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Chapter 6

DC machinepart 1ELECTRICAL MACHINESDr. Radu Bojoi & Prof. Maurizio RepettoPolitecnico di Torino Dip. Ingegneria Elettrica

*contentsmachine structureinductor windingworking principlecomputation of emf and torqueequivalent circuitelectro-mechanical characteristicsseparately excited machineself-excited series machineDC machine efficiencycommutation

*machine structureDC electrical machine can alternativelywork as a motor by converting in mechanical power the power received from a DC supply sourceorwork as a generator converting in DC electrical power the power received at its shaft by a prime source of mechanical power

*while the use as generator is seldom found, DC electrical machines are widely used in electrical traction for tramways, subways, trains etc.

machine structure

*speed regulation of tooling machinesrobotics for small powerautomotive (starters, central locking system and other servo-mechanisms )machine structure

*DC machines are slowly replaced by AC machines which are more robusta particular kind of DC machine (universal motor) can be used also with AC supply and this fact is important for household applicationsmachine structure

*DC machine is made by three parts:inductor winding on the fixed part of the machineinduced winding on the rotating parttsegmented commutator for supplying induced windingStatorRotorCommutatormachine structure

*DC machine needs the creation of a static magnetic flux which, interacting with the moving parts, can give rise to emf and forcesrotor

Inductor winding

*for small machines the excitation field can be created also by permanent magnetsthe number of poles (couple of poles) can be varying from 2 to 10pole width= angular width of a poleNp = number of polesInductor winding

*excitation by windingpole width = 90excitation by surface permanent magnetsDC machine with 4 polesSSNNNSMagnetInductor winding

*by considering a 2-poles machine, the space distribution of magnetic field isRotore

NSmagnetic field lineStatore

neutral axis

polar axis

Ampre theoremNelg air gap lengthNeInductor winding

*if no magnetic saturation occurs[ A/m]magnetic flux density can be considered almost constant under poles while it goes quickly to zero outside them. On the neutral axis the field is zero[T]stator and rotor form a magnetic circuitInductor winding

*by considering the air gap length as a constant and Bt >0 under N pole Bt

*working principleputting a conductor on the rotor surface its interaction with magnetic flux density gives rise to two effects caused by Lorentz laws:

forces on currents immersed in magnetic field

if the conductor is turning, electromotive forces induced at terminals of conductor moving through the magnetic field

*considering a two poles machine, a rectangular winding with current Ia is placed on the rotor (for sake of simplicity rotor iron has not been drawn)Lorentz law imposes that a force is created on the two pieces of winding parallel to the rotation axis (1) and (1)NSBtIa11working principle

*mechanical force (Lorentz):Bg gap inductionl axial length of conductor

machine cross section: field line are drawn not considering magnetic field created by Ia[N]mechanical torquer radius of turn[Nm]working principle

*mechanical torque makes the rotor turningSNSFF111NFF1working principle

*SNwhen the neutral axis is reached the force becomes zero because Bg=0if by inertia the winding goes beyod the neutral axis, a negative torque will bring it again to the zero force positionSNF1111Fworking principle

*in order to make the machine turning, the torque should not invert its sign, this can be obtained by changing the sign of the currentneutral axis

working principle

*NSBIa11L1L2SNRotor11IaL1L2I1-1practically, current inversion is obtained by a sliding contact: a segmented commutator L1-L2 solidal with the rotor in contact with static conducting parts (brushes)working principle

*current changing sign sequenceI1-1 commutation of current (always in upper part of rotor and in the lower one) allows to keep a unidirectional torqueworking principle

*if a winding not supplied is put in rotation by an external torque, induced motional emf appear at the winding terminalsworking principle

* winding angular speedBg magnetic flux density at the air gapl axial length of conductorstotal emf at the winding terminals is[V]emf has the same sign of B so it is alternatedworking principle

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0

180

360

90

270

E1-1

induced emf at winding terminalsworking principle

*if winding is connected with the same system of commutation introduced in the previous case, voltage becomes unidirectionalSN11L1L2SN11L2L1SNL111L2+-+---++ABABAB=0working principle

*by considering the angular speed as positive, emf has the following behavior

0

180

360

90

270

EAB

by changing the sign of the angular speed polarity of emf changesEAB voltage is unidirectional with two pulses per revolutionworking principle

*segmented commutator acts as a mechanical rectifiertwo times for each revolution the brushes short circuit the winding creating a short circuit current during commutationto avoid these high currents, commutation must be made when emf is zero so when the winding is along the neutral axis of the machine (B=0 E=0) working principle

*armature winding and commutatorif more than one winding is set under the pole, both forces and emf-s can be increasedso the induced (armature) winding of a DC machine is made by many coils placed in slots on the rotor, all coils make the armature winding

*rotor iron is made by lamination because, due to turning, it is subject to an alternating flux and so hysteresis and eddy currents are present even if exciting field is statictoothslotslottootharmature winding and commutator

