減速機(jī)詳細(xì)的選型計(jì)算及練習(xí)資料

DriveselectionDriveselection19.02.2219.02.22#GotzProduct-SupportProduct-Support制動(dòng)單元1(Brakingunit1)求轉(zhuǎn)動(dòng)慣量(Calculationofthemomentofinertia)下式適于圓柱固體轉(zhuǎn)動(dòng)慣量的計(jì)算(Forasolidcylinderthefollowingformulaapplies)：(4.11)-r2=0.0625kgm2(4.11)從而可得缶$aresultthetotalinertiais)Jtotal=J+JJtotal=J+JLMotor(4.12)Jtotal=0.0635kgm2(4.13)運(yùn)動(dòng)學(xué)分析：(Kinematics)延遲Delay:abraked3延遲Delay:abraked32?冗?dndt60-dt=261.8—s2(4.14)M=JM=J-a=16.62Nmdyntotalbrake制動(dòng)時(shí)，動(dòng)態(tài)傳輸轉(zhuǎn)矩按下式計(jì)算：(Whenbraking,thedynamicprocesstorqueiscalculatedasfollows)(4.15)(4.16)(4.16)(4.17)總制動(dòng)轉(zhuǎn)矩(Thetotalbrakingtorque)M=Im-M=13.62Nm31frictiondyn1相應(yīng)的制動(dòng)功率峰值：(Thecorrespondingpeakbrakepoweroftheprocess)P=M-3=3565.72WProzess,brake3

Product-SupportProduct-Support(4.18)直流母線上的制動(dòng)功率：(ThepeakbrakepowerattheDCbusis)(4.18)P=PF—P=2592.58W

brake,maxProzess,bakeMotorV連續(xù)制動(dòng)功率：(Calculationofthecontinuousbrakingpower)Pbrake,ave=Pbrake,ave=1.P2brake,maxTcycle.’brake=185.18W(4.19)由于制動(dòng)功率是連續(xù)的，因此不允許使用制動(dòng)模塊，必須使用制動(dòng)斬波器。(Duetothecontinuousbrakingpower,itisnotpossibletouseabrakingmodule.Thebrakingchopper9352hastobeused.)制動(dòng)電阻最大值按下式計(jì)算：(Themaximumbrakingresistoriscalculatedasfollows)R<

brake,maxR<

brake,maxU2—threshold(725V1=202。P2592.58Wbrake,max(4.20)制動(dòng)電阻最小值(Calculationoftheminimumbrakingresistor)R>brake,minUR>brake,minU—thresholdImax,Chopper725——H18。42A(4.21)求制動(dòng)電阻熱容量：(Calculationoftherequiredthermalcapacitanceoftheresistor)(4.22)W=1.P-t=1296.29WS(4.22)brake2brake,maxbrake制動(dòng)電阻值必須介于RBrakemin和RBrakemax之間，且其熱容量應(yīng)大于所需制動(dòng)能量，但是，制動(dòng)電阻必須滿足連續(xù)制動(dòng)及制動(dòng)功率峰值要求。(TheresistorvaluemustbebetweenRBrake,minandRBrake,maxandhaveahigherthermalcapacitancethanthebrakingenergyrequired.Moreover,itmustbeabletohandlethecontinuousandpeakpower.)結(jié)論：制動(dòng)電阻值RBrake=180。(Asaresult,thefollowingresistorcanbeused:RBrake=180。)

