.- 

NASA Technical Memorandum 89056 

DYNAMIC ANALYSIS OF THE 

LARGE DEPLOYABLE REFLECTOR 

Robert E. Calleson 

A. Don Scott 

January 1987 

(NASA-TPl-89056) GYNAHIC ANALX5I.S OF THE 

LARGE DEELGYAELE GEFLECTOB [NASA) 34 p 

CSCL 22B 

N87-1C050 

Unclas 

G3/38 43371 

e 

U' 

National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton. Virginia 23665 
DYNAMIC ANALYSIS OF THE LARGE DEPLOYABLE REFLECTOR 

SUMMARY 

The Large Deployable Reflector (LDR), an astronomical observatory in lowEarth orbit, will operate above the Earth's obscuring atmosphere and perform 

studies in the spectral range at wavelengths of 30 to 1,000 um. Current 

planning projects an LDR flight in the mid-1990's. 

The dynamic analysis of two proposed LOR concepts has been conducted. 

Response from chopping and slew excitations was obtained for two 20-meter LDR 

concepts. One concept was developed by NASA Ames Research Center and utilized 

two secondary mirror module support configurations (six strut and triple 

bipod); the other by NASA Jet Propulsion Laboratory utilized a stiff-mast 

mirror support. Chopping, a forced oscillation of the secondary mirror for 

the purpose of subtracting background signals from target signals, was applied 

to the Ames concept. 

applied to both concepts. 

exceed the 0.02-arc-second requirement in the Ames six-strut configuration, 

but module rotation in the triple-bipod configuration was two orders of 

magnitude less. Response of the primary mirror from slewing in all 

configurations was predominantly from reflector rocking relative to the 

spacecraft. An increase in the damping ratio from 0.002 to 0.02 reduced the 

rocking amp1 i tudes to a level less than the 0.02-arc-second requirement within 

the required 1-minute maximum settling time. 

The excitation from slew, a pointing manuever, was 

Chopping excitations caused module rotation to 

INTRODUCTION 

The Large Deployable Reflector (LDR) is to be an astronomical observatory 

orbiting above the Earth's obscuring atmosphere and operating in the spectral 

range at wavelengths between 30 and 1,000 um. The LDR will be used to study 

such astronomical phenomena as stellar and galactic formations, cosmology, and 

planetary atmospheres. With the current state of technology, the LDR will be 

ready in the mid-1990's. 

The LDR will represent a significant change in past observatory design 

and philosophy. The LDR will be the first observatory to be erected and 

assembled in space. This distinction brings with it several major 

techno1 ogi cal chall enges such as the development of ul tra-1 i ghtwei ght 

deployable mirrors, advanced mirror fabrication techniques, advanced 

structures, and control of vibrations due to various sources of excitation. 

The purpose of this analysis is to provide preliminary information about the 

extent of vibrational response due to secondary mirror chopping and LDR 

slew. 

The dynamic response of two 20-meter LDR configurations was studied. The 

first concept was developed by NASA Ames Research Center, the second by NASA 

Jet Propulsion Laboratory. 

investigated for the Ames concept. The first employs a six-strut secondary 

mirror support structure, whereas the second uses a triple-bipod-support 

design. All three configurations were modeled using a tetrahedral truss 

design for the primary mirror support structure. Response resulting from 

secondary mirror chopping was obtained for the two Ames configurations, and 

Two mirror support configurations were 

1 
response of the primary mirror from slewing was obtained for all three 

configurations. The fdlowing sections discuss the LDR requirements and 

structural modeling as well as the modal and response analyses and results. 

01 SCUSS ION 

LDR Requi remen ts 

LDR performance requirements relevant to this study were selected from 

references 1 and 2 and are listed in table 1. A diameter of 20 meters, an 

F/ratio of 0.7, and an assumed parabolic surface determine the size and shape 

of the primary mirror tetrahedral truss support structure. The secondary 

mirror diameter of 1.3 meters is only applicable to the Ames configuration. 

The JPL configuration involves the passive primary, secondary, and tertiary 

mirrors and an active quaternary mirror--the latter three mirrors being 

supported in a relatively stiff mast. 

