Optimizing tuning masses for helicopter rotor blade vibration reduction including computed airloads and comparison with test data

TLDR: In this article, the authors developed and validated an optimization procedure to systematically place tuning masses along a rotor blade span to minimize vibratory loads in a four-bladed rotor system without adding a large mass penalty.

Abstract: The development and validation of an optimization procedure to systematically place tuning masses along a rotor blade span to minimize vibratory loads are described. The masses and their corresponding locations are the design variables that are manipulated to reduce the harmonics of hub shear for a four-bladed rotor system without adding a large mass penalty. The procedure incorporates a comprehensive helicopter analysis to calculate the airloads. Predicting changes in airloads due to changes in design variables is an important feature of this research. The procedure was applied to a one-sixth, Mach-scaled rotor blade model to place three masses and then again to place six masses. In both cases the added mass was able to achieve significant reductions in the hub shear. In addition, the procedure was applied to place a single mass of fixed value on a blade model to reduce the hub shear for three flight conditions. The analytical results were compared to experimental data from a wind tunnel test performed in the Langley Transonic Dynamics Tunnel. The correlation of the mass location was good and the trend of the mass location with respect to flight speed was predicted fairly well. However, it was noted that the analysis was not entirely successful at predicting the absolute magnitudes of the fixed system loads.

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NASA- Tt4- Ioq, /_q
NASA-TM-104194 19920010604
NASA Technical Memorandum 104194
AVSCOM Technical Report 91-B-020
A
Optimizing Tuning Masses for Helicopter Rotor
Blade Vibration Reduction•Including Computed
Airloads and Comparison with Test Data
Jocelyn I. Pritchard
Howard M. Adelman
Joanne L. Walsh __...__
Matthew L. Wilbur , _ ,,_...,.,
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National Aeronauticsand
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OptimizingTuningMassesFor HelicopterRotorBlade
VibrationReductionIncludingComputedAirloads
AndComparisonWithTest Data
JocelynI. Pritchard* 3 1
HowardM. Adelman**
JeanneL.Walsh+
t
MatthewL.Wilbur++
NASALangleyResearchCenter
Hampton,Virginia
Abstract
Thispaperdescribesthedevelopmentandvalidationof massoffixedvalueonablademodeltoreducethehub
anoptimizationproceduretosystematicallyplacetun- shearforthreeflightconditions.Theanalyticalresults
ing massesalongarotorbladespantominimizevibratory werecomparedtoexperimentaldatafromawindtunnel
loads. Themassesandtheircorrespondinglocations test performedin the LangleyTransonicDynamics
arethedesignvariablesthataremanipulatedtoreduce Tunnel.Thecorrelationofthemasslocationwasgood
harmonicsof hubshearfor a four-bladedrotorsystem andthetrendofthemasslocationwithrespectto flight
withoutaddinga largemasspenalty. The procedure speedwaspredictedfairlywell. However,itwasnoted
incorporatesa comprehensivehelicopteranalysisto thattheanalysiswasnotentirelysuccessfulatpredicting
calculatethe aidoads. Predictingchangesin airloads theabsolutemagnitudesofthefixed-systemloads.
due to changesin design variablesis an important
featureof thisresearch.Theprocedurewasappliedto Nomenclature
a one-sixth,Mach-scaledrotorblade modelto place
threemassesandthenagainto place CT coefficientofthrust
f objectivefunction
sixmasses.Inbothcasestheaddedmasswasableto
I numberofconstrainedfrequencies
achievesignificantreductionsin the hub shear. In
J numberoftuningmasses
addition,the procedurewas appliedto placea single
K numberof harmonicsofshearincludedinthe
objectivefunction
Mj jth tuningmass
NP frequencyor loadingat N timestherotational
"ResearchEngineer,AerostructuresDirectorate,MemberAHS
**DeputyHead,InterdisciplinaryResearchOffice,AssociateFellow speedof blade
AIAA,MemberAHS Sk amplitudeofkthharmonicofshear
'ResearchEngineer.MemberAIAA,AHS Xj locationofjthtuningmass
"Research Engineer,AorostructuresDircectorate,MemberAHS _k scalardesignvariablesappearingintheob-

