DC Machine Principles

Contents
➢ Introduction
➢ Construction
➢ Theory of operation
➢ Role of commutators
➢ Equivalent circuit of DC machine
➢ DC machines classifications
 Introduction
➢ The Direct Current (DC) machine can be used as a motor or as a generator.

Magnetic field (flux) Magnetic field (flux)

➢ DC Motors convert electrical energy to ➢ DC Generators convert mechanical energy

mechanical energy in the presence of to electrical energy in the presence of
magnetic field. magnetic field.

Motoring Action Generating Action

 Introduction
❑ Applications of DC machines
DC Generators
➢ Although a DC machine can operate as either a generator or a motor, at present its use as a generator is
limited because of the widespread use of ac power

➢ Applications of DC generators are limited to:

1. Charging batteries

2. Voltage boosting applications in the feeders

for voltage drop compensation

3. Arc welding that requires voltage drop Charging batteries with

DC arc welding generator
and constant current. DC diesel generator
 Introduction
❑ Applications of DC machines
DC Motors
➢ The dc machine is extensively used as a motor in industry. Its speed can be controlled over a wide
range with relative ease.

➢ Applications of DC Motors :

• Large dc motors (in tens or hundreds of horsepower) are

used in machine tools, printing press, conveyors, fans,
pumps, textile mills, and so on.

• Dc motors still dominate as traction motors used in

transit cars and locomotives, and cranes
DC servo motor
• Small dc machines are used primarily as control devices,
such as tachogenerators for speed sensing and 150 KW DC traction motor
servomotors for positioning and tracking
 Construction of DC machine
➢ DC Machine consists of four main parts:

1. Stator Stationary part

• Yoke
• Poles
• Field windings

2. Rotor Rotating part

• Armature core
• Armature winding

3. Commutators

4. Brushes
 Construction of DC machine
1. Yoke

➢ It is the outer frame of the stator

➢ It provides mechanical support for the poles and acts as a protecting cover for the whole machine

➢ It also carries the magnetic flux produced by the poles

➢ The materials used in the yoke are designed with cast iron, cast steel otherwise rolled steel.
 Construction of DC machine
2. Pole Core and pole shoe

➢ It is electromagnet and the field winding is winding among pole

➢ The pole consist of pole cores and pole shoes.

➢ The pole shoes serve two purposes; They spread out the flux in the air gap and also,
being of larger cross-section, reduce the reluctance of the magnetic path.
 Construction of DC machine
3. Field winding (Exciting winding)

➢ The field coils, which consist of copper wire, are former-wound for the correct dimension.

➢ Then, the former is removed, and wound coil is put into place over the pole core

➢ When current is passed through these coils, they electromagnetise the poles which produce
the necessary flux that is cut by revolving armature conductors.
 Construction of DC machine
4. Armature core (rotor core)

➢ It is cylindrical shaped and is built up of usually circular laminations approximately 0.5 mm

➢ Armature core includes a huge number of slots within its edge. The armature conductor is located in these slots.

➢ It provides the low-reluctance path toward the flux generated with field winding.

➢ The materials used in this core are permeability low-reluctance materials like iron otherwise cast.
 Construction of DC machine
5. Armature winding

➢ The armature winding can be formed by interconnecting the armature conductor.

➢ Armature winding is the productive element in DC machine

➢ In generator operation Armature winding is forced to rotate, then voltage is induced on it

➢ In motor operation Voltage is applied to armature, then torque is produced on armature which makes it rotate
 Construction of DC machine
6. Commutator

➢ It is of copper cylindrical structure and is built up of wedge-shaped segments.

➢ These segments are insulated from each other by thin layers of mica.
➢ The function of the commutator is to facilitate collection of current from the armature conductors.

➢ In generator operation It provides unidirectional current to the load

➢ In motor operation It provides unidirectional torque

➢ Number of segments is equal to the number of armature coils. Each commutator segment is connected to
the armature conductor.
 Construction of DC machine
7. Brushes

➢ Brushes in the DC machine collect the current from the commutator and supply it to the exterior load

➢ They are usually made of carbon or graphite and its shape is rectangular.

➢ Brushes wear with time. So. It needs to be inspected regularly

 DC Generator Working Principle
According to Faraday’s law, whenever a conductor is placed in a fluctuating magnetic field
(or when a conductor is moved in a magnetic field) an EMF is induced in the conductor.

