减速机详细的选型计算及练习

目录(Contents)TOC\o"1-3"1 练习简介(Briefdescriptionofthee*ercises) 12 实用工具(Aids) 23 练习(E*ercises) 33.1 构造设计形式为M的减速电机(GearedmotordesignM)33.2 构造设计开工为N的减速电机(GearedmotordesignN)43.3 制动单元练习1(Brakingunit1)53.4 制动单元练习2(Brakingunit2)63.5 传动轴(Spindle)74 练习答案(Solutions)84.1 构造设计形式为M的减速电机(GearedmotordesignM)84.2 构造设计形式为N的减速电机(GearedmotordesignN)104.3 制动单元练习1(Brakingunit1)124.4 制动单元练习2(Brakingunit2)144.5传动轴(Spindle)15练习简介(Briefdescriptionofthee*ercises)主题(Topic)容(Contents)难度(Grade)传动轴驱动Spindledrive往复传动轴(Cyclicspindledrive)需选择：电机、变频器、制动单元(searched:Motor,inverter,brakingunit)高(High)制动单元(Brakingunit)加速传动(Accelerationdrive)一般(Normal)制动单元(Brakingunit)提升，电阻混联(Hoist,resistornetwork)高(High)直流母线(DCbus)直流母线运行实例(E*amplesofDCbusoperation)一般(Normal)减速电机(Gearedmotor)设计形式为M的Lenze减速电机的选型(CatalogueselectionofaLenzegearedmotorinM-design)一般(Normal)减速电机(Gearedmotor)设计形式为N的Lenze减速电机的选型(CatalogueselectionofagearedmotorinN-design)一般(Normal)横切机(Crosscutter)卷曲设备(Winder)提升设备(Liftdrive)传输设备(Travellingdrive)实用工具(Aids)计算器(Pocketcalculator)Lenze选型手册(Lenzecatalogues)Lenze公式集(Lenzeformulacollection)练习(E*ercises)3.1设计形式为M的Lenze减速电机的选型(GearedmotordesignM)减速电机按S2方式进展传动(运行时间=10min)，此时，可采用常规运行方式。[AgearedmotoristodrivealoadinS2operation(operatingtime=10min).Inthiscase,aregularoperationisgiven.]具体数据(Detaileddata):转矩(Processtorque): M2=580Nm速度(Processspeed): n2=100rev/min主电压(Mainsvoltage): VMains=400V主电源频率(Mainsfrequency): fMains=50Hz运行时间(Operatingtime/day): 8h所需部件(Searchedponents):Lenze异步电机(Lenzeasynchronousmotor)GST减速器(Gearbo*GST)3.2设计形式为N的Lenze减速电机的选型(GearedmotordesignN)减速电机按S2方式进展传动(运行时间=10min)，此时，可采用常规运行方式。[AgearedmotoristodrivealoadinS2operation(operatingtime=10min).Inthiscase,aregularoperationisgiven.]具体数据(Detaileddata):转矩(Processtorque): M2=580Nm速度(Processspeed): n2=100rev/min主电压(Mainsvoltage): VMains=400V主电源频率(Mainsfrequency): fMains=50Hz运行时间(Operatingtime/day): 8h所需部件(Searchedponents):Lenze异步电机(Lenzeasynchronousmotor)GST减速器(Gearbo*GST)注：N型减速器可用于IEC连接，作为规则连接，该型电机应为外置式。为便于计算，可选用Lenze电机。(Note:TypeNisdesignedformotorswithanIECconnection.Asarulethesearee*ternalmotors.Tomakecalculatingeasier,Lenzemotorscanbeusedforthiscalculation.)3.3制动单元1(Brakingunit1)Process:利用伺服控制对圆柱型固体进展加速及制动的驱动特性如上图所示。(Asolidcylinderisacceleratedandbrakedbyaservodriveasshownintheabovecharacteristic.)具体数据(Detaileddata):圆柱体质量(Massofthecylinder): m=2kg圆柱体半径(Radiusofthecylinder):r=0.25m摩擦转矩(rictiontorque):MFriction=3Nm最大速度(Ma*.speed): n=2500rpm加速时间(Accelerationtime): t1=2s延迟时间(Delaytime): t3=1s静止周期(Restperiod): t4=1s循环周期(Cycletime): T=7s电机成效(Efficiencyofthemotor): Motor=0.8电机转动惯量(Momentofinertiaofthemotor): JMotor=10kgcm2变频器功耗(Powerlossoftheinverter): PV=260W需选择(Searchedponents):制动单元(Brakingunit,resistor)转矩及功率曲线(Torqueandpowerprofile)3.4制动单元2(Brakingunit2)电机(Motor):两台37kW电机，忽略成效(平安预留)[2motorswith37kWefficiencyneglected(safetyreserve)]控制器(Controller): 两台EVF9200ES，忽略功耗(平安预留)[2piecesoftheEVF9330-ESpowerlossneglected(safetyreserve)]质量(Mass): m=130,000kg高度(Height): h=55m速度(Speed): v=3m/min接触倾角(Nocontactbevelangle)=0°应用围:(Application:Hoistwithoutcounter-weight.)