The measurement and control of helicopter blade modal response using

THIRTEENI'H EUROPEAN WJ.ORCRAFT FORUM

biC

Paper

No.

10

THE MEASUREMEN.I' AND CDNI'IDL OF HELICDPl'ER BLADE IDDAL RESPONSE

USI'l~

BLl\DE-MJUNl'ED ACCELEROMEll'ERS

Nomen

D.

Ham

Massachusetts Institute of Technology,

u.s

.A.

and

Dwight

L.

Balough and Peter D. Talbot

Ames Research Center, NASA,

u.s.A.

September

8-11, 1987

ARLES'

E'RAOCE

THE MEASlJRElolENI' AND CDNI'OOL OF HELICDPI'ER BLliilE

M:lll!\L

RESPONSE USJ:ro BIADE--M:lUNl'ED ACCELEROMETERS

No

man

D.

Bam

Massachusetts Institute of Technology,

U.s

.A.

'Ihe measurenent of helicopter blade flapping. bending. and lag n-odal acceleration and displacenwmt response using blade-toounted accelerarot.ers is described. It is shoWn that knowledge of the blade node shapes is

sufficient to permit separation of the m:XI$1 contdbutioo.s to the accelerareter signals using natrix inversion. 'lhe apPlication of the McKillip filter to the identificatioo of roodal rate respcnse is described. Finally, the de.Gign of flapping, bending, and lag IOOde controllers utilizing the conVI!Iltionlll swash plate is presented.

The uea.sw:enent te::hnique iS Ulust.mted using flight test results obtained using a Black Bawk: helio::pter.

1. I~

'Ihe concept of Individual-Blade-Control (!BC) mbcxUes the control of

·-,~oacband electrohydraulic actuators attached to each blade, using signllls _.i-an sensors noonted oo the bladeS to

aupptY

approptiate eontrol ~

to the actuators. ~te that me involves not only control of each blade independently. but also a feedback loop for each blade in the rotating frame. In this manner it becates p:>ssible to reduce the severe effects of

atrrP~eric turl:ulence, retreat.fn3' blade stall, blade-vortex interaction, blade-fuselage interference, and blade and rotor instabilities. \bile provic'lin3 inproved performmce and flying qualities U-10).

It is e~ident that the

:me

D'jS\:.etl will be noBt effective i f it is carprised of several mb-systems, each controlling a specific mode, e.g •• the blade flapping li'Ode, the first blade fl.atwise bending nxxle, and the firSt blade lag mode {2]. Each sW-system operates in it& awr~iate

frequency band.

Ccnsider the toodaJ. equation of JIOtioo

ll&+ci+kx•F(tl +AF (1)

'obete the rrodal CQ'ltrol fotce /J.F is

'!30 mbstituting {2) into {1}

miC

+ ci: + lex • {1/ CUR)] F{t)

and the modal response is attenuated by the factor 1/Cl-lf:l \oilile the modal danping and natural frequency are unchanged.

For modal dattping augrrentation. only the rate fee:baclt AF •

-KJPC

is

required.

'!he configuration considered in [1-7] mploys an individual actuator and lrultiple feeCb.ck loops to ccatrol ech blade. "nlese actuators and feedback loops rotate with the blades and, therefore, a conventional IMlSh plate is not required. BCMeVer, sane applications of individual-blade-conttol can be achieved by placing the actuators in the non-rotating system and cootrol.l.ing the blades through a conventional owash plate as deSCribed

in Section 6 and in [8].

'Ibis research

was

sponsored by the 1\mes Research center, msA. I.D'lder

and

Dwight L.

Balough

and Peter D. Talbot

Ames

Research Center, NllSA;

u.s

.A.

'!he follCMing sections describe the design of a system controlling

blade flapping. bending, and lag dynamics, and related teatin<] of tm

system on a roodel rotor in the wind tunnel. 'lbe control inpUts considered

are blade pitch changes proportional to blade flappi,n; and bending acceleration, velocity, and d.illplacen'eflt, and lag velocity. It is then sha.m that helicopter gust: alleviation/attitude atabil.iz.ation, vibration alleviation, and lP lag danping augmentation can be achieved using the conventional helicopter swash plate for an No-bladed J:otor Were N>l. For

Ni:l.

all applications

can

be achieved.

