.

6.

6.

6.

6.

6.

1<5<5

134

337

364

423

487

545

747

5333

722Q

1O75

1796

2685

3582

5333

7186

76
APPENDIX B.

DYNAMIC TEST DATA

FOR SAWTOOTH-PATTERN

77
B.I Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 1.

SAWTOOTH PATTERN #1

25 TEETH, TOOTH DEPTH= 2.540mm, GAMMA=0.40

DR. D. CHILDS TEXAS A?/M .JIJN 85

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

1O.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

8"805.

90169.

90078.

9O209.

89791.

90754.

13O501.

129560.

130314.

1299H.

130125.

129369.

16O252.

159272.

160314.

160500.

160508.

160863.

258330. »

258250. »

256932.*

258375. »

CPM

( Cyc/mi n )

1083.

1791.

2691.

3614.

5310.

7186.

1079.

1818.

2740.

3614.

5310.

7186.

1049.

1765.

2661.

3529.

5310.

7186.

1079.

1780.

2661.

3571.

Fr/A

(MN/M)

-.2448

'-I'-i 1 •"»

• A.^. 1 4-

. 0093

. 1494

.^147

1 . 55^2

- . 4867

-.4276

-. 1675

-.2098

. 7649

1 . 6878

-.6790

-.6958

-.5049

-.5190

.5213

1 . 5855

-1.7324

-1.8909

-1.6000

-1.4506

dev.

(MN/M)

. 1O44

. 1O51

.0493

. 0650

. 0806

. 0926

. 0^73

.0501

. 1035

.0967

. 1048

. 1419

. 1516

. 1197

.1030

.1147

. 1513

. 1527

. 1998

. 1371

.0718

.2452

78

Fc./A

(MN/M)

. 4400

.7681

1.0124

1 . 1 853

1 . 7644

1 . 8635

. 6244

1.0543

1 . 6032

1.9245

2.5085

3.2771

.8154

1 . 3235

1.9019

2.5125

3.0896

4.0493

1.2310

2.3353

2.9058

3.9618

dev.

(MN/M)

.0529

.0697

.0516

. 0544

.0792

. 1033

. 15«>2

.0636

. 0685

.0828

. 0898

. 1025

. 1654

. 1038

. 1889

.0973

. 1277

. 1094

.387O

. 1630

. 1449

. 1420

:F:

(KN)

.0665

. 1024

. 1287

. 1520

.2527

. 3089

. 1026

. 1447

.2051

.2462

.3334

.4686

. 1370

. 1904

.2500

.3261

.3984

.5526

.2750

.3821

.4213

.5366
23 .

24.

25.

26.

27.

23.

2*.

30.

25*583.*

255414.*

331780.

330778.

3323 1 1 .

329595.

327*21.

3O6051.

5310.

7186.

1020.

1724.

2586.

3468.

5310.

7186.

. 1003

. 9832

-2.8467

-2.6993

-2.3082

-2.O976

-.6433

.9151

. 1757

. 2682

.2611

.3117

. 1259

. 2624

. 3425

. 3839

4 . 8**4

6.8414

1 . 3522

2.2597

3.4666

4.5248

6.7066

9.0915

.2011

. 1884

.6611

. 1647

-^i -r. <-• ~-»

m _' O O O

.3412

. 2952

. 3254

.6227

. 8786

. 4095

. 4486

.5301

.6345

.8569

1. 1616

ESTIMATED

79
B.2 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 2.

SAWTOOTH PATTERN #2

25 TEETH, TOOTH DEPTH= 2.54mn-,, GAMMA=.40

PR. D. CHILDS TEXAS A?/M ..IUN 85

Case

1.

•-%

^- *

3.

4.

5.

6.

7.

8.

*.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

2O.

21.

22.

Rao

89548.

89*21.

8*800.

*0163.

896 1 7 .

*0531.

13050*.

129673.

12*815.

129854.

12**75.

130246.

160048.

159542.

159750.

129583.

159668.

159823.

255528.*

253785.*

254036.*

252762.*

CPM

(Cyc/min )

1083.

1796.

2685.

3561.

5333.

7186.

1O83.

1796.

26*7.

3593.

5333.

7186.

1O71.

1791.

2673.

3529.

5333.

7229.

1068.

1780.

2661.

3529.

