. .. 1
J UI?
THE EFFECT OF
RIBBON ROTOR GEOMETRY ON
BLADE RESPONSE AND STABILITY
by
WILLIAM GENE ROESELER
S.B., Iassachusetts Institute of Technology
(1965)
Submitted in Partial Fulfillment of
the Requirements for the
Degree of Master of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May, 1966
Signature of Auther
I
-
Department of Aeronautics
and Astronautics, May 1966
Certified by _
Thesis' Supervtis*r
Accepted by
Chairwan, Departmental
Graduate Committee
.... ..
03&
THE EFFECT OF
RIBBON ROTOR GEOETRI ON
BLADE RESPONSE AND STABILITY
by
WILLIAM GENE ROESELER
Submitted to the Department of Aeronautics and Astronauties
on 24 May 1966 in partial fulfillment of the requirements for the
degree of Master of Sei~aee.
ABSTRACT
A stewable retary wing composed of a thin membrane blade supported
wholly by mass forces acting on a specially designed tip pod was built
and tested. Theeretical flutter and divergence boundaries were calculated
using blade element theory and assumed rigid flapping and linear twisting
Blade flapping response to cyd:lie pitch inputs was measured
modes.
and compared with calculated roots of the characteristi equation based
As a result of the analysis and testing, certain
on test roetr geometry.
basic co•strai-ts were discovered which apnly equally to all rotors
of extreme bending and torsioel flexibility.
Thesis Superviser: Norman D. H1am
Title:
Associate Professor of
Aeronauties and Astronauties
ACKNOWLEDGEMN T
The author wishes to express his appreciation to his Thesis
Supervisor, Professor N. D. Ham, for his patient guidance and genuiMe
eaoouragemeit in this work.
Aeknowledgement is
also made to the Model Shop of the Aeroelastic
and Structures Research Lab at M.I.T. for supplyimg the basic test
model, to the staff of the A.S.R.L. Computing Facility for help it
obtaining computer results, and to the staff of the A.S.R.L. Elect ronics
Lab for help in the experimental phases of this project.
LIST OF SYMBOLS
AT
tip pod area
F
&
modulus of elasticity
ashear modulus
blade flapping inertia = m,
Xc
tip ped feathering inertia
blade tersional stiffness
4L-
II
blade element lift force
total moment
A MAv
&
aerodynamie feathering moment
generalized aondimensionalized aerodynamic feathering moment due teo
R
Roter radius
S
.slope-- of cherdwise variation of radial stress
A4,.
G.
aerodyrnamic center
(
center of gravity
E.A.
elastic axis
iE
leading edge
T E
trailing edge
S
blade lift curve slope
lift
curve slope of tip pod
LA,
0u
eofficients appearing in characteristic equation
b
blade chord
T tip pod chord
x seerdinate of T.E. expressed in inches
x coordinate of L.E. expressed in inches
nondimensionalized blade torsional stiffness
b aeredynamie flapping moment
generalized noedimemsionalized blade flapping moment due to.
YV
4r
nII
U
of tip ped
M*
nmass
/,
radial eeordinate
%,
cherdwise eeoordinate, positive ahead of E.A.
,4 x coordinate of blade A.C.
x
'rt
;Z
*1
ooeerdinate of leading edge
x eoerdinate of trail.ig edge
p vertical displacement of E.A.
blade section angle of attaek
C'
pI
6
rigid flapping angle
amplitude of flapping motion
blade leek
number
#
1?
5
Blade thickness
radial strain
a
feathering angle, a small perturbation from flat pitch equilibrium
ST
feathering angle of tip
amplitude of feathering angle
= 'ýplex rest of characteristic equation
9
(see Figure 5)
air density
radial stress
eonstant radia-l stress
flutter frequeney
-i
roter rotational speed
damping ratio
(frattiom of critical damping)
TABLE OF CONTENTS
Page
N..
Introduction
1
Analysis
5
Leeation of the Elastic Axis
5
Trailing Edge Luff
6
Bifilar Stiffness of Ribbon Rotor
8
Aerodynamics
10
Flutter Analysis
11
Consideration of the Second Made
16
Sample Caleulations
18
Experimenta 1 Study
22
Test Model
22
Data
23
Conclusions
26
General Conclusions
26
Sumrary of Ribbon Rotor Feasibility,
27
Figures
1
The Ribbon Rotor Test Model
2
Effect of Variation of I for Blade with
Small Tip Ped
3
Flurtter and divergence Boundaries Based oe
Model Parameters
4
Flutter and Divergence Boundaries for
Adverse Blade A.C. Offset
Page N..
Figures (cent.)
5
Effeet of Tip Pod A.C.--E.A.
