dc machines - montefiore institute · dc machines 1 dc machines...
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DC machines 1
DC machines
Transforms mechanical energy into electricenergy with DC voltage and current (DC generator or dynamo), or conversely (DC motor)
ball bearing
ball bearing brush
brush holder
stator (inductor)collector
rotor (armature)
29/05/2020
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DC generators
Armature or rotor : • stack of thin magnetic sheets (some tenth of a mm)
(perpendicular to the machine axis to reduce eddycurrents) ...
• ... supporting conductors in which electromotiveforces (e.m.f.s) appear when the armature rotates(e = v ´ b) ...
• ... these e.m.f.s are time-varying and change signeach time the collector crosses a neutral line (bissector between 2 successive poles)
Inductor or stator: 2p poles withexcitation windings carrying DC current
Magnetic circuit:stator + rotor + airgap
2 poles
4 poles
Collector: copper strips isolated from each other, and connected to equidistant points of the armature winding. Fixed brushes slide on the collector and rectify (mechanically) the e.m.f.s
DC machines
3
No-load characteristic
Variation of the voltage Ev as a function of theexcitation current Ie, at constant speed and with nodelivered current
îíì
==q
=0I
constantevitesseavec)I(fE
aev
!
No-load characteristic
)I(kE evEv Fq= !
Magnetic fluxproduced by the inductor andseen by the armature winding
Nonlinear with hysteresis
(3) Increasing Ie
(2) Decreasing Ie
(1) First magnetization
DC machines
constant speed with
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Armature reaction
Magnetic phenomena due to the currents in the armature
Armature reaction (magnetic)
)I(EE av y-=
)I(k)I( aEa DFq=y !
+ =Inducto
r field
1. Neutral line shifted(rotated) in the rotation directionÞ decrease of the e.m.f.
2. Local magnetic field reduction (entry part) and increase (exit part) not compensated due to nonlinearityÞ flux and e.m.f. reduction (+ incr. pmag)
armature fie
ld
Total field
e.m.f. with load1. and 2. armature reaction
DC machines
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Armature reaction
aaaa IR)I()I( +y=Y
Total armature reaction
Compensatingwinding
disadvantages:• for a single value of Ia• shift direction depends on
rotation direction• shift direction depends on
operating mode (generator or motor)
Shift of the brushes w.r.t. neutral axis
Reduction of the armature reaction
DC machines
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Exterior characteristics
Variation of delivered voltage U in terms of thedelivered current I, at constant speed and excitationcircuit
îíì =q
=invariable excitationd'circuit
constantevitesseavec)I(fU
!
Exterior characteristic of a generator
Excitation type...
seriesindependent shunt compound
inductor
armature
DC machines
withfixed excitation circuit
constantspeed
e
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Independent excitation generator
IR)I()I(EUII
aev
a-y-=
=
Ra » 0.1 W (110V/50A machine)Compensated armature reaction
Delivered voltage quasi independentof delivered current® Voltage source
+ Y(Ie) ... max. in the magnetizationcurve corner
Excitation current Ie modification Speed modification
IR)I()I( a+y=Y
DC machines
e
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Series excitation generator
Speed modification
Rs << since Ie = I is highcoherent: section >, ns <
Quasi-linear
U almost fixed
I almost constant
Current source
usefulzone
Inductor shunting
( )IRR)I()I( sa ++y=Y
( )IRR)I()I(EUIII
savea
+-y-===
DC machines
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Shunt excitation generator
ed
aaaev
ea
IRUIR)I()I(EU
III
=-y-=
-=
Rd >> to reduce Joule lossesIe < Þ ns >
Picou construction
daea
212e1e
2v1vedaa
1a
eed
aev
RUIIII
UetUIetIEetEIR)I()I()pointparpointprocédure(IPour
)I(UIRconnus)I(et)I(E
-=-=
®®º+Y®Y®
=Y
IR)I()I( aaa +y=Y
no-load
short-circuit
DC machines
known
For (point by point procedure)&
& &
&
10
... the voltage varies however more than for the generator withindependent excitation
Shunt excitation generatorExterior characteristic
Operating point of the generator driving a resitance R
Delivered voltage almost independent of the delivered current® Voltage source
DC machines
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Shunt excitation generatorSpeed modification Excitation circuit modification
Effect of hysteresis
Short-circuit current
2 branches : Ie increasing and decreasing
If the speed is too low of if Rd is too large® no operating point
DC machines
12
Compound excitation generatorMixed excitation: shunt inductor and seriesinductor wound on the same poles
(1) antagonist compound (opposite m.m.f.)(2) shunt dynamo(3) concordant compound (same direction m.m.f.)(4) hypercompound (ns >>)
fdad
sedased InInnInInIn.m.m.f =÷÷
ø
öççè
æ±=±=
÷÷ø
öççè
æ==
Y-=
ad
sfded
afv
InnIRIRU
)I()I(EU
!
÷÷ø
öççè
æ+Y= a
d
sfdafv InnIR)I()I(E !
DC machines
m.m.f.
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Self-starting generator
Self-starting is possible thanks to the remanentmagnetization of the inductor
Condition:Rd+Ra not too large!
yesyes
no
Example: shunt generator
Operatingpoint
DC machines
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If E decreasesÞ the generator receives energy (motor for shunt and compound machines!)
DC network connection
Conditions :E » UE and U in opposition
a
aea R
U)I,I(EI -=
After connexion (1) :
If E <<, Ia >> !
