NASA TECHNICAL MEMORANDUM NASA TM-77330 

A. Y:uckenbrodt, B. Schultysik and J. P. Slehltrctter 

(BASA-TH-77330) IUTLTICU EAHEEB FOB IHP I840 14228 

ARPTE-f &I SATELLITE: EINAL EEECKT [National 

Aeronautics and Space Adrinisttatioz) 2 1 p 

HC AO2/f4P A01 CSCL 22E Un cl as G3/15 42782 

Translation of "~utationsd~mpfer fcr den AMPTEIRM Satelliten : Abschlubericht" . Technology 

Consulting Institute for Applied Research GMBB. 

(West Germany), TC-No. 017-Tru-Scho/sa, 9 Dee. 1982, 20 pp. 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

WASHINGTON, DC 20546 APRIL 1983 
OR~Q~NAL PAGE IS 

OF POOR QUALlrf 

STArtObbO TatLg ?&a 

" kltW~~-77330 1 8. h-~b Aaaondoa MB. 8. Ros~pln@** Coed- me. 

I 1 

4. T~le on4 LbMtle I. Repoet O~H 

NUTATION DX1PER FOR THE 

M4PTE-IRM SATELLITE : FINAL REPORT. 

t. ~wehm4ab 

A. Truckenbrodt, B. Schultysik and J. P. Mchltretter 

L 1 

e. Pootm+*~nm O~amiamtion mom@ ad Addtoem 

SCITRAW 

BQX 5636 

SW Barhrri QQ11fifi 

Jrse*i*# A en Nme md ~U*OB# 

.clonal Aeronaut ico d Spaea MdnL tratioo 

Uuniwton, D.C. 20546 

6. ~wlmrnlna Oqmn~am~lr Cede 

t 

8. ?erfe*mer@ Oea.atnmtIoa Reput NO. 

I l 

I@. .orb Unlc Me. 

I 1. Cmrko~t w 6rrt Me. 

NASr . 3542 I 

1% trw ot Ropw d ?rid C.rotd 

Tramlation 

IL '--r.r(q *#-P U 

. 

I 

IS. b~lrrnrr) None 

Translation of "Nutationsdiimpfer £fir den 

AMPTE-IRE.1 Satelliten: Abschlubericht. ' 

Technology Consulting Institute for Applied 

Research GMBH. (West Germany), TC-No. 017-Tru-Scho/sa, 

9 Dec. 1982, 20 pp. 

I& AbammeThis report describes the design of, computations, 

and testing of the nutatlon damper for the AMPTE-IRE1 

satellite. Tests wers carried out in a pendulum testing 

device and the time constants calculated. Findings 

showed that the damper remained within the originally 

specified values and provided for good dynamic behavior 

of the satellite. 

t 

87. I1.r ~rh mal~ w A,- 

h 

l& mart- W / 

Unclassified - Unlimited 

I 19. kr~cr CIoart (.I .(a 4 

. Uocl~0if id i 

a,' -9 CI~O~. (4 Yn ).~l) n k of 1- ?a*i ' 

Chch88if id 

-- - 
TEHNOUHX 30NSULTING 

INsrITurE FOR APPLIED REsEmH CrZBH 

Nutatim Bmer for the AEPI'E-IFU4 Satellite 

Final Report 

!xMwRY 

This report describes the design of, captations on and testing of the 

rutation damper for the mIRM satellite. A passive liquid danper has been 

&=loped building on the investigations carried irut during the feasibility 

stdy. It consists of a liquid filled &shaped tube system. Ihe rutatfanal 

motions induce liquid oscillations in the tubes; energy is destroyed by 

tube friction, cmtriction of the stream and the formation of turbulence 

which naturally is extracted £ran the satellite movement which is thereby 

darrped* 

The equations of motion (mlinear coupled differential equations 

for satellite rotation velocities and the Be£ lections of damping fluid) are 

derived for determination of the design parameters; using sinulators the 

oscillation behaviaa can be assessed and the parameters fixed. lhis design 

represents a good canpranise with respect to the twelve different satellite 

configurations. Ihe attermation behavim is evaluated using time constants 

( reduction in amplitude to l/e). 

