Lecture 3

DC Motors

A same DC machine can be used as a motor or generator. Construction of a DC motor is same as that of a DC

generator, however, the former converts electrical energy into mechanical energy.

The principle of working of a DC motor is that "whenever a current carrying conductor is placed in a magnetic

field, it experiences a mechanical force". The direction of this force is given by Fleming's left hand rule and it's

magnitude is given by F = BIL. When armature windings are connected to a DC supply, current flows in the

winding. Magnetic field is provided by field winding excitation. In this case, current carrying armature conductors

experience force due to the magnetic field, and this force will produce a torque to rotate the armature, thus rotating

the machine shaft. 𝑻𝑨 =𝒁𝑷

𝟐𝝅𝑨∅𝑰𝑨

I. Operation Principle of DC motor

When the armature of the motor is rotating, the conductors

are also cutting the magnetic flux lines and hence

according to the Faraday's law of electromagnetic

induction, an emf induces in the armature conductors. The

direction of this induced emf opposes the supplied armature

current (Ia), hence it’s called Back emf and given by

the emf equation of DC generator;

EA = 𝐾∅𝜔𝑚, where K=𝑍𝑃

2𝜋𝐴

Torque per conductor;

𝑇𝑐𝑜𝑛𝑑 = 𝑟𝐹 = 𝑟𝐼𝑐𝑜𝑛𝑑𝐿𝐵where, 𝑟: the distance from the conductor axis to the force

point, 𝐹: force applied on conductor, 𝐼𝑐𝑜𝑛𝑑 : the conductor

current, 𝐿: Conductor length, 𝐵: magnetic field density

If there are A current paths in the machine, then the total

armature current IA is split among these paths, so the current in

a single conductor is;

𝐼𝑐𝑜𝑛𝑑 =𝐼𝐴

𝐴

Then the torque per conductor is given by;

𝑇𝑐𝑜𝑛𝑑 =𝑟𝐼𝐴𝐿𝐵

𝐴

The total flux (P∅ ) acting on the armature conductor is given

by;

𝑃∅ = 𝐵𝐴𝑐=𝐵2𝜋𝑟𝐿Where ∅ is the flux per pole, P is total no of poles, and

𝐴𝑐is the conductor area facing the pole

Hence, 𝑇𝑐𝑜𝑛𝑑 =𝑃∅𝐼𝐴

2𝜋𝐴

Total torque developed in armature;

𝑻𝑨 =𝒁𝑷

𝟐𝝅𝑨∅𝑰𝑨= K∅𝑰𝑨.

Where Z: total number of condcutors

EA = 𝐾∅𝜔𝑚 EA 𝐼𝐴 = 𝐾∅𝜔𝑚 𝐼𝐴

Hence, EA 𝐼𝐴 = 𝑇𝐴𝜔𝑚 = Pdev

In the DC motor, the commutator applies electric

current to the windings. By reversing the current

direction in the rotating conductors each half turn, a

steady unidirectional torque is produced. Hence, the

coil will rotate continually in the same direction.

Need of Commutator

III. Power flow diagramDC motors take in electric power and produce mechanical power. The efficiency of a DC machine is defined by

𝐼𝐴2𝑅𝐴 +𝐼𝐹

2𝑅𝐹

DC motors are usually classified of the basis of their excitation configuration, as follows -

•Separately excited (field winding is fed by external source)

•Self excited -

• Series wound (field winding is connected in series with the armature)

• Shunt wound (field winding is connected in parallel with the armature)

IV. DC motor types

Separately excited Shunt Series

𝑉𝑠 = 𝐸𝐴 +𝐼𝐴𝑅𝐴𝐼𝑠 = 𝐼𝐴

𝐼𝐹 =𝑉𝐹𝑅𝐹

𝑉𝑠 = 𝐸𝐴 +𝐼𝐴𝑅𝐴𝐼𝑠 = 𝐼𝐴 + 𝐼𝐹

𝐼𝐹 =𝑉𝑠𝑅𝐹

Speed Regulation, (SR)

𝑉𝑠 = 𝐸𝐴 +𝐼𝐴(𝑅𝐴+𝑅𝑆)𝐼𝐴 = 𝐼𝑆

Generally, three characteristic curves are considered for DC motors which are,

(i) Developed Torque versus armature current

(ii) Speed versus armature current

(iii) Terminal characteristics (Speed versus developed torque)

These characteristics are determined by keeping following two relations in mind.

V. DC motor characteristics

𝐸𝐴 = 𝐾∅𝜔𝑚 𝑇𝑑𝑒𝑣 = 𝐾∅𝐼𝐴

A separately excited dc motor is a motor whose field circuit is supplied from a separate constant-voltage power

supply, while a shunt dc motor is a motor whose field circuit gets its power directly across the armature terminals

of the motor. When the supply voltage to a motor is assumed constant, there is no practical difference in behavior

between these two machines.

When the load increases, the output torque required to drive the load will increase. Hence, the motor speed will

slow down. Consequently the internal generated voltage drops (𝐸𝐴 = 𝐾∅𝜔𝑚 ↓) , increasing the armature current in

motor 𝐼𝐴 = (𝑉𝑠 −𝐸𝐴↓)/𝑅𝐴. As the armature current increases, the developed torque increase (𝑇𝑑𝑒𝑣 = 𝐾∅𝐼𝐴 ↑) and

finally the developed torque will be equal the load torque at a lower mechanical speed of rotation 𝜔𝑚.

