NASA Technical Reports Server (NTRS) 19930012125: The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: McDonnell-Douglas Helicopter Company achievements

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by  NASA Technical Reports Server (NTRS)

THE NASA/INDUSTRY DESIGN ANALYSIS METHODS
FOR VIBRATIONS (DAMVIBS) PROGRAM - MCDONNELL
DOUGLAS HELICOPTER COMPANY ACHIEVEMENTS
Mostafa Toossi *
Richard Weisenburger t
Mostafa Hasherni-Kia t
McDonnell Douglas Helicopter Company
Mesa, Arizona
Abe,rut The guidelines were broken into three different cate-
gories which consisted of those used for modeling of
the stiffness characteristics, representation of the mass
This paper preRnts t summary of some of the
distribution, and consideration of factors affecting the
work performed by McDonnell Douglas Helicopter
accurate representation of vibrational characteristics
Company under NASA Langley-sponsored rotorcraft
of the :node]. Other resources required for performing
structural dynamics program known as DAMVIBS
efficient :node] checkout (2) and techniques used for
(Design Analysis Methods for VIBrationS). A set of
different types of vibration analyses, were also devel-
guidelines which is applicable to dynamic modeling,
op,c] (3.4}. The portion of this effort which is related
analysis, testing, and correlation of both helicopter
to the dynamic aspect of these studies is the subject
airframes and a large variety of structural finite ele-
of this paper.
ment models is presented. Utilisation of these guide-
lines attd the key features of their applications to vi-
In the first section of this paper, the procedures used
bration modeling of helicopter airframes are discussed.
in converting the static mode] into a dynamic model
Correlation studies with the test data, together with are discussed. These include steps such as addition of
the development and applications of a set of efficient
non-structural components and extra grid points for
finite element model checkout procedures, are demon-
the representation of the locations of the heavy mass
strated on a large helicopter a_frame finite element
items and inclusion of additional effects in shear pan-
model. Finally, the lessons learned and the benefits
sis to make them properly effective. For the accurate
resulting front this program are summarised.
representation of the mass distribution, which is akey
factor in adynamic analysis, a procedure is developed
1. Background and Introduction which is discussed next I_). This procedure is used
to systematically distribute the mass data over entire
finite element model. In addition to these changes, a
Under a U. S. Government sponsored contract, Mc- set of model quality assurance procedures is developed
Donnell Douglas Helicopter (MDHO) was one of the which helps the analyst to rapidly identify modeling
four helicopter JJtanufacturers who participated in errors prior to performing any analysis. These proce-
conducting a study of finite element analysis of he- dures are summarised.
licopter airframes for the enhancement of the tech-
nology baJe ,'elated to the area of airframe structural In the second part, the efforts spent on obtaining
dynamic analysis. This work which was sponsored by an experimental database describing the vibrational
the NASA Langley Research Center Structures Direc- characteristics of the aircraft structure and the finite
torate, consisted of planning, development, and the element model enhancement process are discussed re}
documentation of modeling techniques and computa- The procedure used for testing, the criteria used for
tional procedures. Additional tests were performed to mode identification, and a summary of test results
obtain the necessary data to verify the finite element is discussed. A summary of correlation studies per-
model and to develop procedures for correlation stud- formed to check the validity of a finite element model
ies. The modeling and shake test were performed on and the associated modeling assumptions will be dis-
the McDonnell Douglas AH-64A (Apache) PV01 Heli- cussed. As a part of this enhancement process, the
copter. Initially, a structural finite element model was modeling problems that were identified as a result of
prepared (a) correlation studies arepresented. In addition, the gen-
eral application of the test results is discussed.
*lv(hnapr, Member .AI_I[I.
t ltmareh I_.n_nmr, Member AHS. Finally, use of a model reduction procedure for the
| !_mm_b_anginal Msmb_ A.H8,
35
purpose of increasing the computational efficiency for Another task in generating a dynamic model involves
the dynamics optimisation applications is discussed. the development of the mass model. This process gen-
A preliminary study was performed to demonstrate erally consists of following tasks; a) generation of a de-
application of such a procedure. The lessons learned tailed weights record for the weight empty flight con-
from this mtudy which include the development and figuration, b) generation of a detailed listing of use-
•pplication of the model reduction process and the use ful load weights, c.g.'s, and inertias, c) distribution of
of the reduced model in a sensitivity anaJysis study primary structure weight via material density parame-
are summarised. Finally the lessons learned from the ter, d) manual distribution of large concentrated mass
overall DAMVIBS effort _e discussed. items (i.e., main rotor, transmission, engines, etc.),
and e) automatic distribution of remaining mass data
using a systematic and preferrably automated mass
I1. Vibration Modelin_
lumping process.
