A plan was formed for developing a comprehensive, second-generation system with analytical capabilities for predicting performance, loads and vibration, handling qualities, aeromechanical stability, and acoustics. This second-generation system named COPTER (COmprehensive Program for Theoretical Evaluation of Rotorcraft) is designed for operational efficiency, user friendliness, coding readability, maintainability, transportability, modularity, and expandability for future growth. The system is divided into an executive, a data deck validator, and a technology complex. At present a simple executive, the data deck validator, and the aeromechanical stability module of the technology complex were implemented. The system is described briefly, the implementation of the technology module is discussed, and correlation data presented. The correlation includes hingeless-rotor isolated stability, hingeless-rotor ground-resonance stability, and air-resonance stability of an advanced bearingless-rotor in forward flight

Yen, Jing G.

Yin, Sheng K.

English

NASA Technical Reports Server

N88- 2716 1
AEROMECHANICAL STABILITY ANALYSIS
OF COPTER
Sheng K. Yin
Engineering Specialist
and
Jing G. Yen
Manager of Flight Technology
Bell Helicopter Textron
Fort Worth, Texas
Abstract
A plan has been formed for developing
a comprehensive, second-generation system
with analytical capabilities for predict-
ing performance, loads and vibratlon,
handling qualities, aeromechanical stab±l-
ity, and acoustics. This second-genera-
tion system named COPTER (COmprehensive
Program for Theoretical Evaluation of
Rotorcraft) is deslgned for operational
efficiency, user frlendliness, coding
readabllity, maintainabllity, transport-
ability, modularity, and expandability for
future growth. The system is dlvided into
an executive, a data deck validator, and a
technology complex. At present a simple
executive, the data deck validator, and
the aeromechanical stabllity module of the
technology complex have been implemented.
This paper describes briefly the system,
discusses the implementation of the tech-
nology module, and presents correlation
data. The correlation includes hinge-
less-rotor isolated stability, hingeless-
rotor ground-resonance stability, and
air-resonance stability of an advznced
bearingless-rotor in forward flight.
Introduction
Each helicopter manufacturer has em-
ployed several analytical methods of vary-
ing complexity to determine loads and
vibrations, aeroelastic stability, stabil-
ity and control, performance, and acous-
tics. It was the consensus of the U.S.
Army and the U.S. helicopter industry that
these first-generation methods had limited
capability, since they were not generally
applicable to all types and slzes of heli-
copters, were difficult to maintain and
improve, and were not truly comprehensive.
In 1976, a decision was made by USAAMRDL
Presented at the ITR Methodology Assess-
ment Workshop, NASA Ames, June 21-22,
1983.
271
at Fort Eustis to develop the Second-Gen-
eration Comprehensive Helicopter Analysis
System (2GCHAS) using modern software
design techniques and modules for the
technology complex. In order to maintain
its competitive position in the technical
community and assist the government in the
development of 2GCHAS, Bell Helicopter
Textron Inc. (BHTI) Inltiated the COmpre-
hensive Program for Theoretical Evaluation
of Rotorcraft (COPTER).
The COPTER System
The COPTER system is designed for
operational efficiency, user friendliness,
coding readability, maintainability,
transportability, modularity, and expand-
ability for future growth. The system is
divided into an executive, a data deck
validator, and a technology complex. The
source is coded in VS FORTRAN to take ad-
vantage of the structured programming fea-
tures. Each subprogram has a prologue to
explain its function, inputs and outputs,
computational method and sequence, crea-
tion/modification dates, and authors.
Varlous built-in diagnostic options are
available throughout the program.
A user can invoke the executive of
the system at a TSO (IBM's Time Sharing
Option) terminal by typing the command
"COPTER." The executive then presents a
menu on the screen with options available
to the user. These options include edit-
ing input data, running programs inter-
actively, browslng outputs, and submitting
batch jobs. The executlve can also prompt
the user for inputs and interface inter-
actively with the user.
The executive takes advantage of the
System Productivity Facility (SPF), an IBM
product, to invoke the editing and brows-
Ing options. This allows full-screen
edltlng and scrolling of the input data
and browsing the output immediately after
running the programs. Any error messages
will be displayed on the terminal screen.
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The executive drives two programs.
The first program is the Data Deck Valida-
tor (DDV), which reads inputs, interprets
key words, checks for errors, and gener-
ates error messages wherever appropriate.
It also retrieves block data from the
master data base, creates the run data
base, and generates an annotated echo of
the input data. The second program con-
tains the technology modules of the COPTER
system. It reads the run data base as its
input, executes the user-specified tech-
nology modules, and generates engineering
data that can be printed or plotted. The
flow chart in Figure 1 summarizes the
COPTER system.
