Zbirka Pogoni II Izdanje Napravljen PDF Za Stampu

8/3/2019 Zbirka Pogoni II Izdanje Napravljen PDF Za Stampu

1/136

, 13

II

, 2011.


2/136

:

. ,

,

,

II

:. . ,

. ,

:

:

:

, . . .. :

: , . .

:

32000 , 65

www .visatehnickacacak.edu.yu

E-mail: [email protected]

: , 13

.1375-4-3/07 20. 09. 2007.

: ,

: 250

, , 2011.

ISBN 978-86-86139-18-4

.

.

2
http://www.visatehnicka/http://www.visatehnicka/


3/136

2007. ..

.

Matlab,

,

.

.

, ,

,

.

,

.

,

. ,

, a

.

,

.

,

.

,

.

,

.

, , ,

,

.

, 2011. .

3


4/136

4


5/136

5


6/136

I

1. ( ),M + , M+.

:

a)

)

)

:

a) I

) III

) :

. 1.1

0 Mt-Mt +M-M

+

-

6


7/136

2. ( ),M , ,

:

a)

) )

:

a) I

) IV

) :

. 1.2

3.

, .

m 1500 [Nm]M = . t 3250 [Nm]M = . ?

:

m tM M< , .

0 Mt

+M-M

+

-

7


8/136

4. , ,

.

m 260 [Nm]M = , t 410[Nm]M = . :a) ?) ?

:

a) - .

) m t uM M M= +

[ ]u m t 260 410 150 NmM M M= = = .

5. ][min1910 1=n . ?

:

rad/s][20060

19102

60

2 =

=

=

n

6. , 0,3 [m],

]m[9 .

][min 1 ?

:

m/s][9,m][3,0 == v ,

2 ;

60

v nv

= = =

12 60 60 9 286,5 [min ]60 2 2 0,3

n v vn

= = = =

.

8


9/136

7.

2 219,62 [Nm ]GD = .

t 147 [Nm]M = . ,

200 [rad/s]= ?

:

m t

d

dM M J

t= + ,

22 d ; 200 [rad/s]

4 d

G DJ m

g t

= = = ,

2

u

d d 19,62200 100[Nm]

d 4 d 4 9,81

GDM J

t g t= = = =

,

m t u 147 100 247 [Nm]M M M= + = + = .

8. 1.3 2000 [kg].

DB = 0,4 [m],

B = 0,97, 92,0=R . ][min1000

1=n . 25=i . :a) ,

)

2000 kg,

) 2000 kg.

. 1.3

9


10/136

:

a) 1M

B

100040 [min ]

25

nn

i

= = = .

B B B BB

2 0,4 40 0,838 [m/s]

2 60 60 60

D n D nv

= = = = = .

)

B B B B

B

, ,

F vP P M

= =

B B

B

F vM = ,

BBB B B B

B

9,552

60

F v F v F vM

n n

= = =

,

3

B

2 9,81 10 0,8389,55 4046,8[Nm]

40 0,97M

= =

.

B

R

PP=

,

B BM M

R

MM

=

,

B BM B B

M R M R

1 1nM M Mn

= = .

M

40 14046,8 175,95 [Nm]

1000 0,92M = = .

B B

B

MF v =

,

10


11/136

B B BB B

9,55 ,2

60

F v F vM

n n

= =

3

B

2 9,81 10 0,838

9,55 0,97 3807,66 [Nm].40M

= =

B

R

PP=

,M M

B B

R

MM

= ,

B BM B R B R

M M

nM M M

n

= = ,

M

403807,66 0,92 140,12 [Nm]

1000

M = = .

) :

M M MM M M M

2 175,95 100018424 [Nm/s]

60 9,55 9,55

n M nP M M

= = = = =

M 18, 4 [kW]P = .

9.

.

:

}60

4 g

2

38,2

9,55

375

64 7 48

1 44 2 4 43

2 2

pol pol, ,a a

P mD n GD nM t t

n M M

= = =

9,55

38, 2 375,

60 2 4 g2

365

91

3577

6 4 7 4 8

64 7 48

1 4 4 2 4 4 3

2 2 2

2 2, ,V v v

J m mD GDn n n

= = = 91 365 3577 ,

11


12/136


13/136

m V= , , :

( ) ( ) [ ]

( ) ( ) [ ]

( ) ( ) [ ]

2 2 2 2

1 1 2 1

2 2 2 2

2 2 3

2 2 2 2

3 3 4 3

0,5 0,35 0,1 7200 288 kg ,

0,35 0,07 0,05 7200 133 kg ,

0,07 0,035 0,15 7200 12,50 kg .

m R R h

m R R

m R R h

= = =

= = =

= = =

:

[ ]1 2 3 288 133 12,5 433,50 kgzm m m m= + + = + + = .

:2

J m= , , m .

uR uR , :2 2

s u

2

R R+ = .

, , :

2 2 2 221 2

1 1

2 2 2 222 3

2 2

2 2 2 223 4

3 3

0,5 0,35288 53,64 kg m ,2 2

0,35 0,07133 8,50 kg m ,

2 2

0,07 0,03512,5 0,038 kg m ,

2 2

R RJ m

R RJ m

R RJ m

+ + = = =

+ + = = =

+ + = = =

2

1 2 3 53,64 8,5 0,038 62,18 kg mzJ J J J = + + = + + =

.

:2 24 4 62 2440 N m

z zG D gJ g = = = .

:2 24 4 62 249 kg mz zm D J = = = .

13


14/136

11.

1.5.

.

,

400mm . 3

7800 kg m = .

80

30

3

40

4

00

15

3

1

2

60

. 1.5

:

4 4

;2

s uR RJ h

=

2 3 2 2

v g p0,56 kg m , 1,84 10 kg m , 0,153 kg m ;J J J = = =

2

z g p 0,715 kg m ;vJ J J J = + + =

2 2

z z4 28 Nm .G D g J = = 14


15/136

12. 1 - 6

1.6 6,

z

. . 1 1

940 min

, 12 0,8 = , 56 0,9 = 34 1 = . 1 6.

. 1.6n 1 2 3 4 5 6

[ ]2 NmGD 5 20 6 25 6 30

iz 20 57 25 67 25 75

:

:

2

1 1

1n ii n

ii

i

nJ J

n=

=

2

2 2

1 1

1n ii n

ii

i

nGD GD

n=

=

:

62 1 4 2 4

1 2 31 2 3 4 5 6, , ,

zz n z n n

i i iz n z n z n= = = = = = 1 1 2 3 6n i i i n= , .

n1

n2

n4

n6

1

2

3

4

5

6

M

15


16/136

16 3 52 4 11 6 6 1

1 3 5 2 4 6

20 25 25940 41, 022 min

57 67 75

z z z z z z n n n n

z z z z z z

= = = =

( ) ( )2 2 2 2 2 2 21 2 3 4 5 62 2 2 2 2 21 12 1 2 12 1 2 3 12 56

1 1 1 1 1 1 1GD GD GD GD GD GD GD

i i i i i i

= + + + + +

( ) ( )2 2 2 2

2

2 2 2

1 1 1 15 20 6 25 6

0,8 0,857 57 67

20 20 25

1 1 130 9,745Nm .

0,8 0,957 67 75

20 25 25

GD = + + + + +

+ =

:

:

2

1 1

nni

i i

i i

nJ J

n=

=

2

2 2

1 1

nn

i

i i

i i

nGD GD

n=

=

13.

:

, :

u m t

dconst.

dM M M J

t

= = =

dconst.

dt

=

u

d dJ

tM

=

(. 1.7 1-2 . 1.8).

d

0dt

= , .

, const.v = (. 1.7 3 . 1.8).*

* 2 3 polt

.

16


17/136

t

tpol

r

M

nr

MpolMt

1

23

. 1.7 . 1.8

:

pol r

a0 0

t

Jdt dM

= pol r

u

Jt M= .

:2

4

GDJ

g= ,

2

4

mDJ=

2

60

n = ,

:2

r

pol u4 30

GD nt

g M

= .

2

r

pol u4 30

mD nt

M

= .

polt :

2

rpol

a375

GD nt

M= .

2

rpol

u38,2

mD nt

M= .

14.

2500 [Nm],

,

900 [Nm]. 700 [Nm2],

( )

500 [Nm2]. ,

,

, ][min730 1

?

:

17


18/136

2 2

m m2500 [Nm] 700 [Nm ]M GD= = ,2 2

t RM900[Nm] 500[Nm ]M GD= = ,2 2 2

u m t M RMM M M GD GD GD= = + ,2 2

u 1600[Nm] 1200 [Nm ]M GD= = ,2

11p 1

u

730[min ],38,2

nmDt n

M

= =

2

2 2

1 1 1p

u u u38, 2 9,81 38, 2 375

GD

n n nGD GDgt

M M M

= = =

p

1200 7301, 46[s]

375 1600t = = .

15.

]Nm[100 , () , ,

]Nm[50 . ]Nm[222

.

][min9751

.

:

2

2 1k

k375

n nGDt

M

= , k mk t 100 50 150 [Nm]M M M= + = + = .

k

22 975 00,381[s]

375 150t

= = .

16.

10:1.

)

?

) ?

18


19/136

. 1.9

: [ ]n 7.5 kWP = ;1

n 1460 minn = ; pol n 1.8M M = ;

2 2

m 2 NmGD = ;

:2 2

rm 2000 NmGD = ; [ ]rm 1177 NmM = .

:

:

[ ]' rmrm1177

117, 7 Nm10

MM

i= = = ,

( )2

2 2rmrm 2

GD 2000GD ' 20 Nm

100i = = = .

:

[ ]3 3nnn

7,59,55 10 9,55 10 49 Nm

1460

PM

n= = = .

:

[ ]p n1,8 1,8 49 88,2 NmM M= = = ,

[ ]'u p rm2 2 88,2 117,7 58,7 NmM M M= = = .

a) ,

.

:

1 210:1

Mrm

nrm

19


20/136

( )2 2m rmpol

u

2 '

375

GD GD nt

M

+= ,

( )2

rmpol

u375GD nt

M

= .

