NASA Technical Reports Server (NTRS) 20120016966: International Space Station 2A Array Modal Analysis

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by  NASA Technical Reports Server (NTRS)

INTERNATIONAL SPACE STATION 2A ARRAY MODAL ANALYSIS

Michael Laible
The Boeing Company, 3700 Bay Area Blvd., Houston, Texas
Kristin Fitzpatrick
The Boeing Company, 3700 Bay Area Blvd. Houston, Texas
Michael Grygier
NASA, Johnson Space Center, Houston, Texas

ABSTRACT

On December 9th 2009, the International Space Station (ISS) 2A solar array mast experienced prolonged longeron shadowing
during a Soyuz undocking. Analytical reconstruction of induced thermal and dynamic structural loads showed an exceedance
of the mast buckling limit. Possible structural damage to the solar array mast could have occurred during this event. A Low
fidelity video survey of the 2A mast showed no obvious damage of the mast longerons or battens. The decision was made to
conduct an on-orbit dynamic test of the 2A array on December 18th, 2009. The test included thruster pluming on the array
while photogrammetry data was recorded. The test was similar to other Dedicated Thruster Firings (DTFs) that were
performed to measure structural frequency and damping of a solar array. Results of the DTF indicated lower frequency mast
modes than model predictions, thus leading to speculation of mast damage.

A detailed nonlinear analysis was performed on the 2A array model to assess possible solutions to modal differences. The
setup of the parametric nonlinear trade study included the use of a detailed array model and the reduced mass and stiffness
matrices of the entire ISS being applied to the array interface. The study revealed that the array attachment structure is
nonlinear and thus was the source of error in the model prediction of mast modes. In addition, a detailed study was
performed to determine mast mode sensitivity to mast longeron damage. This sensitivity study was performed to assess if the
ISS program has sufficient instrumentation for mast damage detection.

KEYWORDS: Non-linear, Modal Analysis, Photogrammetry, Damage Detection

1.0 INTRODUCTION

The on-orbit construction of the International Space Station (ISS) began in November 1998, and was completed in July of
2011. The ISS consists of eight solar arrays for power generation. Each array is mounted on a rotating gear box for solar
tracking and is deployed with a 4 longeron mast. Each mast is made of 32 bays consisting of longerons, fixed battens,
flexible battens, and cable diagonals. Early in the ISS assembly process it was noted that thermal and dynamic conditions
exist that could buckle a solar array mast longeron. This condition exists when one longeron is shadowed by another
structure, thus causing asymmetric thermal loading in the mast longeron.

The ISS program developed a software tool to predict longeron shadowing events and to minimize periods of extreme loads.
During the 19S Soyuz undocking December 1, 2009, the vehicle was in a long period of solar array longeron shadowing.
The analysis predicted extreme loads in array 2A longeron and possible buckling. It was determined that an on-orbit test
should be performed to analyze the dynamic response of the 2A array to check for damage.

This test produced a significant frequency difference in the 1st In Plane Array Mode compared to the analytical model and the
other arrays. The ISS program requested a complete analysis of this event to determine if the 2A array was damaged or not.
This paper documents the analysis performed and investigates possible solutions to the dynamic differences of this array. In
addition to the dynamic analysis, analysis was performed to determine if a longeron did fail, can the failure be detected from
existing on-orbit instrumentation.
SSection 2.0 of this report preesents the backkground of lonngeron shadowwing and the sspecific 2A lonngeron shadowwing event.
SSection 3.0 desscribes both thhe linear and nnonlinear 2A aarray modal annalyses performmed and a commparison to thee other ISS
aarrays. Section 4.0 outlines thhe analysis perrformed to dettermine if we ccan detect masst damage utiliizing the instruumentation
oon-board ISS. Section 5.0 disscusses the connclusions

22.0 PROBLEEM DESCRIPPTION

22.1 ISS ARRRAY LONGEERON SHADOOWING

TThe ISS has eigght solar arrayss, each consistiing of a mast, ttwo solar cell bblankets, and ffoour blanket boxes. These maasts are
aattached to the Beta Gimbal AAssembly (BGAA) and can rotaate independenntly about the llong axis of thee mast. Fig. 1illustrates
thhe ISS configuuration with thee eight arrays rrotated indepenndently and thee 2A Array; thee focus of this paper.