The absolute pointing requirement is included here for information but is 

not involved in the dynamic analysis, as it is considered to be a control 

system requirement for the LDR as a rigid body. Jitter, however, is the 

dynamic response of the elastic LDR resulting from slew, scan, or track. Of 

these three maneuvers, the slew maneuver requires orders of magnitude more 

control torque and hence is the maneuver related to the jitter limitation of 

0.02 arc seconds allowing 1 minute of settling time. Slewing the LOR 90" at 

an average rate of 45O/minute establishes parameters for the torque profile. 

The purpose of chopping is to subtract background signals from the star 

signals. It is accomplished by chopping or oscillating the secondary mirror 

at 2 Hz with an approximate square wave having a throw or double amp1 i tude of 

1 arc minute. The system is assumed to be 99 percent reactionless that the 

actuated torques are counterbalanced in a way which prevents reactions on the 

module support struts leaving 1 percent of the actuated torque to excite 

secondary mirror module jitter. 

LDR Models 

The JPL and Ames concepts illustrated in figures 1 and 2 provided the basis for 

the three configurations. The two versions of the Ames concept differ only in the 

secondary mirror module support strut design. 

applicable information for developing the three finite element models shown in 

figures 3-5. Note that the figures include only those model grid numbers referred 

to in the discussion. The primary mirror truss model shown in figure 6 is a 

tetrahedral truss design that is comnon to the three configurations. 

modeled by the Interactive Oesi gn and Eva1 uation of Advanced Spacecraft (IDEAS) 

program of reference 3. All structural members were assumed to be fabricated with 4 

graphi te/epoxy composite material with a modulus of elasticity of 130.3 GPa. 

3 Material density for all finite elements, except those representing the shade 

elements, the spacecraft modules, and the secondary mirror module, 3s 1661 kg/m . Shade element densities for the Ames and JPL concepts are 7428 kg/m and 4813 kg/m3, 

respectively. These are fi ti tious densities calculated to reflect the sunshade 

areal density of 0.645 kg/m given in reference 2. Zero densities were assumed for 

the modules and were replaced with nonstructural mass. 

weights are sumnarized in tables 2 and 3, respectively. 

were not available in references 1 and 2, appropriate values were assumed. 

References 1 and 2 provided 

This truss was 

5 

Member sizes and component 

Where sizes and weights 

2 
The spacecraft is composed of two modules: the resource module starting 

at point 110 (figure 3) and the support module which is assumed to end at 

point 31 in the upper surface of the primary mirror truss (figure 6). The 

instrument module and optical system concatenate with the spacecraft with the 

optical system ending at point 134 shown in figure 3. Construction of the 

Ames models is similar except that there is no optical system and the 

instrument module terminates at point 31. 

To simplify the shade modeling and reduce the number of shade modes of 

vibration, the shade is modeled with one frame in the JPL model and two frames 

in the Ames model. Frame members are modeled as beam elements to provide 

shade stability, and the remaining members are axial elements. 

The primary mirror is comprised of many individual segments. The number 

of segments varies with the mirror concept. There is also a wide variation of 

mirror segment weights reflecting choice of materials, structural design, 

method of support, and segment size. eferences 1 and 2 indicate areal 

chosen for this analysis. This was uniformly distributed in the model by 

locating equal point masses at the upper surface truss grid points. 

density varying from 5 to over 50 kg/m h . An arbitrary weight of 20 kg/m2 was 

A sumnary of the LDR mass and moments of inertia for the completed models 

is given in table 4. The inertias were used in determining the required 

torques for the slew maneuvers. 

Modal Analysis 

Modal frequencies and mode shapes were determined by using the 

eigenvalue/eigenvector determination technique. 

eigenvalues and eigenvectors starting with the assumption of undamped free 

vibration giving the equation of motion, 

This method calculates the 

and the resulting eigenvalue/eigenvector equation, 

where K and M are, respectively, the global stiffness and mass matrices 

associated with the finite element model. 

respectively, the matrices of the eigenvalues and eigenvectors, or modal 

frequencies squared and mode shapes, associated with the free vibration of the 

model. Two finite element programs were used in developing and solving equation 

(2): 

3), and the Engineering Analysis Language (EAL), (ref. 4). IDEAS expedited the 

development of the tetrahedral truss--the geometry for which was transferred to 

EAL. Modal solutions from both programs provided confirmation of results. The 

documented results were determined by the EAL program. 

