Direct-current motor is a device that transforms the electrical energy into mechanical energy.

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

DC motor drives some devices such as hoists, fans, pumps, calendars, punch-presses, and cars. The ability to control the speed with great accuracy is an attractive feature of the dc motor.

The voltage induced Va in the armatureof a dc motor is expressed by:

where

Va = armature voltage (V) K = constant ω = speed of rotation of the motor (r/min) Φ = flux per pole (Wb)

KVa (2.1)

Armature is the rotating part of a dc motor

Ia

Vs

+

+

Fig.2-1: Simple circuit of a dc motor.

R

ω

ΦVa

N S

where Z = total number of conductors on rotor a = number of current paths P = number of poles on the machine

The constant K can be calculated from:

a

ZPK

2

whereas total number of conductors can be expressed as:

CNZ 2

where C = number of coils on rotor a = number of turns per coil

(2.2)

(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

asnet VVV (2.4)

and not,

asnet VVV

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:

ase IVP

so,

RIIVP aaae2

The Ia2R term represents heat dissipated in the armature and VaIa is the

electrical power that is converted into mechanical power.

(2.5)

(2.7)

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:

(2.6)RIVV aas

The mechanical power developed by a motor depends upon its rotational speed and torque it develops given by:

indmP

where

τind = induced torque developed by a dc motor (N.m)

ω = speed of rotation (r/min)

(2.9)

Therefore, the mechanical power Pm of the motor in Watt is equal to the product of the cemf multiplied by the armature current:

aam IVP (2.8)

aind IK

aind IK

and so

(2.10)

Combining Eq. 2.8 and 2.9, we obtain

aaind IV

With substituting Va from Eq. 2.1 into Eq. 2.6 and Ia is determined from Eq. 2.10, we obtain

RK

KV inds

Solving for the motor’s speed produces

inds

K

R

K

V 2

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.

Fig.2-2: Circuit of a separately excited dc motor.

If

Field Lf

Rf

Vf

Il

Ia

Ra

VaN S Vs

In circuit of the separatly excited dc motor, the field current If in Ampere is

f

sf R

VI

where

Rf = shunt-field resistance (Ω)

(2.12)

Fig. 2-2 shows that the current generated by voltage source Il is equal to the armature current Ia:

al II (2.13)

Shunt dc motor is a motor whose its armature and field circuit in parallel across terminals of a dc supply.

Vs

Va

Rf

Ra

Field

Fig.2-3: Circuit of a shunt dc motor.

Il

IaIf

Lf

The field current If in Ampere is

f

sf R

VI (2.12) N S

Whereas the current generated by voltage source Il is

fal III (2.14)

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.

Fig.2-4: Schematic diagram of the field resistance control.

This method is frequently used when the motor has to run above its rated speed, called base speed.

Vs

Ia

Il

If

shunt field

Rf

+

R

field rheostat

ΦVa

If a motor is running at its rated terminal voltage, power, and field current, so it will be turning at base speed.

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.

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.

Summary of the cause-and-effect behavior involved in this method of speed control:

Motor

Motor

τind

τload

Load

I

Motor

Motor

τind

τload

Load

I

ω1

Motor

Motor

τind

τload

Load

I

ω2

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.

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.

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

tconsP tanmax

While the maximum torque varies as reciprocal of the motor’s speed.

(2.15)

Fig.2-6: Armature voltage control of a shunt dc motor.

Vs

Va

Rf

Ra

Field

Il

Ia

If

Lf

Variable Voltage

Controller

Vc

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).

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.

If Φ = constant, so the maximum torque in the motor is

max,max aIK

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

maxmax P

(2.16)

(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

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.

However, the insertion of a resistor yields very large losses in the inserted resistor.

Rheostat speed control is a way to control the speed of a dc motor by inserting a rheostat in series with the armature circuit.

shunt field

Vs

If

Ia

armature rheostat

Fig.2-7: Armature speed control using a rheostat.

+Il

R

+

Va

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.

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 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.

A series dc motor is a dc motor whose field windings composed of a few turns connected in series with the armature circuit.

Fig.2-8: a. Series motor connection diagram; b. Schematic diagram of a series motor.

Φ

o Vs

Va

o+ -

Il Il

series field

(a) (b)

Va

O

O

IlRa R L

Vs

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

)( RRIVV alas

The induced torque in this motor is expressed as

aind IK

The flux in this motor is directly proportional to its armature current. Therefore, the flux in the motor can be written as

acI

where c is a constant of proportionality. Thus, the induced torque is

2aaind KcIIK

(2.18)

(2.19)

(2.10)

(2.20)

From Eq. 2.20, the armature current can be given by:

KcI ind

a

Also, Va = KΦω. Substituting this expressions in Eq. 2.18 yields:

)( RRKc

KV aind

s

Or, the resulting torque-speed relationship can be written as

Kc

RR

Kc

V a

ind

s

1

(2.22)

(2.21)

Φ depends upon the armature current and, hence, upon load.

Φ = constant at load, because the shunt field is connected to the line.

Property

samesimilar

Shunt motor

Construction

Series motor

Basic Principles and Equations

Type of

dc motor

Similarities and differentiations between the shunt motor and the series motor

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.

A compounded dc motor is a motor that carries both a shunt and a series fields.

o

Vs

Va

o+ -

I

series field

Ix

shunt field

►

►

Fig.2-9: a. DC compound motor connection diagram;

Va

O

O

Ia Ra R L

Vs

Rf

If

Lf

Il

•

•

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.)( RRIVV aaas

The currents in the compounded motor are related by

fla III

f

sf R

VI

(2.23)

(2.14)

(2.12)