Aeromechanical Stability
In recent years, the helicopter com-
munity has been challenged by the develop-
ment of hingeless and bearingless rotors.
The area of greatest challenge has been
predicting aeroelastic stability chalac-
teristics for such rotors. As a result,
the U.S. Army awarded several methodology
assessment contracts to helicopter com-
panies in 1981. The results were encour-
aging, but inconclusive (References 1 and
2).
Bell has been working toward the de-
velopment of viable hingeless and bearing-
less rotor systems for over a decade. The
effort has led to an experimental hinge-
less rotor (Reference 3), two production
hingeless rotors (e.g., Reference 4), and
a successful advanced bearingless rotor
(Reference 5).
Recognition of Bell's in-house design
requirements and the lack of a comprehen-
sive capability in analyzing stability
characteristics of hingeless and bearing-
less rotors resulted in the decision that
the aeromechanical stability module should
be the first technology module to be im-
plemented in the COPTER system.
Analytical Model
Modal representations are used for
the rotor and the airframe dynamics. A
two-dimensional, strip, quasi-steady
theory is employed for the blade aero-
dynamics. The effects of compressibility,
reverse flow, and stall are modeled using
the aerodynamic table look-up technique.
A dynamic inflow model similar to the one
discussed in Reference 6 is included as an
option. Dynamic coupling between the
rotor and the airframe is achieved by
using time-invariant mass matrix methodol-
DATA lD{CK
ALIDATOR
ANNOTAI_) 1ECHOOF rA
USER I _IERROR
INPUT_ MESSAGES
INTERACTIV_EXECUTIV_
• PROMPTUSER FOR INPUTS
• EDIT DATA
• RUN PROGRAMS (DDV & ffCHNOLOGY COMPLEXI
• BROWSEOUTPUT
I ERRORMESSAGES
DATA RUN
DATA
BASE
BEGIN
PROCESS
i
DATA TECHNOLOGYCOMPLEX
1
I ENDPROCESS
BEGIN END
TASK TASK
TRIM STAff TIME-HISTORY AEROMECHANICAL COMPONENT/ PERFORMANCE
VALUES RESPONSE STABILITY SYSTEM LOADS
Figure i. The COPTER system.
272
QI_,IGINAL PAGE IS
OI_. 1)_9R (_t)ALFI_
ogy (Reference 7). The time-invariant
mass matrix capability also facilitates
the modeling of various hub types, such as
bearingless, hingeless, gimbaled, and
teetering rotors. Hub loads are calculat-
ed by either the mode-deflection or the
force-integration method. At present, the
analysis interfaces with the C81 computer
program to obtain trim values.
Two methods of solution are available
to the analysis: multiblade coordinate
transformation and Floquet transition
matrix. The multiblade coordinate trans-
formation is used for multibladed rotors
in hover, while the Floquet method is used
for two-bladed rotors and all forward-
flight conditions. The solution is pre-
sented in eigenvalue and eigenvector forms.
-4
T
o"
z
_--
-2
=<
A -1
o EXPERIMENTAL
-- COPTER, WIG DYNAMIC
'NFLOW"';>S0
°
0 o
_.//<O INPII_ STRUCTURAL DAMPING,
o: -1_3 SEC-1
CASE A/2 OF ITR METHODOLOGYASSESSMENT
i i i i i
2 4 6 8 10 12
BLADE PITCH ANGLE, deq
Correlations
Validation is one of the most impor-
tant phases in the development of any
analytical design tool. The aeromechani-
cal stability analysis has been validated
by comparing the results with those of
established computer programs and by cor-
relating with measured model data. The
correlations shown in this paper include a
hingeless-rotor isolated stability, a
hingeless-rotor ground resonance, and sta-
bility of an advanced bearingless rotor
with simulated body degrees-of-freedom in
forward flight.
The hovering data of a hingeless-
rotor isolated stability were obtained
from cases A/2 and A/4 of the Army Inte-
grated Technology Rotor (ITR) methodology
assessment contract. A complete descrip-
tion of the two-bladed rotor model is pre-
sented in Reference i. Case A/2 was for a
uniform blade with a soft feathering flex-
ure, but with no precone or droop. Case
A/4 was for the same blade as case A/2,
but with a 5 ° hub precone. Measured and
computed blade lead-lag damping values vs
blade pitch angles were plotted at a rotor
speed of i000 rpm and are shown in Figures
2 and 3 for case A/2 and case A/4, re-
spectively. For both cases, it was found
that the effect of the dynamic inflow on
the blade inplane damping was small. An-
alytical data shown in Figures 2 and 3
were obtained without employing the dy-
namic inflow model.
Figure 2.
-4
T
-3
o"
zB
__ -2
&
Figure 3.
