Control Moment Gyroscope Gimbal Actuator Study

8/17/2019 Control Moment Gyroscope Gimbal Actuator Study

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UNCLASSIFIED

AD NUMBER

AD801885

NEW LIMITATION CHANGE

TOApproved for publ ic re lease , distribution

unl imi ted

FROMD i s t r i b u t i o n au thor ized to U.S. Gov' t .

agencies and their con t rac to rs ;Admins t ra t ive and Opera t ional Use, ExportControl ; Nov 1966. Other reques t s sha l l ber e f e r r ed to the Air Force Fl igh t DynamicsLaboratory, Attn: FDCL, W righ t -Pa t te r sonAFB, OH 45433.

AUTHORITY

AFFDL, per ltr d td 8 Jun 1972

THIS PAGE IS UNCLASSIFIED


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AFFDL-T R-66-158

CONTROL MOMENT GYROSCOPE GIMBAL00 ACTUATOR STUDY

The Bendix CorporationEclUpse-Pioneer Divisirn

Teterboro, New Jersej

TECHNICAL REPORT AFFDL-TR.66-1S8

NOVEMBER 1966

This document is subject to special export controls and eachtransmittal to foreign governments or foreign nationals maybe made only with prior approval of AFFDL (FDCL),Wright-Patterson AFB, Ohio.

Air Force Flight Dynamics LaboratoryResearch and Technology Division

Air Force Systems CommandWright-Patterson Air Force Base, Ohio


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NOTICES

WhenGovernment drawings, specifications, or other data are used for any purposeother than in connection with a definitely related Government procurement operation,the United States Government thereby incurs no rc-sponsibility nor any obligat ion

whatsoever, and the fact that the Government may have formulated, furnisihed, or i.any way supplied the said drawings, spec fications, or other data, Is not to be regardedby implication or otherwise as in any manner licensing the holder or any other personor corporation, or conveying any rights or permission to manufacture, use, or sellany patented invention that may in any way be related thereto.

Copies of this report should not be returned to the Research and TechnologyDivision unless return is required by security considerations, contractual obligations,or notice on a specific document.


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CONTROL MOMENT GYROSCOPE GIMBAL

ACTUATOR STUDY FINAL REPORT

The Bendix CorporationE clipse-Pioneer D ivision

Teterboro. New Jersey

BestAvailableCopy


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~FnRJMRD

- f i i •4 - r fT t vua prepared by The Bendix Corporation,mvJl •ur USAFContract No. AF33(615VA465

a • •.a~s t o d on 8 August1966o The report oovers work,rrl mmary 1966 to September 1966.

a..s rogram sponred by the Air Force Flight DymaziceLaborator, Reoearh and Technology Division, has beendirectedb,- Air Foroe project engineer, FDCL/t D. W. Anderton. It wasoo edt by The BendmixCorporation throu& i t s Ealipse-PioneerDivision in associatlon with the Research Laboratories Division.

KEe Berndi' pergom l who rave mariap4 the program and signi-ficantly oontributed to i t s te1nwics, anooi'-lishments are the Afolowings

L. Morine i. O'Connor J. CarnazzaD. Pool R. D>Laaia M. RitterR. K~acrPski D. Vassalio J. Madurski

H. Varner

'This technial report has boen reviewed and is approvedo

""H. 4. RASHA -

Chief, Control Elemerts BranchFlight Control DivisionAF Flight DynamicsLaboratory

I!I


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ABSTRACT

The purpx.se of this study Is the determr-ation of an optimal g;mba i•ctWtmorfor largedouble gimbal control moment gyros. The optimization study Is divided Into thr-

distinct.phases: wrquera arn tr-am-issions, which together form the actuators, andcontzollers. The DC torquer wad an epicyclic tranenmistion are selected as optimal,on the basis of power, werAt., size, reliability and performance, Pulse widthmodulation of a type de:tg,.ited as single channel if established as the aplt mal con-trolier.

To denonstrý,ce the application of tQ3 optimal antuator configuration, a prelimninrydesign la;out was coi-pleted for mounting at one '.votof a CMGhaving an &,aguiarmome'p.ninof 1000foot-puund.-seconds. The design inciudes all Pecessary structurean,, a tachometer generator, weighs 23 pounds, consumes less than 45 watts at full1orqueand also fulfills oi perturmance requirements. It has a threshold rf 3% and areliability of 0. 9741 for one year and 0. 9953for two months whHiein operation,

It is recommýuded that a brushless DC7 wrquer be considerel in the future for controlmoment gyro gimbal actuation, when ft is better established as state-of-the-art, Ithas tho advantage of very low threshold and pctpntially high reli&bility.

lit


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TABLE OF CONTENTS

3ECTION PAGE

f INTRODUCTION 11.1 General I1.2 Objectives I1.3 Requirements 2

1.3. 1 A Gimbal Actuator Optimization Study 21. 3, 2 Controller Optimization Study 31.3.3 Actuator Design Study 4

1.4 General Requirements 41.4.1 Electrical Power 41.4.2 Reliability 41.4. 3 Environmental Requirements 51. 4.4 DutyCycle 5

1i SUMMARY 0

2. 1 Purpose of Study 62.2 Optimization Study and Preliminary Derign 62. 3 Recommendations 8

ifi APPROACH 9

IV PRELfMINARYTORQUEREVALUATION 124. 1 Eummary 124.2 Evaluation Criteria 12

4.2.1 Elementary Actuator Operation 124.2.2 Basic Assumptions 124. 2. 3 Evaluation Considerations 12

4.3 Parameters of Individual Actuator Types 154.3.1 Electric 15

4.3.1.1 DC Torquer Motor 154.3.1.2 Electromechanical Dynavector Actuator 184.3. 1.3 Brushless DC Torquer Motors 204.3, 1.4 Stepping Motor 204.3.1.5 AC Servomotors 204.3.1.6 Reeponsyn Actuator 21

4. 3. 2 Hydraulic Actuators 224.3.2. 1 Convcntional Systems 224. 3. 2. 2 Dy•navectorllydraulic System 364.3. :.. 3 Stepping Actuators 37

4.3. 3 Pneumatic Actuntors 37

4. 3. 3. 1 Flow Requirements 374.3. 3.2 Pneumatic Power Supplies 404. ,.4 Qualitative Actuator Comparison 42

4..4 Preliminary Conclusions 43

iv


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TABLE OF CONTENTS(continued)

SECTION PAGE

V TRANSMiSSION STUDIES 455, 1 Hertz Stress 455.2 Types and Parameters 47

5.2.1 Spur Gear .475.2.2 Simple Planetary 505.2.3 Compound Planetary 565.2.4 External Epicyclic 635.2.5 Harmonic Drive 64

5.3 Backash 665, 3.1 Spur Ge;,-i 665.3. 2 Simple Planetary Transmisston 705.3.3 Czrmpound Planetary Transmission 715. 3. , Epicyclc " 'ranswission 73

. 3, 5 Harmonic D)rive 745.4 Friction and Efficiency 745.5 Inertia 76

5.5. 1 Spur Gear 765. 5. 2 Simple P1anetary 775.5.3 Compowud Planetary 825.5.4 External Epicyclic 035.5.5 Harmonic Drive 85

5.6 Transmission Comparison 87

Vi ACTUATOR OPTIMIZ7ATION 926. 1 Dynamic Considerations and Analytic Transforms 92

6- 1, 1 Single Order Response 936. 1. 2 Second Order Response 956. 1. 3 Total Actuator Weight Conmparison 976.1.4 Speed RaWig- Co..deratlons 105

6.2 Transrtnl.ason cptimizatiot: 1066.3 Torquer Selection 114

6.3, 1 Sliection Eample 1146.3.2 Characteristlcs for Five Actuator 5bzes 118

VII ELECTRONIC CONTROLLER DECRII-ilON 1227.1 DC Voltage PoYwerAm,diffier 1227.2 Single Channel Pulse Width Mýodulat&'n 1,25

7.3 Diai Channel Pulse Width Moxiulation 1287,4 ON-OFF Controller 1347.5 Two Lvet ON-OFF Con.roller 144

7.6 Pulse Amplitude Wult i lon 147.7 Pulse Frequency Modulption i507.9 Delts Modulation 156


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TABLE OF CONTENTS(continued)

SECTION PAGE

Viii CONTROLLER EVALU,.TION IC?8. 3 Power 9M Efficiency 1632

8. 1. 1 Motor Power 1658.1.2 Bridge Power 1678.1. 3 Efficiency 16H

8.2 Weight and VolumeEstImation 1698,3 Reliability 1738.4 Threshold 17 4

IX SYSTEMOPTIMIZATION 6

9.1 Reviewof Actuator Assembly (iAimtzatior 1769. 2 Controller Optimization 1769.3 Actuator Controller iptimLizatlon 179

X CONCEPTUAL 'USIGN10. 1 Description 1tJ0

10.2 Transmisslon [ e g n •10. 3 Trammission and Gimbal Bearing ,3

X1 CONCLUSIONSAND RECOMMEN"DATIONS11.i Gimbal -611.2 Torquers

11,3 Ti. -ns m i s ios11. 4 DtXdActuator Cortro,11:5 Controllers 711. 6 Recom--endk onb i

APkENrDt A

A. 1 Itnrdu.clonA. 2 Generil Pequiremeuts IH9A. 3 Toprque. Soed Requirn--r•ex-t I

A Z.1 lixvýedA. 3. 2 Tuirqe,

A4 A. 4 1Rate filspose 4.eyi renments ¼

v. 4, 2 T(orque Reqs, e Requfr'rnenewA, 5d &Definition ,

A .5 Gtm tb .! R uo~tti', r ý.40

A 5.2 In.-kertia 1A. 5. 3 Fr &cti,,n 'j-

A. 5. 4 C M G Cro7s Cojp~tri.


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TABIL E (OF"CONTENTS (continuej

APPENDIX PA GE

A 5.5 Phvsical Ste i z)t1A.5,6 V4ight 191

A, 6 Environment 1•A. 7 Mission Time and Reliability 191A. b Expected Load Distribution 191

APPENDIX B

B. 1 bntroduction 1492B. 2 Angular Displaeement Transducers 193

B, 2. 1 Electromagnetic Anguiar Displacement Transducers 193B. ].I Synchro 1,93B. 2.1,2 Resolver 193B. 2. 1. 3 Induction Potenttometer 194B. 2. 1. 4 Ind.uctosyn 195

B. 2. 2 Resistance Potentiometer 195B. 2, 3 Shaft Encoders 195

3 Discussion of DC and AC Ratv Sensors 195B. 3. 1 Tachometric Angular Velocity Transducers 195

B. 3. 1.1 DC Rate Cene-ator 195B. 3.1.2 AC Rate Generator 1 4t,B. 3. 1. 3 Selection of Ovtimum Type TacLbrneter 97

Generator Sensor for C M G Application13. 4 Gyroscoplc Angular Velocity Transducer

b. 4, 1 DeJ;criotion of a Rate Gyvroscope 0B. 4. 2 tte .vriD Skiectton for C' M C Actu ,itorVy tem "'"r.,

if, 5 Summary 2'

APPENDEX (.

