analisis de estructura dinamica para helicopteros

8/10/2019 Analisis de Estructura Dinamica Para Helicopteros

1/47

N O T I C E

THIS DOCUMENT HAS BEEN REPRODUCED FROM

MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT

CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED

IN THE INTEREST OF MAKING AVAILABLE AS MUCH

INFORMATION AS POSSIBLE


2/47

'

EPARTMENT OF

MECHANICAL ^ AEROSPACE

ENGINEERING

(NASA-C8-1627541 AERODXNAlIIC-STRUCTURAL

80-17061

ANALYSIS OF DO AL BLADED HELICOPTER SYSTEIiS

Final Technical Report (tlissouri Univ.

-Rolla.) 46 p HC A03

/ SF A01

SCL OiC 63/05 471035

I N A L T E C H N I C A L R E P O R T

AERODYNAMIC-STRUCTURAL ANALYSIS OF

DUAL BLADED HELICOPTER SYSTEMS

NASA AMES NSG-2375

BY

BRUCE

P.

SELBERG

_

.

D ON AL D L. CRONIN

^^"^^^" "''^''^

KAMRAN ROKHSAZ

`

c

^

JOHN

R.

DYKMAN

R^'CS^ FPC^^.

^,

S^ `

4a

`` ^

Li

^^ `p^

FEBRUARY

19HO

U N IVER SITY O F M ISSO U R I - R O LLA


3/47

. .

AERODYNAMIC-STRUCTURAL ANALYSIS OF

DUAL BLADED HELICOPTER SYSTEMS

Aerodynamic Analysis

Bruce P. Selberg

amran Rokhsaz

ssociate Professor

raduate Research As:i^tant

Structural Analysis

Donald L. Cronin

ohn R. Dylan

arla J. Yager

Professor

esearch Assistant Research Assistant

February 1980

Department of Mechanical and Aerospace Engineering

University of Missouri-Rolla

Rolla, MO

5401


4/47

^{

^,

THIS DOCUMENT SHOULD NOT BE CONStDERED AS AN OPEN PUBLICATION IN THAT IT CON-

TAINS PROPRIETARY INFORMATION THAT HAS BEEN FILED IN A PATENT DISCLOSURE

^-

^^

i


5/47

I

SUtrQrIARY

The a e r o d y n a m i c a n a l y s i s i n d i c a te d s i gn i f s c a n t powe r s a vi n gs fo r the bi r o to r

over the monorotor fc

r St ^ 1.0, Ga ^ 0.26 and either De ^ -4 d egrees or De ^ -b de-

grees. These sav ing s occu red for all th ree rot or radii at De ^ -6 deg rees and for

t h e sev ent een and twent y feet radii at De = -

4

degrees. When these results are con-

-

idered with th e st ru ct u ral analysis which indicat es th at for bot h th e sev ent een and

, -

ou rt een feet cases, where th e birot or and mo norot or are of equal weig h t s, th e biro-

. ,

or def lect ions are of th e same gene ral mag nit u de as th e monorot or with one tip con-

nect ion between th e birot or blade s. The tip connect ion is required becau se of th e

.

u nev en loads on th e upp er and lower rot ors and th e sensit iv it y of th e aerodynamics

to d e c a l a ge a n gl e a n d ga p.

more opt imiz ed st ru ct u ral syst em in which th e blade weig ht is redu ced mig h t

mov e th e blade radiu s of th e birot or closer to 14 feet case. In th is area th e bi-

rot or wou ld weig h less while st ill exhib iting th e imp rov ed aer odynamics for St

s

1.0,

Ga 0.26, and De

s

-

6

d e g r e e s . W h i l e i t i s r e a l i z e d t h a t t h e e n c l o s e d a n a l y s i s h a s

not achieved the optimal aerodynamic struc tural birotor conf figuration it has demon-

st rat ed birot or feasib ilit y in th at th e birot or syst em c an op erat e with sub st ant ial

required power savings with no weight penalty or with substantial weight savings for

the s a m e r equi r e d powe r a s the s i n gl e r o to r.

3


6/47

` - - -

AERQDYKAPIIC SiJAQL4RY

An analytical study was undertaken to assess the aerodynamic fea sibility of the

birot^^r blade concept. The study investigated:

. Inviscid flow field about dual bladed rotor.

. Boundary layer separation on the rotors.

^}

3.

Three dimensional induced drag calculations.

4.

Rotor thrust and power required.

The aerodynamic study led to the following conclusions:

-

. The best aerodynamic res ults for the dual rotor occurred for a blad e stagger

of one chord length, a blade gap o f twenty six percent of the chord length,

nd an angle of attack between the two blades of -6 degreea.

j

^. For blade placement ; i.e. stagger -St, gap -Ga, ar^i decal age angle -De, that

gave the improved aerodynamic results, the boundary layer separated further

back on the dual blades than for the single bladed rotor.

3.

The delayed separation over the dual bladed rotor sy stems results in a lower

pressure and viscous drag than for the single blade.

4.

The induced drag and, hence, induced torque is lower for the dual rotor sy-

stem than the single rotor system when decalage angles are -4 and -6 degrees.

5.

The dual rotor at a Ga 0.26, St 1.0, and De -6 degrees requires signi-

f i c a n t l y low er p ow er lev e l s t h a n t h e si n g l e rot o r. T h e du a l rot o r at t h e

same gap and stagg er, but with De -4 degrees , also requires lower power

lev els.

6.

The dual rotor at a Ga 0.33, St = 1.0, Pe g

-4 degrees and -6 d^^rees re-

quires lower power levels than the single rotor.

