目錄(Contents)TOC\o"1-3"1 練習簡介(Briefdescriptionofthee*ercises) 12 實用工具(Aids) 23 練習(E*ercises) 33.1 構造設計形式為M的減速電機(GearedmotordesignM)33.2 構造設計開工為N的減速電機(GearedmotordesignN)43.3 制動單元練習1(Brakingunit1)53.4 制動單元練習2(Brakingunit2)63.5 傳動軸(Spindle)74 練習答案(Solutions)84.1 構造設計形式為M的減速電機(GearedmotordesignM)84.2 構造設計形式為N的減速電機(GearedmotordesignN)104.3 制動單元練習1(Brakingunit1)124.4 制動單元練習2(Brakingunit2)144.5傳動軸(Spindle)15練習簡介(Briefdescriptionofthee*ercises)主題(Topic)容(Contents)難度(Grade)傳動軸驅動Spindledrive往復傳動軸(Cyclicspindledrive)需選擇：電機、變頻器、制動單元(searched:Motor,inverter,brakingunit)高(High)制動單元(Brakingunit)加速傳動(Accelerationdrive)一般(Normal)制動單元(Brakingunit)提升，電阻混聯(Hoist,resistornetwork)高(High)直流母線(DCbus)直流母線運行實例(E*amplesofDCbusoperation)一般(Normal)減速電機(Gearedmotor)設計形式為M的Lenze減速電機的選型(CatalogueselectionofaLenzegearedmotorinM-design)一般(Normal)減速電機(Gearedmotor)設計形式為N的Lenze減速電機的選型(CatalogueselectionofagearedmotorinN-design)一般(Normal)橫切機(Crosscutter)卷曲設備(Winder)提升設備(Liftdrive)傳輸設備(Travellingdrive)實用工具(Aids)計算器(Pocketcalculator)Lenze選型手冊(Lenzecatalogues)Lenze公式集(Lenzeformulacollection)練習(E*ercises)3.1設計形式為M的Lenze減速電機的選型(GearedmotordesignM)減速電機按S2方式進展傳動(運行時間=10min)，此時，可采用常規運行方式。[AgearedmotoristodrivealoadinS2operation(operatingtime=10min).Inthiscase,aregularoperationisgiven.]具體數據(Detaileddata):轉矩(Processtorque): M2=580Nm速度(Processspeed): n2=100rev/min主電壓(Mainsvoltage): VMains=400V主電源頻率(Mainsfrequency): fMains=50Hz運行時間(Operatingtime/day): 8h所需部件(Searchedponents):Lenze異步電機(Lenzeasynchronousmotor)GST減速器(Gearbo*GST)3.2設計形式為N的Lenze減速電機的選型(GearedmotordesignN)減速電機按S2方式進展傳動(運行時間=10min)，此時，可采用常規運行方式。[AgearedmotoristodrivealoadinS2operation(operatingtime=10min).Inthiscase,aregularoperationisgiven.]具體數據(Detaileddata):轉矩(Processtorque): M2=580Nm速度(Processspeed): n2=100rev/min主電壓(Mainsvoltage): VMains=400V主電源頻率(Mainsfrequency): fMains=50Hz運行時間(Operatingtime/day): 8h所需部件(Searchedponents):Lenze異步電機(Lenzeasynchronousmotor)GST減速器(Gearbo*GST)注：N型減速器可用于IEC連接，作為規則連接，該型電機應為外置式。為便于計算，可選用Lenze電機。(Note:TypeNisdesignedformotorswithanIECconnection.Asarulethesearee*ternalmotors.Tomakecalculatingeasier,Lenzemotorscanbeusedforthiscalculation.)3.3制動單元1(Brakingunit1)Process:利用伺服控制對圓柱型固體進展加速及制動的驅動特性如上圖所示。(Asolidcylinderisacceleratedandbrakedbyaservodriveasshownintheabovecharacteristic.)具體數據(Detaileddata):圓柱體質量(Massofthecylinder): m=2kg圓柱體半徑(Radiusofthecylinder):r=0.25m摩擦轉矩(rictiontorque):MFriction=3Nm最大速度(Ma*.speed): n=2500rpm加速時間(Accelerationtime): t1=2s延遲時間(Delaytime): t3=1s靜止周期(Restperiod): t4=1s循環周期(Cycletime): T=7s電機成效(Efficiencyofthemotor): Motor=0.8電機轉動慣量(Momentofinertiaofthemotor): JMotor=10kgcm2變頻器功耗(Powerlossoftheinverter): PV=260W需選擇(Searchedponents):制動單元(Brakingunit,resistor)轉矩及功率曲線(Torqueandpowerprofile)3.4制動單元2(Brakingunit2)電機(Motor):兩臺37kW電機，忽略成效(平安預留)[2motorswith37kWefficiencyneglected(safetyreserve)]控制器(Controller): 兩臺EVF9200ES，忽略功耗(平安預留)[2piecesoftheEVF9330-ESpowerlossneglected(safetyreserve)]質量(Mass): m=130,000kg高度(Height): h=55m速度(Speed): v=3m/min接觸傾角(Nocontactbevelangle)=0°應用圍:(Application:Hoistwithoutcounter-weight.)