Modal Testing in the Design .i Evaluation of Wind Turbines · Typical Wind-Turbine Mode Shapes...

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SANDIA REPORTSAND87–2461 ● UC–60

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Modal Testing in the DesignEvaluation of Wind Turbines

James P. Lauffer, Thomas G. Carrie, Thomas D. Ashwill

Prepared bySandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, California 94550for the United Statea Department of Energyunder Contract DE-AC04-76DPO0789

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SF2900Q(8-81 )

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Issued by Sandia National Laboratories, operated for the United StatesDepartment of Energy by Sandia Corporation.NOTICE: This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United States Govern-ment nor any agency thereof, nor any of their employees, nor any of theircontractors, subcontractors, or their employees, makes any warranty, expressor implied, or assumes any legal liabdlty or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service bytrade name, trademark, manufacturer, or otherwise, does not necessarilyconstitute or imply its endorsement, recommendation, or favoring by theUnited States Government, any agency thereof or any of their contractors orsubcontractors. The views and opinions expressed herein do not necessarilystate or reflect those of the United States Government, any agency thereof orany of their contractors or subcontractors.

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SAND87 – 2461Unlimited ReleasePrinted April 1988


James P. Lauffer and Thomas G. CarrieModal and Structural Mechanics Division

Thomas D. AshwillWind Energy Research Division

Sandia National LaboratoriesAlbuquerque, NM 87185

AbstractIn the design of large, flexible wind turbines subjected to dynamicloads, knowledge of the modal frequencies and mode shapes is essen-tial in predicting structural response and fatigue life. During design,analytical models must be depended upon for estimating modal pa-rameters. When turbine hardware becomes available for testing, actualmodal parameters can be measured and used to update the analyticalpredictions or modify the model. The modified model can then be usedto reevaluate the adequacy of the structural design. Because of prob-lems in providing low-frequency excitation (0.1 to 5.0 Hz), modaltesting of large turbines can be difficult. This report reviews severaltechniques of low-frequency excitation used successfully to measuremodal parameters for wind turbines, including impact, wind, step-relaxation, and human input. As one application of these techniques, aprototype turbine was tested and two modal frequencies were found tobe close to integral multiples of the operating speed, which caused aresonant condition. The design was modified to shift these frequen-cies, and the turbine was retested to confirm expected changes inmodal frequencies.

DistributionCategory UC – 60

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AcknowledgmentsWe especially acknowledge the efforts of C. M. Grassham, M. D. Tucker, and A. J.

Gomez for assistance in acquiring data and for assembling and maintaining theexcitation, instrumentation, and data-gathering systems.

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ContentsIntroduction ...................................................................................................................................................................... 7Experimental Modal Analysis ......................................................................................................................................... 8

Ste~J.Relaxation ............................................................................................................................................................. 8Human Excitation ............................................................................................................................................ ............ 11Wind Excitation ............................................................................................................................................................ 12Hammer Excitation ............................................................................................................................................ .......... 13

Modal Testing in the Design Process: An Example Implementation ....................................................................... 13Conclusions ............................................................................................................................................ .............. .............. 16References .......................................................................................................................................................................... 16

Figuwes123456789

10111213141516

Sandia’s 17-m Research Turbine .......................................................................................................................... 7Typical Wind-Turbine Mode Shapes ................................................................................................................... 8Step-Relaxation Hardware ..................................................................................................................................... 9Unfiltered Force-Time History .............................................................................................................................. 9at-Coupled Force-Time History ............................................................................................................................ 10FFT Magnitude of Unfiltered Force .................................................................................................................... 10FFT Magnitude of at-Coupled Force ................................................................................................................... 10unfiltered Force With Time Shift ........................................................................................................................ 10FFT Magnitude of Time-Shifted Force ............................................................................................................... 11Typical Frequency-Response Function Measured Using Step-Relaxation ..................................................... 11Driving-Point ASD Measured During Human Excitation ................................................................................ 11Free Vibration Response Measurement ............................................................................................................... 12Acceleration ASD Measured During High Winds .............................................................................................. 13Mode Indicator Function ....................................................................................................................................... 13Accelerometer Locations for Step-Relaxation Test ............................................................................................ 14VAWTpower 185 Fan Plot ..................................................................................................................................... 15

Table1 Modal Frequencies of VAWTpower 185 .............................................................................................................. 14

5-6


IntroductionFigure 1 shows the Sandia 17-m wind turbine,

which was one of the subjects used during this investi-gation. During operation, the blades and tower rotateat a constant speed. The aerodynamic forces acting onthe blades are transmitted through the tower astorques to the electric generator. Because the orienta-tion of the blades in the wind repeats itself at theconstant rotation speed, the aerodynamic forces areperiodic and have large spectral components at inte-gral multiples of the rotation speed. Broadband forcescaused by wind variability also act on the wind tur-bine, and these are added to the discrete frequencycomponents. Because of the discrete frequency natureof the forces, an understanding of the modal charac-teristics of the turbine is needed to prevent the operat-ing speed, or one of its harmonics, from coincidingwith a resonance of the turbine. Understanding themodal parameters is complicated by the differencesbetween the modal characteristics of a parked turbineand a rotating turbine.1 Consequently, the rotationaleffects must be included in the computation of themodal parameters. This has been done by using apreprocessor that operates in conjunction withNASTRAN.2’S

The analytical model is a critical design tool sinceit is used to predict fatigue life, evaluate operationalconstraints (wind speed and rotation speed), and de-termine modal frequencies of the rotating turbine. Asa rule of thumb, modal frequencies must be 10% awayfrom harmonics of the operating speed, although cer-tain modes are orthogonal to forcing functions ofparticular harmonics and therefore are not excited. Asa result, modal frequencies must be accurately known(-3 %). Typical wind-turbine mode shapes are dis-played in Figure 2. Because of the accuracy required,it is critical that a finite-element model, which is usedas a design tool to analyze a wind turbine, be verifiedby a modal survey.