Fr/A

(MN/M)

-.3414

-. 1281

- . 0373

- . O776

. 7436

1.7431

-. 6*36

-.6202

- . 3722

-.3611

.57*7

l.*833

-.8378

-1.0063

-.5890

-.4844

.3460

1.6864

-2. 1022

-2. 1409

-2.0339

-2.0064

dev.

(MN/M)

. 08 1 3

. 0574

.0814

. 09 1 0

. 0*05

.2114

. 1 1*7

. 1 1 39

. 0390

.0572

. OS**

. 2625

. 1242

. 0566

. 1461

. 0498

. 1256

.2483

.2778

. 1589

. 1 270

. 0844

80

Fo/A

(MN/M)

.4149

.8134

.*555

1 . 1 1 86

1 . 8686

2 . 1 500

. 5795

.9721

1 . 42*5

1.8167

2 . 3*9O

3.4890

.6518

1.2021

1.8011

1.9763

3.0979

4.0689

.9059

2. 1335

2.7720

4.0235

dev.

(MN/M)

. 1 022

. 1 2O7

. 0776

. 1 0 30

.0700

. 1034

. 1380

. 0753

. 0675

. 0663

. 0767

. 1592

. 141*

. 1188

.0795

.0630

. 1281

. 1780

. . 5454

. 1265

. 1268

. 118*

;F:

(KN)

. 0700

. 1048

. 1218

. 1428

.2557

-»er -i--»

. 3-3*-.*-.

. 1167

. 1469

. 1876

.2354

.3137

.5105

. 1366

. 1994

.2414

.2585

.3962

.5606

.3004

.3844

. 4370

.5711
23.

24.

25.

26.

27.

28.

2«.

3O.

252745.*

249583.*

334598.

331329.

329779.

330050.

328733.

309540.

5333 .

7186.

1038.

1749.

2626.

3458.

5333.

7186.

— .

•

—3.

-3.

-2.

-3.

-1.

4235

60 1 5

4510

3722

Q444

0300

4692

1576

. 1789

. 3O53

. 40C'9

.2139

.2103

.2133

. 3093

. 4329

cr

_' .

6.

•

-•

_' •

4.

6.

9.

2734

6*45

8 1 65

2343

6 2 SO

925O

8117

4265

. 1588

. 2704

. 82 1 8

.3152

.2196

. 3122

. 3007

. 37 1 2

. 67 3O

. 8546

. 4645

.5145

.5*3*

. 7347

. 886O

1 . 1 988

* ESTIMATED

81
B.3 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 3-

SAWTOOTH PATTERN #3

25 TEETH, TOOTH DEPTH= 2.540mm, GAMMA=0.74

DR. D. CHILD'S TEXAS A?/M .JUL 85

Case

1.

-s

3.

4.

5.

6.

7.

8.

•=>.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

90463.

90533.

90457.

89915.

•=>0071.

90610.

130352.

129747.

129836.

130641.

129477.

13OO73.

16O170.

160523.

159670.

160051.

160025.

160680.

207509.

206466.

209855.

207494.

CPM

(Cyc/mi n )

1083.

1786.

2679.

36O4 .

5333.

7186.

107^.

1818.

2733.

3593.

5333 .

7186.

1071.

1802.

2673.

3571.

5333.

7186.

* 1064.

* 1770.

* 2691.

* 3550.

Fr/A

(MN/M)

-.0933

- . 0354

. 239C>

. 2854

1 . 2 1 34

l.c'311

-.2C'47

-. 1183

. 3341-'

.7144

1 . 3838

2.5423

-.3716

-.4130

.2860

.7262

1.5924

2.7514

-.9253

-.9426

.0717

.225O

dev.

(MN/M)

. 1246

. 0682

. 0880

.0918

. 1200

.2163

. 1606

. 1007

. 1032

. 0893

. 1777

. 2939

. 1668

. 1504

. 1015

. 1384

. 1731

.2875

.2826

. 1349

. 1^74

.2657

82

Fc./A

(MN/M)

. 5255

.9721

1 . 4888

1 . 9O43

2.3630

1.SO10

. 7045

1 . 3789

2.2448

2.8247

4.0861

4.6886

. 8452

1 . 6263

2.2265

3.3371

4.7144

5.9942

.9843

2. 1424

2.5979

4.0082

dev.