7.

As a result of the lift of the upper a nd lower dual rotors bein g different

nd the sensitivity of the results to proper gap and decal age angles, it will

_

e necessary to tie the two rotors together at the tips with a possible adds-

=

ion tie at the position of the second bendi ng moment.

4^

4


7/47

^_ .

. .

AERODYNAMIC-STRUCTURAL ANALYSIS OF DUAL BLADED HELICOPTER SYSTEMS

An aerodynamic-structural analysis was carried out for dual bladed and single

bladed helicopter rotor

systet;a,

At y p i c a l b i r o t o r c o n f i g u r a t i o n , a s i t w o u l d b e

mounted, is shown in figure 1. The upper and lower blades maintain this same posi--

^

ion relative to one another as they rotate . An end view of the blades are sh own

in figure 2. The distance one blade is ahead of the ot her is called stagger i n per-

#

ent of chord, 5t, with a positive stagger indicating the upper blade is forward of

- -

t^e lower blade. The gap, in percent of chord, is desi gnated Ga. The angle of at-

tack between the two blades is called decalag e angle, De, and is negative when the

extended chord lines intersect in front of the two blade elements . The aerodynamic

^

tructural analysis considered the hover mode of operation and all dual bladed sy-

stems were chosen to have the s ame lifting area as the single bladed system. In

addition aspect ratio of the single bladed rotor was selected as 20 and each aero-

dynamic birotor blade was selected such that they had the same aspect ratio as the

single rotor. Three different diameter birotor combinations were chosen to assess

aerodynamic and stru ctural performance, 28, 37, and 40 feet in diame ter. A constant

chord NACA 0012 airfoil section with an 8 degree lin ear twist was selected for all

calculations. The blades had an airfoil sec tion form 0.25R to R where R is the

blade radius from the hub of rotation. Rotor tip velocity for all cases was 600

feet per second. The blade sizes along with the mode of operation are shown in

Table 1.

AERODYNAMIC ANALYSIS

The analysis level can most easily be discussed with respect to four main areas

which are listed below:

1.

Inviscid flow field analysis to investigate aerodynamic characteristics for

various dual rotor blade placement combinations with respect to blade stag-

ger, gap, and angle of a ttack between the two blades.

2.

Boundary layer separation point analysis and subsequent viscous and pressure

drag analysis.

=

. Induced drag calculation for the three dimensional dual and single rotor sy-

stem.

4, Compilation and integration of the above to predic t Chrtist and power require-

ments.

5


8/47

.

^

.

^

.

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^

,

-

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~ ~~~_~ . - _ ~- . - _~- -, .__..~ ---~ _=_.. - _ ~,_ - _, . ,-~- ;

-~ _

~~r

~_--

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--

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^

.

.

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L

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9/47

i

1

4 1

t

W

v

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7


10/47

_ ^ ^ _ -

-

ma

y.

n

r - -

_- -

ABLE

1

AIRFOIL CHARACTERISTICS

A 0012 const nt cho rd blade

A

8 degree li near twist from 0 .25R to R

Rotor tip speed - 600 feat per second

Single rotor blade dimensions

iameter w

40 feet

chord

feet

s

Dual rotor blade dimensions

Case I

^ s

iameter 28

eet

hord

1.415 feet

Case II

diameter 37

eet

^

hord

.175 feet

Case III

diameter ^ 40

eet

chord

1.0 f oot

nviscid A:^alysis

Nenadovitch 1

who did extensive computatio ns and tests with two element airfo ils

btained aerodynamic impro vements for the two element case over the single element

-

a s e on l y in a n a r r ow ra n g e of S t , G a, an d D e. Th is reg i o n w as w h en S t

s

1 . 0 ,

Ga ^ .33 to

.

66,

and De -3 to - 6

d e g r e e s. Fo r ga ps gr e a t e r tha n o n e , n e ga t i v e

z 6

taggers, or for positive decalage angles the two element aerodynamic chara cteris-

tics were degraded with respect to the single ele ment.

, . ^

aplace's equation of the stream function was solved using a f inite difference

p p r o a c h in a C art e s i a n co o r d i n a t e sy s t e m. P res s u r e di s t r i b u t i o n re s u l t s f o r t h e

NACA 0012 airfoil se ction were com pared with those o f Raj

2 , Eppler

3

, and G.-.abedian^

4_

to validate the numerica l technique with agreement being excellent.

The inviscid computational analysis was carried out in this narrow region of

S t , G a, an d D e w h er e N ea d o v i t c h f ou n d ae r o d y n a m i c imp r o v e m e n t s. F ig u r e 3 is t h e

pressure coeff icient, Cp, distribution for the upper and lower elements for a St 1.0,

+

a 0.26, and De -4 degrees for the lower airfoil at a geometric angle of attack

8


11/47

^-

----

UPPFR AIRFOIL OF A

T

VYO AIRFOIL SY STEM

NACA

0012 , S t

= 1 . 0 G o = o . 2 s

e

,1

1

0

------

INGLE' AIRFOIL

^

,

ACA 00 12 , ^s4

rt

^

,_

1

rti

_ yr - r . .... r .r ...

..' .

p

^^.O

--

/C

/.0

----

LO^f

R

A1 RFOlL OF A

T

V^O AIRFOIL SY STE'r l

NACA 0012 , a=a

n

'

0 ` '

^--- SINGLE A1RFD/L

^'^-.__

ACA 0 0 /2 , a=4

-..

-_

-,

C o.o

---

--. - __ .... . . . _ .._ . ,

P

-

^ . _

^

^^

O

1.0

Figure ?