C I Gwnera l4C. 2 Loading ForcesC. 3 Orbit G-oar iBr ln7 2)o4C. 4 InputShaft DearinpsC. 5 Output Shaft BeRrlngo 2?QJ7

PAPPFNDrXD

Relce nc-es 209

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lMST OF ILLUSTRATIONS

VIGURE NO. TITLE PAGE

I Basic Relationship Between Controller Actuator 2

2 Approach to the CMG Actuator Study 10

3 DC Torquer Acturtor Parameter 19

4 Electromechanical Dynaveator Actuator Parameter 19

Hydraulic Power Supply with Constant Flow 23

6 Hydraulic Power Supply with Constant Pressure 24

7 Sorvovalvo Controlled 1yvdraullc Actuator System 25

8 Schematic - Reversible Vane Motor 27

9 Cam Piston Motor 27

10 Gear Motor 28

11 Four-way Valve 31

12 Hydraulic Actuation System Weight and Power Consumption 34

13 Opt mum Actuator Systems - Power Consumption Comparison 43

14 Actuator Weight Comparison 44

15 Spur Gear Transmission Schematic - 350 ft-lb, 64:1 Ratio 49

16 Configuration for Calculating Spur Gear Transmission Volume 51

17 Spur Gear Transmission Weight Versus Overall Ratio 51

18 Spur Gear Transmission Volume Versus Overall Ratio 52

19 Simple Planetary Transmission Weight and Volume VersusOverall Ratio 56

20 Schematic - Simple Planetary Transmission - 87. 5 ft-lb,7.5:1 Ratio 57

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LIST OF ILLUSTRATIONS (continued)

FIGURE NO. TITLE PAGE

21 Schematic - Compound Planetary Transmission -350 ft-lb. 56:1 Ratio 57

22 Schematic - Compound Planetary Transmission -350 ft-lb, 88:1 Rat -) 58

23 Schematic - Compound Planetary Transmission 58

24 Compound Planetary Transmission Weight and Volume VersusOutput Torque 59

25 Schematic - External Epicyclic Tranemission 65

2(; Epicyclic Transmission Volume and Weight VersusOverall Ratio 65

27 Harmonic Drive Weight and Volume Versus Overall Ratio 67

28 Inertia of Spur Gear Transmissions 78

29 Inertia of Compound Planetary and External EplcyclicTransmissions 84

30 Diagram for Determination of wg 84

31 Inertia of HarmonicDrive Transmissions 86

32 Transmission Weight Versus Stall Torque 89

33 Transmission Volume Versus Stall Torque 90

34 Transmission Inertia Versus Stall Torque 91

35 Block Diagram - Inner Gimbal Control System 92

36 Block D)iagram - Actuator Transfer Function 95

37 Schoniatlc Dilafgam - DC Torquer Motor Control Circuit 96

Actuator Weight Versus Minimum Suitable Gear Ratio -":15ft-lb Stall Torque 103

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LISTOF ILLUSTRATIONS(continued)

FIGURENDO. TITLE PAGE

39 Actuator Weight Versus Minimum Suitable Gear Ratio -87.5 ft-lb Stall Torque 103

4.0 Actuator Weight Versus Minimum Suitable Gear Ratio -175ft-lb Stall Torque 104

41 Actuator Weight Versus Minimum Suitable Gear Ratio -262 ft-lb Stall Torque 104

42 Actuator Weight Versus Minimum Suitable Gear Ratio -350 ft-lb Stall Torque 105

43 Motor and Load Torque-Speed Curve 106

44 Epicyclic Transmission 107N N45 Non-Dimensional Parameter - and - Versus Transmission

Ratio N1 N1 110

46 Epicyclic Transmission Efficiency qt for N, = 50 111

47 Epicyclic Transmission Efficiency Y, or N1 = 100 112

48 Epicycltc Transmission Efficiency 1 for 141 = 150 113

49 Schematic - DC Proportional Controller 123

50 Preamp Required to Reduce DeadBand 124

51 Voltage Amplifier Characteristics - Unloaded GainofApproximately 2.8 v/v 124

52 Single PWMPulse Error Signal at t1 125

51; PWM Pulse Train for a Varyirng Error Signal 126

Single Channel Pulse WidthModulator 127

Power Bridge and Driving Stages 1285; Zero Error Waveforms 129

XI


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LISTOF ILLUSTRATIONS {rontinued)

FIGURE NO. TITLY PAGE

57 Positive Error Signal Waveforms 130

58 Single PWNPuls4 - Error Signal at t1 131

59 PWMPulse Train for a Varying Signa 131

60 S•.heratic - DualChainnelPulse WidthM•olulator 132

6i Zero Error Waveforms 133

62 Positive Error Waveforms 134

63 An ON-OFF System 135

64 Ideal Controller Characteristics 135

65 %'ontroller Characteristics with Dead Bard 135

66 An ON-OFF Rate Control System 136

67 A Simplified ON-OFF Rate System 137

68 Phase Plane Trajectory for Standard ON-OFV Sysitem, 138

69 A Position Repeating System 139

7 Polar Ploi of G 1 ( w) and N(E) 144)39

71 ON-OFF Conti'oller in Torque Mod*e 140

72 Equivalent Circuit of Torque Motor 141

73 Response Torqde fo, Command Voltage to Torque Winding 142

74 ON-OFF Cross Compensated fLateSystem 143

75 Solid State ON-OFF 1V3

?6 ON-.OFFWaveforms 144

77 Ideal 2-Level ON-OFF CharA eristics 145

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LISTOF ILLUSTRATIONS (continued)

FIGURE NO. TITLE PAGE

78 Two Level Cmo.,coller with Dead £Bmnd 145

79 2-Level ON-OFF Rate Controi Sy:7tem 146

80 Phase Plane majeentoryfor 2-Level ON-OFF Controllerwith Second Order System 147

81 Schematic - Soild State ON-OFF with Gain Change. 149

82 Equivalent PAMSystem 150

•3 Pulse Amplitude Modulator - Double-Polarily 15 1

84 Schematic - Pulse Amplitud'3 Modulator 152

85 Block Diagram - IPFM with Input and Output WaveShapes 163

86 Schematic - Pulse Frequency Modulation 154

87 Voltage to Frequency Converter 155

88 Wave Shapes from V/F Converter to Power Bridge 156

89 Duty Ratio Versuc Input Magnitude 1.57

90 Schematic - Delta Modulator System 158

91 Voltage Wave Shapes - Zero Erre- Signal 159

92 Voltage Patterns for Error Signal of 1 Volt 160

93 Voltage Pattern for an Error Signal of v. 5 Volt 161

94 LoadCurreni Versus Time for Stop Error 1nput64

:5 Current Pati in Power Switch ). 5 I96 Controller Power Consumption Versus Torque and CNMG Size 169

97 Controller ":ffictency .ýrsus Torque and CMGSize 172 49 Typical PWM Transfer Characteristics 174

2

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F IGUP , 1ýFITLE PAGE

L99kyt lnuie Girnba Actuatwr Asae-ibly 181

flf(t Actuator Outline Drawing 182

1S1 Schematic. -Resolver with SiOg. Phase fnput 193

1.02 Schematic - Induction Potentiometer 194

1.03 Function Diagram - Rate Gyro 20i

104 Epicyclic Transmission 205

105 Loading Forces 205

106 Orbit Gear Bearings 205

107 Output Bearings 208

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LIST `'7 TABLES

TABLE NO. PAGE

Tabulation of DC Torquer Motors and . ransi .ssion Ratios 16

n 'Tabulation of selected Motors and Gear Ratios 17III Respopsyn Actuator Data 22

TV Weight of Twe Hydraulic Gimbal Torquers for n 2000 ft-lb-seeCMG 32

V Efficiencies of the HydraulicComponentsfor a CMG 33

VI Servovale P,.wer Requirements per CMG 35

VII Weight and Volume Requirements of TWO Pneumatic Actuators 40

VIII Applicable Harmonic Drive Transmission Size NumbersVersus Stall Torque and Gear Ratio 66

XI Equivalent Inertia of himple Planetary Transmission withSin Gear Input and Carrier Output 79

X Equivalent Inertia G. Compound Planetary Trans rnlssin withSun Gear Input and Carrier Okitput 83

XI Calculated Inertia Values for l'xternal Epicyclic Trai sai .•-:ns 86

XII Inertia of Harmonic Drive Transwrssions 87

X111 Transmission Evalution 88

XIV DC Torquer - Transmnission Comparison (200 ft-lb-secCMc Size) 98

M, DC'Torquer - Cransrnissian Compnrlson (100 f-bstCM[1 Size) 9

XVi DC Torquer - Transmisston Cemparison (1000 ft-lb-secCM13 Size) i00

XV i DC Tnrquer - Transimiss ion Comparison (1 500 it-lb-secCMG Size) 101

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LISTOFTABLES(continued)

TABLE NO. PAGEXVIII DC Torquer - Transmission Comparison (2000ft-lb-sec

CMGSize) 102XIX Torquer Characteristics for Various CMGSizes 119

XX Torquer Operating Conditions and Actuator Response 120

XXI Estimated Physcial Characteristics of Five Actuator Sizes 121

XXII Brief Summary of Actuator Characteristics 162

XXIII Power Consumption of Eight Controllers 170

XXIV Efficiency of Eight Controllers 171XXV Controller Electronics - Weight and Volume Estimate 172

XXVI Relative Reliability of Electronic Controllers 173

XXVII Controller Threshold 175

Xxvm Summary of Electronic Controller Characteristics 177

XXIX CMGActuator Reliability 179

XX= Epicyclic Transmission Gears184

XXXI Transmission and Gimbal Bearings 185

XXXII Angular Displacement and Velocity Transducers 192

XXXIII Tachometer Generator Characteristics 199

XXXIV Comparison of Floated VS1 Non-Floated Rate Gyros 203

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ImLISTOF ANBREVIATION8AND symB• Le

