(balke et al)tail rotor design part ii structural dynamics.pdf

8/10/2019 (Balke et al)Tail Rotor Design Part II Structural Dynamics.pdf

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Tail Rotor esign

Part II

Structural ynamics

R W. Balke

Assistant Dynamics Group Engineer

R.

L.

Bennett

PhD, Aeromechanics Engineer

T. M. Gaffey

Group Engineer VTOL Dynamics

R.

R. Lynn

Chief of Research and Development

Bell Helicopter Company

Fort Worth, Texas

In this Part

I

of

Tail Rotor Design, the structural dynamics

of stif f inplane tail rotor configurations are considered. First, the

placement of blade natural

frequencies

the method of calcula-

tion and the interaction between the natural frequencies and the

forcing functions are discussed in detail. Specific design guide-

lines are presented for two, three, and four blade rotors.

Second, the theoretical structural loading of a tail rotor is

treated and comparisons of theory and test results are given.

Finally, several aeroelastic phenomena associated with tail

rotors are discussed, including tail wagging, flut ter and di-

vergence, and blade motion stability. Throughout the text, spe-

cific problems which have been encountered are noted.

NOTATION

see Pa rt for notations not given here)

b tip-path-plane lateral flapping

CF

centrifugal forc e

Ip flapping inertia

mac mean aerodynamic chord

n

an integer

R rotor radius

V helicopter forw ard speed

flapping angle

AL perturbation lift

@ perturbation flapping angle

A@ perturbation pitch change

a

pitch-flap coupling angle, positive if pitch is

decreased when the b lade flaps up

advance ratio,

V aR

Presented at the 25th Annual National Forum of the American

Helicopter Society, May

1 9.

p

air density

aR

rotor ti p speed

a

main rotor rpm

a tail rotor rpm

w

fixed system excitation frequency

w

natur al frequency in th e rotating system

w

fundamental drive system natura l frequency

woo

static feathering natural frequency

NATURAL FREQUENCIES

FORMANY YEARS,

it was considered acceptable tail

rotor design practice merely to avoid the coincidence

of blade natural frequencies with rotor excitation fre-

quencies within th e flight oper ating regimes. Because of

the inadequacies of this approach in explaining the

overall behavior of a tail rotor, it was necessary to en-

gage in lengthy and expensive test programs to insure

the integrity of the hardware. Recent studies have

shown th at in addition to the aerodynamic excitahion

frequencies the effects

of

the main rotor , ta i l rotor

mounting, and transient loading must be considered

in defining th e proper frequency placement. Also these

items must he considered when interpreting test data.

With these items considered in the initial design stage

futur e development should be less costly an d tim e con-

suming.

I n the ensuing discussions, the term harmo nic is used

to denote frequencies which are integer multiples of

the ta il rotor rotational speed. The term nonharmonic

relates t o th e noninteger frequencies.



7

OCTOBER 1970 T A I L ROTOR DESIGN PAn l :

STRUCTURAL DYNAMICS

17

Uppel Frequency Lim it

Based on a review of flight data taken during tlic

development of the UH-1 and other Bell Helicopter

Co. helicopters, i t has been found th at oscillatory struc-

tur al loading of th e tail rotor is no t significant a t fre-

quencies greater than 150 Hz. This corresponds to 5

per rev for the UH-1 tail rotor. Since the upper fre-

quency limit will vary depending on tail rotor diameter

and n umb er of blades, it is suggested a nd bclieved t o be

conservative th at the per rev limit of be used in future

tail mtor blade design. Bell s tudies indicate that i t is

generally ade qua te to considcr only th e first four lower

modes of the tail rotor. Th is is somewhat less th an t he

5 per rev or the 150 cps l imit.

Figure l lustrates the above. Presented ar e typical

tail rotor blade bending moment amplitude spectra

11lots thr ou gh 200 1-12 using a system with unattenu ated

response througli 400 Hz. Principal excitation and

natu ral frequencies are noted. Above 100 Hz, for this

case, the higher frequency modes are suppressed by

structural and air damping.

Aeque ncy Placelnent

General Considerations.

The re are five gencral con-

straints on tail rotor frequency placement. These in-

volve consideration of: (1) resonant amplification; (2)

mounting isotropy; 3) fixed-rotating system tr ansfe r;

(4) f ixed system excitation; and (5) main rotor aerody-

nam ic excitations.

Reson ant Amplification. W ~t lii n th e upper fre-

quency limit, tail rotor forcing functions and natural

frequencies must not be coincident for any possiblc

steady-state operating conditions. This includes not

only the normal flight operating regimes and extremi-

ties of rotor spced and pitch, b ut also such conditions a s

ground idle.

For a seesaw two-bladed rotor system with high out-

of-plane rigidity, the first collective mode can easily

fal l coincident with 2-per-rev tail rotor excitations

within the ground idle range. Under certain wind and

pitch conditions, this can result in damaging struc tural

loads which significantly reduce the rotors fatigu e life.

Mounting Isotropy. Du rin g the development of the

UH-1, it was discovered th at out-of-balance or -track,

static phenomena in the rotating system produced large

2-per-rev loading of the blade. This was found to be

rclated to anisotropy or th e nonsymm etrical deflection

cliaracteristics of the tail rotor mounting which is a

func tion of rotor speed. T he unbala nce produced a

steady forcc in the rotating system which resnltcd in

1-per-rev fixed system motion. The elliptical hub mo-

tions at 1-per-rev produced 2-per-rev accelerations in

the rotating system. As the blade na tural frcquency was

close t o 2-per-rev, high struc tur al loads resulted from

the nonisotropy in combination with the m~balance.

Figure shows th at tail rotor inplane 2-per-rev loading

exists cvcn for a w ell balance d rotor.

Fixed-R otating System Transfer. Inpla ne accelera-

tions in t l ie rotating system with a frequency ratio

o,./ntr, can trans fer into th e nonrota ting system a t a

per-rev frequency of W ,

.