Most of the information specified in the above list is
Generally, there are two major tasks involved in the
generally available through the mass database and the
development of adynamic model from a static model.
mass density information of different geometric repre-
First step involves the additional modeling resources
sentation of various model components. For the pur-
necessary to make a static model useful for vibration
pose of distributing the the remaining mass data (i.e.,
analysis. Next is the generation and addition of the
mass distribution to the static model. item e), an automated mass lumping procedure was
established. In the case of Apache model, this proce-
A static model which is primarily used for calcula_ dure was used to systsmaticaJly distribute the mass
tions of internal loads and stresses under static loads data over the specified dynamic model grid locations
generally does not contain a detailed representation of and as a result a set of CONM2 cards were generated
mass information. Prior to its use for dynamic anal- that were used in the dynamic model. The method-
ysis, it is required that additional steps be taken to ology used for the distribution of the finite element
accommodate for the locations of heavy mass items model mass data is discussed in detail in Ref. 5.
such as engines, missiles, etc. In the case of Apache
For the distribution of mass data, the lumping pro-
model, shown in Fig. 1,one of these steps involved the
gram requires two sets of information, namely, the ac-
addition of secondary structures and non-structured
tual aircraft mass data records and the location of the
parts and a set of additional grid locations required
selected grid points of the finite element model. The
for proper representation of masses. These grid points
mass data is organised and stored in a format that is
were properly linked to the
consistent with the MIL-STD1374A. Starting with the
first mass item in the database, the program internally
generates an imaginary volume, referred to as lump-
ing volume, around the mass item. Next, by searching
through the specified grid points, it identifies those
grids which are confined within this volume and then
assigns a different portion of the mass item to each of
the selected grid points. Then, in case where there are
still some remsining portions, the program increases
the sise of the lumping volume and starts assigning
portions of the remaining mass item to the new set
of grids which may now be within the confinement of
the increased volume. This process is repeated until
the mass item is completely distributed to the sur-
Fig. 1. AH-64A Dynamic MSC/NASTRAN Model. rounding grids. This process is repeated for each of
the mass items. However, proper care is taken within
surrounding areas. The next step in this conversion
the program for avoiding the relumping of the mass of
process was to correctly represent the structure for the
those items which have already been accounted for.
in service conditions. In the case of static models, gen-
erally impending fLilure conditions are considered. In Figure 2 represents the general arrangement of the
this case it is assumed that the skins are fully buckled lumping process sad illustrates the input sad out-
and do not carry any tension/compression loads. This put streams of the automated mass lumping program.
assumption needs to be modified for simulation of in Although this program cam accommodate structural
service conditions. Thus, proper steps were taken in mass input, the primary intent in the development
order to make sure that the skins were appropriately of the program was to distribute nonstructural mass
effective.
36
items(e.g. fasteners, wire bundles, etc.) to model tion, where the N-set and F-set stiffness matrices are
grid point locations. This mass lumping process min- being assembled, improper applications of the M,iti-
intiees the human error through automatic generation Point Constraint equations (MPCs) and Single Point
of a set of CONM2 cards which are readily used as Constraints (SPCs) could result in further modeling
errors. Incorrect specifications of these types of con-
straints will result in incorrect representation of the
II_hlll J/]l linear relatio,_ships among different DOFs and over-
• mm |_m:tmJe
constrained boundary conditions, respectively.
I .............. 1
Cholesky Decomposition DMAP
The purpose of this check is to identify singularities or
mechanisnls as well as near singularities or soft spots
in the model at the F-set level. For this purpose, a
DMAP was developed which employs the DCOMP
functional module to perform a triangular decomposi-
tion of the F-set stiffness matrix in the static solution
sequence 12D.After the decomposition, adiagonal ma-
trix results whose elements provide information about
the conditioning of the stiffness matrix. A max factor
Fig. 2. Block Diagram of Mass Lumping Program.
diagonal value (i.e., ratio of the largest diagonal term
to the lowest diagonal term) of over I0s indicates asoft
a part of the NASTRAN bulk data deck. The struc-
spot (i.e., near singularity) while a value over I0t° is
tural mass (e.g. skins and stringers) is calculated via
indicative of a mechanism (i.e., singularity). In ad-
material density cards internally within NASTRAN
to form the total mass matrix. dition to the max factor ratio, another parameter, _,
is calculated. Aside from round-off errors, any large
nonzero value of e is indicative of a singularity in the
[ILM_!e_I _V_tril_i__ _Pr_._a._ stiffness matrix.