Also presented are preJ.iltdna.iy flight test results fran a Black Hawk

hel.ic:opter having two flatwi.Be-oriented acceleraroters m:xmted on one blaDe. 'Ihese open-lc:Jql results are to be used in the design of an active

control system for rotor gust· alleviation and attitude stabilization.

Frcxa Figures 1 and [51, the blade flatwise acceleration at station r due to response of the first two flatwiae modes

is

(r1-e) r~ll1 11<r₁l

'

.

·~

.,_

_{r 1a 11 <r1}>

.,

(1:2-e) r2C2 Tt(t:l) r_{211 11 (r:z>} 2 •

.,

(rl-e) r3c2 11<r₃

>

_{r 311 11 <r3l}

'

.

{r4-e) r4c2 11<r_.> 2 •

••

r_.o 11 <r₄l In lllltdx

notation.

A • M • R

~ the flatw:l.ae rrodal respooaes are given

J:¥

R • l t1 ·A

Note that the elementll of 1("1 are dependent only upaa blade spamdse

statim,

rotor

rotat!ca speed. and bending !!Ode shape,

i.e..

they are independent of flight o::nditic:a.

Silrdlarly. the blade lag acceleration at station r due to respatse

t'

of tbe fimt lag lrl::lde

am

be llhown to be l&l

where

er.,

is

the spsnwise location of the lag hinge. 'lben for aocelerometers nounted at r₁ and _{r 2}

In nD.trix notation

Ar. .. '\ •

1\.

'.Ole lag: 100&1 reEpOOSeS are given by

Since the elem:mts of M'"1 and

"1:, -

1 are independent of flight c<:nditioo, the 80lution for a desil::ed ttcdal t:espcnae involves only tne

s~.tmntion of the products of spmwise acceleroneter signals and their corresponding constant rn!ltrix elements by an analog or djgital device, here

Consider the block diagram ~ in Figure

:z.

For rn::::dU acceleration

X

and m:xbl displacement x determined as above for MfY m:XIe, this diagram represents the following filter equatiCilS from {7 ,9]:

"'

'"

where the hatted quantities are estiirnteCI values, and _K1 and _K2 are constants. Writing the estination error as

e ... x -

k

and differe11tiating equation (3) with respect to tine, there resUlts

LQ

-dt'

d A

-at'

SUbstituting equation (4) into equation (5),

,$.

Q

•

X +

~e

+ _K1C Sinoe

L~-X

dt'

-e.

&;IUlltion (6) becaoes

'"

'"

"'

'nlis expression represents the dynamics of the estinntion error. 'n:le

Referer.ce Ill describes the application of me to helicopter gllst

alleviation. 'lbe feecback blade pitch control was prqlOrtional to blade flapping acceleration and di.nplacsnent, i.e.,

AS., --K (_!+.Ill

•'

A block di.a9ram of the control syst.m~ is .Ghcr.m in Figure 3, Note that each

blade reQUires only two, flatwise-oriented blade-m:xmted acceleramters. Figure 4 shCMs the effect of increasing the open-loop gain K upon the

lBC gust alleviation system performance. Note that the exper:ilrental reduction in gust-induced flawfu3 response is in accordance with the theoretiCAl closed-loop gain 1/(liK),

'!be 1J::.ck n\11'1'ber of the rrcx1cl blaOe was 3,0, For a full size rotor, the increase in dlnping due to the increase in Lcx:k mmber results in the flapping at excitation frequency becaning the daninant respoose. AJ.Bo, with increased blade dlmping it becomes possible to use higher feedback gain for the Mme stability level. and aa a ~ the IOC system perfornanc:e inproves with increasing Lcx:k nl.lllber.

FollCIW'ing the successful alleviation of gust distw:banees using the

:me

systmn. Reference UJ showed the theoretical equivalence of blade flapping respcnse due to abroqheric turbulence and that due to other low-frequency diJJturbances, e.g,, heliCDPter pitch end roll attituder therefore these disturbances

can

also be lll.leviated by the

me

system, as shown in

[8], to provide helicopter attitude stabilization.

corresponding characteristic equation is References [5,8) describe the application of lBC to rotor vibratior,

alleviation. 'nle fee&lack blade pitch control was proportional to blade s2 + K

1

s

+ K2 ..

o

bending acceleration, rate and displacsnent, i.e ..