( )

( )

2rm

u u u2 2m rm

20

2 2 202

GDM M M

GD GD

= =

++,

[ ]u u0,83 0,83 58,7 48,7 Nm .M M = = =

83 oo uM .

17% .

) [ ]117,7 Nm [ ]n2 98 NmM = . .

17. .

,

.

( ) 1980 min

,

2

m 0,15 kgmJ =

. [ ]500 kgm = .

[ ]1,5 m sv = ,

[ ]b 0, 4 mD = . 2

b 2 kgmJ = .

rm 0,8 = . .

:

:

20


21/136

[ ]bb 500 9,81 0, 2 981 Nm2

DM m g= = = .

:

bb

2

Dv = bb

2

60

n = ;

1bb

b

60 60 2 60 1,571,62 min

2 2 2 0,2n v

D

= = = =

, mn , ,v

, :

m bM M= ,

:

rm m m b bM M = .

[ ]b bm b brm m rm m

1 1 1 71,62981 89,6 Nm

0,8 980

nM M M

n

= = = = .

:

m m mP M=

[ ]m m

m -3 -3

89,6 980

9, 2 kW9,55 10 9,55 10

M n

P

= = =

:

2 2

' 2bb b

m rm

1 71,62 12 0,0125 kg m

980 0,8

nJ J

n

= = =

:

21


22/136

2 2m

rm

1 1 1

2 2tJ mv =

2

22' 2

tmm rm rm

1 1 30 1,5 1500 0,1325 kg m

980 0,8

30

v vJ m m

n

= = = =

:

' ' 2b t m 0,0125 0,1325 0,15 0, 295 kg mJ J J J = + + = + + = .

:

2 24 4 9,81 0, 295 11,58 NmGD g J = = = .

:

[ ]a m1 1

89,6 44,8 Nm

2 2

M M= = = ,

[ ]2

mpol

a

11,58 9800,68 s

375 375 44,8

GD nt

M= = = .

22


23/136

II

1.

[ ]60 minT= . ,

1,5

. .

:

p0

n

60min ; 1,5 ; 0QT pQ= = = =

.

00 =

=

T

t

A

Qe1 , nmax doz

Q

A = = ( t ).

p

n

1,5Q

pQ

= = max (. 2.1.)

t,

1,5

[/]. 2.1

23


24/136

p

p

max doz 1 e

t

TQ

A

= =

,

p

pn

1 e

t

TQQ

A A

= ,

p

n

p

1 e

t

TQ

Q

=

,

p p p

p1 1 11 e e 1 e ln

1 1

t t t

T T Ttp p p

p p p p T p

= = = = =

p

1,5ln 60 ln 60 ln 3 66 [min]1 1,5 1

pt Tp

= = = =

p 66 [min]t = . 66[min] .

2.

: ]kW[6 ; 380 [V] ; ]A[3,13 ; ][min950 1 ; 30 [min] . 10 h,

? 60 [min]T= .

:

kr 30[min]t = , . .

[min]600h10 ==t ( )t , .

00 = :

=

T

t

A

Qe1 .

kr 30 [min]t = 60 [min]T=

24


25/136

30 1

30 3060 2doz 1 e 1 e

Q Q

A A

= =

.

t ,

( )trajno trajnotrajno 1 eQ QA A

= = .

trajno

doz trajno = ,

1trajno30 21 e

QQ

A A

=

.

.. 2~ IQ

1

2 2 2trajno 30 1 eI I

=

1

2trajno 30 1 e 13,3 1 0,607 8,34 [A]I I

= = = .

, , 8,34[A], 62,7%

, 30 [min] .

3. :

: ]kW[7=P ; % 77,5 [%] = . : ( kr 60 [min]t = ); 13 [kW]P= ; % 82,5 [%] = .

:

77 2,03 [kW]

0,775

n

n n

PQ P= = = .

()

krkr kr

13 13 2, 76 [kW] 0,825

PQ P= = = .

25


26/136

krT

n

2,761,36

2,03

Qp

Q= = = .

kr ln 1

pt T p= ,

kr

T

T

6045,14 [min]

1,36lnln

1,36 11

tT

p

p

= = =

.

4.

kr 45[min]t = , : 8 [kW]P= ; n 220 [V]U = ; 43 [A]I= ; ][min1500 1=n ;

84,0= ; 30 [min]T= .

:

( )

kr

kr

1 e 1 et

T

n

Q Q =

,

krT

n

Qp

Q=

kr

T 1 e 1t

Tp

=

.

kr

kr kr T

1 e

1 e e 1

t

T

t t

T T

p

= =

,

kr

kr

45

30

T 4530

e e

1,29e 1e 1

t

T

t

Tp = = =

.

kr n T 8 1,28 9 [kW]P P p= = = ,

kr n T

43 1,28 48,8[A]I I p= = = .

26


27/136

5.

12

14 .

.

: 60

0

C, 0,7

.

( )n_trajno n_trajnon_trajno 1 eQ Q

A A

= = , x_trajnox_trajnoQ

A =

( )x_trajnost pr_xQ k P P = + , ( )n_trajnost pr_nQ k P P = + ;

( )

( )

st pr_x st pr_x

st pr_xpr_n pr_n pr_n pr_nx_trajnopr_n

n_trajnopr_n st pr_n stst pr_n

pr_n pr_n pr_n

1

P P P P

k P P P P P P PAk P P P PP PA P P P

+ + + = = =

+ + +

;

st

pr_n

0,7P

P=

2 2

pr_x

pr_n n

101, 44

12

xP I

P I

= = =

;

x_trajno

n_trajno

0,7 1, 441,26

0,7 1

+= = +

.

0 00,26 60 C 15,6 C = = .

Mont-Singer-

:4 0,0887,15 10L e = ( ),

a = + : - ;

a - ; - ;

:

a x_trajno

a n_trajno

0,088 ( )40,088 0,088 15,6x

0,088 ( )4n

7,15 100, 2534 25%

7,15 10

L ee e

L e

+ +

= = = =

27


28/136

, 75%

15,60C. :

80C,

, .

6. [ ]40 kW .

:

k(kW)P 20 30 40 50 60 70

(kW)P 5,6 6,2 6,8 8 10,4 15,7

:

k(kW)P 63 27,5 50 27,5 58 42,5

t[s] 20 20 30 20 20 20

.

:

k(kW) ( )P f t = 2.2

27,5 27,5

5058

42,5

63

20 60 80 100 120 140

20

40

60

40

Pk(kW)

t(s)

. 2.2

(kW) ( )P f t = :

28


29/136

1

70 6070 63 (15,7 )

15, 7 10, 4P

=

[ ]1 12 kWP = ,

2

30 2030 27,5 (6, 2 )

6,2 5,6P

=

[ ]2 6 kWP = ,

[ ]k3 50 kWP = [ ]3 8 kWP = ,

[ ]k4 27,5 kWP = [ ]4 6 kWP = ,

5

60 5060 58 (10,4 )

10,4 8P

=

[ ]5 10 kWP = ,

6

50 4050 42,5 (8 )

8 6,8P

=

[ ]6 7 kWP =

20 40 60 80 100 120 140

5

10

15

P(kW)

t(s)

12

68

6

10

7

. 2.3

:

1 1 2 2 3 3 4 4 5 5 6 6

sr

1 2 3 4 5 6

P t P t P t P t P t P t P

t t t t t t

+ + + + + =

+ + + + +,

sr

12 20 6 20 8 30 6 20 10 20 7 20

130P

+ + + + + = .

[ ]sr 8,15 kWP = .

,

n 40kWP = [ ]n 6,8 kWP = :

sr nP P > .

. T .

29


30/136

7. , , ,

2.4 .

,

1700 [min ]n

.

ZK 200 L-S ( - ), n 15 [kW]P = ,

1720 [min ]n

n= 8,1max ==

nM

Mp .

. 2.4

:

2 2 2 2 2 2

1 1 2 2 3 3e

1 2 3

310 2 100 19 235 9171 [Nm]

2 19 9

M t M t M t M

t t t

+ + + + = = =

+ + + +.

, const=n

ee

171 70012534[W] 12,5 [kW]

9,55 9,55

M nP

= = = = .

:

e 12,5[kW]P = < n 15 [kW]P = - .30


31/136

nn

n

150009,55 9,55 199 [Nm]

720

PM

n= = = ,

e 171[Nm]M = < n 199 [Nm]M = - . :

max n1,8 1,8 199 358[Nm]M M= = = .

]Nm[3101 =M .

]Nm[358max =M > 1 310 [Nm]M = . , .

8. , 2.5.

:30 [kW];1735 [min ]

;

max

n

1,9M

M= ? ]s[7,3;]s[4,2;]s[9,0 321 === ttt .

570

[Nm]

. 2.5

31


32/136

:

t2 je

2 2 2 2

1 1 2 2e2

490 490 265 265

383 [Nm]3 3

M M M M

M

+ + + += = = .

[Nm]

. 2.6

2 2 2

1 1 e2 2 3 3e

1 2 3

,M t M t M t Mt t t

+ + =+ +

2 2 2

e

570 0,9 383 2,4 127 3,7317[Nm].

0,9 2, 4 3,7M

+ + = =

+ +

ee

317 75024895[W] 24,895 [kW]9,55 9,55

M n

P

= = = = .

32


33/136

e 24,895[kW]P = < n 30[kW]P = - .

nn

n

300009,55 9,55 389,8 [Nm]

735

PM

n= = = .

e 317[Nm]M = < n 389,79[Nm]M = - .

max 1,9 1,9 389,79 740,6 [Nm]nM M= = = .

1 570 [Nm]M =

]Nm[5701 =M < max 740,6 [Nm]M = - .

.

9.

: [ ]16 kW ;[ ]380 V ; [ ]38 A ; -1730 min ; 2,4p = .

. :

a)

0,5 = 0,25 = ;b) .

.

M(Nm)

t( s )5 30 25 20

550

100157

. 2.7

33


34/136

:

4 (

).

