1. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
If a shunt dc motor has compensating windings so that flux is constant regardless of load, & motor’s speed & armature current known at any one value of load , then speed at any other load can be determined if IA is known at that load
EXAMPLE-1: A 50 hp, 250 V, 1200 r/min dc shunt motor with compensating windings,
RA =0.06 Ω (including brushes, comp. windings, & inter-poles). The field cct. has a total resistance of Radj + RF of 50 Ω which develops a no load speed of 1200 r/min. There are 1200 turns per pole on shunt field winding

2. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
Find speed of this motor when its input current
is 100 A
(b) Find speed of this motor when its input current is 200 A
(c) Find the speed of this motor when its input current is 300 A
(d) plot torque-speed characteristic of this motor

3. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
EXAMPLE-1;SOLUTION:
EA=K’φn, since IF is constant (VT & RF const.) & since there are no A.R. φ would be constant
 relationships between speeds & internal generated voltages of motor at 2 different load conditions is: EA2/EA1=[K’φn2]/[K’φn1]
constant K’ cancels, also φ canceled 
n2= EA2/EA1 . n1
at no load IA is zero so EA1=VT=250 V
While speed n1=1200 r/min
If internal generated voltage at any other load is determined, motor speed at the load can be determined

4. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
(a) if IL=100 A then armature current :
IA=IL-IF=IL- VT / RF =100 – 250/ 50=95 A
 EA=VT-RAIA=250 –(95)(0.06)=244.3 V
Resulting speed:
n2=EA2/EA1xn1=244.3/250 x1200=1173 r/min
(b) IL=200 A  IA= /50=195 A
EA=250-(95)(0.06)=238.3 V
n2= 238.3/250 x1200=1144 r/min

5. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
(c) if IL=300 A, then IA=IL-IF= /50=295 A
EA = 250-(295)(0.06)=232.3 V
n2=232.3/250 x 1200=1115 r/min
(d) torque versus speed
At no load induced torque is zero
Pconv=EAIA=Tind ω
From this equation Tind= EAIA / ω
IL=100 A 
Tind=(244.3)(95)/ [1173x1/60x2π]=190 N.m.
IL=200 A  Tind= 238.3x195/[1144x1/60x2π]=388 N.m.
IL=300 A  Tind=587 N.m.

6. TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
Torque – speed characteristic of motor

7. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
flux φ & EA of a dc machine is a nonlinear function of mmf
 anything that changes mmf cause a nonlinear effect on EA
mmf should be used to determine EA & mmf determined based on field current and A.R.
magnetization curve is a direct plot of EA versus IF for a given speed ω0  effect of variation in field current can be determined directly from its magnetization curve

8. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
If a machine has armature reaction, its flux will be reduced with each increase in load. The total mmf in a shunt dc motor is the field circuit mmf less the mmf due to armature reaction (AR):
Fnet = NFIF – FAR
magnetization curves are expressed as plots of EA vs field current, normally an equivalent field current is defined that would produce the same output voltage as the combination of all the mmf in the machine
The equivalent field current :

9. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
one other effect must be considered when non linear analysis is used to determine EA of a dc motor
The magnetization curves for a machine are drawn for a particular speed, usually the rated speed of the machine
How can the effects of a given field current be determined if the motor is turning at other than rated speed?
The equation for the induced voltage in a dc machine when speed is expressed as rev/min: EA = K’φn ,
For a given effective field current, the flux in the machine is fixed, so the EA is related to speed by

10. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
EXAMPLE-2:
A 50 hP, 250V, 1200r/min DC shunt motor without compensating windings has an armature resistance (including the brushes and interpoles) of 0.06 .
Its field circuit has a total resistance Radj + RF of 50 , which produces a no-load speed of 1200 r/min. There are 1200 turns per pole on the shunt field winding, and the armature reaction produces a demagnetising mmf of 840 A.turns at a load current of 200A. magnetization curve of this machine is shown next

11. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
Magnetization Curve of typical 250 V dc motor Example -2

12. NONLINEAR ANALYSIS of a SHUNT DC MOTOR
Torque-speed characteristic of motor with armature reaction

13. SPEED CONTROL of SHUNT DC MOTOR
Two common methods:
1- Adjusting the field resistance RF (and thus the field flux)
2- Adjusting the terminal voltage applied to the armature
Less common method:
3- Inserting a resistor in series with the armature circuit

