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California Polytechnic State University ME404 Research Project Winter 2008 Axial and Radial Stiness of a Diaphragm Lente Florian Rehsöft Stefan Author: Supervisor: Prof. Peter J. Schuster March 17, 2008 Contents 1 Project Report 1.1 Abstract . . . . . . . . . . . . 1.2 Introduction . . . . . . . . . . 1.3 Objectives . . . . . . . . . . . 1.3.1 Main objective . . . . 1.3.2 Additional objectives . 1.4 Approximate Solution . . . . 1.5 Model Development . . . . . 1.6 Mesh Development . . .
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  CaliforniaPolytechnicStateUniversity  ME404ResearchProject  Winter2008  AxialandRadialStinessofaDiaphragm      Author:  Stefan  Lente  Florian  Rehsöft  Supervisor:  Prof.PeterJ.  Schuster  March17,2008   Contents   1ProjectReport3  1.1Abstract........................................3 1.2Introduction......................................3 1.3Objectives.......................................4 1.3.1Mainobjective................................4 1.3.2Additionalobjectives.............................4 1.4ApproximateSolution................................4 1.5ModelDevelopment.................................5 1.6MeshDevelopment..................................6 1.7Analyses........................................8 1.8Post-Processing....................................10 1.8.1MeshConvergence..............................10 1.8.2ComparisonofResults............................12 1.9Results.........................................12 1.10Discussion.......................................13 1.11Conclusions......................................14 1.12References.......................................14 1.13Acknowledgment...................................14 1.14Contact........................................15  2ConvergencePlots16  2.1AxialStiness.....................................16 2.2RadialStiness....................................17  3HandCalculations19  3.1AxialStiness.....................................19 3.1.1Approach...................................19 3.1.2Reference...................................19 3.1.3Analysis....................................20 3.2RadialStiness....................................20 3.2.1Approach...................................20 3.2.2Reference...................................21 3.2.3Analysis....................................22 2   1ProjectReport   1.1Abstract  Thisdocumentdescribesaproject,conductedbytwoexchangestudentsfromtheMunich UniversityofAppliedSciences.TheprojectinvolvestheuseofFEAcodesoftware.Itisgoing tobepartofthelearningexperienceoftheME404-AppliedFiniteElementAnalysisclass. TheresearchtopicisgoingtobeapartofaCNCLatheSpindleproducedbytheSpinner MachineToolsCompanyandusedintheTDSeriesTurningCenters.Theprojectisdivided intotwomainparts.Ontheonehandananalysisofamembranewasperformedtodetermine stinessofthatmembraneintheaxialandradialdirections.Resultsofasimilarpartwere available.Thisreferencemodelwasanalyzedrst,tobeabletocompareandvalidatethe resultsofthenewmembrane.Ontheotherhandastudyoftheinuenceofdierentelement typeswasrealizedaswellasthebenetsofsimplifyingoraddingcomplexitytotheanalysis. Theelementtypewhichresultsintoanaccuratesolutionwithalowcomputationaltimeis sought.Withtheknowledgeofthepossiblemodelvariationsandtheelementtypetouse,a recommendationforfutureanalysesonsimilarpartsisgiven.  1.2Introduction  Forstaticdeterminatebearingofthespindletubeacombinationoftwospindleballbearing pairsareused,onexed,theotheroneoating.Toaddtheabilitytomoveaxiallytotherear ballbearingamembranewasusedtomountittothestructure. Duetotheriseintemperatureofthespindleduringoperation,adierenceinlengthbetween thehousingandthespindlerotoroccurs.Thiselongationiscompensatedbytheelasticaxial deformationofthediaphragm(about0.1mmforahotspindle).Thiscauses,dependingon theaxialstinessofthediaphragm,axialloadsontheballbearings,whichcouldinuence theexpectedlifespan,iftheloadistoohigh.Thismeansthediaphragmpreferablyshould beaxiallyveryexible.Ontheotherside,thediaphragmshouldhaveahighradialstiness, toensuresmalldeectionofthespindleaxisduetoradialloads. Twopartswillbeanalyzed,andinthisreportreferredtoasthe Reference and Analysis  part.Thereferencepart(TD-001-008)isadiaphragmforwhichtheresultsoftwoFEAstudies arealreadyavailable,andwillbeusedforcomparison.Theanalysispart(TD-052-010)onthe otherhandisasimilardiaphragmwhichwillbetestedwithasetupbasedontheexperiences gainedintheanalysisofthereferencepart. 3   1ProjectReport  1.3Objectives  1.3.1Mainobjective  Themainobjectiveofthisanalysisistocalculatetheaxialandradialstinessofthepreviously mentioneddiaphragm.Inordertogetagoodprediction,wearegoingtoconductdierent analysesduringwhichwevarymeshrenement,elementtype,boundaryandloadconditions, aswellasloadapplication.  1.3.2Additionalobjectives  Apartfromgettingagoodpredictionofthestinessintheaxialandradialdirections,and ofthestressinthediaphragmforagivenaxialdeection,wewouldliketoextendthescope oftheprojecttowardsaresearchoftheinuenceofthevariationsofsetupoptionsonthe result. Becauseofthecomplexgeometry,especiallythehugedierencesofthewallthicknesses,ne mesheswillbeneeded.Thereforetheinuenceofthenenessofthemeshisgoingtobe analyzed.Furthermoredierentkindsofelementswillbeusedtoseeiftherearechanges andwhatkindofchangesthereareinthesolutions.Shellelementsandthetwodierent continuumelementshexahedral(bricks)andtetrahedralwillbetested. Moreoverdierentkindsofclampingofthepartattheouteredgeshouldbetested.By meansofasimplepossibilityofclampinganaccuratesolutionshouldbefoundbyvarying theparametersasdescribedabove.Afterwardsamorecomplicatedboltedattachmentwitha contactbetweenthepilotdiameterandaxedringshouldberealized.  1.4ApproximateSolution  Thepredictionsofthehand-calculationswerecrosscheckedwiththeresultsofthebothavail- ableFEAanalysesforthereferencemodel.Thiscomparisonyieldedthefollowingresults. Comparetodatafromreferenceanalysesinaxialdirection:  ã HandCalculation:  k = 0 . 924 · 10 6 N m ã ANSYS:  k = F u = 6000 N  0 . 96186 · 10 − 3 m = 6 . 24 · 10 6 N m ã COSMOSWorks:  k = F u = 83 N  0 . 182429 · 10 − 3 m = 0 . 455 · 10 6 N m GiventheassumptionswemadeandtherangeofbothFEAresults,thepredictionbythe hand-calculationisreasonableandgivesagoodfeelingoftheexpectedrange. Comparetodatafromreferenceanalysesinradialdirection:  ã HandCalculation:  k = 1 . 21 · 10 8 N m ã ANSYS:  k = F u = 348 N  0 . 379 · 10 − 6 m = 1 . 01 · 10 9 N m ã COSMOSWorks:  k = F u = 1000 N  0 . 598891 · 10 − 6 m = 1 . 67 · 10 9 N m 4 
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