bringing broadband 6-dof field vibration environments in ... · dof that this algorithm can control...
TRANSCRIPT
BringingBroadband6-DOFField
VibrationEnvironmentsintotheLab–
Tensor18kNVibrationTestSystem
Joel Hoksbergen, Team Corporation1
Abstract
Commercially available vibration test systems able to reproduce and accurately control
multiple-input, multiple-output vibration tests are often constrained by a limited frequency
band due to excessive tare mass and low natural frequencies of the fixtures. Consequently,
their use in Department of Defense test facilities is limited to a select number of test profiles
found in MIL STD documents and/or platform specific tests where the frequency band of interest is
below 500 Hz. This frequency limitation has now been addressed with the introduction of a new
system based upon multiple electro-dynamic shakers hydrostatically coupled to the specimen
mounting table. This system, called the Tensor 18kN, has been designed, built, and tested by Team
Corporation and has been delivered to two sites in the US A. This paper discusses the design,
with an emphasis on mechanical solutions that have increased the frequency bandwidth and
provide multiple points of control authority for performance to 2,000 Hz. Additionally, the
system response for two specific vibration tests is presented in detail with a discussion of the system
control.
Introduction
What is a Tensor? Wikipedia defines a Tensor as “a geometric object that describes the linear
relationsbetweenvectors, scalars, andothertensors. Elementaryexamplesofsuchrelationsincludethe
dot product,thecrossproduct, and linearmap. A tensorcanbe representedasamulti-dimensionalarray
ofnumericalvalues.”[1] Inbasic engineeringyoumay thinkof aTensor in termsof the3-dimensional
stress stateofasolid object. Remember the cube element showing the normal and shear stresses on
each face? Now, invibrationtestingyoucanthinkofaTensorasthesolutiontoreproducinghigh-
frequency,multi-axisvibration“stressstates”inthelab.TeamCorporation’snewTensor18kNisthemost
advancedcommerciallyavailablevibration test system capable of replicating field vibration
environments out to 2,000 Hz. Twelveindependentexcitationinputsarelinearlymappedintosix
controlleddegrees-of-freedom(DOF).
The basic concept of the Tensor 18kN originated in amuch smaller system developed in the mid 2000’s,
namelytheTensor900.Thissystemwasnovelinthattwelveelectro-dynamic(ED)shakerswereconfigured
insuchaway,with theproperbearingarrangement, toprovide6-DOFcontrolout to2,000Hz. In fact, the
users of this system have successfully operated it past 3,000Hz. This is a small system, andwas used to
developthebasicpremiseoftheoverdeterminedcontrolscheme.Ithas200lbfRMSperaxisandan8”x8”
table.ThefirstcustomerswereSandiaNationalLaboratories,whohasoverthelastseveralyearspresented
1J.Hoksbergen,TeamCorporation,11591WatertankRd.,Burlington,WA98233
Email:[email protected]
several papers on the successes they’ve had operating it, and the University of Maryland’s Center for
AdvancedLifecycleEngineering(CALCE),whouseitheavilyastheyresearchthereliabilityofprintedcircuit
boardssubjectedtovariousvibrationenvironments.Figure1presentstheTensor900.
Figure 1: Tensor 900 Vibration Test System
ThedesignoftheTensorvibrationtestsystemiscoveredunderthefollowingpatents:
• U.S.Patent:6860152
• ChinaPatent:ZL03809374.X
• JapanPatent:4217210
Mechanical System
TheTensor18kNexpands thedesignof the Tensor900 to a sizemore practical for the typical user. The
systemisstilldesignedtobeover-constrainedandusestwelvecustommadeEDshakersforexcitationoutto
2,000Hz.However,now900lbfRMSshakersareusedtodrivea30inchsquaretable.Withfourshakersin
eachaxis, thissystemproduces3,600lbfRMSperaxisandhasabaretablemovingmassofnominally430
lbm.Figure2isaphotooftheTensor18kNsystemandTable1liststhesystem’sperformancespecifications.