需選擇(Searchedponents):制動單元，制動電阻(Brakingunit,resistor)3.5傳動軸(Spindle)應用(Application):傳動軸用于延固定軌跡傳送一剛體，此時，傳動往復路徑是一致的，剛體安裝在導軌上。(Thespindleistomoveamassofsteelaccordingtoaspecifiedprofile.Inthiscase,thereturntripisthesame.Themassismountedonrails.)具體數據(Detaileddata):材料質量(Materialmass): 1.5t前進距離(Forwardfeeddistance): 240mm傳動軸材料(Spindlematerial): 鋼(steel)傳動軸傾度(Spindlepitch): 10mm傳動軸摩擦直徑(Spindlefrictiondiameter): 28mm傳動軸類型(Spindletype): 球軸承(ballbearingspindle)傳動軸長度(Spindlelength): 900mm傳輸速度(Traversingspeed): 12m/min加速時間(Accelerationtime): 0.3sto0.5s延遲時間(Delaytime): 0.3sto0.5s靜止周期(Restperiod): 0.1s與導軌之前的摩擦系數(Frictioncoefficientoftherails):b=0.02需選擇(Searchedponents):異步電機(不帶減速器)[Asynchronousmotor(withoutgearbo*)]變頻器(矢量型)[Frequencyinverter(vector)]制動斬波器，制動電阻(Brakechopper,resistor0練習答案(Solutions)設計形式為M的Lenze減速電機的選型(GearedmotordesignM)求傳輸功率(Calculationoftheprocesspower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n1)求kS2＝1.4且Gearbo*,initial＝0.95時所需的電機功率:(CalculationoftherequiredmotorpowerwithkS2=1.4andGearbo*,initial=0.95) (STYLEREF1\n4.SEQGleichung\*ARABIC\n2)根據主電源數據選擇電機電壓及頻率(Motorvoltageandmotorfrequencycorrespondtothemainsdata.)可選擇4極異步電機：112-32(A4-poleasynchronousmotorisselected:112-32.)電機型號(Motorsize)PNnrIrIA/IrV*frcosMrMstallMAJ[kW][min-1][A][A][V]Y/[Hz][%][Nm][Nm][NM][10-3kgm2]112-325.5144012.58.0-/4002)500.788936.5138.7105.922.8供電電壓：400V，連接方式：角接(Deltainterconnectionwith400V.)求減速器速比(Calculationofthesetpointgearbo*ratio): (STYLEREF1\n4.SEQGleichung\*ARABIC\n3)負載等級為I。(LoadclassIisdefined.)由于在S2方式下運行10分鐘，故每小時開關次數很少。(ThenumberofoperationsperhourisverysmallbecauseoftheS2operationof10minutes.)運行因子最大為0.9。(Thisleadstoanoperationfactorkofma*.0.9.)根據"G-motionconst"手冊中14.286.c=1.3查出iactual(SelectionofiactualintheG_Motionconstcatalogueof14.286.c=1.3.)此時(Inthiscase)：ckGST07-2M假設所需傳遞的轉矩傳至電機側，則結果為Gearbo*=0.97(Iftherequestedprocesstorqueistransformedtothemotorside,theresultisasfollows:Gearbo*=0.97) (STYLEREF1\n4.SEQGleichung\*ARABIC\n4)可根據電機的運行值求出C。(Ccouldberecalculatedbasedontheoperatingpointofthemotor.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n5)為校核啟動轉矩，必須將M2*作為MA，為獲得充足的加速裕量，必須確保在所額定值下都能啟動：(MA.Tocheckthestartingtorque,M2*hastobeparedtoMA.Startingisatanyrateensuredbecausesufficientaccelerationreservesareavailable.)S2方式下允許的電機轉矩為：(ThepermissibletorqueofthemotorforS2-operationis) (STYLEREF1\n4.SEQGleichung\*ARABIC\n6)電機不會過載。(Themotorisnotoverloaded.)設計形式為N的Lenze減速電機的選型(GearedmotordesignN)求傳輸功率(Calculationoftheprocesspower)(STYLEREF1\n4.SEQGleichung\*ARABIC\n7)求kS2＝1.4且Gearbo*,initial＝0.95時所需的電機功率:(CalculationoftherequiredmotorpowerwithkS2=1.4andGearbo*,initial=0.95) (STYLEREF1\n4.SEQGleichung\*ARABIC\n8)根據主電源數據選擇電機電壓及頻率(Motorvoltageandmotorfrequencycorrespondtothemainsdata.)