Lead-lag damping vs blade pltch
angle, no precone or droop,
soft feathering flexure, i000
rpm, isolated two-bladed hinge-
less rotor.
o EXPERIMENTAL
-- COPTER, WIG DYNAMIC INFLOW
INPUT STRUCTURAL DAMPING,
o = -1.03 SEC-I 0
CASE A/4 OF ITR METHODOLOGY _ /o
3 2 \ 4 6 8 / ]0 12
BLADE PITCH ANGLE, deg
Lead-lag damping vs blade pitch
angle, 5 ° precone, soft feath-
ering flexure, i000 rpm, isola-
ted two-bladed hingeless rotor.
A correlation with ground-resonance
data measured on a model-scale, three-
bladed hingeless rotor, coupled with body
pitch and roll degrees-of-freedom, was
performed. Descriptions of the experi-
mental model, experimental results, and
analytical representation of the model
hardware can be found in Reference i.
This was case C/I of the ITR methodology
assessment contract. System frequencies,
damping values of lead-lag regressing
mode, and body pitch and body roll modes
were plotted as rotor speeds varied from
0 to i000 rpm. The blade was untwisted
with 0 ° blade pitch angle. The analysis
was conducted with and without the dy-
namic inflow. For this case (coupled
rotor/body), including the dynamic inflow
in the analysis improved the correlation.
273
Data in Figures 4 through 7 show correla-
tions of system frequencies, lead-lag re-
gressing mode damping, body pitch mode
damping, and body roll mode damping, re-
spectively. Analytical results, with and
without the dynamic inflow, are presented
in Figures 5 through 7. Computed system
frequencies depicted in Figure 4 were ob-
tained with the dynamic inflow included in
the computation; those calculations with-
out the dynamic inflow were not as good.
To avoid further cluttering of the data
in Figure 4, computed frequencies without
the dynamic inflow were deleted from this
figure.
It should be pointed out here that
the analytical data shown in these figures
were obtained by using the force-integra-
tion technique in the calculation of hub
forces and moments. The results showed
distinct frequency shifts in the body/
lead-lag crossings when the mode-deflec-
tion method was used. The difference in
the results between the mode-deflection
method and the force-integration method
was attributed to the fact that the mode-
deflection method did not include the com-
plete dynamic coupling terms.
,Ij0' /l _'_P /
d
---COPIIR. Wl DYNAMIC INFLOW /o
6 /
ITR M[THODOLOCY ASSISSMENT /o
/ R
5 /o
.o
_- ,o
0 .000,0_ '_-'0--0 4' -0 _0-0 <>-_C_
.i_;jP @ k\ BODY ROLE l@)
"g_n _ _ o x_ n r_r'Jl_qT r'ru o- 1] "0
14]_,j p_ \ BODY PITCH _rM,o
Ox /
/
" _ "o ,o
II
\ / R _
S
200 400 600 _00 1000
ROTOR SPHD, [pro
30
-2.5
,T -2.0
_z -I.5
i
-I0
-.5
/
/
--COPTER, WlO DYNAMIC INFLOW //
- -COPTER, Wl DYNAMIC INFLOW //
SYMBOLS ARE MEASURED DATA " o
CASE CI] OF ITR METHODOLOGY ASSESSMENT / _ _ [] o
(Qo
208 e_O _0 800 |000
ROIOR SPEED, rpm
Figure 6. Correlation of body pitch damp-
ing, flat pitch.
Figure 4. Correlation of ground resonance
frequencies, flat pitch.
_' -- CORTLR WIO DYNAMIC INFLOW
' _ A COPffR Wl DYNAMIC INFLOW
CA_I ill [If IIR _IRO[X)IOl;Y AbSlbbMlNl _ 'o
R_
ROTOR b l'l I l), rpm
-4.0
-3.5
-).O
/
-2.5 / / /
.'7 -2 0 -_
Ij // ; o
Do _ _- _
COPIER, W/O DYNAMIC INFLOW /_
- COPTER, Wl DYNAMIC INFLOW /
ARE MEASURED 0ATA / /SYMBOLS
/
CASE Cl] OF ITRMETHODO[OOY ASSESSMENT / / "- - - 0 0
0
0
_0 0
ROTOR 3PEID, rpm
Fzguze 5. Correlation of lead-lag regres-
sing mode damping, flat pitch.
Figure 7.
27J4
Correlation of body roll damp-
ing, flat pitch.
ORIGINAL PAGE I8
OF, POOR QUALITY
ORIGINAL PAGE l_
OF_ POOR QUALITY,,
A correlation of aeromechanical sta-
bility in forward flight was made by using
experimental data measured on a one-fifth
scale model rotor with an advanced bear-
ingless hub. Descriptions of the experi-
mental apparatus and procedures are pre-
sented in Reference 8. The particular
rotor and body used for this correlation
effort were the baseline rotor and the
baseline fuselage configurations identi-
fied as R-I and F-2, respectively, in
Reference 8. The rotor had a hub precone
of 2.75 ° with no blade droop or sweep.
