Ground resonance of helicopters with failed lag dampers :|bresults of

(1)

(

TWENTY FIRST EUROPEAN ROTORCRAFT FORUM

Paper No Vl.4

GROUND RESONANCE OF

HELICOPTERS WITH FAILED LAG

DAMPERS.

RESULTS OF

ANALITICAL AND EXPERIMENTAL

INVESTIGATIONS.

BY

Y.A

.

Myagkov, B. S

.

Godes

MIL MOSCOW HELICOPTER

PLANT

MO?COW, RUSSIA

August

30 -

September

1,

1995

(2)

Paper

nr

.

:

VI.4

Ground Resonance of Helicopters with Failed Lag Dampers

.

R

esults

of

Analytica

l

and Experimental

In

vest

i

gations

.

Yu.A. Myagkov; B.S. Godes

TWENTY FIRST EUROPEAN ROTORCRAFT FORUM

August 30 - September 1,

199

5 Saint-Petersburg

,

Russia

(

c

(3)

GROUND RESONANCE OF HELICOPTERS WITH FAILED LAG

DAMPERS.

RESULTS OF ANALYTICAL AND EXPERIMENTAL

INVESTIGATIONS.

Yu. A. Myagkov, B. S. Godes

Mil Moscow Helicopter Plant

Design Bureau

INTRODUCTION

Usually in helicopter ground resonance problem solution the main rotor \\oith the identical characteristics of blades and lag hinge dampers is considered. In this case stability analysis of rotor system positioned on elastic support with two degrees of freedom , along OX and OZ axis's is reduced to solution of four second order linear differential equations with constant coefficients. This approach to the problem permits to get the results satisfactory for practical purposes. However such an approach doeo-n't give an answer the question about ground resonance of helicopter with different characteristics of individual blades and lag dampers of the main rotor. Such dissimilar conditions can take place, for example, when one of rotor hub dampers fails or in tests with simulation of damper failing in accordance with the FAR 29.663 requirements. These considerations make ground resonance analysis of the helicopter with different blade characteristics quite topical. The paper is devoted to the described problem solution.

PROBLEM FORMULATION

A multi-blade rotor with different blades and lag dampers characteristics is analysed in the paper. Such a rotor is not isotropic one, in a sense. Each blade has one degree of freedom -oscillations \vith respect to lag hinge. In this case the rotor support is considered as an elastic· system \vith 2 degrees of freedom in two orthogonal planes.

Mass and stiffness characteristics of such rotor support are assumed to be equal in both directions. The system under consideration includes equations connecting displacements of elastic and damping elements of spring-hydraulic damper (SHD) with typical successive engagement of the spring and hydra-damper. The equations are given in rotating co-ordinate-system and have the follo\\oing form :

~-

2-

~

?.

2~

s.w [(..

2 .

2 )

2rr

k (.. 2 .

2 ) . 2n

k]

o

sk+ nbsct, +vo,co sk+--

y+ cox-coy

cos-

- x- coy-cox sm-

=

· ~w n n

(4)

• s ( ..

2 )

B =

...1l!!l..

I;

k - ill

I;

k

Mz

.

where

x,y- displacements of rotor support system in two mutually orthogonal planes lnw-lag damper offset

mb - blade mass

'

M

z

-mass of rotor with support

Snw, Inw -blade frrst and second moments of inertia relative to lag hinge axis

v0 . non-dimensional frequency of blade oscillations in the plane of rotation (pendulum oscillation fonn)

nb-

relative coefficient of blade damping Po -blade frequency of oscillations ,when (!) =0

no -

relative coefficient of support damping

I; -

angle of enplane blade rotation about lag hinge

<;d -component of enplane blade rotation angle created by deflection of hydraulic part of SHD

z- number of blades k - current blade number

Conclusion about the system stability is dro\Vned basing on the analysis of the signes of characteristically polynom eigenvalues. The rotors 'With 4 (Mi-26, figures l-5) and 5 blades (Mi-28, fig.7-8) have been analysed in this paper. The 8-bladed rotor of Mi-26 helicopter is considered as 4-bladed one with "equivalent" blades. Mass and stiiTness characteristics of such a rotor are recalculated from the characteristics of the eight-bladed rotor so that the non dimentional frequency

V

0 of blade oscillations in the plane of rotation and parameterS remain the same. In tllis case the requirements will be fulfilled if Ceqv and Keqv coefficients (stiffness and damping) and moments of inertia Snw, Inw of equivalent blade of Mi-26 helicopter will be increased twofold.