)2 2 2

1 1 2 2 3 3e

1 2 3 4

M t M t M t M

t t t t + + =

+ + += [ ]197 Nm

[ ]3n16

9.55 10 209 Nm730

M = =

e nM M

)

2 2 2

1 1 2 2 3 3e

1 2 3 4

M t M t M t M

t t t t

+ + =

+ + += [ ]174 Nm

e nM M<

, ,

.

10. . 2.8

.

.

t1 t2

I1

I2

t

i(t)

. 2.8

:

.

34


35/136

.

:2

1

2

1

2 2

2

e

d

d

t

i it i

t

i

i

t

i t I t

It

t

= =

,

( )i f t= . :

2 1

1 12 1

( )I I

i I t t t t

= + . :

2

1

2

2 11 1

2 12

e

2 1

( ) d

t

t

I II t t t

t tI

t t

+ =

,

2 2

1 1 2 2e

3

I I I I I

+ += .

:2

1

2

1

sr

d

d

t

t

t

t

i t

I

t

=

:

2

1

2 1

1 12 1

sr

2 1

( ) d

t

t

I I

I t t t t tI

t t

+ =

, ,

1 2sr

2

I II

+= .

:

e srI I> .

,

.

35


36/136

11. 21[kW]P= ; ][min660 1=n ; n 100[A]I = , %25% =ED

2.9.

100

[A]

95

. 2.9

:

2 2

e1

95 95 53 5375 [A]

3I

+ += = ,

2 2

e3

53 53 100 10077,7 [A]

3I

+ += = ,

2 2

e5

100 100 0 057,7 [A]

3I

+ += = ,

36


37/136

2 2 2 2 2

1 1 2 2 3 3 4 4 5 5e

e e e

p

I t I t I t I t I t I

t

+ + + + = ,

[ ]

2 2 2 2 2

e

75 2 53 3 77,7 2,6 100 5 57,7 3

78,2 A15,6I

+ + + + = =

%ED

p

%

c

15,6100 100 34, 2%

45,6

tED

t= = = .

%25% =ED

e

34,2 34, 278,2 91,5 [A]

25 25I I= = = .

.

12. 2.10

-1

1400 min .

.

20

10

t(min)

15

P(kW)

1 4 1 3

tr to

. 2.10

37


38/136

:

rt :

2 2 2

1 1 2 2 3 3e

1 2 3

P t P t P t P

t t t

+ + =

+ + [ ]e 13,1 kWP =

:

r

c

6% 100 %= 100 % = 66.7 %

9

t

t = .

66,7 %, 60

%. 60 % :

2 2st e=P P , e

st

P P = ,

:

[ ]66.7

13.1 13,8 kW60

P= = .

.

13.

2.11. 1900 min .

.

t(s)

M(Nm)

4 20 6 100

250

10080

. 2.11

38


39/136

:

:

r

c

30% 100 100 23 %

130

t

t

= = =

[ ]2 2 2

e

250 4 100 20 80 6128 Nm

4 20 6M

+ + = =

+ +

ee 3 3

128 90012 kW

9.55 10 9.55 10

M nP

= = =

25 % :

[ ]est

2312 11,5 kW

25P P = = =

.

14.

. J

, - ,

( ) . .

(, , , , ).

( )=0,5 ( )=0,25 .

[ ]8 m s . [ ]30 mH= .

[ ]1, 2 2200 Nk G = , 1, 2k=

. [ ]2500 kgm = . [ ]76, 3 sT= , [ ]0 30 st = .

2

1 const 0,8 m sa = = .

:

:

m t

d

dM M J t

=

:

39


40/136

m

dvF kG m ma

dt = = , . mF kG ma =

) :

m1 1F kG ma= +

[ ]m1 1, 2 2200 2500 0,8 4640 NF = + =

:

[ ]11

810 s

0,8

vt

a= = = .

:

[ ]1 11 1

8 10 40 m2 2

h v t= = =

m1 const.F = , v , :

[ ]1 m1 37,12 kWP F v= = .) :

0a = :

[ ]m2 2640 NF kG= = :

[ ]2 m2 2640 8 21,12 kWP F v= = = :

312

2 2

v tv tH v t

= + + ( ) 21 3 2

2 2

v tvt t t

= + + +

( )2 02

VH t T t = +

2 0

2 Ht T t

V

= +

[ ]22 300

76 3 30 28,7 s8

t

= + =

:

[ ]2 2 229,6 mh v t= =) :

40


41/136

( ) [ ]3 1 2 0 7,6 st T t t t = + + =

[ ]3 31

30, 4 m2

h v t= =

.

m3 0F = , . :

2kG ma = 2 21,2 2200 m

1,0562500 s

kGa

m

= = = -

m3 0F = 3 0P = . :

2 2

m1 1 m2 2e

1 2 3 0

M t M t Mt t t t

+ =+ + +

.

,

. ,

. ,

, n

( - [ ]8 m sv = ):2 2

m1 1 m2 2e

1 2 3 0

( ) ( )n M t n M t n M

t t t t

+ =

+ + + :

1 m1 m1P F v M n= = ,

2 m2 m2P F v M n= = , :

[ ]2 2

1 1 2 2e

1 2 3 0

24,3 kWP t P t

Pt t t t

+ = =+ + +

,

m1 1

e e

37,12=1,53

24,3

M P

M P= = =

.

:

2 2

e1 1 2 2e

1 2 3 0

P t P t Pt t t t

+ = + + + , e1P

1t .

41


42/136

, ,

. 2.12.

tt1 t2 t3 to

v

tt1 t2 t3 to

t

a

t1 t2 t3 to

t

Ft(Mt)

t1 t2 t3 to

t

Pm

t1 t2 t3 to

P1

P2

Fm

( )d

dt

Fm(Mm)

. 2.12

42


43/136

III

1.

: n 220 [V]U = ; pp 5 [A]I = ; a 0, 0163 [ ]R = ;1

n 450 [min ]n= ; n 680 [A]I = . 1n

170 [V]U= , .

. 3.1

:

I

( )n f I= :a a

e e

R IUn

k k

=

.

n=f(Ia) ke

a ae 1

220 0,0163 675 209 V0,46444

450 450 min

U R IEk

n n = = = = =

a a a

e

220 0,0163

0,46444

U R I I

n k

= = a473,7 0,0351n I=

43


44/136

1

a 00 => 473,7 minI n = =

U1=170 [V],

1 a a a1

e

170 0,0163

0,46444

U R I I n

k

= =

1 a366 0,0351n I=

1

a 010 => 366 minI n = = .

[ ] 1n an n pp 1680 A => 675[A]=> 342 minI I I I n = = = = .

500

n [min-1]

n

. 3.2

II

const = .

a an n pp 680 5 675 [A]I I I I

= = = = , .

44


45/136

(ems),

n e n n a anE k n U R I = = (1)

:

1 e 1 a anE k n U R I = = . (2)

(1) (2)

n a an a ann1 n

1 a an n a an

U R I U R I nn n

n U R I U R I

= =

1

1170 0,0163 675450 342 [min ]220 0,0163 675

n = =

.

2. :

n a pp n220 [V]; 0,2 [ ]; 55 [ ]; 104 [A].U R R I = = = = ,

1n 1000 [min ]n = 1700 [min ]n

= . .

:

a ae 1

220 0, 2 100 V0,2

1000 min

U R IEk

n n = = = =

10

a a a a

2201000 1100min220 0, 2 100e

U U Un nU R Ik U R I

n

= = = = = .

pppp

2204 [A] const.

55

UI

R= = = =

an n pp 104 4 100 [A] const.I I I = = = = .

()

n n a an 220 0, 2 100 200 [V]E U R I = = = .

45


46/136

n e nE k n= . (1)

j dR

( )n a d anE U R R I = + (2)

eE k n= . (3)

(1) (3)

n nn

n

700200 140 [V]

1000

E n nE E

E n n= = = = .

(2)

nd a

an

220 1400,2 0,6 [ ]

100

U ER R

I

= = = .

1

n [min

. 3.3

46


47/136

MATLAB

()

:

http :// www .empr .tfc .kg .ac .rs /2.html ( 4)

3.3

3.3

. 3.3

47
http://www.empr.tfc.kg.ac.rs/2.htmlhttp://www.empr.tfc.kg.ac.rs/2.htmlhttp://www.empr.tfc.kg.ac.rs/2.html


48/136

3.

:1

n n n n a14 [kW], 220 [V], 1500 [min ], 73,5 [A], 0,14 [ ]P U n I R= = = = =

. :

) M=0,6 Mn Ia= const. .

) M=0,6 Mn 60%?

) Ia ).

. 3.4

:

n/ 0,1 0,2 0,36 0,5 0,625 0,8 0,94 1

p pn/I I 0,05 0,1 0,2 0,3 0,4 0,6 0,8 1

:

a ae 1

220 0,14 73,5 V0,1398

1500 min

U R IEk

n n = = = =

1

0e

220

1573,7 min0,1398

U

n k

= = =

obob m a e a a

e

9,559,55

MM k I k I I

k= = =

a a

e n e n

R IUn

k k=

( )a

ob2

e n e n9,55

RUn M

k k=

(1)

ob2220 0,140,1398 9,55 0,1398n M=

ob1573,7 0,75n M=

48


49/136

) ob m aM k I= M=0,6 Mn Ia =const. n0,6 =

( )n an ananobn

n n

9,55 9,55U R I I E I

M

n n

= =

( )[ ]obn

220 0,14 73,5 73,59,55 98,134 Nm

1500M

= =

( ) ( )a a

ob ob2 20,69,55 9,55 0,6e ee e

R RU Un M M

k kk k= =

( )

1

2

220 0,1498,134 2418,3 min

0,6 0,1398 9,55 0,6 0,1398

n = =

) n1,6n n= n0,6M M=

( )a

ob29,55e e

RUn M

k k=

( )

2

ek

( )2 a

n e e obn1,6 0,69,55

Rn k U k M =

( )2

e e

0,142400 220 0,6 98,134 0

9,55k k =

( )2

e e2400 220 0,86317 0k k =

e 0,087560,0041

k =

ep pn

e n

0,087560,626. 3.1 0,4

0,1398

kI I

k

= =

)

ob2

220 0,14

0,08756 9,55 0,08756

n M=

ob2512,6 1,912n M=

49


50/136

[ ]obob m a a a0,6 98,134

9,55 70,41 A9,55 9,55 0,08756

MM k I k I I

k

= = = = =

1,4

1,8n/nnnn=1500 [min

-1]; Mobn= 98,134 [Nm]

. 3.5

4.