需选择(Searchedponents):制动单元，制动电阻(Brakingunit,resistor)3.5传动轴(Spindle)应用(Application):传动轴用于延固定轨迹传送一刚体，此时，传动往复路径是一致的，刚体安装在导轨上。(Thespindleistomoveamassofsteelaccordingtoaspecifiedprofile.Inthiscase,thereturntripisthesame.Themassismountedonrails.)具体数据(Detaileddata):材料质量(Materialmass): 1.5t前进距离(Forwardfeeddistance): 240mm传动轴材料(Spindlematerial): 钢(steel)传动轴倾度(Spindlepitch): 10mm传动轴摩擦直径(Spindlefrictiondiameter): 28mm传动轴类型(Spindletype): 球轴承(ballbearingspindle)传动轴长度(Spindlelength): 900mm传输速度(Traversingspeed): 12m/min加速时间(Accelerationtime): 0.3sto0.5s延迟时间(Delaytime): 0.3sto0.5s静止周期(Restperiod): 0.1s与导轨之前的摩擦系数(Frictioncoefficientoftherails):b=0.02需选择(Searchedponents):异步电机(不带减速器)[Asynchronousmotor(withoutgearbo*)]变频器(矢量型)[Frequencyinverter(vector)]制动斩波器，制动电阻(Brakechopper,resistor0练习答案(Solutions)设计形式为M的Lenze减速电机的选型(GearedmotordesignM)求传输功率(Calculationoftheprocesspower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n1)求kS2＝1.4且Gearbo*,initial＝0.95时所需的电机功率:(CalculationoftherequiredmotorpowerwithkS2=1.4andGearbo*,initial=0.95) (STYLEREF1\n4.SEQGleichung\*ARABIC\n2)根据主电源数据选择电机电压及频率(Motorvoltageandmotorfrequencycorrespondtothemainsdata.)可选择4极异步电机：112-32(A4-poleasynchronousmotorisselected:112-32.)电机型号(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供电电压：400V，连接方式：角接(Deltainterconnectionwith400V.)求减速器速比(Calculationofthesetpointgearbo*ratio): (STYLEREF1\n4.SEQGleichung\*ARABIC\n3)负载等级为I。(LoadclassIisdefined.)由于在S2方式下运行10分钟，故每小时开关次数很少。(ThenumberofoperationsperhourisverysmallbecauseoftheS2operationof10minutes.)运行因子最大为0.9。(Thisleadstoanoperationfactorkofma*.0.9.)根据"G-motionconst"手册中14.286.c=1.3查出iactual(SelectionofiactualintheG_Motionconstcatalogueof14.286.c=1.3.)此时(Inthiscase)：ckGST07-2M假设所需传递的转矩传至电机侧，则结果为Gearbo*=0.97(Iftherequestedprocesstorqueistransformedtothemotorside,theresultisasfollows:Gearbo*=0.97) (STYLEREF1\n4.SEQGleichung\*ARABIC\n4)可根据电机的运行值求出C。(Ccouldberecalculatedbasedontheoperatingpointofthemotor.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n5)为校核启动转矩，必须将M2*作为MA，为获得充足的加速裕量，必须确保在所额定值下都能启动：(MA.Tocheckthestartingtorque,M2*hastobeparedtoMA.Startingisatanyrateensuredbecausesufficientaccelerationreservesareavailable.)S2方式下允许的电机转矩为：(ThepermissibletorqueofthemotorforS2-operationis) (STYLEREF1\n4.SEQGleichung\*ARABIC\n6)电机不会过载。(Themotorisnotoverloaded.)设计形式为N的Lenze减速电机的选型(GearedmotordesignN)求传输功率(Calculationoftheprocesspower)(STYLEREF1\n4.SEQGleichung\*ARABIC\n7)求kS2＝1.4且Gearbo*,initial＝0.95时所需的电机功率:(CalculationoftherequiredmotorpowerwithkS2=1.4andGearbo*,initial=0.95) (STYLEREF1\n4.SEQGleichung\*ARABIC\n8)根据主电源数据选择电机电压及频率(Motorvoltageandmotorfrequencycorrespondtothemainsdata.)