'nle bandwidth and datrping of the estilration process are determined by the choice of the ccnstants :K₁ and _K2•

Since the elettent.s oJ: th~ filter flho.ll'l. in FigUre 1 are indepentlent of flight condition, the estilmtion of modal rate response involves only the :integration of the products of conat:ants and the nr&WUred trodal re.spc:noes

by an analog or digital device, here called

a

Mcltillip filter. NX:e that an inproved estiJmte of the modal displacement x is alSO c:btaine:'l. due to

the double integration of nxxlal acceleration i mbodi.ed in the filter. Also, note that no kn~ledge of the rotor or its flight condition is required in designing the filter.

As d:izcUmled in the Introduction. the modal controller voltage output to the blade pitch actuator is proportional to nodal acceleration, rate, and displacement:

where KA, RR' and Kp are constants and therefore independent of flight condition.

For nochl. &mQing a~tation only,

'·

1be solver. McKillip filter, and controller described in Seetioos 2-.1

are carbined to form the me syste:n for a given m:xle. 'nl.e carb:ined functions of the solver and the McKillip filter are here called the •ooserver•. Sare applications are described belOI</, including experimm.ta.l results obtained at MIT fran a four-foot--dialreter wind tunnel m:xlel rotor, using me.

6-10-2

A block diagram of the systun is Gha.m in Figure 5. Note that each blade requires four flatwise-ori«Lted bl.ade-1tounted a.ceelerareters.

Preliminary experimental results presented in Figure 6 show the effect of incrcatd.ng the me open-loop gain K fran

o

to 3 upon ·the fla.twise

bending

m:?de

respcnse, Note that the experimental reduction in vibratory bending response is in accordance with the theoretical clOsed-loop gain

l./(1 + K).

Since a mjor srurce of helicopter higher hanoonic vertical vibration is the blade flatwioo bending reeporwe to the inpulsive loading due to blade-vortex or blade-fusela.ge interaction, if the blade fla.twise bending response is controlled, the higher harnmic vertical vibration will be

corrCBpX~dingly reduced, as shown in Figure 7, fran [111 •

It Mould be noted that suppression of blade fhfping and flatwise

bending responses and their correapcnding in-plane Coriolis forces

wii,'

tend to alleviD.te in-plAne vibratioo as a beneficial by-product of vertical vibration allwiation.

Reference [6] describes the awJ.ication of me to rotor lag danping augmentation. 'lhe feedback voltage to the blade pitch c:ootrol actuator

was

proportional to blade lag rate, i.e •• -rV + V .,

-R,af

Mlere the tim delay is required for Closed-loop stability. A blOCk diagram of the syst.B'!I is shown in Figure 8, tete that each blade requires two lagwi.Be-oriented blade-munted acceleranetertl.

Figure 9 shcMs the effect of increasing the IBC oper~-loop gain on experimental blade lag chnping. 'lbe figure showS a rotation of the slcpe of the

t:bllBe

angle

versus

frequency

curve

at lag resol'W'ICe, in

the

direction of increased lag dMping, as KR is increased. 'n:le increase in

'·

'lhe preceding sections have den'Dnntrated that the use of blade-m::ulted acceleraneters as sensors nakes possible the control of the flapping,

flat..lise bending, and lag nodes of each blade individually. Tnis control technique is awlicable to helioopter rotor gust alle'liation, attitude Btabilization, vibratioli. alleviation, and lag

c:'lanving

augmentation.

For rotors having three blades, any arbitrary pitch time history can

be applied to each blade individually using the conventional !Mlsh plate. Rotors with nore than three bladeS require individual actuators for each blade for sane awlicationst other applications such as gust alleviation, attitude stabilization, vibration alleviation, and 1P lag drurping augn-entation can be adlieved using 1:1. OOilV8ltionaJ. S\<iash plate, as sho..n belOW" and in [81.

I f the control requirement for the ml:h blade of an fH)laded rotor is em, determined using blade-mounted acceleramters as de:scribea in Section 2, thm the correspc:nding control re:}U.irenent for the IM!lsh plate is

e .. e

₀+

e

₁ CODf +

e

₁

siny

+

e

l

c c

Using the llllthemtics of [lZ}, P, .!Sl, the oontrol laws are

1 N

•, -- r

N , . , 2 N e 18· -N lll"'l

I

e

m

sint

m

•Ounl.easn•pN±t el - o unless n .. pN

±

N/2 [111, P. 341 Were p .. any integer

n .. rotor harm:nic mmber

'lhe ~ysical significance of the above equations is that

:me

of an

N-bladed rotor having a conventional swash plate is possible for those IElC

fwx:tions involving the zeroth (quasi-Bteady), first, Nth, and (N±1)th hamonics of rotor speed, e-.9·• 9\lSt allwiation {p-Ol, atti'o:.de stabilization (p-0). vibration a.lleviation (p-1), and 1P lag dMpil'g augnentation (p-O) •

Note that all bammics and in general any arbitrruy tiDe history of

control are adlievable with a three-bladed rotor using a conventional tMUib

plate.