Magnetic field (flux)

➢ Field winding is connected to DC supply

For magnetic flux production

➢ Armature winding is forced to rotate by external prime mover

For providing mechanical input power

The induced voltage is called the generated armature voltage (Ea)

 DC Generator Working Principle
❑ The generated voltage is AC or DC ?
➢ Faraday’s law states that when a conductor is moving in a magnetic field, EMF is induced on the
conductor and having the following formula:

𝒆𝒎𝒇 = 𝑩 ∗ 𝒍 ∗ 𝒗

➢ According to right hand rule, the direction of the induced current is determined

➢ The flux is perpendicular on the velocity of the conductor

 DC Generator Working Principle
❑ The generated voltage is AC or DC ?
➢ Faraday’s law states that when a conductor is moving in a magnetic field, EMF is induced on the
conductor and having the following formula:

𝒆𝒎𝒇 = 𝑩 ∗ 𝒍 ∗ 𝒗
➢ If the flux is not perpendicular on the velocity of the conductor, then the following formula is used:

𝒆𝒎𝒇 = 𝑩 ∗ 𝒍 ∗ 𝒗 ∗ 𝒔𝒊𝒏(𝜽)

𝜽 = 𝒕𝒉𝒆 𝒂𝒏𝒈𝒍𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒕𝒉𝒆 𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒄 𝒇𝒍𝒖𝒙 𝒂𝒏𝒅 𝒕𝒉𝒆 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚

 DC Generator Working Principle
❑ The generated voltage is AC or DC ?
➢ Let's study the one coil operation in
one complete cycle
• At position A: Linear velocity is
parallel to the flux direction (𝜽=0),
emf =0
• At position B: Linear velocity is
perpendicular to the flux direction (𝜽=90),
emf =maximum

• At position C: Linear velocity is

parallel to the flux direction (𝜽=0),
emf =0

• At position D: Linear velocity is perpendicular to the flux

direction (𝜽=90), and linear velocity direction is reversed,
emf =maximum and reversed
 DC Generator Working Principle
❑ The generated voltage is AC or DC ?
➢ Let's study the one coil operation in
one complete cycle

• The generated voltage is AC voltage

 DC Generator Working Principle
➢ Without commutator segments, slip rings are used and the generated voltage is AC
 Role of commutator in DC generators
• It is clear that the current obtained from this simple
generator reverses its direction after every half
revolution.
• Such a current undergoing periodic reversal is
known as alternating current.

➢ For making the flow of current unidirectional in the external circuit, a conducting cylinder which is cut into two
halves (segments) insulated from each other by a thin sheet of mica are used

➢ The coil ends are joined to segments a and b

on which rest the carbon brushes.

Commutator are used to rectify the

armature voltage and concert it to a
DC voltage
 Role of commutator in DC generators
❑ How can commutators rectify the armature voltage ?

First half of revolution Second half of revolution

• current flows along (ABMLCD) • The direction of the induced current in the coil has reversed (DCMLBA).
• The brush No. 1 in contact with • But at the same time, the positions of segments ‘a’ and ‘b’ have also reversed
segment ‘a’ acts as the positive end of
the supply and ‘b’ as the negative end. • As a result, brush No. 1 comes in touch with the segment which is positive
(segment ‘b’ in this case)
• Current in the load resistance flows
from M to L. • Hence, current in the load resistance again flows from M to L.
 Role of commutator in DC generators
❑ How can commutators rectify the armature voltage ?

➢ As no of commutator segments increase, the output voltage is more rectified (ripple free))
 DC Motor Working Principle
When a current-carrying conductor is placed in a magnetic field, the conductor
experiences a mechanical force.

Magnetic field (flux)

➢ Field winding is connected to DC supply (Vf)

For magnetic flux production

➢ Armature winding is connected to DC supply (Vt)

For current flowing in armature

Torque is produced on the armature hence, the armature core rotates

 DC Motor Working Principle
➢ Without commutator segments, slip rings are used and the torque is bidirectional

➢ The direction of rotation is reversed at each half cycle

 DC Motor Working Principle
➢ With commutator segments, the torque is unidirectional

➢ The direction of rotation is constant

DC Machine Equivalent Circuit

Field circuit Armature circuit

𝑹𝒇 : 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑓𝑖𝑒𝑙𝑑 𝑤𝑖𝑛𝑑𝑖𝑛𝑔 𝑹𝒂 : 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑛𝑑𝑖𝑛𝑔

