Three topics are covered dealing with the frequencies of a rotating beam, the use of the fundamental mode of a uniform cantilever beam, and the analysis of resonance dwell. Immensely high peak loads were generated by the code for resonance dwell indicating further need for including structural damping and for transient analysis capability. The effect of structural damping, newly incorporated in the code, is described

Yu, Y. Y.

English

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EXPERIENCE ON THE USE OF MOSTAB-HFW COMPUTER CODE FOR HORIZONTAL-AXIS WIND TURBINES
Yi-Yuan Yu
Rockwell International
Energy Systems Group
Canoga Park, California 91304
ABSTRACT
Experience gained from the dynamic analysis of horizontal axis turbine rotors based on the use of
the MOSTAB-HFW computer code is described. Three topics are covered, dealing with the frequencies of a
rotating beam, the use of the fundamental mode of a uniform cantilever beam, and the analysis of reso-
nance dwell. Immensely high peak loads were generated by the code for resonance dwell, indicating
further need for including structural damping and for transient analysis capability. The effect of
structural damping, newly incorporated in the code, is finally described. : _
INTRODUCTION
_IZ_±!!_::_ The ,_IOSTAB-HFWComputer code was developed
by Paragon Pacific under support from NASA Lewis
_=±= L_: Resea_c_ Center for the dynamic analysis of
........... h6rizon_al-axis Wind turbine rotors. Experience
on the use of the code is described in this paper.
Three topics are covered.
FREQUENCIES OF ROTATING BEAM
iTThe first topic deals with the frequencies
of a rotating beam, which are needed as input to
the MOSTAB-HFW code. Based on the numerical
results of Yntema (Ref. I), a simple expression
= has been derived relating the frequency of a
rotating beam to that_the same beam without
rotation. For wind turbine blades with commonly
_used:_imens_ns, the expressioh is very conven-
ient _nd accurate enough for preliminary design
and analysis purposes. The derivation is pre-
It is noteworthy that, for the wide range of
linear mass and stiffness distributions these
coefficients lie within limited ranges:
1.17<K01 < 1.26, 1.57<Kli<1.93
Thus, K01 already lies within a very narrow band.
Although Kll does not, we note that the offset
ratio e is seldom greater than 0.1 for wind
turbines. Hence, by assuming a maximum value of
e = 0.1, we have
0.157 < Klle < 0.193
and, for e_0.1
1.17<(K01 + K11e) < 1.45
This interesting result shows that (K01 + K11e)
has only a limited variation for e_0.1. Within
== ii.... 11 per cent accuracy W_l_ropose to take simply
Yntema (Ref. I) has given the frequency of
a rotating beam by the equation
_Rn 2 : _NRn 2 + (Kon +Klne)_ 2
where _Rn and _NRn are frequencies of the
:r_ bea_ with and without rotation, respectively,
_Sn and Kln are dimensionless coefficients, the
subscript n denotes the mode, e is the ratio
between the offset and the beam length, and _L
the rotation speed. This equation is quite gene-
ral and applicable to nonuniform beams with a
large Variety of mass and stiffness distributions.
For linear mass and stiffness distributions
Yntema calculated KOn and Kln for the first
three modes of hinged and cantilever beams. The
linear distributions vary from a beam with
constant-mass and/or constant-stiffness to a
beam whose mass and/or stiffness diminishes all
the way down to zero at one end of the beam.
Yntema's results for. K01 and K1 for the
fundamental modes of cantilever beams _eserve
special attention, because these modes play an
important role in the dynamics of wind turbine
blades and are needed in the MOSTAB-H_ code.
Such results are given in his Figs. 15 and 16.