Def~nltion. Dimension

A - Distance from centerline of planet carrier to centerline Inchesof sun on simple planetary transmission

AL Eqnivalentleakage area in1Linear backlash between mating teeth inches

C - Correction factor dependent upon machining errors

Cc - Flowcoefficient 5 ~secCp - Specflc heat at constant pressure BTUAb-" R

CPA - Current power amplifier

CT - Center tap

fDre - Output shaft diameter inches

DG - Pitch diameter of gear Inches

Di - Pitch diameter of external (ring) gear in second-stage mesh inches

% = Motor displacement in 3 /rev

Do - Pitch diameter of Internal reaction (output) gear in second- inchesstage mesh

- Pitch diameter of pinion inches

Dpa - Planet gear axle diameter Inches

Dr - Planetary ring gear pitch diameter inches

Ds = Planetary sun gear pitch diameter Inches

d = Radius of gyration inchesE - Maximum pulse voltage amplitude volts

EHD - Integrated motor and harmovic drive transntislon

EHD/tr - Harmonic drive with external transmissionx

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LwTor AswmEVAToN AiD SYMBOLS(coovaned)

ff blDefintion Diumenson

fa a- MotorcutofffrequencyCP

fu6 - Motor viscous torque coefficient at rantinrshaft ft-lb-esec

-T Total viscous torque coefficient at motor shaft ft-lb-sec

9 Gravitational acceleration ft/soc 2

IC C. M.G. size ft-lb-sec

h RaJti~oof gear diameter to gear width

I - Gimbel moment of Inertia ft-lb-sec02

- Avertge motor current under duty cycle amperesL1~~ Average motor current required for umaimumdesired ames

torque

=~ Peak motor current amperes

IP Maximummotor current available amperes

IL Load current amperes

a Motor current amperes

::IPFM = Integral pulse frequencymodulation

je Equivalent transmission inertia at motor shaft ft-lb-sec 2

JG Inertia of a mass about an axis ft-lb-sec 2

JL Load inertla ft-lb-sec 2

=o Inertia of output ring gear ft-lb-sec2

JMMotor inertia ft-Ib-setu

J RTa c h o m e t e r momentof inertia ft-lb-sec2

JT Totalinertia at motor shaft ft-lb-sec 2


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LST OF ABBREVIATIONSAND8YMBCZS(continued)

ymbol Definition Dimension

fc Motor citoff frequency cp6

fM Motor visooux torque coefficient at motor shaft ft-lb-ew c

fr Total viscous torque coefficient at motor shaft ft-lb-sec

g Gravitational acceleration ft/sec 2

C .M.G. ,r'ze ft-lb-sec

h Ratio of gear diameter to gear width

I Gimbelmoment of inertL, ft-lb-sec 2

Iv Average motor current under duty cycle amperes

imax Average motor current required for ni.dmum desired amperestorque

IMp Peak motor current amperes

Ip Maximum motor current availalle amperes

Loadcurrent amp,'j tes

Motor current azmpereb

:IPFM Integral pulstefrequencrymodulation

Je Fquivt-ent tran5mission inuertiaat motor shaft ft-)-sec2

JInertia of a mass aixmt an axi-.

J L.Load inertia ft b-sec-

Inertia of output ring gear ftr-lb--ec-

JM Motor inerlia ft-lb-sec-

JR Tachometer moment of iner-tia ft ib-sec'-

J r Total inertia at rnotor sWaft ft--lb--sec-,

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LI3T OF ABBREVIATIONS AND SYMBOLS (continued)

Symbol Definition Dimension

K Hydraulic system dimensional constant watt-sec/in-lb

Error amplifier gain volt/volt

Motor back - emf constant volt-sec/rad

KG Feedback tachometer gain volt-sec/rad

It =- Density ratio of a mesh

1j Dimensional constant lb-sec 2 /ft 4

Km Motor constant Vft-lh-secx 10-2

KT Motor torque constant ft-lb/amp

KTY Motor gain constant of inner gimbal torque ft-lbs/amperes

KVyl Inner gimbal effective back em constant volts/rad/sec

KVy2 Inner gimbal tachometer constant volts/rad/sec

AJSimple planetary transmission face-width scalin,6 factor

K2 = Simple planetary transmission welg. a.•MirigLactor

K 3 Simple planetary transmission weight scaling factor

K4 = .c-,ple planetary transmission volume scaling factor

kI Stall torque input constant ft-lb/volt

L Length inches

La, Ly = Motor winding inductance henries

Lmr Motor inductance henry

t Length of line-of-action incheti

Carrier flange thicknessinches

Input shaft length inches

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LIST O ABBREVIATI)NSANDSYMBOLS(eout7ied)

Symbol Definition Dimesion

o Output s1111A length inches

= Planet gear ae length inchesm = Mass lb-sec 2ft

ntr Ratio of one mesh

M Maximumoutrut of ON-OFFcontroller volts

m Instantaneous torqý,. motor input voltage volts

my Millivolts

ML Load torque-speed curv•e slope ft-lb-sec

NM = Motor torque-speed curve slope ft-lb-sec

m = Ratio of one mesh

N = Number of teath i, contact

NG = Number of teeth in gear

NL = Load spee& RPM

NM Motov speed RPS INp Number of teeth in pinion

n = Number of planet gears

PA Average actuator output power watts

PAM = Pulse amplitude modulation

PFM = Pulse frequency modulation

PW% Pulse wid'•h modulation

PWM - Pulsubwidth modulation, single channel

PWM2 Pulse width modulation, dual channel

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LMT OF ABBREVIATIONS ANDSYMBOLS (continued)


v Motor input power under duty cycle watts

'anvg Average power required watts

•]t Switching bridge power consumption watts

- Motor input power watts

I-d LDiametralpitch

P1, - Hydraulic leakage power loss watts

Pm Mechanical losses watts

PMm Motor input power to deliver maximum desircil torque watts

Pp Motor input power to deliver peak torque watts

PPMI Parts per million hours

PS Hiydraulicpower required at servovalves watts

Ps 1 - Power required at maximum speed watts

Power required at 0.5 maximum speed watts

P4 - Power required at 0.25 maximum speed watts

PT - Total C. M.G. hydraulic system actuator power watts

Pt Total power consumption in motor and controller watts

V'r' 1 Power required at maximum torIque watts

'T 2 =- Power required at 0. 5 maximutrmtorque watts

Power required at 0. 25 maximum torque watts

11Pneumaticmotor inlet pressure psi

-- Pneumatic downstream pre,;surl p:l

A Hydraulic inotor differential prestiurv pri


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Li8T OF ABBREVIATIONSANDSYMBOLS continuedM)

5yvmboi Dcf1•ttlcon Dimension •

SQ Ratiofac•tor

TotW hydraullc system leakage inYisec

QLM Total hydraulic motor leakage ind/sec

( W p Votal pump leakage ýcbargeable per contivl moment Ln3isec

gyrosc,_Ve)

QLV = Total eervoveive leakage in3 /sec

R Resistance ohms

R, Ry= DC motor resistance ohms

Rm Motorresistance ohms

RS Internal resistance of voltage source ohms

RG Transmission overall ratio

Gas constant in/O R

G = Pitch radius of gearinches

rp Pt.ch radius o. pinion or planet inches

rr Ring gear pitch radius inches

rsf=sSun gear pitch radius inches

S = Laplace operator sec-1

IS2S34 = Power switches

Sb = Beam (Lewis) stress psi

,c ,c Hertz stress psi

T Gas temperature o R

Tern - Stedly -state motor torque ft-lb

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LISTGU ABBREVIATIONSANDSYMBOLS(continur _'ý


TF ITot coulomb friction torque at motor shaft ft-lbs

TLM -- &mumdmnu trannmis-ion output torque (stall torque) ft-lb

TM Instantaneous motor output torque ft-lb

Tm = Maximum reqW,'redoutput torque f-lbs

TMp = Torquer. rate.' peak torque output ft-lbs

'MSE Maximrtumnm.or stall torque ft-lb

Tiansmission stall torque ft-lb

t = Time see

T = Pulse period sec

Period of clock pulse sec

V TransmieAon volume iD3

V/F Voltage-to-frequency

V1 = Tooth pitch line velocity ft/mWn.

VPA Voltage power amplifier

W = Transmission weight pounds

Wa WeigLh of actuator lh

w- Specific weight of material lb/In 3

W = Gas weight flow lb/sec

Y Form iactor

Gimbal position angle radia,

Gimbal rates rad/sec

[iDampit g factor

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I


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IUltF OF AXBREV!ATIONSANDSYMBOLS(cOAtliUed)

ymboll Definition Dimension

Trransmtisson efficiency percent

Ratio of inertia seen by outer gimbal and Inner gimbaltorquers

SCompressor efficiency percent

= Motor efficiency percent

r Time constant see

JA Dynamiccoefficient of friction

•c =Car r i e r velocity rad/sec

c = Motor cutoff frequency rad/sec

i = input angular velocity rad/sec

Vm•locityof a mass about an axis rad/see

= Natural frequency rad/sec

wo Maximum gimbal rate tad/sec

w = Planet gear velocity rad/sec

ws Sungear veiocity rad/sec

o = Output angular velocity rad/sec

W = Ring gear argular velocity (about its center) rad/sec

* = CGeartooth pressure angle deg. es

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SECTION 1

INTRODUCTION

1. 1 GENERAL

The useof large control morrent gyroscopes (CMGs~)ior the stabilization of

mannedspacecrafton longdurationmissionsh- beenthe subjectof considerabletheo-etical study. It is expectedthat the use of large CMG systems will leadto a notable

improvement In attitudecontrol accuracies andweightsavings whencompared to the* ~conventional£eactionjetcontrolsystemsfor longterm missions.

There is presently a great dealof interest in thedoublegimbaltype of CMG.NASA Langleyhas a program to fabricate and test a large doublegimbalCMG to pro-

* vide verification of previous theoretical studies. One of these studies recommendedthat a studyc.' gimbaltorquers be carried out to select an'orxlmalCMG gimbaltorquerdesign. The Flight ControlDivisionof the Air Force Flight DynamicsLaboratory atWright- Patterson Air Force Base decidedto undertakesucha torquer studyto corn-plementthe NASA LAn-gleyCMG program.

To illustrate the problem, the,NASA LangleyC MG gyrowheelhas an ang~darmomentumof 1000 ft-lb-sec and req-ir%ýsgimbaltorques up to 175 ft-lb. A direct-drive DC torquer witha 175 ft-lb rating ccald weighover 300 poundsand also consumea maximumof over 600 wattsof continuous nower.Other typesof torquer8 andspeedreductiontransmissions were therefore investigated for this application.The com-binedCMG torquer transmission assembly shall be designated as a CMG actuator inthis report.