Tests carried out in a pendulun testing device to check aut the theory 

and to determine friction loss rmbers shaw the anticipated dependency of 

the time constants on the respective excitation (= nutation) frequency 

and good confomity with the theory. 

Alq with this, the time constants for the satellite are calculated. 

For the design selected (overall length = 572mn, weight = 1165 g, nuunting 

radius = 375mn) values of 5.6 to 12.3 min result; they are significantly 

mder the specified value of 30 min. 'herefore, £ran the standpoint of the 

nutatianal motions, the reliable execution of the mission is assured. 

This study was prepared by Dr. A. TNckenbrodt (Project Manager , Dr. B. Scholt- f 

ysik and Dr. J.B. Mehltretter (scientific advisor) under the overall respansibility of J.M. Mehltretter. i b 

* ~wnbers in the margin indicate pagination of foreign text. 

1 1 -- -- .'.,..---.,..+,..-.-... 2 . ." -. 1 ,_ .-.a>- . ,.. ".,l. .... _ --* ,.. " ". - 1. - .- - " . 'y . . - - .-• 
1. 1mxON 

2. DESCrZZE*rION OF THE NurATION DI\MPER 

2.1 Fhctiml Principle 

2.2 Denper Design and Stmctural Canfiguration 

3. THMlRY 

3.1 Equations of Motion 

3.2 Time Constants 

4. TESTDEVLCE 

5. TIME CXXWNB FOR THE SATELLITE 
l'he intended objective was the &sign, manufacture and testing of a 

mtation darrper for the AMETFiIRM satellite. In accordance with the results 

achieved in the feasibility study, a passive fluid danper was developed. 

'ke errphases of the tasks described in this finel report are 

a) adaptation of the various danper parameters ( dimensions, fluid, etc) to the 

specified carditions, thgt is to: 

r 12 different configxations of the satellite ( with respect to mments 

of inertia, rotational velocity) , 

mdmn permissible darrping time constants; 

b) experimental testing of the theoretical data and the determination of 

the importani. damper parameters. 

?he satellite configurations and the most impartant requirements,refered to the feasibility study, are bxnght together in the following: 
OWOnuAL PAQ# B 

OF POOR QUALITY 

A,B,C are munents of imrtia with respect to the dn axes x,y,z 

Wz spin velocity 

v nutation freplency of the udenped satellite 
ORlOlNAL PAGE IS 

OF POOR QUALITY 

- + 3' for cabiguratiau 3-12 

rrsidual -ion angle: - + 0.2' 

time ccmstants t ,< 30 mirutes, 15 mirutes preferred 

wight :: 1 kgldenper 

2. DESCRIPTION aF 'IHE m1ON lxMPm 151 

2.1 Fbctional Principle 

'Ihe mtation darrper shown in F'igure 1 consists of a closed tube system 

that is canstmcted of tm long thin tubes ( lltube") and two short thick 

tubes ("cap"). Zhe damper is partially filled with a fluid. Based an the 

centrifugal acceleratian through the rotation ( JJ, aroud the satellite spin 

axis, the fluid is located in the tube the -st remaved from the spin 

axis and in the adjacent areas of the caps. The nutation motions of the 

satellite excite fluid oscillations in the damper tubs; kinetic energy is 

&strayed (i.e. converted to heat) thragh the folldng effects: 

tube frictian or' the flawFng liquid in the tube 

constriction of the stream by cross-sectimal chaqge fran 

cap to tube 

formation of turbulence by stream enlargement thrwgh crosssectional me fran tube to cap. 

This energy loss is extracted from the satellite such that the nutation 

moticm is reduced. 

Figure 1 Passive Fluid mtim Denper 
ORIHNAL PAGE IS 

OF POOR QUALltV 

The effectiwss of the denper increases with the arrplituk 161 

of the fluid oscillation. For this reason, the best denping effect is achieved in 

the case of resonance tmi% (i.e. the rutetim frequency v = characteristic 

frequency of the fluid oscillation WF 1, see Figure 2. Moreover, one can 

see from Figure 2 that in case of increasiw danping the effectiveness of the 

nutation denper 

a falls off in proximity to the reresonwce point ( v/uF I , , correspads 

to coolfigurations 3-12) 

a increases for frecpncy ratios << 1 (carresponds to 

diguraticms 1 and 2) 

a is less stxmgly influenced by the frecpzxy ratio v~w~, . 