(K01 + Klle) = 1.31 for e_<0.1
The fundamenta! frequency of a rotating
cantilever beam is then given by
2 2 + 1.31 _ 2
_R1 = _NRI
For some blades analyzed by the use of this
equation, the accuracy on _RI has be_n found
to be within l per cent.
USE OF FUNDAMENTAL
CANTILEVER MODE
The next topic is associated with the natural
modes of vibration of the blade which are also
needed as input to the MOSTAB-HFW code. Although
the code can accommodate coupled modes including
flapw_se and chordwise bending together with
twisting of the blade, the use of the fundamental
mode of a uniform cantilever beam for both flap-
wise and chordwise bending has been found to be
satisfactory for quick calculation of the dynamic
loads. This is essentially to apply the classical
221
https://ntrs.nasa.gov/search.jsp?R=19820015833 2020-03-21T17:04:46+00:00Z
Rayleignprocedurein structuraldynamics
to thecomputercomputation.
Theuseof thefundamentalcantilevermode
simplifiestheexecutionof theMOSTAB-HFWcodegreatly. Themodeis well knownandcanbe
enteredas inputoncefor all, regardlessof
thevaluesof theassociatedbendingfrequencies.
Theadvantageof this is obvious,particularly
duringpreliminarydesignandanalysisof the
rotor blade,whenmanychangesmaybeneeded.
Theuseof thefundamentalcantilevermode
in thecodehasbeencomparedwith theuseof
coupledmodesin samplecalculations. Differ-
encesbetweentheresultingbladepeakandcyclic
loadsrangedfrom8 percentfor thetwisting
momentto 23percentfor theflapwisebending
moment.Theseareconsideredsatisfactory,
sincetheloadsgeneratedbytheMOSTAB-HFW
codecandeviatefromthetest databyasmuch
as 25percent,asreportedbySpera(Ref.2).
RESONANCEDWELL
Thethird topic in this paperdealswith
resonancedwell. Thisis whentheratio between
a naturalfrequencyof thebladeandtherotor
speedis aninteger. Sucha situationis natur-
ally to beavoidedin thedesignfor thenormal
operationof a windturbine. However,it cannot
beavoideduringa transientoperationsuchas
start-up,shut-down,or emergencyshut-down,when
therotor speedvariesandpassesthroughreso-
nanceswith theblade. Resonancedwel!represents
the limiting caseof constantrotor speedor zero
rotor accelerationandcanbehandledbythe
MOSTAB-HFWcode,althoughthecodedoesnot treatthegeneraltransientcasewitha non-zero
acceleration.
Theimportanceof accommodatingtransient
operationsin thedesignof windturbinescannot
beoveremphasized.Dynamicloadsontheblades
of theMOD-OAwindturbinesweremeasuredduring
actualtransientoperationsandfoundto befour
to five timestheloadsduringnormaloperation(Ref.3). Hightransientloadshavealsobeen
reportedbyDugundji(Ref.4), whotesteda small
windturbinemode!in awindtunnelat MIT_
It hadbeenhopedthat, in thedynamic
analysisof a windturbine,resultsof trim
analysisduringresonancedwellbasedontheuse
of theMOSTAB-HFWcodewouldshedsomelight on
whatmighthappenwhentherotor speedwas
varyingandpassingthrougha resonance.Unfor-
tunately,thepeakloadsgeneratedbythecode
for resonancedwellturnedout to betoohigh
to berealistic. Forinstance,in onecaseof
resonancedwellthecodegeneratedamaximum
flapwisebendingmomentin theblade36percent
higherthanthat for normaloperatingspeed,a
maximumchordwisebendingmomentmorethan5
timeshigher,anda maximumshaft torquemore
than16timeshigher.
Theveryhighloadsfor resonancedwellgivenbytheMOSTAB-HFWcodeweredueto lack
of structuraldampingin thecode. Theresults
reflect theextremesensitivity of thestructurally
undampeddynamicsystemastreatedbytheoriginal
code.Theypointto theneedfor includingstruc-
tural dampingandfor transientanalysiscapabi-lity.
EFFECTOFSTRUCTURALDAMPING
In viewof its apparentimportance,struc-
tural dampingwasrecentlyincorporatedin the
MOSTAB-HFWcodebyParagonPacific, in addition
to thealreadypresentaerodynamicdamping.Thesamecaseof resonancedwellmentionedbefore