6
Effect of Variatioe
Zero Area Tip Pod
7
of*
A
Offset
32
fer Blade with
Effect of Increasing Radius
33
34
INTRODUCTION
The rotating wing has one important structural advantage over nonrotating types--the capability of relieving beading moments by using
components of the centrifugal force.
must still
But conventional rotor blades
have sufficient bending strength to accommidite 'the
negative
lead factors involved in ground handling and gust disturbances of the
stopped rotor system.
The resulting beam-like spars add considerable
weight, are often excessively thick for maximum aerodynamic efficiency,
and are susceptible to fatigue failure. in the severe vibration environment.
Blades which can be retracted into the hub as rotor speed decreases
need not have any bending strength and thus can be much lighter and
offer less profile and parasitic drag than thicker blades.
Although
retractable rotors have been designed with blades of appreciable bending
and/or torsional stiffness, the most compact system for stowing a long
thin blade would seem to be on a drum.
coiled on smaller drums,
More flexible blades can be
so maximum bending flexibility is desired in
blades designed for drum stowage.
Thus part of the motivation for
flex rotor research is the possibility of achieving bettoer structural
and aerodynamic efficiency by using rotor blades which are not selfsupporting in thL non-rotating system.
Additionally,
the stowability feature of some flex rotor types may
give rise to controllable,
autorotative recovery systems which could
replace parachutes in many applications.
This same feature,
combined
with potential light weight and the high hover effieiency inherent in
(a)
rotors of large diameter and low disc loading may inspire the development
of powered flex rotor systems for VTOL types of the stopped and stowed
rotor category.
The cepability of gradually changing the diameter of
the rotor makes the reelable flex rotor an attractive candidate for
nearly all types of powered and unpowered rotoreraft.
Flex rotor research dates back almost as far as the helicopter itself,
Theodorsenlland others having had patent claims
types as far back as 1939.
allowed on flex rotor
The capability for light weight construction
of airscrews having flexible blades was recognized by airship manufacturers
in the 1940's.
The resulting blades were held extended during flight
by centrifugal forces on tip weights but hung limp from the hub when
the engines were stopped, no attempt being mrad
to roll them neatly
into a compact unit which could be stowed and deployed easily.
More recent efforts in flex rotor research include model tests
carried out at Kellett Aircraft,
Martin Company?
12
Vidya Corporation,
4 &6
and the
Research at Vidya, carried out under the direction of
Dr. J. N. Nielsen and inspired by the flexirotor invented by Mr. D. T.
Barish treated a stowable cable rotor of porous sail cloth.
coenern in their design were a set of anti-luff criteritr
high chordwise tensieon in the sail cloth.
Of primary
requiring
Although the flexirotor
holds some promise as a r!covery system and controllable parachute,
its relatively poor aeredynamic efficiency seems to make it impractical
for powered rotercraft.
Efforts at the Kellett Aircraft Corporation confirmed the potential
of the cambered two dimensional blade in providing high CT/o in a light
gauge steel flex rotor.
The research program carried on at the Martin
lSuperseriTts refer to bibliographic referenees.
(2)
Co. indicated that the second mode flutter problems encountered in tip
powered flox roetrs of low solidity could be effectively eliminated
by means of proper adjustment of the elastic axis position and the blade
section centers of gravity.
However, the Ma•rtin Co. analysis treated
a flex reter of conventional blade thickness and weight, with only the
bending and torsion stiffness reduced greatly from conventional rotor
standards.
The first torsion flutter mode involving large tip pod
excursions was analyzed on the analogue computer, but apparerftly the
significant tip pod aerodynamies were not included.
Thus although flexible rotors do not represent entirely new technology,
no flex reter has been developed which offers both stowability and a better
thrust to weight ratio than conventional rotor systems.
Although
flex rotor flutter boundaries have been established for a certain reter
type,
no general treatment including control mode blade response has
been undertaken.
The ribbon rotor investigated here is a flei rotor type which
combines the advantages of stowability and high structural efficiency,
the blade being composed of a thin, homogeneous rSbbon of uniform thickness
and essentially zero porosity having neither bending nor camber line
stiffness.
The ribbon rotor is different from the flex rotors discussed
above because no cables are present and the radial stresses are distributed
over all the blade material.
An ultimately light rotor blade results
which is readily stowable as a cylinder rolled abhout the hub or tip
chord line.
(3)
The centrifugal force on the tip pod center of gravity iwmprts a radial
leading to the ribbon.
This radial loading imparts both torsional
and bending stiffness to the blades, and eliminates camber line or panel
6
flutter even though the Vidya anti-luff criteria 6 are not satisfied.