Figure 2: Tensor 18kN Vibration Test System
ThemaincomponentsoftheTensor18kNsystemare:
• (12)customEDshakers
• 30inchx30inchvibrationtable
• Highlydampedreactionmass
• Verticalpreloadactuator
• Hydraulicpowersupply
• Poweramplifierset
Thedesignoftheshakersisbasedonastandardfieldcoilandvoicecoildriverset.However,beyondthisthe
similarities with standard ED shakers end. The armature flexures have been replaced with hydrostatic
journalbearings.Thereisnospecimenmountingsurface,butrathertheendofthearmatureincorporatesa
versionofTeamCorporation’ssignaturehydrostaticpadbearings.Thesebearingsonlytransmitthearmature
force through the pad’s axis, and allow the table to move unrestrained in the other 5-DOF about each
armature. IncorporatinghydrostaticpadbearingsdirectlyintothearmaturefreesupthenecessaryDOFto
the systemsuch that twelve shakers canbeused todriveall6-DOFwithoutmechanically lockingup. The
hydrostatic connection to the table is an extremely stiff and friction-free interface, providing for high
frequencyresponseandnomechanicalwear.
ThemechanicsoftheTensor18kNrequiretheshakerarmaturestobepreloadedagainstthetableforproper
operation. To accomplish this, each shakerhas apreloadmechanism integrated into its armature. In the
horizontalaxes,opposingshakersreacteachother’spreloadtoremaininstaticequilibrium. Inthevertical
axis, a preload actuator is required tohold the tabledownagainst the armaturepreload. This actuator is
hydraulically controlled and includes a variety of hydrostatic bearings to keep the system kinematically
sound. The vertical preload actuator is essentially a soft springwith a large static load capacity and has
minimal effect on the control of the system. Figure 3 shows the layout of the ED shakers relative to the
vibrationtable.
Figure 3: Tensor ED Shaker Configuration
Inadditiontopressurizingthehydrostaticbearings,hydraulicoil isalsousedtoremovetheheatgenerated
fromboth the fieldandvoicecoilsof theshakers. Hydraulicoilprovidesmoreeffectiveheat transfer than
forcedairconvectionusedinmostshakers,andtheTensor18kNisconfiguredtohandletheflowofoiland
keep it properly contained. A furtherbenefit of oil cooled coils is that the shakers aremuchquieter than
conventionalshakersbecauseanexternalblowerisnotrequired.
TheEDshakers,vibrationtable,andverticalpreloadactuatorareallintegratedintoahighlydampedreaction
mass.Thisreactionmassrestsonairisolatorsandcreatesasystemthatisself-containedandisolatedfrom
theexistingfacility.Noadditionalreactionmassisrequiredforoperation,onlyafloorcapableofsupporting
thesystemweightofnominally17,000lbm[7,700kg].Thisallowsforasystemthatiseasilyintegratedinto
anexistinglaboratoryfacility.
Ahydraulicpowersupply(HPS)providestherequiredhydraulicpressureandflow,whileabankoftwelve
PowerAmplifiersprovidestheelectricvoltageandcurrenttotheshakers.Bothofthesesub-systemscanbe
locatedremotelyfromtheTensor18kNtominimizethenoiselevelspresentinthelab.This,alongwiththe
oilcooledcoils,providesforlowambientnoiselevelsinsidethelaboratory.
Table 1: Tensor 18kN Performance Specifications
Specification(perAxis) EnglishUnits SIUnits
PeakSineForce 4,800lbf 21.4kN
RMSRandomForce 3,600lbf 16,0kN
MovingMass 430lbm 195kg
PeakVelocity 50in/sec 1.3m/sec
DynamicStroke 1.00in.p-p 25mmp-p
StaticStroke 1.50in.p-p 38mmp-p
Max.Rotation ±4.0deg ±4.0deg
Control Scheme
The Tensor 18kN requires an advanced multiple-input, multiple-output (MIMO) vibration test controller,
capable of controlling twelve shakers using, at a minimum, twelve control accelerometers. To date, two
commercially available vibration controllers have been used to successfully control the Tensor systems;
namely the Spectral Dynamics Jaguar and the Data Physics SignalStarMatrix. The data presented in this
paperwascollectedusingtheDataPhysicsSignalStarMatrixcontroller.