Model verification process is one of many tasks re- Multi-Level Strain Energy DMAP
quiring a substantial amount of time. Thus, it is very
In contrast to the Choleski Decomposition Check,
desirable to have tools that can facilitate and auto-
Multi-Level Strain Energy Check provides informa-
mate thl, process u much as possible. A series of
tion about modeling problems at all three levels (i.e.,
computational procedures were developed in the form
G-set, N-set, and F-set) of model formation in NAS-
of DMAPs. These DMAPs were used to identify both
TRAN. Through a DMAP, the stiffness matrix, and
modeling errors and also provide certain information
the rigid body modes obtained from the grid point
regarding identification of modes, energy _umciated
geometry of the structure, are used to calculate the
with each mode and calculation of modal participation
strain energy of the structure at each of the three
factors. The latter two DMAPs were developed prior
levels of model formation. The same information is
to start of DAMVIBS program at the MDHC. How-
also used to calculate another parameter referred to as
ever, due to their high level of effectiveness and also
the nodal strain to provide further information about
for the sake of completeness they are included here
modeling problems at each of the levels (2). As a
and are briefly discussed in the following sections.
result, any problems which might be caused by the
As a result of applications of these modeling check- improper grounding of the structure (i.e., G-set), in-
out DMAPs to a variety of structures, a common set correct application of MPC equations (i.e., N-set), or
of sources of errors has been identified. Those errors incorrect definition of the SPC constraints (i.e., F-set)
which occur during the a_embly of the G-set stiffness will be identified through examination of these nodal
matrix are due to; (a) the improper specification of strain energy at each level. To demonstrate the ap-
the coordinate couplings where two components which plicability of this powerful tool, it was applied to the
AH-IG NASTRAN model (z). Examination of the N-
are located in different coordinate systems are cou-
pled together improperly, (b) the use of a short beam set strain energy matrix, shown in Table I, revealed
element next to a long beam element, (c) use of a some problems associated with the rotational degrees
large or improper aspect ratio for plate elements, or of freedoms (i.e., the third through sixth diagonal el-
(d) the use of CELAS elements between noncoinci- ements of the matrix are much larger than I0) which
dent points. Each of these modeling practices will are indicative of incorrect application of MPC equa-
result in the ill-conditioning of the G-set stiffness ma- tions. To further identify the degree of freedom as-
trix. In the second and third levels of model forms- sociated with the MPC equation, another matrix, re-
37
furred to as N-set nodalstrain matrix was examined. This technique wu initially applied during dynamic
The lut analysis of the Hughes Advanced Attack Helicopter
(AAH). At the time of application, the model had 9792
ll_ll| liOm fOliO _ t|| , II • |O&L I _l•O_l | e io_ |q_gl_R| _|1
I degrees of freedom. To identify the modal characteris-
iN
it -I.|tOie-t4 I |till-el -t I,lel-eo -I.@SOII4S -I |till-el t.oOt,l-e,
MLII | 0OIl _IOO | ................................... tics of the model, an eigen analysis was performed up
|J i._0ee|-O, .e es_te-e$ _.o|t_OoOO d e4tTo-o$ , 6150|-o_ -|.iiiuo-e_ to 25 Ha. Within this frequency range, eighty seven
| _ viol I ...................................
NI t! -e._oo_|-0t -t.lSOll-•@ -1 t||lo-ot -•.el|•|-o| t tgt41-@l -t.6T4ll-06 modes were calculted where each mode contained an
lOW eigenvector containing 10000 values. Through appli-
$, -O.JODO|olO | lille-Of -|lQl|ode iIHtI_O1 l.ele|l,el $tloJo¢e|
INR g |SO0 _glNg 4 ................................. cation of the kinetic energy DMAP, a filtered modal
il -I.tttlO-t| t I|T|D-O$ 0.$411|°0| a.elell*e| , t?i40_et -i ll4il*Ol
04,W 6 _l fide I ................................... kinetic energy matrix was obtained which contained
only a set of larger values for each mode (4). A quick
Table I. N-set Strain Energy Matrix. examination of the filtered modal kinetic energy ma-
trix revealed candidates for the local or actual struc.
three columns of this matrix, shown in Table 2, which
rural modes. A structural mode is generally identified
were representative of the rotational degrees of free-
by a column containing many large numbers, since the
dom revealed the location of the troublesome grid and
energy is distributed and large portion of structure
the associated degrees of freedom (i.e., grid points
moves together. In the case of local modes, only a few
750g and 15218). Once the associated MPC equation
elements of the matrix have very large values, indicat-
was corrected the DMAP was again applied and sim-
ing only a local area of structure is moving. Figure 3
ilarproblem associated with the MPC equation used
shows a sample of astructural mode identified through
for the engine support location was identified. This this procedure.
problem was then corrected.