However,
the ribbon rotor is quite susceptible to bending torsion flutter
and trailn:
-dge luff unless ce-tain design considerations are satisfi-d.
The objects of this work havw been to establish the critical ribbon
rotor geometry for stability and to ootimize the controllability of the
ribbon rotor.
Figure 1.
The Ribbon Rotor Test Model
(4)
ANALYSIS
Loeation of the Elastic Axis
The elastic axis is defined here as in conventional blade analysis
as the line along which anplied forees produce no pitching moment.
Reference 5 gives the total tersional moment in a twisted narrow beam
under applied leogitudinal lead as:
h=
bG6
tb
+ 4c2.$
e
JEt
e
(1)
In conventional blades, the first term involving shear stresses dominates;
and blade torsional properties are determined by the shear modulus and
the blade eross seetieo
pqlar moment of inertia.
The elastic axis
in conventional blades lies along the locus ef shear centers of the
blade cross sections.
But in the case of the non-rigid rotor, the
last term im (1) may be several orders of magnitude higher than either
of the other terms,
in this analysis.
for this reason, it
is the only term recognized
The significant results of this property of
eno-rigid
blades is that the elastie axis rigrates from the shear center to the
centroid of the radial stress field.
Goldmam3 and others recognized
that the elastic axis for the eable roetr passed through the C.G. of the
tip pod, so this result is simply a generalization on the previous theory.
In massless articulated neon-rigid blades, the line from the C.G. of the
tip pod to the lag pin defines the elastie axis.
If no lag pin is
present, the projection of the elastic axis must intersect the axis of rotation.
(5)
Rile the cable roetr requires no lag pin, the cables being free to
pivot about hub and tip attachment points and not generally restrained
reter
in differential motion by the blade ribs and covering, the ribbeo
must be articulated in-plane to prevent eoupling of in-plane dynamies
with blade torsional dynamics.
Siose
the ribbox roetr, unlike the cable
retor, is stiff in-plane, the blade reot position of the elastic axis
may be varied•
independently from the tip pbsition of the elastic axis.
In this manner the first torsieon mode shape may be controlled, the ease
of linear twist eecurring only when the chardwise position of the E.A.
is
eonstant along the span of a rectangular blade.
If the E.A.
is not
parallel with the leading and trailing edges, a parabolic twist distribution
results, the greater twist per unit length of blade occurring at the
end where the elastic axis is most remote from the area centroid.
Trailinp Ege Luff
As will be shown later, elimination of flutter requires that the
blade elastie axis be well ahead of the mid eherd.
Thus more centrifugal
lead must be taken in the leading half chord than in the trailing half
Ehord.
As the alastic axis is shifted forward, the stress in the trailing
edge fibers is reduced and will eventually go to zero.
Ihen this happens,
the trailing edge will tend to buckle, and air leads will cause severe
luffing.
To eliminate trailing edge luff, the trailing edge fibers
must be kept in tension.
Neglecting blade mass,
the total centrifugal force is:
(2)
(6)
By definition of the elastic axis:
) T rEo/X
(3)
,= 0
LE
Since both ends of the ribbon are rigidly clamped, the ehordwise
strain distribution has the following form for the ease of an undeflneted
node line.
o 5,
= 6•(')
t
(4)
,
The quadratic term arises from a linear twist.
The exaet expression
for E(Jin the presen e of node line bending is vastly more eomplex,
but additional terms are believed to be of higher order for this analysis.
In fact, for tip pod angular exeursions of the order of ten degrees,
even the quadratie term becomes insignificant, since it is over two
orders of magnitude smaller than the first terms in the eases studied.
Thus a chordwise linear distribution of radial stress was used
for this analysis.
t=.±•
(5)
The trailing edge luff boundary is given by:
which oecurs when
Thus the expression for stress becomes
(7)
and the relationship between
)(
-I
-
a•nd
is given by:
)j
=
(9)
Examination of (9)yields the following important relationship for
non-rigid blades of homogeneous cress section.
ic,
the maximum allowabl
between the E.A. and the
distinaee
T.E. is given as the ratie of the second snd first Prea moments sbout
Location of the E.A. aaw.d of this point will cause trailing
the E.A.
edge luff.
Bifilar Stiffness ef Ribbon Reter
The term "bifilar " is used here because it
is used in flex rotor
literature, even though the radial leads are not earried by distinct
filaments but by the entire ribbon.
As mentioned previously, the blade
torsional properties are determined primarily by the radial stress field,
and shear stresses are neglected.