9


12/47

_

_____a_=

rte-_

- - -s -__

_

. y

of 4 deg rees. Superimp osed is th e pressu re dist rib u t ion for a sing le airf oil ele -

ment at 4 degree geom etric angle of attack. Even though the upper airfoil is a-. a

sero geomet ric ang le of att ack with resp ect to th e freest rsam vsioeit y

v sct or it

has

a

pressure disti^ibutian and hence a lift that corresponds to approximately 4 de-

g ree ang le of att ack. The resu lt ing lif t vsct os on th e upp er airf oil is thu s rot at ed

^ ^

iving an effective thrust or negative drag with respect to the direction of nation.

The loner airf oil has a Cp dist rib u t ion slig h t ly less th an th e 4 deg ree sing le air-

oil case. The net resu lt for th e comb ined two elemen t s is small ch ang es i n tot al

lif t coef f icient along with a neg at iv e indu ced two dimensional drag coe f f icient ,

CD z i

. At an 8 deg ree geome t ric ang le of att ack a simi lar dist rib u t ion is s h ows in

figure 4. Again the upper airfoil, due t o the f

] aw int eract ion, is act ing lik e a

single airfoil at a angle of attack greater than

$ degree even though the geaaetsic

ng le of att ack is only 4 deg rees. Alth oug h th e lower airf oil has a Cp dist rib u t ion

orresponding only to a four degree angle of attack the total lift coefficient stays

nearly th e same while th e indu ced two dimensional drag coef f icientCD

2i is aignif i-

cant and benef ic ial. Figu re 5 shows th e indu ced two dimensiona l drag coef f icient as

a fu nct ion of lif t coef f icient for dif f erent decala g e ang les. Both th e

- 4 and 6 de

g ree decalag e cases d emonst rat e good imp rov ement s at all an g les of att ack while th e

De ^ -2 degree case only gives a negative induced drag at

low

lif t coef f icient s. Fig-

ure 6 illustra tes the effect of gap for the - 4 and - 6 degree decalag e cases, Both de-

calag e cases demonst rat e th at th e hig h est neg at iv e indu ced drag coef f icient lev els are

btained for the narro west gap investigated with improvements falli ng off as the gap

increases . Gap s of less th an 0.26 cou ld not be obt ain ed becau se th e aub mat rix of

^

ach ding

s flow field wou ld ov erlap cau sing nu merical comp u t at ional prob lems. Far

the De ^ ^4 degree case at Ga ^ 0.26 the effects of stagger w e r e

investigated. These

are shown in figure 7. Again the St ^ 1.0 case dem c^r

:

Etrates the best results.

Boundary Analysis and Sep arat ion

. ,

A sep arat ion and viscou s flow analysis aft er E. Truck enb rodt

5

was used to pre-

diet sep arat ion point s and th e viscou s ,drag ov er th e sing le and du al element cases.

Figure 8 shows separation points results on the upper surface of the upper airf oil as

a fu nct ion of x/c and De in comp ar ison with th e sing le r ot or. For St ^ 1.0, and

Ga - 0.26 th e sing le rot or sep ara t es bef ore th e birot or in al l inst ances. The lower

rot or does not hav e any sig nif icant sep arat ion ov er eit h er it s upp er or l ower su rf ace

and i

^ not sh own. The sep arat ion prob lems which do hap p en for th e sing le rot or o ceu r

when C > 0.6. Thus the differences b etween the birotor and single ro tor will be

i^

more pronounced for bl ades with either a larger geometric twist than 8 degrees or f or

_

0


13/47

_ -_

^^. _ _

`

3

.0

---

NACA O 0 2

PPER

A JRFOlL OF A

t

^

'^^ 'YO

AiR

FO /L SYST E 11

^

t=

/, 0 , G

o

= 0.26 ; ^^,="4

^ ^

_

^

----- SINGLE AlRFOL

- 1 ,0 ,,

A CA 001 2 ,

a =

8

-

-

1

^

~ ' ^

1`

/ / ^ - _

V

^^.

. . . . . , .

--

:

I. O

. f

.

/C

^

i

.

. 0

----- L O

y

Y E R

A I

RFOIL OF A

T1

'YO A/RF41L SYSTEA^

NACA O0/2 ,

Q's8

$r=

l.0,

Go

=

0.26 , ,De -q.

-I .D

^ .

- ----

i l Y G

LE

A IRFOIL

_

ACA 0012 , a=4

a

i

^/c

.0

FigurN 4

17.


14/47

_a__.

.00s

k l

U

,

004

w

U

,002

4

Cp

23

4

N

-002

w

v

O -004

..

S

t= t.00

Go= 0 2 6

l^ D Q

=-2

p

D e

,^-fie

o D e = ^ 6

. 4

.6

8

.0

-os

Figure 5

iz


15/47

_

._

..__:;

___

:_

-r .. _

e

n _

-

e__

-

==_ ..=ar.

x

^

_

__

-

.

E

F

^.

s^ = i o

=^ ^

^ . 0 0 4

v a

4

De=^6o

^

t

G

v

G

o

w

D

2 6

^ .26

v

.002

.33

. Q

33

c^

^

O .46

^ .46

4

Cfl2i

o

_2

o

s

8

cv

.002

P

W

-:004

a

:oos.

a

s -

ooa

^ }

Figure 6

; -

i

3


16/47

^_

^

i

Q

^ ,

9

i

W

v

w

0

U

^ I

j

v

Q

:002

N

i

t

st

:004

U

C3

ti^

rOO^

Ga 0.26

Da =-4

o st=o .7s

V St=0.86

O

S

t

=1.40

Q

S^-

1112

0

Y.4

6 LOC

Figure 7

14


17/47

-- .^

--

^:

^.