Ill Ill I4 I| -IIol II I_ I! _4
Iq -14 Iq -t_i II -I_4
|It In 14 I| -114 II I,I4 Ill iIINI_
In LtI4
_I II_l I-- II -IOllII_
Table 2. N-set Nodal Strain Matrix.
Kinetic Ener][_ _DMAP
One of the key recent improvements in the dynamic
analysis of large finite element models is the devel-
opment of efficient and accurate eillenvalue extraction
techniques. Introduction of such techniques has re-
suited in their applications to more complex systems
and consequently much larger FEMs. As a result, for
the prediction of structural modal characteristics, the
Fig. 3. AAH First Torsion Mode.
analyst is often confronted with the identification and
post processing of large number of high density modal Modal Participation DMAP
vectors. For very large and detailed models: this pro-
cuss is rather tedious and time consuming. C;onse- An important information during studies of the dy-
quently a DMAP was developed which is referred to namic structural response of linear systems is the con-
as Kinetic Energy Check DMAP (3.4). Application of tribution of different structural modes to the total re-
this DMAP results in the caculation of the modal ki- sponse of & selected point or a finite region of the
netic energy associated with each mode and rapidly structure. Such information generally provides valu-
identifies the candidate structural modes. Addition- able insight into the vibrational characteristics of the
ally, such results provide the neceesary information to system and points out areas where structural modifi-
identify the local modes and any possible modeling er- cations could result in improved reeponm. In cur, in
rors. Since the development of this DMAP, it has been applications, such data provides the necessary infor-
applied to a large number of different structures and mation for the identification and selection of an opti-
hu resulted in a substantial saving of man|ours and mum location for vibration control devices. For this
the elimination of costly and time consuming plotting purpose, a DMAP was developed which calculates the
process of the local/trivial modes. modal participation factors associated with response
of a selected location of the structure iT). For the ap-
38
plicationofthisDIVlAPf,requencryespons(eSOL30) Test Procedure
is
used. Application of this technique to a vibration
During excitation, data was taken over a frequency
reduction study is discussed in detail in Ref. 5.
range of 3.75 to 50 Hs except for the tail rotor in-
put cases which extended this range to 200 Ha. The
IV. Experimental Efforts frequency was stepped up in increments of 0.5% and
the input dwelled for a few seconds at each frequency
step to allow the response to come to quasi-steady
Test Objective state. Data was taken for all accelerometers at each
frequency step. Each dwell and measurement step
The main objective of the shake test was to obtain an
took about 5 seconds to complete, so an entire test
experimental data base describing the vibration re-
(3.75 to 50 Ha) could be run in less than 45 minutes.
sponge of the test vehicle. This data base consisted
mainly of transfer functions of response acceleration instrumentation
to input force versus input frequency for various men-
surement locations throughout the fuselage structure. A total of 102 accelerometers were mounted on the
Although the test was not a modal survey test, the aircraft at 39 locations and four were mounted on the
major airframe modes were extracted from the test gantry and suspension system. Each accelerometer
data. These modes provided insight into the basic vi- was tested in a mechanical system, comprised of a
bration characteristics of the fuselage and aided in the load cell and a known free mass. The mass was driven
correlation with NASTRAN model. in the test frequency range. The resulting transfer
function from each unit was used by the computer to
Test Vehicle convert voltage to acceleration and to adjust the phase
at each frequency step.
The test vehicle used was the U.$. Army's AH-64A
Advanced Attack Helicopter. The testing was per- The accelerometer locations were chosen based on
formed with the vehicle in the primary mission con- three criteria: (1) to identify the response at key lo-
figuration le_ The main rotor hub and blades were cations such as pilot seats, engines, hubs, etc.; (2) to
replaced with a rigid steel fixture which was attached describe fundamental modes of the airframe; and (3)
to the static mast in a manner similar to the actual to identify important local modes such as those of the
hub. The dummy structure was equivalent to 100_ wings.
of the weight of all of the actual items except for the
rotor blades. The blade weight was reduced to 60% The accelerometers were mounted on one inch cubic
of the actual weight to more closely represent the dy- fiberglass blocks which were epoxied to the airframe.
namic equivalent of the rotating system. The blocks were oriented such that their faces were
aligned with three orthogonal axes of the ship. Each
Setup block had one to three accelerometers attached to it.