The symbols u2 and + are, 

the Interactive Design and Evaluation of Advanced Spacecraft (IDEAS), (ref. 

Modal frequencies for the first 25 modes of each configuration are given in 

tables 5-7 for the JPL, Ames six-strut, and Ames triple bipod strut configurations, 

respectively. As the LDR models are free from any support constraints, as in space, 

the first six modes are rigid body modes with zero frequencies. The remaining modes 

are flexible body modes, and of these the most significant in this analysis are 

modes involving primary reflector rocking and secondary mirror module motion. 

3 
Selected mode shapes are shown in figures 7-30 for the three 

configurations. 

24. Note that in all the mode shape figures, for clarity only the upper 

surface tetrahedral truss members are plotted. Secondary mirror module 

rotation is shown in the 11th mode, figure 18, for the six-strut 

configuration, but this rotation is not obvious in modes for the triple-bipod 

configuration. Module translation but not rotation is apparent in mode 21, 

figure 27; however, examination of the eigenvector output shows rotation as 

well. Some of this rotation is from reflector rocking. The presence of 

module rotation will be shown in the discussion of response. 

The reflector rocking modes are shown in figures 7, 15, and 

Forcing Functions 

In the examination of jitter response, two forcing functions or excitations were applied to the LDR models. One is from chopping of the secondary 

mirror in the Ames configurations (fig. 31), and the other is from slewing or 

rotation of the LOR to a desired position (fig. 32). 

Chopping.- Application of the requirements for secondary mirror chopping 

involved the following assumptions. The 2-Hz "square" wave was modified to 

include a rise time of 10 percent. The 1-arc-minute throw is a doubleamplitude rotational displacement of the secondary mirror with the zero 

displacement position (8 = 0) located at one of the mirror stops. 

"reactionless" system is such that the mirror inertial torque is 

counterbalanced in a manner that is 99 percent contained; the remaining 

1 percent is reacted by the LDR structure. 

the calculated torque acting on the mirror is used as an excitation. 

The 

In other words, only 1 percent of 

Reference 2 describes the secondary mirror assembly or module as being 

3 meters in height, 1.3 meters in diameter, and supported by triple-bipod 

struts or six struts as shown in figure 31(a). 

inertia based on an assumed 1000-kg solid cylinder. These were included in 

the model for the modal analysis as a concentrated mass at points 115 and 113 

as shown in figures 4 and 5. 

mirror moment of inertia (I) is calculated as 21.13 kg-m by assuming a solid 

disk with a diameter of 1.3 meters. 

Included are module moments of 

For the ZOO-kg mass as giv n in reference 2, the 5 

A 10-percent rise time in a 2-Hz displacement square wave requires the 

assumption of a 0.025-second pulse of torque every 0.25 second as shown in 

figure 31(b). The magnitude of the torque (T) must equal the product..of the 

mirror mass moment of inerti9 (I) and angular acceleration (e), T = 18. 

Integration leads to e = Tt /21. Since T is a constant and e is a 

maximum (emaX = 1 arc min) at t = 0.025 second, 

'max = Tt2/21 = 1 arc min = 0.291E-03 rad 

and 

T = 0.9311 

As previously shown, I = 21.13 kg-m 2 . Therefore, T = f19.67 N-m (f174 inlb). For a 99 percent reactionless system, T = f0.197 N-m (f1.74 in-lb). 

This excitation torque was applied at point 115 in figure 4 and point 113 in 

figure 5 for the two Ames configurations. 