^

_

. w

1.0

^

INGLE

~

O T O R

W

8

U

W

Q -

0 26

V

D,^ - 4

. 2

4 De=-sp

.2 46

.0

X/C

.^

Figure 8

w

5


18/47

^_

t h e 8 deg ree case considered but at hig h er ang les of att ack , i.e. from 12 degrees Co

4 deg rees inst ead of from 8 deg rees to 0 deg rees or 9 deg rees to 1 deg ree as consid-

ered herein. The birot or is not se p arat ing sig nif icant ly ev en for C1 as hig h as 1.2

for St ^ 1.0, De ^ -4 deg rees and -6 deg re es and for all gap e considered . Figu re 9

sh ows th at as gap increases th e birot or mov es in th e direct ion of th e sing le rot or

alt h ou g h not ra p idly. Figu re 10 sh ows th e eff ec t of st ag g er. Except for St ^ 0.76

the separation point does not demonstrate any trend s or move signif scantly.

It was anticipate d that viscous and pressure dra g after separation would be ^=:.-

cu lat ed. Howev er, du e to comp u t at ional prob lems in pred ict ing th e pressu re drag af-

ter separation , the viscous and pressure drag were obtaine d from two dimensional 3a;;^

fo r a s i n gl e r o to r at the s a m e C

1

. Thus the be n e fi ts fr o m the l a te r s e pa r a ti o n c c e

t h e birot or do not app ear in th ese final th ru st-power required cu rv es. When th ese

correct ions are app lied, th e birot or will hav e ev en lower power required resu lt s and

hi ghe r l i ft r e s ul ts tha n tho s e r e po r te d Her e i n.

Three Dimensional Indu ced Drag

Finit e asp ect rat io rot or indu ced drag calcu lat ions were made using th e classi-

cal vort ex filament analysi s. This analysis was app lied between 0.25R and R since

t h e analysis is symmet ric with resp ect to th e hub. Figu re 11 sh ows indu ced torque

resu lt s for a St = 1.0, Ga 0.26 as a fu nct ion of decala g e ang le and ro t or radiu s.

Except for th e -2 deg rees decalag e ang le th e indu ced torque for th e birot or is less

t h an th e sing le rot or. While variat ions du e to rot or radi u s are small th ere is a

sig nif icant variat ion in indu ced torque with resp ect to decalag e a ng le with th e -6

deg ree decala g e ang le hav ing th e least in du ced torque. Some of^ t h e indu ced torque

t h at occu rs as th e decalag e an g le get s more neg at iv e is prob ab ly du e to th e lower

r o to r l i ft tha t exits at the s e d e c a l a ge a n gl e s.

Thrust and Power

When th e sect ional C

i

s are int eg rat ed ov er R, as well as th e sect ional valu es

of

CD Zi'

CD

v iscou s' CDindu ced we get th ru st an d required power. Figu re 12 shows th e

required power versu s th ru st as a fu nct ion of decalag e ang le at a St ^ 1.0 and a

Ga = 0.26 for th e th ree birot or and m onorot or radii . As wou ld hav e been expect ed

from the previou s results, the De -2 degrees case requires birotor p ower that is

essent ially th e same as th at of th e monoro t or. Howev er th e -4 deg rees and -6 deg rees

decalag e cases sh ow sig nif icant ly lower required Bower lev els th an far th e sing le ro-

t o r c a s e . W h e n t h e - 6 d e g r e e s d e c a l a g e a n g l e r e s u l t s a r e

linearally extrapolated to

^#

6


19/47

.

Y

I.0

t^

_

^

v

r/

.6

J

. 4

. 2

ms .

_, -- >.^__ .: ^-

.

_ _ . _ s., -^ _ _,

_ - _ - _

_.- .___ _ _ _

_ _ _ '

` ` __, - _ -` ;_ _ __

_ .^_ _z = __ ,

_ _ .__ .^___ ,

--

^

_

_____

-

.z

^

s

s

.a

/c

Figure 9

-

17


20/47

.

i .

t

I

O

^

^ n

3

3

9

^-

LU

U

W

U

^

J

i.^

.6

.4

C^

__ __

_

__ __ -ff-_ .. _ _ _

__a

._ __

"> __-__

_

_

Ga = 0 . 2 6

D 4

SIPICLE

R O T O R

a S

t

= 0 .76

o S

t =

0.88

A S=J.00

Q S t= 1 . J2

.2

4

6

^{/ C

Figure 10

. 8

.0

18


21/47

soo

J

^

400

O T O R

_

j

OD

^

t

^ I.O

G

a = 0.2 6

200

w

ROTOR RADIUS = 14 ft.

.

RoroR

RADIUS

^

7

ft.

o

oo

^

ROTOR RADIUS = 2 o f t.

_ I

2

3

4

5

S

DECALAG.^

A3'lGL

De

o

Figure 11

i

Y

1

19


22/47

4

0

`

s

t

=^. o

G =0.26

O ^

/

o

4NOROTOR

d

,

w

t^

p

e

^

2 0 .

^

lr

^^e

= 4

^

^

^

p

e

=

6

^ R

-- . --

,Rodius=14.15 Ft.

^

Ro diuJ= l7 Ft,

o

^'

^

o diu^ =20 Ft .