Mechanical Load ↑ 𝜔𝑚 ↓, 𝐼𝐴 ↑ , 𝑇𝑑𝑒𝑣 ↑

I. Separately excited/ Shunt DC motor

Torque vs. armature current

Generally, the developed torque is directly proportional to armature current and the relationship is in the form of a

straight line, assuming the field flux Φ to be constant as the supply voltage is constant.

Since, heavy starting load needs high starting current, shunt motor should never be started on a heavy load.

Speed vs. armature current

𝑉𝑠 = 𝐸𝐴 +𝐼𝐴𝑅𝐴 𝑎𝑛𝑑 𝐸𝐴 = 𝐾∅𝜔𝑚 »» 𝑉𝑠 = 𝐾∅𝜔𝑚 + 𝐼𝐴 𝑅𝐴 »» 𝜔𝑚 =(𝑉𝑠− 𝐼𝐴𝑅𝐴)

𝐾∅

As flux Φ is assumed constant, the speed decreases with armature current increase. But practically, due to armature reaction, Φ

decreases with increase in armature current, and hence the speed decrease slightly. Hence, a shunt motor can be assumed as a

constant speed motor.

Torque vs. speed

𝜔𝑚 =(𝑉𝑠 − 𝑇𝑑𝑒𝑣 𝑅𝐴/𝐾∅)

𝐾∅As flux Φ is assumed constant, , the speed decreases with developed torque increase. But practically, due to armature reaction, Φ

decreases with increase in armature current, and hence the speed decrease slightly. Thus, at heavy loads, the motor speed is

almost constant.

(𝑇𝑑𝑒𝑣 = 𝐾∅𝐼𝐴)

2. Adjusting the field resistance 𝐼𝐹 =𝑉𝑠

𝑅𝐹(and thus the field flux). This can be applied to separately excited and shunt

motors

Hence, for a constant supply voltage, at a certain load, increasing the flux decreases the motor speed.

3. Inserting a resistor in series with the armature circuit. This can be applied to separately excited and shunt motors

Hence, for a constant supply voltage and fixed flux, at a certain load, increasing 𝑅𝐴 decreases the motor speed

Speed Control of Separately excited and shunt DC Motors

1. Adjusting the supply voltage applied to the armature without changing the voltage applied to the field. Hence,

the flux is kept constant. This can be applied to separately excited motors only.

Hence, at a certain load, since the flux is fixed, increasing the armature voltage , increases the motor speed

𝜔𝑚 =(𝑉𝑠 − 𝐼𝐴 𝑅𝐴)

𝐾∅

II. Series motor

In the DC series motor, the flux is directly proportional to the armature current. As the motor load increases, the armature

current increases hence the flux increases ∅ = 𝑐𝐼𝑓 = 𝑐𝐼𝐴

Torque vs. armature current

The developed torque is directly proportional to the square of the armature current and the Tdev-IA curve is parabola for smaller

values of IA.

Speed vs. armature current

𝑉𝑠 = 𝐸𝐴 +𝐼𝐴(𝑅𝐴+𝑅𝑠) 𝑎𝑛𝑑 𝐸𝐴 = 𝐾𝑐𝐼𝐴𝜔𝑚 »» 𝑉𝑠 = 𝐾𝑐𝐼𝐴𝜔𝑚 + 𝐼𝐴 (𝑅𝐴+𝑅𝑠) »» 𝜔𝑚 =𝑉𝑠

𝐾𝑐𝐼𝐴−

(𝑅𝐴+𝑅𝑠)

𝐾𝑐

Hence, for series motor, the speed is inversely proportional to the armature current as shown in the speed-armature current curve.

When armature current is very small the speed becomes dangerously high. That is why a series motor should never be started

without some mechanical load

Torque vs. speed

𝑇𝑑𝑒𝑣 = 𝐾𝑐𝐼𝐴2 ≫≫ 𝐼𝐴 =

𝑇𝑑𝑒𝑣

𝐾𝑐»» 𝜔𝑚 =

𝑉𝑠

𝐾𝑐 𝑇𝑑𝑒𝑣−

(𝑅𝐴+𝑅𝑠)

𝐾𝑐

𝑇𝑑𝑒𝑣 = 𝐾∅𝐼𝐴 ≫≫≫𝑇𝑑𝑒𝑣 = 𝐾𝑐𝐼𝐴2

For series motor, the speed is inversely proportional to the square root of the torque

Speed Control of series Motors

𝜔𝑚 =𝑉𝑠𝐾𝑐𝐼𝐴

−(𝑅𝐴+𝑅𝑠)

𝐾𝑐1. Adjusting the supply voltage applied

At a certain load, increasing the supply voltage , increases the motor speed

2. Inserting a series resistor into the motor circuit

At a certain load and certain supply voltage, increasing the circuit resistance, decreases the motor speed

Applications

• Separately excited DC motors are often used as actuators in trains and automotive traction applications.

• For their constant speed characteristics, shunt DC motors are used in fixed speed applications such as fans.

• Since the series motors can give high torque per ampere (since their toque is directly proportional to the

square of armature current), they can be used in applications that require high starting torque. Examples of

these applications include; starter motors in cars, and elevator motors.

• Discuss the theory of operation of DC motor

• What is the need of commutator for DC motor ?

• What are different DC motor types?

Draw their equivalent circuits

Draw their torque-armature current characteristics

Draw their speed-armature current characteristics

Draw their speed-torque characteristics

How to control their speed?

State their applications