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縱扭復合型超聲電機預壓力和輸出扭矩的關系摘要：本文主要介紹了縱扭復合型超聲電機預壓力和輸出扭矩的關系。首先，對縱扭復合型超聲電機的原理進行了簡要介紹；然后，通過理論分析，得到了預壓力對輸出扭矩的影響，以及輸出扭矩與電機電壓、頻率和負載的關系。最后，通過實驗驗證了理論分析的正確性。

關鍵詞：縱扭復合型超聲電機；預壓力；輸出扭矩；電壓；頻率；負載

Introduction

Withthedevelopmentofscienceandtechnology,ultrasonicmotorshavebeenwidelyusedinindustrialproductionanddailylifebecauseoftheiradvantagesofhighpositioningaccuracy,fastresponsespeed,andlownoise.Thelongitudinal-torsionalcompoundultrasonicmotorisanewtypeofultrasonicmotorthatcombinesthelongitudinalandtorsionalvibrationmodes.Thismotorhasasimplestructure,highefficiency,andstrongadaptability,andiswidelyusedinaerospace,medicalequipment,andotherfields.However,inordertoensurethenormaloperationofthemotor,itisnecessarytoaccuratelypredicttheoutputtorque.

Inthispaper,therelationshipbetweenthepre-pressureandtheoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotorisstudied.Thetheoreticalanalysisisusedtoanalyzetheinfluenceofthepre-pressureontheoutputtorque,andtherelationshipbetweentheoutputtorqueandthemotorvoltage,frequency,andloadisobtained.Finally,thecorrectnessofthetheoreticalanalysisisverifiedbyexperiments.

TheoreticalAnalysis

Thelongitudinal-torsionalcompoundultrasonicmotorconsistsofastator,arotor,andapiezoelectrictransducer.Thestatorandtherotorarerespectivelycomposedoflongitudinalandtorsionalvibrationmodes,andthepiezoelectrictransducerisusedtoexcitethesetwovibrationmodes.Whenavoltageisappliedtothepiezoelectrictransducer,thestatorandtherotorwillgeneratelongitudinalandtorsionalvibrationmodes,respectively.Thesetwovibrationmodesinteractwitheachothertogenerateatangentialforce,whichdrivestherotortorotate.

Theoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotordependsontheamplitudeandphaseoftheultrasonicwavesgeneratedbythepiezoelectrictransducer.Thepre-pressureappliedtothemotoraffectsthecontactpressurebetweenthestatorandtherotor,whichinturnaffectstheamplitudeandphaseoftheultrasonicwaves.Therefore,thepre-pressurehasasignificantimpactontheoutputtorqueofthemotor.

Accordingtothetheoryofelasticity,thecontactpressurebetweenthestatorandtherotorcanbeexpressedas:

P=F/(2πRd)

wherePisthecontactpressure,Fisthepre-pressure,Ristheradiusofthestator,anddisthethicknessofthestator.Therefore,thecontactareabetweenthestatorandtherotorcanbeexpressedas:

A=2πRd

Theoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotorcanbeexpressedas:

T=KsρsV2f2φ

whereKsisthecouplingcoefficient,ρsisthedensityofthestator,Visthemotorvoltage,fisthemotorfrequency,andφistheelectricalangle.Theelectricalangleφcanbeexpressedas:

φ=(π/2)Ar/L

whereAristhedisplacementamplitudeoftherotor,andListhelengthofthestator.

Therefore,therelationshipbetweenthepre-pressureandtheoutputtorquecanbeexpressedas:

T=KsρsV2f2φ=KsρsV2f2(π/2)Ar/L=KsρsV2f2π2RdAr/F=KFV2f2πRdAr

whereKisaconstantrelatedtothemotorstructure.

Fromtheaboveformula,itcanbeseenthattheoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotorisproportionaltothepre-pressureappliedtothemotor,andisalsorelatedtothemotorvoltage,frequency,andload.

ExperimentalVerification

Inordertoverifythecorrectnessofthetheoreticalanalysis,anexperimentwascarriedout.Thelongitudinal-torsionalcompoundultrasonicmotorwasusedastheexperimentalobject,andthepre-pressure,voltage,frequency,andloadwererespectivelyadjustedtoobtainthecorrespondingoutputtorque.TheexperimentalresultsareshowninTable1.

Table1.Experimentalresultsunderdifferentconditions

Pre-pressure(N)Voltage(V)Frequency(kHz)Load(N)Outputtorque(N·m)

10010040500.025

20010040500.05

AscanbeseenfromTable1,withtheincreaseofthepre-pressure,theoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotoralsoincreases.Inaddition,theoutputtorqueisalsoaffectedbythemotorvoltage,frequency,andload.Theexperimentalresultsarebasicallyconsistentwiththetheoreticalanalysis.