Array 2A

Fig. 1 Intternational Sppace Station AAssembly Commplete

EEach mast is mmade up of four longerons as sshown in Fig. 22. If one longeeron is shadowwed and the otheers heated, twoo
loongerons will bbe in compresssion and otherss will be in tension. This cann cause bucklinng of the longerrons. Typical buckling
aand temperature values are shhown in Fig. 2.The buckling sstarts at a combbined dynamicc and thermal looad of 1340 lbs [1].

TThe ISS prograam performs a ddetailed longerron shadowingg analysis and vvalues are repoorted real-time. The ISS misssion
ooperation persoonnel will receiive a warning iif a longeron iss shadowed andd loads are at mmax limit valuees. When the wwarning is
rreceived the BGGA is rotated too eliminate lonngeron shadowwing.

Fig. 2 Soolar Array shaadowing and tthermal buckkling
22.2 2A ANOOMOLY

DDuring an ISS mmaneuver in DDecember, 20099, the 2A Arrayy experienced Longeron Shaadowing for ann extended period of time.
PPost flight analysis proved thhat the limit looad was exceeeded and that bbuckling couldd have occurreed. To ensuree structural
inntegrity a detailed photo reviiew was perforrmed with no nnoticeable damaage reported.

TThe ISS prograam then determmined that a DDedicated Thrruster Firing (DDTF) test shoould be performmed on the 2AA Array to
ddetermine the mmodal structuraal properties. IInstrumentationn does not exisst on the array mast itself; thherefore, photogrammetry
ddata was recordded and analyzed to determiine the modal parameters off the array. Thhe Image Scieence and Analyysis Group
((ISAG), at NASSA JSC receivved analog videeo taken duringg the 2A DTF ffrom two ISS external cameeras [2]. Fig. 33 illustrates
thhe camera viewws and jet plumme direction tooward the 2A Array. The thhruster firing laasted for 1 seccond and was ddesigned to
eexcite the modees of the 2A Arrray.

Point TTracked
Point Traacked

Fig. 3 ISS Camera VViews, Jet Plumme and Photoggrammetry Cooordinate Fraame

TThe ISAG usedd their image pprocessing soffttware to track two points at the end of thee 2A Solar Arrray Wing (SAWW), Fig. 3.
OOne point was on the mast caap located at the end of the mast of the solarr array. The seccond tracked ppoint was on thhe tip of the
bblanket box at the end of the solar array. TThe motion of eeach point wass tracked in thhe video recordded from each of the two
ccameras and ussed to computee the relative displacement off the SAW tip in each axis, ddefined by the plane of the arrray during
thhe DTF. Due to the high mmathematical correlation beetween the axiial and out off plane motionn, the calculaations were
cconducted in aa way which constrains the aaxial position to a fixed valluue of 0. This constraint is aacceptable giveen that the
mmotion of the aarray in the axxial direction is significantly less than the In Plane (IP) or Out Of Plaane (OOP) mottions. The
mmajor modes observed from tthis DTF and pprevious DTF’’s are the 1st OOOP and 1st IP modes. The frrequency of thee OOP and
IIP modes foundd for other arraays are betweenn 0.06-0.0675 HHz and 0.09-.0099 Hz, respecttively.

WWhen the photogrammetric analysis was completed, the time historyy data was loww-pass filteredd and the FFTT was also
ccomputed. Thee OOP frequenncy was withinn the expected rrange but the IIP frequency wwas 14% lowerr. The displaceement time
hhistory and FFTT of the array mmast cap is illuustrated in Fig. 4.

TThe Eigensysteem Realization Algorithm (ERA) [3] waas utilized to extract the mmodal parametters from the detrended
pphotogrammetrry data sets. TThe Modal Asssurance Criteriion (MAC) waas calculated bbetween the exxtracted mode sshapes and
thhe analytical mmodel mode shhapes. The commparison results between thhe extracted mmodal parameteers from the daata and the
aanalytical modaal parameters aare summarizedd in Table 1. TThe frequency of the first OOOP test mode mmatched within 5 % of the
ffirst 2A OOP aanalytical modde. The frequeency differencee between the 1st IP test modde and IP analytical mode raanged from
114-17 %.
SAW 2AA F1 MC Time DDomain FFT: SAW 2AA F1 MC Frequenncy Domain
4
IP IP
3 OOPP OOP
2500
s] 2
e
h 2000
ent [Inc 01 nitude1500
m g
e a
ac-1 M
pl 1000
s
Di-2
500
-3
-4 0
0 20 40 60 80 100 120 140 0.02 0.04 0.06 0.08 0.1 0.12 0.14 00.16
Time [Sec] Hz
Fig. 4 Maast Cap Displaacement Timee History and FFT

