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7/26/2019 Fundamentos de mquinas elctricas DC
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MAQUINA CD 6 - 1
Captulo 6 LA MAQUINA DE CORRIENTE DIRECTA (CD)
6.1 FUNDAMENTOS DE LA MAQUINA DE CD
.
A ,
CD .
L CD
,
.
CD
: , .
E .
E ,
, 3
N-m/m ,
.
C 2
.
.
.
L 6.1 CD 6 .
L CD . ,
CD . D ,
.
.1
CD.
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MAQUINA CD 6 - 2
L 6.2 CD 4 ,
:
C ()
B ()
( )
B
C
E , 0.35 0.6.
E ,
.
, , 3 :
E .
E
.
E ,
.
G 4.
2 ,
( 6.3), f k kN I H= =F .
.2
CD 4
D
D
I
C
E
C
D
A
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MAQUINA CD 6 - 3
fI , CD 2 kH ,
( )k kB H . E
, .
kH, CD 2 .
, 2 , .
.2
E ( )aI ,
. L aI RA ,
(A)
C ( 6.4), RA
.
E .
L 6.3 CD ( 0)aI =
p =
fI =
fV =
aV =
aI =
=
.
( )= R .
( )B ( ) .
C ,
( )gB ( 6.4).
.
CD .
/2p
/2p
/2pp
/2p
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MAQUINA CD 6 - 4
,
( )aB .
a gB B .
L 6.5
. L pB .
L 1v 2v (F 6.5)
.
E a (F 6.5) :
netap p aB A B x = =
A L I F 1= pB =
( )p ap a p a
d B xd d xe N B B v
dt dt dt
= = = =
(6.1)
L (6.1) .
A (6.1) 6.5, mv r=
.
D
CD .
.
.Bobina y conmutador
se mueven juntos
Escobillas fijas
Conmutador
o colector
Bobina del devanado de
armadura
x
pB m
a 1v 2v
cv
aV
( )gB
pB
pB
/2 3 /2 2
m
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MAQUINA CD 6 - 5
1 2 p a mv v B r= = (6.2)
a
( 6.5).
L 1v 2v ( 6.5) .
E ( 6.5) :
1 2 2c p a mv v v B r= + = (6.3)
D (6.3) cv ( )pB mt = ( 6.6).
6.5 6.6
:
20 m a ct V v
< < =
32 2m a c
t V v < < =
32
2m a ct V v < < =
D ( )aV 6.7.
E
6.6 CD.
C , ,/2 3 /2 =
( 0)cv = .
.
F 6.5.
.
CD
F 6.5.
cv
2 p a mB r
/2
3 /2
2 mt
2 p a mB r
aV
2 p a mB r
/2 3 /2 2 mt
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MAQUINA CD 6 - 6
L 6.7
.
E CD . L 6.8
4 . E 4 .
6.3,
( )B , ( ) .
L 6.9 ( )gB CD 6.8.
L 6.10 4 . E
. CD:
.
CD 4
.
.
D
CD 4
F 6.7.
aV
m
4v 1v 2v
3v
, 2
.
( )gB
pB
pB 2
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MAQUINA CD 6 - 7
C gB , , , ,1 2 3 4v v v v 4
, 90 ,
( 6.11).
A 2 6.8,
( )aV 4 :
1 220 m at V v v
< < = +
4 12 m at V v v < < = +
3 432m a
t V v v < < = +
.10
D
CD F 6.6.
.11
4
CD
F 6.8.
aV aIaI
4v 1v 2v 3v
m
2
32
52 2
1v
4v
3v
2v mt
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MAQUINA CD 6 - 8
2 332
2m at V v v < < = +
E ( )aV 6.12.
, 12 15,
,
, .
L 6.13 CD.
:
Z= (
).
a = ,
.
E :
[V]0a
a p a mI
ZE V B r
a== (6.4)
E (6.4) :
F... DC.
F.... DC.
.12
CD
F 6.8.
.1D
CD.