.

:

nn

n

140009,55 9,55 89,13 [Nm]

1500

PM

n= = =

( )n an ananobn

n n

9,55 9,55U R I I E I

Mn n

= =

( )[ ]n anobn

n

220 0,14 73,5 73,59,55 9,55 98,134 Nm

1500

E IM

n

= = =

o obn n 98,134 89,13 9,004 [Nm]M M M= = =50


51/136

I :1

0 ob1573,7 0,75 1573,7 0,75 9,004 1566,9 minn M = = =

nn=1500 [min-1]; Mobn= 98,134 [Nm]

n

. 3.6

II :

0a0 an a0

obn

9,00473,5 6,74[A] 6,74[A]

98,134

MI I I

M= = = =

0 n a a0 220 0,14 6, 66 219, 06 [V]E U R I = = =

10n n0 n

0 0 n

219,061500 1566,9[min ]209,71

EE n n nE n E

= = = =

0i

n

-1

n

209,71 V0,1398

1500 min

Un

k

Ek

n

=

= = =

10i 220 1573,7 [min ]

0,1398n = = .

51


52/136

5.

:110 [V] ; 22,5 [A] ;1390 [min ]

;

a 0,7 [ ]R = . 100 [V] 1360 [min ] .

,:

a) 100 [V]

,

) 110 [V]

,

) 100 [V]

5 [ ] 2 [ ] ,) ,

).

:

a) n n a an e nE U R I k n= = ,

n a ane 1

n

110 0,7 22,5 V0,2417390 min

U R Ikn = = =

1

0i

100414 [min ]

0,2417

= = =e

Un

k

) ]V[110 1

0i

110455[min ]

0,242n = = .

)

. 3.7

52


53/136

( 100 [V] )

e 0, 2417 360 87 [V],E k n= = =

a

a

100 87,118,57 [A],

0,7

U EI

R

= = =

aob

87,1 18,459,55 9,55 42,9 [Nm].

360

E IM

n

= = =

a

a a E R I R I + = (1)

p a aU R I E R I = + + (2)

a I I I = + (3)

(1), (2) (3)

pa a

p p

R RRE U R I

R R R R

= + + +

5 10100 0,7 18,57 31,9 [V].

7 7E

= + =

eE k n= ,

1 1

e

31,9132 [min ], 132 [min ].

0,2417

En n

k

= = = =

) , Ia=0,

p

5' 100 71, 43 [V]

7

RU U

R R= = =

+

1

0i

' 71,43295,5 [min ]

0,2417

Un

k

= = = .

53


54/136

6. f ( )n I= obf ( )n M= ,

:

) p1 pn=I I , ) p2 pn=0,5I I ) p3 pn=0,25I I

: [ ]3,2 kW , [ ]220 V , [ ]18 A , -11500 min ,

[ ]a =1,05R . f ( ) = .

0,1

1

1

/n

Ip/Ipn

. 3.8

:

pf ( )I = :

n p pn

1 0,11 ( 1)

1I I

= ,

n p pn0,9 0,1I I = +

[ ]3 3nnn

3,29,55 10 9,55 10 20,4 Nm

1500

PM

n= = = ,

n a ne n 1

n

220 1,05 18 V0,134

1500 min

U R Ik

n = = =

,

m n e n

Nm9.55 1, 2797

Ak k

= = .

:

1n0

e n

2201642 min

0,134

Un

k

= = =

,

54


55/136

:

e

n

0,134k

= , m n

1,2797k

= ,

f ( )n I= obf ( )n M= :an

n n

0,134 0,134

RUn I=

,

a obn

n n n

0,134 0,134 1,2797

R MUn =

,

.n n1642 7,836n I

=

2

n nob1642 6,123n M

=

) p1 pn/ 1I I = 1 n 1 =

1642 7,836n I= ,

ob1642 6,123n M= ;

) p1 pn/ 0,5I I = 2 n 0,55 =

2985 14,247n I= ,

ob2985 20,241n M= ;

) p1 pn/ 0,25I I =

3 n

0,325 =

5052 24,111n I= ,

ob5052 57,969n M= .

7.

,

:

)

-1

1=1100 minn ;)

-1

2 =200 minn ;

55


56/136

) -1

3 =200 minn ;

( )fn M= .

n = , [ ]k=40 AI .

: [ ]8,5 kW , [ ]220 V , [ ]48 A , -1870 min ,

[ ]a 0,426R = .

:

[ ]3 3nnn

8,59,55 10 9,55 10 93,3 Nm

870

PM

n= = = ,

-1n a ne n

n

220 0, 426 480,2294 V min

870

U R Ik

n

= = =

,

-1n0

e n

220960 min

0,2294

Un

k = = = ,

a dn

e n e n

( )R R I Un

k k

+=

,

n e nd a

U n kR R

I

= .

0n > 0I< , . [ ]40 AI= .

)

:

[ ]n 1 e nd1 a220 1100 0,2294

0,426 0,382540

U n kR R

I

= = =

;

) 0U= . :

[ ]2 e nd2 a200 0,2294

0, 426 0, 72140

n kR R

I

= = =

;

)

[ ]n 220 VU U= =

[ ]3 e nd3 a 220 200 0, 2294 0, 426 6, 22140

U n kR RI

= = = ;

56


57/136

500

100

200

300

400

700

800

900

1000

1100

600

10 20 30 40 50 I(A)-10-20-30-40-50

n(min-1

)

-100

-200

-300

-400

-500

-600

-700

-800

-900

-1000

(1)

(2)

(3)

. 3.9

57


58/136

8. : 29 [kW],

440 [V], 76 [A] ,11000 [min ]

.

:

- 3000 kgm =- B 0,2 [m]r =- 20=i-

7,0=

() ,

1,5 [m/s], ?

. 3.10

:

nn

n n

290000,87

440 76

P

U I

= = =

.

aR

50%

:

( ) na nn

0,5 1U

RI

.

58


59/136

( ) ( )na nn

4400,5 1 0,5 1 0,87 0,376 [ ]

76

UR

I = = .

e nk

n a ne n 1

n

440 0,376 76 V0,41142

1000 min

U R Ik

n

= = = .

nn

n

290009,55 9,55 276,95 [Nm]

1000

PM

n= = = .

1,5 [m/s]v = BB

v

r = ,

B BB

6060

2 2

v

rn

= =

,

1BB

B

60 30 30 1,5 201432 [min ]

2 0, 2

v

ir v in n i

r

= = = = =

.

B BRM

g,

G r m r M M

i i

= = =

RM3000 9,81 0,2 0,7 206,01 [Nm].

20M = =

n anobn n a an

n

9,55 ; 440 0,376 76 411,42[V]E I

M E U R I n

= = = =

59


60/136

obn

411, 42 769,55 298,61 [Nm]

1000M

= = ,

0 obn n 298,61 276,95 21,66 [Nm]M M M= = = .

a 3.11.

ob 0

M M M= +

.

.3.11

, , . 3.12.

. 3.12 : ob 0M M M= .

obk RM 0 206,01 21,61 184,35 [Nm]M M M= = = .

obkn

obn

184,3576 46,92 [A]

298,61

MI I

M= = = .

60


61/136

( )e n a dk n U R R I = + +

ed a

0,41142 1432 4400,376 2,803 [ ]

46,92

nk n U

R RI

= = = .

1000

1500

. 3.13

9. ,

( ) 0,5 [m/s] .

:

je

1

k

B

30 30 0,5 20477,5 [min ]

0,2

v in

r

= = = .

61


62/136

.

. 3.14

( )k a kE U R R I = + ,

( )k a kek n U R R I = +

( )e k

k a

440 0,41142 477,5

0,376 13,189 [ ]46,92

U k n

R RI

= = = .

62


63/136

500

1000

1500

n [min-1]

. 3.15

10.

: 5 [kW]; 220 [V]; 28 [A]; 1500 [min-1]; Ra = 1 [].

38 [Nm] ( ]Nm[3 ).

.

a) ,

,

)

,

d 10 [ ]R = .

:

a)

nn

n

50009,55 9,55 31,83 [Nm]

1500

PM

n= = =

n n a an 220 1 28 192 [V]E U R I = = =

n anobn

n

192 289,55 9,55 34,23 [Nm]1500

E IMn = = = .

63


64/136

0 obn n 34, 23 31,83 2, 4 [Nm]M M M= = = .

ob T 0 38 2,4 40,4 [Nm]M M M= + = + = .

obn m an

ob m a

(1)

(2)

M k I

M k I

= =

obM , (2) (1)

oba an

obn

40,428 33,047 [A]

34,23

MI I

M

= = = , :

n a a 220 1 33, 047 186, 95 [V]E U R I = = = .

n nE n

E n= , n

n

En n

E= , . 1

186,951500 1460,5 [min ]

192n = = .

a( )n f I=

a a

e e

R IUn

k k

=

.

n e nE k n=

ne -1

n

192 V0,128

1500 min

Ek

n

= = = ,

1

0i

2201718,75 [min ]

0,128n

= = .

0a0 an

obn

2,428 1,96 [A]

34,23

MI I

M= = =

(ems)

0 n a a0 220 1 1,96 218, 04 [V]E U R I = = = .

100 n

n

218,041500 1703, 437 [min ]192

En nE

= = = .

64


65/136

1400

1600

2000n [min

-1

]

. 3.16

)

( )a d ak

E U R R I = +

obkak an

obn

MI I

M= .