Figure 1. Sandia’s 17-m Research Turbine

If the finite-element model is not accurate, it mustbe corrected to reflect the measured modal properties.A subsequent analysis of the wind turbine, includ-ing rotational effects, may indicate modal frequen-cies coinciding with one or more harmonics of theoperating speed, indicating the need for a designmodification.

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First blade flatwise First blade flatwiseantisymmetric symmetric

Second tower Second towerout-of-plane in-plane

Figure 2. Typical Wind-Turbine Mode Shapes

Experimental ModalAnalysis

(lxFirst towerout-of-plane

Second bladeflatwisesymmetric

Performing a modal test of a parked wind turbinecan be difficult for several reasons. First and mostimportant is the size. Typical turbine rotors range insize from 17 to 100 m tall; therefore, mounting andmoving accelerometers requires the use of a crane,which can be time consuming. Second, the modalfrequencies are very low, requiring long sampling peri-ods. On the Sandia 17-m research turbine, 11 modesare in the range of O to 8 Hz. Because of this low-frequency range, each time record requires over aminute. Even so, because of light damping, exponen-tial windowing had to be applied to the data to avoidsubstantial leakage errors when performing the fastFourier transforms (FFTs). Third, windy or inclementweather can lengthen the test duration. Consequently,a complete survey typically requires two people work-ing two weeks. This time requirement can prolongproduct development time or affect testing schedules.

This excessive time required to perform a com-plete modal survey made it necessary to devise atechnique that would yield sufficient data to confirmthe accuracy of a model in a minimum amount of time.

oFirst towerin-plane

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Second bladeflatwiseantisymmetric

Rotortwist

Third towerout-of-plane

This led to the “mini-modal” concept. In a “mini-modal,” a small number of response measurements areused in conjunction with a reasonably accurate analyt-ical model to determine the modal frequencies andidentify the mode shapes that correspond to the mea-sured frequencies. The advantage of this technique isthat it requires substantially less time than perform-ing a complete modal survey.

Because speed was of the essence, it was necessaryto use an excitation technique that would minimizethe test time. Four excitation techniques were consid-ered: step-relaxation, human, wind, and hammer im-pact. A pendulum-style impact technique was consid-ered but not pursued because it required an additionalcrane to support the impact mass.

Step-RelaxationThe step-relaxation method of structural excita- .

tion involves applying a static load to a structure andthen suddenly releasing this load. This process isanalogous to plucking a violin string. Step-relaxationexcitation has been critically reviewed in previouspapers4’5 and used for testing a rotating wind turbine.GIt is a technique that has seldom been used because it

8

can be mechanically difficult to implement and be-cause problems are involved in performing an FFT onthe Heaviside function (also referred to as the stepfunction). However, the low-frequency content of theHeaviside function, which rolls off as I/frequency, andthe large amount of strain energy that can be input tothe structure make it ideal for testing large structureswith very low natural frequencies (such as wind tur-bines). Also, implementing this technique for large,flexilblestructures is mechanically straightforward.

In using step-relaxation, the loads were applied byusing a winch and a reasonably light steel cable,depending upon the ultimate load. The winch waskept at ground level. A quick-release device was in-stalled between the winch and the cable to allow animmediate relaxation of the applied load. A load cellwas placed close to the structure in-line with the cable.It is important that the load cell be close to thestructure so that it senses the force actually beingapplied to the structure. All joints in the load pathwere taped to avoid rattling. The entire setup isdisplayed in Figure 3.

Blade

1)

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— Cargo Straps

+ Load Cell

—— Steel Cable

Y.

\

&aic::Release

/

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Winch

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zzsyzmGround

Figulre 3. Step-Relaxation Hardware

;Steel cable, rather than nylon rope, was used totransmit the force because it allows a crisp release ofthe force. If the force is relatively low (<1000 lb), it iseasily applied with a hand winch. For higher forcelevels, a powered winch is more convenient to use. Theload-cell amplifier contained a digital readout of theforce to allow precise setting of the input level. Thekey to the setup was the quick-release device which,upon the cue of the tester, released the load.

In testing the turbines, two methods have beenevaluated for attaching the excitation source to thestructure: using a fixture or using a cargo strap that

conforms to the shape of the structure. Although bothmethods yield comparable results, using a cargo strapis preferred because mass loading is negligible and nospecial fixturing is required.

Because these large turbines have low modal fre-quencies, their acceleration responses were low. Also,the transducer cables were quite long, making noise aspecial consideration. To address this problem, re-sponse of the structure was sensed by very high sensi-tivity accelerometers (1000 pC/g) with low noise

cables.The accelerometers were bonded in place with

synthetic putty for easy attachment and removal.Response measurements were made normal and paral-lel to the blade. All signals were low-pass filtered byusing external analog filters to remove out-of-bandresponse and allow for optimal use of the analog-to-digital converters (ADCS).

Special consideration must be directed to thesignal processing used for the force signal because theHeaviside (step) function cannot be Fourier trans-formed without tremendous leakage. To alleviate thisdifficulty, the force signal was at-coupled at the inputof the FFT analyzer. The at-coupling is a high-passfilter with a 3-dB down point at 0.8 Hz. Such couplingconverts the Heaviside function into a pulse with arapidly decaying trailing edge, making the force-timehistory Fourier transformable without leakage. Thisat-coupling also creates a pulse that allows repeat-able triggering. To illustrate the leakage, which canresult without the at-coupling filters, Figure 4 showsan unfiltered force-time history Figure 5 is theat-coupled version of this force-time history. Themagnitudes of the Fourier transforms of these timehistories are displayed in Figures 6 and 7, respectively.

1000 , , I , , , , , m , , ,

T7=3.33 s

aoo -

-T1 +

zSoo -

=m0

:~ulo -

2W -

0 -

,

0 Time (s) 32

Figure 4. Unfiltered Force-Time History

, , , , , , ,

a(

– 200 -

E:–400 -

0:u.

–coo -

–s00 -

-l.~o Time (s) 32

Figure 5. ac-Coupled Force-Time History

‘*FTTT7E=alv

&u.

