The Equivalent Circuit of a DC Motor
• Internal generated voltage is given by
E A = Kφω
• Induced torque was found to be
τ
Chapter 8
ind
= KφI A
DC Motors and
Generators
Figure 8-2
(a) The equivalent circuit of a dc motor (b) A simplified equivalent circuit eliminating the
brush voltage drop and combining Radj with the internal field resistance.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
2
Separately Excited DC Motor
The Magnetization Curve of a DC Machine
E A = Kφωm
Magnetization curve ( Φ vs. F)
τ
Magnetization curve expressed
as a plot of EA vs. IF, for a fixed
rotor speed
ind
= Kφ I A
IF =
VF
RF
VT = E A + RAI A
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3
IL =I A
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
4
1
Shunt DC Motor (Same as S.E.)
Shunt DC Motor Torque-Speed Characteristic
ω =
m
VT
RA
−
2 τ ind
K φ ( Kφ )
V
RA
E A = Kφωm
→ ωm = T −
2 τ ind

K φ ( Kφ )
τ ind = KφI A
V = E + R I
 T
A
A A
I A =IL − IF
IF =
VT
RF
Torque-speed characteristic of a shunt dc with and without
armature reaction
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
5
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
7
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
6
8
2
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
9
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
10
11
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
12
3
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
13
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
14
Accounting for Armature Reaction
• The mmf of the main magnet is reduced by the
equivalent mmf of the armature reaction, FAR
Fnet = NF IF − FAR
• The reduced mmf results in a reduced induced voltage
which may be calculated by locating and equivalent field
current, IF* as
IF* = IF −
The Torque speed characteristic of the motor in
Example 8-1
15
FAR
NF
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
16
4
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
17
19
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
18
20
5
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
21
22
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
23
24
6
Speed Control of Shunt DC Motors
• Torque-speed equation
ω =
m
VT
RA
−
2 τ ind
Kφ ( Kφ )
VT
Kφ
slope = −
Speed Control by Changing the Armature-Voltage
RA
Note: Must change VA w/o
effecting the flux field Φ.
( Kφ ) 2
Changes the intercept but not the
Slope of line.
• For any given load, The load line and hence speed may
be varied by
1. Terminal Voltage VT applied to armature.
2. Main magnet
Flux. Adjust Field via RF
3. Adjust Armature resistance RA (not common)
φ
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
25
m
26
Speed Control by Inserting a Resistor in Series With
the Armature Circuit (not common)
Speed Control by Changing the Motor Flux (via RF)
ω =
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
VT
RA
−
2 τ ind
Kφ (Kφ )
ω =
m
VT
RA
−
2 τ ind
Kφ (Kφ )
Only slope effected
As RA
*Slope and intercept effected
As RF
, ω
,Φ , ω
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
27
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
28
7
250
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
29
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
30
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
31
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
32
8
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
33
34
Series DC Motor
Series DC Motor
• Equivalent circuit
• Torque-Speed Characteristics
φ = cI (assuming linear magnetization)
τ = KφI = KcI
A
2
ind
A
IA =
τ
A
ind
Kc
VT = E A + I A ( RA + RS ) = Kφωm +
τ
ind
Kc
(R
A
+ RS )
Solving for ωm ,
ω =
m
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
35
( R + RS )
VT
− A
Kc
τ ind Kc
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
36
9
߱௠ =
்ܸ
‫߬ܿܭ‬௜௡ௗ
−
(ܴ஺ + ܴௌ )
‫ܿܭ‬
The torque-speed characteristic of a series dc motor.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
37
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
38
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
39
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
40
10
The Compound DC Motor
• A motor with both shunt and series field windings
See text figure 8-23, page 500
n {rpm}
T {Nm}
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
41
The Compound DC Motor
Figure 8-24
The equivalent circuit of a compound dc motor: (a) long-shunt connection; (b) short-shunt
connection
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
42
Torque-Speed Characteristic of a Compounded DC Motor
VT = E A + I A ( RA + RS )
I A = IL − IF
IF =
Same full load speeds
VT
RF
Fnet = FF ± FSE − FAR
IF* = IF ±
NSE
F
I A − AR
NF
NF
Same no load speeds
+ Comulatively Compounded
− Differentially Compounded
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
43
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
44
11
262
236
4.4
5.6
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
45
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
46
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
47
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
48
12