TherearethreeMIMOcontrolschemesthatcanbeusedtocontroltheTensor18kN. Thesearecommonly
referredtoas:
• SquareControl–Equalnumberofdriveandcontrolpoints.
• RectangularControl –Unequal numberof drives and control points,withmore control thandrive
points.
• Coordinate Transformation – Linear mapping of both the drive and control points to some pre-
determinedDOFsusedforcontrol.
TheresultspresentedinthispaperwereproducedusingCoordinateTransformationControl.Thenumberof
DOF that this algorithm can control is limited in theory by the number of drive points, but a test can be
configuredtocontrolfewer.InthecaseoftheTensorthislimitistwelveDOF.Typically,themappedDOFofa
‘VirtualPoint’arechosentobetherigidbodyDOFofinterest.ThelocationoftheVirtualPointisdefinedby
theuser.AdditionalDOFcanbedefined,uptothenumberofdrives.TheseDOFmaybeflexiblebodymodes
of the table. The intent of adding flexible body DOFs to the control is to give the system more control
authorityoverthetablesoitcanworktosuppresstheseparticularvibrationmodes.
Fourtri-axialaccelerometerswereusedasthecontrolpointsoftheTensor18kNandwereplaceddirectlyin-
linewith the shakers, as shown inFigure4. TheCoordinateTransformationmethodwasused tomap the
responseofthetwelvecontrolaccelerometerstotheVirtualPoint,whichwaschosentobethecenterofthe
table’stopsurface. The transformationsweredefinedsuchthatthe linearandangularaccelerationsofthe
VirtualPointwerethereferencepointsforthe6-DOFcontrol.
Figure 4: Tri-Axial Control Accelerometer Placement
TheCoordinateTransformationscheme, ina certain sense, is aMIMOaveragingmethod. Fora single-axis
vibrationtest,itiscommontoaveragetheresponseofmultiplecontrolaccelerometerstoachieveacceptable
responseofagivensystemandcontrol throughvibrationmodes. Thissingle-axisaveraging isdone in the
frequency domain on the magnitude of the response power spectral density (PSD) at each frequency
measurement. SincethePSDcontainsonlythemagnitudeofthespectrum,noconsiderationisgiventothe
phaseof the response signals. In aMIMOvibration test, however, theCoordinate Transformation scheme
averagesboththemagnitudeandphaseoftheresponses inthetimedomain. Consideringthephaseinthe
MIMOcase is important because it is possible for the responses tobedrivenout of phase, even as a rigid
body, due to the nature of themulti-axis equipment. This is in contrast to single-axis systems,which are
mechanicallyconstrained,orguided,anddonotallowresponsestobedrivenoutofphase.Forthisreason,
theCoordinateTransformationmethodprovidesamoreaccurateaverageresponsemeasurementofaMIMO
system.
Vibration Tests
TwospecifictestswererunontheTensor18kNtodemonstratethesystem’scapabilities.Thedetailsofeach
aregivenbelow.
Test 1–ModifiedVersionofMIL-STD810gCompositeWheeledVehicleTest(Method514.6,AnnexC,Table
514.6C-VI)[2]
• SimultaneousexcitationofeachlinearDOF
• Bandwidth:15-500Hzeachaxis
• X-Axis(Longitudinal)
o Acceleration:3.2g-rms
o Velocity:10.0in/secpeak
o Displacement:0.08inchespeak
• Y-Axis(Transverse)
o Acceleration:3.2g-rms
o Velocity:16.9in/secpeak
o Displacement:0.15inchespeak
• Z-Axis(Vertical)
o Acceleration:3.2g-rms
o Velocity:15.2in/secpeak
o Displacement:0.13inchespeak
• Case1:Activesuppressionof3rotaryDOF
• Case2:Activeexcitationof3rotaryDOFatalowlevel
Test 2–5-2,000HzBroadbandRandomProfile
• SimultaneousexcitationofeachlinearDOF
• Bandwidth:5-2,000Hzflatprofileeachaxis
• Acceleration:4.5g-rmseachaxis
• Velocity:8.0in/secpeakeachaxis
• Displacement:0.14inchespeakeachaxis
• Activesuppressionof3rotaryDOF
Composite Wheeled Vehicle Test Results – Case 1
Asnoted,thistestisamodifiedversionoftheprofilesdetailedinMIL-STD810gMethod514.6AnnexC[2].