2.2 hper Design and Smtural Configuration 

In oder to approach resonance tuning as closely as possible for configuratians 312, a relationship for the fluid characteristic frequency uF to 

the spin frequency w, of 

w~/w~~ = 0.4928 

was used. This freplency relationship, given a mounting radius r, = 375nn 

is achieved with the fclldng darrper geunetry: 

'Me length = 47h 

'rube interior 

diameter = 19mn 

Cap l%th = 8(mn 

Cap interior 

diameter = 48.- 

Figure 3 shms the structural farm of the nutation danper. Since a 

-tic material is required , and on weight gmuds as well, the 

was made of alunLrun. Off-the-shelf aluninun tubes were used for the 

tubes. he to the law wall thickness, the tubes and caps were not joined by 

wlding but by adhesives. For this ream, the caps are fabricated canplete 

with the cauplings needed for the adhesion. 

Ihe filling of the denper with the fluid takes place at ambient pressure so that in space an overpressure of 1 bar prevails. Before gluing on 

the cover, kliun is piped into the denper so that a heliun tightness test 

can be carried out. An alunCmxn fixhne semes to anchor the denper in 

the satellite. 
ORlUNAK PAGE I8 

OF POOR QUALITY 

of the Dmnping on the Effectiveness of the 

1 

~reqtmq ratio v'Yb 

flgure 2 : Inflwnce of the Frecpency Ratio v/uF ad 
In the case of the rutatim daper &sign (Figure 3): 

a Overall weight (filled denper with raaatiqg) - 1165 g 

a Olnerall length P 572.2 mn 

Cap outside diraensians: Dianeter - 51.6 nm 

= 90m 

The fluid )Tlutec PP3" is used to fill the damper: 

a Nll level in cap: = 40 nm 

a Fluid urolune: = 282.2 an 3 

OkidW':91. PAGE IS 

OF POOR QUALITY 

3.1 Equations of Motion 

The equatiars of mbtian for satellite and damper are contained in the 

feasibility sMy in linearized fm. For an acxurate estimete of the influence 

of the mlinearities, the general equations of motion were &rived for the 

dnates 

( o = satellite rotational velocities, zl, 3 fluid deflection in tubes 1,2) ; 

in gerreral written fon they read: 

Here, in addition to the laminar tube friction, energy losses 

=re also taken into accant which are caused by the in and art stredm fmm 

tube into cap (stream mtrictim, turbulence fonnatian) eKt Merit tube 

friction (alternatively to the lmdnar tube friction) , all in the interest of 

bmadening the &scriptian of the energy reanoval used in the feasibility study. 

For the energy loss of a denper it is thus found, see equation 

(13) in the feasibility study, that 

with the loss term , fich is only -1ly detenuixmble. Ihe dqer 
ORIOPJAL PAGE IS 

OF POOR QUAL.ll'Y 

equatiars nust therefore, in accordance with equaticm ( 13) of the feasibility 

study be supplemented by the tenns . 

Estimations with 5 = 2 shaw that the energy loss characterized by is /lo/ 

excessive at large rutation ampliMes. It decreases quadratically with 

decreasing ampliMe in favor af the linear term of thp ldnar tube frictim. 

3.2 Time "bnstarlts 

On accunt of the non-lirrearity of the equaticms of motion, the enplieude 

history is no longer characterized by an exponential finction with ccnstmt 

eqxxmts. Therefore, it is inpossible to define time constants indepedent of 

the anpliMe. Eqslly, a sufficiently accurate energy-sink appmdmtion is 

n, lqer possible. Iherefore, the "theoretical" time constants are ascertained 

by the followLng procedure: 

1. Simdation of carglete -linear equations of motion 

2. Conversion of the enplitude term A A after an "examination period" 

.A.t into an equivalent emtial furtion or time constant 

3. Time mtant 

I T=- At/ ln Ah 

The time constants derived with this procedure are collated in Section 5. 