The test vehicle was suspended from agantry. Air sus- The use of a large number of fixed accelerometers
pension springs located at the top of the gantry pro- proved to be much more effective than a few roving
vided vibration isolation between the test vehicle and accelerometers, as is usually done in this type of test-
the gantry structure. This method minimised feed- ing. The chief reasons for this are as follows. The
back from the gantry modes of vibration into the test accuracy of accelerometer positioning was greatly in-
aircraft. Link chain was used to attach the air spring creased. Errors in mounting and polarity were min-
system to the dummy main rotor hub. This technique imised because the accelerometers remained fixed in
removed the tendency for the aircraft to yaw. Sinu- position for the entire test. Moreover, the time re-
soidal vibration excitation was applied to the test ve- quired for testing was greatly reduced because only
hicle at the main rotor hub and at the tail rotor. Three one frequency sweep was necessary for each test case.
forces (longitudinal, lateral and vertical) were applied
to the main rotor hub, as well as two moments (pitch Data Acquisition and Control
and roll). These forces and moments were applied
The system used for data acquisition and control
at the vertical and station positions equivalent to the
was 100% computer controlled and exclusively used
blade plane and the center of rotation. Three forces
Hewlett Packard instrumentation. At the heart of the
were applied at the tail rotor location: longitudinal,
system was the HP9836 computer/system controller.
lateral and vertical. The tail rotor excitation point
was at the center of rotation and at a lateral position At each frequency step, all data channels were scanned
which is half way between the two rotor planes. The and 16 readings were taken over one cycle of vibration.
flight tail rotor equipment was on the aircraft during This data was then sent from the HP6942A scanner
the entire shake test.
39
to the HP9836 computer where magnitude and phase tion tends to deteriorate gradually as the frequency of
data was extracted by means of a Discrete Fourier the response increases. A comparison of natural fre-
Trandorm. By this method the first harmonic was quencies found by test and calculated by NASTRAN
extracted while the higher harmonics, up to the 8th, is given in Table 3. Typical response correlation plots
wore rejected. are shown in Fig. 6.
TEST
TA_I./XX_TORSION
4.42 4.28 -3.2
LYeVE_ICAL 8_DDIG
5.45 5.39 -1.1
Igm_ATERAL_
9.39 8.79 -6.4
10.07 9.78 -2.9
12.11 12.26 1.2
12.48 12.74 2.1
S'04_'TRICWIN_8DIDIlqO 13.38 15.15 13.2
/¢rFI-SYHt_. _ mini143 13.85 15.37 Ii.0
STABILM_ 20.44 17.78 -13.0
Table 3. Correlated Modes
The problem areas in the correlation were the en-
gines, stabilator, and the wings. However, much in-
provement was obtained in the vertical response of the
Fig. 4. Fuselage First Vertical Bending, 5.45 He. wings based on the preliminary correlation results. In
addition to improving the existing finite model, much
knowledge gained in the correlation effort will be ap-
The essential results of the shake test were the re- plicable to future analyses. Shake test results can of-
ten be used to refine an existing finite element model.
sponse transfer functions. Additional results include
This is accomplished by comparisons of experimental
natural frequencies and mode shapes which were
and analytical melts. Tiffs comparison initially in-
gleamed from the transfer functions. Although not es-
dicates whether or not there are errors in the model
sential, this data ,dded in the correlation of the NAS-
and mists in locating probable areas in which these
TRAN model and provided insight into the vibration
characteristics of the aircraft. A sample mode shape errors may reside. If an error has been caused by an
incorrect assumption, then the correlation study can
from the test data k presented in Fig. 4. Natural
provide a guide as to how the problem might be cor-
frequenies were estimated from the data by mesas of
an indicator function 1o}. When the value of the first rected. Finally, the test comparison provides a stan-
function approaches unity, a natural frequency is in- dard by which the degree of enhancement can be mea-
dicated. Sample indicator function results are shown sured. The following discussion describes an example
of how shake test results were utilised to enhance the
in Fig. 5.
NASTRAN finite element model of the AH-64A air-
frame.
IIlltlllll Irlill III
l,lll1111111111 I IIMI + hlll+ Pu. iiii.._i_ l+._.._.,_
Initial comparison of the frequency response curves
$
obtained from the test with those predicted by NAS-
TRAN indicated that, for some cases, there were dis-
creptncies between the two sets of results. The most
s,
noticeable problems appeared in the responses of the
i wings, the engines and the stabliator.
"I
e' Examination of the deflected shapes obtained from
test and analysis helped to farther localise and idea-
|
tify errors in the model. A specific example of such er-
,:11 I_l.l@ 'I11.£P4 li II Ii ..IS I),M 4_1,1'1 !
ror is a mode at approximately 8.5 Hs which is shown
Fig. 5. Simple Indicator Function Results. in Fig. 7. This mode is predominantly a wing mode
although it is significantly lower in frequency than the
wing modes found in the teat results. In addition, one
V: Correlation and M_qd_F_nhancement
wing ks undergoing pare vertical bending, while the
other is experiencing nearly pure wing torsion. Such
An excellent correspondence between test and NAS- asymmetric behavior was not found in the test results.