Toremainwithin thedisplacement limitsof theshakers, thebreakpointsbelow15Hzonall threeprofiles
were removed. Twoseparatecaseswereconducted for thisparticular test. Case1excitedall three linear
DOF,X,Y,Z,simultaneouslyandactivelyworkedtosuppresstherotataryDOF,roll(Rx),pitch(Ry),yaw(Rz),
to anullRMS reference level of 0.70 rad/sec2 (3-DOFexcitation). Case2 controlled the linearDOF in the
samemanner,however,nowallrotaryDOFweresimultaneouslyexcited(6-DOFexcitation).Theprofilefor
therotaryDOFexcitation,inthiscase,wasdefinedtobeaflatprofilewithaRMSlevelof8.50rad/s2from15-
500Hz.It’simportanttonotethatbothcasesarefull6-DOFtestsbecausealltwelveshakersarebeingdriven
tocontrol(exciteorsuppress)rotationsaswellastranslations.
Figure5-Figure7showthelinearresponseofeachaxisandFigure8showstherotaryDOFofallthreeaxes
for Case 1. The graphs of the linear DOF plots the individual acclerometer responses in addition to the
responseoftherespectiveVirtualPointDOF.ThegraphofrotationsshowsallthreerotaryDOFoftheVirtual
Pointrelativetothenullreferencelevel.
Figure 5: Test 1, Case 1, X-Axis Response
Figure 6: Test 1, Case 1, Y-Axis Response
15.0 100 500 500µ
1.00m
10.0m
100m
800m
X-Axis Response
Hz
LogMag, g²/Hz
ControlX
Rms:3.17
AccelX1
Rms:3.22
AccelX2
Rms:3.11
AccelX3
Rms:3.25
AccelX4
Rms:3.16
15.0 100 500 1.00m
10.0m
100m
1.00
Y-Axis Response
Hz
LogMag, g²/Hz
ControlY
Rms:3.17
AccelY1
Rms:3.23
AccelY2
Rms:3.11
AccelY3
Rms:3.14
AccelY4
Rms:3.26
Figure 7: Test 1, Case 1, Z-Axis Response
Figure 8: Test 1, Case 1, Rotary DOF Response
Overall,thesystemperformedverywellinthelineardirections,withsomeminordeviationaround35Hzin
theXandYaxesoftheindividualaccelerometers.ThecontroloftherotaryDOFscannotbesuppresseddown
tothereferencenulllevelandtheybegintodivergebelow100Hz,withapeakat35Hzalso.Thisfrequency
istheshakerpreloadresonance,andthecontrollerhasdifficultysuppressingitsresponsewiththerotation
referencelevelssetsolow.Theexplanationforthisisthatthereferencenulllevelissetbelowthenoisefloor
of the instrumentation. As a result, the controller isunable to resolve the signalswell enough for control.
Case2addressesthisproblem.
Composite Wheeled Vehicle Test Results – Case 2
The control of the rotaryDOFwas altered inCase2 of theCompositeWheeledVehicleTest such that the
rotationswereexcitedtoalowlevelslightlyabovetheaccelerometernoisefloor.Thedifferencebeingthat
now thecontrollerattempts todrive the rotations rather thansuppress them to anull level. It is a subtle
differenceandcanbethoughtofasa6-DOFexcitationtestcomparedtoa3-DOFexcitationtest.