T pmT

M M M= + ,

38 3 35 [Nm]T

M = = .

,

obk T pm 0 35 3 2,4 29,6 [Nm]M M M M = = = .

obkak an

obn

29,628 24,21 [A]

34,23

MI I

M= = = ,

( )220 1 10 24, 21 46,31 [V]E= + = .

65


66/136

( ) 1kk n

n

46,311500 361,8 [min ]

192

En n

E

= = = .

n [mi

. 3.17

11.

Un = 220 [V]; Ian = 150 [A]; Ra = 0,2 []; Rpp = 10 [];Pn = 27 [kW].

1o 2000 [min ]n

= :

pp[AI 2 4 6 7

8

,

5

1

0

,

5

1

3

,

5

1

7

,

7

2

4

[0E4 8

12

0

14

0

16

0

18

0

20

0

22

0

24

0

1

k 120 [min ]n=

n

1,1M M= . ( ),

.

66


67/136

:

n n a an 220 0, 2 150 190 [V]E U R I = = =

n e nE k n= (1)

0 e 0E k n= (2)

(1) (2)

nn 0

0

En n

E= .

npp

pp

22022 [A]

10

UI

R= = = .

0

(240 220)(22A) 220 (22 17,7) 233,64 [V]

(24 17, 7)E

= + =

,

1nn 0

0

1902000 1626,4 [min ]

233,64

En n

E

= = = .

n anobn

n

190 1509,55 9,55 167,3 [Nm]

1626,4

E IM

n

= = = .

nn

n

270009,55 9,55 158,5 [Nm]

1626,4

PM

n= = = .

0 obn n 167, 3 158, 5 8,8 [Nm]M M M= = = .

67


68/136

obk 0 n 01,1 1,1 158,5 8,8 165,55 [Nm]M M M M M = = = = .

obkak an

obn

165,55150 148 [A]

167,3

MI I

M= = = .

k

k 0

0

En n

E=

( )k

k 0

0

120233,64 14 [V]

2000

nE E

n

= = = .

( )k n a d ak E U R R I = + ,

( )a d ak n k R R I U E + = ,

( )n k

d a

ak

220 140, 2 1,38 [ ]

148

U ER R

I

= = = .

12. , ,

.

:

1) () 140%

;

2) , %80

( n0,8 = ) a2R R= .

?

:1220 [V]; 74 [ ]; 1150 [min ]A

,

a 0,2[ ]R = . . 3.18

68


69/136

. 3.18

:

( ) ( )a an anobn

n

220 0, 2 74 749,55 9,55 126,1 [Nm]

1150

U R I I M

n

= = = .

n1,4 1, 4 126,1 176,54 [Nm]M M= = = .

( 1M )

101 n01 n

n a n

2201150 1233 [min ]

220 0,2 74

n n Un n

U E U R I

= = = = .

101 n 1233 1150 83 [min ]n n n

= = =

)(Mfn =

01

n

831233 1233 0,6582

126,1

nn n M M M

M

= = = .

( 2M ) .

69


70/136

10102

n

12331541,25 [min ]

0,8 0,8 0,8

nUn

k

= = = = .

nn

n n n n

M I MI IM I M = =

)(Mfn =

a a a n02 02

n n n

2

0,8 0,8 0,8

R R R R In n I n M

k k M

+ += =

.:

3 0,2 1233 741541,25 1541,25 3,0834

0,8 0,8 220 126,1n M M

= =

.

1 2 176,54 [Nm]M M M= + = , ( 21 nn = ),

1 2 1 21233 0,6582 1541,25 3,0834n n M M = = = .

2 1176,54M M=

1 263,1 [Nm]; 113,44 [Nm]M M= = 1

1 2 1191,47 [min ]n n n= = = .

n=f(M1+M2),

.

1 1 1

1233=f( )=1233-0,6582

0,6582 0,6582

nn M M M =

2 2 2

1541,25=f( )=1541,25-3,0834

3,0834 3,0834

nn M M M =

1 2

1233 1541,25

0,6582 0,6582 3,0834 3,0834

n nM M+ = +

( )1 21287,23 0,54241n M M= +

, 1 2 0M M+ =

70


71/136

1

0 1287,23 minn =

. 3.19

1200

1400

1600

n [min-1]

n

. 3.19

13.

. :

I: [ ]220 V , [ ]10 kW , -11000 min , [ ]5,5 A , [ ]a 0,46R =

II: [ ]220 V , [ ]20 kW , -11500 min

, [ ]106 A , [ ]a 0,19R =

[ ]223 Nm , -11000 min . :

) pR

II, ;

) ( )n f M= .

71


72/136


73/136

[ ]t n1 n2223 95, 5 127,5 NmM M M = = 2 n2I I= .

- :

( )n 2 22 a pe 2 e 2

U I

n R Rk k

= + ,

n2 e 2 2p a

2n

220 0,1332 1000=0,19

106

U k nR R

I

= , [ ]p 0,63R = .

:

M1:nn1=1000-1

min , n01=1130-1

min , Mn1=95,5 [ ]Nm ;

-1

01 n11 01 1 1 1

n1

1130 1000 min1,36126

95,5 Nm

n nn n K M K

M

= = = =

,

1 11130 1,36126n M= 11130

1,36126

nM

= .

M2: nn2=1500-1min , n02=1650

-1min , Mn2=127,3 [ ]Nm ;

-1

02 n2

2 02 2 2 2

n2

1650 1500 min

1,17833127,3 Nm

n n

n n K M K M

= = = = ;

2 21650 1,17833n M= ;

2M : n2n =1000

-1min , n02=1650

-1min , [ ]n2 127,5 NmM =

-1

02 n22 02 2 2 2

n2

1650 1000 min' 5,098127,5 Nm

n nn n K M K M

= = = =

,

73


74/136

2 2' 1650 5,098n M= 21650

5,098

nM

= ;

1 2M + M : 1 2 1130 1650 1153,77 0.93071,36126 5, 098n nM M n + = + =

1212 12 121153,77

1239,68 1,074460, 9307 0, 9307

Mn n M = = .

. 3.21

: . (

) .

n

m

n

Mk

I = .

m e9,55k k = .

74


75/136

14. ,

, -1

1 600 minn = -1

2 650 minn = , [ ]550 VU= [ ]40 A .

[ ]0,35 . .

[ ]550 V , [ ]40 A .

M1 M2

. 3.22

:

ek :

0e 1 -1

1

550 0,35 40 V= =0,893

600 min

U R Ik

n

=

0e 2 -1

2

550 0,35 40 V= =0,825

650 min

U R Ik

n

=

:

[ ]1 2 VU U U+ = (1)

1 2n n = (2)

75


76/136

(2) :

1 0 2 0

e 1 e 2

=U R I U R I

k k

(3)

(1) (3) :

[ ]e 1 0 e 2 e 11e 1 e 2

( )285,33 V

U k RI k k U

k k

+ = =

+

[ ]2 1 264,66 VU U U= =

-11 01 2

e 1

285, 33 0, 35 40303,8 min0,893

U R In n k = = = =

76


77/136

IV

()

1. e :

1

m p a n n n0,325 [ ], 46 [A], 1200 [min ], 220 [V]R R R I n U = + = = = = .

:

a) ,

1

1 950 [min ]n= ,

?) ?) n=f(I).

.

. 4.1

:

a) n n p a n( ) 220 0,35 46 205 [V]E U R R I = + = =

n n

1 1

,E n

E n=

11 n

n

950205 162,29 [V]

1200

nE E

n= = = .

77


78/136

n 1 n p a d( )U E I R R R= + + +:

n 1d p a

n

220 162,29( ) 0,325 0,92956 [ ]

46

U ER R R

I

= + = = .

)

2

cu p a( )P I R R= +

2

cu p a d( )P I R R R= + + . ,

p a d d

p a p a

0,9351 1 3,87

0,325

R R R R

R R R R

+ += + = + =

+ +.

) n=f(I)

e eE k n k k I n= = , mE U R I =

m m

e e e e

R I RU Un

k k I k k I k k I k k

= =

3n me

-1

220 0,325 V3,714674 10

1200 46 1200 min A

U Rk k

n I n

= = =

m

3 3

e e

220 0,325

3,714674 10 3,714674 10

RUn

k k I k k I = =

5922587,5n

I=

78


79/136

1200

1400

n [min-1

]

nn

. 4.2

MATLAB

( ) :


4.2

4.2

79


80/136

. 4.2

2. :

n a p500 [V], 0,12 [ ], 0,08 [ ]U R R= = = . ,.

]Nm[176=M 41[A]I= ][min1000

1=n .:

a) (ems) .

) 11 ,EI 1n M1 = 87[Nm].

80


81/136

:

a)

p a( )U E I R R= + + ,

p a( ) 500 41(0,12 0,08) 491,8[V]E U I R R= + = + = .

)

2 2

m mM k I k k I c I = = = ,

2 21 m 1 1 m 1 1M k I k k I c I = = = ,

2

2

1 1

M c I

M c I

=

1

1

8741 28,8 [A]

176

MI I

M= = = .

(ms)

1 1 p a( ) 500 28,9 0,2 494,2 [V].E U I R R= + = =

1 11

e e e 1 e 1

,E EE E

n nk k k I k k k I

= = = =

1

11

1

1

I

I

E

E

I

E

I

E

n

n== ,

111

1

494,2 411000 1430 [min ]

491,8 28,8

E In n

E I

= = = .

81


82/136


83/136

2

1 1 2

2 2 1m

M E n

M E n

=

,

1 1

2 2v m

M M

M M

=

,

2

1

2

2

1

2

2

1

=

n

n

E

E

n

n,

1 1

2 2

n E

n E= ,

2n

22 1

1

En n

E= .

K 8% 2 10,92E E=

112

1

0,921500 1439 [min ]

En

E

= = .

n. 4.3

83


84/136

4.

: 5,5 [kW]; 1200 [min-1]; 220 [V]; 31[A]; Ra = 0,6 [];Rp= 0,3 []. a ,

110 [V] , kR .

dR

, kR

n2I .