The nondimensionalized blade torsional
stiffness is:
=
e
AKr
l=
(11)
Where
kJO
(8)
The moment at any blade station due to the radial stress field is:
N
(13)
j
L:5.
d/E
T
Since in general
ads
5-
may be a function ofiz,
rE
)
~
I
rA)
(it)
_
But in the particular ease of linear twist
S
S7rpr-l
~
C9 7
SonstB.
(15)
New assuming
Lcr&4z
(16)
o;-1 5 ,
y
The total radial force io:
(17)
And from (3),
(i1)
/
Thurs
(19)
(9)
And (17) becomes:
-
Lx,~dj~-lx,)
M-A z 8?
(20)
Evaluating (20)
+4-
/b Szi
)
mrk%9
(21)
±3I'
((22
substituting
or
er substitutirg
j
14
---
x(,
f=O•1
? ").!2
d
=
Ix'7-F')-
"
/-. ll
(23)
-
Thus the nondimensionalized blade stiffness is seen to be independent of
retor retational speed.
Aeredy namies
For this analysis, blade seetion aerodynamics of the ribbon roter
have been approximated by flat plate charaeteristics investigated in
Reference
8 .
The flat plate has a lift curve slope of 7.16 up to a
stall angle of about 8 degrees.
The center of pressure for the flat
plate moves aft of the 1/4 chord as separation occurs on top of the
blade aft of the leading edge.
The aeredynamie eenter has been taken
at the 25% eherd for this stability boundary analysis, although blade
(10)
section eamber and leading edge separation may eause the A.C.
to be
further aft.
The tip pod aerodynamics are considered separately.
in references ,9
and
Discussions
10) of the aerodynamics of low aspect ratio delta
wings indieate that the lift
in the experimental ribbeo
curve slope for the balsa tip pod used
rotor model is between 1.57 and 1.43.
The
second component of lift, that proportional to sin 2 G0 dominates for
e
greater than five degrees, but only the first component is signifieant
for flutter analysis near flat pitch equilibrium.
The aerodynamic center
for the tip pod lies at 36% of the mean aerodynamie ehord for 60 degrees
sweep back, or at 56% of the root chord.
Thus the highly swept delta
shape is seen to be particularly suited for providing aerodynamie
damping for first mode torsion because of the aft leeation of the A.C.
For this reason the aerodynamic characteristics of the balsa tip pod
will be used throughout this analysis, even though other tip pod
geometry might be mere suitable for particular ribbon rotor applications.
Flutter Analysis
Assume :--non-rigid blade
zero steady coning
no in-plane motion
quasi-static aerodynamies
zero flapping roller offset
Neglecting apparent mass terms the aerodynamic forces acting en eaeh
blade el'ement are:
(11)
the aerodynamie center due to the angle
a forcej•pA'rAbat
a)
at the rear neutral point
of attack q
b)
a foreep
a•cting at the rear neutral point
Here, as in the case of conventional blades,
the A.C. is taken at the
1/4 chord and the R.N.P. at the 3/4 ehord, a procedure valid only
when camber and angle of attack are small.
Then
(24)
Jwt r)+s:4
force at the 1/4 chord beco
andc
tlhe
at
fo~rce
ALa
the
1/L:
sherd
beBomesJ~B:
. 5b--a)
I 2, 1
8
4-z
(25)
3
Thus the feathering moment at4t due to the air leads on the blade element
•
is given by
,./,--,
.
(26)
+X/
and the flapping moment is given by:
A/t-
PA A
A9
Where the
0
beeause e
is of the order
(27)
term inAt has been neglected in the.*Ad
and
b<
(12)
A
expression
New assuming mode shapes
(28)
SZ = t 9
0-r
S=ir
The generalized aerodynamie forces for the first mode become:
Q
§•
zA
,
p
b
r
AA.
(29)
r
1
j/1~d
+ b -P AR 8
(30)
/r4A "'Y.AAlr~JtJ- A-)4%
lr er
kc,~
4R
(bRT
*17i
TbR
I
C
A?''
= P
)
(31)
R
MA ()
)jpixb
0~2 e
(6r
-.
A-P
)cttc
4
(32)
nAb ()
8
These generalized forees may be nendimensionalized by dividing bylbt
Then
MA (1)
ML
a xd
+
t27.- 1
GrI
9
g· R
(33)
(34)
7
r
r
hb
8herea
M9
S.~P·
8
/0
(35)
(13)
067
tj
(36)
r
(38)
Or when tip pod aerodynamics are included,
U-
r
iAr
;r
(39)
r
ped, where the me shapes are unity.
Thus the
ss ters in the blade40)
(412)
Since a massless blade is assumed, all mass moments originate at the tip
pod, where the mode shapes are unaity.