14. SPEED CONTROL of SHUNT DC MOTOR
Changing the Field Resistance
If the field resistance increases, field current decreases (IF↓ = VT/RF↑), and as the field current decreases, flux decreases as well.
A decrease in flux causes an instantaneous decrease in the internal generated voltage EA↓ (=Kφ↓ω), which causes a large increase in the machine’s armature current since

15. SPEED CONTROL of SHUNT DC MOTOR
Induced torque in a motor is given by ind =KφIA since flux in machine decreases while current IA increases, which way does the induced torque change?
Look at
this example: 
armature
current flow is
IA=(250V-245V)/
0.25Ω= 20A

16. SPEED CONTROL of SHUNT DC MOTOR
What happens in this motor if there is a 1% decrease in flux?
If the flux decrease by 1%, then EA must decrease by 1% too, because EA = Kφω Therefore, EA will drop to:
EA2 = 0.99 EA1 = 0.99 (245) = V
armature current must then rise to
IA = ( )/0.25 = 29.8 A
Thus, a 1% decrease in flux produced a 49% increase in armature current

17. SPEED CONTROL of SHUNT DC MOTOR
back to original discussion, the increase in current predominates over the decrease in flux so, ind>load , the motor speeds up
However, as the motor speeds up, EA rises, causing IA to fall. Thus, induced torque ind drops too, and finally ind equals load at a higher steady-sate speed than originally
Summarizing behaviour:
1- increasing RF causes IF (=VT/RF) to decrease
2- decreasing IF decrease φ

18. SPEED CONTROL of SHUNT DC MOTOR
3 – Decreasing φ lowers EA(=Kφω)
4 - Decreasing EA increases IA (=VT-EA)/RA
5- increasing IA increases Tind (=KφIA), with change in IA dominant over change in flux
6-increasing Tind makes Tind>Tload & speed ω increases
7-increase in ω, increases EA= Kφω again
8-increasing EA decreases IA
9-Decreasing IA decreases Tind until Tind=Tload at a higher ω
Effect of increasing RF on O/P characteristic of a shunt motor shown in next figure

19. SPEED CONTROL of SHUNT DC MOTOR
Effect of RF speed control on a shunt motor’s torque-speed (over motor’s normal operating range)

20. SPEED CONTROL of SHUNT DC MOTOR
Effect of RF speed control on a shunt motor’s torque-speed (over entire range from no-load to stall conditions)

21. SPEED CONTROL of SHUNT DC MOTOR
According to equation of speed presented before:
(a) no-load speed is proportional to reciprocal of flux in motor
(b) while slope of the curve is proportional to reciprocal of flux squared
Therefore a decrease in flux causes slope of torque-speed to become steeper
over this range, an increase in field resistance increases motor’s speed
For motors operating between no-load & full-load conditions, an increase in RF may reliably be expected to increase operating speed

22. SPEED CONTROL of SHUNT DC MOTOR
In previous figure (b) terminal characteristic of motor over full range from no-load to stall shown
In figure can see at very slow speeds, an increase in field resistance will actually decrease speed of motor
This effect occurs because at very low speeds, the increase in armature current caused by decrease in EA not enough to compensate for decrease in flux in induced torque field resistance
Some small dc motors used for control purposes operate at speeds close to stall conditions
For these motors, an increase in RF might have no effect or it might even decrease speed of motor
Since the results are not predictable, field resistance speed control should not be used in these types of dc motors. Instead, the armature voltage method should be employed

23. SPEED CONTROL of SHUNT DC MOTOR
CHANGING ARMATURE VOLTAGE
This method involves changing the voltage applied to the armature of the motor without changing the voltage applied to the field
If the voltage VA is increased, then the IA must rise [ IA = (VA ↑ -EA)/RA]. As IA increases, the induced torque ind =KφIA↑ increases, making ind > load , and the speed of the motor increases
But, as the speed increases, the EA (=Kφω↑) increases, causing the armature current to decrease This decrease in IA decreases the induced torque, causing ind = load at a higher rotational speed

24. SPEED CONTROL of SHUNT DC MOTOR
Effect of armature voltage speed control

25. SPEED CONTROL of SHUNT DC MOTOR
Inserting a Resistor in Series with the Armature Circuit
If a resistor is inserted in series with the armature circuit, the effect is to drastically increase the slope of the motor’s torque-speed characteristic, making it operate more slowly if loaded. This fact can be seen from the speed equation:
The insertion of a resistor is a very wasteful method of speed control, since the losses in the inserted resistor are very large. For this reason, it is rarely used