1

, _

-

'

^^

^000

o00

o0o

T N R V S ;

b

Figure 12

20


23/47

- -_-,__-

--

- -

--

z--------

-^

---__---=-

-__ ----

--=

- -

r

he same thrust levels as those of the sin gle rotor the required power levels are

st ill sig nif icant ly b elow t h ose of t h e sing le rot or. Th is is t ru e f or all t h ree

birotor radi i conside red. In figure 13 the same power required thrust curve are

_

hown except for a Ga 0.33. The same general trends occurs as for the Ga 0.26

case except the required power levels are slightly higher for the birotor cases.

^ ,

ig u re 1 4 ag ain illu st rat es p ower requ ired v ersu s t h ru st t rends excep t f or a Ca 0.4 6.

However, except for the -6 degrees decala ge case the required power levels are of

the same or higher than the single roto r. A linear extrapola tion of the -6 degrees

^ `

esults yields lower required power only fvr the 40 feet and 34 feet diameter blades .

In figure 15 the results for stagger are sho^m. For a Ga = 0.26 and De 4 degrees

^

he stagger is varied from 0.76 to 1.12. The St 1.0 yields the best results fol

lowed b y St = 1.12, St = 0.88, and f inally St 0.76.

ue to the sensitivity of the required power results to both gap and decala ge

angle it is necess ary that spacers attac h the upper and lower rotor together. This

is required because the upper and lower rotors are carrying significantl y different

loads when the rotors are positio ned for the best power required results. The struc-

tural analysis ind icates that with one tie at the tip of the rotor blades the change

in decalage angle is insigni f icant while the change in 'gap is acceptable for the 17

f oot rot or b lades. Two t ies, one at t h e t ip and t h e ot h er at t h e second b ending mo-

ment p rodu ced insig nif icant ch ang es in b ot h g ap and decalag e ang le. Th e added drag

these ties would cause can be minimized by cove ring the tie with an airfoil section

that is free to rotate and align itself with the incomin g flow.

21


24/47

^.. .,

^

_

-- __- _-.

g-

_ __

_

x

t =1. o

,, '

= 0.33

^

/

NI DNOROTOR

^

o

Q = 2

^ i

t

C^

^

^

--" ' -- ' Radius = l4.1 ,^ F1 '.

L^

-----

Radius= 7 Ft.

e

^------- Rad

us

s

20

Ft.

uu

s

P ^

/^

^^^

_ _

^

o 0 0

o o 0

voo

T H

}^JJST

b

Figure 13

22


25/47

P

^ '

^ P

/ ^^

^'

/ A ' ' ,

:Q

i .

i .

`

1

^,

t

= i.o

o

^ aas

4

'

o N O R

OroR

^V

= . o ^

D e

=2

o

D

e

=

ad

D

e

c -

_ w

otor

" _ -'" Rodius

i

`^ l5 Ft.

2

_ _ _ _ Rotor ^ ^ ? Ft.

w

odiu

T

ar

P

R

otor

=20^'t.

^ n

- ^

odiva

w

0

Q .

S000

000

000

THRUST ^ ^

Figure 14

23


26/47

1 O

,.

^

^^

^^

3

i

t

L . .Y

P

p

.^

a

:^

T.

. ,.. _

^-

G a

= 0.26

Dwwp

t

^ .o .

o S

t

= l.12

e

^

't

= 0

es

n S t = 0.76

- - - - - - RADIUS

3

14 .13 f t.

-- `

RADIUS =1 ? ft.

'--'

'- RADIUS =20 f t.

j

^

0

PR

3

0

o ^

loo0

000

000

THRUST T 1 b

Figure h5

24


27/47

STRUCTURAL SU^tARY

An analytical study was undertaken to assess the structural feasibil ity

of the birotor helicopter blade concept.

The study focused on two aspects of structural performance:

1.

Response of a representative birotor to loading characterizing

a steady-state hover.

2.

Natural frequencies of a representative birotor.

o order to evaluate birotor structural perfotôance, birotor br.havior

was compared to that of a baseline s ingle blade. Criteria for birotor

structural feasibility included:

1.

Blade

otresse

for the birotor do not exceed values consis tent

with current aerospace practice as exemplified by stres ses in

the baseline blade.

2.

Hub loads produced by the birotor do not exceed values consistent

with current aerospace practice as exemplified by loads pro duced

by the baseline blade.

^ ^

. S ig n i fi c a n t nat u r a l f r equ e n c i e s of t h e b i r o t o r f a l l g e n e r a l l y in

the neighborhood of significant natural frequencies of the baseline

blade.

`

he study led to the following conclusions:

1.

The birotor is in theory a dynamicall y balanced configuration.

True balance may, therefore, be achieved by the add ition of small

c o r r e c t i o n w eig h t s. St ab i l i t y an d co n t r o l p r o b l e m s f o r t h i s

configuration are, therefore, not anticipated.

2.

The birotor without structural spacers between blades is n ot a

3 feasible configuration. One spacer connecting blade tips produces

acceptable structural performance and may be acceptable aerodynam-

ical ly. Two spac^.r; -- a

p

e conneeting blade tips and one connecting

- blades near the eeco

û .

. r'_'

hp

bending anti

p

ode -- lead to deflections

in steady

-

state ho^êr which aze acceptable from the aerodynamic stand -

point.

__

5


28/47


29/47

^

^

ce__

`

3 .ocal hub loads for the birotor are higher than those for ':ie

baseline single blade.

s a consequence of non-zero stagger, the

individual blade center of mass will be either forward or aft of

the radial axis along which the blades will interface with the

hub.

entrifugal loading, therefore, leads to transverse shear

and in-plane bending stresses which must be reacted at the hub.