可選擇4極異步電機：112-32(A4-poleasynchronousmotorisselected:112-32.)電機型號(Motorsize)PNnrIrIA/IrV*frcosMrMstallMAJ[kW][min-1][A][A][V]Y/[Hz][%][Nm][Nm][NM][10-3kgm2]112-325.5144012.58.0-/4002)500.788936.5138.7105.922.8供電電壓：400V，連接方式：角接(Deltainterconnectionwith400V.)求減速器速比(Calculationofthesetpointgearbo*ratio): (STYLEREF1\n4.SEQGleichung\*ARABIC\n9)負載等級為I。(LoadclassIisdefined.)由于在S2方式下運行10分鐘，故每小時開關次數很少。(ThenumberofoperationsperhourisverysmallbecauseoftheS2operationof10minutes.)運行因子最大為0.9。(Thisleadstoanoperationfactorkofma*.0.9.)在"G_Motionconst"手冊中查閱N型減速器數據，查出iactual。(SelectionofiactualintheG_MotionconstcataloguedesignN.)特性(Characteristics)：M2permn1IEC連接(IEC-connection)iactual=14.286 GST07-2NM2perm=624NmM2*k假設所需傳遞的轉矩傳至電機側，則結果為Gearbo*=0.97(Iftherequestedprocesstorqueistransformedtothemotorside,theresultisasfollows:Gearbo*=0.97) (STYLEREF1\n4.SEQGleichung\*ARABIC\n10)為校核啟動轉矩，必須將M2*作為MA，為獲得充足的加速裕量，必須確保在所有額定值下都能啟動：(MA.Tocheckthestartingtorque,M2*hastobeparedtoMA.Startingisatanyrateensuredbecausesufficientaccelerationreservesareavailable.)S2方式下允許的電機轉矩為：(ThepermissibletorqueofthemotorforS2-operationis) (STYLEREF1\n4.11)電機不會過載。(Themotorisnotoverloaded.)制動單元1(Brakingunit1)求轉動慣量(Calculationofthemomentofinertia)下式適于圓柱固體轉動慣量的計算(Forasolidcylinderthefollowingformulaapplies)： (STYLEREF1\n4.SEQGleichung\*ARABIC\n11)從而可得(Asaresultthetotalinertiais) (STYLEREF1\n4.SEQGleichung\*ARABIC\n12) (STYLEREF1\n4.SEQGleichung\*ARABIC\n13)運動學分析：(Kinematics)延遲Delay: (STYLEREF1\n4.SEQGleichung\*ARABIC\n14)制動時，動態傳輸轉矩按下式計算：(Whenbraking,thedynamicprocesstorqueiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n15)總制動轉矩(Thetotalbrakingtorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n16)相應的制動功率峰值：(Thecorrespondingpeakbrakepoweroftheprocess) (STYLEREF1\n4.SEQGleichung\*ARABIC\n17)直流母線上的制動功率：(ThepeakbrakepowerattheDCbusis) (STYLEREF1\n4.SEQGleichung\*ARABIC\n18)連續制動功率：(Calculationofthecontinuousbrakingpower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n19)由于制動功率是連續的，因此不允許使用制動模塊，必須使用制動斬波器。(Duetothecontinuousbrakingpower,itisnotpossibletouseabrakingmodule.Thebrakingchopper9352hastobeused.)制動電阻最大值按下式計算：(Thema*imumbrakingresistoriscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n20)制動電阻最小值(Calculationoftheminimumbrakingresistor) (STYLEREF1\n4.SEQGleichung\*ARABIC\n21)求制動電阻熱容量：(Calculationoftherequiredthermalcapacitanceoftheresistor) (STYLEREF1\n4.SEQGleichung\*ARABIC\n22)制動電阻值必須介于RBrake,min和RBrake,ma*之間，且其熱容量應大于所需制動能量，但是，制動電阻必須滿足連續制動及制動功率峰值要求。(TheresistorvaluemustbebetweenRBrake,minandRBrake,ma*andhaveahigherthermalcapacitancethanthebrakingenergyrequired.Moreover,itmustbeabletohandlethecontinuousandpeakpower.)結論：制動電阻值RBrake=180(Asaresult,thefollowingresistorcanbeused:RBrake=180)制動單元2(Brakingunit2)驅動所需時間：(Timerequiredforonedrive)制動運行時，發電模式產生的功率為：(Whenmovingdownwardsagenerator-modepowerof)此時，制動功率持續上升，必須使用多臺控制斬波器。(Thebrakingpowerarisescontinuouslyandhastobedissipatedbyseveralbrakingchoppers.)9352制動斬波器可處理19kW連續制動功率，這意味著需4臺9352。[Thebrakingchopper9352canhandle19kWcontinuously.Thismeansthatatotalof4brakingchoppersareneeded.Eachchopperhastodissipateaquarter(appro*.16