TRAN results was obtained for the frequency re- Therefore, it was concluded that there were errors in
sponses up to 13 Ha. This includes the first six modes the wing portion of the finite element model.
found in the shake test. Above 13 He, the correla-
4O
Afterclose
scrutiny of the wing portion of the model,
problems were identified and corrected. The problems °1
were mainly uymmetries in the lumped muses and
element products of inertia, overly stiff modeling of
the pylons, and the omi_ion of the trailing edge. The O_[O ,00|?
wing trailing edge wu ignored in the static model be-
cause it wM considered secondary structure.
fIST
- -- NASTIAM
- o GRIO 900055
erie
FREOUENCY CHZ}
t_
w E_CITAfIO_ _O_GITUOIN_ • _PR _ASI 22-SEP-O_
w_
PILOt SEAT. _0NGI_UOIN_ N[SPONS[ _3_J9.33
e._o
h-
I
(c) Longitudinal Response at
Pilot Seat
o
r_sy
. -- NAS_NAN
8
_a tI}.00 _e. 00 3O,OO 40.00 50, G_IO 24g0_
I:REOUENC_'(HZ)
C3
I[I¢ITATIOII, L0JIG|T_INM. e M/I IqAIT a_-llP-lS
"IAIgl PlOIOII O_. LQFIIeIfUOIIIAI. IllP_qS[ _I,_6, oS
(s) LonqLtudimtl Response st Naln
Rotor Hub
o o
TEST
- - I&IIIAN
"Ja_
° O' GNID 351J
, ,,,,,./
0
I O • •
g
_'.oo
,O. 30 _0. O0 _0.00 _0. O0 _,0.0:3
r_[OU[NC_ (HZ)
EgCITAT|Oq, 1[R/ICq. • q/l qASt 235[P-86
•olr ENGINE (AFr}. fENflC4L q[SDOlSE
.d It b (d) Vertical Response at: Enqine
_0 ¸
/in I1
-0. O0 _0.00 _0.00 _0._0 *0.00 50.30
FREOUEMC?(_Z9
iNCITATION. LONGIT_INAA, • _/_ MASr
FUS|LAG| SYAYIO# 3S, V|NYICAL RiSPON$i
(b) Vertical Response at Aircraft
Nose
Fig. 7. Wing Mode at 8._ HE.
41
Witlz the improvements made to the model, the ana- static model for dynamic analysis was generally suc-
lyst can use the entire inventory of test results such as cessful, some of the assumptions made for statics were
frequency response plots, deflected shapes, and modal not good for a dynamic model. Two examples were
frequencies to examine the effect of the improvements. ignoring the trailing edge structure of the wing sad
An excellent example of this is the improvement of the the frictional load carrying capability of bolts. Some
vertical response of the wing as s result of the changes assumptions made for statics were previously recog-
implemented in the model. See Fig. 8. nised and corrected to meet dynamics requirements.
!o f An example of this was the shear panel effectivity.
-- ,¢lf IAIIRN Ul0 }0]1, Regarding the mass distribution, some of the assump-
flllT - -FIN_
tions and methods were not strictly correct. For ex-
ample, the automated mass lumping routine does con-
sider connectivity when lumping the masses, nor does
it rigorously account for rotational mass moments of
inertia.
0o VII. Vibration Reduction Studies
D
m
Generally, use of model reduction procedures for the
purpose of increasing the computational efficiency is
j / t
of great interest in a dynamic analysis. This is espe-
,m s w FIlE_M Cv o(sN.0@Z) _NLO@ cially true in dynamic optimisation applications. Con-
I|¢IIAIiD, LaNI|WIIIlaL • _ i_S! sequently, a preliminary study was done to explore the
S|MmIMNI viN. t_l[Iflt m HHSt applicability of &reduction procedure to a vibration
Fig. 8. Improved Correlation of
reduction study. A model reduction procedure was
Vertical Response at Wing Tip.
initially developed and was used in vibration study.
Model Reduction Procedtlr__
VL Ge_nera/AAp.plication of Test Results
A computational procedure for the reduction of large
airframe finite element models was developed is). This
A comprehensive shake test, such as the one per-
procedure, which has been implemented as a set of
formed under this program, not only helps to enhance
DMAPs, results in a significantly reduced model while
an existing finite element model of the test specimen,
retaining the .essential dynamic characteristics of the
but also provides valuable guides for enhucing other
full-sized model. This procedure was applied to a
models and future modeling efforts. Test results may
slightly modified version of the airframe dynamic fi-
be used to verify modeling practices used in the past,
nite element model of AH-64A Attack Helicopter. A
to identify questionable assumptions and practices,
mathematicaly reduced model with significantly less
and to provide a reasonable level of confidence in the
DOFs was obtained. This reduced model, is shown in
analysis.