4. TESTDEVICE 

Denping tests were carried out with 

plexiglass rutation danpers with various filling levels 

the ultimateflight model 

to check the themy and to experinmtally &tennine the lnss term r, ;these 

were dare using the test device &scribed in the feasibility study.hith the 

plexiglass danpers, the stream processes dd be clearly observed. 

Ihe test mechenimn (F'igure 4) consists of a permidun (total mssm 

ges 

1111 

suspmxIed at point A. By displacemat of Uu peddun tube d of th 

wights 2, th center of gravity intcmal s ad the he of inertia 

0, M be changed with respect to the appnt pint A. In Me my the period 

of oscillation T of. the petndulun can be dunged. 
ORlGtlJAL PAGE fS 

OF POOR QUALITY 

Figure 4 : Test kkchanism for Wation Ihmper 

Ihe rutation damper ND is fid an the perxiulun at interval a fran the 

pivot A. 

At different pendulun geetries , (i .e. different characteristic frequencies 

of the pmdulun), the oscillation behaviaur for an initial anp1ih.de of 

8, = 15' was recorded with a rotary potentianeter and recorder both 

with and withcut the rutation danper. Without the mtation damper the 

effect of bearing friction and air resistance is determined. 'Ihe time constants 

amcxnt here to about 200 to 850 sec depending on the pedulun mment of 

inertia. In the measurarrents with the nutation dartper, the interval a 

was set at: a = 37hn = ro, corresponding to the installation in the 

satellite. 

F'ran the tiroe constantsmeasured for air resistance ad bearirg friction /I2/ 

T L+L (in the case of canstant pendulun gemetry) and the time constants 

measured for the nutation danper + air resistance + bearing friction 

MkbL follow the time constants r nf the pendulun only with 

p,m the nutation danper: 

Figure 5 shows the time constants of the pendutun thus detdned, relative to the potential initial energy of the pendulun. 
E = m g s (I - cos Bo) Pot, 0 ees 

It is recognized that the effectiveness of the nutaticm clanper is at 

its greatest (i.e. smallest time cmstant 1 wben the pendulun (= excitation) 

freqwncy f coincides with the characteristic frerpmncy fE of the fluid P 

oscillation. Ihe characteristic frequency on earth amounts to 

In contrast, in space there follw: 

in configurations 1 d 2 : fE = 29.568 oscillations/min 

in ocnfigurations 3-12 : fE = 9.8% 19 I I 

ztus, in space the relatiunship between the atation £requmcy v aml 1131 

the characteristic freqmq fE amounts to 

in configurations 1 ard 2 : V /fE = 0.41-0.48 

in cdigurations 3-12 : V/fE = 0.89-1.09 

'Ihese ftequency ratios w re achieved on the test mechanism (on earth) 

with the pendulun frequencies 

f = 9.7- 11.4 osc. /min. configurations 1 and 2 

P 

f~ = 21.1 - 25.9 osc. /min. f configurations 3-12 
Figure 5 : Time Canstants of the Test Mechanism Perkiulun, relative to the 

potertial initial energy, as a fmction of peddun frequacy. 

0 NDI 

KO2 

po :15* 

I fE = 2 3.7c. L: L . . . --.., - 1-- ---- . 

C 5 !C i5 23 25 35 oscillations/min 

pendulm frequency f,. 

* . _* -- . . .--_ .. - -.. - . -. - 

. .. f2 Ifc 

5 G.7 C.l.OY.C.F, C,-. I I., 1.2 

canfigmatian I,? configurations 3-12 
Both the identically constructed rutation dampers of the satellite ("ND 1" 1141 

and "ND 2" were used in the measurements on the test mechanism. It is recognized 

that the findings on both lutatim dampers correspand well, as wmld be 

expected. Moreover, the limited deviatiars irdicate that measurenmt and 

evaluatim errors in the investigations on the test tllechanism are also small. 