4 .

lthough blade loads for the birotor are higher than for the base-

line single blade, maximum blade stresses are similar, since the

centrifugal loading described above is reacted by portions of the

blade structure which are typically lightly loaded by aerodynamics.

5 .

ignificant natural frequencies for the birotor configuration are

generally in the range of significant natural frequencies for the

baseline blade.

he more complicated birotor structure leads to

more modal activity in this range ai.3 significant coupling of

in- and out-of-plane bending, and torsion.

In summary, although detailed blade and hub design were beyond the scope

of the study, the work done lead s the writer to cone Lade that, in s pite of

higher loads described above, the birotor concept is structurally feasible.

Soc^e redesign of the blade structure may be required to efficiently

react transverse shear and in-plane bending.

he hub will, moreover,

require additional structure to react birotor loads.

erodynamic perfor-

mance may be traded-off (by reducing blade stagger) to reduce loads and the

consequent need for added structure.

The birotor concept is, additionally, attractive to the dynamicist

since added latitude for tailoring natural frequencies and associated mode

shapes is afforded by varying the location, stiffness, and end conditions

of the structural spacers needed for a feasible birotor design.

27


30/47

I

I

I

I

I

Table I -- Properties for Baseline Blade

f

^

,^

---

,

o.

I

sB

Material: Stainless, E - 28 x 10

6

, G ^ 12.5 x 10

6p si

^.

rea . 5.39 in2

I

y y

3.89 in4

I

.63 in4

zz

I

8.94 in4

xx

includes factor to account for warping of,non-circular cross-sections.

r

28


31/47

.-

:

3

i

s

Table II -- Properties for Birotor Blade

ti

-^

Material: Stainless, E

8 x 10 6 , G

3

12.5 x 10

6

p si

17' birotor

Area

.19 in2

I

9.06 in4

YY

I

.941 in4

zz

I

xx

.84 in

14' birotor

Area

.70 in2

I

3.53 in4

I

.16 in4

zz

I

.746 in4

xx

includes factor to account for warping of non-circu]ar cross-sections.


32/47

f .

Hover Loads

D ur i n g t h e ae r o d y n a m i c p o r t i o n of t h i s st u d y , ae r o d y n a m i c lo a d s rep r e s e n t i n g

a steady-state hover condition were develope d for the blades described in the

previous section. These loads are given in Fig. 16 for the ba seline blade,

and are exemplified for a birotor

(

17' case) in Figs . 17 and Fig. 18.

The given aerodynamic loads were combine d with gravity loading and

centrifugal loading corres ponding to a blade tip speed of 6 00 f t/sec. in

order to develop the results de scribed below.

Composite hub loads, i.e., loads due to a single bas eline blad e or to a

^ e

air of birotoc blades are summ arized in Table III. Six birotor cases were

investigated.

The one -t i e b i r o t o r ca s e s in c o r p o r a t e a si n g l e st r u c t ur a l sp a c e r co n n e c t i n g

_

he tips of the biro tor blades. The two-tie birotor case inco rporates a tip

s p a c e r an d a sp a c e r at rou g h l y t h e se c o n d in

-

p l a n e b e n d i n g ant i

p

ode. The

m u l t i-t i e ca s e in c o r p o r a t e s a t ot a l of ni n e sp a c e r s p o s i t i o n e d at ev e r y ot h e r

m o d e l n o d e po i n t (

approximately 2 feet apart).

, -

The unique loading produced by birotor oper ation is represen ted in

Table III by the torque directed along the blade , T x

. Thi s i s a gy r o s c o p i c

torque developed as a cons equence of the fact that the ro

* .

or spin axis is

n o t pa r a l l e l to a s y m m e t r y ax i s o f a bi r o t o r bl a d e pa i r.

(

The opposed blade

pair produces an equal and opposite gyroscopi c torque so that gyroscopi cs

are reacted entire ly within the hub assembly.)

The study requirement that birotor tip speed be equal to baseline blad e

t i p sp e e d le a d s t o a h ig h e r sp i n rat e f o r t h e b i r o t o r , an d , t h e r e f o r e , t o

a proportionally higher birotor axial force, Fx.

The higher lift, F

y

, seen for the 17' birotor leads a s a consequence to

a higher tangential tor que, T

z

. It is worth noting that thi s torque component

i n c r e a s e s le s s t h a n p r o p o r t i o n a l l y w ith F

y

when the 17' birotor and baseli ne

blade are compared.

Worst case local hub loads, that is, worst case loads at a theoretical

individual blade

-

hub interface , are summarized in Table IV. Clearly seen is

the significant influe nce of spacers on the in-plane bending torque, T

y

, and

the out

-

of-plane bending torque, Tz.

30


33/47

t4

^

O

N

..

' O

^ O

w

Q

O

^

O

m

w

N O

^o

^,

^

^o

,,

w

i

t

^^^ -

U -

1N3i^0

j lhldtV^tQ0^3^y

V

O

N

-

.

NO

p

r

^q -

30 ^

0 .^

l t^dAl^ oo

?^3d

d010^1N3^

31


34/47

i

r

^_

^ -

t t

Q

j

O

-

N

-

O

t

^ qf

-ui

--

Al3f'VOpy

o r w d n r^ c a o ^ 3 d

d

O

...

h

a

a

.^

w

Q

d

m

O

W

N

o

t

^q^ - . oô .^

rûdnrôo^3d ^d

aro^.te^^

32


35/47

^ q 1 - u 1

1J^3S^Oyy

J^l

bJy^100^3 'b '

c ^ U

o

^

w

d.

-,.