Similarly, mo-

tions in t l ie f ixed system transfer into the inplane ro-

tati ng system a t a per-rev frcquenc y ratio of (o,/Ot,)

=k 1.Accelerations a t these frequencics a re related t o

the cyclic modes. Symmetrical out-of-plane accelera-

t ions in the rotat ing sys tem t ransfer di rect ly to the

fixed system and vice versa without change in fre-

quency. These are related t o t he collective modes.

By considering these freqnency transfers, a simple

out-of-balan ce can procluce 0, 2, 4, 6 per-rev cyclic

excitations in the rotating system. Du e to system dam p-

ing, th e energy of th e higher modes is usually nil unless

tlie frequency transfer is reinforced by system reso-

nances. Th us it is clear, homever, th a t th e louver even-

harmonic transfer frequency can be amplified by the

cyclic mode tail-rotor na tu ra l frequencies which ar e lo-

cated t o avoid t he odcl pcr-rev forcing functions of tlie

two-bladccl rotor. This phcnomcnon should bc con-

sidered in design and during test.

Fized System Excitation. Bell s tudies show sig-

nificant contributions of stead y sta te and transient

fixccl system excitation to tail rotor loading. Fuselage

and fin accelcrations are particularly important when

their effectsare amplified b y the h ladc response.

Stea dy am plitude fuselage response is forced a t fre-

quencies equal to the m ain rotor speed n,,) and mnl-

tiples of th e blade passngc freq uency (nbn,,,,, w here n is

an integer and b is the number of main rotor blades).

Unless tlie fuselage responsc to a given main rotor fre-

quency a t he tail rotor location is qnite small, accelera-

tions a t th at frequency will be transferred into th e tail

ro tor system. S t l~ ~c tu ra l lyorne main rotor excitations

transfer directly,

om,

nd nbn,,,,, for the symmetrical

out-of-plane situa tion and a t in,,, n,,l and

InbCl,3,,

z

R,,I fo r th c cyclic inpla ne case.

Transient fuselage response that is caused by gusts

or rapid manenvers occurs at all the lourer values of

of the natu ral modes of vibration of the fuselage.

Consequently, the tail rotor is subjected to transient

accclcrations a t thos e frequencies. The se fixed system

excitations are reflected into the tail rotor rotating

system, as described before, to produce transient in-

plane blade structural loading with frequencies of

Jot, .

nt,J,

nd transient out-of-plane loacls a t fre-

quencies of

w

The forced and free fuselage vibrations give rise to

tail rotor hub response which is generally a spatial

motion resolvable into vertical and horizontal com-

ponents. Therefore, thcse motions m ay affcct both th e

inplanc and out-of-plane bladc loading. Generally,

the situ ation is agg rava ted because for a11 of t h e lower



..

R A LK E , B E N N E W , G A F F E S A N D IdYNS

JOURNAL O F THE ABIEIIICAN H ELICOPT ER SOCIETY

8

OUT OF PLANE AT 0 . 2 2 R ; 1 0 8 K NO TS L EV EL F L I G l l T

a .

2 7 . 5 1 1

2 4 0 j n = 3

b

OUT OF PLANE AT 0 .2 2R ; LEFT TURN ENTERED FROM 1 0 8 KNOTS: a,, 2 7 . 1 HZ

n=

1 2 0

1 S T OUT OF PLANE SYMMETRIC

2ND OUT OF PLANE SYMMETRIC

6 0 1 S T BEAM ASYMMETRIC 7

4 0

0 0

FREQUENCY - HZ

C

I N

P L A N E AT

0 . 0 5 ~ ; 108

KNOTS LEVEL

F L I G H T ;

n,,

2 7 . 5 H Z

4 0 0

n=

3 2 0

n=3

2 4 0

1

n=3

I

1 6 0

,

=

v

T 7

n = 1

m

n - 2

v

0

2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

& FREQUENCY - HZ

t

d

IN PLANE AT 0 . 0 5 ~ : LEFT T U R N

E N T E R E D

FROM 1 0 8 K N O T S ;

ntr

2 7 . 1 H Z

C

2 4 0 =I

v

n.2

v

LST OUT OF PIANE ASYllMETRIC

n = 3

n= v

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

FREQUENCY HZ

FIGURE

Tail rotor

lndc

bending moment n~nplitudespectra l>lots for UH-1E helicaptcr



fuselage niorles, the tail ro tor is locatetl a t or nea r a n

antinode. Thus, s ignificant transient tail rotor hub

accclerations occur for essentially all fuselage natural

frequencies and significaut stead y am plitud e responses

occur for most main rotor excitations in the low-

frequency range. Since good design practice requires

placement of the fuselage natura l frequencies so as t o

avoid coinciclencc with the primary liiain rotor forcing

frequencies, tlie trans ient respouse occurs a t frequencics

between tlie n. and

? ~ b n , ~ , ,

xcitations.

With numerous natural frcquencics in close prox-

imity to the ta il rotor ro tationa l s1,eeds and higher

harmon ics, the possibility of beating phenom ena

should be considered. F or instance, drivc systcm , fusc-

lage and rotor flapping frequencies can interac t to pro-

duce non-harmonic beating. I some cases, beating

modcs can couple strongly, producing subharmonic

aeroe lastic problems such as tail wagging discussed

latcr. Otlier beating phenomena occur and dissipate a t

random , suggestive of gust distnrbances. This has little

implication with respect to structural dcsign other tha n

th at its recognition is necessary fo r ]~ossible ate r cor-

rective action.

Main Rotor Aerod?lnaoaic Excitations.

Figurc

1

shows the existcnce of main rotor I-, 2-, 4-, and 6-per-

rev frcquencies in tail-rotor loads during steady state

and maneuver flight. Also the data show the existcnce

of a ma in rotor 3-per-rev reflected in th e rotatin g sys-

tem. During maneuvers, the tail rotor out-of-plane

loads occurring a t main rotor 2-per-rev and the inplane

loads associatcd with the main rotor 3-per-rev are

most significant. Analytical studies discussed later

show most of these occurrences and indicate a cause to

be the main rotor wake a t the tail rotor location. The

relat ive contr ib~~t ionf tlie aerodynamic and fuselage

cffects is unknow n.