1.2 OBJECTIVES

The objectiveof this studyis to determine optimalactuators for control momentgy~roscopes having angu ar momentumis ranging from 200 to 2000fl-lb--sec. This studymust also detormine optimal controllers (control electroniesi for the correspondingrangeof actuators, includingany interface relationships betweenthe controller andactuator. A diagram -tepresenting relationships betixeenthe controller and actuator isshownin figure 1.

Theoptimization stidyshall be madeon the basis of the fcllowingchar acte rist1c'4:

(a) Powerconsumption

(6) Roliability

(c) Weight

(d)I Volume

(e) Performrance3


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More detai on required perfornawe~ to glivn In para: taj*t 1.3.

POWER

INPUJT

CM

Figure 1. Basic Relationship Betu' en Controller and Actuator

In addition to the optimization study, a preliminary design study for an aigularmomei&.umof 1000 ft-lb-sec is needed to examine Its applicability to the NAS.ALangley CMG.

1.3 REQUIREMENTS

The study can be divided into three parts:

(a) A gimbal actuator optimization study

(b) A controller study

(c) A destii -study for the NASA LanglreyIt;OOft-lb-see '-4G.

1.3.1 A Gimbal Actuator (kitimizationi Study

The CMGgimbal actuator wrqiier and transmission st;udy is requirod forthe angular mcomentumeiage from 200 to 2000ft-lb-sec. T he following s.pecific re-quL'ements are tco be consid~rted:

(a) 14axdrum gimal.,- rate less thfin:0. 17.5 raidýsee (approx. *10 deg/see).

(b) Minimum gimbal iiite greater thati 0, 000175 radi'sov (approx. 0. 01 deg/secý).

(c) Threshold torque le.ý than 0. (X' of maximulmtorquer output.

(d) Tcorqueoutput linearity ,4hallbe within ±57 of ttie ma~ximumoutput torque.


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Pctuator Desiga tudyta result of the gimbalactuator optimization study andthe controllera•udy., a detaflld set of requirements for a control actuator for use on the NASA

ngloy 1 0 0 ft-lb-seo CMG will be examined. As a result of this, a preliminary de-aige wfll be prepared which will optimize the performance of the gimbal actuator forthis p9lt•ation. This preliminary desig will include layout and outline drawings.'The cu•lin3 drawing shall include dimensioning for all Interfaces with the NASALang-l.ey C•iG Inner gimbal.

The gimbal actuator shall be capable of developing a maximum torque ofS175 ft-lb with either a torque or rate mode configuration. In addition to the specific

reoqui•ments listed in paragraph 1.3.1 for the actuator optimization study, the designmust vlso meet the following performance requirements:

Threshold torque 0. 2 ft-lb

Output torque resolution 1.75 ft-lb

The actuator design will allow for modular-mounting or dismounting ofthe torquer, a tachometer generator and the complete actuator. It must also be Inter-chanriable with the presently designed NASA CMGtorquers,

1.4 GENERAL REQUIREMENTS

In addition to the above, some general requirements and other design objectiveswere dictated: such as, type of electrical power, reliability, environment and dutycycle operation.

1.4.1 Electrical Power

Allphases of the study will

bebased upon the following types of electri-cal power:

DC - Regulated, 28 * 0.5 volts

Unr•gulated, 24 to 31 volts

AC - 115/200 volts 2%

400 cps, three-phase wye

1. '.2 Roliability

A design objective of the CMG actuator will be a reliability of better thanu.99 for ono year of continuous operation. With annual scheduled service, the mini-mum oporational life shall be five years.

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1.4.3 Environmental Requirememts

The CMG actuator should be oapable of conttnu•us operqtion in the following envLronment:

Ambient temperature: 7Q;F to120'F

whilevL•rafional

Pressure. 10 to 1.0 atmosphere (operational),

lo 11 atmosphere (nun-operational)

Radiation: negligible

Acceleration: 0to Ig (operationai)

1.,I4 Duty Cycle

The duty cycle of the CMG act~vtor wiflie assumed as follows:

1% of operation time -- Full required torque

3N( of operational time -- One-haif full requirýd torque

69%,of operatiomal time - One -quarter full required torque


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SECTIONII

SUMMARY

2.1PURPOSE

OF STUDY

The purpose of this study is to determine optimal gimbal actuators for largedouble glbtal CMG's with angular momentums from 200 to 2000 ft-lb-sec. Elec-trical, hydraulic and pneumatic actuators, along with five different types of mech-anical transmissions, were Investigated with respect to power requirements, weight,size and complexity.

In addition to the actuator study, it is desirable to deterrnine an optimal con-troller for driving the CMGactuator.

2.2 OPTIMIZATION STUDYANDPRELIMINARY DESIGN

Anoptimal actuator and controller was selected on the basis of minimum powerconsumption, minimum weight and size, maximum reliability and satisfaction ofperformance requirements. The actuator optimization is actually two studies:torquers arndmechanical transmissions. Once the optimal torquers were selected,the transmission optimization study followed.

To demonstrate both physical and performance characteristics of a typicallyoptimal actuator for the CMGapplicaticn, a preliminary design of the actuator forthe 1000 ft-lb-sec CMGsize is developed. A layout drawing End tabulation of itsperformance characteristics are presented. A summary of the design's character-istics follows:

Design load torque 175 ft-lb

Design load velocity 0. 175rad/sec

Transmission gear ratio 60

Peak power consumption 43.1 watts

Dutycycle avg, power consumption 5.5 watts

Weight 23 lb

Envelope volume 380 cu in.

Reliability: I year 0.9741

2 months 0.9956

Threshold 3%

Actuator response 123 rad/sec

Damping factor 1.27

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The major difference between this optional acthator design (175 ft-lb torque forthe 1000ft-lb-sec size) and that used for the NASA Langley CMGis the mechanicaltransmission. The actuator In this study uses an epicyclic transmission, while theone used on the NASALangley CMGactuator is basically a simple two-stage planetary.The optimal actuator design has a number of significant advantages over the NASALangley CMGactuator, mainly on the basis of the characteristics of the transmissionused: namely,

(a) The number of teeth of each driven gear which are in engagement with its drivergear are much greater, thereby Improving reliability.

(b) Lower Hertz stress in engaging teeth, thereby improving wear Lndlife.

(c) Less overall weight.

(d) Smaller volume.

(e) Lower reflected moment-of-inertia back to the motor shaft, thereby minimi-zing problems in achieving response and dynamic stability.

(f) Higher gear ratios are available per gear pass (simple planetary is limitedto 10 per stage).

Except for problems of switching high inductiwe loads and having high rippletorques, a DC brushless torque motor would be an optimal torquer. It has a lowerthreshold and potentially high reliability. But until this problem is solved, the DCtorquer is considered optimum.

An excellent second choice for tle mechanical transmission is the compoundplanetary transmission.

With regard to controller optimization, the single channel pulse width mod-ulator was selected. An excellent alternate is delta modulation, particularly wherea vehicle's attitude control system requires a digital computer for determining thedesired torque output at each CMG's pivot.

The single channel pulse width modulation controller has the following charac-teristics for the 1000ft-lb-sec CMG:

*Peak power consumption 50.9 watts

*Average power consumption 8.8 watts

Weight 2.5 ounces

Volume 2.5 cu. In.

Reliability (1 year, operational) 0.9775

(2 months, operational) 0.9962*Including actuator power

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2.3 RECOMMENDATIONS

The recommendations are that:

(a) The optimal actuator shall inoluwea DC torquer and an epicyclic transmission.

(b) The optimal controller be a single channel pulse width modulator.

(e) Delta modulation be considered as an alternate controller when a digitalcomputer is used for resolving torque commands at each CMGpivot.

(d) Brushless DC torquers should be considered for CIMG gimbal actuation inthe future when It may be closer to being established as "state-of-the-art".

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SECTION MI

APPROACH

The approach to the CMG actuator study is summarized in Figure 2. As pre-

viously described, the program was divided into three major categories:

(a) Actuator optimization

(b) Controller optimization

(c) Preliminary CMG actuator design

The actuator optimization is actually divided into two distinct studies: torquersand transmissions. As shown in Figure 2, all types of electrical, hydraulic andpneumatic torquers or motors were evaluated in a preliminary sense. This was toeliminate any torquers which were obviously inadequate for this CMG applicationbefore selecting nn optimal torquer-type. Th s evaluation, which was based uponpower required, weight, size, reliability, and performance, is presented in SectionIV.

A number of trznsmission types for the CMG actuator application were alsostudied, namely: spur gears, simple planetary, compound planetary, epicyclic andthe harmonic drive. The study was made for five different actuator torque outputs:35, 87. 5, 175, 262, and 350 ft-lb. The transmissions were evaluated on the basis ofweight, volume, reflected moment of inertia to torquer, efficiency, threshold andbacklash as a function of torque output and gear ratio. This study is made in Sec-tion V.

Other aspects of the actuator optimization are given in Section VI. Once the

torquer and transmission types have been selected, the actual torquer type and sizeand the transmission sizing are determined for the five actuator sizes. Final char-acteristics of the five actuators are then tabulr.ted.

Controller candidates for the optimum actuators are described in Section VII.They include the following:

(a) DC proportional

(b) Pulse width modulation, single channel (PWM 1 )

,(c) Pulse width modulation, double channel (PWM 2 )

(d) ON-OFF

(e) ON-OFF with two gain levels

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I

r;-

!00

'0 0 1" w

2- ,

@1~v -'a

N 0ýva0 0 .

Z., 0)aa0vt

M4


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(f) Pulse amplitude modulation

(g) Pulso frequency modulation

(h) Delta modulation

Power dissipation, reliability, threshold, weight and volume are determinedfor all eight controllers in Section VIII. Final selection of the optimal controller Ismade in Section IX, where the optimal actuator is also reviewed.

A preliminary design of a 175 ft-lb CMG actuator can then be made on the'configuration determined in the optimization study.

Included in the design are the selected torquer, transmission, tachometergenerator and associated hardware for mounting to the structure and gimbal. Alayout drawing and an outline drawing are then prepared. This preliminary designis presented in Section X.

Three appendices are needed to support the preliminary design of the CMGactuators is in Appendix A. A study of the types of gimbal displacement and ratesensors is g1ven In Appendix B. Appendix C contains a brief analysis for the selec-tion of bearings for the actuator design.

