Using
Determination
of the Model LJncertainty Factor
Cross-Orthogonality
sod Overall I.“ad Factor Decomposition
M. A. Blair
Lockheed Technical Operations
Greenbelt, MD 20770
.I. W. Sills, Jr.
Co. Lockheed Technical Operations
Greenbelt, MD 20770
Abstract
dynamic
math
for
Structural
models
used
performing
Space Shuttle coupled
loads analyses
are required to bc test verified.
Generally, this is
accomplished
using a flight
configuration
modal
test
and subsequent
math
model
correlation.
Model
verification
is usually
evidenced
by
comparison
of the measured and predicted
mode
shapes and frequencies
with different
acceptance
criteria
for
“primary”
and “secondary”
modes.
Since the purpose of the modal correlation effort is
to develop a model which more accurately predicts
flight
generated
structural
loads, it is important
to understand
how different
levels
of modal
correlation
relate
to the accuracy
of internal
loads.
A methodology
has been developed in which the
mode shape correlation,
as measured by the crossorthogonality
comparison,
is used along
with
modal
decomposition
of overall
payload
load
factors to determine a model uncertainty factor.
Introduction
To the degree that any model falls short of
the NASA/JSC
requirement
for a fully
model
(the
main
two
being
mass
orthogonality
of 0.9
or greater
and
frequency errors of 5% or less for primary
Reference 1, the use of a Model Uncertainty
(MUF) will be applied.
meeting
verified
crossnatural
modes),
Factor
This memo documents the results of an analytical
study undertaken
to develop a Model Uncertainty
Factor (MUF) for the HST Flight Support System
(FSS) Finite Element Model.
The FSS has completed
its system level modal test and the results of the
model correlation
are represented in Figures 1 and
2.
These clearly show that the model has not
achieved the standard 90% or greater correlation
expectations to fully validate a model.
In this case
a MUF should be systematically
ascertained,
oat
613
Co.
A. Semple
Fairchild Space & Defense Corp.
Germantown,
MD 20874
arbitrarily
applied
as for a completely
verified
model. To develop a MlJF for the FSS tw” measures
of model
uncertainty
were employed:
interface
load and overall
center
of mass accelerations
during lift-off
and landing.
The ioterface
load
measure is useful to identify
uncertainty
in the
trunnion/STS
longeron
loads and the coupling
of
the FSS to other payloads.
The center of mass
acceleration
measure
is useful
to estimate
the
uncertainty
in the FSS internal stresses, since for
the FSS the stresses are calculated based on this
measure.
These measures are calculated
using a
decomposition
of the interface
loads
and cg
accelerations
mode by mode for both lift-off
and
landing
coupled
with cross-orthogonality
values
from Figures
1 and 2 or overall
error in the
reconstructed
modal test transfer
functions
using
the final “verified”
FSS model.
MUF
Application
The MUF will be applied to the load responses by
multiplying
the Loads
Transformation
Matrix
(LTM)
by a single scalar value.
For the load
factors
recovered
during
the load
cycle,
the
NASAIGSFC
environmental
verification
specification
document
states that STS analyses
which combine load factors for any phase of launch
contain
the summation
of the low and high
frequency
dynamic
components
superimposed
upon the steady state component.
IIowever, for STS
liftoff
there
is B negligible
steady
state
acceleration in both the Orbiter Y and 2 axes. The
Orbiter X-axis load factor contains approximately
1.5 g’s due to the steady state lift off acceleration.