Correlation of blade regressing in-
plane frequency (fixed system) and lead-
lag damping (rotating system) vs rotor
speed at a tunnel speed of 27.7 kn and ig
rotor thrust is shown in Figure 8. Mea-
sured data for body pitch and roll mode
frequencies were not available. However,
computed body pitch and roll frequencies
are included in Figure 8 to indicate the
rotor speeds where the regressing inplane
mode crosses the body modes.
A correlation of regressing inplane
frequency (fixed system) and blade lead-
lag damping (rotating system) vs rotor
thrust at 750 rpm and a 27.7-kn tunnel
speed is presented in Figure 9.
6
z
-n
o 4
u_
2
Z
z 0
_D
O
I I
O 1.0 2.0
THRUST, g
8
5
4
2
>-
x
-- 0500La.
8
=--
Z
-- 4
._ 2
_C
o
508
Figure 8.
REGRESS ING IN-PLANE
" _ o_ 80DY _ITCH
/ BODY ROLL
I I I 1 I
600 700 800 9O0 10O0
ROTOR SPEED, rpm
% : 2.750
SHAFT TILTED 30 FORWARD
TUNNEL VELOCITY • 27.7 KN
o MEASURED
COPTER
o o
i i i i
608 7O0 8OO gO0
ROTOR SPEED, rpm
I
lOo0
Correlation of frequency and
damping vs rotor speed in for-
ward flight, ig thrust.
E
o
z
6
4
2
0
a = 2.750
o
SHAFT TILTED 3o FORWARD
TUNNEL VELOCITY = 27.7 KN
o MEASURED
-- COPTER
o
o
o
I J
O 1.0 2.0
THRUST, g
Figure 9. Correlation of inplane frequen-
cy and damping vs rotor thrust
in forward flight, 750 rpm.
Concluding Remarks
A second-generation comprehensive
aeromechanical stability analysis has been
developed as part of the overall technol-
ogy capabilities of the COPTER system.
The technology complex of the system is
modularized. The system, therefore, has
great potential for growth and improve-
ment, and new physics can be incorporated
at any point of the COPTER life cycle.
The use of dynamic inflow improves
the ground-resonance correlation.
The mode-deflection method usually
does not include the complete dynamic
coupling terms, as does the force-inte-
275
gration method. Its application to theground-resonanceanalysis may lead to
erroneous rotor/body crossing and incor-
rect damping.
Application of the Floquet transition
matrix to aeromechanical stability in for-
ward flight produces eigenvalue and eigen-
vector solutions. This eliminates most of
the shortcomings associated with a time
history solution.
Acknowledgement
The authors would like to acknowledge
the contribution of Mr. P. Y. Hsieh and
Dr. Tom Waak in the Scientific and Tech-
nical Computing Department and Dr. Gene
Sadler in the Rotor Dynamics Group at Bell
to the planning and design of the COPTER
system and implementation of the aero-
mechanical stability analysis.
8. Weller, W. H., "Correlation and
Evaluation of Inplane Stability Char-
acteristics for an Advanced Beaing-
less Main Rotor," NASA CR-166448, May
1983.
References
1 .
2.
3.
4.
5.
6.
7.
Yen, J. G., "Integrated Technology
Rotor Methodology Assessment," Final
letter report by Bell Helicopter
Textron Inc. to Contract No. NAS2-
10872, ii December 1981.
Anonymous, "ITR Methodology Assess-
ment Workshop," NASA Ames, 21-22 June
1983.
Cresap, W. L., Myers, A. W., and
Viswanathan, S. P., "Design and
Development Tests of a Four-Bladed
Light Helicopter Rotor System,"
Journal of the American Helicopter
Society, January 1979.
Cresap, W. L., and Myers, A. W.,
"Design and Development of the Model
412 Helicopter," Preprint No. 80-56,
American Helicopter Society, May
1980.
Alsmiller, G. R., Sonneborn, W. G.
O., and Metzger, R. W., "The All-
Composite Rotorcraft," Preprint No.
A-83-39-61-I000, American Helicopter
Society, 9-11 May 1983.
Peters, D. A., "Hingeless Rotor
Frequency Response with Unsteady
Inflow," NASA SP-352, February 1974.
Sadler, S. G., Corrigan, J., and Yen,
J. G., "Component Coupling with
Time-invariant Mass Matrix for Non-
isotropic Rotating and Nonrotating
Systems," Preprint No. 82-0731, AIAA
SDM Conference, May 1982.
276


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