Field operation of the Mod-0 and Mod-1 wind turbines is described. Operational experience shows that 1 per rev excitation exists in the drive train, high aerodynamic damping prevents resonance response of the blade flatwise modes, and teetering the hub substantially reduces the chordwise blade response to odd harmonic excitation. These results can be used by designer as a guide to system frequency placement. In addition it is found that present analytical techniques can accurately predict wind turbine natural frequencies

Sullivan, T. L.

English

NASA Technical Reports Server

A REVIEW OF RESONANCERESPONSE IN LARGE, HORIZONTAL-AXIS WIND TURBINES
Timothy L. Sullivan
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
E
ABSTRACT
Field operation of the Mod-O and Mod-I wind turbines has provided valuable information concerning
resonance response in large, two-bladed, horizontal axis wind turbines. Operational experience has
_ Shown that ] per rev excitation exists in the drive train, high aerodynamic damping prevents resonance
res;_nse Of the blade flatw!se modes and teetering the hub substantially reduces the chordwise blade
INTRODUCTION
in any mechanical system, vibrations are
undesirable and possibly dangerous if the
z vibratory motion becomes excessive. However, in
=_: a Potating system, like a wind turbine,
vibrations are unavoidable. Hence, one of the
keys to good design of wind turbines is to
mini_ize vibrations. This is done by avoiding
resonance.
: Resonance is a phenomenon which occurs in a
structure when an exciting or forcing frequency
equa}s or nearly equals one of the natural
frequencies of the system. It is characterized
byalarge increase in displacements and
interna_ loads. In a rotating system the
exciting frequencies are integer multiples of
the rotational speed. In a wind turbine the
-- _mportant natural frequencies that must be
considered are those associated with the blades,
the tower (including yaw drive) and the drive
train.
?h_purpose of this report _s to'review _hat has
becn learned about resonance response from
: operation of the Mod-O and Mod-I wind turbines.
Based on this Field experience, conclusions will
be _adeconcerning when resonance will occur in
a two-bladed, horizontal-axis wind turbine. In
addition analysis and design approaches to avoid
resonance will be discussed.
ANALYTICAL APPROACH TO RESONANCE
A useful tool in the analysis of resonance
potential of complex rotating systems is the
frecuency plot or Campbell diagram. A Campbell
diaQram for a hypothetical wind turbine, typical
of _ind turbines like the Mod-O and Mod-l, is
shown in Figure l. In this diagram system
natural frequencies are plotted versus
rototional frequency. The radial lines are
plots of integer multiples of the rotational
frequency and represent exciting frequencies.
Therefore, a potential for resonance exists
whenever lines cross. This type of diagram is
particularly useful for analyzing wind turbines
designed no operate at variable rotational
speeds.
response to odd harmonic excitation. These results can be used by the designer as a guide to system
freq_;ency placement, In addition it has been found that present analytical techniques can accurately
predict wind turbine natural frequencies.
System natural frequencies like those shown in
Figure ] can be calculated using finite element
computer codes such as NASTRAN. Modeling
considerations and natural frequency results for
the Mod-O tower, bed plate and blades are
presented in reference l and for the Mod-O drive
train in reference 2. Experimental methods
using vibration analyzers (ref. 3) are available
for verifying calculations. Agreement between
measured and calculated frequencies within 5
percent are not uncommon for,the lower frequency
modes that are of primary interest in wind
turbines.
For a wind turbine with a single operating
speed, another type of frequency diagram can be
constructed and this is illustrated in Figure
2. This diagram was presented at the Mod-2
preliminary design review. The radial "per rev"
lines of Figure l are now vertical lines with an
avoid range applied. The required width of the
avoid ranges is not precisely known. Here they
were conservatively set at _0.5 per rev for the
even harmonics and +0.25 per rev for the odd
harmonics. Calculated system frequencies are
also shown. All the system Frequencies are
clear of the avoid ranges except the off-line
drive train frequency. Because the rotor is a
node point for this mode, the rotor cannot
excite it. Therefore it is permissible to be
within the avoid range for this case.