Thus the mass terms in the blade
equations of motion are identical with these for the case of rigid torsion
and rigid flapping analyzed in Reference
2
Thus assuming
(43
-
(14)
The coupled equations of motion are:
pr
%e &jt
p
]
(44)
(45)
fr
The characteristic equation is found by setting, the determinant of
oeefficients equal to zero.
61 )4
+j 6k))
St
+ 6I
C
(40)
WIhere
614
= i
(47)
(49)
a3
I21 +
e
(49)
Me
a~ fe9
a@
I~~
mntM1
(50)
(51)
Alp;
E
The stability boundaries of Figures (2), (3), and (4) were found by
using Routh's criteria.
The boundary of statie stability being given
(15)
by:
0(52)
0 =o
and the boundary of escillatery stability;
a0
6 2- -"
0
(53)
Reoots of the characteristic equation pletted in Figures (5), (6), and
(7) were obtained from I.B.M. 1620 computer solutions.
Consideration of the Second Mede
The analysis of the low solidity flex reter in Reference 3 indiested that the second coupled mode involving mid radius oscillations
similar to these encountered in a fixed-fixed beam was most troublesome
for the flex retor and that blade stability depended upon the leastion
of the A.C. aft of the E.A. to nrevent divergence and leoation of the
0.G. ahead of the E.A. to prevent flutter.
These conditions are irmpssible to
aehieve in the ribbon rotor of uniform thickness since:
1. The blade C.G.
eccurs at the mid chard, which is necessardly
aft of the A.C.
2.
Trailing edge luff is eneountered ahen the E.A.
is ahead of
the 25% cherd.
However, the ribbon rotor tested seems to be virtually free of
second mode instability, and the coupled first mode escillations ahich
oecur can be eliminated by adjusting tip pod aerodynamies
high aerodynamie damping.
to provide
A number of facters eantribute to this
apparant discrepaney between the present ribben roter results and the
Martin Co. research.
(16)
It
is noteworthy,
for instance, that Figure 6 of Reference 3 indicates
that a reduction in rotor radius seems to eonsiderably alleviate the
divergence problems, allowing the E.A. to be located aft of the 30%
chord before divergencn
is encountered.
In the ribbon rotor of this
analysis, the solidity Is much higher, and second mode static divergence
ceases to be a problem.
Divergence of the first mode is prevented
by placing the tip pod A.C. well aft of the E.A.
The absence of
osenid mode flutter in the ribbon retor is probably
due to the dependence of this coupled bending--tersion phenomenon on force
couples acting en a rigid chord.
Any second mode analysis for the ribbon
roter would need to include the cambering dynamics.
For these reasons the second made was not analyzed as a part of this
project, even though there are indications that it could become significant,
especially in rotors of low solidity or of rigid chord.
(lit
~.&(
/
SAMPLE CGALCULATIONS
14*(
Aq
0
l
-0·--
4-
2-·
J
A
.1
4¼
-1
4z3
F-j
1 f -
(I73F-A) tF.-A')
4-
P2.4:=
f'-cO
f+-a(it
go
Sgxzx2 8- 9x 8X• )
I
£V
K28 - i8X 6-/
4x
•.,
Ap
I
C
/f
4j -45
I 3. /
/0
R
j-/c-44
-4
0 0o238x Z7
rn,"
.b473
• ÷73 8 •
I
* 4.73x .1x.
-7.-yI
,,Ar
bJr
a;-
7AX
7./4~
/0
-4
X R2.
A'
*oo230X%/-K
601 KSe
R.
(18)
2.
r
me~
.0 5B
.4
%~
MA
/1
--I-
-iv
f
t
-
0
Kr li
A'~~·
oft/I1
VtT
rM
VT)
~T ~i-s~
R /t9A
. o(97
2.
0 1?
a
iTr
Bcuj,
1T.
'x~2.
Nor- sotting
.0o'9
0
Me
P1
64
5.
n=fi:
p/
-
19 -*4t~ =
p
r
i
x1
.6 o
p
%
.r~r;3P
S9·
. c0r4F)
I
$2
+o
-4-
9.063?
x
.063'7
o
"
(19)
. 3xo0-
.$x o0
OG
o =
()o 1- 2R3.1
A
+e 9
ci,' +,h,4 it,)
4, ;4
Ca
(. 6:2 R" 9.
*1/ý.
.o63 ()oR
2 3.
(4?d
~%:
-
4
f9P 3) -
*23./
A . ,R) r'/-
/oR')
r,. ~gp
-4-
Setting
(:
i
0 4+23. /
+ 4. ),r
+-.037
(.
42
+
s-23.I
(Ly.
6A 4
7
t
O x/0
1-
.
38x lo-
-4
aZ)X/ o
-4.