F ~ g n rc 0, in a later section, shows calculated tail

rotor spectra with and mithout main rotor wake in-

cluded. These main rotor aerodynamic effects shonld

be ack~iowlcd ged in ta il rotor design by avoiding

placement of tail rotor natural frecluencies coincident

with the first scveral main rotor liarmonics (n,,,,,

nbn,,,,,

Inn.,,

-c a,, ,and

\nhR,, n,,

for n

1

2, and 3).

Additional work is required to define the number of

harmonics that should be considered as a function of

~iu mb cr f main rotor blades, tail rotor location and

the per t inent tai l rotor parameters . In Ref . 1 , i t

is

noted t ha t high inplane stresses and low bladc life will

result due to aerod ynam ic effects if t he in plane nat ura l

frequency is located a t

bn,?,, n .

Th e UH-I series uses a noninteger gcar ratio bctween

the main and tail rotors. With a nonintegcr ratio, the

relative position of t he main and ta il rotor blades con-

tinuously changes, placing them in close proximity

about I/second. During many of the tests with this

machine unusual tail rotor loading lias been observed

as spikes in t l lc blade out-of-plane tra cc n~b ich ome-

times occur n'hen the blades are in closest proximity.

Th e loading varies from flight to flight and even during

the same flight, so a definite cause-effect relationship

has been elusive. The loading is important, howcver,

and mnst be includcd in the aircraft's fatigue spectrum.

Tlie phenomenon is presented h ere as a m atte r of record

and to alerl tcst and stluctures personncl to i ts ex-

istence.

F ~ e q z ~ e n c ulacenaent Design Guides.

Followillg are

the frcquency place ment guides developed for tlie gen-

era l case of tail roto r design.

A)

For conventional semi-rigid tail rotor design

and construction methods, all vibration modes occur-

ring bclow 150 H z should be considered.

(B) IIrit1iin this frequency limit, tail rotor n atu ral

frequcncies should not be coincident with nor in close

proximity to exciting force frequcncies for any steady

sta te operating conditions including ground idle specd.

(C) I n acldition to the tai l rotor per-rev frcquencies,

an attc mp t should he made to avoid na tural frequencies

coincident mith the excitation sources s l i o ~ nn Tablc I

for values of n and i of 1 and 2, a t least.

The above general rules are i l lustrated for a t~vo-

bladed rotor by Fig. 2.

Tes t Dn tn and C ompavisons.

For the tcst case

-shown by Fig. la a n d l o n 5.4 Hz, a,, = 27.5 Hz

and the principal main rotor induced vibrations art

given by n = 1, 2, 3, and 4. Based on these frequencies

and us ing Table I steady st ate tail rotor inplane bend-

ing

moments

a t frequen cies of 5.9, 16 .7, 22.1, 32.9, 38.3,

43.7, 49.1, 54.1, 59.9 and 70.7 Hz would he anticipated.

Similarly steady state out-of-plane moments at 5.4,

10.8,21.6,32.4, and 43.2

Hz

could b e expected.

Tlie turo principal UH 1E vertical fuselage motles

i= 1 and

2

ar e located a t 6.7 to 7.0 and 15.0 to 15.9

Hz depending on gross wciglit, ballast and fuel loading.

TABLE I

Summary

of

Excitation

Sources

Sarrrce anisotropy

and urnbalance F~ eqoencies

n l ~ d e ode?

and

out-of-t~.nck

nbn .

innlane

cvelic

Fixed

system excitation

Steady state

collective

1 Inplane cyclic

UP Ont-of-nlnne

collect,ivc

Main r t r

nbn n /

Inplsne cyclic

neradynxmio n ntr S w

escitation nbn.... ... Out-of-nlnne

collective



RALICE BENNETT

G A F F E S ND

L Y N N

NORMAL O R R A T I N 3

SPEED

FIGURE

.

Excitnbion sources

of

a typical tmo-blncled stiff

inldnue rotor.

Based on Table

I

for the le ft turn shown in Figs. I b

and id with

n . = .3

Hz and at =

27.1

Hz transient

inplane hcnding moments at frequencies of

12.5 20.4

33.8 and 42.5 would be an ticipated duriug the maneu-

ver and in term ittently durin g level flight in response to

gusts. Similarly transient out-of-plane response could

be expcoted a t 6.7 and 15.0

Hz.

A review of Fig. 1 shows that a number of these do

in fac t occur and a re quite s igni f i can tpa r t i cu la r ly a t

44

Hz where the tail rotor first illplane cyclic natural

frequency is near

3n

n a t

43.7

Hz. Other fre-

quencics of interest include the first drive system tor -

sional mode

o

t

3.3

Ha the first out-of-planc cyclic

JOUIINAL OF THE A M E R I C A N HELICOPTER SOCIETY

mode varying from

88.3

to

96.6

over the normal col-

lective pitch and rotor speed rangc and th e first out-

of-plane collective mode which varies from

35.0

t o

36.7

Hz. The conclusion is simply that these non-

harmonic frequencies must not be coincidcnt with the

nat ura l frequencies of th e blade.

A

detailed examination of th e harmon ic and non-

harmon ic conteut of ou t-of-p lane bendiug moment

traces for a typic al rotor as a fu nction of flight speed

is given by Fig.

3.

Th e nonharmonic frequencies match

those listcrl above within the accu racy of the equipm ent

used to screen the d ata. Significantly the m agnitude of

the nonharmonic moments is generally th e same order

as those of the harmonic moments.