:

. 4.4

np

n

p d

UI

R R=

+,

np

p d

n

UR R

I+ = ,

1100,3 3,25[ ]

31d

R = = .

(ms)

n n a p n( ) 220 (0,6 0,3) 31 192,1 [V]E U R R I = + = + = .

j nn n= n = ( ), n 192,1 [V]E E= = .

(. 4.5).

,

, aR kR .

84


85/136

11200 [min ]n

= .

n 192,1 [V]E E= = , n2I , n2M , kR ,

nk n

a k

2 EI IR R

= =+

n nk a a

k n

192,10,6 2,5 [ ]

2 2 31

E ER R R

I I= = = =

.

1400

180

. 4.5

5. ( )

e :

110 [V], 90 [A], 600 [min-1]. 0,11 [ ] , 0,06 [ ] .

90[A]

500][min 1

, 90 [A]

1320 [min ]

.

.

85


86/136

, ,

50 [Nm] ,

1150 [min ]

?

( ) 4,7 [Nm].

, .

:

m a p 0,11 0,06 0,17 [ ]R R R= + = + =

a m

e e a

U I REnk k k I

= = ,

a me -1

a

110 90 0,17 V0,0017537

600 90 min A

U I Rk k

n I

= = =

.

-1

e

11062724 min A

0,0017537

U

k k

= =

-1m

e

0,1796,94 min

0,0017537

R

k k = =

n=f(I)

-16272496,94 minn

I =

a m

e

U I Rn

k

=

,

a m dd

e

( )U I R Rnk

+= ,

86


87/136

d m

d a m d( )

U I Rn

n U I R R

=

+ ,

d1a m a m

d1

a

( )n

U U I R I RnR

I

= .

. 4.6

l. a an 90 [A]I I= = 1500 [min ]n

=

d1

500110 (110 90 0,17) 90 0,17

600 0,175 [ ]90

R

= = .

II a an 90[A]I I= = 1320 [min ]n

=

d2

320110 (110 90 0,17) 90 0,17

600 0, 491 [ ].90

R

= =

e

m

2 1 0,104760 9,55

kk

= = = ;

87


88/136

e

m0,1047

kk = em -1

0,0017537 V0,01675

0,1047 0,1047 min A

k kk k

= = =

.

[Nm]50 ]Nm[7,4 ,

m 50 4,7 45,3[Nm]M = = .

2

m m a m aM k I k k I = = , :

ma

m

45,352 [A]

0,01675

MI

k k= = =

.

, , . 1150 [min ]n

=

e a

a a

110 0,00175367 52 1502,378 [ ]

52

U k k I nU ER

I I

+ = = = = .

d3 m 2,378 0,17 2,208 [ ]R R R= = =

88


89/136

400

600

n [min-1]

. 4.7

6.

8000[kg]m = , 4.8.

n 400[A]I = , a 0,15 [ ]R = , rp 0,05[ ]R = , n 300 [V].U = 0 33,2 [Nm]M = , 10=i .

][min10001

0

=n :

[ ]0 VE 40 120 180 220 240 260 280 300

[ ]AI 20 60 90 120 160 220 300 420

[ ]ob NmM 76,75 222,51 326,82 426,49 552,17 725,25 927,6 1168

89


90/136

. 4.8

:

a) v D) , .

:

( ) ( )n n a rp n 300 0,15 0,05 400 220 [V]E U R R I = + = + = .

]A[400 , 4.1 0E ,

:

0 280300 280

420 300 400 300

E =

,

V][67,2960 =E .

0 0

n n

E n

E n= n

1n

n 0

0

2201000 741,56 [min ]

296,67

En n

E

= = = .

n n

n obn 0 0

n

9,55E I

M M M M n

= = .

n

220 4009,55 33, 2 1133,2 33, 2 1100 [Nm]

741,56M

= = =

90


91/136

n n n 1100 741,56 85421,58W30 30

P M n

= = =

1n n n 300 400 120000WP U I = = = .

n

1n

85421,580,7118.

120000

P

P = = =

a)

n P F v = , gmF = ,

n P m g v = ,

n 85421,58 0,7118 m0,77 [ ]8000 9,81 s

Pv

m g

= = =

.

1n

B

741,56

74,156 [min ]10

n

n i

= = = .

BB

2

60

n =

B2

Dv =

: B2v

D = , :

B22

60

nv

D

= ,

B

60 60 0,770, 2 [m]

74,156

vD

n

= = =

.

ob

0 0

M I

M I= ,

0

76,75 2033,2 I

= ,

91


92/136

0 8,65 [A]I = .

( )0 0

0

4020

E II

= , ( )0 0 17,3 [V]E I = .

() 0I

( ) ( )0M a rp 0 300 0,15 0,05 8,65 298, 27 [V]E U R R I = + = + = .

:

( )0 0 0

0 0MM

E I n

E n=

:

( )10M

oM 0

0 0

298,271000 17241 [min ]

17,3

En n

E I

= = = .

( . ).

7. (.6) :

a) 30% ,

) ,

) ,

.

:

a) 30%I

30% n0,3 0,3 400 120 [A]I I= = = . ()

0E ]A[120=I 0 220 [V]E = .

( )300 0,15 0,05 120 276[V]E= + = .

92


93/136

n

n

E

E 00 =

1

0

0

2761000 1254,55 [min ]

220

En n

E

= = = .

) ,

pM TM M> .

n p

p

n

9,55E I

Mn

=

p

a rp

3001500 [A]

0,2

UI

R R= = =

+ ,

p

220 15009,55 4249,5 [Nm]

741,56M

= = .

T

0,28000 9,81 7848 [Nm]

2 2

DM m g= = = ,

[ ]TT7848

1102,56 Nm10 0,7118

MM

i = = =

.

p TM M> ,

]A[1500 , ,

.

)

pm TM M

n p

Tn

9,55E I

Mn

93


94/136

T np

n

1 1 1102,56 741,56389,155 [A]

9,55 9,55 220

M nI

E

= = .

p

a rp d

UIR R R

=+ + ,

a rp d

p

3000,771 [ ]

389,155

UR R R

I+ + = =

,

d 0,771 0,2 0,571 [ ]R = .

8. ,

, ,

][min6001

, ],[min6501

][V550 ][A40 .

m 0,35 [ ]R = . ,

4.9. () 550 [V] , 40 [A] . .

:

:

e

U R Ik

n

= ,

:

e 1 1

1

e 2 1

2

550 0,35 40 V0,893

600 min

550 0,35 40 V0,825 .

650 min

U R Ik

n

U R Ik

n

= = = = = =

. 4.9

94


95/136

,

, A][40 ,

, e 1k e 2k , 1U 2U

1

e 1

U R In

k

= ,

2

e 2

U R In

k

=

1 2 550 [V]U U U+ = = .

1 e 1

2 e 2

,

.

U R I k n

U R I k n

= =

( )1 2 e 1 e 22U U R I k k n+ = + ,

:

11 2

e 1 e 2

2 550 2 0,35 40 522303,8 [min ]

0,893 0,825 1,718

U U R I n

k k

+ = = = = + + .

1 1 0,893 303,8 0, 35 40 285, 3 [V]eU k n R I = + = + = .

2U

2 1550 550 285,3 264,7 [V]U U= = = .

95


96/136

V

1.

: , [ ]380 V , [ ]22 kW , -1980 min , [ ]43 A ,cos =0,87 ,

p n =6,65I I , p n =3M M , pr n =3,2M M , =0,89 ,2 2=32 kg mm D ,

[ ]345 kg . .

:

:

3 nn

n

9,55 10P

Mn

= ,

[ ]3n22

9,55 10 214 Nm980

M = = ,

[ ]pr n3,2 =3,2 214=685 NmM M= ,

[ ]p n3 =3 214=642 NmM M= .

-1

s 1000 minn = ,

n

1000 9800,02

1000s

= = .

:

prpr

pr

2=

M

ssM

s s+

prM

M k :

2 2

pr pr 2 0s s k s s+ = .

96


97/136

:

( )2pr 1s s k k = , (1)

( )2pr 1s s k k = + , (2)

ns s= pr

n

3,2M

kM

= = :

( ) ( )2 2pr n 1 0.02 3,2 3,2 1 0,125s s k k = + = + =

( ) ( ) 1pr s pr 1 1000 1 0,125 875 minn n s = = =

:

1) =0n =1s p=M M

2) k=n n pr= =0,125s s pr=M M

3)

:

prpr

2=

M

sM

s

pr

1 2=

sk

s

pr 2s k s= .

97


98/136

:

clearsk=0.125; Mk=685; ns=1000;syms n s mmehmmeh_linearizovan_klosov_obrazac=2*s*Mk/sk;mmeh_uproscen_klosov_obrazac=2*Mk/(s./sk+sk./s);figure(1)ezplot(mmeh_linearizovan_klosov_obrazac,[0,1])grid on; axis auto; hold onezplot(mmeh_uproscen_klosov_obrazac,[0,1])

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

s

1370/(8 s + 1/(8 s))

X: 0.02079

Y: 221.7

X: 0.1247Y: 685

prema uproscenom klosovom obrascu

prema linearizovanom klosovom obrascu

. 5.1

5.1

.

,

, (

642 [ ]Nm o .

98


99/136


100/136

1

s

60 60 50600 [min ]

5

fn

p

= = = .

( 5.2):

=

0

n

s=1

s=2-ns

. 5.2

( )s

s

600 29005,83

600

n ns

n += = =

]Hz[5,2915083,52 ==f .

4. :

]kW[10=P ;

][min14501

=n ;

p

n

5I

I= ;

max

n

2M

M= ;

p

n

1, 2M

M= .

:

a) ;

100


101/136

) maxM pM ;

)

, 85%,

? 380[V] .

:

a) 1500=sn

s

60 60 502

1500

fp

n

= = = ,

( 42 =p ).

s nn

s

1500 14500,0333

1500

n ns

n

= = = .