2 3
2 5
2 2
aV
mt
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MAQUINA CD 6 - 9
p
p , :
2 [Wb/m ](2 / )
p p
p
p a
BA r p
= =
(6.5)
(6.5) (6.4)
[V]2
p m p m
pZE K
a= =
(6.6)
[V-s/Wb]2
p ZK
a=
(6.7)
E K .../.
/A.
L 6.10 () , a p= .
,
, 2a= .
Ejemplo 6.1: L DC 4 54
.
. C ?
. C ...
. C 2 , , 54.
.C , 4a p= = . E 2 .
L:
2 54 108Z= =
A (6.7),
V-s/Wb4 108
17.192 2 4
p ZK
a
= = =
Tarea 6.1: E [lb-ft] [rad/s]
550
m mTHP
=
A W1 746HP= , 1.356 Tk k=
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MAQUINA CD 6 - 10
E CD
... ( )E aR ,
6.14 6.15.
, , (6.6)
2 : ( )p ( )m .
L aR
.
A aL ,
. .
E 6.14 ,
:
: m m mP T= : V F V mP T =
: F VT
: dT
: d aP E I=
: a aP V I=
D , 6.15 CD
.
.1
C
CD
.
.1
C
CD
.
aI
aV
E
d aP E I= m m mP T=
F VP
d
m
T
F VT
aR
mT
m m mP T= VP
m
mT
V dT T
aV
aR
E
d aP E I=
aI
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MAQUINA CD 6 - 11
L ,
a aP V I= m m mP T= .
L E 6.14 6.15
() (). A (6.6)
[W]d a p m aP E I K I= = (6.8)
L F VP
dP mP , :
Generador: Motor:d m F V d m F VP P P P P P= = + (6.9)
E :
[N-m]dd p am
PT K I= =
(6.10)
E (6.10) ... (6.7),
. , (6.10) /A.
E dT , m .
Ejemplo 6.2: L DC 6.1 Wb0.1p = ,
0.14aR = V200 .
D rpm1100 .
dT , (6.10)
dP, (6.8). L,
.... E (6.6) aI ,
6.15.
V17.19 0.1 1100 / 30 198.02p mE K= = =
L :
A200 198.02 14.140.14
aa
a
V EIR = = =
A (6.8) :
W198.02 14.14 2800d aP E I= = =
F, (6.10)
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MAQUINA CD 6 - 12
N-m2800
24.311100 / 30
dd
m
PT = = =
E 17.19K= 6.1:
N-m17.19 0.1 14.14 24.31d p aT K I= = =
A ,
d dT P , .
.TIPOS
CD
6.14 6.15.
L
CD, .
( 6.16)
E
E
L
( )f fI ( )I=F .
( ) fR .
E
CD.
.1
CD.
sN
Excitacin
serie
fN
Excitacin en
derivacin
Armadura
aIf
I1S 1F 2F 2S
fN sN
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MAQUINA CD 6 - 13
E ( )sN
fI ( )I=F . L
( ) f .
E ,
.
D 6.16,
5 CD:
CD .
CD .
CD .
CD
CD
E
CD, F 6.17.
(F 6.18).
.
.1
CD
.
.1
CD
,
.
a
aI
t aV V=
fR
fI
1F 2F
GEN
MOT
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MAQUINA CD 6 - 14
E CD ,
, F 6.19.
E CD , F 6.20
L CD
, F 6.21.
E
:
p f s = + (6.11)
.1
CD
.
.20
CD
.
.21
CD
.
fI
E2F 1F
a
aI LI
fI
f
R
t aV V=
GEN
MOT
GEN
MOT
E S S
aR
aI
sR
tVaV
GEN
MOT
E
2 1
aR
aI
s
tVaV f2F 1F
f s
LIGEN
MOT
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MAQUINA CD 6 - 15
L CD ,
,
F 6.22. D :
p f s = (6.12)
.
E 6.2 ,
.
E . E
, fE I . E
, ( )aI ,
( RA ).