'llle m.mm.tions of individual blade sensor signals required to c:bta.in ie swash plate collective and cyclic pitch ca!pCI'lents provide a filteril'g

hion

such that cnly the desired blmtatics OP, lP,

re,

and <N±l>P remdn after 8\mll'&tion, i.e .. no .epecific barm:xdc analysis is required.

Since all sensing is done in the blades, no transfer natrices frail non-rotating to rotating system are requiredt therefore .no upchting of these I!Dtrices is required, and no non-linearity pr<blemG result frau the linearizatiOn required to obtain the transfer matrices. Also. blade: state measuremnt.s all.ow tighter vehicle control since rotor control can lead fuselage r~se: this lead ahould provide: roore effective gust alleviation and permit higher control Authority without inducin; rotor instabilities than would be p:>Ssible without rotor state feedback [13].

A bloci(. diagram of an active control systB!I for the conventional S'leSb plate of a helicopter rotor having four blades A, B, C, and D is sho.in in

Figure 10. 'lhe control voltages VA-D are generated fran blade-m:xmted accelerometer signals, as descr.ibed in preceding sections. A schemtic showing all the carponents of such an active control sy6tem is shown in Figure 11 for the special case of vibration alleviation.

7, FLIG!n' TEST EQJIPMENr AND P.ocx::.EIXlRE

Recently, the first ~se of a joint N!\SA-U.S, Ar1!rf flight test progrlllll involving the UH-60A Black Bawk helicopter was coopleted. 'nle fligh.t test p:c~ram, conducted fr<l\'o Januacy tht:Oillilh .Jun~ H£1 at ~tds Air Force Base, California, was part of the NASA Ames Re.seatch Center's Modem Technolo;y Rotors Program (Ml'R) • 'lhe Ml'R program calls for a series of flight investigations using cw:rent, state-of-the-art :cotor systens.

'Jlle ptesent program, involving the UB-60A Black Ba~. is the first of two pvu:es to be carried out by ~. in conjunction with the

u.s.

Arllrf

Aviation .Ellgineering Flight Activity (USMEFA). 'lhe Phase I flight program included an evaluation of rotor aerodynamic limits, handling qualities and

baseline acoustic rreasuremnts of the UH-60A, It shoold be noted that the flight data contained herein are preliminary in nature.

'lhe instpmentation for this flight test included a variety of aircraft state and operating condition nenso:cs, bub and fuselage acceleraneters, and a strain~auge-eguipped blade. 'lhe strain~auged blade alsO carried a blade II'Otion sensot syBtBil capable of independently ueasuring blade position, and two blade-mounted acceJ.erC~Ieters. 'lhe acceleta!K':ters used during the flight test program were Entran Model

J:X>A-125-D (danped), and were located near the root and the tip of the blade, as

shown in Figure 12. '!tie root and tip accelerometers bad ranges of ±5g and +2.50g, respectively. 'lhe acceleranete:cs were I!O.mted alon:J the blade feathering axis to reduce pitch

cOupling

effects. 'lhe IOOUllting angles of the acceleraneters relative to the blade were chosen to best reflect a variety of flic;Jht speeds and conditiona, i~e~, blade collective settings.

'Iherefore, the accelerateters were placed SUCb that at mid-collective position, they were at zero pitch angle and their sensitive axes were in the b~ing direction. 'nlis a.rrangerrent is depicted in Figure

u.

'Jlle sensor used to independently determine blade position was the Sikorsky blade-relative-m:~tion hardloare system. 'Ibis unit allows meaauremnt of blade-flapping angle at the blade root, relative to the min roto.r shaft axis. 'nl.e blade-tootion system also allaw& measurement of the blade root pitch and lead-lag angles.