可选择4极异步电机：112-32(A4-poleasynchronousmotorisselected:112-32.)电机型号(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供电电压：400V，连接方式：角接(Deltainterconnectionwith400V.)求减速器速比(Calculationofthesetpointgearbo*ratio): (STYLEREF1\n4.SEQGleichung\*ARABIC\n9)负载等级为I。(LoadclassIisdefined.)由于在S2方式下运行10分钟，故每小时开关次数很少。(ThenumberofoperationsperhourisverysmallbecauseoftheS2operationof10minutes.)运行因子最大为0.9。(Thisleadstoanoperationfactorkofma*.0.9.)在"G_Motionconst"手册中查阅N型减速器数据，查出iactual。(SelectionofiactualintheG_MotionconstcataloguedesignN.)特性(Characteristics)：M2permn1IEC连接(IEC-connection)iactual=14.286 GST07-2NM2perm=624NmM2*k假设所需传递的转矩传至电机侧，则结果为Gearbo*=0.97(Iftherequestedprocesstorqueistransformedtothemotorside,theresultisasfollows:Gearbo*=0.97) (STYLEREF1\n4.SEQGleichung\*ARABIC\n10)为校核启动转矩，必须将M2*作为MA，为获得充足的加速裕量，必须确保在所有额定值下都能启动：(MA.Tocheckthestartingtorque,M2*hastobeparedtoMA.Startingisatanyrateensuredbecausesufficientaccelerationreservesareavailable.)S2方式下允许的电机转矩为：(ThepermissibletorqueofthemotorforS2-operationis) (STYLEREF1\n4.11)电机不会过载。(Themotorisnotoverloaded.)制动单元1(Brakingunit1)求转动惯量(Calculationofthemomentofinertia)下式适于圆柱固体转动惯量的计算(Forasolidcylinderthefollowingformulaapplies)： (STYLEREF1\n4.SEQGleichung\*ARABIC\n11)从而可得(Asaresultthetotalinertiais) (STYLEREF1\n4.SEQGleichung\*ARABIC\n12) (STYLEREF1\n4.SEQGleichung\*ARABIC\n13)运动学分析：(Kinematics)延迟Delay: (STYLEREF1\n4.SEQGleichung\*ARABIC\n14)制动时，动态传输转矩按下式计算：(Whenbraking,thedynamicprocesstorqueiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n15)总制动转矩(Thetotalbrakingtorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n16)相应的制动功率峰值：(Thecorrespondingpeakbrakepoweroftheprocess) (STYLEREF1\n4.SEQGleichung\*ARABIC\n17)直流母线上的制动功率：(ThepeakbrakepowerattheDCbusis) (STYLEREF1\n4.SEQGleichung\*ARABIC\n18)连续制动功率：(Calculationofthecontinuousbrakingpower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n19)由于制动功率是连续的，因此不允许使用制动模块，必须使用制动斩波器。(Duetothecontinuousbrakingpower,itisnotpossibletouseabrakingmodule.Thebrakingchopper9352hastobeused.)制动电阻最大值按下式计算：(Thema*imumbrakingresistoriscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n20)制动电阻最小值(Calculationoftheminimumbrakingresistor) (STYLEREF1\n4.SEQGleichung\*ARABIC\n21)求制动电阻热容量：(Calculationoftherequiredthermalcapacitanceoftheresistor) (STYLEREF1\n4.SEQGleichung\*ARABIC\n22)制动电阻值必须介于RBrake,min和RBrake,ma*之间，且其热容量应大于所需制动能量，但是，制动电阻必须满足连续制动及制动功率峰值要求。(TheresistorvaluemustbebetweenRBrake,minandRBrake,ma*andhaveahigherthermalcapacitancethanthebrakingenergyrequired.Moreover,itmustbeabletohandlethecontinuousandpeakpower.)结论：制动电阻值RBrake=180(Asaresult,thefollowingresistorcanbeused:RBrake=180)制动单元2(Brakingunit2)驱动所需时间：(Timerequiredforonedrive)制动运行时，发电模式产生的功率为：(Whenmovingdownwardsagenerator-modepowerof)此时，制动功率持续上升，必须使用多台控制斩波器。(Thebrakingpowerarisescontinuouslyandhastobedissipatedbyseveralbrakingchoppers.)9352制动斩波器可处理19kW连续制动功率，这意味着需4台9352。[Thebrakingchopper9352canhandle19kWcontinuously.Thismeansthatatotalof4brakingchoppersareneeded.Eachchopperhastodissipateaquarter(appro*.16

