MAchine a courant continu

A Conventional DC Machines and Universal Motor 45
When you have completed this exercise, you will be able to demonstrate the
main operating characteristics of a separately-excited dc motor using the
DC Motor/Generator.
Simplified equivalent circuit of a dc motor
Previously, you saw that a dc motor is made up of a fixed magnet (stator) and a
rotating magnet (rotor). Many dc motors use an electromagnet at the stator, as
Figure 2-8 shows.
Figure 2-8. Simplified dc motor using an electromagnet as stator.
When power for the stator electromagnet is supplied by a separate dc source, of
either fixed or variable voltage, the motor is known as a separately-excited
dc motor. Sometimes the term independent-field dc motor is also used. The
current flowing in the stator electromagnet is often called field current because it
is used to create a fixed magnetic field.
TheSeparately‐ExcitedDCMotor
Exercise2‐1
EXERCISE OBJECTIVE
DISCUSSION
Stator
(electromagnet)
 NS
Rotor
(armature)

Ex. 2-1 – The Separately-Excited DC Motor  Discussion
46 Conventional DC Machines and Universal Motor A
The electrical and mechanical behavior of the dc motor can be understood by
examining its simplified equivalent electric circuit shown in Figure 2-9.
Figure 2-9. Simplified equivalent circuit of a dc motor.
In the circuit,  is the voltage applied to the motor brushes,  is the current
flowing in the armature through the brushes, and  is the resistance between
the brushes. Note that , , and  are usually referred to as the armature
voltage, current, and resistance, respectively.  is the voltage drop across the
armature resistor. When the motor turns, an induced voltage proportional
to the speed of the motor is produced. This induced voltage is represented by a
dc source in the simplified equivalent circuit of Figure 2-9. The motor also
develops a torque
T proportional to the armature current  flowing in the motor.
The motor behavior is based on the two equations given below. Equation (2-1)
relates motor speed
n and the induced voltage . Equation (2-2) relates the
motor torque
T and the armature current .
K
 (2-1)
where  is the motor rotation speed, expressed in revolutions per
minute (r/min).
K
is a constant expressed in /
.
is the voltage induced across the armature, expressed in
volts (V).
K
 (2-2)
where  is the motor torque, expressed in newton-meters (N·m) or in
pound-force inches (lbf∙in).
K
is a constant expressed in ∙
 or 
∙
.
is the armature current, expressed in amperes (A).
+
+

Ex. 2-1 – The Separately-Excited DC Motor  Discussion
A Conventional DC Machines and Universal Motor 47
Relationship between the motor rotation speed and the armature
voltage
When a voltage  is applied to the armature of a dc motor with no mechanical
load, the armature current  flowing in the equivalent circuit of Figure 2-9 is
constant and has a very low value. As a result, the voltage drop  across the
armature resistor is so low that it can be neglected, and  can be considered
to be equal to the armature voltage . Therefore, the relationship between the
motor rotation speed
n and the armature voltage  is a straight line
because  is proportional to the motor rotation speed
n . This linear
relationship is shown in Figure 2-10. The slope of the straight line equals
constant K.
Figure 2-10. Linear relationship between the motor rotation speed and the armature voltage.
Since the relationship between voltage  and the rotation speed n is linear, a
dc motor can be considered to be a linear voltage-to-speed converter, as shown
in Figure 2-11.
Figure 2-11. DC motor as a voltage-to-speed converter.
Motor speed
n
(r/min)
Armature voltage 
(V)
Slope  K
Output  motor rotation speed
n
Input  armature voltage K1

Ex. 2-1 – The Separately-Excited DC Motor  Discussion
48 Conventional DC Machines and Universal Motor A
Relationship between the motor torque and the armature current
The same type of relationship exists between the motor torque T and the
armature current , so that a dc motor can also be considered as a linear
current-to-torque converter. Figure 2-12 illustrates the linear relationship between
the motor torque
T and the armature current . Constant K is the slope of the
line relating the two. The linear current-to-torque converter is shown in
Figure 2-13.
Figure 2-12. Linear relationship between the motor torque and the armature current.
Figure 2-13. DC motor as a current-to-torque converter.
Motor torque
T
(N·m or lbf·in)
Armature current 
(A)
Slope  K
Output  motor torque
T
Input  armature current  

Ex. 2-1 – The Separately-Excited DC Motor  Discussion
A Conventional DC Machines and Universal Motor 49
Relationship between the motor rotation speed and the armature
voltage
When the armature current  increases, the voltage drop  (
) across the
armature resistor also increases and can no longer be neglected. As a result, the
armature voltage  can no longer be considered equal to , but rather the
sum of  and , as Equation (2-3) shows:
 (2-3)
Therefore, when a fixed armature voltage  is applied to a dc motor, the voltage
drop  across the armature resistor increases as the armature current 
increases, and thereby, causes  to decrease. This also causes the motor
rotation speed
n to decrease because it is proportional to . This is shown in
Figure 2-14, which is a graph of the motor rotation speed
n versus the armature
current  for a fixed armature voltage .
Figure 2-14. The motor rotation speed drops as the armature current increases (fixed armature
voltage ).
Armature current  (A)
Fixed armature voltage  
Motor speed
n
(r/min)