Significance The implications of the many aero-

dynamic and dynamic excitation sources are far

reaching. Wind tunnel tests of isolated tail rotors

cannot be cspcctcd to produce structural loading data

representative of actu al flight conditions; the need to

introduce significaut structural damping in the rotor

blade design is readily apparent; flight-test tail rotor

s t r ~ ~ c t n l . a lata will vary dependent on main-rotor

balance and track and the particular response char-

nctcristics; for n~ ean ing ful ail-rotor structural anal-

z

'

300

2

200

5

m

100

IRSPEED

N

IRSPEED - KN

FIG~IRE

.

Typical harmonic and nonhnrmanic bending moments

1 8 airspeed for UII-1E.



OCTOBER 1970

TAIL

ROTOR DESIGN

PART

: STHUCTURAL UYNAIIICS 21

Y

yses, fuselage response characteristics mu st be in-

cluded. Final ly, an at tempt s l~ouldhe made in de-

fining the configu ratio~l o increase th e isotropy o f the

tail rotor mounting.

If

this cannot be donc, some form

of tail rotor isolation may be desirable to attenuate

fixed system responses and increase th e isotropy.

Specific Requ iremen ts, Two-Bladed Roto r.

For a

two-bladed tail rotor, as indicated in Fig.

4,

I-,

3-

and 5-per-rev tail-rotor frequencies must be avoided

by thc cyclic modes and 2-,

4-,

and 6-per-rev hy the

collective modes. AtIargins of 0 .10-per-rev ar e ncccssa ry

dcpending on the modes. Usually greatcr nlargins are

required for tbe lower I~armonics.Th e shaded regions

in Pig. 4 show ma rgins of 0.25-per-rev. An atte m pt

sllonld be made to avoid natural frequencies coinci-

b

CY CLIC

MODES

WOWL

OPERATIEX:

SPE E D

F~oune .

Typical

frequency

plots

for an inplane

stiff

Lwo-

bladed tai l

rotor.

0

2 5 50 7 5

100

N O W O P E P A T I f f i S P E E D

FIUUHI.;. St~ onp cam-chord coupling with blade

pitch due

to

close proximity

of

out of plnnc

a ~ l d

ll plan^

mnd~s

dcnt \\,it11 the other significant excitations discussetl

earlicr.

I n the exanlple of F ig. 4, two near resouant con-

clitions are shown: the first inplane cyclic mode with

2-per-rev in the overspeed rang e (A ), and th e first

out-of-plane collcctivc mode with 2-per-rev at ground

idlc ( B ) . As shown on the figurc, these conditions

sl~oulclnot be a problcm; llowever, they do require

attention during developmental testing.

A further constraint that exists for t l le two-bladed

rotor is that t l lc f irst inplane symmetrical mode and

out-of-],lane S-ing mode mu st be separa ted from one

another so that in- and out-of-plane coupling is re-

duced and th e variation in natur al frequency with

collective. pitch is minimized. Th e consequences of

placing these modes close togcthcr are shown by

Fig. 5. For the case shown, the natural frequency of

both modes va ry ovcr 1 2 Hz (12 to

19 )

a s t h e

collective

pitch is changed from 0 to 15 . This broad

spread in frequency wit11 normal collective pitch values

makcs it very difficult to avoid resonances and other

source excitations cven with small rotor speed varia-

tions.

This situation can be avoided simply in theory.

In practice it is difficult because, for a practical sys-

tem, the simultan eous avoidanc e of all of t he cyclic

excitation sources is more of a n ar t- han a science.

Th e preferred approac h, wliich is different to th at

discussed above, involves placing t he S-in g mode below

3-per-rev and t he inplane mode well above 3-per-rev.

This is desirahle as i t te nds to decouple the frequencies

with bladc pitch, thus reducing the frequency varia tio~l

and permitting better placement. The inplane, out-of-



22

BALKE, BEUNETT GAFFET A N D LYNN

2 5

50 75 100

N O W

OPERATINO SPEED

PIOURE

.

Typical

frequency

plots

for

an i11plnnc stiff three

bladcd

tai l

rotor.

plane coupling also causes the S-ing modc frequency

to decrease with pitch, thus moving the system away

from resonance a t high pitch. Another approach t o

separate the first S-ing and inplane symmetric modes

involves placing the S-ing mode well above 3-per-rev

and the inplane mode below 3-per-rev. This has been

done successfully using high be am stiffness inboard.

Three-Bladed Rotor. Fo r three-bladed gimballed

rotors, many of the same considerations apply. The

placement of the cyclic modes is again the most dif-

ficult since

1-

2-, 4-, and 5-per-rev must be avoided

as well as the other forcing function frequencies noted

JOURNAL OF

THE

IEKIC N HBLICOPTER SOCIBTY

earlier. Figure Ga illustrates th e cyclic freque ncy plots

for a three-bladed rotor. Since less coupling exists,

location of both th e first bcam an d chord cyclic modes

betwecn 2- and 4-per-rev is preferred although the

boundary conditions make this less tractable. Place-

me nt of t h e collective modes, Fig. Gb, is no t a difficult

task whcn only the tail rotor aerodynamic excitations

are considered. Higllcr blade natural frequencies are

dictated, however, by th e o ther excitation sources.

Pour-Bladed Rotov.

For a four-bladed gimballed

ro tor , the p lacement of the cycli c modes i s al so t h

most difficult. With this configuration, the rigid or

scissoring modes mnnst also be tre ate d. Fig ure 7 shows

a typical frequency plot for a stiff inpla ne four-blader1

rotor. Typical f ixed system and aerodynamic source

excitations a re shown t o i l lustrate t he pro ble ~n of

frequency placement.

Significant 2-pcr-rev inplane forces occur in multi-

bladed rotors that are not gimbal mounted. These are

the Coriolis forces due to 1-per-rev flapping. For stiff

inplane designs, the resulting 2-per-rev loads will be

high and modes subject to this excitation must bc

ke pt well clear of 2-per-rev . In a three-blad ed rotor

this is the first inplane cyclic mode; for a four-bladed

rotor, it is th e inpla ne scissoring mode. I n four-blade.1

rotors, relief from the Coriolis loading may be gained

by allowing diffcrential action between th e two pa irs of

blades. Fignre 7c shows these rigid modes for the case

wherc 2-per-rev resonance occurs at opera ting rpln

( A ) . With proper design this situation can be avoidcrl

Frequency Detevmination

A

discrete element analysis for a rotating beam such

as My klcstad's2 or ih a t of Ref. 3 gives satisfactory re-

sults for purposes of frequency determination pro-

viding a sufficient num ber of blad e segments is used,

inplane-out-of-plane coupling is included and the

proper elemental stiffness parameters are used. Tor-

sional coupling for the rigid inplane design has been

found to be of sma ll consequence.