CD
(), p fI . L (6.6) E p m .
m , fE I , .
L
(CC) ( ), .
.22
CD
.
.2C CC
CD,
.
fI
E
aR
0aI =
aV
fR
fI
1F 2F
constantem =
E
1S 2S
aR
sR
aV
s
aI
tVfR 2F 1F
f
LI
fI
GEN
MOT
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MAQUINA CD 6 - 16
CC CD
F 6.23. H
, aV E= ,
fI .
E 0f
I = ,
.
E CD ( )
... C
,
.
Ejemplo 6.3: L F 6.24 CC
CD V - rpm600 1200 , rpm1200 rpm800 .
E .
A (6.6), E p
22 2
1 1 1
p m m
p m m
KEE K
= =
(6.13)
p , ( )fI .
22 1
1
m
m
E E
=
(6.14)
.2
E
CC.
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MAQUINA CD 6 - 17
E (6.14) :
2 1 1
800 2
1200 3E E E= =
L F 6.24.
L . C
fE I , CD
.
E CD ,
, ( )aI .
L ( )aI , ( )a ( )p ,
,
(A).
L A CD
D .
.
L (L) ( )p , ...
. L F 6.25 L CD 2 .
E F 6.25 ( )d ( )q ,
. E
.2
L
CD .
Lnea neutram
d
q
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MAQUINA CD 6 - 18
.
L F 6.26 ( )a (A)
( )p CD.
E p , a
,
F 6.27, L CD
.
(F 6.27)
,
.
E ( )aI .
C ?
E
L, ...
( )E ( 6.6 6.7).
.2
C
CD
.
.2
I
CD
.
Lnea neutra
sin carga
Lnea neutra
con cargaLnea neutra
sin carga
Lnea neutra
con carga
a
p
a
Flujo polar
m
Flujo de armadura
Flujo resultante
reforzado
Flujo resultante
debilitado
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MAQUINA CD 6 - 19
L, ... 0E ,
, ,
.
E L
. E
CD .
, ,
.
, 6.28.
A A400 ,
200A.
C ,
. 800 50
, ( )ct :
s160
0.075800
vueltat = = s0.075 / 50 0.0015ct = =
A H0.1L = ,
.2
E
,
.
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MAQUINA CD 6 - 20
V3400
0.1 26.67 100.0015
gi
d iv L
d t= = =
A L ,
.
E ,
, .
E . ,
....
a a a mE V I R K= = (6.15)
L ( )
( )m . E ( )m m mP T= ,
, .E CD.
L F 6.29
CD, A.
.2
D
,
A.
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MAQUINA CD 6 - 21
E 3
L, A:
D .
I .
D .
H
, L .
E ,
.
, CD
, .
E ,
, A.
L F 6.30 ... CD
H ,
CD. E
.
.0
D
... CD,
.
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MAQUINA CD 6 - 22
L L,
, ( )aI ,
.
, (F 6.31).
L F 6.29 .
3 A: L ( 6.27),
( 6.28).
E 3 A, :
L,
.
,
.
, ,
, A (F 6.32). E
.
E ,
, A.
.1
F
.
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MAQUINA CD 6 - 23
...
F 6.33 fE I
, A. E
F 6.34.
.2
E
CD.
Lnea neutra no
desplazada con carga
.
E A
...
CD.
.
D
A CD.
constantem =
1F 2F
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MAQUINA CD 6 - 24
D tV
fI aI . E ... :
t a aE V I R= + (6.16)
.
E
,
CD CD .
, CD
, ,
. .
C 6.17 6.22
CD, .
L F 6.35 CD,
.
E
: en mP P= .
,
: en m f fP P V I= + .
E F 6.17 t LV I
F 6.36, .
L F 6.36 60600
ALAB, F 6.17,
0.25aR = F 6.34.
.
D
CD.
enP sal L LP V I=
F VP 2
a aI R
d aP E I=
excP
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MAQUINA CD 6 - 25
Ejemplo 6.4: L (CC) F 6.34 t LV I F 6.36.
