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FINITEELEMENTANALYSISOFAUTOMOBILECRASHSENSORSFORAIRBAGSYSTEMSABSTRACTAutomobilespringbiascrashsensordesigntimecanbesignificantlyreducedbyusingfiniteelementanalysisasapredictiveengineeringtool.Thesensorsconsistofaballandspringscasedinaplastichousing.Twoimportantfactorsinthedesignofcrashsensorsaretheforce-displacementresponseofthesensorandstressesinthesensorsprings.Inthepast,sensorsweredesignedbybuildingandtestingprototypehardwareuntiltheforce-displacementrequirementsweremet.Prototypespringsneedtobedesignedwellbelowtheelasticlimitofthematerial.Usingfiniteelementanalysis,sensorscanbedesignedtomeetforcedisplacementrequirementswithacceptablestresslevels.Theanalysisprocedurediscussedinthispaperhasdemonstratedtheabilitytoeliminatemonthsofprototypingeffort.MSC/ABAQUShasbeenusedtoanalyzeanddesignairbagcrashsensors.Theanalysiswasgeometricallynonlinearduetothelargedeflectionsofthespringsandthecontactbetweentheballandsprings.Bezier3-Drigidsurfaceelementsalongwithrigidsurfaceinterface(IRS)elementswereusedtomodelball-to-springcontact.Slidelineelementswereusedwithparallelslidelineinterface(ISL)elementsforspring-to-springcontact.Finiteelementanalysisresultsfortheforce-displacementresponseofthesensorwereinexcellentagreementwithexperimentalresults.INTRODUCTIONAnimportantcomponentofanautomotiveairbagsystemisthecrashsensor.Varioustypesofcrashsensorsareusedinairbagsystemsincludingmechanical,electro-mechanical,andelectronicsensors.Anelectro-mechanicalsensor(seeFigure1)consistingofaballandtwospringscasedinaplastichousingisdiscussedinthispaper.Whenthesensorexperiencesaseverecrashpulse,theballpushestwospringsintocontactcompletingtheelectriccircuitallowingtheairbagtofire.Theforce-displacementresponseofthetwospringsiscriticalindesigningthesensortomeetvariousaccelerationinputrequirements.Stressesinthesensorspringsmustbekeptbelowtheyieldstrengthofthespringmaterialtopreventplasticdeformationinthesprings.Finiteelementanalysiscanbeusedasapredictiveengineeringtooltooptimizethespringsforthedesiredforce-displacementresponsewhilekeepingstressesinthespringsatacceptablelevels.Inthepast,sensorsweredesignedbybuildingandtestingprototypehardwareuntiltheforcedisplacementrequirementsweremet.Usingfiniteelementanalysis,thenumberofprototypesbuiltandtestedcanbesignificantlyreduced,ideallytoone,whichsubstantiallyreducesthetimerequiredtodesignasensor.Theanalysisprocedurediscussedinthispaperhasdemonstratedtheabilitytoeliminatemonthsofprototypingeffort.MSC/ABAQUS[1]hasbeenusedtoanalyzeanddesignairbagcrashsensors.Theanalysiswasgeometricallynonlinearduetothelargedeflectionsofthespringsandthecontactbetweentheballandsprings.Variouscontactelementswereusedinthisanalysisincludingrigidsurfaceinterface(IRS)elements,Bezier3-Drigidsurfaceelements,parallelslidelineinterface(ISL)elements,andslidelineelements.Thefiniteelementanalysisresultswereinexcellentagreementwithexperimentalresultsforvariouselectro-mechanicalsensorsstudiedinthispaper.PROBLEMDEFINITIONThekeycomponentsoftheelectro-mechanicalsensoranalyzedaretwothinmetallicsprings(referredtoasspring1andspring2)whicharecantileveredfromarigidplastichousingandasolidmetallicballasshowninFigure1.Theplastichousingcontainsahollowtubeclosedatoneendwhichguidestheballinthedesireddirection.Theballisheldinplacebyspring1attheopenendofthetube.Whenthesensorisassembled,spring1isinitiallydisplacedbytheballwhichcreatesapreloadonspring1.Theballisabletotravelinonedirectiononlyinthissensorandthisdirectionwillbereferredtoasthex-direction(seetheglobalcoordinatesystemshowninFigure2)inthispaper.Onceenoughaccelerationinthex-directionisappliedtoovercomethepreloadonspring1,theballdisplacesthespring.Astheaccelerationappliedcontinuestoincrease,spring1isdisplaceduntilitisincontactwithspring2.OnceFigure1.Electro-mechanicalautomobilecrashsensor.contactismadebetweenspring1andspring2,anelectriccircuitiscompletedallowingthesensortoperformitsfunctionwithintheairbagsystem.FINITEELEMENTANALYSISMETHODOLOGYWhencreatingafiniteelementrepresentationofthesensor,thefollowingsimplificationscanbemade.Thetwospringscanbefullyrestrainedattheirbasesimplyingaperfectlyrigidplastichousing.Thisisagoodassumptionwhencomparingtheflexibilityofthethinspringstothestiffplastichousing.Theballcanberepresentedbyarigidsurfacesinceittooisverystiffascomparedtothesprings.Ratherthanmodelingthecontactbetweentheplastichousingandtheball,allrotationsandtranslationsarefullyrestrainedexceptforthexdirectionontherigidsurfacerepresentingtheball.TheserestraintsimplythatthehousingFigure2.Electro-mechanicalsensorfiniteelementmesh.willhavenosignificantdeformationduetocontactwiththeball.Theserestraintsalsoignoreanygapsduetotolerancesbetweentheballandthehousing.Theeffectoffrictionbetweentheballandplasticisnegligibleinthisanalysis.Thesensorcanbeanalyzedbyapplyinganenforceddisplacementinthex-directiontotherigidsurfacerepresentingtheballtosimulatethefulldisplacementoftheball.Contactbetweentheballandspringsismodeledwithvariouscontactelementsasdiscussedinthefollowingsection.Anonlinearstaticanalysisissufficien