'lhe data acquisition system used during the tH-60A flight test prog:cam was the USMEFA HiO:Ip PO!. data system. Both accele:caooters and the independent m.in rotot flapping sensor were sanpled at a rate of 517 sanples per

second.

'Ibis rate allowed reliable resolution of the &ta up

to 80 Hz, Since the rotor rotational speed of the Ult-60A is raJghly 4 ,3 Hz, the &ta sanpling rate provided inforJIBtion well beyond the present frequency range of interest UP and bel<ML

••

'lhe objective of the flight measuremnts was to carpare the root and

tip acceleration IOOllSUt:emnts with values predicted by the silrple rigid-blade mxlel and to ooopare estirn!tted fllq:lping with that ~T~ePured by the

root""""IIOnted fllq;ping transducer~

Figures 14 and 15 shc:M the tilre histories and frequency spectra of the two acceleraroterB and the flapping transducer for an 80 kt. level flight

trim condition of the OH-60A helicopter. ~tiple harmonics of rotor speed

(4.3 Hz) are evident in the record, with 1P and 3P contribUtions being particularly strong. In order to estinBte flapping for purposes of controll.ing flight clynmnics, only the lower frequency respa1.ses at D-lP are of interest. ~e acceleraneter spectra, however, indicate significant 1P response due to bending, ilrplying the likelihood of additional contributions to the local values of blade slope and blade acceleration, Wich to;!ether detennine the accelerareter responses.

Fo:c sinple barnonic motion of a rigid blade at 1P with mean flapping

•

..,pJ;r..-ilo and~jll' the expected acceleraneter response is easily calculated. Using the IOOasured f~ing values for an so kt. trim. the estine.ted and neasured

tip acceleration are shown in Fig. 16(a). 'lbe result indicates that the anplitude of the rneamlred tip acceleration respawe is greater than the sinple roodel. prediction by a factor of five. It is likely that the increased output is due to the local slope and acceleration due to blade bending. 'lhe root accelerareter output was a.lm:lst identical to the expected respcnse, as shown in Figure 161bl.

'lbe rreasurements showed a significant P"mse lilift between tip and root ac-celeraneter signals [Fig. 16(c)]. 'Ihe tip signal appears to lead the root signal by 50 to 60 degrees of rotor azinuth in sare fligbt CXJnditions. and this lead was present in all the data to

sane

degree. Independent confirnntion of the existence of

Fhaae

differences due to bending can be seen in the analysis of Ol.-H blAde respc:nne calculations by Esculier and

BOUmran 1141.

'Ihe following analyuis, including blade bending in the acceleraneter signal, shows the physical basis for the above pbenaM:nll.

'Ihe flatwise acceleraneter signal including blade bending is

(8)

Were 11lxl • bending m:xle shape

gltl .. bending mX!e displacement

Assume .fJ ., iieiwt, g • §eiwt,

~

•

~

eiwt Were

ji

and

g

are

wi

RD2

catplex to accoont for phase. Also take l)(X) • 4 {

t l )

2 - 3{

t l

1-l: 1-l: where f(x,t) {10)

Equation {10) indicates that the blade-bending contribution to the acoolerometer 1P signal increases as the square of the opemd.se

accelel:(l(N!ter location x, Wile the flapping lP contribution is .invariant with span. For the data of Figure 15, the following lP flapping and

bending anplitudes were estinated, using equation {10):

IP

1 1 o.044 rad.

1911 .. 0.0038

~lji11

..

0.0021

f(x,tl

!s

₁1 .. -

o.ooo5o

(:inboard> f(x,l:l

19

₁

1

o.olS !outboard)

It is seen from equation (2) that the :inboard 1P acoeleraneter signal is flapping-d:::minated, while the out:board 1P accelero;ooter signal is

bending-dootinated.

For lP excitation, blade bending (natural frequency =:JPl has a srro.ll phase lag, and flapping !natural frequency l::1.Pl has a large phase lag. 'Iherefore the bending-d:::minated tip acceleraneter signal 1P catpOnent can

6-10-4

be expected to have a substantial lead over that of the fl.apping-daninated root acceler~er signal.

'lhe aOOve results su;gesl:. that blade 0-lP flapping estinntion can be acoooplished by using two inboard acceleraneters to minimize the blade bending contribution to the accelerareter signals. Alternatively, the blade flapping and bending response can be determined by using four spanwise acceleraneters and the I!Cthodology of Section 2 to solve for flapping lllld/or bending res:pawe.