kW)ofthetotalpower.]每臺制動斬波器配備的制動電阻值為：(Thecorrespondingbrakingresistorperchopperiscalculatedasfollows)又因為電阻的阻值應在18

到32.85

之間，同時，制動電阻應可消耗16kW連續制動功率。(Theminimumbrakingresistoris18.Theselectedresistorvalueshouldbebetween18

and32.85

.Moreover,thebrakingresistormustbeabletohandle16kWcontinuously.)可行方案為將6支18

電阻按下列圖混聯。(Apossi‰blesolutionisagroupconnectionofatotalofsi*18

resistors.)總制動電阻值為：〔Inthiscase,twotimes3resistorshavetobeconnectedinseriesandbothseriesconnectionshavetobesetinparallel.Thisresultsinthefollowingresistorvalue〕這樣，每支制動電阻制動可消耗3kW連續制動功率，共計18kW。(3kWarecontinuouslypermissibleperresistor.Thiscorrespondstoatotalof18kW.)結論(Conclusion)此例中，需4臺9352制動斬波器，每臺9352需配備6支各18的電阻組成的電阻橋做為制動電阻。(Atotalof4brakingchoppers9352areneeded.Eachchopperreceivesaresistornetworkwithsi*18resistors.)傳動軸(Spindle)計算轉動慣量Calculationofthemomentofinertia一局部轉動慣量產生于傳動軸的幾何形狀：(Momentofinertiaarisingfromthegeometryofthespindle)傳動軸用于圓柱體傳動時：(Forasolidcylinderapplies) (STYLEREF1\n4.SEQGleichung\*ARABIC\n23)該固體為鋼質時：(Forsteelapplies) (STYLEREF1\n4.SEQGleichung\*ARABIC\n24)另一局部轉動慣量產生于負載質量及傳動軸與其軸閂之間的摩擦：(Momentofinertiaarisingfromthemassoftheloadandthespindleboltwithreferencetothespindle) (STYLEREF1\n4.SEQGleichung\*ARABIC\n25) (STYLEREF1\n4.SEQGleichung\*ARABIC\n26)總轉軸慣量為：(Asaresult,thetotalmomentofinertiaisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n27) (STYLEREF1\n4.SEQGleichung\*ARABIC\n28)運動學分析：(Kinematics)本例中的速度曲線如下列圖所示，由于該曲線在往復過程中是一致的，故在此僅對前向運動中的數據進展計算。(Thediagramshowsthespeedprofileoftheapplication.Sincetheprofileisthesameforforwardandbackwarddriving,itissufficienttoe*amineforwarddrivingonly.)求加速及延遲時間：(Calculationofaccelerationanddelay) (STYLEREF1\n4.SEQGleichung\*ARABIC\n29)隱藏距離：(Distancecovered) (STYLEREF1\n4.SEQGleichung\*ARABIC\n30)這說明在恒定傳動中存在0.18m的隱藏距離，傳動速度為12m/min時，這段距離需用0.9s。(Thismeansthat0.18mhavetobecoveredduringconstantdriving.Incaseof12m/min.,thistakes0.9s.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n31)圖中各段時間為：t1=0.3st2=0.9s t3=0.3s t4=0.1s T=1.6s。(Theindividualtimesare:t1=0.3s t2=0.9s t3=0.3s t4=0.1s T=1.6s.)線速度與角速度的轉換為：(Thetranslatoryvariablesaretransferredtotherotatoryvariablesasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n32) (STYLEREF1\n4.SEQGleichung\*ARABIC\n33)因而，角速度為：(Asaresult,theangularvelocityisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n34)又因為該角速度對應轉速為n=1200rev/min。