)

nn

n

100009,55 9,55 65,86 [Nm]

1450

PM

n= = = .

max n2 2 65,86 131,72 [Nm]M M= = = .

p n1,2 1, 2 65,86 79 [Nm]M M= = = .

) , :

2

n nM k U= . 15% :

( )2 2

p n n n1,2 0,85 1,2 0,85 0,867M k U M M = = = .

15%. p nM M< , .

5. T ][V220=U ,

101


102/136

: R1 = 0,46[],

R2 = 0,02[], X1 = 2,24[] 2 0,08[ ]X = . 36,192

21== NN , n1 n20,932, 0,955K K= =

3=p . 21 qq = , :

a) p1I p2I , pM ,

, .

.

) 1I 2I obM ,

s % 3= % .

) xr

, , ,

, p maxM M= , 1I 2I .

) prs ,

.

:

a)

1 n1e i

2 n2

192 0,9325,2

36 0,955

N Km m

N K

= = = =

.

2 2

2k(1) e 2 5,2 0,02 0,54 [ ],R m R= = =

2

2k(1) 5,2 0,08 2,16 [ ],X = =

k 1 2k(1) 0,46 0,54 1 [ ],R R R= + = + =

k 1 2k (1) 2,24 2,16 4,4 [ ],X X X = + = + =

2 21 4,4 4,5 [ ].kZ = + = , , 1=s ,

fp1

k

220 48,78 [ ]4,51

UI AZ

= = = ,

102


103/136

p2 i p1 5,2 48,78 253,66 [ ]I m I A= = = . 3=p

1

s

60 60 501000 [min ]

3

fn

p

= = = .

( )

2 2p2 2cu2

ps0

3 253, 66 0, 0236,87 [Nm].

2 2 10001

6060

q I RPM

nss

= = = =

) % 3= % ( )03,0=s s

R2 ,

2 221 2(1) 1 e

0,020,46 5,2 18, 49 [ ],0,03

= + = + = = RR R R R ms

2 2 2 218, 48 4, 4 19 [ ].= + = + = Z R X

f1

22011,58 [A]

19= = =

UI

Z,

2 i 1 5,2 11,58 60,22 [A]I m I = = = . obM ( T )

2 2

2 2 2ob

0

3 60, 22 0,0269, 26 [Nm]

2 10000,03

60

q I RM

s

= = =

,

) 1=s ,

( )

2k(1)

pr2

2

1 1 2k(1)

Rs

R X X

=+ +

,

, pr 1s = , xr ,

( )

2k(1) (1)

pr2

21 1 2k(1)

1x

R rs

R X X

+= =

+ +.

103


104/136

( )2

2

2k(1) (1) 1 1 2k(1)xR r R X X + = + + ,

( )

22 2 2

(1) 1 1 2k(1) 2k(1) 0, 46 4, 4 0,54xr R X X R= + + = + ,

[ ](1) 3,88xr = ,

(1)

2 2

e

3,880,143 [ ]

5,2

x

x

rr

m= = = .

,

fp1

k

UI

Z= ,

2 2

k k kZ R X = + .

: k 1 2k(1) (1)xR R R r = + + ,

( ) ( )p1

2 2 22

1 2k(1) (1) k

22033,48 [A].

0, 46 0,54 3,88 4,4

f

x

UI

R R r X

= = =+ + ++ + +

2pI

p2 i p1 5, 2 33, 48 174 [A]I m I = = = .

) pr 1s s= = .

6. : R1 = 1,4 [],

[ ] [ ] [ ]2k(1) 1 2k(1) 1f 1 , 2 , 1,5 , 380 [V]R X X U = = = = ,

1

n

3, 960[min ]p n= = ,

]W[5840 =P . .:

104


105/136

a) cos ,

) n 0,5M = , .

:

22k(1) 1f

ob 2

n 2k(1) 2

1 k

n

2=

+ +

R UpM q

f s RR X

s

.

nn

s

9601 1 0,04

1000

ns

n= = = ,

2

ob 2

2

3 1 3803 145,82 [Nm],

2 50 0,04 11,4 3,5

0,04

M = = + +

0

0

n

9,55 5849,55 5,82 [Nm]

960

= = =

PM

n,

n ob 0 140 [Nm]M M M= = .

n n nn n n n

2 140 960

14073,3 [W]60 9,55 9,55

n M n

P M M

= = = = = .

:

*

1nn 1fS q U I = ,

[ ]j7,551f1n2k(1)

1 k

n

38014,27e A

11,4 j3,5j

0,04

UI

RR X

s

= = = + ++ +

o

,

( )j7,55 j7,55n 3 380 14,27e 16267,8e 16126,77 j2137,45 [VA]S = = = +o o

,

105


106/136

1n 16126,77 [W].P =

a) n n7,55 , cos 0,9913 = =o

.

nn

1n

14073,30,873

16126,77

P

P = = = .

)

2 2

1fpr

2 2 2 2

1 1 k

3 3 380400 [Nm]

2 2 2 50 2 1,4 1,4 3,5

Up qM

f R R X = = =

+ + +.

ob pr 1 200[Nm]2

M M= = ,

2

2

2

5,31

4,1

38013

502

3200

+

+

=

s

s ,

.

68,2025,121

4,1

2

=+

+ s

ss

68,2025,1211

8,296,12

=+

++ s

sss ,

sss

s =+++ /68,2025,121

8,296,1

2 21,96 2,8 1 12, 25 20,68s s s s + + + = ,

0188,1721,14 2 =+ ss ,

007,026,1

2 =+ ss ,

2

07,0458,126,1 =s ,

2

14,126,1 =s ,

106


107/136

1 1,2s = 2 0,06s =

0 1

2 0,06s = .

( ) ( ) 1s 1 1000 1 0,06 940 [min ]n n s

= = = .

1 1,2s =

( ) ( ) 1s 1 1000 1 1, 2 200 [min ]n n s= = = .

.

. 5.3.

n [min -1]

. 5.3

7.

: U1 = 380[V], nn = 1440 [min-1],

f = 50 [Hz], R1 = R2k(1) = 1 [], X1 = X2k(1) = 4 [], n 4222 [W]P = ( ). .

:

a) 0n ,

107


108/136

)

, , ,

1 60 [Hz]f = , . 1,1m = .

. .

) ,

).

:

a)n

n

n

4222

9,55 9,55 28 [Nm]1440

P

M n= = = .

( )

( )

22k 1 1nf

obn 2

n 2k 1 2

1 k

n

2

R UpM q

f s RR X

s

=

+ +

2

obn 2

2

380

2 1 33

2 50 0,04 11 8

0,04

M

=

+ +

: ( )k 1 2k 1 8 [ ]X X X = + = ,

nn

s

14401 1 0,041500

nsn

= = = ,

obn 31,06[Nm]=M .

o obn n 31, 06 28 3, 06 [Nm]M M M= = = .

0n

108


109/136

( )0

pr 0pr

0 pr

2 1

2

M

s sM

s s

+ =

+ + ,

( )

1pr

2k 1

Rs

R = .

( )2k 1

pr2 2 2 2

1 k

10,124

1 8

Rs

R X= = =

+ +.

( ) ( )1

pr pr s1 1 0,124 1500 1314 minn s n

= = = .

10,124 0,124

1 = = .

2

2

1nfpr

2 2 2

1 1 k

380

2 3 3 50,72 [Nm]2 50 2 2 2 1 1 8

Up qMfR R X

= = = + + + +

.

s

( )

0

0

2 1 0,1243,06

0,12450,722 0,124

0,124

s

s

+=

+ +

00

0

0,124 2,248 50,720,248 / 0,124

0,124 3,06

ss

s

+ + =

2

0 04,58961 0,015376 0s s + =

12

2

0

4,58961 4,58961 4 0,015376

2s

=

01 020,0034, 4,586s s= =

.

109


110/136

( ) ( ) 10 0 s1 1 0,0034 1500 1494,9 [min ]n s n= = = .

)

( )

( )

22k 1 1nf

obn n 02

n 2k 1 2

1 k

n

2

R UpM q M M

f s RR X

s

= = +

+ +

,

( )

( ) ( )

( ) ( )

22k 1 d 1 1nf

obn n 02

1 1 2k 1 d 1 2

1 k

1

2

R R Up

M q M Mf s R RR X

s

+

= = + + +

,

0M ,

.

, .

( )

( ) ( )

( ) ( )

( )

2

2k 1 d 1 2

1 k

2k 1 1n 0 1 1

2

n 0 n 2k 1 d 1 2k 1 2

1 k

n

R RR X

R sM M f s

M M f s R R RR X

s

+ + + + = +

+ +

, (*)

],Hz[50,Hz][601 == ff 1

k k k k

601,2

50

fX X X X

f = = = .

1

sk60 60 60 1800

2fn

p = = = , ,

8,11800

144011 =+=s .

(*)

110


111/136

( )

( )( )

2

2d 1

2

d 1 2

11 1, 2 8

1,828 3,06 60 1,8 1

28 3,06 50 0,04 1 11 8

0,04

R

R

+ + + + =

+ + +

.

x= ( )d 11 R+ ,

2 51,69527 301,838 0x x + =44,9856

6,7097x

=

( )d 143, 9856 [ ]R = ,

.

( )d 1

d 2

43,985636,352 [ ]

m 1,21

RR = = = .

1500

1800

n [min -1]

. 5.4

111


112/136

MATLAB

:


5.4

5.4

. 5.4

)

112


113/136

( ) ( )

2

1nf2(1)k 2

2k 1 d 1 2

1 k

1

UI

R RR X

s

=+

+ +

( )

2

1nf2(1)n 2

2k 1 2

1 k

n

UIR

R Xs

=

+ +

( )

( ) ( ) ( )

22

2k 1 2 21 k

n2(1)n

2 2

22(1) 2k 1 d 1 2

1 k1

11 8

0,040,964

1 43,98561 1,2 8

1,8

+ + + + = = =

+ + + + + +

RR X

sI

I R R

R Xs

2(1) 2(1)n 2(1)n

11,037

0,964= =I I I

8.