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SECTION IV

PRELMNITARY tTOQER~EVALUATION

The results of the iritial phase efforts Indicatedthatk the DC torquer motors wereoptinAulcandidates for control m~omentgyroncopm,3LmYbd actuator application, Brush-loee 1)C torquer motors, electromagnetle. harmoniCdrlvea;,a1nd electromechanicglDYn'XECTOR14are. includedin the broad eategory of DC torquer motcirs. Ha"wever,thes* tater threzet -psa gea l ; t aotstate -A -tic -art. Currently, commutationand,the required -controlelectronics are the eoxnmonproblems associated -withallthree types.

The graphcal psower"14 woightrenults of,this section indicatethe total require -mneoftwoactuators per CMG, one for each axis. Throughoutthe remainder of the

report, all paarametersare presented on a per actiator basis.

4.2 EVALUATION CRITERIA

4. 2". Elementary Actuator Operation

Each 0,uble gianbalgyrobuopehas twoactuators, onefor the outer gimbalan(,'one for the Innergimbal. Thefunctionof the actuators are twofold,but both func-tions are not required simultaneously on anyone actuator. Thefirst functionIs toexert torques at stall. rhe secondfunctionis to provideglmh&Iratteswithinertia andfriction loadingonly. The actuattorthat is not exerting stal to,.rqueis required to pro-viderates proportional to theaiall torque exerted by the other actuator of a doubleginmbalgyroscope.

The datapreae 'nd in this section illustr:~te the total r~equirementsfortwoactuators per CMG.

4.2.2 Basic ..ssumpttons

The control momentgyroscope size iterations usedin the studyare the200, 500, 1, 000, 1,500 and2,000 ft-lb-sec sizes. The specification used asa guide%s"Specifications for Control MomentGyroscope,."NASA SpecificationNo. L-5298,

dated2 Augustl'465.

4. 2. 3 'Evauatic-" Considerations

P~imary consider-at.ionsfGr the initial qualitative studyof actuators areaverage powerdemandto moet;iteady-state torque -speedrequirements of the load,

*DYNAVECTORis a regboteredtrade name 'A The BendixCorporation

12


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physical sLe andweight,efficiencyand system complexity. The secondory corsIderit-tions for the prelimuinaryevaluation,re gross 'Limitationson expa.,,ctedresponsc underrate modeof operationm Thepurpoeeof this phaseof the stdy was to eliminate Spe-citic typesof torquers havinggross limitations in application to the control moment

For purposes of uniformity, the transmission weightestimate per actu-ator wasequalizedfor all actuator types as a functionof maximtumtransmission outputtorque TLM. Theassumed expressions for external transmission weightsusedwere.-

For ratios between15 and 100:1

W - 0' "29b/ft-lb TM + 3. 5 )- (4-1)

For ratios between100 and 200A.

W 0).035 lb/ft-lb, TLM 4.2& b (4-2)

These twoexpresslionsar'e empirically formulated becauseof the scarcity of the re~-quired data. The formulation includedapplicationof engineering judgeirient- neetransmission weight dataavailable minudedt weightof the housing,and, further.the bearings and gear face widths -werenotdirectly applicable to thelife requiremrentsof the CMGs. rhes~eequations, though notrigorously justifiable, served a useful pur-pose in permitting the use of a commontran.smission baseline for comparing the vari-ous torquer types, andpermitting the c'ompletionof the preliminary qualitativeevaluation.

Theweightsof the e c. romnechanicaland hydraulic DYNAVECTORSwereestimated from datamadeavailableby the DYNAVECTOR prog-ramcurrently beingconductedby TheBendixCorpotration.

For purposes of the preliminary evaluation,the transmission efficiencywas assumed to be 90 percent.

The torque -speedc,?quireincntsof t'.,egimbalactuators are definedforthe fiveCMIG sizes tinderconsideration, withmaximumspeedbeingcommonfor allsizes at 0. 175 rad/sec and stall torquebeinfrthe CMG size thimesthe maximumspeed.Theminmumnspeed,capability required is 0. 000175 rad/sec, Otherpertinent specifi-cations derived duringthis studyare illustrated in AppendixA.

The averagesteady-state operation powerrequirements per CMG derivedin this studywerebase on the followinrgloaddistribution:

PA%0 . 1 P +"U+03(P P T + .4.)(FIl, p3)

C(WMG 'Ti 1) T2.( S2 6P S3

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where

• power required at maximxumtorque"T"

:PT power requirbd at 0.5 of maximumtorque

P T3 powerrequired at 0.25 of maximum torque

P powerrequi-d at maximumsweedra

S•S2 powerrequired at 0.25 omaximumspeed

P • power required a",0. 25 of maximum speed

Equation(4-3)states that the average powerrequired for a twoactro.torCMGIs the sumof the average powerrequired to provide the stall torques abovebyone actuator andthe average powerrequired to provide proportional speedby the other.This arbitrary load distribu*!onis slightly more stringent thanthat distribution used inthe "ControlMomentGyroscopeDesignReport" prepared for NASA/LangleyResearchCenter by Ecl.pse-Pioneer Division,datedI November1965.

The response of the actuator can beobtainedby considering that under therate modeof operation, the actuator transfer functionwillhaveeither of the followingforms:

Single Order:

NL(S) ___L - (4-4)

Em (S) i.S•- (

SecondOrder:

NL (S) 2n__. . ..(4-5•)

Em (S) S2 4V 2 ~ra(S 4. 2rwo S f Wn n

If a single order transfer function governs the actuator, then the required r must be

0. 05 seconds. However,if a secondorder transfer functiongoverns the actuator, the.tep response mustbe within+3 percent of the final valuewithinthe same thi:. inter-v41 that a single order system with a time constant of 7 0. 05 seconds rlaches 97percent at its final value. The required settling frtquency of the second order systemmust al-o be less than 100cps. The required time to reach -3 percent of filal vpluefor botU types is 0. 175 seconds. For a second order system with an assumed

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r 0, 7, this -orresponds to a natural frequency w of 5 c ps and a settling frequencyof 3.5 cps, which is considerably less than the required 100 cps.

Under torque mode of operation, :0 percent of final value within 0. 175seconds is not s8.ingent, and therefore is not considered to i a respon.;e problem.

4.3 PARAMETERS OF INDIVIDUALACTUAT'ORTYPES

4.3.1 Electric

4.3.1.1 DC Torquer Motor

DC torquers were sized to meet the maximum torque and maxi-mum speed requirements and a'lo to minimize the difference between the maximumand minimum suitable gear ratio. The suitable gear ratios were tabulated using vari-ous DC motors for each of the five s&,parateactuator requirements. The optimumfixed gca. ratio was estimated to be in the range of 100:1to 200:1 with the higher gearratio requirement for the smaller CMGsizes.

Table I illustrates the motors and transmission ratios consid-ered, and the preliminary data on weight and volume.

The resulting gear ratios of several CMG sizes were higher than2100:1. Subsequent discussions with the motor manufacturer indicated that minor modi-fication of motor internal construction details would result in a change in the slene ofthe motor's torque-speed curve, without materially altering the motor's external con-figuration or package weight. The resulting increase of the motor' s stall torque capa-bility permitt d slight reductions of the overall gear ratio.

The motor cizing criteria used were:

(1) Minimum actuator weight consistent witl, required performance.

(2) Transmission ratio ol 200:1or less

(3) The product oi ma:ximumme;torspeed and motor stall torque must be •reaterthan the maximum load stall torque squared divided by the slop.eof the loadtorque-speed curve. Expressed mathematically

N xI'-M

max M

The final selected ratios for each CMG size are show>ýinTable 1.

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.e p .a.4 --- a a 4 *

'S. - *.. a 0 -

1- 6 -4 '4

4 4 4 :.-7 _____4 I

.i- ---. ---- 4----

I 'S * 4 . 2 1 4.,- - -

B-

*- - of-B I -. 5,

I- _________ --- ________

41

- 4 __ YI- *I 4

4* .

____

14 __

t _______ 2 ::i .42B-- I2 :, 4 ,a .1 .4 9- .4z

- at ____ 5.4,

'-4 -ri: - : : - ao ia e.fT7l _____

I- '4

0 4, 4-w -- .a -* B.

C)' - - - ----4.- r- - . - - - - - - I4 0

H >---

0 -------. >1++'I2 * -..- * .44 5

H 0 C - I - *oj ..

-, .4 **

I . -

K. .- t t$ I tI I

1.1:

12*1

. j7iI-__________ . . _______ L :1

16


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TABLE H

TABULATIONOF SELECTED MOTORSANDGEAR RATIOS

C M G Inland GearSize Model Number Ratio

200 T-2170 160

500 T-2171 200

1000 T-2950 200

1500 T-5134 100

2000 T-5135 100

The average power (Pavg) required for tho DC torquer was basedon the load distribution given in equation (4-3). The average value is given by the fol-lowing integration:

Pavg (t) dt (4-6)

0

where t Is time, r is the period of operation, and P (t) the instantaneous power.

Since the power, P, required in a DC motor at stall Is pure 12

Rloss, using equation (4-6)

Pag 7(I (t) dt (4-7)

0

For DC torquer motors,

TIM

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Since the assumed loading is given in three discrete steps, the value of Pavr per actu-ator can be obtained from the following summation:

avg j m(-

( )2 (0. KT ) (0.25 )2]P 01 + 0.3 + 0.69

avg K

(4-9)

= (0.1281)

2P ag= I mxR (0. 1281)

For two actuators, assuming the same duty cycle on each, thetotal averagepower required per CMG (Reference: equation (4-3)) becomes:

P /CMG = 0.26 I2 R (4-10)avg max

Actuator parameters using DCtorquer motors for a double gim-bal CMGare illustrated in Figure 3 as a function of CMG size.

4.3.1.2 Electromechanical DYNAVECTORActuator

The information presented in this paragraph was extracted fromscaling factor data made available by the DYNAVECTORefforts currently being con-ducted by The Bendix Corporation. The volume, weights and power consumption, as afunction of CMGsize, are shownin Figure 4. The weight and volume requirements ofthe associated commutation circuitry have not been included in the data illustrated inFigure 4.

The transmission ratio used was 840:1. Noexternal transmis-sion was required since this ratio is integrated with the electric DYNAVECTOR.Ingeneral, the system weight tends to decrease as the transmission ratio is further in-creased. However, with very high transmission ratios, the transmission life is do-

creased by the high velocities of some of the transmission parts. If very hightransmission ratios are used, the system should havea two-ratio transmission witha clutching or shifting mechanism to reduce the transmission ratio for high speedoperation. Transmissions with the ratio selected should be capable of long life andwould not require a clutch.

