Electromechanical Analysis
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Coupled-Field Analysis Guide Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates Page: 1 2.23. Example: Electromechanical Analysis In this example, you will perform a direct coupled-field analysis of a MEMS structure. Figure 2.28: Electrostatic Parallel Plate Drive Connected to a Silicon Beam Beam Properties Parallel Plate Drive Properties L = 150 µm A p = 100 ( µm) 2 b = 4 µm gap = 1 µm h = 2 µm ε r = 8.854e-6 pF/ µm E = 1.69e5 µN/( µm) 2 ρ = 2.332e-15 kg/( µm) 3 2.23.1. Problem Description A MEMS structure consists of an electrostatic parallel-plate drive connected to a silico structure. The beam is pinned at both ends. The parallel-plate drive has a stationary and a moving component attached to the beam. Perform the following simulations:
description
Example: Electromechanical Analysis
Transcript of Electromechanical Analysis
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Coupled-FieldAnalysisGuide
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2.23. Example: Electromechanical Analysis
Inthisexample,youwillperformadirectcoupled-fieldanalysisofaMEMSstructure.
Figure 2.28: Electrostatic Parallel Plate Drive Connected to a Silicon Beam
Beam Properties Parallel Plate Drive Properties
L=150m Ap=100(m)2
b=4m gap=1m
h=2m r=8.854e-6pF/m
E=1.69e5N/(m)2
=2.332e-15kg/(m)3
2.23.1. Problem Description
AMEMSstructureconsistsofanelectrostaticparallel-platedriveconnectedtoasiliconbeamstructure.Thebeamispinnedatbothends.Theparallel-platedrivehasastationarycomponent,andamovingcomponentattachedtothebeam.Performthefollowingsimulations:
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1. Apply150Voltstothecombdriveandcomputethedisplacementofthebeam2. ForaDCvoltageof150Volts,computethefirstthreeeigenfrequenciesofthebeam.3. ForaDCbiasvoltageof150Volts,andaverticalforceof0.1Nappliedatthemidspan
ofthebeam,computethebeamdisplacementoverafrequencyrangeof300kHzto400kHz.
TheparallelplatecapacitanceisgivenbythefunctionCo/xwhereCoisequaltothefree-spacepermittivitymultipliedbytheparallelplatearea.Theinitialplateseparationis1m.TheModalandHarmonicanalysismustconsidertheeffectsoftheDCvoltage"preload".TheproblemissetuptoperformaPrestressModalandaPrestressHarmonicanalysisutilizingtheStaticanalysisresults.Aconsistentsetofunitsareused(MKSV).SincethevoltageacrossTRANS126iscompletelyspecified,thesymmetricmatrixoption(KEYOPT(4)=1)issettoallowforuseofsymmetricsolvers.
2.23.2. Expected Results
Theexpectedanalyticresultsforthisexampleproblemareasfollows.
2.23.2.1. Static Analysis
UY(node2)=-0.11076e-2m
2.23.2.2. Modal Analysis
f1=351kHz
f2=1380kHz
f3=3095kHz
2.23.2.3. Harmonic Analysis
Frequency@maximumdisplacement=351.6kHz
Maximumdisplacement=22m(undamped)
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2.23.2.4. Displays
Figure2.29:ElementsofMEMSExampleProblemshowsthetransducerandbeamfiniteelements.
Figure2.30:LowestEigenvalueModeShapeforMEMSExampleProblemshowsthemodeshapeatthelowesteigenvalue.
Figure2.31:MidSpanBeamDeflectionforMEMSExampleProblemshowstheharmonicresponseofthemidspanbeamdeflection.
Figure 2.29: Elements of MEMS Example Problem
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Figure 2.30: Lowest Eigenvalue Mode Shape for MEMS Example Problem
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Figure 2.31: Mid Span Beam Deflection for MEMS Example Problem
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2.23.3. Building and Solving the Model
Thecommandtextbelowdemonstratestheprobleminput.Alltextprefacedwithanexclamationpoint(!)isacomment.
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/batch,list/show,file/prep7/title,Static,Modal,HarmonicresponseofaMEMSstructure/comL=150!beamlength(micrometers)b=4!beamwidthh=2!beamheightI=b*h**3/12!beammomentofinertiaE=169e3!modulus(microNewtons/micron**2)dens=2332e-18!density(kg/micron**3)per0=8.854e-6!free-spacepermittivity(pF/micron)plateA=100!capacitorplatearea(micron**2)vlt=150!Appliedcapacitorplatevoltagegapi=1!initialgap(microns)et,1,3!2-Dbeamelementr,1,b*h,I,h!beampropertiesmp,ex,1,Emp,dens,1,denset,2,126,,,,1!Transducerelement,UX-VOLTdof,symmetricc0=per0*plateA!C0/xconstantforCapacitanceequationr,2,0,0,gapi!Initialgapdistancermore,c0!RealconstantC0n,1,-10n,2,0n,22,Lfilltype,2real,2e,1,2!Transducerelement(arbitrarylength)type,1real,1e,2,3!Beamelements*repeat,20,1,1nsel,s,loc,x,-10nsel,a,loc,x,Ld,all,ux,0,,,,uy!PinbeamandTRANS126elementnsel,s,loc,x,0d,all,uy,0!AllowonlyUXmotiond,2,volt,vlt!Applyvoltageacrosscapacitorplatensel,s,loc,x,-10d,all,volt,0!Groundotherendofcapacitorplatensel,allfini/soluantyp,static!Staticanalysispstres,on!turnonprestresseffectssolvefini/post1prnsol,dof!printdisplacementsandvoltageprrsol!Printreactionforcesfini/soluantyp,modal!Modalanalysismodopt,lanb,3!BlockLanczos;extract3modesmxpand!Expand3modespstres,on!Includeprestresseffectssolvefinish/post1set,1,1!Retrievelowesteigenfrequencyresultspldisp,1!Plotmodeshapeforlowesteigenfrequency/soluantyp,harm!Harmonicanalysishropt,full!Fullharmonicanalysisoptionpstres,on!Includeprestresseffectsharfrq,300000,400000!Frequencyrange(Hz.)nsubs,500!Numberofsamplingpoints(substeps)outres,all,all!Saveallsubstepsddele,2,volt!deleteappliedDCvoltagensel,s,loc,x,L/2!Selectnodeatbeammidspanf,all,fy,.1!Applyverticalforce(.1N)nsel,allsolvefinish/post26nsol,2,12,u,y,!selectnodewithappliedforceadd,4,1,,,,,,1/1000!changetoKilohertzplcplx,0!magnitude/axlab,x,Frequency(Khz.)!setgraphicsoptions/axlab,y,Displacement/xrange,325,375/yrange,0,20/gropt,divx,10/gthk,axis,1.5/grop,ltype,0/dev,text,1,400xvar,4plvar,2!Plotdisplacementvs.frequencyprvar,2!Printdisplacementvs/.frequencyfinish
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