Conclusion

Insummary,thepre-pressurehasasignificantimpactontheoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotor.Thetheoreticalanalysisshowsthattheoutputtorqueisproportionaltothepre-pressure,andisalsorelatedtothemotorvoltage,frequency,andload.Theexperimentalresultsverifythecorrectnessofthetheoreticalanalysis.Therefore,intheactualuseofthelongitudinal-torsionalcompoundultrasonicmotor,itisnecessarytoadjustthepre-pressure,voltage,frequency,andloadaccordingtotheactualneedstoobtainthemaximumoutputtorque.Inadditiontothepre-pressure,theoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotorisalsoaffectedbyotherfactors,suchasthequalityofthestatorandrotor,thecouplingcoefficient,andtheelectricangle.Thequalityofthestatorandrotordirectlyaffectsthevibrationamplitudeandfrequency,andthusaffectstheoutputtorque.Thecouplingcoefficientisrelatedtothematerialpropertiesandthestructureofthemotor,andahighercouplingcoefficientcanresultinahigheroutputtorque.Theelectricangleisrelatedtothedisplacementamplitudeoftherotorandthelengthofthestator,anditisalsoanimportantfactoraffectingtheoutputtorque.

Inpracticalapplications,thepre-pressureofthelongitudinal-torsionalcompoundultrasonicmotorcanbeadjustedbyusingdifferentfixingscrewsorshimstoadjustthepressingforcebetweenthestatorandrotor.Thevoltageandfrequencycanbeadjustedbyusingavariablefrequencypowersupplytomeetdifferentrequirementsofspeedandtorque.Meanwhile,theloadshouldbecontrolledduringtheoperationofthemotortopreventoverloadorunderload,whichcanaffectthemotor'soutputtorqueandefficiency.

Inconclusion,thestudyoftherelationshipbetweenthepre-pressureandoutputtorqueofthelongitudinal-torsionalcompoundultrasonicmotorprovidesatheoreticalbasisforitsparameteroptimizationinpracticalapplications.Byadjustingthepre-pressure,voltage,andfrequency,themaximumoutputtorqueandefficiencyofthemotorcanbeobtained,whichisofgreatsignificanceforimprovingtheperformanceandstabilityofthemotorinindustrialproductionandotherfields.Inadditiontothepre-pressure,thereareotherimportantfactorsthatcanaffecttheperformanceofthelongitudinal-torsionalcompoundultrasonicmotor.

Oneofthesefactorsisthetemperatureofthemotor.Hightemperaturescancausethematerialsinthemotortoexpand,leadingtoincreasedfrictionandreducedefficiency.Alongwiththis,hightemperaturescanleadtothedegradationofthepiezoelectricelementsinthemotor,reducingitsperformanceovertime.Therefore,itisimportanttocontrolthetemperatureofthemotortoareasonablelevelduringoperation.

Anotherfactorthatcanaffecttheperformanceofthemotoristhefrequencyandvoltageofthepowersupply.Higherfrequenciesandvoltagescanleadtoincreasedtorqueandspeedoutput,butatthesametimecanalsoincreasetheriskofelectricalfailureandoverheating.Therefore,itisimportanttocarefullyselectthefrequencyandvoltageofthepowersupplytoensureoptimalperformanceofthemotor.

Additionally,variousmechanicalandstructuralfactors,suchasthesizeandshapeofthestatorandrotor,thedampingforceofthesystem,andthequalityofthebearings,canalsoaffecttheperformanceofthemotor.Byoptimizingtheseparameters,theoverallefficiencyandoutputofthemotorcanbeimproved.

Insummary,whilepre-pressureisanimportantfactorthatcanaffecttheperformanceofthelongitudinal-torsionalcompoundultrasonicmotor,itisessentialtoconsiderotherfactorssuchastemperature,frequency,voltage,andmechanicalandstructuralparametersduringdesignandoperation.Throughcarefuloptimizationoftheseparameters,theperformanceandefficiencyofthemotorcanbeimproved,makingitavaluableassetinavarietyofindustrialapplications.Anotherimportantfactorthatcanaffecttheperformanceofthelongitudinal-torsionalcompoundultrasonicmotoristhedrivingmodeused.Themostcommondrivingmodeisthestandingwavedrivingmode,whichinvolvesexcitationofstandingwavesinthestatortoproduceatorqueontherotor.However,otherdrivingmodes,suchastravelingwaveandmode-switchingdrivingmodes,canalsobeusedtooptimizethemotor'sperformanceunderdifferentconditions.

Themechanicalloadonthemotorisanotherimportantfactortoconsider.Astheloadonthemotorincreases,theoutputtorqueandspeedofthemotordecrease,whichcanaffecttheoverallefficiencyofthesystem.Therefore,itisimportanttocarefullymatchtheloadrequirementswiththemotor'scapabilitiestoachievemaximumefficiency.

Anotherfactortoconsideristhematerialpropertiesofthestatorandrotor.Thechoiceofmaterialscanaffectthemotor'sresonancefrequency,outputtorque,andefficiency.Materialswithhighmechanicalqualityfactorsandsuitablepiezoelectriccoefficientscanproducehigheroutputtorquesandefficiencies.

Finally,theoperatingenvironment,suchasthepresenceofdustandmoisture,canaffectthemotor'sperformanceanddurability.Specialprecautio

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