(MN/M)

.0415

. 0464

. 1010

. 0856

.0^10

. 159-3

. 3 258

.0701

. 1 72 3

. 1040

. 1051

. 1826

. 1220

.0841

.2118

. 1404

. 1221

.2635

. 2380

. 1730

. 1364

.2089

I F:

O N)

. 06^7

. 1238

. 1910

. 2449

. 3378

.3359

_ QQOQ

. 1762

. 2883

. 3702

. 5485

. 6784

. 1196

.2140

.2854

.4341

. 6326

.8383

. 1773

.2977

.3310

-511O
23.

24.

25.

26.

27.

28.

29.

30.

204*79.*

204067.*

242003.*

245605.*

247074.*

245880.*

248256.*

24 1 63 1 . *

5333.

7186.

1031.

1749.

2632 .

350*.

5310.

7186.

1 .

3.

-1.

-1.

-.

•

2.

3.

•-'454

1251

2208

3699

6109

13O1

1437

9646

.2581

. 3990

. 3241

.21 33

. 1846

. 1489

.2507

. 4594

6. 269O

7.6711

. 8348

2. 1724

3. 2563

4.7979

7.2223

•3.87O3

. 2243

. 28--' 7

. 2228

. 1 538

. 1845

. 1774

.21O8

.5116

.3346

1.0534

. lc'2>:>

. 3274

. 42 1 6

. 6099

. 0573

1 . 3523

* ESTIMATED

83
B.M Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator *4.

SAWTOOTH PATTERN *4

25 TEETH, TOOTH DEPTH= 2.540mm, GAMMA=O.74

DR. D. CHILDS TEXAS A?/M AUG 1*85

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

9O618.

*O530.

89851.

89743.

89926.

8*59* .

12**37.

130381.

129253.

1 3O697 .

129751.

12*524.

160453.

160511.

159848.

160202.

160190.

159617.

209748.

21O384.

209743.

210152.

CPM

( Cyc/mi n )

1060.

1775.

2673.

3550.

5333.

7186.

1071.

17*1.

2673.

3571.

5333.

7186.

1075.

1775.

2703.

3593.

5333.

7229.

1068.

1791.

2691.

3604.

Fr/A

(MN/M)

- . 0568

. 0567

. 2928

. 4470

1 . 1 1 46

2.5*88

-. 1088

-.0573

. 32O9

. 7306

1 . 5260

2.8747

-.3616

-.3052

.2015

.8448

1 . 7033

3.2465

-.7225

-.4774

.0695

.8771

dev.

(MN/M)

. 1O94

. 0407

. 0448

. 0568

.0981

. 1400

. 1326

. 1273

. 0939

.0678

.1185

. 1730

. 1863

. 0636

. 0930

.0903

. 1544

. 1990

. 1387

. 1364

. 1956

. 1201

84

Fn/A

(MN/M)

.4415

. 8 1 68

1. 1848

1.5136

2.2336

2.5614

.6948

1. 1142

1.7020

2. 1936

3.4033

4.2220

.7194

1 . 3966

2.0047

2.7989

4.0309

5.3656

.6905

1 . 7642

2.4081

3.4811

dev.

(MN/M)

. 0696

. 048O

. 0403

. 0576

.0701

.1112

. 0559

. 0588

.0741

. 0*48

. 1073

. 1574

. 1007

. 1028

.1104

.0743

. 1093

.2071

.3073

. 1474

.2199

. 1679

:F:

(KN)

.0581

. 1041

. 1552

. 2006

.3173

. 463*

. 090*

. 1427

. 2204

. 2*38

. 4740

. 64* 1

. 1052

. 1817

.2561

.3714

.5560

.796*

. 1321

.2328

.3067

.4562
23.

24.

25.

26.

27.

28.

29.

30.

209659 .

21O445.

263412.

262697 .

264503.

263296.

261772.

260437.

5310.

7136.

1068.

1786.

2661.

3571.

5310.

7186.

1.

4.

-1.

" ~ •

-.

•

2.

4.

9344

1539

3852

8476

3776

8929

O120

1070

.22O1

.3010

. 2035

. 1329

. 0990

.2176

. 3024

.3788

5.

7.

•

1.

2.

4.

5.

7.

1243

0545

7521

9696

7347

2451

9830

9955

. 2565

. 3265

. 28O4

. 1736

. 1O82

. 1581

. 2993

. 4096

. 6962

1 . 04O8

. 20 37

. 2729

. 3508

.5516

. 8027

1. 1425

85
B.5 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 5.

SAWTOOTH PATTERN #5

105 TEETH, TOOTH DEPTH= 1.016mm, GAMMA=0.64

DR. D. CHILDS TEXAS A?/M SEPT. 1^85

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

8^694.

