abb变频器的计算公式

ABBAutomationTechnicalguideNo.7-Basicformulas基本公式Roadshow3JukkaJuottonenABBAutomationPage2TechnicalguideNo.7-BasicformulasPurposeofthepresentation内容Showthetypicalformulasusedinbasicdimensioning说明基本选型公式Thetargetsofthepresentationarethatyou:目的Candoalsomanualcalculationsofbasicdynamicalsystems(e.g.accelerationtime)动态系统的手工计算Purposeandtargetsofthepresentation内容和目的ABBAutomationPage3TechnicalguideNo.7-BasicformulasMotor’smechanicaloutputpowercanbecalculatedfromspeedandtorque:通过速度和力矩计算电机的输出功率ACmotor-Power交流电机的功率9550m]T[Nm]*n[rp[kW]PoutMotor’sinputpowercanbecalculatedfromvoltage,currentandpowerfactor:通过电压，电流和功率因数计算电机输入功率)cos(*][*][*3][AIVUWPins][radT[Nm]*[W]Pout/][*602/rpmns][radWkW10001ABBAutomationPage4TechnicalguideNo.7-BasicformulasMotor’sefficiencyisoutputpowerdividedbyinputpower:电机效率是输出功率/输入功率ACmotor-Power交流电机的功率inoutPPAtnominalpointACmotor’soutputpoweris:电机额定点的输出功率nnnnnoutAIVUWPWP*)cos(*][*][*3][][orElectricpowerinput电磁功率输入Mechanicalpoweroutput机械功率输出Thermalpowerlosses热损耗9550][[rpm][Nm]*nT[kW]PkWPnnnout轴头电功率轴头机械功率ABBAutomationPage5TechnicalguideNo.7-BasicformulasOneofthefundamentalequationsforanelectricmotoris:电机转子的加速规律ACmotor-MechanicallawsofrotationalmotionAC电机的转动原理loadTTdtdJMotortorqueconsistsofdynamicandloadcomponent.Dynamiccomponentchangesthespeed:电机力矩包含动态力矩分量和负载力矩分量loaddynTTTTorqueSpeedABBAutomationPage6TechnicalguideNo.7-BasicformulasDynamictorquecomponentchangesthemotorspeed:动态力矩分量影响电机转速dtsraddkgmJNmTdyn]/[*][][2Inpracticethedynamiccomponentiscalculatedasfollows:动态分量的工程计算][][*602*][][2strpmnkgmJNmTdynThetotaltorqueneededinaccelerationisthus:加速过程中总的力矩是loadloaddynTstrpmnkgmJTTNmT][][*602*][][2ACmotor-MechanicallawsofrotationalmotionAC电机的转动原理ABBAutomationPage7TechnicalguideNo.7-BasicformulasExample:ACmotor’sandload’stotalmomentofinertiais3kgm2.Constantloadtorqueis50Nm.举例：电机和负载的总转动惯量是3kgm2，恒定负载力矩50NmA)Whatisthetorqueneededtoacceleratethemotorfrom0rpmto1000rpmspeedin10seconds?问题A)：电机转速在10秒内从0加速到1000rpm，需要多大力矩？B)Iftheelectricsupplyisswitchedoffat1000rpmspeedhowfastwillthemotordecelerateto0rpmspeed?问题B)：如果电机运行在1000rpm时，停止供电，那么电机减速至0rpm要多少时间？ACmotor-MechanicallawsofrotationalmotionAC电机的转动原理ABBAutomationPage8TechnicalguideNo.7-BasicformulasSolution:答案A)Thetotaltorqueneededforaccelerationisthesumofdynamicandloadcomponents.加速过程中总力矩是动态和负载力矩之和1060Nm.NmNm**TTTloaddyn48150100023B)Themotordeceleratesbecauseoftheloadtorque(50Nm)，Actualmotortorqueiszero.Then:减速过程中，仅靠负载力矩起作用(50Nm)，电机本身没有任何力矩起作用ACmotor-MechanicallawsofrotationalmotionAC电机的转动原理ssst28.6501000*602*3][loadTstrpmnkgmJ][][*602*][2ABBAutomationPage9TechnicalguideNo.7-BasicformulasMomentofinertia&gears惯性矩和齿轮箱的因素‘Inertia’(momentofinertia)isimportanttoknowinmanydimensioningcases.选型时必须知道惯性(转动惯量)。GenerallyJ[kgm2]canbegivenbymotorandmachinemanufacturers.制造厂通常给出转动惯量：J[kgm2]Sometimesitcanbecalculatedquiteeasily.Foracylindershapethemomentofinertiaisproportionaltomassandquadraticallyproportionaltoradiusofthecylinder:J=m*r2.转动惯量很容易计算。圆筒型的转动惯量与其质量和半径的平方成正比：J=m*r2Energystoredtoarotatingmassis:E=0.5*J*2旋转体储存的能量是：E=0.5*J*2ABBAutomationPage10TechnicalguideNo.7-BasicformulasMomentofinertia&gears惯性矩和齿轮箱的因素Whengearisusedpower,torque,momentofinertia,springconstantofashaft,etc.mustbereduced.使用齿轮箱时，功率，转矩，转动惯量，轴的弹性系数等必定会减小÷÷1221*nnTT21221*nnJJ21PPDirectionofenergy能量传递方向2nn12P1P2T1TABBAutomationPage11TechnicalguideNo.7-BasicformulasCalculationexample计算举例Afanhasfollowingloadcharacteristics一个风机有如下的负载特性20.012.98.69.114.422.532.444.157.672.990.001020304050607080901000102030405060708090100Speed(%)Torque(%)ABBAutomationPage12TechnicalguideNo.7-BasicformulasCalculationexample计算举例Afollowingmotorhasbeenselected:电机选型如下Pn=110kWUn=400VIn=202Acos(fn)=0.83nn=991rpmJmotor=5kgm2FansmomentofinertiaisJfan=995kgm2风机转动惯量：Jfan=995kgm2ABBAutomationPage13TechnicalguideNo.7-BasicformulasCalculationexample计算举例Task1:Whatisthenominaltorqueofthemotor?Whatisthenominalefficiencyofthemotor?电机的额定力矩是多少？电机的额定效率是多少？Task2:Estimatethestartingtimefrom0to100%speedifacceleratingisdonewithnominaltorque.如果以额定力矩加速，估算电机转速从0上升到100%的额定速度的起动时间。SolutionABBAutomationPage14TechnicalguideNo.7-BasicformulasCalculationexampleTask3:Estimatethedecelerationtimefrom100%to0%speedifitisassumedthattheaveragebrakingtorqueoverthewholespeedrange(ingeneratingmode,fluxbrakingisutilised)is4.5%.Hint:Dividethespeedrangeintosectorsandcalculatethetimesoverthesectors.