液压泵外文报告加翻译Word格式.docx

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Experimentsforderivedfactorswithapplicationtohydraulicgearpumps

C.J.Sexton,S.M。

LewisandC。

P.Please

UniversityofSouthampton，UK

［ReceivedJune1999.RevisedOctober2000］

Summary.Forexperimentsonmechanicalproductscomposedofseveralcomponents,suchasahydraulicgearpump,conventionalmethodsofdesigningandimplementingfactorialexperimentscanbeimpracticalbecauseoftheprohibitivecostsofobtainingcertaincomponentswithfactorssettoprespecifiedvalues.Afurtherdifficultyisthatoftensomeofthefactorsthatarebelievedtoinfluencetheproduct’sperformancearenotfeaturesofasinglecomponentbutarederivedasfunctionsofthedimensionsofseveralcomponentsarisingfromtheproduct’sassembly.Experi-mentsareproposedwhichuseasampleofmeasuredcomponentstoexploretheinfluenceofsuchderivedfactors.Analgorithmicmethodforobtainingefficientdesignsispresentedandappliedtofindingplansforstudiesonthegearpump。

Anexperimentonthepumpisdescribedwhichinvolvedbothconventionalandderivedfactors。

Thisexperimentledtonewknowledgeonhowtoimprovetheengineeringdesignofthepumpand，inparticular，onhowtoimproveitsrobustnesstothevaryingpressuresthatareexperiencedinoperation.

Keywords:

Algorithm；

Components;

Factorialexperiment;

Mechanicalengineering；

Optimaldesign;

Qualityimprovement;

Robustness

1.Introduction

Thedesignofaconventionalfactorialexperimentspecifiesthelevelsofeachfactorandhowtheyshouldbecombinedtoformruns。

Whentheobjectiveoftheexperimentistoinvestigateandimprovetheperformanceofaproductassembledfromseveralseparatecomponents，e。

g。

amechanicalorelectricaldevice,twomethodsofobtainingtherequiredcombinationsoffactorlevelstorealizethedesignarecommonlyused.Oneapproachistomanufactureone-offcomponentstohavethefactorvaluesthatarerequiredfortheexperiment。

Alternatively，samplesofthevariouscomponentscanbetakenfromproductionand，throughmeasur-ingthefeaturesofinterest,componentsfoundwiththerequiredproperties。

Typically,therequiredfactorlevelsareat,ornear,theextremesofthefactorrangesobtainedinproduction，solargesamplesofcomponentsmustbemeasuredtofindsufficientfortheexperiment。

Forsomeproducts，thecostsoftheseapproachesareprohibitive.AnexampleisthehydraulicgearpumpshowninFig.1，wheremachiningtheindividualgearteethonthedriveanddrivengearstoprecisespecifications,ormeasuringtheirprofiles,isslowandcostly.Afurtherdifficultywithmechanicalproductsisthatoftenacomponentcannotbeusedinmorethanoneexperimentalproduct,e。

whenrunningandtestingtheproductproducescomponentwear，asinthegearpump.

Forsuchsituations，weproposeanapproachwhichtakesamuchsmallerrandomsampleofcomponentsfromproduction,measurestheirrelevantfeaturesandassemblesthemto

Addressforcorrespondence：

C.J.Sexton,DepartmentofMathematics,UniversityofSouthampton,Highfield，Southampton,S0171BJ,UK.

E—mail:

C。

J.Sexton＠maths。

soton。

ac.uk

2001RoyalStatisticalSociety0035-9254/01/50155

formasetofprototypesfortestingthatgivesasmuchinformationaspossibleonthefactorialeffectsofinterest.Thusfullcontrolissacrificedoverthevaluestakenbyafactor,butsomeControlisretainedoverwhichfactorvaluesarecombinedintheexperiment。

Suchfactorscanberegardedassemicontrolled;

seealsoHarville（1974）。

Anaddedcomplicationformanymechanicalproductsisthatthemeaningfulfactorsarenotthemeasuredfeaturesofthecomponentsbutfactorsderivedfromthem,suchasadistancebetweentwocomponents,orotherfunctionsofseveralvariablesthatrelateinengineeringtermstotheproduct'

sperformance。

Wepresentanalgorithmicmethodofobtainingefficientdesignsforexperimentsinvolvingderivedfactors。

InSection2thehydraulicgearpumpisdescribed,andSection3definesthedesignproblem。

AnalgorithmforgeneratingdesignswhenallthefactorsarederivedisgiveninSection4;

thisalgorithmhasbeenusedtofindadesignforapilotstudyonthepump.Section5considersanexperimentwheresomefactorscanbefullycontrolledandotherscannot.Anextensionofthealgorithmisusedtoobtainadesignforthisexperiment。

InSection6theanalysisofthedatafromtheexperimentisoutlined,togetherwiththenewknowledgegainedonhowtoimprovetheengineeringdesignofthepump。

2.Thehydraulicgearpump

Hydraulicgearpumpsareusedinawidevarietyofmachines,e。

g.agriculturalandconstructionvehiclesandaeroplanes,toprovideflexiblepowerfromtheenginetoliftinggearorancillaryequipment.Thepumpunderinvestigationhereformspartofthepowersteeringmechanismofanagriculturaltractor。