kW)ofthetotalpower.]每台制动斩波器配备的制动电阻值为：(Thecorrespondingbrakingresistorperchopperiscalculatedasfollows)又因为电阻的阻值应在18

到32.85

之间，同时，制动电阻应可消耗16kW连续制动功率。(Theminimumbrakingresistoris18.Theselectedresistorvalueshouldbebetween18

and32.85

.Moreover,thebrakingresistormustbeabletohandle16kWcontinuously.)可行方案为将6支18

电阻按下列图混联。(Apossi‰blesolutionisagroupconnectionofatotalofsi*18

resistors.)总制动电阻值为：〔Inthiscase,twotimes3resistorshavetobeconnectedinseriesandbothseriesconnectionshavetobesetinparallel.Thisresultsinthefollowingresistorvalue〕这样，每支制动电阻制动可消耗3kW连续制动功率，共计18kW。(3kWarecontinuouslypermissibleperresistor.Thiscorrespondstoatotalof18kW.)结论(Conclusion)此例中，需4台9352制动斩波器，每台9352需配备6支各18的电阻组成的电阻桥做为制动电阻。(Atotalof4brakingchoppers9352areneeded.Eachchopperreceivesaresistornetworkwithsi*18resistors.)传动轴(Spindle)计算转动惯量Calculationofthemomentofinertia一局部转动惯量产生于传动轴的几何形状：(Momentofinertiaarisingfromthegeometryofthespindle)传动轴用于圆柱体传动时：(Forasolidcylinderapplies) (STYLEREF1\n4.SEQGleichung\*ARABIC\n23)该固体为钢质时：(Forsteelapplies) (STYLEREF1\n4.SEQGleichung\*ARABIC\n24)另一局部转动惯量产生于负载质量及传动轴与其轴闩之间的摩擦：(Momentofinertiaarisingfromthemassoftheloadandthespindleboltwithreferencetothespindle) (STYLEREF1\n4.SEQGleichung\*ARABIC\n25) (STYLEREF1\n4.SEQGleichung\*ARABIC\n26)总转轴惯量为：(Asaresult,thetotalmomentofinertiaisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n27) (STYLEREF1\n4.SEQGleichung\*ARABIC\n28)运动学分析：(Kinematics)本例中的速度曲线如下列图所示，由于该曲线在往复过程中是一致的，故在此仅对前向运动中的数据进展计算。(Thediagramshowsthespeedprofileoftheapplication.Sincetheprofileisthesameforforwardandbackwarddriving,itissufficienttoe*amineforwarddrivingonly.)求加速及延迟时间：(Calculationofaccelerationanddelay) (STYLEREF1\n4.SEQGleichung\*ARABIC\n29)隐藏距离：(Distancecovered) (STYLEREF1\n4.SEQGleichung\*ARABIC\n30)这说明在恒定传动中存在0.18m的隐藏距离，传动速度为12m/min时，这段距离需用0.9s。(Thismeansthat0.18mhavetobecoveredduringconstantdriving.Incaseof12m/min.,thistakes0.9s.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n31)图中各段时间为：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.)线速度与角速度的转换为：(Thetranslatoryvariablesaretransferredtotherotatoryvariablesasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n32) (STYLEREF1\n4.SEQGleichung\*ARABIC\n33)因而，角速度为：(Asaresult,theangularvelocityisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n34)又因为该角速度对应转速为n=1200rev/min。