89595.

8'r'452.

9059 1 .

90043.

•30474.

13024*.

130350.

129535.

130166.

130483.

12*0*2.

159518.

159971.

160017.

160239.

159924.

160463.

250029.

250449.

250586.

250478.

CPM

( Cyc/mi n )

1075.

1786.

2661.

3571.

5333.

7186.

1068.

1786.

269 1 .

357 1 .

5333.

7186.

1083.

1796.

2709.

3561.

5310.

7186.

1060.

1760.

2661.

3529.

Fr/A

(MN/M)

-.2429

-. 1O85

.0378

.2555

1.351O

2.5731

-.5128

-.4305

-. 1723

. 1453

1 . 2595

2.6*07

-.6480

-.5469

-.2921

-.2920

1.0018

2.7271

-1.9164

-1.7491

-1.5988

-.7748

dev.

(hN/M)

.0543

. 0668

. 0277

. 0509

. 1082

. 1 432

. 1041

. 1100

.0681

. O793

. 1 1 62

. 1*73

.6164

. 0788

. 1330

. 1422

. 1054

. 1926

. 1608

. 1457

.O860

. 1445

86

Fo/A

(MN/M)

.4239

. 5396

. 8228

1. 1804

1.5101

1 . 6044

.577*

. 9528

1 . 3277

1 . 7362

2.3494

2.7045

.5621

1. 1539

1.6712

2.2013

3. 1932

3.4986

1.O751

2.0047

2.6131

3.3906

dev.

(MN/M)

. 1015

. O835

. O363

. 0662

. 0*47

. 1232

. 0670

. 0905

. 1277

.07*2

. O765

. 1 1 80

. 6032

.0840

. 1314

. 1349

.0900

. 1596

.2632

. 1357

.2015

. 1794

!F!

a N)

. 0627

. 0705

. 1O47

. 1535

. 2578

. 3855

. 09*2

. 1 334

. 1701

. 22 1 5

. 3390

. 4848

. 1382

. 1626

. 2163

.2826

.4253

.563*

.2815

.3385

.3891

.4421
23.

24.

25.

26.

27.

28.

29.

30.

24^919.

250552.

342151.

341964.

341768.

348323.

345254.

346465.

5310.

7186.

1083.

1780.

2679.

3509.

5286.

7186.

. 5785

1 . 9629

-3.6912

-3.4752

-3.2849

•'"i *~i «""» t~* *~i

*L. m s-*OC'«— '

-.716O

1.415*

. 20O5

.2

. 3

.2

~>

373

356

534

143

. 2487

.3

. 3

336

•=•09

4.

6.

1.

— i

3.

4.

7.

9.

8939

2416

1616

9152

7743

8151

0402

1342

. 1 998

. 2082

. 42O6

. 1977

. 1441

. 1*25

.2415

. 3375

. 6265

.8315

. 4l7'52

. 5773

. 6 363

. 6833

. 8997

1. 1752

87
B.6 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 6.

SAWTOOTH PATTERN #6

SO TEETH, TOOTH DEPTH= 1.016mm, GAMMA=0.4*

DR. D. CHILDS TEXAS A?/M SEPT. 1*85

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

89904.

89559.

8994*.

9O408.

90398.

90536.

12*814.

12*670.

13O19S.

130323.

130529.

12*843.

16O478.

159645.

159797.

159824.

159728.

159795.

250011.

249754.

250207.

249704.

CPM

( Cyc/mi n )

1075.

1780.

2667.

3561.

531O.

7186.

106O.

1802.

2740.

365*.

5310.

7186.

1095.

1796.

2685.

3571.

5286.

7186.

1064.

1813.

2685.

3582.

Fr/A

(MN/M)

- . 2428

-. 1640

. 1 258

.2513

1 . 3542

2.6642

-. 600*

-.4*5*

-. 1752

. 10*7

1 . 2352

2.8381

-.8296

-.6893

-.4222

-. 1495

1.0656

2.8270

-2.O770

-2. 1234

-1.7311

-1.2256

dev.

(MN/M)

. 0452

. 020 1

.0266

.0243

.0*28

. 1474

. 0554

. 0322

.0535

. 0298

. 2000

. 1 246

. 0870

.0360

.O582

.O800

. 1075

. 1435

. 1488

.0698

.0991

. 1176

88

Fo/A

(MN/M)

. 3*22

.8101

1 . 05*9

1. 104*

1 . 5974

1 . S295

. 6237

1 . 1 285

1 . 5935

1 . 8638

2.5946

2.*4*5

. 80*4

1 . 4355

1 . 7799

2.4869

3.3844

3.9111

1. 1664

2.4083

3. 1476

3.9961

dev.