1

0.10.01 0.1 1

Frequency (Hz]

Figure 6. FFT Magnitude of Unfiltered Force

The effect of at-coupling the force is to generate awaveform that is totally observable within the samplewindow, whereas the unfiltered signal is not. As aresult, no leakage error is associated with transform-ing the filtered signal. The finite sample time causesthe unfiltered force to appear as a rectangular pulsewhose width is shown as T1 in Figure 4. Varying thedelay period (Figure 8) has the effect of changing thepulse width, thereby altering the form of the Fouriertransform magnitude (Figure 9). The holes in theFourier transform magnitude appear at multiples ofthe inverse of the pulse duration (I/T).

10

1

0.1

k , , , ‘

0.01 0.1 1 10

Frequency (Hz)

Figure 7. FFT Magnitude of at-Coupled Force

T2--1

z 600 -=al0zk 400 -

200 -

Io Time (s) 32

Figure 8. Unfiltered Force With Time Shift

The response signals were also at-coupled to can-cel the effects of high-pass filtering of the force signalwhen computing the frequency-response functions.This at-coupling of the channels did not induce adetectable phase shift between channels.

An alternative to at-coupling the channels wouldbe to differentiate both the input and response signalin the time domain.7 This would result in the excita-tion appearing as sharp pulse. The resulting responsewould be the time derivative of acceleration (jerk).This technique was not pursued because it requiresadditional data processing and tends to increase noise

10

levels, whereas the first method can be directly imple-mented by using standard data-acquisition tech-niques After at-coupling, the resulting input andresponse signals are not unlike those obtained byimpact testing and can be processed in a similarmanne:r. For example, one can apply a force or expo-nential window. Exponential windowing is particu-larly important for removing structural responsecaused by wind excitation, after the response causedby the intended excitation has diminished. If theresponse of the structure to wind excitation is notsignificant, comb filtering could also be used toeliminate leakage.6 A typical frequency-response func-tion measurement using step-relaxation is shown inFigure 10.

‘!E-- 1 II II\

I

0.$ ~ * I I J’,l/, ,,, J0.1 1 10

Frequency (Hz)

Frequency-response functions are the desiredquantities being measured during a step-relaxationtest. These functions are curve-fitted to extract themodal frequencies, damping, and mode shapes. Per-forming a “mini-modal” testis identical to a completemodal survey except that fewer frequency-responsefunctions are measured. Consequently, modal fre-quency, damping, mode vector entries, and modalmass can be determined by standard curve-fittingalgorithms. The obvious drawback to this techniquewith respect to a complete modal survey is that adetailed mode-shape description is not available.Therefore, some confusion might arise when modesare closely spaced.

Human ExcitationHuman excitation is exactly what its name

implies—a person shakes the turbine directly or witha rope. This technique has been applied to moderate-size turbines; application to large turbines may not beeasily implemented. Either of two types of tests can beperformed: forced response or free vibration decay.Forced-response testing is equivalent to performing asine dwell test. The person supplying the force shakesthe turbine and synchronizes in on the natural vibra-tion. The turbine is then driven at this frequencyat a constant response level while an accelerationpower spectrum of the driving-point response is mea-sured. The resultant peak in the power spectrumoccurs at the resonance frequency. A typical exampleof a power spectrum measured in this manner is shownin Figure 11.

Figure g. FFT Magnitude of Time-Shifted Force

1 2 8

Frequency (Hz) 4

0 2 4 6

Frequency (Hz)

Figure 11. Driving-Point ASD MeasuredExcitation

8 10

During Human

Figure 110. Typical Frequency-Response FunctionMeasured Using Step-Relaxation

11

Free-decay measurements are similar to forcedresponse except that after the turbine is excited to thedesired steady-state level, the input excitation ishalted, and the vibrational decay of the structure ismeasured. Curve-fitting algorithms can then be usedto extract modal frequency and damping from thisfree decay of the structure. A typical free-decay curveis shown in Figure 12.

@

(~ 0“0*

.-0.10

0 32

The (s)

Figure 12. Free Vibration Response Measurement

Either of these two techniques is repeated atdifferent directions and locations and at various fre-quencies until all of the modal frequencies of interestare determined.

Because the mode-shape characteristics of theturbine are known before the test from the finite-element model, the tester actually tries to excite oneparticular mode when he shakes the wind turbine.This is accomplished by exciting a point in a directionwhere a particular mode has a large participation andother modes participate very little. The fact that thetester has excited a particular mode is verified byvisually observing the deformation pattern. In fact,the mode can be studied in some detail while thestructure is being excited. Because it is relatively easyto excite any point on the structure, this is an excellentmethod for decoupling closely spaced modes.

The low-frequency modes are extremely easy toexcite because the vibration amplitude is large and the

motion of the turbine is slow enough for the exciter totrack. In fact, the amplitude of vibration for thesemodes can be as much as a foot. Exciting the higher-frequency modes, above 4 Hz, is more difficult becauseconsistently maintaining the higher frequencies isphysically demanding and the exciter eventually fallsout of sync. Also, because of the higher frequencies,the displacement of a given mode is smaller, makingthe deformation pattern harder to observe. In thisinstance, more reliance is placed on the model todetermine the mode shape. Exciting the structure atfrequencies above 5 Hz was virtually impossible.

An original concern was that the human excitermight mass-load the structure. Yet, this did not occur,presumably because the individual exciting the struc-ture did not simply go along for the ride; he sensed thevibration and applied a force that was -90° out ofphase with the displacement and sufficient to main-tain motion. As a result, mass loading was negligible,evidenced by the fact that natural frequencies deter-mined by this method and by step-relaxation wereessentially the same. The only instruments used werean accelerometer, transducer cable, amplifier, andan FFT analyzer, all of which could be placed in theback of a ‘pickup truck, from which the test could bedirected.

Benefits of human excitation include fast results,accurate natural-frequency information, and qualita-tive mode-shape information. The negative aspectsare that modal frequencies above 4 Hz were difficultto obtain and quantitative mode-shape informationwas not available.