Then, increase E (2)Þ the generator produces energy
operating point
Slope should be large (to reduce the currentvariations dues to voltage perturbations)Þ compound antagonist generator OK
DC machines
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DC motorsMain principle
aa IREU +=
Total e.m.f. (E) on brushes is equal to the integral ofthe electromotive field along the armatureconductors
... in the armature conductors as soon as they rotate,opposed to the current
Electromotive force (e.m.f.)
The armature conductors are subjected to themagnetic flux density created by the inductor
Excitation current Ie and armature current Ia
... hence to the Laplace force bjf ´=
... hence to a torque that tends to make the armaturerotate
DC machines
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Armature reaction
aaaa IR)I()I( +y=Y
Total armature reaction
)I(EE av y-=
)I(k)I( aEa DFq=y !e.m.f. with loadarmature reaction
DC motor DC generator
aa IREU += aa IREU -=
aaaa IR)I()I( -y=Y
DC machines
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Motor torque
aaavaa IR)I(EIREU +y-=+=
( ) 2aaaav
2aaaa IRI)I(EIRIEIU +y-=+=aI´
Electric power provided to the armature
Joule losses in the armature
Electromagneticpower
q=
q= !!
aelm IEPC
Electromagnetic torque
[ ] aaevEaaeE I)I()I(kI)I,I(kC DF-F=F=
DC machines
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Mechanical characteristics
Motor speed in terms of the electromagnetic torque,with fixed voltage and excitation circuit
îíì =
=qinvariable excitationd'circuit
constanteUavec)C(f!
Machanical characteristic of a motor
Excitation type...
independent or shunt series compound
inductor
armature
!
DC machines
withconstant
fixed excitation circuit
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Shunt excitation motor
[ ])I,I(fC
I)I()I(kC
ae0
aaevE=
DF-F=
1)I(
)I()I()I,I(fev
aevae £
FDF-F
=
with
C0 = torque produced by the motorif there was no armature reaction
(Ie constant)
[ ] aaaevEaa IR)I()I(kIREU +DF-Fq=+= !
[ ] )I,I(f1
)I()I(kIRU
ae0
aevE
aa q=DF-F
-=q !!
)I(kIRU
evE
aa0 F
-=q!
aevE0 I)I(kC F=
Speed almost independentof torque
DC machines
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Shunt excitation motor
Influence of Ie
Stable and unstable zones
Small perturbation: e.g. speed increase
From P:motor torque P'' < resisting torque P'Þ speed decreases, back to P Þ stable
From Q:motor torque Q'' > resisting torque Q'Þ speed increases! Þ unstable
Limited speed range (saturation)DC machines
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Shunt excitation motor
Influence of the voltage U
Poor efficiency!
+ power electronics...
)I(kU
evE F»q!
High dynamic torque control (since la <<)
DC machines
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Series excitation motor
( ) asaaE
aaE
IRR)I(kUI)I(kC
++Fq=
F=!
( ) asaaME
2aME
IRRIkU
IkC
++ql»
l»!
Non saturatedmachine
Saturated machine
( ) asaSE
aSE
IRRkU
IkC
++qF»
F»!
sa
SESE RR
kUkC+
qF-F»
!
No loadÞ runaway!
Maximumcurrent !
( ) 2
2
ME2
saME
2
MEU
k1
RRk
UkCql
»++ql
l»!!
DC machines
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Series excitation motor
Influence of the voltage source UShunting the inductor
+ power electronics...
aa'ss
's
e IIRR
RI £+
=
)I(II'I)I( aaMaMeMe F=l£l=l»F
MM'ss
's
MRR
R' l£l+
=l
Typical useElectric traction and lifts (large startup torque)
DC machines
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Series excitation motor
BrakingaaE I)I(kC F=
Change the sign of the torque to work as a brake
Electric power changes sign(recovers energy)
DC machines
Different modes
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Compound excitation motor
Mixed excitation: shunt and series inductor woundon the same poles
fd
ad
sed
ased
In
InnIn
InIn.m.m.f
=
÷÷ø
öççè
æ±=
±=
DC machines
m.m.f.
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DC motor startup
>>=a
a RUI
a
E
aa R
kUREUI Fq-=
-=
!
Shunt motor Series motor
Zero speed at startup Þ zero e.m.f. E
Induced current Ia limited only by the armature resistance Ra
Startup rheostat(value progressively reduceddown to short-circuit)
Startup rheostat in series with the armature (to limit Ia) (One allows Ias = 1.5 Ian)
DC machines
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Inverting the rotation direction
aeE I)I(kC F=
Shunt motor Series motor
Modify the direction of the current in theexcitation circuit w.r.t. the rotor
Torque changes sign
Samedirection
Oppositedirection
DC machines
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Losses in DC machines! Mechanical losses
– friction losses in bearings (÷ v) (v = speed)– windage losses (÷ v2)– friction losses from brushes on the collector (÷ v)
! Magnetic losses– eddy current losses in armature (÷ v2, ÷ bmax
2)– hysteresis losses in armature (÷ v, ÷ bmax
1.5 ® 2)
! Electric losses– Joule losses in armature, inductor and brushes (÷ I2, function of
temperature)
! Supplementary losses– due to skin effect in the rotor and sparks at brushes/collector contact– increased magnetic losses due to the magnetic reaction
DC machines