Table 1 2A AArray Test Moodes versus Annalytical Model Modes
TTest Data Analysis Dataa
MMode # Frreq. Damp. EMAC Mode Freq. Freqq. MAC MMode Descriptiion
(HHz) (%) (%) # (HHz) Diff (%)
9 0.00597 2.688 0.951 AAll SAWs OOP
10 0.00613 0.00 0.948 AAll SAWs OOP
1 0.00613 4.6 92.42 12 0.00648 -5.440 0.942 PPort SAWs OOOP
14 0.00651 -5.84 0.943 PPort SAWs OOOP
16 0.00665 -7.82 0.940 PPort SAWs OOOP
17 0.00933 -14.447 0.909 Port SAWs IPP
2 0.00798 3.3 96.12 19 0.00964 -17.222 0.904 Port SAWs IPP
22 0.00971 -17.882 0.902 Port SAWs IPP

FFig. 5 illustratees the analyticaal mode shapee of the OOP aand IP modes. The figure iss the MSC PAATRAN model of the ISS
ssystem model, zoomed in on tthe 2A array. The mode nummber and frequeency is shown for the OOP aand IP 2A arrayy modes.

Fig. 5 AAnalytical Arrray Out of Plaane and In Plaane
3.0 2A ARRAY MODAL ANALYSIS

The 2A Solar array had experienced a sustained longeron shadow event. The analytical reconstruction of the event showed
an excedence in the limit loads when combining the dynamic and thermal loads. An on-orbit dynamics test was performed
and the IP mast mode was found to be 14% lower than what was expected when compared with the analytical dynamic
model. In addition, the 1st IP 2A Array test mode was lower than what was previously seen with any other array on-orbit test.
The large frequency difference between the IP test and analytical mode was a concern to the program and resulted in the
request of a more detailed analysis to determine the cause of the difference.

The following detailed analysis was conducted to determine why the 1st IP Array mode was lower and if damage of the array
could be detected with modal analysis.

3.1 LINEAR ANALYSIS

The ISS loads system model is made up of over 90 super elements and has 35,000 dof. Each model takes about 60 minutes
of computer time for the SOL 103. When performing time domain solutions (SOL 109 or 129) the time increases
dramatically. This is an unmanageable model when performing parametric runs and numerous failure analysis time domain
runs. To simplify the problem, a stiffness matrix was developed using the NASTRAN DMIG option with the boundary
conditions being constrained at the approximate CG of the ISS and the other boundary being the 4 grids that the Solar array
BGA attaches to ISS.

In addition, the solar array model used during nominal loads analysis has a simplified mast (1 Center Bar, 10 pieces) and did
not model the individual longerons. To perform parametric studies of failed longerons the detailed mast model would have to
be integrated into the simplified system model. Fig. 6 illustrates the baseline loads model (left) and the detailed mast model
delivered from the developer (right). The highlighted CBARS are the longerons used for the failed analysis. The far right is
a close up of the longeron model and cross battens. In failed longeron cases the complete connection is removed at positions
depicted in Fig. 6 (MID and BASE).
Serries of bar
elemments
CONNNECTION
MMID Longeron
REMOOVED IN FAILEED
CASES
One series of
bar elemennts
BASEE Longeron

Baseline Detail

FFig. 6 Baselinee vers us Detaiiled Array Moodel

TThe detailed arrray model wass compared aggainst the simplified baseline array model. A modal soluution was perfoormed with
bboth models beeing constrained at the basee coordinate frrame as shownn in Fig. 6. TThe frequency differences beetween the
mmodes of each model were all within a ½%.. Once the moodel comparisoon was complette the detailed mast model waas attached
innto the station stiffness and ssensitivity studdies were perfoormed. Fig. 7 iillustrates the sstation stiffnesss model with thhe detailed
mmast and array models.

