减速机详细的选型计算及练习资料

DriveselectionDriveselection19.02.2219.02.22#GotzProduct-SupportProduct-Support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)：(4.11)-r2=0.0625kgm2(4.11)从而可得缶$aresultthetotalinertiais)Jtotal=J+JJtotal=J+JLMotor(4.12)Jtotal=0.0635kgm2(4.13)运动学分析：(Kinematics)延迟Delay:abraked3延迟Delay:abraked32•冗•dndt60-dt=261.8—s2(4.14)M=JM=J-a=16.62Nmdyntotalbrake制动时，动态传输转矩按下式计算：(Whenbraking,thedynamicprocesstorqueiscalculatedasfollows)(4.15)(4.16)(4.16)(4.17)总制动转矩(Thetotalbrakingtorque)M=Im-M=13.62Nm31frictiondyn1相应的制动功率峰值：(Thecorrespondingpeakbrakepoweroftheprocess)P=M-3=3565.72WProzess,brake3

Product-SupportProduct-Support(4.18)直流母线上的制动功率：(ThepeakbrakepowerattheDCbusis)(4.18)P=PF—P=2592.58W

brake,maxProzess,bakeMotorV连续制动功率：(Calculationofthecontinuousbrakingpower)Pbrake,ave=Pbrake,ave=1.P2brake,maxTcycle.’brake=185.18W(4.19)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：(Themaximumbrakingresistoriscalculatedasfollows)R<

brake,maxR<

brake,maxU2—threshold(725V1=202。P2592.58Wbrake,max(4.20)制动电阻最小值(Calculationoftheminimumbrakingresistor)R>brake,minUR>brake,minU—thresholdImax,Chopper725——H18。42A(4.21)求制动电阻热容量：(Calculationoftherequiredthermalcapacitanceoftheresistor)(4.22)W=1.P-t=1296.29WS(4.22)brake2brake,maxbrake制动电阻值必须介于RBrakemin和RBrakemax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,maxandhaveahigherthermalcapacitancethanthebrakingenergyrequired.Moreover,itmustbeabletohandlethecontinuousandpeakpower.)结论：制动电阻值RBrake=180。(Asaresult,thefollowingresistorcanbeused:RBrake=180。)

Product-SupportProduct-Support驱动所需时间：制动单元2(Brakingunit2)驱动所需时间：(Timerequiredforonedrive)s55s55mV3mmin=18.3min制动运行时，发电模式产生的功率为：(Whenmovingdownwardsagenerator-modepowerof)制动运行时，发电模式产生的功率为：(Whenmovingdownwardsagenerator-modepowerof)P=m-g-sin9-v=130000mmkg・9.81一・1・0,05一=63765WP=m-g-sin9-v=130000mmkg・9.81一・1・0,05一=63765Ws2s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(approx.16kW)ofthetotalpower.]每台制动斩波器配备的制动电阻值为：asfollows)(ThecorrespondingbrakingresistorperchopperiscalculatedU2―thresholdPcontinuos(725V1/=32.85。16kW又因为电阻的阻值应在18Q到32.85Q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18Q电阻按下图混联。(Apossi%oblesolutionisagroupconnectionofatotalofsix18。resistors.)卜18QI—I18。II18。II18QI总制动电阻值为：(Inthiscase,twotimes3resistorshavetobeconnectedinseriesandbothseriesconnectionshavetobesetinparallel.Thisresultsinthefollowingresistorvalue)Rtotal111=27Q+3-18Q3-18Q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18Q的电阻组成的电阻桥做为制动电阻。(Atotalof4brakingchoppers9352areneeded.Eachchopperreceivesaresistornetworkwithsix18Qresistors.)Product-SupportProduct-Support传动轴(Spindle)计算转动惯量Calculationofthemomentofinertia一部分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)(4.23)(4.24).兀(4.23)(4.24)J=——•d4•l•pS32s.该固体为钢质时：(Forsteelapplies)J=123•10-9・r4・l=123•10-9•(14mm)4•900mmS=4.25kgcm2另一部分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)J=m•TransgesJ=m•Transges2=1500kg•(4.25)(4.26)Jtotal=J+J(4.26)Jtotal=J+JTransS(4.27)Jtotal=42.25kgcm2(4.28)J=38kgcm2Trans总转轴惯量为：(Asaresult,thetotalmomentofinertiaisasfollows)