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o600

u d

d 000

hi 100- 30

jGoamams

00

0 40 M M10020

6 60

Q

3 0-

33 __ _ ___ _ _

1019


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4.3.1.6 *RESPON9YN Actuator

Servo actuators designated as RESPONSYN actuators have beenbuilt by the United Shoe Machinery Corporation, Beverly, Massachusetts. These unitsemploy a rotating magnetic field which deflects the flex spline of a harmonic drivetranomission. One of two design variations could be utilized. One approach utilizesan integrated motor and harmonic drive transmission and is designated as the EHD.

The second approach uses an external transmission in addition to the integrated pack-age and is designated as the EHD/Tx.

RESPONSYN actuater % arc avaflable with stators having distrib-uted windings for operation as synchroraous motors or with stators having discretewinding•&for operation as stepping motors, The current state-of-the-art Includes twoRESPONSYN actuator sizes that are past the development stage. They are the 6 and120 in-lb sizes. Other sizes have been built for special applications.

Table MI Illustrates data furnished by the manufacturer. Thefollowing requirements were used in the sizing estimate:

(1) Stall torque - 0. 175 x CMG size

(2) Maximum output speed - 2 rpm

(3) Operating voltage - 30 VDC

(4) Cooling - without external fans

The estimates presented in Table III are not fully optimized forthis application, but are useful for comparative tradeoff purposes throughout the CMGsize range. The weight, power and size estimates are for the RFSPONSYN actuatoralone, excluding electronics for controlling the field in the stator and the required ex-ternal transmission for EHD/Trx approach.

The approximate dimensions of a stepping actuator that was builtfor a special application( 2 ), are a cylinder having a 4-inch diameter and 4-inch lengthconnected to another cylinder having an 8-inch diameter and 4-inch length. Its weightIs only 22 pounds (as compared with 180 pounds for the size 500 CMG submitted by themanufacturer). This unit had an overall ,fficiency of 35 percent, a maximum outputspeed of 18 rpm, and a holding torque capability of 100 ft-lb. The size, weight andpower consumption requirements of the motor commutation electronics packages werenot supplied by the manufacturer and are not included in the above data.

*RESPONSYN actuator Is a catalog term used by the Harmonic Drive Division. UnitedShoe Machinery Corporation.

"(2Sce Reference No. 2, Appendix

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TABLE M

RESPONgYN ACTUATORDATA

C AM Sine ift-lb-see) 200 S00 1000 1500 Z000

WeightZlD Motor (lbs) 70 1 0 350 510 690END/ Tx Motor 13 '0 0.6 Z.6 7 3,only (lbs)

Power

DO@max tall50 960 1500 1940 2400torque (watts)END/Tx *rnsx. @tall 22 56 110 160 220torque (watts)

Power at maximum speed is approximately 1/4of the power at maximum stall torque

Slse

EHD Motor

Diameter (in) 9.5 12 14 15.5 17""nth (in) 14 18 z2 23 {

.%HD/TA Motor only .Diameter (in) 2.5 3.5 5 6.5 8Length (in) 3.7 5 7.5 9.7 13

Additional Requirements

External TransmissionRatio using the EHD/Tx 80 35 25 20 1iApproach

4.3.2 Hydraulic Actuators

4.3.2.1 Conventional Systems

There are several basic types of hydraulic actuation systemsthat could be considenred as possible candidates for application to the CMG. Amongthese are the constant flow system, the servo pump system and the servovalve system.

Constant flow systems as shown in figure 5 were discarded froT..

further constderation as candidates for the CMG. Their operation is poorly adapted toapplication to two or more. independent systems eperating simultaneously from theoamo supiply. This is especially true for the CMG, where one gimbal operates underlow prosBure, high flow conditions (rate control), and the other -timbal operates underhigh pressure, tow flow conditions (torque control).

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SYSTEM I.I-- -- ---- - - -

SERVO MOTOR-VALVE IMTi

1PRESSURE MOTORLFI~SOURCE F

L __ .I

SYSTEM 3.

7E'i• MOTOR],I

Figure 5. Hydraulic Power Supplywith Constant Flow

The electrical system analogy of the constant flowhydraulic sys-temi is constant current operation. The constant flowsystem wouldbe sized to providethc high flowv rcquircrnent of nne gimbal and the high pressure requirements of the sec-ond gimbal. The resulting extra auxiliary control equipment increases overall weightand decreases reliability. Furthermore, the operation of such a system is very Inef-ficient In overall power consumption, and would bev?ry nonlinear. Servo performancecharacteristics wouldat best be only fair.

Variable displacement pumps or servo pumps also were not con-s'dcred for several reasons. The servo pump power efficiency is greater than servo-valve efficiency on a single axis system comparison basis. However, for the CMG,two axes must be connected to a single servo pump or one servo pump must be usedwith each gimbal. An example Is shownfor a constant pressure system in figure 6.

Since use of multiple servo pumps (oneper axis) is not practicalfromnthe size and weight viewpoint, a sin~tleservo pumpmust be used for each CMG.Th1s3ervo pumpwouldbe sized to provide the peak pressure requirements. Loadtflow,rccquiremonts, within the range of maximum demand required by the load profile,

II

would be obtained by varying pump displscement. Auxiliary equipment In the form of

23


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SYSTEM I.

__rSERI MOTOR 6

• SYSTEM 2.

CONSTANT I [,7v. v , .o7oV

SYSTEM 3.

P UALVE OTOr-

Figure 6. Hydraulic Power Supplywith Constant Pressure

pressure reducing valves and switching valves wouldbe required to implement the con-trol circuit. Use of pressure reducing valves wculd lower the overall power efficiencycapability of the servo pump. The extra equipment adds additional weight and physical

size requirements, and reduces reliability. Finally, the larger volume of fluid undercompression In the servo pump system lowers the "hydraulic spring" rate, and gives alow control response. This response generally is several times lower than an equiva-lent servovalve system.

A servovalve controlled hydraulic actuating system (Seefigure 7)for the CMG would, in general, consist of the following elements:

(1) Sorvovalve

(2) Rotary actuator

(3) TI'ransmission

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ACCUMULATOR

POSITION _L SERVO VALVECOMMAND

MECHANICALi1 ROUTARLOAD eIT$N=I=IO ROTARYTASISO ACTUATOR

TRANSMISSION

Figure 7. Servovalve Controlled Hydraulic Actuator System

(4) Auxiliary Power Unit (A. P. U.) coa~sistingof:

(a) Electric motor

(b) Pump

(c) Accumulator

(d) Reservoir

(e) Valves, fittings, lines, etc.

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0P

Unl.ess a suitable hydraulic power supply is available, the penal-ties of added weight and vicrficeis in efficiency and reliability incurred In the conver-aton from electrlcal to hydraolio power must be charged to the hydraulic actuators.

The fact 3iat the pxcosed units will operate over exteadedpeT•lodsof time precludes the possbilty of operating the ys tm entirely fron achafed aoc'tmulstor. Anoptimum actuator would most likely contain an A. P.11U. con-mistint of a motor-pump-accumulator w•th suitable on-off controls to meet the averageand peak power demands of the syste_

Prellminazy cowsideratioas of system characteristics seem toindicate the need for certain redundancies If the hydraulic actuator is to meet the reli-ability Teqdrnments of a mission of this nature. The ele~tric driving motor possessessufficient reliability potential, and, becaise of stringent wetightrequirements, wouldnot be dupUcated. However, it is felt that two pumps sho-ild be provided. Onepumpwould be held on a gtandby basis and would be clutched to the common .Aectric motorin the event that the prima7,mpawnap -ereunable to roiasin sjy e•emp r e s s u r e . Slmui-taneoms declutching of the prlnary pump would alas be reqiirei An over-rurmingtype mechanism coui be designed to accomplish this taek.

Standby rocudancy of the hydraulic actuator would be desirable.from a reliability standpoint but would be difficult to Implement without intrfucing 'ax-cessive weight and unbalance to .he system at the load.

Duplicatlon of the servovalve would most likely not be justifiedby the small resultant increase in reliability since a valve inactive for long periods iftime would be susceptible to seizing.

The criteria of evaluation are limited to torrque-speed capability.power consumption based on an average torque of 33 percent of maximum torque andan average speed of 33 percent of maximum speed [Refer7nce: equation (4-3)], sys-tem weight and system response. Hydraulic systems are well knownfor their responsecapabilities. Consequently, response was not considered at this time.

The preliminary evaluation of an actuator for the large (2000ft-lb-sec) CMGactuators will be car. led out in some detail and will serve to illustratethe .rtAhod sed for evaluation of all five CMGsizes. Graphical results are presentedfor all sizes.

The :360 degree and :80 degree outt-c and inner gimbal rotationrequirements, and the interchangeable actuator requirements for both gimbals eliminates any 4 the rotary types nvarlable which are not capable of meeting this require-

m-nt, and Indicates the use of a vane or piston-type continuous rotaticn motor. r'gure8 shows a functional diagram of a reversible vane motor. One example of a pi',Eon-type motor it the cam piston motor sh')wn in figure 9. Gear types, as shownkn figure10, were not considered because of thoir relatively large leakage at stall conditto._

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Figiir, B. Schematic -Reversible Vane Motor

*a top%/

Figure, 9. Caul Piston Motor

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Figure 10. Gear Motor

The YrrIimumnopen servo ioop smioothspeed of hiydraulicvatioand piston-typo motors Is csttmated by motor mnanufacturers to be in the range of 5 to10 rpm. This mninimumrange capability Is primarlyx due to the combined effects ofcoulomb friction, imperfect inotor displacement per revolution, anO differences inmotor leakage as a function of output shaft po~sition. Ulseof well compensated sc~ioycontrol locrs will per-nit smooth closed-iooý) operation a.ý ltowas 0. 1. rpm. Using, thlýclosed loop low speed practical limit, the minimum reduction ratio wouldWe60. an'dthe minimum, smooth, closed-looyp output bp)eedi of the actinat~r wouildbe' 0. 0001,75 rad/spe.

Thme displacement. flowpower requiredI by,a byvd~r~aulicmotor i.Oven 'my:

P K~p D 11 N 4-DAn m4-11

Where

PA !9piacc-en~l~t flowp)ower (watts)

A) differential y:ressure kpst)

D) motor (1 ;placeinemi.(in/evm

11 grear ratio (di niens f ioess )G1


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N M output speed (rev/see)m

K - dimensional constant = 0. 113 watt-sec/in-lb

The minimum value of RC, has been determined from the motorlimitations, and Nm is fixed by the output speed specifications.