RESULTS OF INVESTIGATIONS

One can see from the paper (figures l-4) that 10-20% diiTerence in SHD characteristics has small effect on ground resonance boundaries. Figure l illustrates variations of the real and imaginary part of eigenvalues of the system of equations under consideration as a function of main rotor speed. In comparison with Fig.! Figure 2 and 2a show eigenvalues of similar system of equations but stilT ness coefficients of damper elastic element are reduced by 20%. This was done for one of dampers on Fig.2, and for two of dampers on Fig.2a. Figures 3 and 3a illustrate sinlilar changes of damping part of dampers. Figure 4 presents eigenvalues of equations describing the system, in which one of damper has a reduced by 20% coefficients of elasticity and damping.

Ii is needed to be aware that when one is talking about one or two dampers of equivalent 4 -bladed rotor this is corresponding for two or (our dampers of neighbour blades.

Figures 5 and 7 show correspondingly the results of equation solution for the system 'With one failed blade damper for the Mi-26 and Mi-28 helicopters. It is seen from analysis of the calculation results for the Mi-26 helicopter (represented on Fig.8) that though for the case of simulation of two dampers failing the instability boundary is practically unchanged, but increment of oscillation in the centre of the instability area is increased twofold (q = +0.06 instead of q=+0.03). Figure 6 shows

(5)

values of real and imaginary parts of eigenvalues of characteristical equation for the Mi-28 helicopter which has equal characteristics of all dampers ,and Fig. 7 shows the results for the system, where one of dampers has zero values of stiffness and damping coefficients. For these cases Fig.9 shows separated eigenvalues having positive real part. Comparison of these roots shows that at rotor speeds distant at 15-20% from instability boundary oscillation decrements may have difference in several times. For comparison of analysis and test on these figures are plotted also the values of logarithmic decrement of blade lead-lag oscillations obtained from special ground resonance tests of the Mi-28 helicopter.

In these tests Mi-helicopter pilot excited blade oscillations about lag hinge by cyclic stick movement in lateral direction. The oscillation frequency had been set so that one of the combinatory frequencies corresponded to blade natural frequency in rotating system. Needed degree of coincidence had been reached by multiple training. After the excitation halting the oscillations faded away. The oscillation amplitude was used to defme logarithmic decrement of blade oscillations. The tests have been performed at different rotor speeds in the range from its minimal to maximal permitted exploitation values. The test results are shown on FigureslO,ll and 12. Simulation of one damper failing performed by pouring off working liquid from valves case in such manner that it's piston moved in cylinder practically \vithout resistance. This was controlled by tests recording of moments on dampers . Figure I 0 presents an example of the test recording, showing practically zero moment on simulated fail blade damper. Figure!] shows this recording after high frequencies filtration. Figure 12 has on horizontal axis values of rotor speed and on vertical axis values of blade oscillation logarithmic decrements. It is seen from the figure that oscillation decrements of blade \Vith "failed" damper are less than decrements of blade \Vith normal damper prepared in accordance \vith standard requirements. The difference between values of these blades decrements becomes small \vith the increasing of rotor speed and bottom boundary of instability region is reached approximately on the same rpm. both for the rotor corresponding standard and rotor \\ith simulated failing of one damper.

