Download Lecture 02-DC Motor

Direct-current motor is a device that transforms the electrical energy into
mechanical energy.
DC motor drives some devices such as hoists, fans, pumps, calendars, punchpresses, and cars. The ability to control the speed with great accuracy is an
attractive feature of the dc motor.
There are five major types of dc motors in general use:
• The separately excited and shunt dc motors
• The permanent-magnet dc motor
• The series dc motor
• The compounded dc motor
The voltage induced Va in the armature
of a dc motor is expressed by:
Ia
R
ω
+
N
+
Vs
Va  K
S
Va
Fig.2-1: Simple circuit of a dc
motor.
(2.1)
Φ
where
Va = armature voltage (V)
K = constant
ω = speed of rotation of the motor (r/min)
Φ = flux per pole (Wb)
Armature is the rotating part of a dc motor
The constant K can be calculated from:
ZP
K 
2a
(2.2)
where
Z = total number of conductors on rotor
a = number of current paths
P = number of poles on the machine
whereas total number of conductors can be expressed as:
Z  2CN
where
C = number of coils on rotor
a = number of turns per coil
(2.3)
In the case of the motor, the induced voltage is called counter-electromotive
force (cemf) because its polarity always acts against the source voltage Vs.
In sense that the net voltage acting in the series circuit of Fig. 2-1 is
Vnet  Vs  Va
and not,
Vnet  Vs  Va
(2.4)
Referring to Fig. 2-1, the electrical power Pe in Watt supplied to the armature
is equal to the supply voltage Vs multiplied by the armature current Ia:
Pe  Vs I a
(2.5)
According to the Khirchhoff’s voltage law (KVL), the source voltage is equal
to the sum of Va plus the IaR drop in the armature:
Vs  Va  I a R
(2.6)
Pe  Va I a  I a2 R
(2.7)
so,
The Ia2R term represents heat dissipated in the armature and VaIa is the
electrical power that is converted into mechanical power.
Therefore, the mechanical power Pm of the motor in Watt is equal to the
product of the cemf multiplied by the armature current:
Pm  Va I a
(2.8)
The mechanical power developed by a motor depends upon its rotational speed
and torque it develops given by:
Pm   ind
where
τind = induced torque developed by a dc motor (N.m)
ω = speed of rotation (r/min)
(2.9)
Combining Eq. 2.8 and 2.9, we obtain
 ind  Va I a
 ind  K I a
and so
 ind  KI a
(2.10)
With substituting Va from Eq. 2.1 into Eq. 2.6 and Ia is determined from
Eq. 2.10, we obtain
Vs  K  
 ind
K
R
Solving for the motor’s speed produces
Vs
R



2 ind
K K 
where
R = armature resistance = internal resistance (Ω)
(2.11)
Separately excited dc motor is a motor whose field circuit is supplied from
separate constant-voltage power supply.
Ra
If
Ia
Rf
Vf
N
Field
Il
Va
S
Lf
Fig.2-2: Circuit of a separately excited dc motor.
Vs
In circuit of the separatly excited dc motor, the field current If in Ampere is
Vs
If 
Rf
(2.12)
where
Rf = shunt-field resistance (Ω)
Fig. 2-2 shows that the current generated by voltage source Il is equal to the
armature current Ia:
Il  I a
(2.13)
Ra
Shunt dc motor is a motor whose its
armature and field circuit in parallel
across terminals of a dc supply.
Ia
Il
If
Rf
The field current If in Ampere is
Vs
If 
Rf
(2.12)
N
Va
S
Vs
Field
Lf
Whereas the current generated by
voltage source Il is
Il  I a  I f
(2.14)
Fig.2-3: Circuit of a shunt dc motor.
There are three ways to control the speed of a shunt dc motor:
1. Adjusting the field resistance Rf and thus the field flux Φ.
2. Adjusting the armature voltage Va.
3. Inserting a resistor in series with the armature circuit.
Field resistance control is a method to control the speed of a dc motor by
connecting a rheostat with a shunt motor.
