Post on 25-May-2018
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Key information May2010edition/subjecttochange
maxon DC motor and maxon EC motorKeyinformation
The motor as an energy converter
TheelectricalmotorconvertselectricalpowerPel(currentIandvoltageU)intomechanicalpowerPmech(speednandtorqueM).Thelossesthatarisearedividedintofrictionallosses,attributabletoPmechandinJoulepowerlossesPJofthewinding(resistanceR).IronlossesdonotoccurinthecorelessmaxonDCmotors.InmaxonECmotors,theyaretreatedfor-mallylikeanadditionalfrictiontorque.Thepowerbalancecanthereforebeformulatedas:
Thedetailedresultisasfollows
Electromechanical motor constantsThegeometricarrangementofthemagneticcircuitandwindingdefinesindetailhowthemotorconvertstheelectricalinputpower(current,voltage)intomechanicaloutputpower(speed,torque).Twoimportantcharac-teristicvaluesofthisenergyconversionarethespeedconstantknandthetorqueconstantkM.ThespeedconstantcombinesthespeednwiththevoltageinducedinthewindingUind(=EMF).Uindisproportionaltothespeed;thefollowingapplies:
Similarly,thetorqueconstantlinksthemechanicaltorqueMwiththeelectricalcurrentI.
Themainpointofthisproportionalityisthattorqueandcurrentareequivalentforthemaxonmotor.Thecurrentaxisinthemotordiagramsisthereforeshownasparalleltothetorqueaxisaswell.
Seealso:Technology–shortandtothepoint,explanationofthemotor
Motor diagrams
AdiagramcanbedrawnforeverymaxonDCandECmotor,fromwhichkeymotordatacanbetaken.Althoughtolerancesandtemperatureinfluencesarenottakenintoconsideration,thevaluesaresufficientforafirstestimationinmostapplications.Inthediagram,speedn,currentI,poweroutputP2andefficiencyhareappliedasafunctionoftorqueMatconstantvoltageU.
Speed-torque lineThiscurvedescribesthemechanicalbehaviorofthemotorataconstantvoltageU:– Speeddecreaseslinearlywithincreasingtorque.– Thefasterthemotorturns,thelesstorqueitcanprovide.Thecurvecanbedescribedwiththehelpofthetwoendpoints,no-loadspeedn0andstalltorqueMH(cf.lines2and7inthemotordata).DCmotorscanbeoperatedatanyvoltage.No-loadspeedandstalltorquechangeproportionallytotheappliedvoltage.Thisisequivalenttoaparallelshiftofthespeed-torquelineinthediagram.Betweentheno-loadspeedandvoltage,thefollowingproportionalityappliesingoodapproximation
whereknisthespeedconstant(line13ofthemotordata).
Independentofthevoltage,thespeed-torquelineisdescribedmostprac-ticallybytheslopeorgradientofthecurve(line14ofthemotordata).
Derivation of the speed-torque lineThefollowingoccursifonereplacescurrentI withtorqueMusingthetorqueconstantinthedetailedpowerbalance:
TransformedandtakingaccountofthecloserelationshipofkMandkn,anequationisproducedofastraightlinebetweenspeednandtorqueM.
orwiththegradientandtheno-loadspeedn0
UnitsInallformulas,thevariablesaretobeusedintheunitsaccordingtothecatalog(cf.physicalvariablesandtheirunitsonpage42).42).).
Thefollowingappliesinparticular:– AlltorquesinmNm– AllcurrentsinA(evenno-loadcurrents)– Speeds(rpm)insteadofangularvelocity(rad/s)
Motor constantsSpeedconstantknandtorqueconstantkMarenotindependentofoneanother.Thefollowingapplies:
Thespeedconstantisalsocalledspecificspeed.Specificvoltage,generatororvoltageconstantsaremainlythereciprocalvalueofthespeedconstantanddescribethevoltageinducedinthemotorperspeed.Thetorqueconstantisalsocalledspecifictorque.Therecip-rocalvalueiscalledspecificcurrentorcurrentconstant.
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