Product-SupportProduct-Support运动学分析：(Kinematics)运动中的数据进行计算。本例中的速度曲线如下图所示，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行计算。(Thediagramshowsthespeedprofileoftheapplication.Sincetheprofileisthesameforforwardandbackwarddriving,itissufficienttoexamineforwarddrivingonly.)求加速及延迟时间：(Calculationofaccelerationanddelay)v——maxt1v——maxt10.2m-8-=0.6667—0.3ss2(4.29)隐藏距离：(Distancecovered)11m——•a•11m——•a•12——•0.6667—•212=0.03m(4.30)s2这段距离需用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.)s-2•s0.24m一2•0.03mg0svmax=0.9ss-2•s0.24m一2•0.03mg0svmax=0.9s0.2ms(4.31)图中各段时间为：t1=0.3st2=0.9st3=0.3st4=0.1sT=1.6s。(Theindividualtimesare:t1=0.3st2=0.9st3=0.3st4=0.1sT=1.6s.)线速度与角速度的转换为：(Thetranslatoryvariablesaretransferredtotherotatoryvariablesasfollows)3—2•兀(4.32)aa—2•兀•_h(4.33)因而，角速度为：(Asaresult,theangularvelocityisasfollows)0.2m1v13—2•兀•-max—2•兀•——125.66—h0.01ms(4.34)又因为该角速度对应转速为n=1200rev/min。(Thiscorrespondstoaspeedofn=1200rev./min)Product-SupportProduct-Support因此，该角速度为：(Asaresult,theangularvelocityisasfollows:)a0,6667m/s2a=2•a0,6667m/s2a=2•兀•一二2•兀•0,01m=418,91/s2(4.35)动态传递转矩如下式计算：Mdyn(Thedynamicprocesstorqueiscalculatedasfollows)=J・a=0.004225kgm2•418.9—=1.77Nmgess2(4.36)首先，静态转矩为：(Determinationofthestationarytorque)(4.37)m(4.37)F=m-g-R=1500kg-9.81m-0.02=294.3Nfrictiontotalbs2Mstatfriction2.冗—=294.3Mstatfriction2.冗—=294.3N-ns0.01m2•兀0.92—=0.51Nm(4.38)制过过程中，静态转矩可用下式求出：torque)制过过程中，静态转矩可用下式求出：torque)(Duringthebraking,thefollowingappliestothestationarystatfriction2.冗-n=294.3-001-0.92statfriction2.冗-n=294.3-001-0.92=0.43Nms2-兀(4.39)传动轴功效可按下式计算：(Thespindleefficiencyiscalculatedasfollows)1-K平1-0.1137・0.011+工0.1137=0.92(4.40)ith兀•d兀•28mm(4.41)(4.42)(4.43)(Thecalculatedvaluesforthetotaltorquearelistedbelow)时间(Period)(4.42)(4.43)(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摩擦系数取决于传动轴的类型(Lenzeformulacollection,s=0.01)。[Thefrictioncoefficientofthespindleresultsfromthespindletype(Lenzeformulacollection,人=0.01).]总传递扭矩为动态转矩与静态转矩之和。(Thetotalprocesstorquecanbefoundbyaddingthedynamicandthestationarycomponents.)M(t)=M(t)+M(t)totaldynstat其对应的功率为：(Thecorrespondingprocesspower)P(t)=M(t)-3(t)totaltotal总传递转矩的计算值如下所示：有效转矩取决于所选电机。(Theeffectivetorqueisrelevantforselectingamotor.)

Product-Support；M2•t+M2•t+M2•t+M2・tM=.■—1——12~23——34——(4.44)eff\T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230丫，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(Axis)heighth(mm)额定转速(Speed)nr(min-1)额定转矩(Torque)Mr(Nm)额定功率(Power)Pr(kW)额定电流(Current)I(A)电源电压(Connection)VoltageV(V)额定频率(Frequency)(Hz)MDXMA7112711355/1.5400/23050电机型号(Motortype)功率因子(Power)功效(Efficiency)堵转转矩(StallTorque)张紧转矩(TighteningTorque)启始电流(StartingCurrent)转动惯量(Momentofinertia)重量(Weight)factorMrMAIA/IrJMcos①n(Nm)(Nm)(kgm2)(kg)MDXMA71120.700.60.00065.9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。behigher.)(Owingtothetorqueofthemotor,thedynamicstresswill(4.45)(4.46)因此，可按下式求出新的动态转矩：(Thenew(4.45)(4.46)因此，可按下式求出新的动态转矩：(Thenewdynamicprocesstorqueisasfollows)J=J+J

total,newtotalMotorJ=48.25kgcm2total,new(4.47)(4.47)(4.48)M=J-a

dyn,newtotal,newM=0.004825kgm2-418.9—=2.02Nmdyns2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=1.35NmProduct-Support在计算电流值时，应进一步校核负载能力。(Loadcapacitycanandshouldbeexaminedmoredetailedwhencalculatingthecurrent.)此时，应根据转矩曲线求电流曲线。profile.)(Inthiscase,thecurrentprofileiscalculatedfromthetorque电流Ia,r及If,r得自额定数据。(ThecurrentsIa,randIf,rresultfromtherateddata)I=I-cos9=1.5A-0.7=1.05Aa,rtotal,r(4.49)I=：I2-12=丫6.5A)-(1.05A}=1.07A(4.50)f,rtotal,ra,r根据下表的等式，可由转矩求出有效电流。(Owingtothefollowinggeneralrelation,thecorrespondingeffectivecurrentcanbecalculatedfromthetorqueM.)MIra,r(4.51)总电流为：(Thetotalcurrentcanbecalculatedasfollows)(4.52)时间(Time)t[s]转矩(Torque)Mtotal[Nm]有效电流(Activecurrent)L[A]盲电流(Blindcurrent)If,N[A]总电流(Totalcurrent)ItotalMt1=0,3M1=2.531.471.071.81t2=0,9M2=0.510.31.071.11t3=0,3M3=-1.59-0.931.071.42t4=0,1M4=001.071.07i=Ji2+12totalaf,N以上小结如下：(Thisresultsinthefollowingvalues)电机有效电流1tota[,eff=1-33A。(TheeffectivemotorcurrentiscalculatedwithItotaleff=1.33A.)电机未过载。(Themotorisnotoverloaded.)Product-Support首先，可根据电机额定功率进行粗选。选择变频器Selectionofthefrequencyinverter:首先，可根据电机额定功率进行粗选。(Whenselectingthefrequencyinverter,itispossibletomakearoughselectionbasedontheratedmotorpower.)但是，应仔细计算电机平均电流(算术平均值b[Themeanmotorcurrent(arithmeticmeanvalue)has,however,tobecalculatedindetail.]ave.「Lotal,2ave.「Lotal,2.t2+1total,3.tA、Lotal,4■t1=1.3A(4.53)i=1求制动电阻：斩波频率为8kHz时，选E82EV251_2B就足够了，且不会造成过载。(Withachopperfre