Product-SupportProduct-Support驅(qū)動(dòng)所需時(shí)間：制動(dòng)單元2(Brakingunit2)驅(qū)動(dòng)所需時(shí)間：(Timerequiredforonedrive)s55s55mV3mmin=18.3min制動(dòng)運(yùn)行時(shí)，發(fā)電模式產(chǎn)生的功率為：(Whenmovingdownwardsagenerator-modepowerof)制動(dòng)運(yùn)行時(shí)，發(fā)電模式產(chǎn)生的功率為：(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此時(shí)，制動(dòng)功率持續(xù)上升，必須使用多臺(tái)控制斬波器。(Thebrakingpowerarisescontinuouslyandhastobedissipatedbyseveralbrakingchoppers.)9352制動(dòng)斬波器可處理19kW連續(xù)制動(dòng)功率，這意味著需4臺(tái)9352。[Thebrakingchopper9352canhandle19kWcontinuously.Thismeansthatatotalof4brakingchoppersareneeded.Eachchopperhastodissipateaquarter(approx.16kW)ofthetotalpower.]每臺(tái)制動(dòng)斬波器配備的制動(dòng)電阻值為：asfollows)(ThecorrespondingbrakingresistorperchopperiscalculatedU2―thresholdPcontinuos(725V1/=32.85。16kW又因?yàn)殡娮璧淖柚祽?yīng)在18Q到32.85Q之間，同時(shí)，制動(dòng)電阻應(yīng)可消耗16kW連續(xù)制動(dòng)功率。(Theminimumbrakingresistoris18。.Theselectedresistorvalueshouldbebetween18。and32.85。.Moreover,thebrakingresistormustbeabletohandle16kWcontinuously.)可行方案為將6支18Q電阻按下圖混聯(lián)。(Apossi%oblesolutionisagroupconnectionofatotalofsix18。resistors.)卜18QI—I18。II18。II18QI總制動(dòng)電阻值為：(Inthiscase,twotimes3resistorshavetobeconnectedinseriesandbothseriesconnectionshavetobesetinparallel.Thisresultsinthefollowingresistorvalue)Rtotal111=27Q+3-18Q3-18Q這樣，每支制動(dòng)電阻制動(dòng)可消耗3kW連續(xù)制動(dòng)功率，共計(jì)18kW。(3kWarecontinuouslypermissibleperresistor.Thiscorrespondstoatotalof18kW.)結(jié)論(Conclusion)此例中，需4臺(tái)9352制動(dòng)斬波器，每臺(tái)9352需配備6支各18Q的電阻組成的電阻橋做為制動(dòng)電阻。(Atotalof4brakingchoppers9352areneeded.Eachchopperreceivesaresistornetworkwithsix18Qresistors.)Product-SupportProduct-Support傳動(dòng)軸(Spindle)計(jì)算轉(zhuǎn)動(dòng)慣量Calculationofthemomentofinertia一部分轉(zhuǎn)動(dòng)慣量產(chǎn)生于傳動(dòng)軸的幾何形狀：(Momentofinertiaarisingfromthegeometryofthespindle)傳動(dòng)軸用于圓柱體傳動(dòng)時(shí)：(Forasolidcylinderapplies)(4.23)(4.24).兀(4.23)(4.24)J=——?d4?l?pS32s.該固體為鋼質(zhì)時(shí)：(Forsteelapplies)J=123?10-9?r4?l=123?10-9?(14mm)4?900mmS=4.25kgcm2另一部分轉(zhuǎn)動(dòng)慣量產(chǎn)生于負(fù)載質(zhì)量及傳動(dòng)軸與其軸閂之間的摩擦：(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總轉(zhuǎn)軸慣量為：(Asaresult,thetotalmomentofinertiaisasfollows)

Product-SupportProduct-Support運(yùn)動(dòng)學(xué)分析：(Kinematics)運(yùn)動(dòng)中的數(shù)據(jù)進(jìn)行計(jì)算。本例中的速度曲線如下圖所示，由于該曲線在往復(fù)過程中是一致的，故在此僅對(duì)前向運(yùn)動(dòng)中的數(shù)據(jù)進(jìn)行計(jì)算。(Thediagramshowsthespeedprofileoftheapplication.Sincetheprofileisthesameforforwardandbackwarddriving,itissufficienttoexamineforwarddrivingonly.)求加速及延遲時(shí)間：(Calculationofaccelerationanddelay)v——maxt1v——maxt10.2m-8-=0.6667—0.3ss2(4.29)隱藏距離：(Distancecovered)11m——?a?11m——?a?12——?0.6667—?212=0.03m(4.30)s2這段距離需用這說明在恒定傳動(dòng)中存在0.18m的隱藏距離，傳動(dòng)速度為12m/min時(shí)，這段距離需用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)圖中各段時(shí)間為：t1=0.3st2=0.9st3=0.3st4=0.1sT=1.6s。(Theindividualtimesare:t1=0.3st2=0.9st3=0.3st4=0.1sT=1.6s.)線速度與角速度的轉(zhuǎn)換為：(Thetranslatoryvariablesaretransferredtotherotatoryvariablesasfollows)3—2?兀(4.32)aa—2?兀?_h(4.33)因而，角速度為：(Asaresult,theangularvelocityisasfollows)0.2m1v13—2?兀?-max—2?兀?——125.66—h0.01ms(4.34)又因?yàn)樵摻撬俣葘?duì)應(yīng)轉(zhuǎn)速為n=1200rev/min。(Thiscorrespondstoaspeedofn=1200rev./min)Product-SupportProduct-Support因此，該角速度為：(Asaresult,theangularvelocityisasfollows:)a0,6667m/s2a=2?a0,6667m/s2a=2?兀?一二2?兀?0,01m=418,91/s2(4.35)動(dòng)態(tài)傳遞轉(zhuǎn)矩如下式計(jì)算：Mdyn(Thedynamicprocesstorqueiscalculatedasfollows)=J?a=0.004225kgm2?418.9—=1.77Nmgess2(4.36)首先，靜態(tài)轉(zhuǎn)矩為：(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)制過過程中，靜態(tài)轉(zhuǎn)矩可用下式求出：torque)制過過程中，靜態(tài)轉(zhuǎn)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)傳動(dòng)軸功效可按下式計(jì)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)時(shí)間(Period)(4.42)(4.43)(Thecalculatedvaluesforthetotaltorquearelistedbelow)時(shí)間(Period)t[s]轉(zhuǎn)矩(Torque)Mtotal[Nm]t1=0.3M1=2.28t2=0.9M2=0.51t3=0.3M3=-1.34t4=0.1M4=0摩擦系數(shù)取決于傳動(dòng)軸的類型(Lenzeformulacollection,s=0.01)。[Thefrictioncoefficientofthespindleresultsfromthespindletype(Lenzeformulacollection,人=0.01).]總傳遞扭矩為動(dòng)態(tài)轉(zhuǎn)矩與靜態(tài)轉(zhuǎn)矩之和。(Thetotalprocesstorquecanbefoundbyaddingthedynamicandthestationarycomponents.)M(t)=M(t)+M(t)totaldynstat其對(duì)應(yīng)的功率為：(Thecorrespondingprocesspower)P(t)=M(t)-3(t)totaltotal總傳遞轉(zhuǎn)矩的計(jì)算值如下所示：有效轉(zhuǎn)矩取決于所選電機(jī)。(Theeffectivetorqueisrelevantforselectingamotor.)