Neglecting leakage, no power would be dissipated by one actu-ator at stall since no flow is required. The entire power dissipation would take placein the second actuator.

If Nm in equation (4-11) is taken as Nayt "- 0. 33 Nmax. equation(4-11) becomes the expression for the average ideal power dissipation of the actuators,and

P - (0.113) Ap D R (0.33) (0.0279 rev/sec)A m G

or

P = 10.4x 10-4 Ap D R (4-12)A m G 4-2

The minimum differential pressure at which a hydraulic motorcan produce torque Tmax (in this case, 350 ft-lb or 4200 in-lb) Is given by:

2rTA - max (4-13)

min D RG

Combining equations (1-12) and (4-13) yields:

PA = 10.4 x 10-4 (2rT max) watts (4-14)

where

T is in in-lbmax

It is seen from equation (4-14) that the average power dissipatedin the actuator for a hydraulic system is a function of the level of stall torque only;thus, the selection of values of Ap, Dmi and RG must be based on considerations otherthan minimizing the average ideal power dissipation.

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The total average power consumption of the system can be writ-ten as:

T A L m (4-15)

where

PT total average power consumption of the actuator system for a single CMG

(watts)

PA = ideal power required by the actuators (watts)

P L = leakage flow power (watts)

P = mechanical losses (watts)m

For the selection of any combination of values of Dm, Ap, andH0 , which satisfy. the maximum torque requirement in equation (4-13), the PA term inconsumption indicates selecting Ap. Dm, and RG to minimize the system leakage lossterm PL" Since leakage flow is proportional to the differential pressure across anelement, it can be minimized by selecting a system pressure as lowas possible whilenot compromising torque demand.

A system pressure of 500psi was selected. While pressureslower than 500psi woulddecrease leakage flow, motor physical size and weight wouldincrease since a larger motor displacement wouldbe required to offset the reducedpressure. The optimum system is in the 500-psi range whenboth the overall weightand the total power demand are considered.

With the supply pressure fixed, the selection of D and RG canbe r. de on the basis of minimum weight. The minimum gear ratio has %.ready beendeter-.iined as 60 and the stall torque as 4200in-lb. Dy rearranging equation (4-13),the following relationship results:

2rTD H max (4-16)

m G p

It is seen that increasing RG permits the use of a smaller andlighter motor. Under the transmission assumption made in equation (4-1), the weightof the LX, . - , in iUs lof , for a particular stall torque value, is constant for ratios to 100.In this case, the transmission weight wouldbe 13.5 pounds. Thus. a ratio of 100 may

be used without an additional increment of weight. Using equation (4-16) with RG 100,Lho necessary minimum motor displacement is 0. 528 in /rev.

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A suitable motor would be the Vickers Model 911 aircraft-typeaxial piston motor which has a displacement of 0. 598 in3 /rev and a weight of 6. 8pounds.

Substituting the selected values of D , R,, and Ap into equation(4-12) yields an average ideal actuator power dissipation J'31..7 watts.

Suitable miniaturized servovalves are manufactured by BendixCorporation, Lear-Siegler. and Moog Servo Controls, among others. Sales literatureIndicates the weight of such a valve to be approximately 1/3 pound. A four-way servo-valve is shown in figure 11. This servovalve is usually used as a second-stage for anelectrically energized low level valve, such as a flapper valve. An electrical or me-chanical feedback from the four-way second stage valve to a low-level first stage valveis usually packaged as one complete servovalve.

No data is immediately available on suitable hydraulic powerunits since these are nonstandard items. Conversations with manufacturers of similarequipment indicate that, for the purposes of this study, 25 pounds might be a reason-able estimate of the weight of such a unit. In arriving at a system weight per CMG, itwas assumed that 3 gyros will be supplied from the same A. P. U. and therefore 1/3 ofthe weight was charged to each.

POWERSOURCE

•, • INPUT

"LOAD

Figure 11. Four-way Valve

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~k c~t!sat1 t ~e 'Yan , .mi , 1 t t Tt'in,-LO1 n l o f l en t . FrC7- I able TV this dght Is r;1. 3 p u n d s .

The power consumption of the syste'm Is evaluated on an avet ageb)a!.is,. It is assumed that an accumulator capable of providing peak demands Is In-cludied In the hydraulic power unit.

The PA portion of the total power consumption has been com-puted as 31.7 watts.

The leaka e flow for the 911 hydraulic motor is given by theVickers Corporation as 0. 129 n' /sec/1000 psi. Assuming the supply pump to have

F about the same characteristics, the leakage flow for the two motors and the pump at500 psi Is:

+2 (1/2 x0 ' + 1/3 (1/2 0. 128 23)(4-17)

- 0. 149 in3

/sec

Leakage flow for the Lear-Slegler servovalve is given as typi-cally 0. 1 GPM/4000 psi or 1/2 (QLV) - 0.05 in 3 /scc at 500 psi, or QLV = 0. 10 in3 /Sec.

Total system leakage is the sum of pump, motor and servovalveleakage:

QL = QLV + LM ' LP (4-18)

Total system leakage Is then 0. 249 in 3 /sec at 500 psi. In termsof power, this represents about 15 watts.

TABLE IV

WEIGHT OF TWO HYDRAULIC GIMBAL TORQUERS FORA 2000 FT-LB-SEC CMG

Z Motors 13.6 lb

Z Transmi ialons Z7.0 lb

Z Se rvovalves 0.7 lb

Sub-Total 41.3 lb

1/3 (A.P.(J .+Misc. Valving) 10.0 lb

TOTAL 51.3 lb

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Ihus f:.r. 31. 7 - 1I or 46,- 7 watts rmsuast1' 3pplled W the avs-" : •:• ,•.•: :zxiuds v.otumetric. but not mechanical. tnbefftcienries.

The efficiency of conversion from electrical to hydraulic powerwas taken as 40 percent. This figure is in line with the claims of manufacturers of4ircraft A. P, U. 's (e. g., Eastern Industries of Ha~mdon,Connecticut). Reasonableefficiencies were assumed for the other components and are listed in Table V.

The total power consumption, PT Is obtalined by dividing thepreviously found power requirement of 46.7 watts by the overall system efficiency toyield:

48.7 wattsP = 0. w.t = 259 watts

Values of actuator system weight and power consumption forCMG of other sizes were calculated in a similar manner and are illustrated in figure 12

Should a hydraulic power supply be made available, it would benecessary to imow the power required at the hydraulic servovalves. The power re -

quired at the servovalves, Ps. is the actuator power plus total leakage power less theleakage power of the pump, all divided by the mechanical efficiency of the valve andactuator. Thus

PA + PL - K Ap QLP

S 0 .8x0 .8x0 .7 (4-19)

Total power required, as previously defined, is the sum of actuator and leakage powerdivided by component and A. P. U. efficiencies. That is, from equation (4-15),

TABLE V

EFFICIENCIES OF THE HYDRAULIC COMPONENTS FOR A CMG

Hydraulic Motor (2) 70 percent

Transmission (Z) 80 percent

Servovalve (2)' 80 percent

The Overall Efficiency 45 percent(less A.P.U.)

A.P.U. 40 percent

The Overall Efficiency 18 percent(including A.P.U.1

Basic servovalve losses have been Included In thedetermination of the average Ideas power, PA '

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40*WRIGHT (COMVEPTIOHAL)

.4 j-WEIGHT (DYNAVECTON)

100*

0

CMGSIZE (PT-L11.SEC)

Figure 12. Hydraulio Actuation SystemWeight and Power Consumption

PA +PL(41aPT O 4x0.8x0.8x&.-7(45a

04 PA +PLPT = . 8x 0. 8 x0.7

Substituting this relationship into equation (4-19), the latter becomes

P =O4P - KAp QLPS T. 4 0T8x0LP (4-19a)

The pump leakage power (K,6p QLP~Is based on average values given by manufacturers.

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What equation (4-19a) 8ayA, In effect. is this: If a hydraulicIpw'er t'lupjdIl In already available, then the A. P. I. efficiency does not have to e.taken Into account. Thus the hydraulic power required is only 40 percent of the pre-v ourly calculated total input power to the A. P.U. (This accounts for the term 0.4 PT.)Ftilrther, since a pump Is not required, the leakage power of the pump (divided byefficiencies) is subtracted from the 0.4 PT term to determine the hydraulic power thatwould be required at the servovalves.

A tabulation of hydraulic power requirements at the servovalvesof a control moment gyroscope is shown in Table VI. This table represents power re -quired for a 500 psi constant pressure servovalve system controlling a two actuatorCMG. Note that it neglects the electric-to-hydraulic conversion losses.

TABLE VI

SERVOVALVE POWER REQUIREMENTS PK'RCMG

C M G Size PT 0.4 PT QLP Ap QLp g Psft-lb-sec watts watts in 3/sec watts watts

Z000 259 104 O.OZ 1.2 1031500 186 74 0.015 0.9 731000 152 60 0.015 0.9 59

500 97 39 0.009 0.5 38

200 75 30 0.009 0.5 ,29

Ordinarily, one of the greatest advantages of a hydraulic systemis its smaller size and weight for given power capability. This is fully exploited bydesigning systems to operate at high pressure levels. In this case, however, whereleakage flow represents a very high proportion of system power consumption, somecompromise in size and weight is indicated in order to reduce system pressure and,thus, leakage losses. The highly inefficient high pressure operation is due to the lowpower demand of the system, much lower than those of systems for which hydraulicsare usually considered.

The following sample computation serves to demonstrate the un-foasibility of 3000 psi operation for this application. Using a small displacement

motor, for example the Vickers Motor Model Number 906, the unit has a displacementof 0. 095 in 3 /rov and, for two units per CMG, displacement flow power of 32 watts(from equation 4-14). Each of the Model 906 motors has aleakage flow specification

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SyMetmwelghtj aire plotted in equation 4-3. showing the welght savings when a DYNA-VECTOR unit replaces the hydraulic motor and planetary transmission of the conven-tloral hydraulic system. Power consumption for the DYNAVECTOR system Isassumed to remain essentially the same as that for conventional hydraulic systems.

4.3.2.3 Stepping Actuators

The smallest eloctrohydraulic stepping motor manufactured byFujitsu, Limited, would be suitable for the largest CMG when coupled with a 200:1gear ratio since it is capable of a 30 ln-lb stall torque and a maximum speed of 50 rad/seC. The motor size is 3 inches in diameter and 10 inches in length. Thus, when usedwith a. 200:1 transmission, it is considerably larger than the equivalent DC torquermotor system. Further, the unit's relatively large length-to-diameter ratio does notreadily fit itself to the general "pancake" construction philosophy required by the con-trol moment gyroscope.