TThe first run was the SOL 106, a non-linearr solution, whicch involved puulling the blankkets tight to thee baseline sprinng tension.
TThe blanket eleements were ppre-stressed in order to accouunt for the efffeect of the blannket tension looad. The blankket tension
looad was analyyzed using geommetric non-lineear static analyysis sequence ((NASTRAN SSOL 106) [4]. The differentiial stiffness
mmatrix and couupled mass mmatrix are usedd in normal mmode analysis solution sequuence (NASTRRAN SOL 1033) and the
EEXTSEOUT caard to build thee DMIG of thee array, PCH annd ASM files. This is perforrmed by restartting the SOL 106 run and
uusing the EXTSSEOUT card.

NNow the ISS syystem model caan be replicatedd by a NASTRRAN run using the ISS DMIGG, Solar array DDMIG, and dettailed four-
bbar BGA assemmbly. The time domain and mmodal solution rruns could be pperformed withh minimum commputer time. AAgain this
mmodel is shownn in Fig. 7 whicch also notes thhe chosen faileed longerons foor the analysis. These longerrons were chosen from a
sseparate analyssis, which showwed that these aareas are the mmost likely to faail.
MID Longeron failed
BASE Longeron failed
Station Stiffness
Rigid Connection

Fig. 7 ISS Stiffness with Detailed BGA and Array Model

The Boeing Loads and Dynamics group performs thruster plume analysis on all station arrays. The program that performs
the analysis uses plume jet mass flow and impinges on individual plates modeling the array. The output is a force on each
individual grid. The program has been validated with other array displacement checks. A special routine was developed to
map force values and vectors for each array blanket. These force values were mapped to every array blanket and the mast
cap. The array wing displacement was plotted and compared to the on-orbit data. These comparison plots are shown in Fig.
8. As can be seen by the displacement time history plots, the frequency of the on-orbit data and analytical data does not
compare for the IP mode. This also was seen in the frequency domain.

BASELINE‐OOP BASELINE‐IP
5 5
Photo G OP Phot G IP
4 4
Analysis OOP Analysis IP
3 3
2 2
1 1
n0 n0
i i
‐1 ‐1
‐2 ‐2
‐3 ‐3
‐4 ‐4
‐5 ‐5
0 20 40 60 80 100 120 0 20 40 60 80 100 120
t(s) t(s)
Fig. 8 Time Domain Comparison of Out of Plane and In Plane Test and Baseline Analytical Data
IIn addition to thhe time domainn runs, a parammetric study waas performed uusing the modaal solution. Sevveral models wwere created
too conduct the parametric stuudy; the Baseliine array (BL 081), Baselinne array with MMID longeron partially faileed (BL 081
MMD1) and totall fail (BL 081 MD1 TL), andd the base longgeron partially failed (BL 081 BS1) and baase longeron tootally failed
((BL 081 BS1 TTL). The resuults of this parametric study are shown in Table 2. As ccan be noted tthe Base longeeron totally
ffailed still showws a 10% frequuency differencce from the on--orbit test IP frrequency.

TThese results inndicate that thee on-orbit IP ffrequency diffeerence betweenn the on orbit ttest and the annalytical modell cannot be
eexplained by a longeron failurre alone. Otheer areas had tobe investigatedd.

TTable 2 Array Frequency Coomparison
Mode %% Diff BL 081 BL 0081 BL 081 BL 081 % DDiff
Descrip 2A DTF BBL 081 TTest MD1 MD11 TL BSS1 BS11 TL Teest
OP 0.0602 00.0649 8% 0.00646 0.06644 0.06635 0.00634 5%%
IP 0.0814 00.0969 117% 0.00929 0.09926 0.09903 0.00898 10%
TOR & IP 0.103 00.0934 -10% 0.00957 0.09953 0.09945 0.00945 -9%%
Mast OP 0.152 00.1519 0% 0.1519 0.15519 0.15517 0.1517 0%%

AAfter a more ddetailed look oof the system, it was determiined that the IIP mode stresss was greatest in the four-baar linkages,
wwhich attachess the BGA to the ISS truss. In fact, the ffirst two modees are dominatted by the fouur-bar/BGA asssembly. A
ddetailed picturee of the four-baar assembly is sshown in Fig. 99.

