Fundamentos de máquinas eléctricas DC

7/26/2019 Fundamentos de mquinas elctricas DC

1/39

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.


2/39

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


3/39

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


4/39

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


5/39

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


6/39

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


7/39

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


8/39

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


9/39

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=


10/39

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


11/39

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)


12/39

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


13/39

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


14/39

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


15/39

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


16/39

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.


17/39

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


18/39

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


19/39

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

,

.


20/39

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.


21/39

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,

.


22/39

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

.


23/39

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


24/39

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


25/39

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

.


26/39

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


27/39

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)


28/39

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


29/39

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


30/39

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

.


31/39

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

.


32/39

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

,

.


33/39

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


34/39

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 .


35/39

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


36/39

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

.


37/39

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


38/39

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


39/39

E CD CA.

,

, 6.49.

G

: , ,

6.50, (1.500 15.000

).

.

C

.

.0

.

Fundamentos de máquinas eléctricas DC

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Transcript of Fundamentos de máquinas eléctricas DC