𝑳𝒇 : 𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑓𝑖𝑒𝑙𝑑 𝑤𝑖𝑛𝑑𝑖𝑛𝑔 𝑳𝒂 : 𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑛𝑑𝑖𝑛𝑔
𝑽𝒇 : 𝐹𝑖𝑒𝑙𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑬𝒂 : 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝑰𝒇 : 𝐹𝑖𝑒𝑙𝑑 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑽𝒕 : 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝑰𝒂 : 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
 DC Machine Equivalent Circuit

Field circuit Armature circuit

➢ For Generator • Armature terminals connected to load

• 𝑰𝒂 flows from 𝑬𝒂 to 𝑽𝒕
• 𝑬𝒂 > 𝑽𝒕

➢ For Motor • Armature terminals connected to DC supply

• 𝑰𝒂 flows from 𝑽𝒕 to 𝑬𝒂
• 𝑽𝒕 > 𝑬𝒂
 Types of Armature winding
➢ In DC machine, the armature conductors (in the form of coils) are placed in the slots around the surface of cylindrical
armature core.

➢ The coils are connected in series through the commutator

segments such that their EMFs are added to each other.

➢ In DC machines, two types of armature windings are used:

1. Lap Winding

2. Wave Winding

➢ The difference between these two is merely due to the end connections and commutator connections of the conductor.
 Types of Armature winding
❑ Basic definitions and rules

1. A turn consists of two conductors.

2. A coil is formed by connecting several turns in series, with two ends (S=start & F=finish).
Therefore, each coil has two coil sides.

3. A winding is formed by connecting several coils in series.

 Types of Armature winding
❑ Basic definitions and rules
4. Back pitch (YB): It is the distance between the two coil sides (S and F) of one coil

5. Front pitch (YF): It is the distance between the Finish (F) coil side of one coil and the Start (S) coil side of next coil

6. Winding pitch (Y): it is the distance between the beginnings of two consecutive turns.
 Types of Armature winding
1. Lap Winding

➢ In lap winding, the successive coils overlap each other.

➢ The two ends of a coil are connected to adjacent commutator segments.

➢ The armature coils are connected in such a way that the armature winding is divided
into as many parallel paths as the number of poles of the machine

No of parallel paths = no of poles

➢ No of brushes equal to no of poles

 Types of Armature winding
1. Lap Winding
➢ Let's define:

𝒂: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑝𝑎𝑡ℎ𝑠 𝑜𝑓 𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑛𝑑𝑖𝑛𝑔

𝟐𝑷 ∶ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠
𝑰𝒂 ∶ 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑰𝒂
𝒂 = 𝟐𝑷 𝑰𝒄 =
𝑰𝒄 ∶ 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝟐𝑷

➢ Applications of Lap winding

❑ This type of winding used to achieve

• low voltage high current DC generator

• low voltage high torque DC motor
 Types of Armature winding
2. Wave Winding

➢ In this type of connection, winding always travels ahead avoiding overlapping. It

travel like a progressive wave hence called wave winding.

➢ In other words, all the coils which carry emf in the same direction are
connected in series.

➢ The armature coils are connected in such a way that the armature winding is divided
into TWO parallel paths regardless of the number of poles

No of parallel paths = 2

➢ Only two brushes are used

 Types of Armature winding
2. Wave Winding
➢ Let's define:

𝒂: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑝𝑎𝑡ℎ𝑠 𝑜𝑓 𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑛𝑑𝑖𝑛𝑔

𝟐𝑷 ∶ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠
𝑰𝒂 ∶ 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑰𝒂
𝒂=𝟐 𝑰𝒄 =
𝑰𝒄 ∶ 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝟐

➢ Applications of Lap winding

❑ This type of winding used to achieve

• High voltage low current DC machines

 Generated EMF Equation
➢ Consider the following DC machine

➢ Let's define:
𝐷 = 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑑𝑖𝑎𝑚𝑒𝑛𝑡𝑒𝑟
𝐿 = 𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝐿𝑒𝑛𝑡ℎ (𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑙𝑒𝑛𝑛𝑔ℎ𝑡)
∅ = 𝐹𝑙𝑢𝑥 𝑝𝑒𝑟 𝑝𝑜𝑙𝑒
2𝑃 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠
𝜏𝑝 = 𝑃𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ
The peripheral distance between centers of two adjacent poles

➢ The induced emf on an armature conductor is given by:

