DC MACHINES - Florida International...

Energy Systems Research Laboratory, FIU

DC MACHINES

(c) Copyright by Prof. Osama A. Mohammed. All Rights Reserved. 18-1

Lecture (18)

Energy Systems Research Laboratory, FIU (c) Copyright by Prof. Osama A. Mohammed.

All Rights Reserved. 18-2

Example on EMF Equation

P = 6

n = 1150 rpm

There are120 slots, and 8 conductors / slot. Calculate the flux per pole if the machine has:

a. Lap Winding ( a = P ) b. Wave Winding ( a = 2)

1) A dc machine has: E a = 230 V

I a = 25 A



Parallel Paths in DC Machines

a=2 or a=P (always is the case based on the winding type)

Lap winding (concentric) a=P (#of Poles) Wave Winding a=2



a) For Lap winding

E a = 230 V

I a = 25 A

φ p = ?

m p a a PZ E ω φ π 2

=

( ) ( )

( ) 60 1150 2

6 2 8 120 6 230

π φ π p

× =

φ p = 12.5 mWb

a=6 lap winding

( ) 60

n 2 π m= ω



φ p = ?


=

( ) ( )

( ) 60 1150 2

2 2 8 120 6 230

π φ π p

× =

φ p = 4.17 mWb

a= 2 Wave winding

E a = 230 V I a = 25 A

a) For Wave winding



Calculate the electromagnetic torque:

m

a a

m e

I E P T ω ω

= =

a m p m

e I Z P T ω φ

ω × =

a p e I Z P T φ =

f f f

p I R

I N R

mmf φ −−−−> = = Proportional to

a) π (2

a)π(2Also we can write



( ) 25 10 5 . 12 960 6 3 × × × = −

e T

m N T e 7 . 47 =

Wave Winding:

( ) 25 10 17 . 4 960 6 3 × × × = −

e T

m N T e 47.7 =

Lap Winding:

2 π (6)

2 π (2)



DC Machines Connections

Ra

V t I a E a

+

-

R f

I f

Separately Excited, DC Generator



Rf

If

Separately Excited, DC Motor

Ra

V t I a E a

+

- T e , ω m



Ea , VS

Ia

(1) (2)

(3)

(4)

(5)

(1) Series (2) Shunt (self excited) (3) Differential Compound (4) Commulative Compound (5) Separately Excite

Performance Characteristics



Ra

Vt Ia Ea

+

-

Rf

Series DC Generator Ra

Vt Ia Ea

+

-

Rf

Series DC Motor Te , ωm

Series Connection



Series

Separately Excited Te

Speed

Torque-Speed Characteristics



Ra

Vt Ia Ea

-

Rf

+

Shunt Generator

If

It

Ra

Vt Ia Ea

-

Rf

+

Shunt DC Motor

If

It

Te , ωm

Shunt Connection



Rs

Vt

S1

Ea

-

φf

+

Comulative Compound (Short Shunt)

Ia It

φS

Ra

S2

F1

F2

A1

A2 Shunt Field Winding

Series Field Winding

Compound Connections



Difference between Shunt and Compound dc Machine Connection:

Shunt dc machine has: Armature Resistance, Field Resistance.

Compound dc machine has:

Shunt field resistance, Series field resistance, Armature resistance.



Vt

S1

Ea

-

φf

+

Differential Compound

Ia It

φS

Ra

S2

F1

F2

A1

A2



Compound DC Motor

S 1

E a

-

R f

+

Short Shunt

I a

I t

R S

Ra

S 2

F 1

F 2

A 1

A 2



S1

Ea

-

Rf

+

Long Shunt

Ia

Vt

RS

Ra

S2

F1

F2

A1

A2

It



Examples

1.

E a

-

+

Separately Excited dc Machine

I a

V t

Ra

R f

I f



V no load = 125 V = E a

I f = 2 A

N = 1780 rpm

No load characteristics

Linear

Non Linear V

I f



a) Find E a if I f goes to 2.5 A, with n = 1780 rpm.

b) Find E a if I f goes to 2.75 A, with n = 1650 rpm.

a)


=



m p a a K E ω φ =

m f a a K E ω Ι ' = ( )

( )

=

60 1780 2 5 . 2

60 1780 2 2

125 '

'

π

π

a

a

a K

K

E

( ) 5 . 2 2 125 a E =

E a = 156.1 V



b) ( )

( )

=

60 1650 2 75 . 2

60 1780 2 2

125 '

'

π

π

a

a

a K

K

E

E a = 159.3 V

Example 2.

V t = 230 V connected to 10 kw load R a = 0.1 Ω R f = 150 Ω

Shunt DC Generator

Brush voltage drop of 2 V. Find E a



Ra

Vt

Ia Ea Rf

+

Shunt DC Generator

If

It

- -

+

10 kW

The following Two Diagrams are the same !!!



Ra

Vt Ia Ea Rf

+

Shunt DC Generator

If

- -

+ 10 kW



A I t 48 . 43 230

000 , 10 = = A I f 53 . 1 150 230 = =

I a = 43.48 A + 1.53 A = 45.01 A

E a = V t + R a I a + V BD = 230 + (45)(0.1) + 2 = 236.5 V

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