The MI-28 helicopter tests have confmned the conclusions obtained through analy1ical methods that instability boundary is changed insignificantly when one damper is shut off (failed). This boundary change consists of 3-4 % for the examined model parameters when potential instability region are above operational range of rotor speeds. At the same time the blade oscillation decrements \vith normal and failed damper can differ in several times "(see fig.9) in operational range of rotor speed (20-30% below of instability boundary). Taking in account these results one can see that tests with simulation of damper failing, required by FAR 29.663, appears not to be validation criterion, because of needed margin of rotor r.p.m to instability boundary \Vith account of all operational circumstances must be equal or more then 10-15 %. Tllis circumstance is more essential for multibladed rotors, when the number of blades is 5 or more

2 .2

_.03

"'

_1.6

"'

-;;; :>

"

"'

0 )

_1.2

·o; ~ 0 ~

.8

~

"'

0..

c

"'

4

"

·s,

"'

.§

0

~ <>

-.2

:=; -;;; > _c

-.4

"'

OJ) '8 '

--.6

0 t:

"'

p..

-.8

-;;; ~ r I

.

'

~

\

;:

7

/ .

.d-'

\

:.xr\

~

-1

0

2

3

0 .5

1.5

2

2.5

3

main rotor speed w main rotor speed Til

Fig.l Eigenvalues of the system "itb equal characteristics of dempers.

(6)

2 . - - , - ·

~

03 1 .6 > a

•

-~ 1.2 0 t .8 2. tl'

~

~-a

•

0> ·;;; '--_"-... ~ ~

§

2 3 .5 2 2.5 3

.

_• ~ 2 > ~ 1.6

•

0 1.2

[

c

-~

"'

§

•

v .!l .4 0 0

main rotor speedm _{main rotor speed}_m Fig.2 Eigctmtlucs of I he syslcm lt:n·lng reduced s!iffcnc:>s of ouc of nil d:unpcrs.

tl'

~

_~-.2 .S!> _<lJ _·-.4 0 " •

"

-;;; ~ 2 3 5 .s 2 2.S

main rotor spccdl:il

main rotor speedm

Eigcm·alucs of the system hal·ing reduced stiffcncss of 1 1ro of aU dampers.

Fig.2a tl' ~ ~

.---.,---,

_"

I~ ~ ~ l.G

•

0 1.2 t 3, .B

~

.4

I

~=':::::'

lz:7'--l

f

o

I 0 1 2 3

main rotor speedUJ

~ § -.2 .9' w -. 4 1----Y--1' (j "

•

~-.sl~r ~~ m " -1 0 . ~) 1.5 2

main rotor speed m 2.~

1<1~.3 Ei~cm·a[u!.'s of 1!1c system h:!.Yiug reduced cod. of dampinJ! of one dampcr.

3 :; Q) 2 r-·-··---·;.r ~ ~ 1.6 •

"

• I 2 0 .. [ .n

c

• 4

t

oi___Lf;::~J. ~J

0 I 7 3

main rotor speech:<~

0' 0 -~- ----~ ··.7. ~ --.1 d g, -.G -0 -.8 ----

-••

1l .

1

·---"

";;j 1.2 -[I! --1 iJ ---- ~-0 .:) 1. ~) /. 25

main rotor speed 1:il

Fig.3a EigcnYalucs of the systcrn h:ning reduced cocf. of damping of l•rnt rotor d:tmpcrs.

• 2

·7]··-··-·· ....

0 B ~ 1 6 - - - -.. - ·

~

! ./ - --- ·-0 .. .. ···'7''

~-

p,

""·{-£: --

"--v

-v~

_l

·--~j

~-

_,

---~~

'h s,

§

0 0 ~~~-~~-~-2 .l muin rotor spccdm tr • 0 I" .2 ~ ₂ d

•

-~ -.1 0

'.J

--.G n, ro --.s ~

.s

1.5 2 2.5

moin rotor spccd:iJ

Fig.4 Eigcnrnlucs of the S)'slcm haring reduced cocf. of damping and stiff cues._" of one d:unpcrs .

g

2

•

> _g 1.6

"'

~I 0

-~ =---l~-==

·--~- ---· --··.-":~ v~-[ .8

f-"'---1---c~~

i

'1·~,.-/

.