Fig. 9.
it is usually necessary to make assumptions in prepar-
ing a finite element model. The validity of these
assumptions must be verified by testing. In this
particular case, the test results confirmed many of
the assumptions used in modeling the AH-64A heli-
copter. For example, the assumption that stringers
and longerons carry axial loads while skins and webs
cm'ry shear loads was verified. The effectiveness of
using a static model for dynamic analysis with dy-
namic reduction was also confirmed. Good correlation
emociated with main rotor mast responses confirmed
our modeling technique regarding the main rotor sup-
port structure ud the overall representation of the Fig. 9. Apache Stick Model.
airframe.
This model is an accurate representation of the global
The correlation of the test results revealed some as- behavior of the full model. The resulting reduced
sumptions and practices which were not quite correct. model resulted in a substantial reduction in the com-
The following are some examples. Although using a putation time. This reduced model which has g3 grid
42
pointsand atotalof498 DOF isonlya mathematical the totalresponse of each location,were calculated
representationofthe reduced (stick)model (i.e.t,he {7}.Subsequent tothe identificatioonf thedominant
elasticpropertiesaredefinedinterms ofstiffnesmsa- modes, a designsensitivityanalysisstudy (SOL 53)
trixratherthan physicalelementssuch as bar,beam, was performed toidentifythepertinentmodel param-
etc.).However, furtherstepscouldbe takento caxry eters{e.g.,crosssectionalarea,areamoment ofiner-
thismathematical reduced model one stepfurtherand tia,etc.)which havethemost effecton thevibrational
developan equivalent"physical_reduced model. This responseattheselectedlocations.Once theseparam-
processwas not pursued. Instead,the Umathemati- eterswereidentifiedc,ertainincrementalchanges were
cal"reduced model was adapted forsensitivitaynaly- made to each ofthem individuallyor a combination
sisstudy which willbe discussedinthefollowingsec- oftheseparameters toreduce thevibrationatthese-
tion.Followingthereductionprocess,an eigenanal- lectedlocations.
ysiswas performed toevaluaetheaccuracyofthedy-
namic reduced model. Figure 10,representsthe first Inconjunctionwiththevibrationreductionstudy,the
verticalbending mode. contributionofeachmode tothetotalresponseofthe
selectedportionofthestructurewas determined atthe
locationofinterest.This locationwas thetipofthe
verticaltailofthe AH-64A reduced model. For this
purpose, an in-house DMAP (7)program was used
inconjunctionwith the MSC/NASTRAN modal fre-
quency response solutionsequence (SOL 30). Figure
•11 shows the four modes with the largestcontribu-
tionstothetotalresponseoftheselectedpoint,when
theaircraftissubjectedto afour-per-revverticalhub
excitation.
Fig.I0.StickModel FirstVerticalBending.
(TIP OF VEWrlCAL TAIL)
I0
To furtherquantifythedegree ofcorrelationbetween
thetwo models, an in-housecomputer program which
provided a systematicway ofchecking thedegree of
correlationbetween frequencies,mode shapes or a
combination ofthe two,was used (s}.Table 4 shows "1 e2
theresultingcorrelationmatrix between thetwo mod-
[email protected]
els.
FRF-_UENC¥ (HZ) Monl_ SHAPE
MODE., FULL STICK CORRELATION"
TAILBOOM TORSION $4S $12 OM
15"I' VF_T BENDING tCO SIS 0_
IST LATI_ItAL BENDING l0 70 97Q 084
SYM ENG|Nf, YAW AND PITCII It 44 II (7 0g0 @_ •Bin @,_6@ O.le_ql_uBz.M(Os@_ O.Nnm D,@_e e._ elm
VF,RT TAIL iX)NG. BF,,NDING 1197 12.31 091
MAST i_)NC, BF_NI)IH(; 13,41 1433 087 ,<nlc K _I)LrL
ANT_YM [NGINF, YAW 1416 1643 070 MO_-I?, I0 e03 [q'L -- -_- •, 6II_ R]L
,_rYABILATOR YAW 2963 IgmO 081 M01_-20.21,9110 ilZ -- - IIIOOE 15 1?2e@IIZ
Fig.11.StructuralModal Response.