AsshowninFig。

1,itconsistsofadrivegearandadrivengearwhichsitintwobearingblocks,floatingwithinahousing,withaflangeplateononesideandacoverontheothertopresstheblocksontothegears.Asthedriveshaftturns，thegearteethmeshanddrawhydraulicfluidthroughthepump.However，atendencyforsomeofthefluidtoleakbackaroundtheinternalcomponentscanleadtoareductionintheefficiencyofthepump。

Toimprovetheengineeringdesignbyreducingsuchleakage，themanufacturerwishedtoinvestigatetheinfluenceofthemanygeometricalaspectsofthecomponentsonpumpleakage，definedasthedifferencebetweenthetheoreticalandactualflowratesoffluidthroughthepump。

Becauseoftheveryhighpressuresthatareexperiencedbythehydraulicfluid，thedesignmustaccommodatetheflexingofcomponentswhichwouldotherwisecreatesubstantialgapsbetweencomponentsandresultinhighleakage.Withinthepump，theflexingispartlycontrolledbyacarefuldesignofregionsontheflangeandcoverplateswherehighpressurefluidisallowedtoenter，andtherebytobalancetheforcescreatedbythepumpinginthebearings。

Suchbalancedfloatingbearingsarecentraltotheoperationofthepump.Attemptstomodelthebehaviourofthesepumpsbyusingmathematicalmodelshavenotbeenverysuccessful,primarilybecauseofthestrongrelationshipbetweenfluidflowandflexingmovementandthedynamicnatureofthegearmotionwithintheoil.Consequentlyexperimentsonasoftwaremodel（e。

g.Aslettetal。

（1998））arenotanoptionforthistypeofstudy.Realprototypesmustbeusedwhichincurcostsofmanufacture，measurementandtesting，andleadtorestrictionsonthesizeofanexperiment。

Thefinalpartofthemanufacturingprocessinvolvesrunningthepumpsothatthegearscutintothebearingblocks，creatingasealagainsttheleakageofoil.Thisbedding-inprocesscreatesanadditionalrestrictionasitchangesfeaturesofthecomponentsofacompletedpumpsothatitscomponentscannotbereusedinanotherprototype。

Forexample,whenatestedpumpisdisassembled,abrasionandpittingcanbeseenonthewallsofthebearingblocks。

Asafirstattempttoexperimentonthepump，asmallpilotstudywasplannedtoestablishlaboratorytestingprocedures，andtogainsomeinsightsintohowtheleakagemightarise。

Inthisstudyonlyfeaturesrelatedtothedrivegear,thedrivengearandthetwobearingblocks（knowncollectivelyasthegearpack）werevaried,andalltheotherfeatureswereheldconstant.Asampleofcomponents,sufficienttomake12pumps,wasavailable。

Therelevantdimensionsofthesecomponentswerecarefullymeasured,andadesignwasthenneededtospecifywhichcomponentsshouldbeselectedandassembledtomakeeachofthe12pumps.Althoughthespecificreasonsforleakagearenotknown，theengineersidentifiedthreepossibleleakagepathsthroughthepump.Foreachpathaderivedfactor（side-gap，clearanceandgearform）wasdefinedgivingthesizeofthepathasanexplicitformulaintermsofthegeometricaldimensionsofthecomponents。

Theclearanceisbasedonthedifferencebetweenthediameterofthedriveshaftandthatofthejournalbearingintowhichitfits,thegearformisafunctionoftheprofileofthegearsandtheside-gapcorrespondstothesizeofthegapsbetweenthegearsandbearingblocks.Anaimofthepilotstudywastoobtaininformationonwhichofthesederivedfactorsmightbeimportantforleakagesothatmoredetailedfollow-upexperimentscouldbefocusedontheappropriateleakagepaths。

3。

Thedesignproblem

Todemonstratetheimportanceofsolvingthisproblem,Table1givestwoofthemanypossibleplansforthepilotstudyon12gearpacks。

Herethevaluesofeachderivedfactorarescaledsothattheirminimumandmaximumpossiblevalues，calculatedacrossallvaluesthatcanbederivedfromallpossibleassembliesofthecomponents，are一1and1respectively.Thesedesignsarerealizablefromthesamesetsofmeasuredcomponentsthroughdifferentchoicesofthespecificcomponentsforassemblyintoeachofthe12gearpacks。

Fig.2showseachofthedesignsasasetofpointswithinthethree-dimensionaldesignspaceforthederivedfactors。

Thecurrentexperimentalpracticeistoassembleprototypesatrandom.Thedisadvantagesofthisapproachareillustratedbydesign1ofTable1whichoffersverylittleinformationonhowvaryingthesizeofclearanceaffectstheleakage;

11ofthe12clearancesliebetween0。

23and0.30,andsevenofthesehavevalue0。

27.Incontrast,design2exploresthisfactoracrossamuchwiderrangeofpracticalimportance,namelyfrom-0。

49to0。

91。

Fig.