Wind ExcitationWind can be used as an excitation source because

of its availability and its ability to excite thestructure—the vibration of wind turbines can be visu-ally observed during moderate winds. For a fullyinstrumented prototype, all necessary response datacan be collected on the parked turbine during highwinds. Response auto-spectral densities (ASD) andcross-spectral densities (CSD) can be used to deter-mine modal frequencies and mode shapes. Figure 13shows an acceleration ASD measured during highwinds for the 100-m EOLE turbine, displayed using alog scale. The peaks clearly indicate the presence ofmodes at the frequencies of the peaks.

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0.0 FREQUENCY (HZ) S.o

Figure! 13. Acceleration ASD Measured During HighWinds

The procedure for performing wind-excitationtesting is similar to that used in performing step-excitation testing. One significant difference is thatthe forces acting on the structure are not measured.Several reference degrees-of-freedom (DOFS) are se-lected based upon their degree of participation in eachof the mode shapes. The complete set of referencesshoulcl strongly participate in all of the modes of thestructure within the frequency band of interest. Fromthe response measurements, ASDS of the referenceDOFS are evaluated, and CS13Sare computed betweenthe reisponse DOFS and the reference DOFS.

The modal frequencies are determined from thepeaks in the ASDS of the reference DOFS and thepeaks of a mode-indicator function. The indicatorfunction is created by summing the magnitudesquared of response ASDS. Particular modes can beenhanced by selecting response DOFS baaed upon aknowledge of the mode shape. Shown in Figure 14 is atypical mode-indicator function calculated to enhancethe flatwise blade modes. The mode shapes are thencomputed from the ratios of the CSDS and a referenceASD. The values from these ratios at the resonantfrequency are taken as the corresponding componentsof the mode-shape vector.

Hammer ExcitationHammer excitation has been attempted with a

PCB 12-lb impact hammer on a moderate-size tur-bine. Although reasonable success was obtained withthis technique in that frequency-response functionscould be measured, the drawbacks were considerable:(1) Because of the low-frequency range of interest,excitation could not be properly shaped by adjustinghammer tip stiffness and hammer mass. Also, foam

pads used to decrease the hammer tip stiffness yieldedinconsistent results. (2) Impacting at oblique angles tothe blades would require special fixturing. (3) Incon-sistent impacts overloaded the ADC, requiring addi-tional averages that took more time. (4) For largerturbines, it may not be possible to input enoughenergy to excite the structure sufficiently. It was feltthat these problems could be overcome or tolerated;but because the other techniques worked well andrequired little time, this excitation method has notbeen pursued.

Modal Testing in theDesign Process: AnExample Implementation

A typical application of the use of modal testing aspart of the design process was the VAWTpower 185.The excitation techniques used were human excita-tion and step-relaxation.

For the step-relaxation portion of the test, onedriving point was used. It was on a blade at an angle of-45° with respect to the plane defined by the bladesand the tower. From this location, all modes of inter-est could be excited. Frequency-response functionswere measured at three points on the turbine, usingthree triaxial accelerometers: at the driving point, onthe second blade at a point opposite the driving point,and at the midpoint on the tower. The accelerometermounting locations are shown in Figure 15. Of thenine frequency-response functions measured, onlyfive were required to identify the modal parametersfor the VAWTpower 185; the other four were obtainedwith no additional effort because triaxial accelerom-eters were used.

I I I I I I

0.0 FREQUENCY (HZ) 5.0

Figure 14. Mode Indicator Function

13

Blada 2 Blade 1

Figure 15. Accelerometer Locations for Step-RelaxationTest

The frequency-response functions measured onblade 1 revealed the first and second flatwise modes,first tower in-plane, and first and second tower out-of-plane. The edgewise frequency-response functionsmeasured for blade 2 yielded phase information toseparate and identify the third tower out-of-plane andthe rotor twist mode. The in-plane frequency-response functions measured for the tower indicatedthe second tower in-plane mode. All of these modesare illustrated in Figure 2. Proper modal identificationwas cross-checked by reviewing each of the frequency-response functions to determine whether they wereconsistent with the assumed mode shapes. The num-ber of frequency-response functions could have beenreduced to three (those on blade 1) if only the first sixmodes were required. From start to finish, this “mini-modal” test took just one day, including setup time,data interpretation, and mode-shape identification.

After the modal data were identified using step-relaxation, the turbine was tested using human excita-tion. The human exciter gained access to the turbineby standing in a manbucket and being lifted intoposition by a crane. The bucket was positioned atvarious points of the turbine where the modes ofinterest had large participation factors. At these loca-tions, accelerometers were mounted and the structurewas excited by hand. Using an FFT analyzer,the accelerometer output was processed into auto-spectral densities. The crane positioned the bucket atthree locations, from which all modes of interest wereexcited.

Both excitation techniques took about the sametime (less than one day) and yielded virtually identicalresults. The modal frequencies determined usinghuman and step-relaxation excitation and finite-element analysis are listed in Table 1.

Table 1. Modal Frequencies ofVAWTpower 185 (Hz)

Finite FiniteElement Step Element

Description (Initial) Relaxation Human (Final)Propeller 0.44 0.45 0.43 0.44First bladeflatwisesymmetric &anti-symmetric 1.72 1.36 1.35 1.37

First towerout-of -plane 2.34 1.75 1.75 1.72

Fjrst towerm-plane 2.84 2.53 2.54 2.58

Second bladeflatwisesymmetric 3.77 3.17 3.15 3.14

Second towerout-of -plane 4.01 3.20 3.20 3.21

Second bladeflatwiseanti-symmetric 3.80 3.23 3.15 3.23

A comparison of the finite-element analysis andtesting results revealed that the initial finite-elementmodel needed to be corrected. The model was re-viewed in detail and several changes and correctionswere made. The resultant model predicted modalfrequencies within 3% of the measured modal fre-quencies for the parked turbine (see Table 1). As afurther check on the accuracy of the model, the modesof the turbine, including the effects of rotation, werecomputed and compared to the modal frequenciesdetermined from turbine operating data. The agree-ment was very good.