(Thiscorrespondstoaspeedofn=1200rev./min)因此，該角速度為：(Asaresult,theangularvelocityisasfollows:) (STYLEREF1\n4.SEQGleichung\*ARABIC\n35)動態傳遞轉矩如下式計算：(Thedynamicprocesstorqueiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n36)首先，靜態轉矩為：(Determinationofthestationarytorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n37) (STYLEREF1\n4.SEQGleichung\*ARABIC\n38)制過過程中，靜態轉矩可用下式求出：(Duringthebraking,thefollowingappliestothestationarytorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n39)傳動軸成效可按下式計算：(Thespindleefficiencyiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n40) ith (STYLEREF1\n4.SEQGleichung\*ARABIC\n41)摩擦系數取決于傳動軸的類型(Lenzeformulacollection,s=0.01)。[Thefrictioncoefficientofthespindleresultsfromthespindletype(Lenzeformulacollection,s=0.01).]總傳遞扭矩為動態轉矩與靜態轉矩之和。(Thetotalprocesstorquecanbefoundbyaddingthedynamicandthestationaryponents.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n42)其對應的功率為：(Thecorrespondingprocesspower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n43)總傳遞轉矩的計算值如下所示：(Thecalculatedvaluesforthetotaltorquearelistedbelow)時間(Period)t[s]轉矩(Torque)Mtotal[Nm]t1=0.3M1=2.28t2=0.9M2=0.51t3=0.3M3=-1.34t4=0.1M4=0有效轉矩取決于所選電機。(Theeffectivetorqueisrelevantforselectingamotor.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n44)根據上表中數據：T=1.6s；Meff=1.21Nm。(IfthevaluesshowninthetableareusedwithT=1.6s:Meff=1.21Nm.)所選電機為：(Selectionofthemotor)電源電壓230V，角型連接的MDFMA71-12電機。理由：其額定轉矩大于本例中所需之有效轉矩，額定轉速明顯大于本例中所需傳遞速度。(MDFMA71-12becausetheratedtorqueishigherthantheeffectivetorqueoftheapplication.Theratedspeedisslightlyhigherthantherequestedprocessspeed.Themotorisdelta-connectedwith230V.)電機型號(Motortype)軸高〔A*is〕額定轉速(Speed)額定轉矩(Torque)額定功率(Power)額定電流(Current)電源電壓(Connection)額定頻率(Frequency)heightVoltagehnrMrPrIV(mm)(min-1)(Nm)(kW)(A)(V)(Hz)MD*MA71-127113551.80.250.85/1.5400/23050電機型號(Motortype)功率因子(Power)成效(Efficiency)堵轉轉矩〔StallTorque〕緊轉矩〔TighteningTorque〕啟始電流〔StartingCurrent〕轉動慣量(Momentofinertia)重量(Weight)factorMrMAIA/IrJMcos(Nm)(Nm)(kgm2)(kg)MD*MA71-120.700.613.43.43.80.00065.9校核電機負載能力Checkofmotorloadcapacity:由于電機轉矩，會產生較高的動態應力。(Owingtothetorqueofthemotor,thedynamicstresswillbehigher.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n45) (STYLEREF1\n4.SEQGleichung\*ARABIC\n46)因此，可按下式求出新的動態轉矩：(Thenewdynamicprocesstorqueisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n47) (STYLEREF1\n4.SEQGleichung\*ARABIC\n48)因而，總轉矩如下表所示：(Asaresult,thetotaltorqueisasfollows)時間(Period)t[s]轉矩(Torque)Mtotal[Nm]t1=0.3M1=2.53t2=0.9M2=0.51t3=0.3M3=-1.59t4=0.1M4=0有效轉矩為：(Theeffectivetorqueisasfollows) Meff=1.35Nm在計算電流值時，應進一步校核負載能力。(Loadcapacitycanandshouldbee*aminedmoredetailedwhencalculatingthecurrent.)此時，應根據轉矩曲線求電流曲線。(Inthiscase,thecurrentprofileiscalculatedfromthetorqueprofile.)電流Ia,r及If,r得自額定數據。(ThecurrentsIa,randIf,rresultfromtherateddata) (STYLEREF1\n4.SEQGleichung\*ARABIC\n49) (STYLEREF1\n4.SEQGleichung\*ARABIC\n50)根據下表的等式，可由轉矩求出有效電流。(Owingtothefollowinggeneralrelation,thecorrespondingeffectivecurrentcanbecalculatedfromthetorqueM.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n51)總電流為：(Thetotalcurrentcanbeca