= 8. 33,YX0
fx0
:- 48
ie:~j
= 5.
4 1/r/o
_-4
(20)
- 4-
/xi0
f/
Y/It
2-)x le- #
.r~9~.i4'
S(4
/0
) x
0 7) Yio
S
g9R
S()o
a3
*, dý
-4.
£
-io
New forming the discrimixant
SS5 K
cA,
c<
8x.S
3
)- OX 8.33 X*'.33
= £ 5x55y
2.5Zi
4Thus this is
2=50
38
non flutter poet g
3
n by:-
Thus this isa non flutter point givn by-:
I
/~,-
S
,Zzz
f
A-T
;
bR
.I
The divergence boundaries may be found. by expressi ng MA in terms of
r
i44
ix·otj
2$,
4 '? ý ý 4 7 1 19
The divergence boundary is given by:
4~~x
Josaie
IP6A 7"
S3.1
4----/
This sample point and divergence boundary appear in Figure 2.
(21)
=32
EXPERIMENTAL STUDY
Test Model
The ribbon rotor test model consisted of two ribbons of type A
mylar plastic .005 inehes thiek, of.4 inch eherd and three feet radius.
The blades were elamped at the hub to a pair of 5/8 inch diameter
rollers which were articulated in lead lag and in feathering, the lag
pin being adjustable from the root 20% chord to the 60% chord.
A
conventional swash plate was used to control the pitch of the blade
rollers, thus controlling the pitch of the blade reoots in a 1/rev
harmonic.
The rollers were eriginally conneeted through flexible cables and
a common gear train to a non-linear spring which restrained the unrolling
of the blades.
A pair of leaded aluminum tip weights caused the blades
to extend gradually as rotor speed was increased.
However, the aerodynsmic
and mass properties of the aluminum tip pods prevented the achievement
of torsional stabilitysinee it
was impossible to makeO4~negative.
A
balsa fairing was constructed to enclose one of the tip weights and
data was taken with the rotor in a single blade configuration.
A clock
spring with linear characteristies replaced the more complicated non-linear
restraining mechanism, and the blade extended at a predetermined speed
of about 150 RPM.
The balse fairing was made as light as possible and a serew mechanism
was instailed which moved the balsa along the tip ehord so that different
tip aerodynamic eenter offsets could be achieved.
However, the mass
of the balsa and associated hardware proved to be a substantial part
(22)
of the total tip mass,
so tip C.G. loeeation varied along with the
Thus the tip pod adjustment mechanism proved
aerodynamic center offset.
more valuable in
eeafirming the trailing adge luff boundary than in
The flutter characteristics
regulating blade flutter characteristies.
were regulated by combining tip pod position adjustments with slight
mass additions to the tip pod trailing edge.
Thus both flutter boundaries
and trailing edge luff boundaries could be established experimentally
for different blade A.C.,
tip A.C. offset and different root •E.A. leeations
The test rotor was mounted in an enclosed area, the expansion
chamber of a low speed wind tunnel, to prevent injury in the event of
blade failure during tests.
Power was supplied by a 20 hp hydraulic
system, and rotor RPM was regulated by metering the flow of oil to the
retor motor.
Structural considerations prevented testing at rotor speeds higher
than 350 RPM for the two blad" rotor and 200 RPM for the single blade
rotor.
Tests were generally earried out as sooeen as possible after blade
extension, because blade fatigue caused thes
lar to fail along the sharp
clamping edges after sustained testing in the presence of flutter.
Attempts to test blades of reinforced leading edges were hindered
by the buckling of the blade material during rolling.
As a result,
no data Are presented for the blades of double and triple thick leading
edges which were made.
Data
Two metheds were conceived for measuring the time to half
amplitude of the blade flapping motion.
The first involved mounting
a remotely controlled 16 mm movie camera on the hub and photographing
the tip pod.
The blade was exeited by applying a square pulse of eyelie
(23)
pitch at the blade rest.
After the pulse, the awash plate was trimmed
normal to the spindle, and the subsequent tip ped and blade motion were
reeorded on the film.
The film was analyzed on a mierometric enlarger
which enabled measurement of the tip pod position to approximately
Two time references were
1% of the maximum amplitude of eseillation.
available,
the camera speed and the roetr rotational speed.
Since
both of these reference times were known within 10%, the average of the
two was used in measuring the flutter frequeney.
The damping ratio
was measured by counting the eyeles to half amplitude and comparing
with standard plets for second order systems.
The results of these
measurements are presented in Figure 5, superimposed on the analytical
curves based on the test reter geometry.
Film reserds were also made with the,eamera
both above and below the rotor tip path plane.
mounted
Hfowver,
off the rotating hub
results of
this procedure were less accurate than visual observations of the decay
or growth of the weaving motion.