The updated model then predicted that twomodal frequencies occurred near harmonics of theoperating speed, causing high stresses in the prototypeturbine. The two modes causing the problem were thefirst flatwise symmetric and the first tower in-plane(see Figure 2). These two modes had their modalfrequencies at nearly two and three times the turbinerotation speed (0.84 Hz). The occurrences of resonantconditions are clearly revealed in the fan plot displayof Figure 16. This plot shows the modal frequencies

..

14

versus turbine operating speed with the harmoniclines superimposed on the plot. Wherever modal fre-quencies approach a harmonic line, resonance canoccur.

13ecause the resonant conditions caused highstress and reduced the fatigue life of the turbine, adesign modification of the turbine was required. Thefinite-element model was used to investigate possiblestructural improvements to the turbine. The firstdesign iteration involved stiffening the blade-to-towerjoints with an added strut between the tower and eachblade. A mini-modal, using human excitation, was

1

quickly performed to determine experimentally theshifts in the modal frequencies. An additiond mini-modal survey was conducted to determine the effectsof decreasing cable tension, which reduces cable stiff-ness. The final modifications to the turbine includedthree design changex (1) stiffening the blade-to-towerjoints by adding struts, (2) increasing the guy cablestiffness by doubling the cable cross-section, and (3)reducing by one-half the length of the tower betweenthe base and the blades. These alterations to theturbine have eliminated any near-resonance problem.

I I I I ‘:i

OPERATiNG ISPEED 50.5 rpm~~

/“’,

SECOND BLADEFLATWISE ANTIRVM

/

/’

—, . .. ----- .. .

-- . . ..—- SECONDT5LADE =tUJN

FLATWiSE, SYM OUT-OF-PLANE ,/ ,/”/

; // /“

/ ,/

~ FiRST TOWER ,0/ ##

/iN-PLANE /“

,/’ /’ ,/ POTENTiAL- FiRST TOWER~OUT-OF PLANE ,/ ,/’ / PROBLEM AREAS .

/ / //”,0

~

~.

;/

/I

/

FiRST BLADE / //I

FLATWiSE //” II

3YM &/’.’ /“

// I

ANTiSYM // ; ---

.’;”:/’ //”=-.- -e --

/0/ ./---

—---i1

iLER. / /“ --–

,+,’O#’/ti~--

--4:”=: ----

-/-1

~ PIROPEiI

I

o 10 20 30 40 50 60

n=s

n=4

n=3

n=2

il=l

ROTOR SPEED (rpm)

Figurc~ 16. VAWTpower 185 Fan Plot

15

ConclusionsOf the different approaches to exciting a wind

turbine for a modal test, human excitation, step-relaxation, and wind are the most useful. For mini-modal testing, human excitation is preferred becauseit is the fastest method and requires no special instru-mentation or fixturing and little user interpretation.Use of this technique is limited because small turbineshave natural frequencies too high to be excited man-ually and larger turbines may be too massive to excite.

For a standard modal test or a mini-modal, bothwind and step-relaxation testing methods work ex-tremely well, although they require more time thanhuman excitation. Step-relaxation methods requirepretest analysis for sizing of excitation hardware andsignificant ground support. Both methods require acrane and personnel to mount the accelerometers.Step-relaxation testing requires a higher dependenceon the site workers. However, damping information isnot as readily available from the power spectra ob-tained from wind excitation as it is from FRFs ob-tained using step-relaxation testing. Finally, and mostimportantly, we were able to extract modal data fromFRFs measured, using step-relaxation, during highwinds. However, it would not be possible to obtainmeaningful wind-response measurements during com-pletely calm days.

References‘T. G. Carrieet al, “Finite Element Analysis and Modal

Testing of a Rotating Wind Turbine,” AIAA Paper 82-0097,23rd Structures, Structural Dynamics, and Materials Con-ference, Part 2, New Orleans, May 1982, pp 335-47.

‘J. S. Pate and S. M. Seltzer, “Complex EigenvalueSolution to a Spinning Skylab Problem,” NASA TMX-2378,Vol II (Springtleld, VA National Technical InformationService, Sept 1971).

3D. W. Lobitz, Dynamic Analysis of Darrieus VerticalAxis Wind Turbine Rotors, SAND80-2820 (Albuquerque,NM: Sandia National Laboratories, May 1981).

4D. L. Brown, G. D. Carbon, and K. Ramsey, “Survey ofExcitation Technique Applicable to the Testing of Automo-tive Structures,” SAE Paper 770029, International Automo-tive Engineering Congress and Exposition, Detroit, MI, Feb1977.

5D. L. Brown, “Grinding Dynamics,” PhD Thesis, Uni-versity of Cincinnati, 1976.

W. G. Carrie and A. R. Nerd, “Modal Testing of aRotating Wind Turbine,” Proc Sixth Biennial Wind EnergyConf and Workshop, Minneapolis, MN, June 1983, pp825-34.

7G. F. Mutch et al, “The Dynamic Analysis of a SpaceLattice Structure via the Use of Step Relaxation Testing,”Proc Second International Modal Analysis Conf, Orlando,FL, Feb 1984, pp 368-77.

8C. Van Karson and R. J. Allemang, “Single and Multi-ple Input Modal Analysis, A Comparison of AveragingTechniques,” Proc Second International Modal AnalysisConf, Orlando, FL, Feb 1984, pp 172-78.