1. 'lbe flight test results described above indicate that the use of bla.de-m:lunted accelerometers to est.i.nl!lte blade flapPing lllld flatwise

bending is feasible in terms of signal size and repeatability. 2. Inboard G-lP acceleraneter aignals are flapping-daninated.

'·

••

OUtbOard

G-lP ac:celerateter signals are bending-dominated.

Blade 0-lP flapping estinntion can be accatplished by using two :inboard accelerometers to minimize the bending contribJtion to the acceleroneter signals.

5. Blade O-lP flapping and bending estinntlon can be acCO!!plished b .. using four D~erometers. In this case, the bending a:ntribution to

the acceleraneter signal.&

can

be accounted for in estilro.ting blade

1.

f.lapplng.

Kretz. H., "P.eaearch in J.Ulticyclic and Act:i~ Control of Rotary Wings.• ~. 95-105, 1916.

2. Bam, N.D .. "A Sil'tple Systen for Helicopter Individual-Blade-Control USing K:x1aJ. Deoonposition", Vertica,

±•

23-28, 1980.

3, Ham, N.D. and McKillip, R.M., Jr., "A Sinple Systen for Helicopter Indlvidual-Blade-Ccntrol and Its Application to GJst Alleviation". Proc. 'lbirty-Sixth AHS Annual Nlltional Forum, washington. D.c •• May

1980.

4. Ham, N.D. and QJackenbush, T.R .. "A Sinple System for Helicopter Individual-Blade-Caltrol and Its Application to stall-Induced Vibratioo Allevia.tion", Proc. 1IHS Naticnal Specialists' Meeting oo Helicopter Vibratioo, Bllrtford,

cr.

Novenber 1981.

5. Bam, N.D., "Helicopter Individual-Blade-Control and Its A{:plications", Proc. 'Ihirty:Ninth MIS Mnual National Forum. St. Louis, I'D, May 1983.

6. Bam, N.D .. Behal, Brigitte L. and McKillip, R.M., Jr., "Helicopter flotor Lag Drurping Augtrentation 'nl.rough Individual-Blade-Control". Vertica,

1•

361-371. 1983.

7. M::Klllip, R.H. Jr .. "Periodic Control of the Individual-Blade-Centro. Helicopter Rotor•, Vertica.

!•

199-224, 1985.

8. Bam, N.D., "Helicopter Q.lfit Alleviation. Attitude Stabilization, and

Vibration Alleviation USing Individual-Blade-Control 'lb.rough a Conventional SWash Plate", Proc. Forty:First ABS Annual National

~· Fort w::>rth, Texas, M!l.y 1985.

9. McKillip. R.M. Jr •• "Kinematic Observers for Rotor Vibration Control." Proe. Forty:Second AH5 Annual Naticnal Forum•. June U86.

10. Bam, N.D., "Helicopter Individual-Blade-Control Research at MIT 1977-1985." Vertica 11, 109-121, 1987.

11. ~e. P.F .. "A Method for Reducing Helicopter Vibration,• JABS

.!•

3, July 1957.

12. Johnson,

w ..

Helicopter 'Iheory. Princetoo O.P .. 1980.

13. D...!Val. R.W .. •tJse of J.Ultiblade sensors for On-Line Rotor Tip-Path-Plane Est.imtion,• JABS 25, 4, Octcber 1980.

14. Esculier. J.E., and Bousm.n, w.G .. •calculated and Measured Blade structural Response on a FUll-scale Rotor•, Proc. Forty-second ABS

BLADE

X

Figure 1. Blade Flatwise Inertia Forces

I

I

: CONTROLLER

v

PITCH

1---OBSERVER

_ACIUATOR

~

6

Figure 3. Block Diagram of Flapping IBC System

6-10-5

+

Figure 2. Block Diagram of McKillip Filter

SUPERHARMONIC

1!.8

KEY,

<>1!.8

•

!m!.

...IL

:..

D

IJ

v

... 8.4

A

I

a

0

dl.

II.

2

_l

J

v

a

A

A

..

1

II.

1!.8

EXCITATION FREQUENCY

<>1!.8

:..

... 1!.4

_a

a

a

a

i

dl.

II.

2

l I

I

l

II.

SUBHARHONIC

:..<>1!.4! ... 1!.2

dl.

a.