The speed of dc motor is controlled by varying the field flux Φ and keeping
the armature voltage Va constant. Thus, if Φ is incresed ---- ω will drop, and
vice versa.
In order for the armature current limit not to be exceeded, the induced torque
limit must decrease as the speed of the motor increses.
In field resistance control, the lower the
current flowing through the armature,
the faster the armature turns and the
higher the field current, the slower it
turns . Because an increase in armature
current causes a decrease in speed.
Il
+
field
rheostat
Ia
Rf
R
If
This method is frequently used when the
motor has to run above its rated speed,
called base speed.
If a motor is running at its rated terminal
voltage, power, and field current, so it
will be turning at base speed.
shunt
field
Vs
Va
Φ
Fig.2-4: Schematic diagram of
the field resistance control.
Summary of the cause-and-effect behavior involved in this method of speed
control:
1. Increasing Rf causes If (=Vs/Rf ↑) to decrease.
2. Decreasing If decreases Φ.
3. Decreasing Φ lowers Va (= K Φ↓ω).
4. Decreasing Va increases Ia (= (Vs – Va↓)/Ra).
5. Increasing Ia increases τind (= K Φ↓Ia ↑↑ ), with the change in Ia dominant
over the change in flux.
6. Increasing τind makes τind > τload, and speed ω increases).
7. Increasing ω to increase Va (= K Φω↑) again.
8. Increasing Va decreases Ia.
9. Decreasing Ia decreases τind until τind = τload at a higher speed ω.
Load
Load
τload
Load
τload
τload
ω1
I
Moto τind
r
Motor
I
Moto τind
r
Motor
ω2
I
Moto τind
r
Motor
Fig.2-5: A load coupled to a motor by means of a shaft. (a) Shaft is
stationary τind = τload. (b) Shaft turns clockwise τind = τload. (c) Shaft turns
counterclockwise τind = τload.
Since the torque limit decrease as the speed of the motor increases, and the
power out of the motor is the product of the torque developed by dc motor and
the rotation speed (see Eq.2-9), then the maximum power out of a dc motor
under field resistance control is
Pmax  cons tan t
(2.15)
While the maximum torque varies as reciprocal of the motor’s speed.
Warning…..!!
This method can only control the speeds of the motor above base speed but
not for speeds below base speed. Because to achieve a speed slower than
base speed, the armature requires excessive field current, possibly burning
up the field windings.
Ra
Variable
Voltage
Controller
Il
If
Ia
Rf
Va
Vs
Vc
Field
Lf
Fig.2-6: Armature voltage control of a shunt dc motor.
The speed of dc motor is controlled by varying the armature voltage Va using
a variable voltage controller and keeping the flux in the motor constant.
The lower the armature voltage on dc motor, the slower the armature turns
and the higher the armature voltage, the faster it turns . Since an increase
in armature current causes an increase in speed (see Eq. 2.1).
If Φ = constant, so the maximum torque in the motor is
 max  KI a ,max
(2.16)
Since the power out of the motor is the product of the torque developed by
dc motor and the rotation speed (see Eq.2-8), then the maximum power of
the motor under aramture voltage control is
Pmax   max 
(2.17)
Summary of the cause-and-effect behavior involved in this method of speed
control:
1. An increase in Vc increases Ia (= (Vc ↑ - Va)/Ra).
2. Increasing Ia increases τind (= KΦIa ↑).
3. Increasing τind makes τind > τload increasing ω.
4. Increasing ω increases Va (= KΦω ↑).
5. Increasing Va decreases Ia (= (Vc ↑- Va)/Ra).
6. Decreasing Ia decreases τind until τind = τload at a higher ω
+
Rheostat speed control is a way to control
the speed of a dc motor by inserting a
rheostat in series with the armature circuit.