I n using such analy tical techniques, care must be

taken to obtain t he proper effective stiffness across the

grip-yoke bearing region. I n series of similar de-

signs, where empirical data are available to definc

radial hearing stiffness, good correlation between cal-

culated and measured frequencies has been achieved

for the first two collective and cyclic modes.

Wit h each change in hearing design or arrangement,

new elnpirical factors must be determined to obtain

correct frequencies from the analysis . The empirical

facto rs mu st account for complexities such a s bearing

play and centrifugal stiffening. Other empirical fac-

tors may be necessary to account fo r hub impedance

and isotropy. O ften these effects ar e q uitc nonlinear.

The principal problem in calculating exact fre-

quencies is th e definition of the above effect- which are



OCTOBER 197 PALL

LlOTOR

DESIGN P A R T : STKUCTZTHALDYNAXICS 23

oat

amenable to precise analysis. For this reason, a

very useful design technique is to incorporate pro-

visions for varying the effective stiffness across the

huh region (e.g., bearing spacing). These same factors

often negate the value of nonrotating frequency re-

sponse tests or measured whirl stand rlata. Blade fre-

qucncics should be dcterrnined by slolv rpm sweeps

with the helicopter on the ground, noting bending

moment response to determine the crossover points

where th e blade frequency is coincident with ~. ot or x-

citation frequencies.

STRUCTUR L

LO A D I N G

Excessive structural loading of tlie tail rotor has

been a problem du ring tlie develop mcnt of m an y single

F ~ a m s

. Frequency plots

far

an inplane sti iour bladed

tail

rotor

rotor he1icol)ters. Du e t o th e high ro tatiolial speeds

common to most designs, tlie number of loading cycles

accumulates rapidly on a tail rotor. This can lead to

short service life if the system stresses are not below

th e component s en durance lim it. Efficient and effective

design practice requires analytical techniques capable

of predicting accurately the structural loading.

nal l~ t ical pproach and i l t e thods

T he primary objective of this alialytical effort a t

Bell is to develop a time-variant aeroelastic-rotor-

response program capable of predicting the structural

loading and behavior of a tail rotor during stead y-

state and accelerated flight conditions. Although the

program is in its ear ly stages of developm ent ant1



24

BALKE, BENNETT, G FFEY

AND

LYNN

7

STEADY

CALCULATED

EASURED

T R U E A I R S P E E D ,

KN

F ~ o u n c

.

Comparison

of

calculated and test UH-1

tail

rotor

bending moments.

there are many improvclncnts yet to he made, the

results obtained and the ease with wl~ ich hey ma y be

interpreted portend an extremely useful computer rou-

tine for design and research purposes. I n the following

par agr al~ hs, he dy namic and aerodynamic aspects of

this simulation techniqu e are discussed in general term s

to acqu aint tlle reader with th e items considcrcd a nd in

somc cases , to s t a te n~hycertain apl)roaches were

adopted.

D?~710?1aics. he analytical technique used is com-

monly referred to a s the modal approach. This m ethod,

which is derived in Refs.

4

and

5,

involves the simnl-

tancous time variant solution of a system of equations

representing the selected normalized modes of vibra-

tion which a re treated as inpu t variables. The inpu t

elastic modes and frequencies are obtained by the

Myklestad technique mentioned earlier.

I n a n earlier section the upper frequency limit for

conventional tail rotor design was defined to be 150

Hz for medium size helicopters. This usually requires

the first four lower modes be considered. Th e effect of

vary ing the numb er of modes was investigated by

JOURNAL OF THE A h l E R l C A N HELICOPTER SOCIETY

simulating the behavior of a main rotor in a wind tu n-

nel. Up to eight modes were used in the analysis. The

results showed t b at su ch items as flapping, power, etc.,

were no t appreciably affected b y th e number of modes

used. Structural loads were found to vary only slightly

as thc ntnnb cr of modes were increased above fou r. A

typical ou t-of-plane blade bending moment varied only

10

as the

nodes

were increased from

4

to 7. The in-

vestigation ind icated t h at inclusion of t he fir st four

modes was sufficient for representation of stea dy st ate

main rotor behavior. Based on this main rotor study

an d a review of th e test da ta presented herein, it is be-

lieved tha t the tail rotor is adequately represented by

considering only the first four modes. This numhcr is

used in the analy tical results presented herein.

Aero~ l yna~~a i c s

he aerodynamic behavior is simu-

lated by use of classical techniq ues with t he local

blade segment aerodynam ic coefficients defined as a

function of Mach number and angle of attack, and

th e inclusion of such effects as main rotor wake, rigid-

body fuselage yaw motions, fin interference, induced

flo~v, and elastic feedb ack velocities. Tim e var yin g

li ft ancl dra g forces ar e calculated for each of 40

blade segments tip to tip) for the two-bladed rotors

studied. These forces are used in conjunction with

the input no rm al mode shape to def ine the t ime

depend ent forcing functions.

T he cffects of blade segment aerodyn amic pitchin g

moments and velocities associated with elastic mo-

tion of the fuselage ar e not included in th e aero-

dynam ic simulation. Recent work by Pau lT has indi-

cated that nonlinear destabilizing aerodynamic pitch-

ing moments ran produce a self-excited ti p path planc

oscilla .tion a t advan cing tip Ma ch nu mbers g reater

t ha n

0.92

for certain blade configurations. Recent

modifications of th e Bell program have included th e

effects of the aerodynamic pitching moment. The

effects of t he elasti c fuselage lnotions are expected to

be small from the aerodynamics standpoint; however,

STEADY OSCILLATORY

P

P

A Calculated A Calculated

Measured Measured

T R U E A I R S P E E D KN

F l o u n ~ . Control

loads.