~

0

-"~"';"

.... ..! " 0 2 3

muin rotor speed@

tl' " I~ ~ -.2 a ru .:2' --.4 ru 0 ₆ ru 0._.8 -;;; ~ ₁L.~L~-' 0 .5 .:) 2 main rotor spccdw

F'ij!,S Eigcn1·aluc-s of I he ~ysl<'m h:1.ving OtiC <.l:!mpcr f;1ilcd.

2.:) 3

"

_{..,._}

>

3 :1

(7)

5

""'" V> v ~

'1

~-8 "!1 'o .G h ~ ~.

c

~

·5t

2 ~ 8 -- 0 0 .4 .8 1.7 LG 2

main rotor speed co

~ .05

"

.

!--0~1~~

' h

g_ -.

1

51 /<61'11 \l

-;;;

~:

I'

1/

='

I

A .8 1.2 1.6 2 ~ tett value!

main rotor speed w

Fig.6 Eigcn\·a)uc.s of the syslcm with cqu:tl characteristics of dampers for Mf-28

g .6

l

~ .4 ~ .3 ~ >. ~ I . " -~ 1 -~ .0 0 main rotor cpccd w ·"" l"""?r~-, .04 - - - - · - - 1 / ' - - " · f

~ ~2~~~~~~~~~~~

> 0 ~-0? -:_: -:o< ~"--- +=. ;¢.;, ., ~ -.06 -- - --· ----:..., ~ 'EP,.;

~ !'~

_"

-

:5~2'~

...:

__

;,

""\ -.1-4- ~ -.16

I::Z

.2 .4 .6 .8 1.2 1A 1.6 1.8 main rotor cpccd w a test values

Fig. 7 Eigcm·:ducs of the system h:ning one damper f:ti!cd.

I )Cr faild one' amJ·~·-·---·--\ _

-~--·-~ --~--·-~-~--·-~ -~--·-~-JE--~--·-~-~--·-~.--~--·-~-~--·-~-~--·-~-~--·-~-~--·-~-~--·-~--=_

!l,

02 - ·

-~

• • - - - · - - - ..

~---

! 0 0

-~

--··1

.. IJG '-···-·· () .) _1.5 main rotor speed 0)

Fi~-:.8 Comp:trison of unsl:~ih!c roots

of system wilh nonn:~! d:uupers

:wd S)'S!crn with one failed

d:uupcr fur Mi-26 hdit(I[Jlcr

1 v

"

~ 5

"'

·o ~ 0 t • ~ -~.:_~~~~per~~~~ .06 .0'1 .1>! 0

s

-.04

"

·,;,

.§

_{• OH} 0 ·.4 .13 .2 1.6

main rotor speed (I)

'

Fig.9 Comp:nison ofunstaih!c routs

of system with nonn:!l dampers :md system l'>ilh one f:tilcd

dampn for Mi-28 hdicoplt·r

#M~\wN'VWVVtwVV\\VVV\~hV~;

"4'ir~«~lit-../0J\N\fVV'Iy¥/v\A.ivANW"'

.

I

~~~.4._~f{llyi)/WlYv*f

·:~w~~\~J~fv~~Vv~ANv·VYvvv'"

·; -~----~~;···---~-~~--t-····---- -;,---~~-... -···. --~...-;---. ··;,. Fig. I o Exam pi of non (iltered record of the night regime

c,

2,25

r-

4,5<

~81

~~ ~ -1,6 Mct 70

moment on non-operated damper (without working liquid)

so~~~~

Mct'"

400 200

0

moment on operating damper

3 5 7 ') I I 13 15 _seQ;T

(8)

0 detected demper

*

o-

_normal

_demper

_,

!t

>:: _~normal

_rotor

O.l

_-.03

El

1--O.l _.& H u 0 O.l

_-.06

_.& ₀ '0 ~

*

<d u

"'

0 0 .~

El

-.09

_"'

.c

+

_, .~ H 0 <d

8'

-.12

@ ~ ~ ® 0

+

-.15

0

90

95

100

105 %

Rotor speed

co

Fig.l2

VI .4 -6