4 
Slew maneuver.- This analysis assumes the same condition considered by 

JPL in reference 1; that is, a total slew angle of 90' is assumed complete in 

2 minutes, which complies with the requirement. The control torque, 

accomplished with control moment gyros (CMG), is assumed to vary as a versine 

function (fig. 32). The torque profile is defined as follows: 

T = A(l - COS wt) 0 < t < 60 sec 

T = -A(1 - COS wt) 60 < t < 120 sec 

where w equals 2n/120 rad/sec and A is a constant to be determined for 

each configuration. The torque (T) must also equal the product of the mass 

moment of inertia (I) and the angular acceleration (e). Equating Ie to each 

of the above expressions for T yields 

integrated to yield the following equat 

ll (1-cos 60 t)] 

n 

3600 

2 

A tL: 120t + 3600 + - (1-cos 

e = -Tk- n 

differential equations which can be 

ons for the slew position or angle, e: 

0 < t < 60 sec 

& t)] 60 < t < 120 sec 

By substituting t = 120 sec and 0 = n/2 in the second equation for e, the 

maximum torque (2A) for each configuration (see fig. 32) is determined as 

Tmax = 2A = nI/3600. In addition to the torque profile and slew position, 

figure 32 includes a sumnary of T for the three LDR configurations. The 

respective torque profiles were ap7:ed at points 115, 112, and 111 about the 

y-axes of the models shown in figures 3, 4, and 5. 

Response 

The dynamic response of the various LDR models depends on the results of 

the modal analysis, internal damping, and the external forces. The following 

equations defi ne the dynamic response of the model s : 

(3) T .. 

q + 2zoq t w2q = I# f 

Y = wi (4) 

where z, W, q, I#, f, and y are the matrices of the viscous structural 

damping ratios, modal frequencies, generalized displacements, mode shapes, 

forcing function and true nodal displacements, respectively. The external 

force or forcing function is applied at the desired nodal location. The 

structural damping ratios, which vary with the modal frequencies, currently 

can only be determined through experimentation. Therefore, the damping ratio 

was assumed to be contant throughout the modal frequency range. 

Response analysis determined with the EAL program (ref. 4), is limited to 

the response of the secondary mirror module due to chopping and to the 

response of the primary reflector due to slewing. 

given: one for the 0.002 damping ratio and another for the 0.02 damping 

ratio. Jitter displacements at significant points in time for the three 

configurations are given in table 8. Displacement time histories are shown in 

figures 33 through 37. 

Two sets of results are 

5 
Response is limited to the two Ames configurations which 

differ -- on y in the way the secondary mirror module is supported. The sixstrut configuration exhibits orders of magnitude greater module rotation than 

the triple-bipod-strut configuration (table 8) because the centerlines of the 

six struts intersect at the module center of mass, and provide resistance to 

rotation only through strut bending and twist. The triple-bipod-strut design 

provides a much stiffer resistance through strut axial stiffness, as is 

normally found in a truss. As a result, the six-strut configuration exceeds 

the requirement of 0.02 arc second by an order of magnitude, whereas the bipod 

configuration exhibits module rotation two orders of magnitude less than the 

requirement. 

Examination of the response shown in figures 33 and 34 for both configurations shows that the higher damping significantly reduces the time required 

for the transient vibration to damp out. The remaining steady state or 

forcing vibration amplitude is over half of the maximum, but still much too 

high in the six-strut configuration. In the triple-bipod configuration, the 

amplitudes with both levels of damping are almost insignificant. 

case, the determining factor in meeting the requirement was not an increase in 

damping, but rather one of structural configuration. 

In this 

- Slew.- The response of the primary reflector from slewing in all three 

configurations is predominantly from reflector rocking which can be seen in 

the seventh mode (figs. 7 and 15) of the first two configurations and the 

ninth mode (fig. 24) of the triple-bipod-strut configuration. 

first and third elastic modes, respectively. Because of the structural 

similarity of the three configurations, it is not surprising to see the 

similarity in responses shown in table 8 and figures 35 through 37. The 

effect of increasing the damping ratio one order of magnitude to 0.02 clearly 

(see table 8) brings the reflector pointing deviations to well within the 

requirement of 0.02 arc second 1 minute after slew. 

These are the 

CONCLUSIONS 

Jitter response of three large deployable reflector (LDR) configurations was 

examined. Two forms of exci tation were applied. One is from chopping or 

oscillation of the secondary mirror for the purpose of subtracting background 

signals from star signals. The other is from slewing the LDR to a desired position. 

Because of insufficient definition of the JPL optical system, chopping response 

is limited to two Ames configurations which differ only in the way the secondary 

mirror module is supported. Module rotation in the six-strut configuration exceeds 

the 0.02-arc-sec requirement by an order of magnitude, but module rotation in the 

triple-bipod configuration is two orders of magnitude less than the requirement. 