..__A

__,l.___,i!,___,a.__,l_

II.

1!.2 1!.4 1!.8 6) /

0

GAIN EFFECT

ON

Fl.AI'P!NG

MU-.4

II.

1!.4 1!.8 1.2

~~

oasERVER

I

:

: CONTROLLER

v

PITCH

ACTUATOR

Figure 5. Block Diagram of Bending IBC System

...

• Flisbt Telt D.c•

•

•

•••• •••••••••••• 0

... ···

··¥~-,.~~.--~-.-~-...~---,

DAWri:DAWrUnCA'fiOH rA.CTOk

(J!I TO 1ST FLAP IEHDINC)

Figure 7. Effect of Blade Bending lmplification Factor on Maximum Cockpit Vibration level

OBSERVER CONTROLLER

v

PIJCH

ACTUATOR

Figure B. Block Diagram of lag IBC System

~

e

e

6-10-6

TIP ACCEL, VARIOUS FEEDBACK <14HZ)

2.

51

2.

j

1. 5

I

1. -~-

1-

r

T

I

I""'

,,.,;"'1""''

I

l

iii·-1--.1----1---J--..(.!..--1

313.

4121.

513.

60.

70.

80.

FREQ <HZ>

Figure 6. Open and Closed loop Flatwise Tip Accelerometer Response to White Noise Pitch Input in Hover

LAG ACCELERATION

DUE TO

PITCH

p.•0.27,

KR•0.3

"'

---.

I

I

----,---,

~

-20

----1---J

~I

I -

Opu Loop

1

o Closed Loop -40~---~---_J 0 I 2

LOG FREQ (RAD/S)

180

~

_,

- 0 - - , -

:::::)

"'

90

- - -

-

---j

w

_I

-0

--1

=I=

-w

0

I

lf)

_,_

<[

=~=

-I

:z:

_-90

a.

- I -

-I

-180

0

I

2

LOG FREQ (RAD/S)

Figure 9. Open and Closed Loop Acceleration Response to White Noise Pitch Input {p " 0.27)

figttre

10.

COLU!C!WE ' _ _ _

,..n

ACTUATORS t" f ti(l LATERAL

=

AC11JATORS

1---_,. e,

c

Block Diagram of F1<lPPi11!h ll~nding, or Lag Control System U5ing the Conventional swash Plate: Four-Bladed Rotor

ATI'ACHMENT

POINT

FEATiiElUNG

AXIS

Figure ll. Schematic of Bendfng Control System Using the Conventional

S'Wnh Plate:

Fnur-B-hded

Rotor {Drawn

lzy

.R.H.

lt:K:Hlip Jt.)

ACCELEROMETER

NOTE: BLADE Slml"CH NGr TO SCAlE

ELASTOMERIC

SEARING

Figure ll.

Root

and

Tip

Accelerometer locations an 00·60A !;lade

6-10-7

UH-60A LEVEL FLIGHT, 80 kt

"I:JJ UH-60A LEVEL FUGHT. 80 kt

·Ek:=3?::4v:+EF-+l-lll--+-L.--+1J-!\.

--1--c-L-+-J

---4

~"<fl!~bidfl.iLJlLLLt

0

<

o

L1J

i

;E::T:::£::4

_{1:11J "··}

L ..

J

..

J.

' " !

1

1.2

1.4

1.6

_{. o}

₁₀

_{20 .}

₃₀

₄₀

TIME.

sec

_FREQUENCY, hz

Figure 14. Typical Flapping Transducer and Accelerometer Time Histories Figure 15. Typical Flapping Transducer and Accelerometer Frequency Spectra

""

z

0

0.~

l"eJ

"'

()

~

UH-60A LEVEL FLIGHr, 80 kt

0

....

0

(a)

_MEASURED, ~·· 5 HZ FILTER--,..---... ~

"'

0

/

""'

/

i\_

/

"'

:;:rC---

--

../.--

--

;;~~---:-'-.../

-~ ESTIMATED/ 0 ~ ~~---.---~---,

<ol

(oJ

/

1-,

=-

_...__

'

//

/

/

_i\

r\

'

/

_{__,.}

'-...._/

_"'-./

PHASE SHIFT

=

-1.2

1.4

TIME, sec

Figure 16. Estimated Rigid-Blade-Model and Measured lP Accelerometer Time Histories

6-10-8

~

-!.6

so