15.0 100 500 600µ
1.00m
10.0m
100m
1.00
2.00
Z-Axis Response
Hz
LogMag, g²/Hz
ControlZ
Rms:3.16
AccelZ1
Rms:3.15
AccelZ2
Rms:3.17
AccelZ3
Rms:3.16
AccelZ4
Rms:3.17
15.0 100 500 200µ
1.00m
10.0m
100m
1.00
10.0
Virtual Point Rotary DOF Response
Hz
LogMag, (rad/s²)²/Hz
Ref Rz
Rms:697m
ControlRx
Rms:2.57
ControlRy
Rms:1.42
ControlRz
Rms:10.6
Theresults for the linearDOFofCase2aregiven inFigure9 -Figure11andthe rotaryDOF inFigure12.
Exciting the rotations created a significant improvement in the overall control of the system. Now, the
controller isabletomaintaincontrolovertherotationsatthereference levelover thefullbandwidth. The
change to the rotary control also improved the responseof the system in the X andY axes at 35Hz. The
resonance at this frequency is very well controlled, and the virtual point and individual accelerometer
responsesforeachaxismatchesthereferencelevelsextremelywellovertheentiretestbandwidth.
This test provides a clear example of how important it is to properlydefine aMIMOvibration test and to
understand the capabilities of the system. Each shaker input of the Tensor 18kN has an effect on all
accelerometer outputs (per the geometric definition of a Tensor – linear mapping), resulting in a closely
coupledsystem.Ifareferencelevelissetoutsideofthesystem’slimits(highorlow),mostlikelytheresponse
ofotherDOFwilldegradeasthesystemisunabletocontroltheDOFwiththeunreasonablereference.This
test highlights how a very minor increase in one parameter can significantly improve the control of the
overallsystem.
Figure 9: Test 1, Case 2, X-Axis Response
Figure 10: Test 1, Case 2, Y-Axis Response
15.0 100 500 500µ
1.00m
10.0m
100m
800m
X-Axis Response
Hz
LogMag, g²/Hz
ControlX
Rms:3.17
AccelX1
Rms:3.20
AccelX2
Rms:3.09
AccelX3
Rms:3.26
AccelX4
Rms:3.17
15.0 100 500 1.00m
10.0m
100m
1.00
Y-Axis Response
Hz
LogMag, g²/Hz
ControlY
Rms:3.16
AccelY1
Rms:3.21
AccelY2
Rms:3.10
AccelY3
Rms:3.13
AccelY4
Rms:3.24
Figure 11: Test 1, Case 2, Z-Axis Response
Figure 12: Test 1, Case 2, Rotary DOF Response
Broadband Test Results
Thefocusofthebroadbandrandomvibrationtest,Test2,wastoexcitetheTensor18kNsystemoveritsfull
bandwidthtoshowcasethesystem’sabilitytocontrolthevibrationspectrumtohighfrequenciesusingthe
CoordinateTransformationcontrolmethod. Asnoted, this testexcitedall three linearDOFsimultaneously
andsuppressedtherotationstoanulllevel.TheprofileofeachaxiswasflatwithanRMSaccelerationlevelof
4.5g.
The improvement to the control detailed in Case 2 of the previous test was not implemented for the
broadbandtestsimplybecauseitwasnotrealizeduntilaftertheresultsofthistestwerecollected. Future
testingwiththissystemwillimplementthesesubtlechangesanditisexpectedthatthesameimprovements
canbegainedforthebroadbandtest.