The avoid ranges shown in Figure 2 are
relatively wide, resulting in rather small
windows for the designer to place system
frequencies. Another point to note in this
figure is that for the drive train no avoid
range is shown for the odd harmonics. The
significance of this will be discussed in the
following section.
A similar diagram for the Mod-I wind turbine for
35 rpm operation is shown in Figure 3(a). Here
a slightly different approach to the avoid
ranges was taken. The avoid ranges are not as
wide, allowing the designer greater flexibility
in frequency placement. The justification for
the very narrow avoid range for the flatWise
237
https://ntrs.nasa.gov/search.jsp?R=19820015835 2020-03-21T17:04:52+00:00Z
blademodeis thehighaerodynamicdamping
associatedwith this mode.Onlyoddharmonic
avoidrangesareshownfor thebladechordwise
modebecausenoevenharmonicexcitationis
expected.Thetheoreticalbasisfor this canbe
found_nreference4. Thebladetorsion/pitch
changemechanism(PCM)moderequireshigh
stiffnessto avoidflutter. Thenatural
frequencyof this modeshouldbedesignedto be
sohighthat resonanceis nota consideration.
Measuredandcalculatedsystemfrequenciesare
comparedin Figure3(a), showingthedegreeof
correlationwhichcanbeexpected.The
calculatedbladefrequenciesincludetheeffect
of centrifugalstiffening. Themeasuredblade
frequencieswereobtainedbyapplyingan
analyticallyderivedcorrectionfactor to the
measurednon-rotatingfrequencies.In general
theagreementbetweenmeasuredandcalculated
valuesis good,whichis typicalof experience
to date.Whendifferencesdooccur,theycan
usuallybeexplainedbymodelingassumptions
that werenotreatizedin theas-builtwind
turbine. Forinstance,thedifferencein the
off-line drivetrain frequenciescomesfromthe
assumptionf nobacklashin thedrivetrain.
Thedifferencein thetowerbendingfrequencies
is relatedin part to theassumptionf a
flexible foundation,whentheactualwindturbinewasattachedto bedrock.
A condensedversionof Figure3(a) is showni
Figure3(b) for thepresentoperatingspeedof
theMod-l,23rpm. Themeasurednatural
frequenciesareclearof theavoidrangesexcept
for thebladeflatwisemode.Becauseof high
aerodynamicdamping,this is noconcern.Note
that thecalculateddrivetrain modenowis very
closeto l perrev. Theimplicationsof this
arediscussedin thefollowingsection.
FIELDEXPERIENCEWITHRESONANCE
Becauseit is a researchmachinetheMod-Owind
turbinehasprovidedmuchexperiencewith
resonance.TheMod-Ihasprovidedadditional
experience.In this sectionthis experience
will bereviewedfor thedrive train, rotor
support(tower,yawdrive)andblades.
DriveTrain
Fora perfectlybalancedrotor, onlyeven
harmonicexcitationwouldbeexpectedin thedrivetrain of a twobladedrotor. Forthis
reasonavoidrangesin Figures2 and3 areshown
onlyontheevenharmonics.However,mass,
stiffnessor aerodynamicunbalancefrombladetobladecancauseoddharmonicexcitationas
well. Thiswasvividly demonstratedwhentheMod-Irotor speedwasreducedfrom35to 23rpm
whichplacedits naturalfrequencycloseto l
perrev° Theoutputpowerof awindturbinecan
varyaboutameanpowerlevel. Figure4
comparestheamplitudesof cyclic power
variationfor 23and35rpmoperations.Examinationf thereal timedatafor 23rpm
operationshowedthecyclic frequencywasclose
to l perrev. Thesourceof the l perrev
excitationin thedrivetrain is presentlybeinginvestigated.However,theresponseseenhere
is notpeculiarto theMod-l. Synchronous
operationof theMod-Oat 35rpmplacedits
drive train naturalfrequencycloseto l per
rev. A timehistoryof outputpoweris showni
Figure5. Theresponsehereis verysimilar to
that seenwith theMod-l.