*the segmented commutator allows the supply of the armature winding by means of the contact between segments and brushesbrushes made in graphite (soft material) in order to reduce mechnical stress on segmentsarmature winding and commutator

*construction of rotor with terminals of rotor winding ready to be soldered on the segmented commutatorarmature winding and commutatorsegmented commutator

*technically more than one layer of conductors is placed in the slotupper layerlower layercommutatoractive parts of windingsfront connectionsarmature winding and commutator

*1234NSslotsneutral axis

building example of a 2 poles machine with 4 turns (8 active conductors)armature winding and commutator

*parallel working of the machine112233441234NSIaS1S2neutral axis

S1S211224433IaAB0.5Ia0.5IaEa = 0E emf induced in one turnarmature winding and commutator

*22331144NSIaS1S2S1S211224433+-+-IaAB0.5Ia0.5Ia1234 = 45neutral axis

Eaarmature winding and commutator

*112233441234NSIaS1S2S1S211224433IaAB0.5Ia0.5Ia = 90neutral axis

Eaarmature winding and commutator

*22331144NSIaS1S2S1S211224433+-+-IaAB0.5Ia0.5Ia1234 = 135neutral axis

Eaarmature winding and commutator

*112233441234NSIaS1S2S1S211224433IaAB0.5Ia0.5Ia = 180neutral axis

Eaarmature winding and commutator

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0

180

360

90

270

Ea

45

135

225

315

the induced voltage does not fall to zero but at of the maximum valueemf is doubled with respect to the case of one winding4 pulses per periodarmature winding and commutator

*in a first approximation (neglecting dynamic effects due to commutation and voltage drop on brushes) the model of the machine becomes:S1S2IaAB0.5Ia0.5Ia+-+-+-+-+-+-current always finds two ways Ea

torque and emf computation

*if the armature winding has Z active conductors:total torque produced:[Nm][V]emf induced in one turnnumber of turns per current waycurrent in one internal waytorque and emf computation

*the value of computed emf is valid only if the magnetic flux density B is uniform under the whole poleactually this fact is not exactly true due to effect of slots (air gap is not uniform) reaction of the armatureas a result B is not uniform under pole expansion

torque and emf computationefficient B at the gap

*slot effectthe effect is a lowering of B and an effect of non constant torque produced (vibration problems)torque and emf computation

*armature reactionneutral axisBt,induceda090180270atorque and emf computation

*if magnetic material is linear, superposition of effects holdsneutral axisBt,risaaBt,ris,media090180270torque and emf computation

*the new behavior can be used to define an average value of B under the pole090180270aBt,ris,media()360Bt,media(0-)torque and emf computation

*this value can be used to compute the flux through the rotorneutral axis

NuBt,ris,media()RotorRotorflux linerotor surface

torque and emf computationneutral axis

*this value of average magnetic flux density can be used in the formulas for the evaluation of torque and of emf[V][Nm] Ea and T are average values of emf and of torquetorque and emf computation

*in the most general case of a machine with p couples of poles and with a internal ways for current[V][Nm] winding constantu average flux at air gap per polefundamental equations for evaluation of machine performancestorque and emf computation

*in this way flux depends on Iecc and on Iaexcitation windingarmature reactionif armature reaction can be neglected or it is canceled out by some suitable modification to the magnetic circuit, thentorque and emf computation

*BABAIaRaLaEaIaVadynamic circuit for a two-poles machine becomesS1S2IaAB0.5Ia0.5Ia+-+-+-+-+-+-E+- La armature inductance Ra armature resistance++Vamachine equivalent circuit

*IaRaLaEain steady state Ia = cost. brushes voltage drops are usually negligibleDCIa = cost.IaRaEaVaVaArmatureVaIa+-+-++machine equivalent circuit

*equivalent circuit for excitation windingIeccReccLMDCIecc = cost.IeccReccVeccVeccfieldVeccIecc+-+- LM excitation winding inductance Recc excitation winding resistancemachine equivalent circuit

*electro-mechanical conversionelectro-mecahnical conversion in one DC machine, is ruled by the following equation:emf sign depends on the sign of wtorque sign

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DC machineTEaIaelectrical powermechanical powerConversionTEaIaworking as motorworking as generator (brake)electro-mechanical conversion

DC machineelectrical powermechanical powerConversion

*since and Ea are proportional as well as T and Ia characteristics can be drawn in both plane which are coincident a part some constantsTIaEamotormotorgenerator (brake)0electro-mechanical conversiongenerator (brake)

*electro-mechanical cahracteristics: all curves linking torque and angular speed, efficiency as function of speed etc.DC machine is nowadays seldom used as generator so the study of its working as a motor will be privilegedin a DC machine armature and excitation coils can be independent or connectd, in this last case the machine is often called as self-excited. electro-mechanical characteristics

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