Damping is required to decay transient vibrations. In this case, the determining 

factor in meeting the requirement was not an increase in damping, but rather the 

structural con f i gura t i on. 

The response of the primary mirror from slewing in all three configurations is 

predominantly from reflector rocking relative to the spacecraft. The similar 

response is primarily the result of similarity in the models and mass distribution. 

The order of magnitude increase in damping ratio to 0.02 reduced the rocking 

amplitudes to less than the requirement of 0.02 arc sec within the required 1 minute 

maximum settling time. 

damping, some additional form of damping or active control may be required. 

As 0.02 is considered relatively high internal structural 

6 
REFERENCES 

1. Swanson, Paul N., "A Lightweight Low Cost Large Deployable Reflector (LDR), A 

Concept Study by the Jet Propulsion Laboratory," JPL D-2283, June 1985. 

2. NASA Ames Research Center, "Large Deployable Reflector (LDR) Systems 

Concept and Technology Delimition Study," GP-00865, Volumes I, dated March 15, 

1985 and Volume 11, dated February 28, 1985. 

3. Garrett, L. Bernard, "Interactive Design of Future Large Spacecraft Concepts," NASA TP-1937, December 1981. 

4. Whetstone, W. D., "ElSI-EAL Engineering Analysis Language Reference Manual," 

Engi neer i ng In format i on Sys terns, Incorporated , 3u 1 y 1983. 

7 
TABLE 1. - SELECTED LDR PERFORMANCE REQUIREMENTS 

FOR DYNAMIC ANALYSIS 

Parameters Requirements 

Diameter 

F/ratio 

Absolute pointing 

Jitter 

Slew 

Scan 

Track 

Chopping 

20 m primary, 1.3 m secondary 

F/0.7 primary 

0.05 arc sec 

0.02 arc sec - within 1 min after slew 

20" - 5O0/min 

i"~1" - linear scan at i"/min 

O.T/hour (for comets E 25"from Sun) 

2 Hz square wave, 1 arc min throw 

(reac tionless) 

* Selected from reference 1. 

TABLE 2. - STRUCTURAL MEMBER SIZES 

Tubular Components 

Resource module 

Support module 

Instr. module 

Optical system (1) 

Primary mirror truss 

Upper surface 

Diagonals 

Lower surface 

Frames 

Shade 

Diagonals 

Verticals 

(1) For JPL model. 

Tube 

Diameter 

(mm) 

4500 

4500 

4500 

3800 max 

1100 min 

39.4 

20.2 

39.4 

152.4 

70.4 

78.4 

Tube 

Thickness 

(mm) 

2.0 

2.0 

2.0 

2.0 

2.0 

0.66 

0.66 

0.66 

0.66 

0.66 

0.66 

Length (mm) 

JPL 

6600 

3000 

6800 

7000 

2956 

1744 

2934 

11582 

12629 

12292 

AMES 

(2) 

(2) 

(2) 

- 

2956 

1744 

2934 

11582 

11123 upr 

9927 Iwr 

9496 

(2) Total length of Ames modules assumed to be 9910 mm. 
Figure 1. - 3pL Concept 

9 
X= 11.58m 

(456 in) 

110 

Figure 3. - 3pL Model 

57 
PAGE IS 

CW POdR QUALf7V 

57 

l”f 110 

Figure 5. - h Triple-Bipod Strut Model 

57 

Fim 6. - Primary Mrror Truss 

11 
Table 3.- LDR COMPONENT WEIGHTS (kg) 

Configuration 

JPL 

AES six strut 

MS triple bipod 

Component 

Mass (kg) 

23477 

2 1309 

21309 

Modules 

Resource module 

Support module 

Instrument module 

Total 

Primary mirror (20 kg/m2) 

Secondary mirror module 

Optical systems less primary 

Primary mirror truss 

Secondary mirror struts 

Sunshade C.645 kg/m3) 