Thefield experiencedescribedaboveprovides
strongevidencethat windturbinedrivetrains
containl perrevexcitation. In addition,
Mod-Odrivetrain resonanceausedbyevenharmonicexcitationis documentedin reference
2. Therefore,drive train naturalfrequencies
mustavoidbothevenandoddharmonicsuntil the
sourceof the l perrevexcitationis better
understoodandreducedor, hopefully,
eliminated.
RotorSupportStructure
In its initial configurationtheMod-Ohada
relatively flexible yawdrive. Thenatural
frequencyof thenacelleandrotor aboutheyawdrivewascloseto 2/revat theoperational
speedof 40rpm. Thisresonancer sultedin
largeyawoscillationswhichin turnresultedin
anamplificationof bladeloads. This
amplificationwasof majorconcernbecause,if
allowedto continue,it wouldsignificantly
decreasebladelife. Modificationswere,
therefore,madeto Mod-Oto increaseits yaw
stiffness. Figure6 showscyclic bladeloadsas
a functionof yawdrivestiffness. Themeasured
dataarecomparedto loadscalculatedusingtheMOSTAS-Bcomputercode(ref. 5). Thenear2 per
revresonancein theyawdrivecausedboth
edgewiseandflatwisebladeloadamplification.
Thisamplificationhasbeenreducedbyeither
softeningtheyawdrive(freeyaw)or by
stiffening it bymeansof adualyawdrive(ref.
6) andby lockingthebedplateto thetower
withbrakes.
Becauseit is a researchmachine,theMod-Ohas
beenmodifiedin severalwaysprimarilyto
supportadvancedwindturbineprojectslike the
Mod-2.Amongthesemodificationsarereduction
of thetowernaturalfrequencybyplacingit on
a springfixture (ref. 7) andreplacementof the
rigid hubwitha teeteredhub(ref. 8). The
effectof thesemodificationsonresonance
responsewill bedescribednext.
TheoriginalMod-Otowerhada first bendingfrequencyof about2.1Hzandwascharacterized
asbeing"stiff" becausethis frequencywasgreaterthanthebladepassingfrequencyof
2/revwhenoperatingat 40rpm. Becauseof
interestin moreflexible towers,primarilyfor
economicreasons,thefrequencyof theMod-O
trusstowerwasreducedbyplacingthetoweron
a springfixture. Thedetailsof this fixture
aregivenin reference7. Withthefixture the
towerbendingfrequencywasreducedto about0.8Hzor 1.5/revat thepresentoperationalspeed
of 31rpm. Towerswithbendingfrequencies
238
=between I/rev and 2/rev are classified as "firm"
towers. One of the operational characteristics
with firm towers is that the machine passes
through a 2/rev tower resonance going up to and
coming down from operation speed. The effect of
this resonance on blade and tower loads was a
concern.
Figure 7 shows the envelope of peaks from a time
history of the response of the M6d=O with a firm
tower during a typical start-up, shut-down
2. Odd harmonic content is present in the
drive train and can cause significant resonance
response.
3. Resonance associated with yaw drive
flexibility causes blade load amplification;
resonance associated with tower bending
f_exfbflity does not cause blade _oad
amplification.
cycle.
passing through the tower resonance, blade loads
were not adversely affected and tower
deflections were not excessive. More details of
this test can be found in reference 9. Initial
operation of the first Mod-2 wind turbine at
Goldendale, Washington, confirms the results of
the Mod-O firm tower tests.
In summary, this test showed that when ...... 4. Odd harmonic excitations up to and
including 5/rev can cause significant blade
chordwise resonance response; teetering the
rotor will reduce this response substantially.
Blades
Blade resonance response can be determined by
running a speed survey in which the wind turbine
is operated over a wide range of rotor speeds.