The application of the MUF for all load factors in
all directions will be applied to the transient low
frequency component ooly as shown helow:
N x max = -1.5 + [( 1.4~~~ Transient * MIJFI + 13 +
Random
Vibx + trumlion
misalignment
loads)2
+ (friction
loads)2]0.s
N x min =
-1.5 - I( {AMin
Random
Vib,
l”ads)z
NY =
+I-
[( (Ay
Transient * MUFF + 1.5 +
+ trunnion
misalignment
+ (friction
* MUF)
trunnion
misalignment
loads)210,5
N, =
+/-
[( (A,
* MUF)
trunnion
misalignment
l”ads)210.5
loads)2]0.5
+ Random
loads)*
Viby
+ (friction
+ Random
l”ads)2
+
Vib,
+
+ (friction
Displacements,
stresses, and forces produced
for
lift-off
are calculated in a similar manner with the
MUF
applied
to the low-frequency
transient
component
only.
The maximum loads at landing for the STS are to be
considered as a combination
of the low frequency
transient
landing
loads,
trunnion
misalignment,
friction,
and
thermal
induced
loads.
The
application of the MUF for landing will be applied
to the low frequency transient component only.
FSS
Structure
The Flight Support System was initially
developed
as a reusable,
primary
interface
between
the
Multi-mission
Modular
Spacecraft
and the Space
Transportation
System
for launch,
deployment,
servicing,
and landing
operations.
This initial
system coosistcd of three cradles, a Berthing and
Positioning
System (BAPS), mechanisms,
avionics,
and associated
mechanical
and electrical
ground
support
equipment.
The FSS is currently configured
for servicing the
HST. The HST servicing configuration
consists of a
single cradle, avionics, mechanisms, and the BAPS,
Figure 3. Once the HST is berthed to the PSS, the
BAPS will be used to orient the HST for serviciug
and to react loads induced by reboosting
the HST
to a higher orbit.
Methodology
In order to determine
MIJF,
two comparisons
model and test results
frequencies
were in
available test measures
a reasonable
value for a
between
the analytical
were made.
Since natural
good
agreement,
the two
of mode shape correlation
614
were used.
The first comparison
involves
the
cross-orthogonality
diagonal
terms
while
the
second involves the frequency response functions.
The general approach was to assign an error value
for each mode of the FSS.
This error was then
applied to both the average net cg acceleration and
to the average interface
force percentage.
Thus,
modes
which
are critical
contributors
to the
overall loads carry much more weight than those
which are insignificant
as far as overall
loads.
The interface
force decomposition
was chosen
because of its relevance to the Orbiter and because
these loads are less sensitive
to internal
FSS
modeling
errors.
The “et cg accelerations
are
critical
because
the stress analyses
are based
upon quasi-static
load environments.
In order to obtain the STS landing and liftoff loads
decomposition,
a series of “base drive”
analyses
were
performed
in
which
the
interface
accelerations
and displacements
were applied
to
the FSS analytical model and both interface forces
and net cg accelerations
recovered.
The peak
result for each response item was then decomposed
into the response
per flexible
and rigid
body
mode.
This gives an indication
of which flexible
modes are excited by the input transients.
LOad
Decomposition
Results
The results of the load decomposition
study are
shown in Figures 4-l.
These include both the net
cg accelerations and interface forces for both STS
liftoff and landing events.
The “et cg results were
averaged
across all directions
to obtain
and
average net cg acceleration
percentage
from O-SO
HZ. This data was used in the MUF comparisons.
In &meral, the treuds hetween net cg response and
interface force are similar.
The interface
forces
are dominated
by the rigid body and first three
flexible modes while the net cg accelerations show
more flexible mode behavior.
Model
Uncertainty
Factor
As discussed above, the methodology
for determining a MUF was to compute the error percentage
by mode and scale this by the percentage of load
which is attributed
to that mode.
The Root Sum
Square (RSS) of these errors gives the error margin
which is then added to 1.0 to give the MUF.
Orthogonality
Figure 8 shows the results of the MUF calculation
for the orthogonality
errors with the net cg loads.
Using the primary
mode diagonal
orthogonality
terms, an orthogonality
vs. frequency
comparison
was made.
Overlaid upon this plot is the average
net cg accelerations
for both liftoff
and landing.
At each mode, the average load percentage
was
scaled by the interpolated
orthogonality
error (lorthogonality)
to arrive at a modal error value.