6 RALKE, BENNETT, GAFFEY

AND

YNN

FIGURE1 Oscillagraph trace o tail r,ag.

responds to the natural frequcncy of the first inplane

cyclic mode, th e majo r component of th e total transie nt

loading; the second frequency is thc 1-pcr-rev forcing

function.

Frequency placement has been a primary design

tool used t o avoid or reduce oscillatory load levels.

Th e above indicates th at much futu re research and

development effort should be directed toward increasing

the structural damping in tail rotor blades. Whenever

a practical method for increasing structural damping

is achieved, a new tool will be available to reduce

oscillatoly loading.

AEROELASTICITY

Stability

M ain roto r flapping instabilit y has been of concern

recently because of t he increase in helicopter speed a nd

the conc ept of slowing th e rotor on compound lielicop-

ters. Since the ta il rotor generally operates a t abou t

the sam e advance ratio as the main rotor, i.t is also sub-

ject to flapping instabili ty. Pure flapping instabili ty is

less of a problem fo r th e tail rotor because of i ts lower

Lock number; however, additional considerations arise

because of i ts mounting on the tai l hoom. There a re

strong aerodynamic and inestia couplings between

the tail rotor flapping and tail boom modes which can

cause instabili ty. Tail rotor aeroelastic phenomena

u~hichhave been encountered a t Bell and the ir ex-

planations are given in this section.

Tail Wagging

During the flight tests of several

experimental tail rotors, a n instabili ty was encountered

where the tail rotor flapping coupled with a tail boom

JOURNAL OF THE A b I E R I C A N HELICOPTER SOCIETY

latcral bending-torsion mode. This coupling produces

a sensation in the cabin th at the tai l boom is wag-

ging; hence, th e name.

A similar phenomenon which has been encountered

is related to the engine exhaust. Fo r ce rtain conditions,

the hot engine cxhaust impingcs on the tail rotor

causing oscillatory thr ust and flapping. This has often

been mistakenly identified a s tail wagg ing; however,

i t is of very Ion. amplitude and disappears at higher

speeds or if the helicopter is yawed. Minor changes in

the engine exhaust nonzle hav e corrected th is situation.

Tail wagging nonnally

increases

in ampli tude as

airspeed increases so that the crew is alertetl before

the amplitude reaches a dangerous level;

how eve^.

in

several cases it was encountered without warning, and

appeared to bc divergent. An

oscillograph recording

of one occurrence of tail wagging is shown in Fig.

11

In the case shown, a Model 47 tail rotor with the

pitch-flap coupling,

$,

increased from +45' to

+581/20 was being evaluated.

A

pedal displacement at

100 mph initiatcd a limit amplitude wagging, which

could bc stopped only by redncing airspeed. The fre-

quency of wagging was 7.2 Hz n ~h ic h s close to the

Model 47 tail hoom sccond lateral hending-torsion

natural frequcncy.

Pitch-flap coupling has been identified as the canse

of tail n~agging.This can bc explained as follows:

a t the tail boom na tural frequencies, tail rotor f lapping

lags the tail Boom angular motion. This is due to the

tail boom natural frequencies being much higher than

the fixed system flapping natural frequency. For

example, the UH 1 tail rotor flapping frequency is

1.088-per-rev in th e rotating system.

I n

th e fixed sys-

tem thi s appe ars a s a 0.088-per-rcv, ~vllich s 2.4 H z .

TAIL

B W H

BENTIN

VELOCITY

b) swnce

1

DESTABILIZ~G

THRUST DAMPI

F ~ o u ~ a2

Tail

boom mode shape and EOUtCe

of

negative

damping.



OCTOBER 1970

TAIL E O T O R DESIGN PART

T he tai l boom first coupled late ral be nding-torsion

mode natural frequency is about 6.5 Hz. The mode

shape of this mode is shown in Fig. 12% If tl:e system

were undamped, flapping would lag the tail boom

motion by 180 ; however, flapping is heavily damped,

abo ut 12 to 1 5% of critical in the rotating system, so

th e lag is less tha n 180'. Thus, when th e tail boom is a t

its maximum bending velocity (Fig. 12b) there will be

some lateral (bl) f lapping. Sincc a moment balance

must be maintained on the advancing b ladc, the force

associated with the moment will be proportional to

b l n R

V 2 an

Sg

and on the ret reat ing blade to

b , ( n R )2 t a n

S3.

Since thesc forces are not equal,

a changc in tail rotor th rus t is generated. Th is change

in thrust is proportional to bl tan

S3

and for conven-

tional pitch-flal~ oupling acts in the sam e direction as

the tail boom bending velocity. Since it tends to in-

crease tlie tail boom motion. thc thrust constitutes

negativc damping.

Figu re 13 shows ?vIodcl UH -1 calculated tail boom

latera l bending-torsion mode dam ping versus airspeed

for several values of pitch-flap coupling. For this m a-

chine wli~ ch as S3 +3S0, no problem is indicated

within the possible flight regime.

It

i s apparen t tha t

one solution to tail wagging is to rcduce the pitch-flap

coupling or to use unconv entional, negativc S3.Another

solution is to reduce tlie am oun t of struc tural coupling

by either stiffening tlie tail boom torsionally or by

relocating the tail rotor closer to the boom neutra l axis.

Ncgative

Sa

appears to be the bcst so lut io~ i ince i t

increases the damping of the tail boom modes. Ex-

tensive flight testin g of t ai l rotors with neg ative

8s

has been made to prove its suitabili ty. Flapping and

loads nrcre essentially identical t o those of a sim ilar

tail rotor with conventional positive Sa.