SimilartoTest1,theCoordinateTransformationmethodwasusedforcontrollingthemappedVirtualPoint
tothereferenceprofile.Forrigidbodymotionitisexpectedthattheindividualaccelerometerresponseswill
closelymatchthevirtualpointresponse. However,whenthesystemhitsaresonantfrequencythismethod
acts to control the virtual point to be the average of the accelerometer responses, in bothmagnitude and
15.0 100 500 600µ
1.00m
10.0m
100m
1.00
2.00
Z-Axis Response
Hz
LogMag, g²/Hz
ControlZ
Rms:3.15
AccelZ1
Rms:3.16
AccelZ2
Rms:3.21
AccelZ3
Rms:3.15
AccelZ4
Rms:3.13
15.0 100 500 30.0m
100m
600m
Virtual Point Rotary DOF Response
Hz
LogMag, (rad/s²)²/Hz
Ref Rz
Rms:8.53
ControlRx
Rms:8.55
ControlRy
Rms:8.53
ControlRz
Rms:8.49
phase. Thismethodology issimilar to thesingleDOFcasewhenaveragingofaccelerometermagnitudes is
usedtoimprovecontrolofavibrationmode.Approachingthecontrolinthismannerislogicalbecauseitis
extremelydifficultandcostly todevelopa largestructure that isresonant free throughthe fullbandwidth,
especiallyforhigh-frequencytests.Although,itshouldbenoted,thatinthedesignoftheTensor18kNevery
attemptwasmadetopushthefirstmodeofthetableasfaroutinfrequencyaspossible.
Figure13-Figure15plottheresponseofthevirtualpoint’slinearDOFforeachaxis.Theseplotsshowthat
thecontrollerisabletomaintainexcellentcontroloftheVirtualPointacrossthefullbandwidth. Figure16
givestheVirtualPoint’sresponseforalloftherotaryDOF.Note,again,thatthecontrollerisunabletobring
therotationsdowntothereferencenulllevelbecausetheprofileisbelowthenoisefloor.ImplementingCase
2ofTest1shouldimprovethisresponse.
Figure 13: Test 2, Virtual Point X-Axis Response
Figure 14: Test 2, Virtual Point Y-Axis Response
Figure 15: Test 2, Virtual Point Z-Axis Response
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
X-Axis Virtual Point DOF
Hz
LogMag, g²/Hz
ControlX
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
Y-Axis Virtual Point DOF
Hz
LogMag, g²/Hz
ControlY
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
Z-Axis Virtual Point DOF
Hz
LogMag, g²/Hz
ControlZ
Figure 16: Test 2, Virtual Point Rotary DOF Response
Figure17-Figure19plottheindividualaccelerometerresponsesforeachaxis.Theseplotsshownicecontrol
uptoaround800Hz. This indicatesthatthesystemisresonantfreetothispointsincetheaccelerometers
closely match the Virtual Point. Above this frequency, three resonances show up in the accelerometer
responses. The first andsecondmodesof the systemoccurat810Hzand930Hz, respectively. The first
modeshapeisthetypicaltorsionmodeofasquareplatewherethecornersofeachsidemoveoutphase.The
secondmodeshapeisanin-planeshearmodewherethesquarestructuredeformstoa‘diamond’shape.This
isduetothevibrationtablehavingsignificantdepthandnolongerbehavingasathinplate.
Themostdifficultmodetocontrol isat1,620Hz,whichisactuallythesixthsystemmode. Themodeisan
out-of-planemodesimilartothefirstmode,butnowthecenterofagivenedgemovesoutofphasewiththe
centerofeachadjacentedge. Thismodeissometimesreferredtoasa ‘saddle’or ‘potato-chip’modeshape
and it is the firstmodewhere there is not a shaker acting against the high response regions of themode
shape,resultinginthecontrollerhavingthemostdifficultyminimizingitsresponse.
The third, fourth, and fifthmodes are all in-planemodes andwere found by a finite elementmodel of the
system.Thesemodesdonotcauseanyoutoftoleranceresponseoftheindividualaccelerometers.Theyare
easily controlled by the system and/or do not affect the top surface response because they are in-plane
‘breathing’modeshapes.