. ,

^

O

J

^

^`

^

^

V

^

O

N

1

^

O

O

. ^

: ^

^

o

c

0

o

^

.

^

w

c^

^

^r

o

g

r

^ ,

o

^qj --

^Q2^0^

^l^l^^^JA00^13^y

^JQ10^11fY3^

33


36/47

--

__z_-_ -

_---

-

-

^.

^.

^_

Table III -- Composite Hub

Loads

}

^-

'^

X

Case

FZ

TX

y

Tz

X

y

(pounds)

(

inch

-

pounds)

Baseline

104000

10

0

1770

137000

All 17' cases

123000

020

0

12700

149000

All 14' cases

146000

40

0

28800

105000

34


37/47

Table IV -- Worst Case Local Hub Loads

}

d

^.

Case

Fx

Fy

(pounds)

^ y

Baseline

104000 810

17' No tie

61000

690

17' One tie

6 4 0 0 0

600

^ ~

17' Two ti e

6 6 0 0 0

54 0

^ ;

17' Nine ti e

71000

620

. -

^ -

14' No tie

73000

58 0

. -

^

14' One tie

720A0

50 0

r -

^ .

{

{

^ }

35

x

F Z

Tx

Ty

TZ

(inch-pounds)

0

1770

0

137000

+4200

-770

+432000 96700

+26 00 2600

127000

(_gg000)

74600

+1800

3700

83000

67500

+ 650

k500

83000

58100

+7200

-1020

+620000

69000

+4500

5750

(166000)

53000

-

149000


38/47

z,. _ ---

-

-_ R- - - = --

.^ _

The spacers are also seen to produce with increasi ng number a reduction

in tangential shear, F

z

and an increase in ra dially directed torque, Tx.

In Table V are aum.^arized, for the several birotor configurations,

worst case deflections of one birotor blade with respect to the other.

Inspection of this table revea ls why structural spacers ar e required. The

^ _

hange in gap for the untied l7' blades, for example, is roughly four

times the intended gap and the change in s tagger is roughly equal to the

i n t e n d e d st a g g e r. A ero d y n a m i c s wil l b e sev e r e l y inf l u e n c e d an d b l a d e

i m p a c t i n g se e m s a ce r t a i n t y. Th e si n g l e sp a c e r ca s e p r o d u c e s a w or st ca s e

change in gap of approximately 20X of gap for the 17' case and 14 x of gap

f o r t h e 14 ' ca s e. T h es e co n f i g u r a t i o n s ar e ac c e p t a b l e st r u c t u r a l l y an d ma y

e acceptable aero dynami cally. The 17' two spacer configuration appea rs

fully acceptable from both standpoints and additional spacer s offer no

great advantage.

^

orst case bla de stresses are exemplified in Table VI for the 17'

.

case. These strESSes were developed f or the cross

-

section properties illus-

trated in Tables I and II and are presented for comparative purpose s only.

Calculations are given i n the Appendix.

Worst case spacer loading is summarized in Table VII. Loading given

=

or the 17' two spacer case was employed to size a spacer in ord er to assess

t h e p ot e n t i a l ef f e c t s of sp a c e r s on b i r o t o r ae r o d y n a m i c s. T h e w or st ca s e

n

ormal stress will be approximately equal the sum of the stress due to bending

G -

I c

1)

and the stress due to axial loading

Q2 s A

2)

For a uniform circular cross-section of rad ius r, eqs. (1) and (2) may be

summed to yield

g

n

7854 r^

.1416 r^

3)

Given a working normal stress o f 50 ksi, and Table VII values for M

and P of 16900 inch

-

pounds and 2480 pounds respectively, eq. (3) may be

written in r

36


39/47

_

_ ee^ .a

__

__

_

^

'

^

^

Table V ^Torst

Case Relative Deflection

^ .

Caee

D Gap

D Stagger

D i'wist

(inch) (inch)

(r)

17' No tie

17.6

16.7

0.004

17'

One tie 0.733

0.728

0.002

17' Two ti e

0.220

0.187

0.002

17' Nine ti e

0.200

0.050

0.001

3

14' No tie

13,6

7.3

.001

i

14' One tie

0.633

0.190

.004

^ -

^ -

. .

. -

37


40/47

Table VI -- Worst Case Blad e Stresse s

Case

Normal Stress

Normal Stress

Bottom of Blade

leading edge

(ksi)

( i)

Baseline

61.9 ^O

17' No tie

iuv.

79.2

17' One ti e

87.1

37.7

^

17' Two ti e

81.4

32.2

17' Nine ti e

74.5

33.8

i4' No tie

7.6

11.2

14' One tie

3.2

9.2

38


41/47

t

Table VII -- Borst Case Spacer Loads

Case

ending Moment

hear

xial

ar^ua

3

(inch-pounds)

pounds)

pounds)

inch-pounds)

plane 1 plane 2

plane 1

plane 2

17'

One tie

8300 2500

2700

31 0

1570 900

17'

I

Two tie

5900

4 6 0 0

2300

430

2480

220

17' Nine tic 10500

750

1400

100

50 0 170

14 '

One tie

110

10300

6 00

1050

2660

520

39


42/47

r 3

- 0.01579 r - 0.43035 - 0

4)

Th e only real solu t ion t o eq. ( 4 ) is

r 0.7620 inch

It f ollows t h at t h e requ isit e sp acer h as a diamet er of rou g h ly an inch and

a half .

Dynamics

^ -

Modal analyai: wan p erf ormrd f o; t h e b aseline conf ig u rat ion and f or t h e

six birotor configurations described in previous sections.