𝒆𝒄 = 𝑩 ∗ 𝒍 ∗ 𝒗 𝐵 = 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

𝑙 = 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
𝑣 = 𝑙𝑖𝑛𝑒𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
Armature
 Generated EMF Equation
𝒆𝒄 = 𝑩 ∗ 𝒍 ∗ 𝒗

∅
𝑩= 𝒗=𝒘 ∗𝒓
𝑨
𝟐𝝅𝒏
𝑨 = 𝑨𝒓𝒆𝒂 𝒑𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓 𝒕𝒐 𝒇𝒍𝒖𝒙 𝒘 = 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅 =
𝟔𝟎
𝑨 = 𝝉𝒑 ∗ 𝒍 𝑫
𝒓 = 𝑨𝒓𝒎𝒂𝒕𝒖𝒓𝒆 𝒓𝒂𝒅𝒊𝒐𝒖𝒔 =
𝟐
𝝅𝑫
𝑨= ∗𝒍
𝟐𝑷

𝝅𝒏𝑫
∅ ∗ 𝟐𝑃 𝒗=
𝐵= 𝟔𝟎
𝜋𝐷 ∗ 𝑙

∅ ∗ 𝟐𝑷 𝝅𝒏𝑫 ∅ ∗ 𝟐𝑷 ∗ 𝒏
➢ Then, 𝒆𝒄 = ( ) ∗𝒍 ∗( ) 𝒆𝒄 =
𝝅𝑫 ∗ 𝒍 𝟔𝟎 𝟔𝟎
Armature
 Generated EMF Equation
∅ ∗ 𝟐𝑷 ∗ 𝒏
𝒆𝒄 =
𝟔𝟎

➢ Let 𝑍 = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑠

➢ Let the total number of conductors 𝒁 are divided into a parallel paths

➢ Then, the generated voltage across the machines (Ea) is:

∅ ∗ 𝟐𝑷 ∗ 𝒏 𝒁
𝐸𝑎 = 𝒆𝒄 ∗ 𝒁ൗ𝒂 𝐸𝑎 = ∗ ൗ𝒂
𝟔𝟎

𝒁 ∗ 𝟐𝑷 𝒏 𝟐𝝅
𝑬𝒂 = ∗∅ ∗ ∗
𝒂 𝟔𝟎 𝟐𝝅

𝒁 ∗ 𝟐𝑷 𝟐𝝅𝒏
𝑬𝒂 = ( ) ∗∅ ∗
𝟐𝝅𝒂 𝟔𝟎
 Generated EMF Equation
𝒁 ∗ 𝟐𝑷 𝟐𝝅𝒏
𝑬𝒂 = ( ) ∗∅ ∗
𝟐𝝅𝒂 𝟔𝟎

𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝒁 ∗ 𝟐𝑷
𝑲𝒂 = 𝑨𝒓𝒎𝒂𝒕𝒖𝒓𝒆 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 =
𝟐𝝅𝒂

∅ = 𝑭𝒍𝒖𝒙 𝒑𝒆𝒓 𝒑𝒐𝒍𝒆

𝟐𝝅𝒏
𝝎 = 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅 =
𝟔𝟎
 Developed Torque Equation
➢ When armature conductors of a DC motor carry current in the presence of
stator field flux, a mechanical torque is developed (𝑻𝒅𝒆𝒗 )

➢ The torque is the quantitative measure of the tendency of a force to

cause a rotational motion

➢ From the circuit representation of DC motor

𝑽𝒕 = 𝑬𝒂 + 𝑰𝒂 𝑹𝒂 (∗ 𝑰𝒂 )

𝑽𝒕 𝑰𝒂 = 𝑬𝒂 𝑰𝒂 + 𝑰𝟐𝒂 𝑹𝒂

Input electrical power = Mechanical power developed by the armature + armature losses

➢ Thus, let’s define: 𝑷𝒅𝒆𝒗 = 𝑴𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍 𝒑𝒐𝒘𝒆𝒓 𝒅𝒆𝒍𝒐𝒑𝒆𝒅 𝒃𝒚 𝒂𝒓𝒎𝒂𝒕𝒖𝒓𝒆 𝒄𝒐𝒊𝒍