(MN/M)

. 03 1 0

.0291

.0214

.0291

. 0732

.1115

. 0564

.03*3

. 0624

. 0286

. 1 085

. 1312

.0*01

. 0526

.0715

.0607

. 0949

. 1550

.2411

. 0723

. 1238

.0975

:F:

<KN)

. 059O

. 1050

. 1356

. 143*

. 266 3

. 4 1 07

. 1 1 04

. 1566

. 2037

.2371

. 3661

.5201

. 1480

.2023

.2325

.3166

.45O9

.6132

.3045

. 4O79.

. 4564

. 53 1 0
ORIGINAL PAGE IS

OF POOR QUALITY

•*" ~* •

24.

25.

26.

27.

28.

29.

30.

250461.

250472.

319217.

3 1 8603 .

318386.

3180*7.

317*45.

326332.

5286.

7186.

1075.

1 765 .

2661.

3561.

5286.

7186.

. 4805

2.6422

-3.3762

-3.3778

-2 . 8058

-1.9027

-.3880

1 . 5*06

. 2202

.2691

.2210

. 0865

. 1318

. O823

.2977

. 3084

5.

7.

1.

•^i

3.

5.

7.

9.

6431

2731

2037

0166

7299

2254

1193

0815

. 1813

. 2907

. 5337

. 1084

. 1 588

. 1094

. 2252

. 28 1 6

.7199

. 98 3 3

.4610

. 5752

. 593O

. 7064

. 9063

1. 1714

89
B.7 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 7.

SAWTOOTH PATTERN #7

55 TEETH, TOOTH DEPTH= 1.016mm, GAMMA=0.34

DR. D. CHILDS TEXAS A?/M SEPT 1*85

Case

1.

2.

3.

4.

5.

6.

7.

8.

*.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

(

90146.

80900.

89730.

90333.

89795.

89490.

12*942.

129885.

1 29600 .

129474.

130412.

ISO 163.

16O491.

159935.

160023.

159689.

159637.

1598O2.

249864.

249995.

249438.

249675.

CPM

Cyc/mi n )

1O49.

1760.

2655.

3614.

5310.

7186.

1103.

1818.

27O3.

3647.

5310.

7186.

1079.

1807.

2697.

3604.

5333.

7186.

1068.

1786.

2697.

3604.

Fr/A

(MN/M)

-. 1885

-.0180

. O386

.2395

1. 1*3*

2 . 58*2

-.5291

-. 2062

- . 1 603

. 1 373

1.0*33

2.7070

- . 6738

-.5266

-.2680

-.0182

1.0791

2.6591

-1.6280

-1.3198

-1. 1767

-.8644

dev.

(MN/M)

.0331

.011*

. 0220

. 0285

.0513

. 0950

. 08 1 8

. 0278

. 0426

.0436

. 0746

. 1394

. 1 1 00

.0336

. 0457

.0493

. 1307

. 1383

.2281

.0658

.0881

. 1157

90

F.I./A

(MN/M)

•

•

•

1.

1 .

1.

•

1.

1.

1.

— t

4- m

*_ •

•

1.

1.

2.

2.

3.

1.

2.

2.

3.

4O38

527*

8061

0822

3 393

4332

7O82

0784

3887

8324

2487

6*7*

8992

2131

6512

3575

9079

5114

3813

1552

8528

8050

dev.

(MN/M)

.0212

.0131

.0151

. 04 1 2

.0521

. 0942

. 0636

. 0426

. 0507

.0473

. 0886

. 1284

. 0845

.0356

.0439

. 0908

. 1099

. 1135

.2740

.O7O8

.0736

. 1453

:F:

(KN)

. 0568

.0671

. 1025

. 14O3

. 2280

. 3761

.112*

. 1395

. 1776

. 2 334

. 3176

. 4857

. 1438

. 168O

.2125

. 2995

. 3942

.5596

.2748

.3211

.3921

.4957
""• If

-_ _• •

24.

25.

26.

27.

28.

29.

30.

250001.

250387 .

360377.

3590S7.

368740.

360040.

361107.

360998.

5310.

7 1 86 .

1060.