: 600 100A,
A. 0.25a = .
A (6.16),
V600 100 0.25 625t a aE V I R= + = + =
0aI = F 6.34, A,
:
A1.6fI
A100aI = , A, :
A1.75fI
,
1.75 1.6100 9.4%
1.6
=
A. 5% 10%.
Ejemplo 6.5: L
F 6.17 0.4aR = 100fR = .
W600 rpm1200 . L (E / I)
rpm1200 F 6.24,
6.37. L 6.1.
.
C L aV I
CD
.
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MAQUINA CD 6 - 26
Tabla 6.1 Datos para generar la curva Ef v/s If
. D , rpm1500 ,
A1.0fI =
.E aI , mP ,
dT, A1.5fI = ,
rpm1200m = 15LR = .
. ALAB (E / I) , rpm1200
F 6.37. L :
>> Vtnom = 600; Pnom = 60e03; Ra = 0.4; Rf = 100; DProt = 600;
>> Ianom=Pnom/Vtnom; %corriente nominal
>> load curvaEIf % Carga valores de Ef v/s If
>> %inicialmente se guard como save(curvaEIf,E,If)
>> E=curvaEIf(:,1); If=curvaEIf(:,2);
.
C (E / I)
CD
,
rpm1200 .
I E I E I E I E
0,00 5,0000 0,80 415,3789 1,60 6250,0000 2,40 685,23080,05 33,7549 0,85 434,0303 1,65 632,3741 2,45 686,4170
0,10 62,5000 0,90 451,7487 1,70 639,1112 2,50 687,5000
0,15 91,1482 0,95 468,6036 1,75 645,2446 2,55 688,5133
0,20 119,6124 1,00 484,6643 1,80 650,8078 2,60 689,4902
0,25 147,8058 1,05 500,0000 1,85 655,8341 2,65 690,4641
0,30 175,6412 1,10 514,6684 1,90 660,3568 2,70 691,4684
0,35 203,0318 1,15 528,6799 1,95 664,4094 2,75 692,5363
0,40 229,8904 1,20 542,0331 2,00 668,0252 2,80 693,7014
0,45 256,1302 1,25 554,7267 2,05 671,2375 2,85 694,9970
0,50 281,6640 1,30 566,7594 2,10 674,0798 2,90 696,4563
0,55 306,4049 1,35 578,1297 2,15 676,5854 2,95 698,11290,60 330,2658 1,40 588,8365 2,20 678,7876 3,00 700,0000
0,65 353,1599 1,45 598,8782 2,25 680,7199
0,70 375,0000 1,50 608,2536 2,30 682,4157
0,75 395,7252 1,55 616,9613 2,35 683,9082
= 1200
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MAQUINA CD 6 - 27
A1.0fI = , F 6.37,
V1200 485E . ALAB V1200 484.66E = :
>> If1=1; E1=interp1(If,E,If1)
E1 = 484.6643
, (6.14):
V15001500
485 606.31200
tV E= = =
. rpm1200 F 6.37 A1.5fI = ,
V1200 608.5E . ALAB V1200 608.25E = :
>> If2=1.5; E2=interp1(If,E,If2)
E2 = 608.2536
L, F 6.17:
A608.5
39.510.4 15
a
a L
EI
R R= = =
+ +
A F 6.35,
:
kW HP30.6 608.5 39.51 10 24.64 33m F V aP P E I
= + = + =
C
kW2 2 324.64 (1.5) 100 1 0 24.87en m f fP P I R = + = + =
kW2 2 3( 39.51) 15 10 23.42sal a LP I R = = =
23.42100 100 94.17%
24.87
sal
en
P
P = = =
E :
N-m608.5 39.51
191.321 200 / 30
d ad
m m
P E IT
= = = =
. E
.
L (6.6),
:
( ) ( ) ( )g p g gd
e t K t K t Kdt
= = = (6.17)
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MAQUINA CD 6 - 28
E F 6.19
,
.
,
,
. E ...
F 6.38.