Total 

AMES 

Total is 

uniformly 

distributed 

over 9.9 1 m 

10000 

9124 

1000 

136 

51 

998 

2 1309 

JPL 

7999 

1237 

3393 

12628 

9124 

1126 

136 

463 

23477 

TABLE 4. - LDR MASS AND INEFITIA PROpERTlES 

Distribution 

Uniform over 6.6 m 

Uniform over 3.0 m 

Uniform over 6.8 m 

Concentrated masses on 

truss upper surface joints 

Concentrated mass 

Uniform over 7.0 m 

Uniform 

Uniform 

Reflected in fictitious 

material density 

Moments of Inertia (kg*m2) 

Ix lY lz 

939,000 939,000 70 1,000 

1 , 130,000 1,130,000 770,000 

1 , 155,000 1,155.000 769.000 
TABLE 5. - JPL MODAL FREQUENCIES (Ht) 

Mode Freq 

1 .oo 

2 .oo 

3 .oo 

4 .oo 

5 .oo 

6 .OO 

7 .54 

8 .54 

9 .61 

10 .61 

11 1.34 

12 1.54 

13 1.97 

14 2.73 

15 2.73 

16 3.27 

17 3.27 

1% 3.31 

19 3.61 

20 3.61 

21 3.74 

22 3.74 

23 3.93 

24 3.95 

25 4.41 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Reflector rocking plus shade motion 

Same 

Shade frame motion 

Same 

Same 

Symmetrical reflection motion 

Shade motion 

Same 

Same 

Unsymmetrical reflector motion plus shade motion 

Same 

Symmetrical reflector motion 

Unsymmetrical reflector motion plus shade motion 

Same 

Unsymmetrical reflector motion plus shade motion 

Same 

Shade motion 

Unsymmetrical reflector motion plus shade motion 

Same 

TABLE 6. - AMES SIX-STRUT MODAL FREQUENCIES (Ht) 

Mode Freq 

1 .oo 

2 .oo 

3 .oo 

4 .oo 

5 .oo 

6 .OO 

7 .68 

8 .6% 

9 1.43 

10 1.47 

11 1.52 

12 1.52 

13 1.72 

14 1.74 

15 2.12 

16 2.51 

17 2.51 

1% 2.54 

19 2.77 

20 2.81 

21 2.85 

22 3.01 

23 3.09 

24 3.09 

25 3.75 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Reflector rocking plus shade motion 

Same 

Shade frame motion 

Symmetrical reflector motion 

Sec. mirror assy. rot. about y axis 

Sec. mirror assy. rot about x axis 

Shade frame motion 

Shade frame motion 

Sec. mirror assy. rot. about z axis 

Shade frame motion 

Same 

Same 

Same 

Same 

Same 

Symmetrical reflector motion 

Unsymmetrical reflector and shade motion 

Same 

Same 

13 
TABLE 7. - 

Mode Freq 

1 .oo 

2 .oo 

3 .oo 

4 .oo 

5 .oo 

6 .OO 

7 .55 

0 .56 

9 .65 

10 .65 

11 1.17 

12 1.43 

13 1.48 

14 1.09 

15 1.90 

16 1.94 

17 2.51 

18 2.51 

19 2.85 

20 2.98 

21 2.98 

22 3.04 

23 3.59 

24 3.59 

25 3.74 

LDR 

Configuration 

JPL 

Ames six 

strut 

Ames triple bipod 

AMES TRIPLE-BIPOD MODAL FREQUENCIES (Hz) 

Damping 

ratio 

.002 

.020 

.002 

.020 

.002 

.020 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Rigid body 

Shade frame motion 

Shade frame motion 

Spacecraft module rocking rei. to reflector 

Spacecraft module rocking rel. to reflector 

Shade frame motion 

Shade frame motion 

Sym. reflector motion 

Shade frame motion 

Shade frame motion 

Strut motion 

Shade frame motion 

Shade frame motion 

Shade frame motion 

Reflector, strut & secondary mirror assy motion 

Reflector, strut & secondary mirror assy motion 

Sym. reflector motion 

Unsym. reflector & strut motion 

Unsym. reflector & strut motion 

Strut motion 

87C 

.205 (4) .120 (5) 

.000069 (4) .000059 (5) 

TABLE 8. - JITTER DISPLACEMENTS DUE TO CHOPPING & SLEW 

A (microns) 

838.200 

0.508 

6 85.800 

0.21 1 

787.400 

0.122 

Slew Chopping (211 (31 

@ (sic) 

14.9 

12.2 

14.0 

.0090 

,0038 

.0022 

(1) Requirement 5.02 sec. 