1796.

2614.

3550.

5333.

7186.

. £.Q04

2 . 867O

-3 . 268 1

-2.6127

-2.4214

-2.2686

-. 3481

2.2756

. 1 446

.2401

. 3720

. 1456

. 1 505

. 1 354

.4651

.4110

5.

6.

-t

O •

4.

5.

7.

10.

OS 1 6

6076

3414

5660

5741

4884

6058

3391

.1413

. 2204

. 50 33

. 1585

. 2273

. 1414

. 1924

.3861

.6517

.9155

. 5 1 64

. 56 1 8

. 6576

. 7545

. 9689

1 . 3456

91
B.8 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 8.

SAWTOOTH PATTERN #8

60 TEETH, TOOTH DEPTH= 1.524mm, GAMMA=0.48

DR. D. CHILDS TAMU NOV l'-'S5

Case

1.

?..

3.

4.

5.

6.

7.

8.

•-',

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

9O421.

90240.

89601.

90342.

8

C

'617.

9O30O.

129835.

12*<:>13.

ISO 188.

13O034.

129444.

130024.

159844.

160109.

160300.

159739.

159515.

159826.

219832.

219848.

220500.

219671.

CPM

(Cyc/min )

10*9.

1835.

2685.

3670.

5310.

7186.

1064.

1840.

2697.

3571.

531O.

7229.

1071.

1802.

2685.

3659.

5310.

7186.

1075.

1796.

2697.

3540.

Fr/A

(MN/M)

- . 277O

-. 1495

. 02O6

.2531

. 8006

2.607O

-.4438

-.4145

-.0148

. 2459

. -3025

2. 1307

-.6408

-.6945

-.2018

. 1987

1.0132

2.6380

-1.3020

-1.0907

-.8263

-.3139

dev.

(MN/M)

. OS 2 2

-O251

. 0265

. 06OO

. 0576

. 125O

. Q*4*

.0413

.03*1

. 0524

. 0776

. 530*

. 1023

.0322

.O502

. 0852

. 1077

.2436

. 1946

.0683

. 080O

. O668

92

Fo/A

(MN/M)

.51*8

. 9470

1 . 2509

1.6433

2.28*2

2 . O36*

. 6878

1.2*21

1.8158

2.3934

3.3057

4. 1654

. 8040

1 . 4635

2.2265

3.2O30

4.3521

5. 1616

.9744

2.0583

2.9492

3.9239

dev.

(MN/M)

. O477

. 0247

. 02 1 6

. 03 1 8

.0518

.121 8

. 064*

. 0847

.0343

.0711

. 1 06 1

.2ir'71

. 0855

. 0309

.0439

.0699

.0960

.2330

.2594

.0834

. 0857

. 1324

:F :

(MM)

. O75S

. 1213

. 1589

.2113

. 3O8O

. 4204

. 1 050

. 1724

. 2307

. 3056

. 4 35 3

.^•37

. 1316

. 2058

.2840

.4076

.5677

.7368

.2105

.2959

.3891

.500O
*_.!•.

24.

25.

26.

27.

28.

2*.

30.

220501.

2195*0.

275O99.

274109.

278546.

282887.

287765.

29482*.

531 0.

7186.

1079.

1807.

26*1.

3582.

531O.

7186.

1.

2.

-2.

-1.

~" 1 •

-1.

•

O •

1 67 1

980 1

008*

6003

7119

0689

5992

0728

.2184

. 3276

. 1760

.0841

. 1002

. 1 *2O

. 3132

. 3*46

5.

7.

•

2-

3-

5.

7.

10.

7964

5675

*477

5623

7772

2721

5331

4945

.2415

. 2975

. 3658

.O681

. 0369

. 1331

.2457

.3536

.7515

1.0337

. 2867

. 383*

. 5268

. 6836

. *6O5

1 . 38*8

93
B.9 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 9.

SAWTOOTH PATTERN tt^

60 TEETH, TOOTH DEPTH= 1.524mm, GAMMA=.6S

DR. D. CHILDS TAMU NOV l^'Sf.

Case

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

90025.

90385.

89822.

9O204.

90524.

8

C>57'=>.

130238.

12«722.

129504.

130339.

130226.

130349.

160522.

160448.

160071.

160217.

159832.

160556.

219844.

220184.

219780.

219943.

CPM

(Cyc/min)

1075.

1813.

2697.

3636.

5286.

7186.

1O64.

1813.

269 1 .