jectivefunctionandconstraints
labor-intensiveeffort,however,mathematicaloptimiza-
p, advanceratio(ratioofforwardflightspeedto
tip speed) tion techniquesallowforefficientandthorough searches
ofthe designpossibilities while satisfyinga large num-
0)i ith natural frequency berof conflicting design requirementsfrom manydiffer-
_i ,O)i / _
_li lower bound on _i ent disciplines. For example, reference 9 used optimi- '.
zation methods to study the interaction of structural
_ui upper bound on _i propertieswith airload distributions indesigning blades
rotational speed of rotor blade for low vibration. The structural properties included
mass and stiffnessdistributions. The airload distribu-
Introduction tions included higher harmonic lift components and
Since helicopter vibration is transmitted from the aerodynamic pitching moments which are the primary
rotor blade to the fuselage through a time dependent sources of vibration in helicopter rotor blades. Corn-
shear force atthe hub, methods for reducing vibration parison of the vibration characteristics from three ana-
through reduction of hub shear have long been a lyticaldesignstrategiesshowedthebenefitsofusingan
subject of study. An example ofthis is vibration reduc- automated structural optimization procedure with a
tion of rotor blades through passive control. For in- coupled aeroelastic analysis. Another examplewhere
stance, pendulum absorbers 1, active isolationdevices optimization was successfully applied to the design of
2,additionaldamping 2-3,andvibrationabsorberswhich low vibration rotor bladeswas reported in reference 10
create anti-resonances 4-5 have all shown promise in and 11 where severalalternative optimization formula-
reducing blade vibratory response. Historically, fre- tions were investigated and their benefits revealed.
quency placement has beenthe principal technique for References10 and 11 did not use computed airloads in
passively reducing blade vibration 6. Another form of the analyses. Reference 12 discusses an optimization
passive control is to after the mass and stiffness distri- procedure for designing a low vibration rotor blade.
butions of the blade. These modifications tailor the Wind tunnel tests of the blade showed that the design
mode shapes to achieve orthogonalityto the airloading proved to be better than a rotor designed using the
thereby reducingthe generalizedforce andresponseof traditional approach of frequency placement. A com-
the blade7. This is generally done in a latestage ofthe parison between the analytical results and test data
design process, revealed that the trends and reductions in load levels
The currenttrend inengineering designofaircraftis were predictedwell butthe absolute values of the loads
to incorporate critical requirements from all pertinent at given airspeeds were predicted less accurately.
disciplines into an early phase of the design processto Reference 13 described a procedure for placing
avoid costly modifications after a problem has been and sizing tuning masses at strategic locations along
detected 8. In the preliminary stage of design, a large the blade span to tailor the mode shapes. This proce-
number of design variables are free to be chosen in dure used formal mathematical programming tech-
order to satisfy important multidisciplinary consider- niques in conjunction with a finite element program to
ations. Itis inthis stagethat passive control of vibration model a simplified blade and calculate the dynamic
can play an important role. The design process is a response. The airloads used in the analysis repre-
2

sentedasetof harmonicstypicalofafour-bladedrotor ables,_k whichalsoappear in the constraintsas
system7. Theloadsdidnotvarywithchangesinthe "upperlimits"ontheshearharmonicamplitudes,Sk.
massesortheirlocations.Thepurposeofthispaperis
to describethe enhancementandvalidationof the Sk/13k--1 < 0 k = 1,2....,K (2)
methoddescribedinreference13.Theenhancements
includetheincorporationofacomprehensivehelicopterK representsthe numberof shearharmonicsto be
analysisCAMRAD/JA14 intotheoptimizationproce- includedinthe objectivefunction.Byconventiona
durewhichyieldsa morerealisticblademodeland constraintissatisfiedifitsvalueislessthanorequalto
calculatedairloads.Thevalidationisaccomplishedby zero.Consequently,theoptimizerwilltendtodecrease
comparingtheanalyticalresultswithexperimentaldata thevaluesof{3k tominimizetheobjectivefunctionbut
fromwindtunneltests, willalsotendtoincreasethevaluesof13ktosatisfythe
constraints.Thisresultsinacompromiseonthevalues
ProblemDefinitionandFormulation of_k whichforcesa reductioninthevaluesofSkthus
reducingthehubshearharmonicswhile incurringthe
smallestpossiblemasspenalty.Additionalconstraints
M1 M2 Mn includeupperandlowerboundsonthenaturalfrequen-
_ Am "= " _ cies of the bladeto avoidresonanceas shownin
Xl X2 _lr'xn _! ,,..V equation(3).
)
/_ui-1 -<0_ i = 1,2,...,1 (3)
Figure1. Designvariabledefinitionforoptimizing
magnitudesandlocationsoftuningmasses 1- _i / _li < 0 J
Thedesigngoalistofindtheoptimumcombina- where_'-'i= °)i / .Q, 0)i istheith naturalfrequency,
tionofmassesandtheirlocations(Fig.1)to reducethe _
t.Ouiand t..01iaretheupperand lowerboundson 0)i
verticalhubshear.Themethodentailsformulatingand
respectivelyandIisthenumberofconstrainedfrequen-
solvingan optimizationproblemin which the tuning
cies.
masses,M'sandcorrespondinglocations,X's arede-
signvariablesthat are manipulatedto minimizethe
Analyses
objectivefunction. Equation(1)definestheobjective
function,f whichis a combinationofverticalhubshear
Theanalysesthatareusedintheprocedurearethe
andaddedmass. comprehensivehelicopteranalysiscode, CAMRAD/
JA14,the optimizationcode,CONMIN15 andan ap-
f = 1+ ,T-,_k 7_,Mj (1) proximateanalysistoreducethenumberofCAMRAD/
k=l )j=l JAanalysesduringtheiterativeprocess.CAMRAD/JA
calculatesrotor performance,loads,vibration mode
Theobjectivefunctionincludesadditionaldesignvari- shapesandfrequencies,aeroelasticstabilityand re-
3

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Q1. What are the contributions in "Optimizing tuning masses for helicopter rotor blade vibration reduction•including computed airloads and comparison with test data" ?

In this paper, the authors developed and validated an optimization procedure to systematically reduce the hub shear for three flight conditions.