𝑷𝒅𝒆𝒗 = 𝑬𝒂 ∗ 𝑰𝒂

𝑷𝒅𝒆𝒗 = 𝑻𝒅𝒆𝒗 ∗ 𝝎
Developed Torque Equation
𝑷𝒅𝒆𝒗 = 𝑬𝒂 ∗ 𝑰𝒂

𝑷𝒅𝒆𝒗 = 𝑻𝒅𝒆𝒗 ∗ 𝝎

𝑻𝒅𝒆𝒗 ∗ 𝝎 = 𝑬𝒂 ∗ 𝑰𝒂

▪ 𝒃𝒖𝒕, 𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝑻𝒅𝒆𝒗 ∗ 𝝎 = 𝑲𝒂 ∗ ∅ ∗ 𝝎 ∗ 𝑰𝒂 𝑻𝒅𝒆𝒗 = 𝑲𝒂 ∗ ∅ ∗ 𝑰𝒂
 Developed Torque Equation

➢ Summary:

Generated emf equation Developed torque equation

𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎 𝑻𝒅𝒆𝒗 = 𝑲𝒂 ∗ ∅ ∗ 𝑰𝒂

𝒁 ∗ 𝟐𝑷
𝑲𝒂 = 𝑨𝒓𝒎𝒂𝒕𝒖𝒓𝒆 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 =
𝟐𝝅𝒂

∅ = 𝑭𝒍𝒖𝒙 𝒑𝒆𝒓 𝒑𝒐𝒍𝒆

𝟐𝝅𝒏
𝝎 = 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅 =
𝟔𝟎
 Example 1
A four-pole DC machine has an armature of radius 12.5 cm and an effective length of 25 cm. The poles cover 75% of the
armature periphery. The armature winding consists of 33 coils, each coil having seven turns. The coils are accommodated in
33 slots. The average flux density under each pole is 0.75T.
1. If the armature is lap-wound,
(a) Determine the armature constant Ka.
(b) Determine the induced armature voltage when the armature rotates at 1000 rpm.
(c) Determine the current in the coil and the electromagnetic torque developed when the armature current is 400 A.
(d) Determine the power developed by the armature.
2. If the armature is wave-wound,
repeat parts (a) to (d) above. The current rating of the coils remains the same as in the lap-wound armature.

1. If the armature is lap-wound 𝒂 = 𝟐𝒑 = 𝟒

𝒁 ∗ 𝟐𝑷 (𝟑𝟑 ∗ 𝟕 ∗ 𝟐) ∗ 𝟒
𝒂 𝑲𝒂 = = = 𝟕𝟑. 𝟓𝟑
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟒
 Example 1
1. If the armature is lap-wound 𝒂 = 𝟐𝒑 = 𝟒

𝒁 ∗ 𝟐𝑷 (𝟑𝟑 ∗ 𝟕 ∗ 𝟐) ∗ 𝟒
𝒂 𝑲𝒂 = = = 𝟕𝟑. 𝟓𝟑
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟒

𝒃 𝑬𝒂 =? 𝒊𝒇 𝒏 = 𝟏𝟎𝟎𝟎 𝒓𝒑𝒎

𝑬 𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝟐𝝅𝒏 𝟐𝝅∗𝟏𝟎𝟎𝟎
• 𝝎= = = 𝟏𝟎𝟒. 𝟕𝟐 𝒓/𝒔
𝟔𝟎 𝟔𝟎

• ∅ = 𝑩𝒂𝒗𝒈 ∗ 𝑨 ∗ %𝒐𝒇 𝒑𝒐𝒍𝒆𝒔 𝒄𝒐𝒗𝒆𝒓𝒂𝒈𝒆 = 𝑩𝒂𝒗𝒈 ∗ 𝜏𝑝 ∗ 𝑙 ∗ %𝒐𝒇 𝒑𝒐𝒍𝒆𝒔 𝒄𝒐𝒗𝒆𝒓𝒂𝒈𝒆

𝝅𝑫 𝝅∗ 𝟐𝟓∗𝟏𝟎−𝟐
• ∅ = 𝑩𝒂𝒗𝒈 ∗ ∗ 𝑙 ∗ %𝒐𝒇 𝒑𝒐𝒍𝒆𝒔 𝒄𝒐𝒗𝒆𝒓𝒂𝒈𝒆 = 𝟎. 𝟕𝟓 ∗ ∗ 𝟐𝟓 ∗ 𝟏𝟎−𝟐 ∗ 𝟎. 𝟕𝟓
𝟐𝑷 𝟒