Product-Support；M2?t+M2?t+M2?t+M2?tM=.■—1——12~23——34——(4.44)eff\T根據(jù)上表中數(shù)據(jù)：T=1.6s；Meff=1.21Nm。(IfthevaluesshowninthetableareusedwithT=1.6s:Meff=1.21Nm.)所選電機(jī)為：(Selectionofthemotor)電源電壓230丫，角型連接的MDFMA71-12電機(jī)。理由：其額定轉(zhuǎn)矩大于本例中所需之有效轉(zhuǎn)矩，額定轉(zhuǎn)速明顯大于本例中所需傳遞速度。(MDFMA71-12becausetheratedtorqueishigherthantheeffectivetorqueoftheapplication.Theratedspeedisslightlyhigherthantherequestedprocessspeed.Themotorisdelta-connectedwith230V.)電機(jī)型號(hào)(Motortype)軸高(Axis)heighth(mm)額定轉(zhuǎn)速(Speed)nr(min-1)額定轉(zhuǎn)矩(Torque)Mr(Nm)額定功率(Power)Pr(kW)額定電流(Current)I(A)電源電壓(Connection)VoltageV(V)額定頻率(Frequency)(Hz)MDXMA7112711355/1.5400/23050電機(jī)型號(hào)(Motortype)功率因子(Power)功效(Efficiency)堵轉(zhuǎn)轉(zhuǎn)矩(StallTorque)張緊轉(zhuǎn)矩(TighteningTorque)啟始電流(StartingCurrent)轉(zhuǎn)動(dòng)慣量(Momentofinertia)重量(Weight)factorMrMAIA/IrJMcos①n(Nm)(Nm)(kgm2)(kg)MDXMA71120.700.60.00065.9校核電機(jī)負(fù)載能力Checkofmotorloadcapacity:由于電機(jī)轉(zhuǎn)矩，會(huì)產(chǎn)生較高的動(dòng)態(tài)應(yīng)力。behigher.)(Owingtothetorqueofthemotor,thedynamicstresswill(4.45)(4.46)因此，可按下式求出新的動(dòng)態(tài)轉(zhuǎn)矩：(Thenew(4.45)(4.46)因此，可按下式求出新的動(dòng)態(tài)轉(zhuǎn)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，總轉(zhuǎn)矩如下表所示：(Asaresult,thetotaltorqueisasfollows)時(shí)間(Period)t[s]轉(zhuǎn)矩(Torque)Mtotal[Nm]t1=0.3M1=2.53t2=0.9M2=0.51t3=0.3M3=-1.59t4=0.1M4=0有效轉(zhuǎn)矩為：(Theeffectivetorqueisasfollows)Meff=1.35NmProduct-Support在計(jì)算電流值時(shí)，應(yīng)進(jìn)一步校核負(fù)載能力。(Loadcapacitycanandshouldbeexaminedmoredetailedwhencalculatingthecurrent.)此時(shí)，應(yīng)根據(jù)轉(zhuǎn)矩曲線求電流曲線。profile.)(Inthiscase,thecurrentprofileiscalculatedfromthetorque電流Ia,r及If,r得自額定數(shù)據(jù)。(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根據(jù)下表的等式，可由轉(zhuǎn)矩求出有效電流。(Owingtothefollowinggeneralrelation,thecorrespondingeffectivecurrentcanbecalculatedfromthetorqueM.)MIra,r(4.51)總電流為：(Thetotalcurrentcanbecalculatedasfollows)(4.52)時(shí)間(Time)t[s]轉(zhuǎn)矩(Torque)Mtotal[Nm]有效電流(Activecurrent)L[A]盲電流(Blindcurrent)If,N[A]總電流(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以上小結(jié)如下：(Thisresultsinthefollowingvalues)電機(jī)有效電流1tota[,eff=1-33A。(TheeffectivemotorcurrentiscalculatedwithItotaleff=1.33A.)電機(jī)未過載。(Themotorisnotoverloaded.)Product-Support首先，可根據(jù)電機(jī)額定功率進(jìn)行粗選。選擇變頻器Selectionofthefrequencyinverter:首先，可根據(jù)電機(jī)額定功率進(jìn)行粗選。(Whenselectingthefrequencyinverter,itispossibletomakearoughselectionbasedontheratedmotorpower.)但是，應(yīng)仔細(xì)計(jì)算電機(jī)平均電流(算術(shù)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求制動(dòng)電阻：斬波頻率為8kHz時(shí)，選E82EV251_2B就足夠了，且不會(huì)造成過載。(Withachopperfre