To &tennine the loss term C , the experimentally determined tine constants 

for the test mechanism ere carpared with the time cmtants ccmputed for 

the Lest mechanism. Here it is shown that with ; =2.2 a very good agreement 

is achieved between canputation ad measummnt ( error about 1.5- 49. in the 

neighborbod of the reme point, that is for fp/fe = 0.9-1.1. For tk 

frequency ratio fp/fE= 0.44-5,an optinun value r, = 4.9 follars. lhese 

different C values rrrake it clear that in the resonance case and with 

subcritical excitation, different stream canditicns are present in the mtation damper. 

5. TIME CXPSBWS FOR ?HE SATELLITE 

With the runerical values that apply to the satellite, the time constants 

shawn in Figure 6 result, as a huon of satellite canfiguration. An initial 

mtatim angle of 6, =20° was used in configurations 1 and 2 for the an+ 

ptaticns ard of Sc, = 3O in the succeeding mnfiguraticns 3-12. Ihe values 

ascertaimd experimentally on the test mechanism were used for the loss 

tern 5 , that is: 

cdigurations 1 and 2: 5 4.9 

configurations 3-12 : 5 =2.2 

0 1 -,-,---. - - -- 

123L56789i3t112 

Satellite Canfiguration 

wZQ: 60 rpm 

, ,=20' 

UZo= 20 rpm 

Po: 3' 

Figure 6 : Cunputed Tim Curstants for Different Satellite Ccnfiguratians 
ORIGINAL liXGZ 

OF POOR QUALITY 

It is seen that in all canfigurations the time constant lies between 

abaut 5 and 12 minutes. In canfigurations 1 ad 2, the higher C value 

produces an inprwement, because at a subcritical excitation the effectimss 

of the rut:. tion damper is inproved with an increase in C (see Figure 2 1 . For campari..m,conpltaticms were also carried out in digurations 1 and 2 

using C : 2.2. In this way the range of time constants which result Mng 

the recluction of a large initial nutation angle down to a small final angle 

is limited. For mnfiguraticms 3- 12 (i.e. for v/fE = 1) one can expect an 

even faster damping at very small mtation qles because then the influence of 

the turb~llr re danping is smaller and near the resonance point a more effective 

danping is achieved with the tube friction (see Figure 2). 

In 7 are sh the final nutation angles after a total damping .- 

tine t~f t= 1000 sec, when the initial rutation angle in canfigurations g=s 1 and 2 B = 20° ard in digurations 3-12, B0 = 3O. 

0 

1161 

Satellite Configuratian 

Figure 7: Nutation Angle of the Satellite after 1000 sec for the Different 

.atellite Mipations 
ORIWAL PAGE f!3 

OF POOR QUALITY 

Ngure 8 shaws for the different configuratians the maxinun initial 

nutation angle which results in a final rutation angle of pdlWO 

after a danping time of 1000 sec. 

0 L -,-- ,--...--4- - -.-,_ *- : -- - 

113LS6789101112 

satellite configuration 

Figure 8 : Maximun Initial Nutation Angle with which after 1000 sec a 

htation Angle of 0.2~ is Achieved, for the Different Satellite 

Configurations 
ORIQINAL PAGE IS 

OF POOR QUALITY 

Ngme 9 shms , using the relatively unfavorable Tie of oonfiguratim 1171 

5 (see Figure 61,that with a change in the characteristic value 5 , the camputed time constant of the rutatioml motion of the satellite remains about 

in the same order of magnitude. This means that the time constants calculated for 

the satellite remain approximtely correct, even when the actual characteristic 

value 5 occurring in space deviates sanewhat £ran the value developed on the 

test device. 

Loss term S 

Figure 9 : Influence of the bss Term z; on the Time Constant of the 

Satellite (ESrample in Configuration 5) 
i 

i With this it is sham that the danper clearly muins within the originally 

specified values, also estimated in the feasibility sMy, and accordingly 

it can prwide for good dynamic behavior of the satellite. 
. 

'7 
Ternperatur ("F) $ 

e1 

___ -I - . - c_- -- __ - 

-20 20 60 100 I40 I80 120 ?60 300 
........ 

......... 

- t -- 

.,. - . 

..... 

..... .. 

.. 

.... 

.. ...... 

...... .. 

..... 

.... -. .. 

... 

. -- 

2