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Battelle-Pacific NorthwestLaboratory

Attn: L. WendellPOI Box 999Richland, WA 99352

Bechtel Group, Inc.Attn: B. LessleyPO, Box 3965

San Francisco, CA 94119

Bonneville Power AdministrationAttn: N. ButlerPO BOX 3621Portland, OR 97208

Burns & Roe, Inc.Attn: G. A. Fontana800 Kinderkamack RoadOradell, NJ 07649

California Institute of TechnologyApplied Mechanics DepartmentAttn: K. KnowlesPasadena, CA 91109

Colorado State UniversityDept of Civil EngineeringAttn: R. N. MeroneyFort Collins, CO 80521

Commonwealth Electric Co.Attn: D. W. DunhamBOX 368Vineyard Haven, MA 02568

CSA Engineering, Inc. (2)Attn: D. A. Kienholz

C. D. JohnsonSuite 101560 San Antonio RoadPalo Alto, CA 94306

M. M. Curvin11169 Loop RoadSoddy Daisy, TN 37379

State of WyomingDepartment of Economic Planning

and DevelopmentAttn: G. N. MonssonBarrett BuildingCheyenne, WY 82002

DOE/ALOAttn G. P. TennysonPO Box 5400Albuquerque, NM 87115

17

DISTRIBUTION (Continued):

DOE/ALOEnergy Technology Liaison OfficeNGDAttn: Capt. J. L. Hanson, USAFPO Box 5400Albuquerque, NM 87115

DOE Headquarters (5)Wind/Oceans Technologies DivisionAttn: L. J. Rogers

P. R. Goldman1000 Independence AvenueWashington, DC 20585

Electric Power Research Institute (2)Attn: E. Demeo

F. Goodman3412 Hillview AvenuePalo Alto, CA 94304

Engineering Mechanics Assoc., Inc.Attn: T. K. Hasselman3820 Del Amo Blvd.Torrance, CA 90503

Dr. N. E. Farb10705 Providence DriveVilla Park, CA 92667

Fayette Manufacturing CorporationAttn: W. ThompsonPO Box 1149Tracy, CA 95378-1149

FloWind Corporation (2)Attn: L. Schienbein

B. Im1183 Quarry LanePleasanton, CA 94566

General Dynamics CompanyConvair DivisionAttrx A. L. HaleMZ22-6020PO BOX 85357San Diego, CA 92138

General Motors Research Labs (3)Engineering Mechanics Dept.Attw J. A. Wolf, Jr.

J. HowellD. Nefske

Warren, MI 48090-9055

Southern UniversityDepartment of Mechanical EngineeringAttn: I. J. GrahamPO Box 9445Baton Rouge, LA 70813-9445

Helion, Inc.Attn: J. Park, PresidentBox 445Brownsville, CA 95919

Iowa State UniversityAgricultural Engineering, Room 213Attn: L. H. SoderholmAmes, IA 50010

West Wind IndustriesAttn: K. JacksonPO Box 1705Davis, CA 95617

McAllister FinancialAttn: M. Jackson1816 SummitW. Lafayette, IN 47906

Jet Propulsion LaboratoriesApplied Mechanics DivisionAttn: J. C. Chen4800 Oak Grove Dr. 157-316Pasadena, CA 91109

Kaiser Aluminum and ChemicalSales, Inc.

Attn: A. A. Hagman14200 Cottage Grove AvenueDolton, IL 60419

Kaiser Aluminum and ChemicalSales, Inc.

Attn: D. D. DoerrPO BOX 877Pleasanton, CA 94566

18


Kansas State UniversityElectrical Engineering DepartmentAttn: G. L. JohnsonManhattan, KS 66506

Kinetics Group, Inc.Attn~ J. Sladky, Jr.PO Elox 1071Mercer Island, WA 98040

KW Control Systems, Inc.Attn: R. H. KleinRD#4, Box 914CSouth Plank RoadMiddletown, NY 10940

L. K. Liljergren1260 ,S.E. Walnut #5Tustin, CA 92680

Bare- WestAttn: L. LiljidahlBuilding 005, Room 304Beltsville, MD 20705

Los Alamos National LaboratoryAttn: N. F. Hunter, WX-11, MSC931PO Box 1663Los Alamos, NM 87545

R. Lynette & Assoc., Inc.Attn: R. Lynette15042 NE 40th StreetSuite 206Redmond, WA 98052

Martin Marietta CorporationAttn: R. F. HrudaMail Stop G-6496PO BOIX179Denver, CO 80201

Massachusetts Inst of Tech (2)Attn: N. D. Ham

W. L. Harris, Aero/Astro Dept.77 Massachusetts AvenueCambridge, MA 02139

US Wind PowerAttn G. M. McNerney160 Wheeler RoadBurlington, MA 01803

Michigan State UniversityDivision of Engineering ResearchAttn: O. KraussEast Lansing, MI 48825

NASA Langley Research Center (2)Structural Dynamics DivisionAttn L. Pinson

B. R. HanksMail Stop 230Hampton, VA 23655

National Rural ElectricCooperative Assn

Attn: W. Prichett 1111800 Massachusetts Avenue, NWWashington, DC 20036

Natural Power, Inc.Attn: L. NicholsNew Boston, NH 03070

New Mexico EngineeringResearch Institute

Attn: G. G. LeighCampus PO Box 25Albuquerque, NM 87131

Ohio State UniversityAeronautical and Astronautical Dept.Attn: G. Gregorek2070 Neil AvenueColumbus, OH 43210

Oklahoma State UniversityMechanical Engineering Dept.Attn D. K. McLaughlinStillwater, OK 76074

Old Dominion UniversityDept of Mech Engineering &

MechanicsAttn: S. R. IbrahimNorfolk, VA 23508

Oregon State UniversityMechanical Engineering Dept.Attn: R. E. WilsonCorvallis, OR 97331

19


Pacific Gas & Electric Co.Attn: T. Hillesland34OOCrow Canyon RoadSan Ramon, CA 94583

J. M. Turner Technologies, Inc.Attn: E. N. HinrichsenPO BOX 1058Schenectady, NY 12301-1058

Public Service Co. of New HampshireAttn D. L. C. Frederick1000 Elm StreetManchester, NH 03105

Public Service Company of New MexicoAttn: M. LechnerPO BOX 2267Albuquerque, NM 87103

Purdue UniversitySchool of Civil EngineeringAttn: J. T. P. YaoWest Lafayette, IN 47907

RANN, Inc.Attn A. J. Eggers, Jr.260 Sheridan Ave., Suite 414Palo Alto, CA 94306

Iowa State UniversityAerospace Engineering DepartmentAttn: R. G. Rajagopalan404 Town Engineering Bldg.Ames, IA 50011

State of California Resources AgencyDepartment of Water ResourcesEnergy DivisionAttn: R. G. FerreiraPO BOX 388Sacramento, CA 95802