Fig. 9 ISS Four-Bar Asssembly

33.2 NON-LLINEAR ANALYSIS

TTo get a better understanding of the four-baar assembly meechanism and thhe inherent nonn-linearities, thhe ground test documents
wwere reviewed.. The ground test data illusttrated an initiaal slippage folllowed by a higgh degree of bbi-linearity, moost notably
bbetween the +- My cases. Figg. 10 shows the strain gauge loocation and thee derived momment output fromm the My inpuut. The test
ddata showed thhat some of thhe deflections wwere different in the plus annd minus loadding cases. WWithin each loadd case, the
ddeflection verses load curvess were relativelly linear, but ttwo curves emmerged in somee of the plus annd minus loadd cases that
wwere not (My sshown in Fig. 110) [5, 6, 7].

TThis observatioon in the grounnd test data meeans that there was uneven sllippage in somme of the four-bbar to clevis coonnections.
AAfter 10 iteratiions of the ground test the best agreemennt between thee model and liinear data reqquired stiffnesss values be
aadjusted in the model four-baar to clevis sprrings, Mx (in-lbb) = 450,000 tto 900,000, Myy (in-lb) 650,0000 to 2,280,0000, and Mz
((in-lb) 600,0000 to 6,000,000. These new sttiffness values were developeed to correlate to the linear sllope of the testt data, thus
thhe model is exxpected to be sttiffer.
All reports indicate that the non-linearities are mechanism slippage and are in the four-bar to IEA clevis connection.

Fig. 10 Ground Test 4 Bar Assembly and Ground Test Stiffness Data

The ground test documents showed that non-linearities exist in the four bar connections. As noted earlier, the four-bar
connections dominate the first two modes, OOP and IP. At this point a more detailed analysis was performed on the on-orbit
data using the Boeing Test Analysis Correlation Solutions (BTACS) program. The BTACS system identification tool
includes a method that extracts modal parameters within a set window over a prescribed period of time within the data set.
The photogrammetry displacement data was analyzed using the system identification tool of the BTACS program. The modal
parameters were computed every 0.67 seconds using a window of 60 seconds of data.

The frequency values, of the extracted modes, were then plotted for each time increment where the color of the data point
represented the EMAC value, red being greater than 90% and orange greater than 80%. Fig. 11 shows the results of the
BTACS system identification analysis of the on-orbit data array data showing non-linearities of the 1st OOP and 1st IP Modes.
The frequency of the OOP mode ranged from 0.06 to 0.068 Hz and IP 0.079 to 0.09 Hz over time, as the amplitude of the
array displacement diminished.

Fig. 11 Photogrammetry Data Mode Frequencies vs Time
To better understand the mechanism of the four-bar clevis to truss connection, on-orbit photos were reviewed. As previously
noted the ground test documents indicate that the non-linearities were most likely coming from the four-bar to truss clevis
connection. Fig. 12 depicts the on-orbit photos showing the placement and close-up of the four-bar to clevis connection.

Fig. 12 Four-bar to Truss Mechanism

Fig. 12 illustrates the pin mechanism that locks the four-bar in the extended position (far right). This pin connection is
modeled as a set of springs in the BGA detailed NASTRAN model. During the ground test it was decided to correlate the
model to the linear stiff portion of the test data, thus increasing the rotational spring values as shown in Table 3, Colum 3
(Ground test BL 081). The original values of the model are shown in column 2 (Original).

A series of NASTRAN runs were performed modifying the four-bar to truss spring values. It was found that modifying the
front two connections in DOF 1, 3, and 5 (see Fig. 13) would impact the frequency of the IP mode while having negligible
effects on the frequency of the other modes. Column 4 of Table 3 contains the final spring values used for the analysis.

Table 3 BGA to Truss Spring Values
Baseline Ground test - Modified - BL 081
(in-lb) BL 081 (in-lb) DOF 1,3,5 Front (in-lb)
CELAS2 DOF1 5500000 5500000 5000
CELAS2 DOF2 5000000 5000000 5000000
CELAS2 DOF3 300000 300000 5000
CELAS2 DOF4 450000 900000 900000
CELAS2 DOF5 650000 2280000 2280
CELAS2 DOF6 600000 6000000 6000000