L A F 6.38, ,
fI
( )f fE I R R= + (6.18)
fR
(F 6.19). E tE V= .
C E:
. E .
L f ( 2)
. 2fR R R+ > , ... (F
6.39). E 2R ( )cR .
.
...
.
( )nomE
( )f nomI
v/st fV I v/s fE I
tf
f
VR R
I+ =
resE
Lnea de
resistencia de
campo
O
P
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MAQUINA CD 6 - 29
,
tV a aI R A.
6.19,
t LV I . ,
, :
A 1: ( )f nomI .
A 2: tV LI
A ,
, ( )f nomI ,
P 6.38, :
( )
( )
t nom
T f
f nom
VR R R
I= + = (6.19)
G ( )t nomV . , (6.19)
( )f nomI .
fE I ( 6.37), ( )f nomI
... ( )nomE , : 0LI = .
, F 6.19, ... ( )nomE
( )L nomI :
( ) ( ) ( ) ( ) ( ) ( )( )nom t nom a nom a t nom L nom f nom aE V I R V I I R= + = + + (6.20)
C ( )f nomI (6.20) (6.19),
( )f nomI
6.38. E 1 :
.
E
...
.
E
0E
1E
3E
fI
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MAQUINA CD 6 - 30
1. A 0fI = .
2. C a f LI I I= + .
3. A (6.20), ( )t L f aE V I I R= + +
4. C E fE I fI .
5. 2 4 fI .
, tV LI ,
fI . D , fI ,
LI , 2, :
1. A 1LI I= .
2. 1 ( )f f nomI I= , ... 1E fE I .
3. C 1fI 1E, :
1 1 1 1( )t L f aV E I I R= + (6.21)
4. C 2fI
12
tf
T
VI
R= (6.22)
5. 2 1f fI I tol ,
(6.21), 1LI ,
t LV I .
6. 2 1f fI I tol > , 1 2f fI I= 4. 6.
E tol (6.22)
.
, ALAB, F 6.40,
kW - V60 600 ,
0.25aR = .
t LV I ,
F 6.33, , en mP P= .
.0C t LV I
DC
.
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MAQUINA CD 6 - 31
E F 6.41, kW - V60 600 ,
kW3.06F VP = rpm1200 .
Tarea 6.2: Aplicando los 2 algoritmos sugeridos anteriormente, obtener las curvas mostradas en las
figuras 6.40 y 6.41.
Ejemplo 6.6: E F 6.19 rpm1200 ,
(CC) F 6.37. L
F 6.19 0.5a = , 200f = 160R= . C
... .
D F 6.37,
(CC)
, :
200 160 360fR R+ = + =
E F 6.42, ALAB,
CC .
B , :
V650E A650
1.81360
fI = =
ALAB ,
6.38. E :
A1.82fI = V653E= .
,
rpm1200 F 6.42. A1fI = V570E ,
570570
1cR =
.1C
DC
.
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MAQUINA CD 6 - 32
, ALAB
6 CC,
571cR = , .
. , CD ,
2 , tV :
CD CD
L CD ,
tV .
E CD,
, : m mT n LI . E
6.19 6.20.
D (6.10), ( )dT DC
( )p ( )aI :[N-m]d p aT K I= (6.23)
, :
[W]d aP E I= (6.24)
E .... , .
.2
C CC
DC
,
.
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MAQUINA CD 6 - 33
m ,
LI , (6.15): p mE K= , .... ( )E
.
E F 6.19, t a aE V I R=
t a am
p p
E V I R
K K
= =
(6.25)
E , (6.25)
sR:
( )t a a sm
p p
E V I R R
K K
+ = =
(6.26)
, (6.25) (6.26) 30 /m m= . A,
CD, LI aI .
m m mT P= , mP ,
F 6.43.
en t LP V I= . L
( )F VP .
E
[N-m] [N-m]d md mm m
P PT T= =
(6.27)
L ( )dP ( )mP (6.27),
F 6.43.