Reynolds Metals CompanyMill Products DivisionAttn: G. E. Lennox6601 West Broad StreetRichmond, VA 23261

National Atomic MuseumAttn: G. Schreiner, LibrarianAlbuquerque, NM 87185

Wind Energy News ServiceAttn: F. S. Seiler, EditorPO BOX 4008St. Johnsbury, VT 05819

Solar Energy Research InstituteAttn: R. W. Thresher1617 Cole BoulevardGolden, CO 80401

Southern California EdisonResearch & Development DeptRoom 497Attn: R. L. SchefflerPO BOX 800Rosemead, CA 91770

Stanford UniversityDept. of Aeronautics andAstronautics Mechanical EngineeringAttn: H. AshleyStanford, CA 94305

Structural Dynamics Research Corp. (2)Attn: M. Baker

D. Hunt11055 RoselleSan Diego, CA 92121

Structural Dynamics Research Corp. (2)Attn: G. Townley

M. Abrishaman2000 Eastman DriveMilford, OH 45150

Synergistic Technology, Inc.Attn: R. C. Stroud20065 Stevens Creek Blvd., Ste. 106Cupertino, CA 95014

State University of NY at BuffaloDept of Mechanical & Aerospace EngrAttn: D. J. Inman1006 Furnas HallBuffalo, NY 14260

Texas Tech University (2)Mechanical Engineering Dept.Attn: J. W. OlerPO BOX 4289

Lubbock, TX 79409

20


Moriah ResearchAttn: K. J. Touryan6200 Plateau Dr.Englewood, CO 80111

TRW CorporationDynamics Dept RB/B240Attn: S. SimonianOne Space ParkReclondo Beach, CA 90278

Tulane UniversityDept. of Mechanical EngineeringAttn: R. G. WattsNew Orleans, LA 70018

United Engineers and Constructors,Inc.

Attn: A. J. KaralisPO BOX 8223Philadelphia, PA 19101

Universal Data SystemsAttm C. W. Dodd50010Bradford DriveHuntsville, AL 35805

University of CaliforniaInstitute of Geophysics

and Planetary PhysicsAttn: P. J. BaumRiverside, CA 92521

University of Cincinnati (2)Mechanical Engineering DeptAttn: D. L. Brown

R. L. AllemangCincinnati, OH 45221

University of ColoradoDe]pt. of Aerospace Engineering

SciencesAttn: J. D. Fock, Jr.Bo,ulder, CO 80309”

University of DaytonResearch InstituteAti,m M. Soni, JPC-326Dayton, OH 45469

University of MassachusettsMechanical and AerospaceEngineering Dept.

Attn: D. E. CromackAmherst, MA 01003

University of New MexicoMechanical Engineering DeptAttn: F. D. JuAlbuquerque, NM 87131

University of OklahomaAero Engineering DepartmentAttn: K. BergeyNorman, OK 73069

The University of TennesseeDept. of Electrical EngineeringAttn: T. W. ReddochKnoxville, TN 37916

The University of Texas at AustinDept of Aerospace Engineering

and Engineering MechanicsAttn: R. D. CraigAustin, TX 78712

USDA, Agricultural Research ServiceSouthwest Great Plains Research

CenterAttn: R. N. ClarkBushland, TX 79012

Virginia Polytechnic Institute andState University ,-.

Dept of Mechanical EngineeringAttn: L. D. MitchellRandolph HallBlacksburg, VA 24061

W. A. Vachon & AssociatesAttn: W. A. VachonPO Box 149Manchester, MA 01944

Washington and Lee UniversityAttn: R. E. AkinsPO Box 735Lexington, VA 24450


Washington State UniversityDept. of Electrical EngineeringAttn: F. K. BechtelPullman, WA 99163

Westinghouse Electric CorporationAttn: S. SattingerSenior Research Engineer1310 Beulah RoadPittsburgh, PA 15235

West Texas State UniversityGovernment Depository LibraryNumber 613Canyon, TX 79015

West Texas State UniversityDepartment of PhysicsAttn: V. NelsonPO BOX 248Canyon, TX 79016

West Virginia UniversityDept. of Aero EngineeringAttn: R. Walters1062 Kountz AvenueMorgantown, WV 26505

Central Lincoln People’s UtilityDistrict

Attn: D. Westlind2129 North Coast HighwayNewport, OR 97365-1795

Wichita State University (2)Aero Engineering DepartmentAttn: M. Snyder

W. WentzWichita, KS 67208

Wind Power DigestAttn: M. EvansPO Box 700Bascom, OH 44809

Wisconsin State Division of EnergyAttn: Wind Program Manager101 South Webster Street, 8th FloorMadison, WI 53702

Wright Patterson AFBAttn: V. B. VenkayyaAFWAL/FIBRDayton, OH 45433

State Univ. of GhentAttm D. VandenbergheSt. Pietersniewstraat 419000 GhentBELGIUM

Pontificia Universidade Catolica-PUC/RjMechanical Engineering DepartmentAttn: A. de Faro OrlandoR. Marques de S. Vicente 225Rio de JaneiroBRAZIL

The College of Trades and TechnologyAttn: R. E. KellandPO BOX 1693Prince Philip DriveSt. John’s, Newfoundland, AIC 5P7CANADA

Indal Technologies, Inc. (2)Attn: D. Malcolm

C. Wood3570 Hawkestone RoadMississauga, OntarioCANADA L5C 2V8

Institut de Recherche d’Hydro-QuebecAttn: B. Masse1800, Montee Ste-JulieVarennes, Quebec, JOL 2P.O.CANADA

Trinity WesternAttn. A. S. Barker7600 Glover RoadLangley, BCCANADA V3A 4R9

Canadian Standards AssociationAttn: T. Watson178 Rexdale Blvd.Rexdale, Ontario, M9W 1R3CANADA

22


National Research Councilof Canada

Energy, Mines and ResourcesAttn: M. CarpenterMontreal RoadOttawa, OntarioCANADA KIA 0R6