][min1455

11

=n , ][min900

1

2

=n . ][06,02 =R . .

:

nM ,

2 22 2 2n 2 2

n 22 2

R R r p pM q I q I

f s f s

+= =

2 2 2

n 2

R R r

s s

+= .

113


114/136

n 2n 2

s s

1455 9001 1 0,03 ,a 1 1 0, 4;

1500 1500

n ns s

n n= = = = = =

22 2 2

n

;R

R r s s+ =

2 22 2 2 2

n n

0,41 0.06 1 0,74[ ];

0,03

s sr R R R

s s

= = = =

2 0,74 [ ].r =

9. .

, :

]kW[11 , ]A[17 , ],[min9601 ]V[380 (),

1p p

n n

6, 1,3I M

I M= = .

,

? ?

:

1p n6 6 17 102 [A]I I= = = .

n

nn

30 30 11000109, 42 [Nm]

960

PM

n= = =

.

p n1,3 1,3 109,42 142, 24 [Nm]M M= = = .

114


115/136

800

900

n [nim-1]

npr

. 5.5

p nM M =

, :

( ) ( )

( )

( )

2k 12 2

2k 1 2 1 p 2 1 n

n2 2

Rp pq R I q I

f f s =

,

p 1s = .

( )

( )2 1 n

2 1 p

n

I

I s = .

nn

s

9601 1 0,04

1000

ns

n= = = ;

( )

( ) ( )

( )

2 1 n 2 1 n

1n2 1 p 2 1 n5 50,20,04

I I

I I I = = = .

115


116/136

kZ ,

( )1f

1pn 2 1 pn

k

UI I

Z= ,

( )

1f 1n 1nk

1pn 1pn 2 1 pn3 3

U U UZ

I I I= = =

.

p nM M=

( )

( )

( )1n

1 k 2 1 p 2 1 p

2 1 pn

3 33

UU Z I I

I = =

,

- ( )2 1 pI - .

- ( )2 1 pnI - .

1n1 1n

1n

55 380 316,67[V]

6 6

UU I

I = = = .

17%.

10.

. : ],V[380

, 110 [kW], 2950 [min-1], 199 [A], ,91,0cos =

pcos 0,5 = ,p

n

6,9I

I= ; p

n

2,M

M= -

pr

n

3,25MM = =

. ,

p 300 [Nm]M = . -?

:

nn

n

1100009,55 9,55 356,1 [Nm]2950

PMn

= = = .

116


117/136

p n2 2 365,1 712, 2 [Nm]M M= = = .

p713

237, 4 [Nm]

3

M = = .

. 5.6

p 300 [Nm]M = ,

p p237,4 [Nm] 300 [Nm]M M = < = , -.

( )

( )( )( )

2 2

1 1

p 2k 1 2k 12 22k

1 k2k 1,2 2

U Up p

M q R q Rf f Z R R X = = + + (1)

( )

( )( )

( )

( )

2

1p 2k 1 2

2

1 d k2k 1

2

1p 2k 1 2 2

k d k

2

.

2

UpM q R

f R R R X

UpM q R

f R R X

= + + +

=

+ +

(2)

117

~


118/136

p

p

M

M (1) (2)

( )2 2

p k d k

2p k .

M R R X

M Z

+ +

= (3) (3)

( )2 p p p2 2 2 2 2 2 2

k d k k k k p k p

p p p

sin sin .M M M

R R Z X Z Z Z M M M

+ = = =

(4)

(4)

p 2

d k p k

p

sinM

R Z RM

= (5)

k k pcosR Z= , (5)

p p2 2

d k p k p k p p

p p

sin cos sin cosM M

R Z Z Z M M

= =

,

kZ (Y),

p 2

kY p p

p

sin cosM

R ZM

=

.

kZ (), 1p 1fp3I I=

1f 1 1k

1p1 p

3 3 3800, 48 [ ]

6,9 6,9 199

3

f n

U U UZ

II I

= = = = =

.

5.7

k

kY

0,480,16 [ ]

3 3

ZZ

= = = .

118


119/136

:

( )22 2

p psin 1 cos 1 0,5 0,75 = = = , :

7130,16 0,75 0,5 0,124 [ ]300R

= =

0,124R =

. 5.7

,

.

11. :

a) ,

) ,

) .

:

a) :

1

f

k

380

791,67 [A]0,48

U

I Z= = =

l f 3 3 791,67 1371, 21 [A].I I= = =

)

( )

1 1 1

f2 2 2 2 2 22

kY kY kY k kYkY kY

3 3 3.

2 2

U U U

I

R R R R X Z R R R R R X

= = =

+ + + + ++ +

2 2 2

kY kY kYZ R X = + .

119


120/136

. 5.8

kY kY cos 0,16 0,5 0,08 [ ]pR Z= = = ,

p kY kY

sin 0,866 ; sin 0,16 0,866 0,138 [ ]p

X Z

= = = = ,

( )f

2 2

380

3890,78 [A]

0,08 0,124 0,138I = =

+ +.

)

( )

2

1p 2k 1 2

k2

UpM q Rf Z= ,

( )( )

2

1p 2k 1 22

k k2

UpM q R

f R X X =

+ +,

p 2 2

kY p p

p

713cos sin 0,16 0,5 0,866

300

MX Z

M

= = ,

120


121/136

0, 0948 [ ].X =

LX = , . LfX = 2

0,09480,0003018 [H] 0,3018 [mH]

2 2 50

XL

f

= = = =

.

-

.

-

.

12. ,

U 50 [Hz] prY 120 [Nm].M = U 60 [Hz],

pr.M

1 0.R

:

2

1pr

2 2

1 1 k2 2

Up qM

f R R X =

+ +,

1R , . 01 R

2

1pr 2

k2 2

Up qM

f X=

.

kX

k k k2X L f L= = .

,

2 2

1 1prY

kY k2 2 2 2 2

U Up q p qM

f X f f L= =

121


122/136

( )2

21

1pr

1 k 1 1 k

3 3

2 2 2 2 2

U Up q p qM

f X f f L

= =

,

2

prY 1

pr

1

3

M f

M f

=

,

2 2

pr prY

1

503 3 120 250 [Nm],

60

fM M

f

= = =

pr 250 [Nm].M =

13.

: ( ) ( ) ( )1 2k 11 j2 [ ], 2 j3 [ ],Z Z= + = + U1n=380 [V], f=50 [Hz], f2=2 [Hz] ( ),

m 1,2= ( ), 0 0, 2.I p = .

300% .

,

.

?

:

ob obn3M M=

( )ob

prpr

pr

2 1

2

M

ssM

s s

+

= + + ,

122


123/136

( )

( )( )

2k 1

pr 22

1 1 2k 1

Rs

R X X

=+ +

( )

1pr

2k 1

Rs

R = ,

( )pr

22

2 0,3921 2 3

s = =+ +

;1

0,392 0,1962

= = .

( )

( )

2

1n

2k 1

obn 2

n 2k 1 2

1 k

n

3

2

URp

M qf s R

R X

s

=

+ +

,

( )k 1 2k 12 3 5 [ ]X X X = + = + = ,

2n

20,04,

50

fs

f= = =

2

obn 22

380

2 2 33 17,5 [Nm],

2 50 0,04 21 5

0,04

M

= = + +

2

1n

pr2 2

1 1 k

3,

2 2

U

p qM

f R R X

=

+ +

2

pr2 2

3802 3 3

75,36 [Nm].2 50 2 1 1 5

M = =

+ +

( )ob

prpr

pr

2 13

2

M

ssMs s

+ =

+ +

123


124/136

( )

,

392,0392,0

392,0

196,012

36,75

5,173

+

+

+=

s

s

=

=

=+

147,0

045,1

2

154,04193,1193,1

0154,0193,1

21

2

21

2

s

s

ss

147,0=s ( ).

1

s

60 60 501500 [min ]

2

fn

p

= = = ,

( ) ( ) 11 1 0,147 1500 1279,5 [min ]sn s n= = = .

p pr M M= pr 1,s = :( ) ( )2k 1 d 1

2 2

1 k

1R R

R X

+=

+,

( ) ( )2 2 2 2

1 kd 1 2k 11 5 2 3,099 [ ]R R X R= + = + = ,

( )d 1

d 2 2

3,0992,152 [ ]

1,2

RR

m= = = ,

d 2,152[ ]R = .

( )( ) ( )

1n

1p2 2 22

k kd 1

380

3 327,82 [A]

3 3,099 5

U

I

R R X

= = =+ ++ +

.

124


125/136

1500

n [min-1]

. 5.9

14. e

( ),

( )nn , . ?

:

k n

n n= k nI I= .

( )

1n

1n2

2k 1 2

1 k

n

3

U

IR

R Xs

=

+ +

,

125


126/136

( ) ( )

1n

k2

2k 1 d 1 2

1 k

k

3

U

IR R

R X

s

=+

+ +

.

: n 0,04s = ,

( ) ( ) 1n n s1 1 0,04 1500 1440 [min ]n s n= = = .

( )nk nk

s s s

14401 1 1 1 1,96

1500

nn ns

n n n

= = = + = + = .

( ) ( ) ( )

1n 1n

1n k2 2

2k 1 2k 1 d 12 2

1 k 1 k

n k

3 3

U U

I IR R R

R X R X s s

= = =+

+ + + +

,

( ) ( ) ( )2k 1 2k 1 d 1

1 1

n k

R R RR R

s s

++ = + ,

( ) ( )k

d 1 2k 1

n

1,961 1 2 96 [ ]

0,04

sR R

s

= = =

,

( )d 1

d 2 2

9666,667 [ ]

1,2

RR

m= = = .

,

126


127/136

( ) ( )

( ) ( )

2

1n

2k 1 d 1

obk 2

k 2k 1 d 1 2

1 k

k

3

2

UR Rp

M qf s R R

R X

s

+ =

+ + +

2

obk 2

2

380

2 2 9

Documents

Zbirka Pogoni II Izdanje Napravljen PDF Za Stampu