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1ALGORYTHMSFORSPEEDANDSTRECHCONTROLOFTHEMAINDRIVESOFANSTRECH-REDUCINGTUBEMILLDorianMACREASCIPROLAMSA,Negustori23,Bucharest,Romania:dorian.macreaiprolam.roCostinCEPISCAPolitehnicaUniversity,Spl.Indep.313,Bucharest,RomaniaAbstract.Thispapershowsthedrivesolution,thespeedreferencescalculationandtheautomaticcontrolofallspeedsrangefortheassemblyofthe24standsbelongingtoastretch-reducingmillforseamlesspipes.Thecorrelationbetweenthespeedcontrolandthestretchingcontroloftherolledpipeisalsoshown.TheexperimentalresultsarerealdataassociatedtothemostrecentprojectthathasbeenexecutedataseamlesspipeplantinChina.1IntroductionTheconceptofcommondrivesofthestandsusingdistributionanddifferentialgear-boxesrepresentsaflexibilitylimitationoftheperformancesofthemillbutusingitwecansensiblyreducethecostsofthedrives1,2.Therefore,whenwearedesigningrollingmillsofthistype,wehavetostudycarefullythenecessityandtheutilityofchoosingindividualdrivesforeachstandorcommondrives3.Ifweareusingacommonreducerdrivenusingmainandoverlappingdrivestherotatingspeedratiosarechangingsimultaneouslyatallstandsbycontroloftherotatingspeedatboth(oroneofthetwo)motorsandmaintainingtheratiosfortherotatingspeedsoftherollingstandsasbeenestablishedbydesigningofthegears.Thus,inthisdrivesystemwecanchangeonlythespeedaverageorthestretchingaverage,butnotthedistributionofthedeformationvaluesintheindividualsequenceofthestands4,5.Ifwemaygiveuptheadvantagesoftheindividualspeedcontrolonthepipedeformationandifweexceptalargerslippingbetweentherollsandtherolledmaterial(acurrentstatusateasierrollingprograms)wecouldacceptacommondrivewithdistributionanddifferentialgears6,7.2Electromechanicaldrivesolution2.1.SpeedcontrolThe4-motordriveconsistsoftwodrivegroupswhicharemechanicallyseparatedfromoneanotherand,therefore,alloweffectivecropendcontrol(CEC)evenwithclosesequencesoftubes.Forthispurpose,theentrymillstandgroupfeaturesexceptionallyhighgearratiostoobtainparticularlylargeelongations(Figure1).Therollspeedsforstandposition(i)arecalculatedas,Intheentrysidedrivegroup:2Distribution&DifferentialGearNo.2RollrotatingspeedSRMRollingstandsDistribution&DifferentialGearNo.1n1frommotor1n2frommotor2tostandn1+n2Motor1Motor2Motor3Motor4CommonvariationofrotatingspeedratiosDD1MD1MD2DD2Figure1:SchematicforSRMwithCommonDrivewithDistributionandDifferentialGears()()11*21*)(IGRDDISDDiIGRSDDIGRMDISMDiIGRSMDispeedRoll+=(1)Withrespecttothedrivegroupontherun-outside:()()22*22*)(IGRDDISDDiIGRSDDIGRMDISMDiIGRSMDispeedRoll+=(2)Thebasisspeedcurveischaracterizedbyhighgearratiosintheentrydrivegrouptoenablepositivedifferentialgearactionalsointhisarea,i.e.identicaldirectionofrotationofbothbasicanddifferentialdrives.Duringthesteady-statephaseoftherollingprocess,thebasicdrivesofthissystemrunatidenticalspeedswhilethedifferentialdriveunitsoperateatexactlysynchronizedspeeds.Thespeedsarerelatedbythefollowingterm:22*22*1IGRDDISDDIKDIGRMDISMDIKMIGRMDISDD+=(3)22*11IGRMDISMDICFIGRMDISMD=(4)wherebyIKMandIKDareconstants.Themotorsaresynchronizedautomaticallyinthebasicautomationsystem.3SpeedrangeforrollingprogramBasicspeedcurveCECreserveFigure2:Speeddiagramsofthetandemdifferentialdrive2.2StrechcontrolThemotorspeedsatchangesinelongationarecalculatedwiththerotationalspeedvaluesresultingfromthecalculationofthechangesinspeed.Thismethodensuresthattheoperatorcaneffectachangeinelongationbymeansofachangeinspeed,ifnecessary,ifmotorspeedlimitsarereachedwithnochangeinspeed.Oneinputvalueisusedforthechangeinelongation.Inputrange:-100.+100%Standard:0%(inrollingprogram)Calculation:ConversionoftheenteredvalueP:100/*100/1maxPPPS+=(5)withPmaxasinternallimitingvalue,e.g.20%intheactualproject.Thefollowingcalculationresultsina“pivoting”ofthespeeddiagramwiththepivotpointIPSPP(Figure2).Onestandpositionisdefinedasthepivotpoint:IPSPP=IPSI.Thishastheeffectthattheentryspeedandthusthethroughputofmaterialremainmoreorlessconstant.Eachgearboxisassignedtoonemotor.Acharacteristicvaluewhichisdeterminedtogetherwiththerollingprogram,determinesthegearstage(0or1).ThecorrespondinggearratiosareindicatedintheTable1.4Furthercalculationofnewmotorspeeds:IGRMD1=1orgearratiooftheswitchingstepchosen.ThesameistobeappliedforIGRMD2,IGRDD1andIGRDD2.ForcalculationreasonswedefinethevariablesX=IKMandY=IKD.Table1GearratioIGRMD1IGRDD1IGRMD2IGRDD2Gearstage0111111111Ifonlythestandgroupontheinletsideisoccupiedbyrollstandsandthedrivesontherunoutsidearenotusedtodriveguidestandsetc.thefollowingapplies:2*112IGRMDIGRMDISMDISMD=andX=0Y=1(6)Finalcalculationofnewmotorspeed:()()1*1111*1IGRDDIPSFIGRSDDICFYRAPIPSIIGRSSDDICFZMWUAVSMDIGSRSDDIGRDIGRSDIGRSMIGRDDISDDIGRMDISMDUAVOSDD+=(7)()()1*111111IGRMDMDIGRSDDIGRSIGRDDOSDDISDDIGRMDISMDOSMD+=(8)()2*11*11*2IGRDDICFIGRMDOSMDXYIGRDDISDDYRAPOSDD=(9)2*112IGRMDICFIGRMDOSMDOSMD=(10)Aftereverycalculationofamotorspeed,limitvaluesarecheckedandcorrectedaccordingly.Thechangeininletandoutletspeedcanbecalculatedwiththebasicequation:IOSAJGIS+=*(11)with:IS-Inletoroutletspeedafterchangeinelongationm/s;G-Gradientrelationshipofinletorou
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