The results of a speed survey between 12 and 40
rpm for Mod-O in the st_ff tower configuration
are shown in Figure 8. In general the chordwise
loads respond to the odd harmonics as expected.
Peak response was expected to occur very close
to the odd per revs. However, the 5 per rev
peak response occurs about 2 rpm higher than
expected_ The reason for this displaced
response is not presently understood. The
response to harmonics greater than 5/rev does
not appear to be significant. Examination of
flatwise blade loads during this same speed
survey snowed no load amplification at any rotor
speed, High aerodynamic damping prevents the
blades from responding in the flatwise direction.
The primary reasons for teetering a rotor is to
reduce flatwise blade loads and torsional tower
loads. As a result hub motions are reduced,
whic_ in turn should reduce the blade resonance
response. This indeed is the case as shown in
Figure 8 for a 5/rev resonance. The load
amp!ification for the teetered hub was about
half that for the rigid hub.
The data shown in Figure 8 have certain
imp!_cations with respect to multispeed
operation of a wind turbine. Operation on 5/rev
and above for a teetered rotor and 7/rev and
above for a rigid rotor could probably be
tolerated. This is based on the fact that the
load magnification for these resonances is less
than 20 percent.
CONCLUSIONS
3ased on the operation of the Mod-O and Mod-I
wind turbines, the following conclusions
concerning resonance response in large,
two-bladed, horizontal axis wind turbines can be
made:
1. The important natural frequencies of
wind turbines can be calculated with reasonable
accuracy,
5. High aerodynamic damping prevents
resonance response in the blade flatwise
direction at all frequencies.
I.
2.
3,
4,
5,
6,
7,
8.
9,
REFERENCES
Chamis, C. C. and Sullivan, T. L.: Free
Vibrations of the ERDA-NASA I00 kW Wind
Turbine, NASA TMX-71879, 1976.
Sullivan, T. L., Miller, D. R. and Spera, D.
A.: Drive Train Normal Modes Analysis for
the ERDA/NASA I00 kW Wind Turbine Generator,
NASA TM-73718, July 1977.
Edgerly, Walter: Instant Replay for
Vibration Analysis, Machine Design, November
22, 1979.
Den Hartog, J. P., Mechanical Vibrations,
2nd Edition, McGraw-Hill Book Company, _ew
York, 1940, pg. 313.
Kaza, K. R. V., Janetzke, D. C. and
Sullivan, T. L.: Evaluation of MOSTAS
Computer Code for Predicting Dynamic Loads
in Two-Bladed Wind Turbines; NASA TM-79101,
1979.
Spera, D. A., Janetzke, D. C. and Richards,
T.R.: Dynamic Blade Loading in the
ERDA/NASA I00 kW and 200 kW Wind Turbines,
NASA TM-73711, 1977.
Winemiller, J. R., et al: Design,
Fabrication and Initial Test of a Fixture
for Reducing the Natural Frequency of the
Mod-O Wind Turbine Tower, NASA _M-79200,
July 1979.
Glasgow, J. C. and Miller, D. R.: Teetered,
Tip-Controlled Rotor: Preliminary Test
Results from Mod-O I00 kW Experimental Wind
Turbine, NASA TM-81445, 1980.
Keith, Jr., Theo G., Sullivan, Timothy L.
and Viterna, Larry A.: Performance of a
Steel Spar Wind Turbine Blade on the Mod-O
lO0'kW Experimental Wind Turbine, NASA
TM-81588, Sept. 1980.
239
3,0
2.5
2.0
1.5
1.0
0.5
MODE:
2NDDRIVE
IST CHORDWISEj
TOWER
IST FLATWISE
IST DRIVE TRAIN-/
0 10 28 30 40 50
ROTOR SPEED, RPM
Figure I - Campbell diagram for a hypothetical
wind turbine.