3604.

5286.

7186.

1087.

1796.

2721.

3604.

5310.

7186.

1068.

1796.

2679.

3571.

Fr /A

(MN/M)

-. 1662

-.0049

. 3533

.5116

1 . 3502

3.0941

-.4046

-.3150

. 1757

. 575 1

1.6127

3. 1037

-.6372

-.4252

-. 1676

.5086

1 . 7967

3.4113

-1. 1798

-1.0163

-.5540

-. 1038

dev.

(MN/M)

.0651

. 024«

.032O

.0510

. 0965

. 1007

. 1062

.O345

. 04 1 7

. 0587

. 1479

. 1153

. 1430

.0542

. 0858

.0922

.2548

. 1852

. 1124

.0818

.0922

.0981

94

Fo/A

(MN/M)

. 4765

. '=>696

1 . 2783

1 . 7293

2.0559

2.5493

. 68 1 1

1 . 3334

1 . 7888

2.4917

3.6O83

4.2306

.7543

1.4571

2.2722

2.8835

4.3549

5.7700

.7985

2. 1634

2.8926

3.8062

dev.

(MN/M)

. 0270

.0344

.0315

. 0674

. 0857

. 0980

. 0672

.0501

.0421

.0581

.1138

. 1549

. 1171

.0632

.0739

.0887

. 1601

. 1507

. 1704

.0940

. 1289

. 1331

(KN)

. 0647

1 ~

I

*^I*-"

1

. 1685

.2291

. 3126

. 50*3

. 1018

. 1741

.2283

.3248

. 5024

. 6667

. 1275

. 1929

.2896

.3720

.5991

.8516

. 1827

.3037

.3742

.4837
23.

24.

25.

26.

27.

28.

29.

30.

219499.

219909.

247822.

248663.

249O55.

25097*.

2569O5.

260000.

5310.

7136.

1099.

1796.

2709.

3604.

531O.

7186.

1.

4.

-1.

-1.

-1.

^ •

1.

4.

8319

4753

5328

3262

0485

2447

41 1 1

1050

. 2489

.2-51

. 1674

. O7 36

.0903

.1139

.3232

.3307

5.

8.

•

2.

3.

4.

6.

9.

7792

2919

7071

5290

296 1

4977

6456

5686

. 1587

.3144

. 32 33

. 0664

.1311

. 1671

. 1830

. 3259

. 7707

1. 1-72

.21-1

. 3628

. 4394

. 5722

.8638

1 . 322C)

c

95
B.10 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 10.

SAWTOOTH PATTERN #10

6O TEETH, TOOTH DEPTH= 1.524mm, GAMMA=O.33

DR. D. CHILD'S TAMU DEC 1*85

Case

1.

--%

*- m

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

9O448.

*0287.

8*865.

90011.

89708.

89970.

1299*4.

129751.

129678.

129671.

12*844.

129959.

160282.

159893.

159895.

160100.

159957.

160393.

219714.

219872.

219994.

219907.

CPM

( Cyc/mi n )

1O7*.

1807.

2721.

3571.

5333.

7186.

1087.

1796.

2691.

3636.

5333.

7186.

10*5.

1802.

2752.

3593.

5310.

7186.

1071.

1813.

2727.

3614.

Fr/A

(MN/M)

-.2791

-.0825

. 0542

.3346

1.4122

3.0426

-.6483

-.4741

-.0844

. 0969

1. 1867

3.0463

-.9556

-.8728

-.4855

-.0225

.9793

2.6540

-1.8094

-1.7343

-1.3052

-.6576

dev.

(MN/M)

.0630

. 0 1 94

.0330

.0272

. 0720

. 0846

. 0874

.0267

. O342

.0334

. 1297

. 131*

. 1365

. 0343

.0417

.0462

.0943

. 1726

. 1471

.0571

.0602

.O773

96

FC./A

(MN/M)

.4582

.6835

1. 1516

1. 1974

1 . 7962

2.5029

.6443

1 . 0775

1 . 6338

1 . *79O

2.*258

3.9278

.7032

1 . 3094

2.0466

2.5504

3.6290

5.2192

.9763

2. 1338

2.6727

3.4937

dev.