(2) Secondary mirror module rotation response from secondary mirror chopping. 

(3) A= reflector truss edge displacements (2) at point 57 (see fig. 

3-5) 1 min. after slew maneuver (t-180 sec.). Based on slew 

of 90"in 2 min. with 1 min. settling time. - 

@= rotation of reflector truss structure (sed. 

(4) Rotation at 19.78 sec-transient plus steady state vibration. 

(5) Rotation at 19.78 sec-transient vibration almost zero. 

b 

c 

14 
I 

Figure 6. - 3% Cantiguratierr, lbtk 9, 0.61 Hz 

15 
Figure 10. - 3pL Contiguratim, Male 16, 3.27 Hr 

16 

- 
figure 11. - 3pL Configuration, Mode 18, 3.31 Hz 

E 

fim 12. - 3pL Configuration, ?Me 20, 3.61 Hz 

17 
Figure 13. - 3X Configuration, Mode 21, 3.74 Hz 

Figure 14. - 3pc Configuratim, btk 24, 3.95 Hz 

18 
4 

Figure 15. - kes SixtStrut eonfiguration, Mode 7, 0.68 Hz 

Figure 16. - kes SixStrut eonfiguration, Mde 9, 1.43 Hz 

19 
Figure 17. - Ams Six-Strut Cmfiquration, Mode 10, 1.47 Hz 

Figure 18. - hes Six-Strut Configuration, Mode 11, 1.52 Hz 

20 

~~ 
Figure 19. - hes SixtStrut Configuration, Me 15, 2.12 Hr 

bnflgcnatlon, Mode 22, 3.01 Hz 

21 
I 

Figure 21. - hes Six-Strut eonfiguration, We 24, 3.09 Hz 

Figure 22. - kes Sin-Strut eonfiguration, IkJe 25, 3.75 Hz 

22 
T 

ORIGINAL PAGE I§ 

OI POOR QUAW 

Figure 23. - ks Triple4ipad-Strut eonfigurat,orr, b 7, 0.56 Hz 

c 

Figure 24. - kes Triple-Bipod-Strut Configuration, !Me 9, 0.65 Hz 

23 
Figure 25. - hs Triple-Bipod-Strut eonfiguration, Mode 13, 1.48 Hz 

Figure 26. - hes Triple-Bipod-Strut 

Ibtfiguratian, bde 16, 1.94 & 

4 

-. 
ORIGINAL PAGL IS 

OF POOR QUALITY 

Figure 27. - hs TripletBipodtStrut fhfiqurath, Me 21, 2.98 Hr 

25 
Figure 29. - hs Triple-Bipod-Strut Confiquration, Mode 24, 3.59 Hr 

i 
r secondary 3 

Module inertias: 

2 M = 1000 kg I, =i2=855.63 kg-m 

rT% Mirror throw 

.5 

t (sed U .025 sec 

(b) Mirror Qlopping Torque and Rotation 

Figure 31. - Secondary Mirror Chopping 

Slow position 

(0)- dog 

- 

- T= -A( l-CO8Wt) 

-2AConfiguration Tmax = 2A N-m (in-lb) 

JPL 820 (7256) 

Am08 six strut 985 (8720) 

Am08 bipod rtrut 1008 (8918) 

Figure 32. - LDR Slewing Torque and Position 

27 
I 

1.2 - 

.8 * 

.4 ' 

n 

u 

2 

0 Y 

E 

0 

Q 

0 

.- 

c 

0- 

a -.4 . 

-.8 * 

-.992 x rad 

(.205 m) 

1 -1.2 4 I I I I I I 

0 4 8 12 16 20 

Time (sed 

(a) 0.002 Oarping Ratio 

x 10'6 

- 

Figure 

-.58 x lov6 rad 

(. 120 SeE) 

.2 I 1 I I 1 1 I 1 1 

0 4 8 12 16 20 

Time (sed 

28 
4 

.335 x 10'' rad 

(.000069 s5) E 

4 

L 

. 