University Laval-QuebecFaculty of Sciences and EngineeringMechanical Engineering DepartmentAttn: H. GerardinQuebec GIK 7P4CANADA

Ecole PolytecniqueDepartment of Mechanical EngineeringAttn: I. ParaschivoiuCP 6079Succursale AMontreal H3C 3A7CANADA

Hydro QuebecAttn: J. PlantePlace Dupuis Ile etage855 est rue Ste-CatherineMontreal, QuebecCANADA H2L 4P5

Atlantic Wind Test SiteAttn: R. G. RichardsPO Box 189Tignish P.E.I., COB 2B0CANA.DA

Shawinigan Engineering Co., Ltd. (10)Attn: H. Benjannet1100 Dorchester Blvd. West, 8th FloorMontreal, QuebecCANADA H3B 4P3

ADECONAttn P. South32 Rivalda RoadWeston, Ontario, M9M 2M3CANADA

NRC-National Aeronautical Estab (3)Low Speed Aerodynamics LaboratoryAttn: R. J. TemplinMontreal RoadOttawa, Ontario, KIA 0R6CANADA

University of Sherbrooke (2)Faculty of Applied ScienceAttn A. Laneville

P. VittecoqSherbrooke, Quebec, JIK 2R1CANADA

Instituto Technologico Costa RicaAttn: K. SmithApartado 159 CartagoCOSTA RICA

Riso National Laboratory (2)Attn: T. F. Pedersen

H. PetersenPostbox 49DK-4000 RoskildeDENMARK

Roskilde University CenterEnergy Group, Bldg. 17.2IMFUFAAttn: B. SorensonPO BOX 260DK-400 RoskildeDENMARK

Institut fur LeichbauTechnische Hochschule AachenAttn: I. H. RuscheweyhWullnerstrasse 7AachenFEDERAL REPUBLIC OF GERMANY

France (2)Attn: D. Bonnecase

J. C. Cromer19 bis Chemin de Mouilles69130 EcullyFRANCE

23


Establissement d’Etudes et deRecherches MeteorologiquesAttn B. de Saint Louvent77 Rue de Serves92106 Boulogne-Billancourt CedexFRANCE

National Technical UniversityDept of Mechanical EngineeringAttn: G. Bergeles42, Patission StreetAthensGREECE

Technion-Israel Institute ofTechnology

Aeronautical Engineering Dept.Attrx A. SeginerProfessor of AerodynamicsHaifaISRAEL

Toray Industries, Inc.Pioneering R&D LaboratoriesComposite Materials LaboratoryAttn: H. S. MatsudaSonoyama, Otsu, ShigaJAPAN 520

University of AucklandSchool of EngineeringAttn: V. A. L. ChasteauPrivate BagAucklandNEW ZEALAND

FFA, The Aeronautical ResearchInstitute

Attn: O. LjungstromBox 11021S-16111 BrommaSWEDEN

National Aerospace LaboratoryAttn: O. de VriesAnthony Fokkerweg 2Amsterdam 1017THE NETHERLANDS

Nederlands Energy ResearchFoundation (E. C.N.)

Physics DepartmentAttn: J. B. DragtWesterduinweg 3Petten (nh)THE NETHERLANDS

Garrad HassonAttn: A. D. Garrad10 Northampton SquareLondon ECIM 5PAUNITED KINGDOM

Imperial College of Science & TechnologyDept. of Mechanical EngineeringAttn: D. J. EwinsExhibition RoadLondon SW7 2BXUNITED KINGDOM

Napier College of Commerce andTechnologyTutor Librarian, Technology FacultyColinton RoadEdinburgh, EH1O 5DTUNITED KINGDOM

Open UniversityAlternative Energy GroupWalton HallAttn: D. TaylorMilton Keynes, MK7 6AAUNITED KINGDOM

Queen Mary CollegeDept of Aeronautical EngineeringAttn: D. SharpeMile End RoadLondon, El 4NS’UNITED KINGDOM

The University of ReadingDepartment of EngineeringAttn G. StaceyWhiteknights, Reading, RG6 2AYUNITED KINGDOM

24


University College of SwanseaDept of Mechanical EngineeringAttn: R. T. GriffithsSingleton ParkSwansea, SA2 8PPUNITED KINGDOM

1520 C. W. Peterson1522 R. C. Reuter, Jr.1522 D. W. Lobitz1522 D. R. Martinez1523 J. H. Biffle1524 A. K. Miller1524 C. R. Dohrmann1524 P. S. Veers1550 R. C. Maydew1552 J. H. Strickland1556 G. F. Homicz2525 R. B. Diegle3160 J. E. Mitchell (15)3162 P. S. Wilson6000 D. L. Hartley6200 V. L. Dugan6220 D. G. Schueler6225 H. M. Dodd (50)6225 T. D. Ashwill (10)6225 D. E. Berg6225 T. C. Bryant6225 L. R. Gallo6225 P. C. Klimas

6225 S. D. Nicolaysen6225 D. S. oscar6225 M. E. Ralph6225 D. C. Reda6225 M. A. Rumsey6225 L. L. Schluter6225 W. A. Stephenson6225 H. J. Sutherland7290 T. S. Church7500 D. M. Olson7531 D. R. Schafer7540 T. B. Lane7541 R. Rodeman7542 T. G. Priddy7543 D. E. Miller7544 D. O. Smallwood7544 V. I. Bateman7544 T. G. Carrie (20)7544 A. J. Gomez (10)7544 J. P. Lauffer (20)7544 A. R. Nerd7544 M. D. Tucker8240 C. W. Robinson8243 M. L. Callabresi9100 R. G. Clem9122 T. M. Leonard8524 P. W. Dean3141 S. A. Landenberger (5)3151 W. L. Garner (3)3154-1 C. H. Dalin (8)

For DOE/OSTI

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Modal Testing in the Design .i Evaluation of Wind Turbines · Typical Wind-Turbine Mode Shapes...

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Transcript of Modal Testing in the Design .i Evaluation of Wind Turbines · Typical Wind-Turbine Mode Shapes...