Th a model b eh av ior f or t h e b aseline b lade is st raig h t f orward and is

summarised in Table VIII.

Modal b eh av ior f or t h e 17' b irot or conf ig u rat ions is su mmarised in

Tab le IX. Modal b eh av ior f or t h e 1 4' b irot or is not inclu ded since i t

exposes nothing new.

An examination of Tables VIII and IX illustra tes that potentia lly

sig nif icant b irot or nat u ral f requ encies are not g reat ly dif f erent f rom

orresp onding b aseline b lade n at u ral f requ encies. Dynamic st ab ilit y and

cont rol p rob lems aniqu e t o t h e b irot or concep t will not b e p resent , at least ,

based upon this preliminar y view.

Th e addit ional comp lexit y of b irot or conf ig u rat ions su g g est s rou g h ly a

dou b ling of modes of v ib rat ion wit h in t h e f requ ency b and of int erest. Rou g h ly

h alf of t h ese modes dep end st rong ly on t h e sp ecif ics of sp acer desig n, locat ion,

and end condit ions. None of t h ese f act ors were inv est i;:

,

a*.ed during the present

st u dy. Spacers, wh ere emp loyed, were assu med t o b e rig idly eonnec t ed at

individual blade centroids.

Spacers,

-

oreou er, modif y symmet ry of t h e b lade conf ig u rat ion and t end,

-

herefore. to couple in-plane bending, out

-of-plane bending, and torsion.

The impact on helicopter flight stability and eontrol of incr@axed

modal active ity and modal coupling associated with the birotor configurati on

-

eserves further study.

40


43/47

Table VIII -- Baseline Simp le Blade Modal Activi ty

Mode

requency(Hz)

Out-c^r

-

Plane Bending

1st

.74

2

nd

0.9

3

rd

0.4

In.-Plane Bending

is

t

.85

2n d

8.8

3r d

35.5

First Torsion

9.3

41


44/47

Table IX -- 11'

Birutor Blade Modal Activity

i

Mode

Frequency(Hz)

No-tie

One-ti e Two-ti e

Nine-tie

In-plane Bending

1 St.38

6.69

6.93

7.91

3

(6.38) (27:5)

(coupled) (coupled)

^

nd

9.7

40.4

40.9

42.2

(39.7)

(coupled) (coupled)

(coupled)

3 rd

11.0

111.2 111.3

112.8

(111.0)

(coupled)

(coupled)

(coupled)

Out-of-Plane Bendin g

1 st

.4 2

1.51

1.57

1.73

(1.42)

(6.58)

(12.5) (22.4)

`

nd

.8 5

9.08

9.27

9.70

? ^

8.85)

(19.4)

(24.3)

(53.9)

3 rd

4.7 24.9

24.9

25.3

(24.7) (36.4)

(37.7)

(75.4)

First Torsion

9.7

87.2

100.8

141.2

(69.7)

(coupled)

(coupled)

(coupled)

Items in parentheses refer

to a mods roughly

c or re sp on di ng , g e ne r al l y

with blades out-of-phase.

42


45/47

--

_

i

f-

Appendix

Stress Calculations

The text, Theory and_ Analysis of Flig h t Stru ct u res, prov ides th e equat ion

^

Mzlyy -

MyIYZ

Y) -

MyIzz - Mziyz (

z

)

11

-

-

xx A

I

YY

I

z

z

- Iyz2

yyizz -Iyz2

If twist is sufficie ntly small, Iyz

a

0, and

z -

^^

6=--

xx A IZ2 IYY

where

P axial load

My : torque ab ou t an axis perp endicu lar to th e

chord intersecting the elastic axis

Mz

: torque ab ou t an axis parallel to th e ch ord

int ersect ing th e elast ic axis

and where I

yv

and I

zz

are according ly def ined.

Sample Calct lation

For the 17' birator with one tie, Table IV gives

Fx

= P 64000 pounds

TY= M

y

127000 inch-pounds

T

z

=

t

z

= 74600 inch-pounds

Table II gives

Area = A = 3.19 inch2

I

yy

= 19.06 in ch4

I

0.941 inch4

zz

^2)

43


46/47

^

On the bottom of the blade

y

1.4 4 i n c h ( 1.44

12 x 14.10/2),

P

z

a

0, and

^

a

64000 +

4600(1.44)

xx

.19941

Q = 87:1 ksi

_

x

^

t the leading edge of the blade of

y

, and z 2.65 inches (

.

188 x 14.10),

^

nd

= 64000 + 127000( 2.65)

6xx

.19

9.06

6 = 37.7 ksi

xx

s

e

i

4 +


47/47

^P^_.

EFERENCES

1 .

enadovit ch, M., Recherches sur les Cellules Biplane Rig ides d'Enverqure

Tnf

ine, Publications Scientifiques et Techniques du Minister de L'Air,

Tnstitut Aerotechnique de Saint-Cyr, Paris, 1936.

_

.

ai, P. and Gray, R. B., Computat ion of Two-Dimens ional Potentia l Flow

Using Elementary Vortex Distribution, Journal of Aircraft, Vol. 15,

=

ctober 1978, pp. 698-700.

3.,4.

reule r, R. J., and Gregorek, G. M., An Evalua tion of Four Single Element

Air-foil Analytic Methods, General Aviation Design and Analysis Center,

The Ohio State Universit y.

S. Truckenbrodt, E., A Method of Quadrature for Calculation of the Laminar and

Turbulent Boundary Layer in Case of Plane and Rotationally Symmetric Flow,

NACA TM-1379, 1955.

i

analisis de estructura dinamica para helicopteros

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