Another possible destabilizing source involves the

tail rotor drive train. When tail wag was first en-

countered it was speculated that i t mas caused by

coupling with th e drive tra in. A lthough tl ie theoretical

s tudies have Shown that this i s not the case in this

instance, there is evidence that the drive system does

have an effect on tail wag. For example, on the

UH-1 a tail rotor drive system natural frequency is

nhout 8 Ha which is close to th e tail boom nat ura l frc-

clucncy. I hovcr, the tail rotor adds considerable

damping to the tail boom mode due to the change in

inflow caused by the boom bending velocity. 'This can

am ou nt to 3-4% of critical dam ping (see Fig. 13).

With the drive system frequency close to th e bending

mode frequency, the tail rotor will speed up and slow

down slightly in response to torque changes which

accompany a thrus t change; this reduces the a~nount

of thrust damping. The net result is a decrease in

the tail wagging stabili ty.

Blade Motion.

Bladr motion instability is a possi-

bili ty if thc lo~v est nplnne natu ral frequency is lo-

11:

STRUCTURAL DYNAMICS

27

...

VELO ITY

Kn

FIGUR

3.

Calculnted UH I

tail-hoom

damping vs speed and

pitch

flap conpline

catccl slightly higher than the flapping natural fre-

quency.O This is primarily a problem with tail rotors

where the inplane mode is located between 1 and

2-per-rev and which use positive

SB

Positive

S3

causes

an increase in flapping natu ral frequcncy a s a function

of advance ratio. Under the adverse conditions noted

above, a t some forward speecl th e flapping a nd inplane

blade bending frequency will become coincident. This

typ c of in stabilit y was encountered with an experi-

mental main rotor where the inplane frequency was

about 1.5-per-rev and a

S3

+39 was used. On the

UH-1 tail rotor, a similar iuplane bending-pitch-flap

coupling exists; however, thc blade motion is very

stable. Thi s is th e rcsult of t he low Lock num ber of

the UH-1 tail rotor wliich reduces the effect of the

pitch-flap coupling on the flapping natural frequency.

Blade motion instability is eliminated for stiff inplane

rotors by using negative

SR

placing the lowest inplane

natural frequency above 2-per-rev, or by reducing the

rotor Lock number.

Flut ter and Divergence

As far as is known classical blade flutter involving

flapping and torsion has never been encountered with a

Bell tail rotor. This may be surprising since Bell tail

rotors are not mass balanced and use large values of

pitch-flap coupling. For example: the UH-1 tail rotor

has a n effective chordwise center of grav ity a t 37.5%

blade chord and its pitch-flap coupling is

S3

+38O.

For a m ain rotor, this com bination of blade center of

gravity and pitch-flap coupling n~ ou ld cause blade

flutter, even with a stiff control system. S tud y shows

that there are three reasons why the Bel l type tai l

rotors are less susceptible to flutter. First, tlie systems

l>ossessa very high stiffness of the blad e control system



28

BALKE BENNElT

GARFEY

AND

LYNN

4

EFFECTIVE

CO

PERCENT

M C

P~ouns14. UH 1 rotor flutter and divergence boundaries

which, in part, results from the lack of cyclic pitch;

second, the damping about the pitch change hearing is

quite high; and third, th e tail rotor is not a s susceptible

to fluttcr or divergence as a main ro tor because of its

higher relative mass. The last reason is primary and

will be discussed in more detail below.

Shown in Fig. 148 ar e calculated flutter and diver-

gence boundaries for the UH-1 tail rotor. These are

for a blade assumed rigid in bending and with all

torsional flexibility concentrated a t the root. In-

clusion of b lade bending a nd torsion flexibility in th e

calculation causes only a slight reduction in tlie bound-

ary. Dam ping for the pitch-change bearing was n ot in-

cluded in tlie calculations. For comparison, calcnlatcd

flutter and divergence boundaries for the UH-1 main

rotor are shown in Fig. 14b. These boundarie are also

for a blade rigid in hending and with all torsion con-

centrated a t the root. For t he main rotor, blade bending

has a more significant effect than for the tail rotor;

particularly blade inplane bend ing, since flutter occurs

first in th at mode. For the purposes of this comparison,

main rotor fiutter and divergence calculations were

made on th e same basis as those of the ta il rotor. It

can be seen that the tail rotor is considerably less

crit ical from the flutter standpoint than the main

rotor.

The differences between the flutter and divergence

characteristics of the main and tail rotors will be

understood when it is realized th at th e ta il rotor is not

simply a scaled-down main rotor. Requiremeiits im-

posed by the tail 's rotor more severe environment rc-

sult in blades th at are relatively

6

times as stiff, and

consequently much heavier than those of a Mach-

scaled main rotor. This increase in relative inertia is

apparent in the UH-1 tail rotor where the Lock num-

ber is about 2 compared to about for the main

rotor. Another significant difference, peculiar to the

UH-I, is the construction methods. For example, the

UH-I, tail rotor has a 0.025 stainless steel abrasion

strip-the same thickness as th a t of the UH-1 main

rotor. This and the lower aspect ratio of t he ta il rotor

blade cause its feathe ring inertia to be much gre ater

relative to the flapping inertia than th at of the main

rotor.

The impact of the tail rotor's heavier construction

on flutter and divergence can he understood by con-

sidering the mechanism of blade flapping divergence.

Similar reasoning can also be used to explain the

difference in blade flutter characteristics. Figure 15

illustrates tl ie divergence mechanism a t the point o f

neu tral static stability-when the inertia an d dam ping

forces are zero. As shown, a perturhation increase in

blade lift, AL will cause the blade to flap upward

through a flapping angle p so that the flapping mo-

ment from the centrifugal acceleration normal to the

hlade is equal to the aerodynamic flapping moment.