(MN/M)

. 0420

.0252

.0249

. 0243

. 0649

.0725

. 0879

. 0279

. 0630

.0304

. 1089

. 1 366

. 1782

.0314

.O787

.0426

. 1218

. 1837

.2811

.0614

.0700

.1142

I F ;

(KN)

.0688

.0875

. 1465

. 1579

.2903

. 5004

. 1171

. 14*5

. 2078

.2517

.4012

.6316

. 1532

. 1999

.2672

.324O

.4776

.7438

.2641

.3493

.3778

.4515
23.

24.

25.

26.

27. "

28.

29.

30.

219754.

219676.

311309.

313196.

313344.

315782.

320554.

326006.

531O.

7186.

1095.

1775.

2709.

3593.

5310.

7186.

. 9285

2.4451

-3.6021

-3.2822

-3.5872

-2. 1249

-.6450

2. 1677

.1199

. 2008

.2571

. 0964

. 1 887

. 1221

. 1 722

.5610

_l m

7.

•

•-.

3.

5.

7.

10.

1 6 1 5

04 1O

•-•'627

5697

5327

2804

5629

6522

. 1052

. 2 1 56

. 7483

. Oc'58

. 1640

. 19Q2

. 172*

. 4559

. 666 1

. 9469

. 48I-:7

. 5296

.63*7

.7231

. 9642

1 . 3826

97
B.11 Test Data: Force Coefficients (average and standard deviations)

and average force magnitudes for stator 11.

SAWTOOTH PATTERN #11

60 TEETH, TOOTH DEPTH= 1.524mm, GAMMA=0.47

DR. D. CHILE'S TAMU .JAN 1*86

Case

1.

2..

3.

4.

5.

6.

7.

3.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Rao

*0088.

8*8*2.

89638.

90252.

00153.

8*817.

12*545.

1304*0.

1 30356 .

12*803.

12**41 .

12*888.

159641.

160328.

159081.

159853.

160505.

159530.

219676.

220351.

220126.

220514.

CPM

( Cyc/mi n )

1060.

1 7-56 .

2685.

3604.

5 357 .

7186.

1O91.

17*1.

2721.

35*3.

53 3 3 .

7229.

1083.

1807.

2721.

3604.

5333.

7186.

1071.

1770.

27O9.

3561.

Fr/A

(MN/M)

- . 3O57

-.2322

-.0261

. 1876

1 . 7287

3.4147

-.6800

-.632'-"'

-. 3023

- . 20 1 2

. 9** 1

2.*023

-1.0642

-1. 1218

-.7751

-.3050

.8702

2.5992

-1.7671

-1.9913

-1.8773

-1.2498

dev.

(MN/M)

.0616

. 0323

.0401

. 05 1 6

. 1312

. O**7

. 0*O 3

.0352

. 0426

. 0565

. 0*47

. 5426

. 09*9

. 0473

. 0569

. 0688

. 1552

. 1678

. 1549

. 0929

.0942

. 1056

98

Fo/A

(MN/M)

. 3893

.**63

1 . 349O

1 . 6780

1.9871

2.7566

. 64 36

1.2873

1 . 7264

2.44*5

3.6536

4.2152

. 7268

1 . 5500

2.0200

2.7808

4.4805

6.0616

.8458

1 . 9625

2.9265

3.5629

dOV.

(MN/M)

. O552

. 043*

.0533

.0701

. 1 1 60

. 1008

. 0*24

.0301

. O6*2

. 0446

. 0876

. 38 1 3

. 1419

. 0483

. 0764

. 0995

. 1045

.2064

.3135

.0955

.1121

-O759

IF:

(KM)

. 0637

. 1300

. 1714

.2145

. 3350

.5575

. 1 2OO

. 1822

. 2227

. 3122

.4812

. 654*

. 1 65 1

.2431

.2749

. 3554

. 58OO

.8378

.2527

.3552

.4417

.4798
23.

24.

25.

26.

27.

28.

29.

30.

219699.

220430.

2683*7.

266227.

26 **80.

271234.

273933.

283076.

5333.

7229.

1075.

1796.

2685.

3582.

5333.

7186.

. 3*23

2 . 1311

-2.<r'964

-2.7212

-2.*058

-1.0866

-.470O

2.2977

.210 3

1.0810

.1241

.1119

. 1385

.0912

. 2866

. 3438

5. 4947

8. 4606

.7*16

2.6429

3 . 5923

4.4325

6.6*10

10.4621

. 1*37

. 3773

. 44*6

. 1211

.1187

. 161*

. 1556

. 3529

. 70O2

1.11 6*

. 3979

. 482O

. 587 1

.6170

. 8526

1 . 3609

99