• I.M : PgRFF_,'T (_)RRELATION
@W : NO CORR£LATION
Table 4.Modal CorrelationMatrix. As can be seen,mode 17 contributesthe most to
thetotalresponse.Inaddition,examination ofother
The correlationfactorsindicatedinTable 4 axebasi- modes and the resultsobtained from the DMAP in-
callyindicativeofthedegreeofcorrelationbetween a dicatedthat the fifteenth mode (i.e., 17.268 Ha) to
pairofglobalmodes. be the next highest contributor to the response of the
point of interest. Therefore, these two modes (i.e.,
VibrationReduction study
modes 15 and 17) were selected to be used in a follow-
ing design sensitivity analysis. This selection process
was repeated for two other types of hub excitations
Inadditiontothedevelopment and applicationofthe
(i.e., longitudinal and lateral excitations) and a simi-
model reductionprocedure,another studywas made
lax pattern was obtained.
to examine the applicabilityof the reduced (stick)
model to a vibrationreductionstudy. For thispur-
To identify those parameters which have the most ef-
pose, the reduced model was subjected to different
fect on the response of selected normal modes in the
four-per-revhub excitationsand themodal frequency
area of interest of the structure, a sensitivity analysis
responses(SOL 30)ofdifferentlocationsofthestruc-
was performed. For this study, the tailboom which
ture,togetherwith the contributionofeach mode to
43
is in the close proximity of the vertical tail was se- VIII. Concluding Remarks
lected. The cross-sectional area, the two area mo-
ments of inertia, and the torsional constant parame-
A summary of the MDHC's effort related to the devel-
ters were selected as the design variables. The two
opment of DAMVIBS dynamic modeling guidelines,
dominant stick model modes (i.e., modes 15 and 17)
testing and the correlation studies has been presented.
which represented mainly the tailboom vertical and
As a result of this work, a set of comprehensive mod-
lateral bendings, were selected as the "constraint" pa-
eling procedure and check out tools have been gener-
rameters. The design sensitivity analysis was per-
ated which have been used in modeling of large air-
formed for all twelve tailboom frame segements and
frame structures. These procedures which been used
a set of sensitivity coefficients obtained. These are
in the ongoing enhancement process of the exiting
shown in Fig. 11 and 12.
MDHC product models, have also been applied to the
newly developed product models. Throughout this
(MODg-Ill. 17_311 Ill) program, a substantial amount of experienced have
been gained in creating other reliable airframe finite
element models (t°) which are used during the design
process. Through such improved modeling capability,
a better estimation for man-hour requirements and
W O@Oa
scheduling process is now possible.
In relation to performing shake tests and efficient use
of this data, our capability has been substantially en-
l hanced. This has been accomplished through use of
experience gained during this program in the preper-
ZO 30 40 50 (JO 70 II.O |+ I§_O IlJ I|.0 ation of better test plans, performing the the shake
X-,_'TATIfllq
.S'I'_K MOI_L tests where issues such as support of test structure,
_J CHANGE
A I-HAI_ ;E applications of loads or load levels are of great im-
II rHANI;[
12 _'XANI;F. portance. Reduction and application of test data to
the model resulted in improved corrolation method-
Fig. 11. Sensitivity Coefficients, Mode 15
ology which also brought into focus the shortcomings
associated with different correlation methods and the
Oln IMi)I)E_IT, ltAm llJ) inaccuracy associated with higher analytical modes.
Further examination of the test data pointed out the
Jbtm degree of structural nonlinearity and provided insight
IL[Il into damping characteristics of the aircraft structure.
The exchange of information between MDHC and
+04 other three companies provided a means to compare
methodologies used by each group and the associated
N
results. Such an exchange of information resulted in
[
improving certain areas of our models. One of these
+. t,,.I L,_ . .I, .....
areas was inclusion of secondary structural compo-
go Z+ _111 40 50 I0 ?+ 1.0 lO lO.l llO l;t.ll
X-+CI'ATIOIq nents which have resulted in improving the correla-
,_'TH'K MC_.L
tion results. Finall, these studies have pointed out
_._A f'|IAN(;[ I_J q-HAN(;I[
III_ Ii"'HIIAAN_G-'_[ new challenges in terms of limitations associated with
FEA which need to be further investigated.
Fig. 12. Sensitivity Coefficients, Mode 17
A summary of the lessons learned during these studies
are listed as follow:
Examination of these figures revealed that the two
area moments of inertia parameters have the most el-
fect on the frequency placement of the two selected The staticfiniteelement model may be usedfor
modes. Consequently, these parameters were altered dynamic analysisaftermaking theproper mod-
which shifted the frequencies of these two modes away ifications.
from the four-per-rev excitation frequency _). This The proper modeling of the mass distribu-
process resulted in a reduction of the vibration level tionand representationofsecondary and non-
at the tip of vertical tail. Similar changes were also structuralcomponents isessentialto accurate
made to the same locations of the full model and the
vibrationmodeling. Automation ofthisproce-
response of the vertical tail was calculated. dure greatlyreducesmodeling time.
44