If the section center of gravity is off of the pitch-

change axis this centrifugal force normal component

produces a torquc about the pitch-change axis. If tlie

center-of-gm vity is af t of t he pitch change axis, this

moment is nose op. f there is control system flexibility,

PITCH C-E XIS

CFP

ZERO FIA PPIN G

REFERENCE

Froun~15. Mechanism

of

flapping divergence



o c l . o n ~ n 970

TAIL

ROTOR DESIGN PART 11: STRUCTITRAL DPNhnIrcs 29

an increase in pitch results which causes a further

increasc in flapping. If the control system is too soft,

flapping will diverge.

Divergence is prcvented by two nose-down moments.

One is the control system; the second is the tennis

racket effect which, by itself, is capable of preventing

divergence (see Fig.

14

for w /n

0 ) .

I n Bell ta i l

rotors the tennis racket moment, which is approxi-

matcly proportional to the blade feathering inertia is

greate r thn n tha t of a scaled main rotor because of th e

blade construction. This is reflected in the

UH-1

ta i l

rotor 's divergence hounda~y,Fig.

14a,

which shows

freedom fro m divergence for effective center of grav i-

ties of ul) to

48%

mac even with zero control system

stiffness ( ~ , / n 0 ) . For comparison, the UH-1 main

roto r would diverg e if the effective center of g rav ity

were a ft of 26.5% mac (Fig. 14b) .

Beal ing Dan~ping.

It was pointed out earlier that

the centrifugal force on mo st present Bell tail rotors is

carried by a thr ust hearing which also acts a s a pitch

change hearing. Considerable mechanical pitch damp-

ing is generated by th is arrangement. Figure 16 shows

the calculated effect of pitch-change bearing damping

on the flutter and divergence boundaries.

It

is seen

that control system frequency requirements are re-

duced significantly as t l ~ e amping is incrensctl .

CRU-

tion m ust be exercised, hon ~ev er, or bearing dampin g

cann ot he relied on to prevent flutter problems if there

is a large amo unt of bncklash in the control system.

Pitch-Flap Coupling and Divergence. Bell tail

rotors normally employ pitch-Hap coupling ratios of

-0.7 to -1.0

a3 35

to 45 ) to rcducc tail rotor

flapping. As noted, t he aerodynam ic effects of 8% re dis-

cussed in Part I

It

is well known that conventional

pitch-flap coupling (hlad e pitch is reduced when th e

E PFE C T N E CG

PERCENI U C

P ~ c u n ~6.

Effect of pitch-axie damping on UH-1 tnil rotor

flutter

characteristics.

EFFE TWE

E PERCENI PUD

FIOURE7 Effcct of pitch-flap eaupliag on UH-1 t n i l ru lor

flutter characteristics.

blade flaps up) has an adverse effe ct on flu tter. Posi-

tive pitch-flap coupling, however, does decrease the

possibility of flapping divergence. Unconventionnl

pitch-flap coupling, or negative S3, has a stabilizing in-

fluence on hlade flutter. With negative Sa, some loss of

stat ic stability (divergence) is incurred bu t this is no t a

problem on most rotors. Figure 17 shows the effect of

pitch-flap coupling on the UW-1 tail rotor's flutter and

divergence boundaries. Thc cffect is much less than it

nrould he on a main rotor because of t he lrigher re1 at ve

illass of the ta il roto r.

Solne atld itio nal discussion of th e effect of unco nve n-

tional pitch-flap coupling is in ortler, especially in view

of comments by several authors t ha t i t can not be used

because of th e divergence problems.1° Thi s is prob ably

true in the case of fully articulated main rotors where

the hlade Lock number is very high. For semirigid

rotors, divergence is not a problem because of th e lower

Lock numbers. Assumii~ga rigid control system, the

pitch-flap coupling ratio that causes flapping diver-

gence can be determined by settin g the flapping nat ura l

frequency equal to zero. The pitch-flap coupling for

flapping divergence is given as

AB/APai

y.rr.c p.

a n

Sn

Wy.

Even though this divergence boundary must be re-

duced somewhat to provide for secondary effects, this

simple approach shows that relatively large values of

unconventional pitch-Hap coupling may be used on

tail rotors where th e Lock numb er is less th an 4.0.

REFERENCES

1. Normand, Y., Diverge7~t Vibration BL Helicopter

ail

Rotors presented nt Inter~ iation al Antomotive Engi-

neering Congress, Detroit ,

Mich.,

1965.



30 BALKE BENNETT GAFFES *XI YSS

JOURNAL

OP

THE AMERICAN

RELICOPTER SOCIETY

2 Myk lestad, N . O., Vibration Analysis, McCram -Hill Book

Co., Inc., Nem I'ork, 1944.

3 Bla~~keush ip ,. L. and Harvcy, I< I1. A D igita l An-

alysis for Helicopter Per form al~c c nd Roto r Blade Bend-

ing Rton~ents, 7,

4)

J. America>& elicopter Society

(Oetobcr 1962).

4.

Etkin, Bernard, Dynanlics of Flight, John Wiley aud

Sons, Inc., New York, 1959.

5. Timosheuko, S., Vibration Problems in Engineering,

D.

\'a.~~N ostrand om pany, Inc., Prinecton, N.J., 1955.

6

Gessoxx., I and Myers,

G. C .

Jr., Aerodynanzics of the

Helicopter, The, Th e AlacMilliam Co., Nexv I'ork, 1952.

i

aul, 11 . F. A Self-Excited Ro tor Blade Oscillation at

High Subsonic Mach Numbers, 14 (1) J . American

Helicopter Society (January 1969).

8. Crimi, P., Theoretical Prediction of the Flow in the

Wake of

a

Helicopter Rotor, CAL No. BB-1994-S-1,

Cornell Aeronautical Laboratory, Inc., Buffalo, N.Y.,

September 1965.

9. Gatiey, T. M., The Etieot of Positive Pitch-Flap

Coupling (Negative S3 on Rotor Blade Motion Sta-

bility and Flapping,

J.

Amelican Helicopter Society,

14 (2) (April 1969).

10. Mil, M. L. et al, Helicopte1.s-Calculation and Design

Volume I Aerodynamics, NASA Technical Translation,

NASA T T F4 94 , September 1967.

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