4.3.3 Pneumatic Actuators

4.3.3.1 Flow Requirements

The calculations in this section are based on the test record of apneumatic gearmotor( 3 ) and are the basis for determining pneumatic system power re -quirements. The motor is approximately the size required for the 2000 ft-lb-seo CMG.Piston motors were not considered in this evaluation. Although piston motors have a-lightly higher volumetric efficiency than gear motors, the overall efficiency is lower.

The weight of gas flow through the motor, using hydrogen sup-ply, is given by:

*= D N + C A 1 lb/sec(4-20)RE0T m m doL VT

The first term on the right is the weight of gas displaced as the motor rotates. Th esecond term is the leakage flow.

AL = equivalent leakage area, In2

C flow coefficient, 4 /sec0

3D = motor displacement, in /rev.m

N = motor speec, rev/secm

(3)See Reference No. 3, Appendix D

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R gas constant, in/ i,0

T gac temperature, 0R

gas weight flow, lb/ c

The equivalent leakage area was calculated by sub,3tiWtingtestdata( 4 ) into equation (4-20). For example,

18r x1002x ýO ;0. 09853600 9270 x 500 0.2 x ;00

A 0. 011 in2

The calculated values of A- using other test points were approxi-mately the same, even using heavier gases such as nitrogen. For constant tempera-,

ture operation, the best improvement that could be expected is a 10 to 50 percentreduction in leakage.

Selectir,ý a 200:1transmission ratio, the required differentiale-ssure is:

2 m 2u- x 350 x 12

1ýT n7mDmR ( U.85 x 0.,86 x 3.2x 200

where n) and n) are transmission and motor efficiencies.

Assuming a back pressure of 19 psta, the motor inlet pressurewill be 75 psi at maximum torque. The peak flow rate. w at stall Is then:

SAL 1l 0.367 x 0.011. x 75-IV . . .. . 0. 0132 lb/ s ec

The mihnimumleakage flow is 47 percent of the leakage at maxi-mum stall torque due to valve leakage. Thus. the average flowat stall is:

(4) lild, See Reference No. 3, Apicndix D

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1.67 rpm x 200 :334 rpm or 5. 56 rpls

The motor inlet pressure at maximum speed will be, aproxi-mately 50 percent of the inlet pressure at n~axtmim stall torque; thus

P = 0.5 x 60 + 15 45psia!The flow rate due to motor displacement is then:

Pl 45 -46 D x 3.2 x 5.56 2.30 x 10 lb/sec

2 R T m in 6 6 2x 5 300

The average value is-

w2 avg = 2.30 x 10-4 (0.01 x 1 4- 0.3 x 0.5 + 0.69 x 0.25) = 7.7 x 105 lb/sec

The minimum leakage flow is 47 percent of the leakage flow atmaximum stall torque. Thus, the leakage, when running at no Load, is:

ý3 .= 0. 47 x 0. 0132 - 0. 0o62 lb/sec

The total average flow at no load Is Lhenthe sum of )'2 avg and

w2 avg + w3 -- 0.000077 4 0.0062 0.606 lb/sec

which is less than stall torque flow rates.

The total flow per CMG is:

I avg 2 avg 3 avg

w 0.0102 ý 0.0063

"w : 0. 0165 lb/sec

For 3 CMGs, the total flow rate iW:

w T __ 3w - 3(0. 0165):: 0. 0495 lb/sec

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4r

1.55 x 10 lb/year

The above flow rate would eliminate the use at a non--circulatingtjytom with the long mission requirewtent uinoe the weight of the gas alone would beexcoasive.

The gear actuator and DYNAVECTOR actuator have about thesame efficiency; therefore, the pneumatic power supply requirement would be the same.However, the vane actuator leakage Is about 46 percent of the gear actuator leakage.Silmo the leakage is a very significant part of the flow, the pneumatic power supplyweight for the vane actuator would be 46 percent of that for tl e gear and DYNAVECTORactuators. Since there is no significant difference between various types of pneumaticactuators, there is no justification for further detailed study of pneumatic actuatorsfor this application.

Table VII illustrates the estimated weight and volurte require-ments for a single control moment gyroscope as a function of the CMG size.

TABLE VII

WEIGHITAND VOLUME REQUIREMENTS OF TWO PNEUMATIC ACTUATORS

C M G Size (ft-lb-sec) 200 500 1000 1500 2000Motor Weight (lbs) 0.23 0.50 0.95 1.40 1.90

Transmission Weight (lbs) 5.90 6.00 11.10 14.20 17.40

Servovalve Weight (lbs) 0.50 0.60 0.70 0.80 0.90

Total Actuator Weight (lb.) 6.63 9.10 12.75 16.40 20.20Total Actuator Volume (in 3 ) 168 212 268 322 380

4.3.3.2 Pneumatic Power Supplies

To determine the electrical power requirements, the followingprocedure is used:

In a recirculating system, the required compressor must besized to supply the average flow requirement. The average flow rate is 0. 0495 lb/sec,and the peak flow rate is 0. 0585 lb/sec. A storage tank must be used to supply theadditional flow when operating at higher than average flow rates and to provide theleakage flow that escapes into the shroud.

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111, 7 7 0 c -

E - 778 x 0.24 x 530 , "0. 286 - (0.0495) 3 W) ft-lb/sec

For estimation purposes, the compressor efficiency was deter-mined from test data for the Gast Model 0211 compressor. (5) This compressor de-livers 0. 5 scfm of air at 10 psig with a 1/6 horsepower motor. The weight flow fo,the compressor is 6.4 x 10- lb/sec.

The power for compression to 10 psig (25 psia) is:

0.268

E -- 778 CpT 1

0.286

778 x 0.24 x 530 [(5) - 1] (0.00064)

10. 0 ft-lb/sec ý 0.018 TIP

The compressor efficiency Is then:

Soutput horsepower - 0.018 -_0.107c input horsepower 0. 167

The clectric motor efficiency is approximately 0.6. Thus, the input electrical pcrequired is:

3, 00 ft-lb/sec x 1.356 watt-sec/ft-lb = 74,000 watts0.107 x 0.6

Higher compression efficiency can be obtained by using a d teacti)g piston type compressor with cooling; however, the compressor weight wou e

(5)"Gast Rotary Vacuum Pumps" Catalog

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considerablyheavier. Asauinbigan 30 percent coinpreniporefficiency,the electricaiInputpowmerwould be:

74. (C1O 2~.=900O Watts

Sincethese powerrquireraenti, are unreasonable, no fu~rtherefforts wereappliedto pneumnaticactuators.

4. 3. 4 QuaflitativeActuatorComparison

Ma' r limnitationsof the mranysys8temsconsidered limit the numberofsystems that require further cletafiedcompat'lson.

AC serv;omotors werefouand to have.frequ~encyrespons;echaracteristicsbelow 5 cps with-outtrzinsmIssions, and,the tlransmissions required for the AC servosystems haveexcessively high gear ratios. Thesetwo factors limit their suitability.

Stepping,notors ahowedweightanid size disadvantages wheacomparedwithDC torq~uersystems. A disadvantagecommonto both AC servornotors and step-ping motors is 'thatvariable frequencyinputsare zequired for goodlinearity betweenrate com-_mandand rate oitput.

The RESPONSYN actuator has isome poteantialadvantageý!ompa~redwvithDC torquer systems for the large CMG units. The particular areas of advantaggeareweightand size. However,additionalelectronic equipmentis required to produ~cethehigh-speed rotating magneticfieldforlyits drive motor. The large numberof additionalelectronic componentsrequiret for EHD systems wouldtendto loweroverall actuatorreliability. Further, the unitis at best !!near state--of-the-art" and requires furtherdevelopmentin phyaicaIsize andweightand commutationelectronics development.Nevertht-Aess,this unit sllouldPotbe eliminated frompossible future application.

The results showniur pneumaticsystems from the standpointof totalpawerconsumption(a minimumof 100 times great~r thanithe equivalentelectr!icsys-tems) Indicatesthatno further consideration is required.

Moredetailedcomparisons are now limited to the followingfive majorcategories-

(1) DIC torquer systlems

(2) DC brushless torquiersystems

(3) Flectrlc DYNAVECTOIRsystemis

(4) Conventionalhydraulic syste ms

(5) HydraulicDYNAVECTOR Systems

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Di fig-ure12 the avaeragepow~errequired per GNIG for titrce oasic svstemsBis gtver.as a funetion cCNIG eize. The powerfor DC brushless torquer systemb Gsassumedto be simihi.rto LICtorquersystems,and the pcr'*'erfor hydrauliicDY-NA -VECTORsysteims15 aL;2um-edto 1besimnilartip conventtont-dhydraulicisysters.

4IM

ILga DYAIC

D C TOMBa

C I O S U F -L - C

Figur 3 pini cutrSaes-PwrCnup nCmaio

figure ~ ~ ~ ~ ~ ~ ~ ucm3 D-hteadltoteeecrcDAAET

Figue ure pt3u Atuato Syfine soe Powntaer for DCptiorqeomparisonw

figure 14 shows that electric andhydraulicDYNAVECTORactuators havea weight ad-vantagefor the larger C'MG sizes.

4.4 Preliminary Conclusiens

Thebroad preliminary studyindicates significant disadvantages in the use offluid systems for longmission requirements. The disadvantages of fluidsystems canbe traced directly to the efficiencyI._converting electric powerto fluidpower,poor

efficiencydueto leakageflows, especially for pneumaticsystems, and the require-mentof slip rings for furnishing fluidpowerto the hinnergimbal.

As a consequenceof this broad preliminary study, further intensive studywasrestricted to DC electric actuators. Secondly,brushless systems (Brushless DC

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Lit.CTROC OYXA' CTUR

CMGSilt (FT- Lb-SC

Figure 14. Actuator WeightComparison

Torquers, Electric DYNAVECTORSand Electromechanical HarmonicDrives' cur-rently are, at best, near the state-of -the-art because of cmnplexities involvedin high-speed electronic switchingof inductiveloads;therefore it is advisable to qualifyanydetafled studyof these types to potential futuireapplications. Also, this initial studyphase indicateda scarcity of dataon various transm~issiontypesfo;: optimal use in thecontrol momentgyroscope.

No cons!ý.'ation was given to theapplicationof clutch-brake mechanismsfor gimballockingpurposes, sinceit is anticipated that cagingpinswillbe availablefor sftaticloc

Control Moment Gyroscope Gimbal Actuator Study

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