Visual observations included the following:
I.
Most prmoounced flutter ocourtd when a 10 gram lead bar was
taped to the trailimg edge of the tip pod.
This eaused the tip ped
0.G. to shift baek to the A.C. while inducing the E.A. to migrate back
past the blade mid eherd.
Flutter so induced was self excited and
caused blade flapping motion to build up to about 1 30 degrees.
(24)
2.
In the moest stable eenfigurations (O&4=0
1AVr
j,
-.18)
the
blade flapping motion dropped to half amplitude in about ene second
after a step or square pulse eyclic pitch input.
m vwuch as as i"n 9I
o pes.t±vev
the test rotor without causing flutter.
'4
soulu be
ar-n Teuonma'Cec wsniT
Thus the single data point
in the flutter region of Figure 4 was actually a stable ease.
Trailing edge luff was encountered in all *enfiguratioas with
E.A. ahead of the quarter ehord, although leeatien of the E.A. between
the quarter chord and the 1/3 chord did not seem to be troublesome.
Trailing edge luff could not be detedted visually, but analysis of the
films taken with the c~mera mounted as the hub confirmed the fact that
the noisy sound of some blade configurations was evidence of trailing
edge luff.
(25)
CONCLUSIONS
Although the experimental phase of this project was confined to
a particular ribbon roter type and the analytical results presented
were based on the model parameters, an attempt was made to provide
analytical tools for other flex rotor investigations.
General Conclusions
Both the analysis and the test program support the fellowing
more general cncalusions:
1. In roter blades of negligible structural stiffness blade torsional
stiffness is directly proportional to the
4square of the rotational 'spee',
and stability boundari-s are independent of roter rotational speed.
2. The effective elastic axis of such men-rigid blades is coincident
with the centroid of the radial stress field.
3.
In non-rigid blades of homegeneous msterial the maximum allowable
distance aft of the elastic axis is given as the ratio of the soeend
and first area moments about the elastic axis.
Location of the E.A.
in violation of this criterion will result ix unloading of the trailing
edge fibers, but tests showed that the E.A.
could be breught slightly
further forward before pronoueed trailing edge luff eoccured.
4.
Stability of non-rigid blades in roters of low solidity generally
depends upon:
a)
Location of mass axis ahead of the elastic axis.
b)
Location of the elastic axis in freont of the aerodynamic
center,
However, ~on-rigid blades which are also flexible in camber may be
less sensitive to these criteria due to aleviation of bending torsion
eoupling through camber-tersion coupling.
(26)
5.
Non-rigid blades in which the E.A. is ahead of the A.C. and
the C.G. is ahead of the A.C. could be expected to be more stable
in roters of low solidity, while blades with E.A. aft ef' the A.C. would
be more apt to experience static divergence and blades with the C.G. Qft
of the E.A. would be more apt to flutter as the radius was increased.
6.
First mode instabiliti~s in non-rigid blades may be eliminated
by the addition of a tip pod with sufficient area and aft A.C. offset.
theory to describe ribbon
7. The use of flat plate aerodynamie
rotor blade characteristics overemphasizes
the relative significanee
of the blade in determining first mode flutter eharacteristics when a
rigid chord tip pod is also present.
less negativeA,
4
Thus a smaller
AT
and one with
may be required to stabilize a blade with positive tZ- 4
than theory predicts since blade camber; gets into the picture as well.
Summary of Ribbon Roter Feasibility
Although the simple ribbon rotor of uniform thickness can be effectively
stabilised in low aspect rstie configurations, second mode instabilities
would probably set in as the radius inereased.
Camber--tersion coupling
would make the ribbon less susceptible to these instabilities than rigid
chord flex rotor types, but the high aeredynamic efficieney of ve-ry
low solidity rotors could not be achiev~d.
In order to fully realize
the potential of ribbeon rotor systems, the leadig edge tensile strength
should be increased to allow elastic axis positions ahead of the
quarter chord.
Any second mode flutter problems which may arise could
probably be handled by making the leading edge additions sufficiently
massive to eause the blade sectien C.G.
(27)
to be located ahea'd of the E.A.
Blades so constructed could still be easily stowed, though a powered
retraeting mechanism would probably be required instead of the spring
leaded type.
Although blade flapping response to root feathering inputs was
stable and fast enough in the rlhbon rotor tested, this scheme of
rotor control may not be best for large diameter reters of low solidity.
Retor tip pitch tabs, activated, perhaps, by the tensile reinfererrent
filaments, may be a better mecns of controlng large flex rotors.