Il
If
The
motor speed is controlled by
adjusting the magnitude of resistance R of
a rheostat.
With
varying R ---- the current flowing
through the armature Ia vary and thus,
voltage across the armature.
Ia
R
armature
rheostat
Vs
+
shunt
field
Va
However,
the insertion of a resistor
yields very large losses in the inserted
resistor.
Fig.2-7: Armature speed control
using a rheostat.
Warning…..!!
This method can only control the speeds above its rated
speed or base speed but not for speeds below base speed.
Because to achieve a speed faster than base speed, the
armature requires excessive field current, possibly
burning up the field windings.
A permanent-magnet dc (PMDC) motor is a dc motor whose poles are made
of permanent magnets.
A PMDC motor is basically the same machine as a shunt dc motor, except that
the flux of a PMDC motor is fixed. Therefore, it is not possible to control the
speed of a PMDC motor by varying the field current or flux.
Compared with shunt dc motors, PMDC motors offer a number benefits.
Since these motors do not require an external field circuit and thus, they do
not have the field circuit copper losses. Because no field windings are
required, they can be smaller than corresponding shunt dc motors.
However, PMDC motors also have disadvantages. Permanent magnets can
not produce as high a flux density as an externally supplied shunt field, so
PMDC motor will have a lower induced torque τind per ampere of armature
current Ia than a shunt motor of same size and construction. In addition,
PMDC motors run the risk of demagnetization.
A series dc motor is a dc motor whose field windings composed of a few turns
connected in series with the armature circuit.
Il
series
field
Va
Ra
R
O
Φ
Vs
Va
Il
+o
L
Il
Vs
(a)
o-
O
(b)
Fig.2-8: a. Series motor connection diagram;
b. Schematic diagram of a series motor.
In a series motor, the armature current, field current, and line current are all the
same. The Kirchhoff’s voltage law equation for this motor is
Vs  Va  I l ( Ra  R)
(2.18)
The induced torque in this motor is expressed as
 ind  KI a
(2.10)
The flux in this motor is directly proportional to its armature current.
Therefore, the flux in the motor can be written as
  cI a
(2.19)
where c is a constant of proportionality. Thus, the induced torque is
 ind  KI a  KcI
2
a
(2.20)
From Eq. 2.20, the armature current can be given by:
Ia 
 ind
Kc
Also, Va = KΦω. Substituting this expressions in Eq. 2.18 yields:
Vs  K 
 ind
Kc
( Ra  R)
(2.21)
Or, the resulting torque-speed relationship can be written as
Vs
Ra  R
1


Kc
Kc  ind
(2.22)
According to Eq. (2.19) the speed of a series dc motor can be only controlled
efficiently by changing the terminal voltage of the motor, unlike with dc
motor.
Similarities and differentiations between the shunt motor and the series motor
Type of
dc motor
Shunt motor
Construction
similar
Series motor
Property
Φ = constant at load,
because the shunt field
is connected to the
line.
Φ depends upon the
armature current and,
hence, upon load.
Basic Principles
and Equations
same
A compounded dc motor is a motor that carries both a shunt and a series fields.
►
►
series
field
shunt
field
Va
Ix
I
Vs
+o
o-
Fig.2-9: a. DC compound motor connection diagram;
Ia
Ra
R
•
L
Il
O
If
Rf
Va
•
Vs
Lf
O
Fig.2-9: b. Schematic diagram of dc compound motor.
Current flowing into a dot produces a positive magnetomotive force.

If current flows into the dots on both field coils the resulting
magnetomotive forces add to produce a larger magnetomotive force. This
situation is known as cumulative compounding.
 If current flows into the dot on one field coil and out of the dot on the other
field coil, the resulting magnetomotive forces subtract.
Vs  Va  I a ( Ra  R)
(2.23)
The currents in the compounded motor are related by
I a  Il  I f
Vs
If 
Rf
(2.14)
(2.12)