The errors for all 23 modes were root sum squared
to obtain the landing and liftoff
MUF’s shown on
the plot (1.11 & 1.12 Respectively).
Rigid body
loads were not subject to error calculations.
The same approach used above was used to obtain
the MUF’s based upon FSS interface forces.
These
results are shown
in Figure
9 with
the final
calculated MUF’s at (1.12 and 1.09).
Frequency
Response
Functions
Frequency
Response
Functions
are a direct
measure of model
perlormance
at tested force
levels.
They
are not
subject
to parameter
extraction
errors
as are
the
orthogonality
comparisons.
The FSS exciter
locations
were
chosen for their ability to excite modes of interest
and for reasons of practicality
such as access and
ease of stinger attachment.
Since the FSS drive
points are not on the primary
load path(s), the
resulting
FRF’s may be prone to local modeling
errors.
For this reason, the FRF calculated MUF
was given equal weighting
with the orthogonality
MUF.
the modal errors was computed to obtain a MIJF.
The resulting MUF’s are 1.12 and 1.11. Again, the
same calculations
were performed
except the load
decomposition
results for the FSS interfaces were
used.
The resulting MUF’s, shown in Figure 12,
are 1.14 and 1.10.
Summary
In an effort to account for possible load errors
resulting from a less than ideal modal correlation
of the FSS, a model uncertainty
factor has been
computed
based upon test to analysis eigenvector
comparisons
coupled
with
load
decomposition
results for the FSS “et cg.
The resulting MIJF is 1.11 is an average of the
MUF’s
calculated
from
both
orthogonality
and
FRF’s using both interface forces and FSS net cg
accelerations.
The scatter on the MUF values is
small, 1.09 to 1.14 which justifies using an overall
average value of 1.11.
It is felt that the procedure
used to develop this value is reasonable as far as
overall loads are concerned.
References
1
Payload
Verification
Requirements,
14046 Rev. B. NASALISC, 29 October
NSTS
1992
The FRF’s for all channels and all three exciter
locations
were compared
on a frequency
by
frequency basis and an overall average analysis to
test FRF ratio computed.
This is shown in Figure
10. Of note is the fact that the analytical model
over-predicts
the response
through
most of the
frequency range.
A normalized FRF ratio was used
to develop the MUF’s.
For all ratio’s greater than
1.0 the ratio
was inverted.
Thus,
a perfect
correlation would result if the ratio was at 1.0 and
the error
value
for
other
ratio’s
would
be
calculated as 1.0 - normalized ratio.
Figure
11 shows
the normalized
FRF ratio
compared to the load decomposition
study average
net cg loads. Using the same approach as employed
for the orthogonality
MUF calculation,
the RSS of
615
Figure
I. Cross-Orthogonality
Modes
History
for
All
FSS
Figure 2.
Figure
3.
Cross-Orthogonality
FSS Modes
History
Flight
Support
System
Servicing Mission
for
for
primary
the
IIST
616
Figure
4.
FSS Interface
Load Decomposition
STS Landing Analysis
For
Figure
5.
FSS Interface
Load Decomposition
STS Lift-Off
Analysis
For
Figure 6. FSS Net CG Acceleration Load
Decomposition
For STS Landing
Analysis
Figure 8. Orthogonality vs. Landing & Lift-Off
Net CG Load Percentage
Figure 7. FSS Net CG Acceleration
Load &Wre 9. Orthogonality vs. Landing & Lift-Off
Decomposition
For STS Lift-Off
Average Interface Force Percentage
Analysis
617
Figure
Figure
10. Average
FRF
Figure
11. Normalized
Lift-Off
Net
Ratio
(AnalysisiTest)
FRF
Ratio
vs. Landing
CG Load Percentage
&
618
12. Normalized
Lift-Off
Percentage
FRF
AWage
Ratio
vs.
Interface
Landing
&
Force