(Thiscorrespondstoaspeedofn=1200rev./min)因此，该角速度为：(Asaresult,theangularvelocityisasfollows:) (STYLEREF1\n4.SEQGleichung\*ARABIC\n35)动态传递转矩如下式计算：(Thedynamicprocesstorqueiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n36)首先，静态转矩为：(Determinationofthestationarytorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n37) (STYLEREF1\n4.SEQGleichung\*ARABIC\n38)制过过程中，静态转矩可用下式求出：(Duringthebraking,thefollowingappliestothestationarytorque) (STYLEREF1\n4.SEQGleichung\*ARABIC\n39)传动轴成效可按下式计算：(Thespindleefficiencyiscalculatedasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n40) ith (STYLEREF1\n4.SEQGleichung\*ARABIC\n41)摩擦系数取决于传动轴的类型(Lenzeformulacollection,s=0.01)。[Thefrictioncoefficientofthespindleresultsfromthespindletype(Lenzeformulacollection,s=0.01).]总传递扭矩为动态转矩与静态转矩之和。(Thetotalprocesstorquecanbefoundbyaddingthedynamicandthestationaryponents.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n42)其对应的功率为：(Thecorrespondingprocesspower) (STYLEREF1\n4.SEQGleichung\*ARABIC\n43)总传递转矩的计算值如下所示：(Thecalculatedvaluesforthetotaltorquearelistedbelow)时间(Period)t[s]转矩(Torque)Mtotal[Nm]t1=0.3M1=2.28t2=0.9M2=0.51t3=0.3M3=-1.34t4=0.1M4=0有效转矩取决于所选电机。(Theeffectivetorqueisrelevantforselectingamotor.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n44)根据上表中数据：T=1.6s；Meff=1.21Nm。(IfthevaluesshowninthetableareusedwithT=1.6s:Meff=1.21Nm.)所选电机为：(Selectionofthemotor)电源电压230V，角型连接的MDFMA71-12电机。理由：其额定转矩大于本例中所需之有效转矩，额定转速明显大于本例中所需传递速度。(MDFMA71-12becausetheratedtorqueishigherthantheeffectivetorqueoftheapplication.Theratedspeedisslightlyhigherthantherequestedprocessspeed.Themotorisdelta-connectedwith230V.)电机型号(Motortype)轴高〔A*is〕额定转速(Speed)额定转矩(Torque)额定功率(Power)额定电流(Current)电源电压(Connection)额定频率(Frequency)heightVoltagehnrMrPrIV(mm)(min-1)(Nm)(kW)(A)(V)(Hz)MD*MA71-127113551.80.250.85/1.5400/23050电机型号(Motortype)功率因子(Power)成效(Efficiency)堵转转矩〔StallTorque〕紧转矩〔TighteningTorque〕启始电流〔StartingCurrent〕转动惯量(Momentofinertia)重量(Weight)factorMrMAIA/IrJMcos(Nm)(Nm)(kgm2)(kg)MD*MA71-120.700.613.43.43.80.00065.9校核电机负载能力Checkofmotorloadcapacity:由于电机转矩，会产生较高的动态应力。(Owingtothetorqueofthemotor,thedynamicstresswillbehigher.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n45) (STYLEREF1\n4.SEQGleichung\*ARABIC\n46)因此，可按下式求出新的动态转矩：(Thenewdynamicprocesstorqueisasfollows) (STYLEREF1\n4.SEQGleichung\*ARABIC\n47) (STYLEREF1\n4.SEQGleichung\*ARABIC\n48)因而，总转矩如下表所示：(Asaresult,thetotaltorqueisasfollows)时间(Period)t[s]转矩(Torque)Mtotal[Nm]t1=0.3M1=2.53t2=0.9M2=0.51t3=0.3M3=-1.59t4=0.1M4=0有效转矩为：(Theeffectivetorqueisasfollows) Meff=1.35Nm在计算电流值时，应进一步校核负载能力。(Loadcapacitycanandshouldbee*aminedmoredetailedwhencalculatingthecurrent.)此时，应根据转矩曲线求电流曲线。(Inthiscase,thecurrentprofileiscalculatedfromthetorqueprofile.)电流Ia,r及If,r得自额定数据。(ThecurrentsIa,randIf,rresultfromtherateddata) (STYLEREF1\n4.SEQGleichung\*ARABIC\n49) (STYLEREF1\n4.SEQGleichung\*ARABIC\n50)根据下表的等式，可由转矩求出有效电流。(Owingtothefollowinggeneralrelation,thecorrespondingeffectivecurrentcanbecalculatedfromthetorqueM.) (STYLEREF1\n4.SEQGleichung\*ARABIC\n51)总电流为：(Thetotalcurrentcanbeca