The
increasing stability with increasing radius trend of Figure 7 is
encouraging ix any ease, and it
is defixitely felt that large diameter
flex roters can be effectively controlled.
Figure 6 indicates that
flex roetrs may be stabilized without large tip pods provided that
the leading edge is sufficiently reinforeed to allow forward shifts
of the E.A.
(28)
0.3
0.2
DIVERGENCE
BOUNIDARIES
T(FEET
0.0
fA P IUS
FLUTT7ER
BOUANDA R Y
-0.1
b
EET)
Ft.
S.33
Ft.
=0
-
AT
o.2
bR
SAMPLE CALCU LA rTNOI
-0.3
Figure 2Z.
stheket
retti"i of 3
(29)
fr
B
wide
with Small Tip Pao
0.3
.=47
b•
b =.33
fA = O
Ar
bR
0.2
I
0
- 1o-3
IT
OINT
NO FLUTTER
0.1
XA (FEET)
0.0
R (FE ET)
CUTTING
PLANE FOR
FIGURE
7
- o.2
C UT 7T INCG PLA NE
FOR
FIGURE
-0.3
Figure 3.
Flutter and PivergeMce
Beundaries Based ot Model Parameters
(30)
5
0.3
-b : ~
T=
7.7F
.33 f•.
z,4 = +.0277 f•
bRF?
o.2_
02
S
0
10 -3
TE ST
CASE
0.1
(FEET)
TTE
o.1
-
-
NO FLUTTER
POINT
0.2
-0.3
Figure 4.
Flutter and Divergence Boundaries for Adverse Blad- A.C. Offset
(31)
br a
ý =.33 4
/I'A = O
0 < /X.,Ar <
Ar
bR
.3
J.0
3
T =10 PL
0.5
- 1.0
SFLT
UTT
17 STA
F0 DENO
DA TA
L
74=
- o.5
CASE
4SE
-0.5
EX PER IMENTAL
-I.0
%Ar :=
Figure 5.
Effect of Ti p Pod A.C.--E.A.
Offset
(32)
I
b,-zi~
IImLJ]
R =3'
rAA
-
.0
-3
ARO
10
%LA=0
(X
A
%x, -0
ARROWS
DIRECT/ON
IND ICATE
OF DECREA.I/NG
0.5'
5 REP]J
i.
-1.0
+-o.
- -0.-5
/
Figure 6.
IErf~ibett -•Y:` t
r
a•
-A ni s Blade With Zera Area Tip Pod
(33)
b,: . 7'
b = .33
/X-A=
T -0.1"
*1
AT
bR
.3
R3
/'< R < )o
-+1.0
- f0.5
R = )o'
RE. )]
-1.O
- 0.5
+0.5
-- 0.5
Figure 7.
Effect of Imereasing Radius
(34)
1.
Flutter";
2.
"Helieopter Blade Vibration and
Miller, R.H.; and Ellis, C.4.;
Ham, N. D.;
"Comparison of Flutter Theory with Test Results from
a Model Helicopter Rotor"; M.I.T. Aer. E. Thesis
3.
I.A.S.
Paper 60-44
Nielsen, J.N.; and Burnell, J.A.; "Wind Tunnel Tests of Model
Flexiroter Recovery System."; Vidya Rept. #70
5.
May 1957
Goldman, R.L.; "Some Observations on the Dynamie Behavier of
Extremely Flexible Rotor Blades";
4.
1956
July
American Helicopter Society Journal;
Timeshenke;
March 1962
Strength of Materials. Ptart II;
New York, 1941
6. Nielsen, J.N.;
D. Van Nostrand Co.;
Burnell, J.A.; and Seeks, A.E.;
of Flexible Roter Systems";
Vidya Rept.
#55
"Investigation
September 1961
7. Gessew,A.; and Meyers, G.C.; Aerodynamics of the Helicopter,
Macmillan Co., New York, 1952
8. W1,k
B.H. ; ;AStudy at the Subsonic Frees & Aoements on an Inlined
Plate of Infinite Span"; N.A.C.A. TN 3221, June, 1954
9. Heerxer, S.F.;
I0.
Fluid Dynanic QDrz;1958
Tosti,L.P.; "Low Speed Static Stability and Damping-in-Rell Characteristics
of Some Swept & Unswept Low-Aspeet-Ratie Wings"; N.A.C.A.
11.
Theodersen, T.; ard Andrews, E.F.;
U.S. Patent #2,172,334;
12.
TN 1468,
1947
"Sustaining Roter for Aircraft";
September 1939
PruyA, R.R.; and Swales, T.G.;
"Development of Rotor Blades with
Extreme Chordwise ~ad Snanwise Flexibility"; A.H.S. Forum May 1964
0(5)