_m
• Tcwwon
Drbxl tr_n two'ion
• On-liM
• Off4_r,e
Rotor: $*..i l_EIm
• nk#d _ (mwl
• Fbx_
• Fkm dmrd
• Fk to,r_on(> 12 _l
Row: e.ompa_m
• flklid _
• fluflm
• Ru d_wd
• Fire ton,l_ (> 141Q )
r¸
-- 6
0 1 2 3 4 15 (I 7
Fmquancy. _ (pmmvOl7.SrlX.)
figure 2 - System resonance avoidance -- the Mod-2 approach.
72
--?
240
DOMINANTMOTION
EQIOELG_
ON-LINE
OFF-LINE
BLA_
FLATWISE
CHORDWISE
TORSION/PEM
I_LLE
BEND]N5
FORE-AFT
LATERAL
TORSION
POGO
NATURALFREQUENCY(ROTATING)IROTORSPEED
-_-+ I I ____F _ _ ip11
0
0 PREDICTED 0 MEASURED i_iiii!]TO BE AVOIDED
(a) 35 rpm
DOMINANTMOTION
BLA_
FLATWISE
CHORI}WISE
TOWER/NACELLE
BENDING
FORE-AFT
LATERAL
O PREDICTED
NATURALFREQUENCY(ROTATING)/ROTORSPEED
-_ _4-+-_-_ _ ,_i_
MEASURED _ TO_EAVOIDED
(b) 23 rpm
Figure 3 - Mod-1 system natural frequencies.
241
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242
=E
-4
TOWERDEFLECTION,]N.
h
-0,5
POD ACCELERATION,G'S
-75 i
BLADEROOTFLATWISEMOMENT,103 LB.-FT.
iiI:IYII:::YIIIiii:YT :::Y:II: :IY:IY i
BLADEROOTCHORD_ISEMOMENT,103 LB.-FT,
50
ROTORSPEED,._PM
Figure 7 - Response of the Mod-O when passing through a
2/rev tower resonance (envelope of cyclic peaks),
1.8
_1.6
,,--1.4
1.2
_i,0
N
--o-- RIGID HUB, DOW_I_
-o-- TEETERED HUB, DOWNWIND
-___- TEETERED HUB, UPWIND
MGRAV= 52,000 LB.-FT.
I
!
!
_. /I
II
gP 7P 5P 3P
___,l , I , L___ , , L
0._ 16 20 24 2_ 32 36 _0
ROTORSPEED'_, RPM
Figure 8 - Blade root chordwise response as a function of
rotor speed for the Mod-O tip-controlled blade.
243
|
=
z-
QUESTIONS AND ANSWERS
T.L. Sullivan
From: K. Hohenemser
Q: Why did you not show the chordwise 3P for the rigid hub?
A: We were afraid of damaging the blades if we ran the rigid hub up to 3P (40 rpm).
From: W.C. Walton
Q: i) Do blade dynamic characteristics (stiffness; natural frequencies) play any role
in the IP drive train resonance (i.e., do the blades just provide the rotation-
al inertia)?
2) In the blooming of tower response (with no accompanying increase in blade load_)
were the tower loads of any concern?
A: I) For the fundamental drive train mode (which is the one of most concern) only
the rotor inertia plays a role in the drive train natural frequency.
2) Tower loads were not of concern. However, the loads in the spring fixture
used to soften the tower were of concern. Hence, the spring fixture was strain
gaged. These strains were within acceptable limits.
From: Anonymous
Q: What is the predominant frequency of the cyclic component of MOD-I power output
(at 23 rpm rotor speed)?
A: Close to I/rev.
From: R. Perley
Q: What is the basis of establishing the avoidance ranges?
A: Presently they are set rather arbitrarily. Heavily damped modes have narrow bands.
Lightly damped modes have wider bands. Additional field experience and computer
studies will allow us to set the avoid ranges more precisely.
From: W. Sullivan
Q: What methods were used to compute MOD-I and 2 resonant frequencies--are all rotating
coordinate system effects included?
A: The only rotational effect taken into account was centrifugal stiffening. This
approach gives good agreement with measured data. •
244


A review of resonance response in large horizontal-axis wind turbines

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