2 n 

U 

2 

Y 

co 0 

cp 

0 

.- 

c 

c 

a -2 

-4 

-6 1. I 1 1 1 I I 1 1 1 

0 4 0 12 16 20 

Time (sed 

(a) 0.002 Darping Ratio 

x 10-10 

4 

2 

n 

U 

!? 

Y 

co 

0 

cp 

0 

.- 

c 

c 

a -2 

-4 

.287 xlO-' rad 

(.000059 S~C) 

I I 1 I I I 1 

0 4 a 12 16 20 

Time (sed 

(b) 0.02 Darping Ratio 

Figure #. - hes Triple-Bipod Strut Secondary Mirror llodule 

Jitter troa Chopphg 

29 
1.52 1 

1.02. 

-51. 

g -1.02 

-2.03 

-1.52 

-2.54 

n 

E 

E - -.51 v) 

C 

c. 

0 

a 

m 

a 

-3.05 4 I I I I 1 1 I I I 1 

40 80 120 180 200 0 

Time (sed 

(a) 0.002 Daqing Ratio 

1.52 

1.02 

.51 

0 n 

E 

y E -.51 

c 

C 

-1.02 

- a -1.52 

n 

m 

a -2.03 

E 

0 

h 

b 

-3.05 1 I I- 

-2.54 . 

1 I I 

I 

0 40 80 120 180 200 

Time (sed 

(b) 0.02 Dimping Ratio 

Figure 35. - 3pL Reflector Jitter fror Slew. 

Displacerent at Reflector Tmss/Shade kint 
1.52 1 

1.02 . 

.51. 

n 0 " 

E 

E 

Y -.51 . c. 

C 

9) 5 -1.02. 

0 

(D 

m 

- 

Q -1.52- 

ii 

-2.03. 

-2.54 

-3.05 

0 40 80 120 180 200 

Time (sed 

(a) 0.002 Darping Ratio 

1.02 

.5 1 

0 

-.51 

n 

Y 

In 

e, g -1.02 

E 

0 -1.52 

a -2.03 

-2.54 

m 

Q 

m 

- 

-3.05 , 1 1 

0 

figure 36. - 

40 80 120 180 200 

Time (sed 

(b) 0.02 Dqing Ratio 

k Six-Strut Reflector Jitter from Slew. 

Displacarent at Reflector T~sdShade 3oint 

31 
1.52 1 

n 

E 

E 

Y 

-1.52 . 

-2.03 . 

-2.54 . 

-3.05 I , 1 

1 1 1 1 

120 180 200 0 40 80 

Time (Sed 

(a) 0.002 Daping Ratio 

1m52 1.02 i 

-.51. C 

Q) 

0 

Q 

E -1.02' 

3 -1.52. .- 

n 

-2.03 ' 

--7 

1 , 1 

180 200 80 120 

Time (sed 

-2.54 . 

-3.05 7 

0 40 

(b) 0.02 Daping Ratio 

Figure 37. - Aus Triple-Bipod Strut Reflector Xtter ftoll SlcWDisplaarrent at Ref lector Truss/Shade 3oint 

? 

. 

32 
1. Report No. 2. Govrrnmmt Accession No. 

NASA TM-89056 

4. Title and Subtitle 

Dynamic Analysis of the Large Deployable Reflector 

7. Author(s) 

Robert E. Calleson 

A. Don Scott 

9. Performing Organization Name and Address 

3. Recipient's Catalog No. 

5. Report Date 

6. Performing Organization Code 

506-49-31-01 

January 1987 

8. Performing Organization Report No. 

10. Work Unit No. 

17. Key Words (Suggested by AuthorW) 

Large Depl oyabl e Ref1 ector 

Primary Mirror 

Secondary Mirror 

Chopping 

S1 ew Response 

NASA Langely Research Center 

Hampton, VA 23665-5225 

National Aeronautics and Space Administration 

Washington , DC 20546-0001 

2. Sponsoring Agency Name and Address 

18. Distribution Statement 

Uncl assi f i ed - Unl imi ted 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

Subject Category - 18 

~~ 

19. Security Classif. (of this report) 

Unclassified 

20. Sccurity Classif. (of this page1 21. No, of Pages 22. Rice 

Uncl assi f ied 33 A0 3 

*. 

c