C (6.27) (6.25) (6.26),
m mT n DC ,
.
.F
DC.
en elecP P= sal mP P=
VP
d aP E I=
excP2
a aI R
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MAQUINA CD 6 - 34
E /
, F 6.44. L
ALAB DC HP - V - rpm80 600 1200 .
L m Ln I t LV I (F 6.40), tV
( A).
E F 6.44 DC
. L :
(0 ) ( )
( )
(%) 100m m pc
m pc
n nReg
n
= (6.28)
A (6.28) F 6.44, :
(0) ( )
( )
1255 1200(%) 100 4.58%1200
m m pc
m pc
n nRegn
= = =
L F 6.45 , ALAB,
, HP80 .
A F 6.43
F 6.19, CD ,
.
C
/
DC
.
.
C
/
DC .
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MAQUINA CD 6 - 35
mP . E
F 6.46.
Ejemplo 6.7: DC : HP, V10 230 ,
rpm, A1350 37.5 . L A0.75fI = ,
0.35aR = W519 .
. , , ....
.
. V230tV = , A20LI = A0.75fI = .
D .
E 6.19 .
. F 6.43
(6.27)
m F Vdd
m m
P PPT
+ = =
N-m10 746 519
56.441 350 / 30
dT +
= =
...., : t a aE V I R= . L
aI , , :
A37.5 0.75 36.75a L fI I I= = =
V230 36.75 0.35 217.14t a aE V I R= = =
F,
.
C
/
CD
.
E2F 1F
a
fI
R
tV
GEN
MOT
GEN
MOTaI
LI
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MAQUINA CD 6 - 36
10 746100 100 100 86.49%
230 37.5
sal m
en t L
P P
P V I
= = = =
. A20LI = . L:
A2 2 20 0.75 19.25a L fI I I= = =
, p
22 p ad
d p a
K IT
T K I
=
N-m22
19.2556.44 29.56
36.75
ad d
a
IT T
I= = =
L ....
V2 2 230 19.25 0.35 223.26t a aE V I R= = =
, .... . L
rpm221
223.261350 1 388.1217.14
m m En nE
= = =
E DC F 6.20 m mn T m LI ,
F 6.47. ALAB
, HP80 , V600 , rpm1200
8 .
E 6.47 DC ,
, .
.
C
m mT m Ln I , DC
.
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MAQUINA CD 6 - 37
C ,
, .
E ,
DC .
L
, . E
, ,
.
L ( )m m mP T= ,
,
, F 6.47 . ,
A, .
F 6.47 , p ,
, F 6.48, ALAB,
, , y4 5 7 10sN = .
A ,
, F 6.48. L
HP80 .
D
, .
.
Ejemplo 6.8: DC HP - VDC40 500 rpm300
A75LI = . 0.4a sR+ = . E
.
L A .
.
C
/ DC ,
.
80 H
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MAQUINA CD 6 - 38
p fI .
VDC600 , .
E 6.20 .
(6.23):
d p aT K I=
A p fI f aI I= , :
2
d m aT K I=
C 0FVP , m dT T . ,
:
2
( 1) (1)m m aT K I= 2
(2) (2)m m aT K I=
C : ( 1) ( 2)m mT T= , :
2 2
(2) (1)a aI I= A(2) (1) 75a aI I= =
, .... . A
:
V1 (1)( ) 500 75 0.4 470t a a sE V I R R= + = =
V2 (2 )( ) 600 75 0.4 570t a a sE V I R R= + = =
A (6.15), :
( 2) (2 )2
1 (1) (1)
570
470
p m m
p m m
KE
E K
= = =
:
(2 ) 2
(1) 1
570
470
m
m
n
n
= =
rpm2 1
570 570300 363.83
470 470n n= = =
E CD (6.10), :
d aT K I=
E , ,
( )p ( )aI
E . E ,
E S S
a
s
tVaV
GEN
MOT
aI
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E CD CA.
,
, 6.49.
G
: , ,
6.50, (1.500 15.000
).
.
C
.
.0
.