Figure 17: Test 2, Control Points X-Axis Response
5.00 10.0 100 1.00k 2.00k200µ
1.00m
10.0m
100m
1.00
Virtual Point Rotary DOF
Hz
LogMag, (rad/s²)²/Hz
ControlRx
ControlRy
ControlRz
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
100m
300m
X-Axis Accelerometers
Hz
LogMag, g²/Hz
AccelX1
AccelX2
AccelX3
AccelX4
Figure 18: Test 2, Control Points Y-Axis Response
Figure 19: Test 2, Control Points Z-Axis Response
Overall,thistestproducedexcellentaveragecontroloftheaccelerometercontrolpointsasshowninFigure
13-Figure15. Therearedeviationsfromthereferenceleveloftheindividualaccelerometersatthreehigh
frequencyvibrationmodes,butthis,toacertainextent,istobeexpectedforthissizeofastructure.Thereare
techniquesthatcanbeappliedtothecontrolsystemtoreducetheresponseatthesefrequencies.However,
due to the time thatwasavailablewith thissystemtheywerenot implemented. Planshavebeenmadeto
continuetestingwiththeTensor18kNasdetailedinthefollowingsection.
Future Testing Plans
TheTensor18kNisanewsystemcapableofperformingadvancedhigh-frequencyvibrationtesting.Thiswas
demonstratedintheresults.However,duetotheoverconstraineddesign,itisinherentlyacomplexsystem
tocontrolandthere isstillmuchto learnregardingthecontrolnuancesthatcanbeappliedtoadvancethe
system performance. Further testing is planned to investigate several subtle changes as well as more
advancedtechniquesusingtheCoordinateTransformationmethod.Afewoftheseare:
• Asymmetric accelerometer locations – All testing to date was done with symmetric locations
measuring the samepoint on the table in each quadrant. Testingwill be done to seewhat effect
asymmetriccontrol locationshaveonthecontrol. Thegoal isthatmeasuringdifferent locations in
eachquadrantwillprovideabetteraveragingscheme.
• Define additional Virtual Point DOFs –TheresultspresentedwereforthesixrigidbodyDOFofthe
VirtualPointintheCoordinateTransformation.TheoverconstraineddesignoftheTensor18kNcan
beexploitedbydefiningvarious flexiblebodymodeshapes tobeadditional controlledDOFof the
VirtualPoint.Thegoalisthatthesystemcouldcontroloutmodeshapesofthetable.Thistestingwill
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
100m
Y-Axis Accelerometers
Hz
LogMag, g²/Hz
AccelY1
AccelY2
AccelY3
AccelY4
5.00 10.0 100 1.00k 2.00k2.00m
10.0m
Z-Axis Accelerometers
Hz
LogMag, g²/Hz
AccelZ1
AccelZ2
AccelZ3
AccelZ4
beginbyaddingonemodeshapeatatime.Theconcernisthatduetothestiffdesignofthevibration
tableitmaytakeexcessiveforcetoaccomplishthiscontrol.
• Apply narrow band notching – This technique could be applied to decrease the response of the
higherfrequencymodesbynotchingthereferenceprofilesandwillbeappliedonly if theprevious
twotechniquesareunsuccessful.
Thistestingwillbeconductedonthefirstsysteminstalled,whichislocatedattheLifeCycleEnvironmental
EngineeringBranchof theNavalAirWarfareCenterWeaponsDivision inChinaLake,CA. The intent is to
publishtheresultsinafuturepaper.
Conclusion
The Tensor 18kN is the newest multi-axis vibration testing system available from Team Corporation. It
expandsanovelconceptofusingtwelveelectro-dynamicshakerstoexciteall6-DOFofavibrationtableto
2,000Hz.TeamCorporationfirstappliedthisdesigninaproofofconceptsystemreferredtoastheTensor
900.TheTensor18kNnowbringsthisproofofconcepttoasizemorepracticalfortypicalvibrationtesting
applications.
The results presented show that this system produces excellent control of the vibration table using the
CoordinateTransformationcontrolmethodology.Varioussubtletieswerediscussedregardingthecontrolof
thesystem,withsuggestionsforpossiblewaystoincreaseperformance. Thisresearchwillcontinueasthe
stateoftheartforvibrationtestingcontinuallyadvances.
References
1. Tensor.(n.d.).RetrievedFebruary13,2013,fromWikipedia,TheFreeEncyclopedia:
http://en.wikipedia.org/wiki/Tensor
2. MIL-STD810gDepartmentofDefenseTestMethodStandard,Method514.6Vibration,AnnexC.(31
October2008).514.6C-11.