wasanalyzedagainbymeansof thecode,only
nowwith 2percentof critical dampingadded
for boththeflapwiseandchordwisebending
modes.Themaximumflapwiseandchordwisebend-
ing momentsin thebladeandmaximumshafttorque
werefoundto be69,18,and12percent,respec-
tively, of their previouslevel for zerostruc-
tural damping.Theloadreductionwas,therefore,drastic.
REFERENCES
I. RobertT. Yntema,SimplifiedProcedures
andChartsfor theRapidEstimationof Bending
Frequenciesof RotatingBeams,NACATechnical
Note3459,June1955.
2. DavidA.Spera,Comparisonof ComputerCodesfor CalculatingDynamicLoadsin Wind
Turbines,NASATM-73773,September1977.
3. ProjectInformationReleaseNo.158,
WindEnergyProjectOffice,NASALewisResearchCenter,1980.
4. J. Dugundji,E. E.Larrabee,and
P.H.Bauer,ExperimentalInvestigationof a
HorizontalAxisWindTurbine,WindEnergyConversion,Vol.V, ASRLTR-184-11,Aeroelastic
andStructuresResearchLaboratory,Department
of AeronauticsandAstronautics,MIT,1978.
222
QUESTIONS AND ANSWERS
Y.Y. Yu
From: G. Beaulieu
Q: Does your constant K values consider the reducing stiffness of the cantilever blade?
..... if not, your resonant frequencies will be shifted.
_ A: The values of Kon and Kln given by Yntema cover a large variety of linear stiffness
{as well as mass) distributions. The final approximate frequency equation in the
paper therefore applies to cantilever blades with such stiffness variations,
From: T. Currin
Q: After rough approximations of input, is using a large code, i.e., MOSTAB, justified?
A: The use of approximate frequencies and mode shapes as indicated in this paper saves
time for preparing input during the early stage of design when a number of configur-
ations may be considered and many changes needed. When the design is narrowed down,
such approximations are replaced by more accurate values while many other inputs to
the code remain the same. The use of the code at an early stage therefore does not
_ add much to the analysis work.
= = F_om2=_ Jack Landgrebe
Q: _o_s y0ur sensitivity demonstration indicate that you can get any answer with dif-
lerent dampings and what answers do you believe?
A: Data on structural damping of wind turbine blades are lacking because little atten-
_k _ ..... _ion has been paid to such damping. When it is better known, the transient loads
=" _ van be estimated more accurately.
:_ :_:_= From: W.C. Walton
_ _= = Q: I) Should results be compared with "normal operating loads" or with design loads?
2) Please explain the term fixed axls.
A: i) The transient loads are compared with normal operating loads because both must
be taken care of as far as structural strength i8 concerned, although their
fatigue effects are different due to the different numbers of cycZe8 during
the life of the wind turbine.
2) The MOSTAB-HFW code assumes a rotor with a fixed axis in space. In other
words, the rotor is assumed to be uncoupled from the other components of
the wind turbine system. In contrast, the MOSTAS code considers the inter-
_ction between the rotor and the other components.
From : Anonymous
: Qi H0_ was damping incorporated into MOSTAB and what is required for input data to
take this into account?
A: Modal damping was introduced for each mode in the form of a viscous damping term.
Damping ratio (percentage of critical damping) i8 assigned to each mode as input.
From: Jack Hoffman
Q: Why did the flap loads go up with damping?
_: A: Th_ flapwise bending moment did not go up. With 2 percent damping, the moment
_- _as 69 percent o_ its value for zero damping.
{
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224


Experience on the use of MOSTAB-HFW computer code for horizontal-axis wind turbines

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