• ∅ = 𝟎. 𝟎𝟐𝟕𝟔 𝒘𝒃
 Example 1
1. If the armature is lap-wound 𝒂 = 𝟐𝒑 = 𝟒

𝒁 ∗ 𝟐𝑷 (𝟑𝟑 ∗ 𝟕 ∗ 𝟐) ∗ 𝟒
𝒂 𝑲𝒂 = = = 𝟕𝟑. 𝟓𝟑
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟒

𝒃 𝑬𝒂 =? 𝒊𝒇 𝒏 = 𝟏𝟎𝟎𝟎 𝒓𝒑𝒎

𝑬 𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝑬𝒂 = 𝟕𝟑. 𝟓𝟑 ∗ 𝟎. 𝟎𝟐𝟕𝟔 ∗ 𝟏𝟎𝟒. 𝟕𝟐 = 𝟐𝟏𝟐. 𝟓 𝑽

 Example 1
1. If the armature is lap-wound 𝒂 = 𝟐𝒑 = 𝟒

𝒄 𝑰𝒄 =? 𝒂𝒏𝒅 𝑻𝒅𝒆𝒗 =? 𝒊𝒇 𝑰𝒂 = 𝟒𝟎𝟎𝑨

𝑰𝒂 𝑰𝒂 𝟒𝟎𝟎
▪ 𝑰𝒄 = = = = 𝟏𝟎𝟎 𝑨
𝒂 𝟐𝒑 𝟒

▪ 𝑻𝒅𝒆𝒗 = 𝑲𝒂 ∗ ∅ ∗ 𝑰𝒂

▪ 𝑻𝒅𝒆𝒗 = 𝟕𝟑. 𝟓𝟑 ∗ 𝟎. 𝟎𝟐𝟕𝟔 ∗ 𝟒𝟎𝟎 = 𝟖𝟏𝟏. 𝟖 𝑵. 𝒎

𝒅 𝑷𝒅𝒆𝒗 =?

▪ 𝑷𝒅𝒆𝒗 = 𝑬𝒂 ∗ 𝑰𝒂 = 𝟐𝟏𝟐. 𝟓 ∗ 𝟒𝟎𝟎 = 𝟖𝟓 𝑲𝒘

 Example 1
1. If the armature is wave-wound 𝒂=𝟐

The current rating of the coils remains the same as in the lap-wound armature

𝑰𝒄 = 𝟏𝟎𝟎 𝑨

𝒁 ∗ 𝟐𝑷 (𝟑𝟑 ∗ 𝟕 ∗ 𝟐) ∗ 𝟒
𝒂 𝑲𝒂 = = = 𝟏𝟒𝟕. 𝟎𝟔
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟐

𝒃 𝑬𝒂 =? 𝒊𝒇 𝒏 = 𝟏𝟎𝟎𝟎 𝒓𝒑𝒎

𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝑬𝒂 = 𝟏𝟒𝟕. 𝟎𝟔 ∗ 𝟎. 𝟎𝟐𝟕𝟔 ∗ 𝟏𝟎𝟒. 𝟕𝟐 = 𝟒𝟐𝟓 𝑽

 Example 1
1. If the armature is wave-wound 𝒂=𝟐

The current rating of the coils remains the same as in the lap-wound armature

𝑰𝒄 = 𝟏𝟎𝟎 𝑨

▪ 𝒄 𝑰𝒄 = 𝟏𝟎𝟎 𝑨 𝑰𝒂 = 𝟐 ∗ 𝟏𝟎𝟎 = 𝟐𝟎𝟎 𝑨

▪ 𝑻𝒅𝒆𝒗 = 𝑲𝒂 ∗ ∅ ∗ 𝑰𝒂

▪ 𝑻𝒅𝒆𝒗 = 𝟏𝟒𝟕. 𝟎𝟔 ∗ 𝟎. 𝟎𝟐𝟕𝟔 ∗ 𝟐𝟎𝟎 = 𝟖𝟏𝟏. 𝟖 𝑵. 𝒎

𝒅 𝑷𝒅𝒆𝒗 =?

▪ 𝑷𝒅𝒆𝒗 = 𝑬𝒂 ∗ 𝑰𝒂 = 𝟒𝟐𝟓 ∗ 𝟐𝟎𝟎 = 𝟖𝟓 𝑲𝒘

 Example 2
An 8-pole DC generator has 500 armature conductors, and a useful flux of 0.05 Wb per pole. What will be the e.m.f.
generated if it is lap-connected and runs at 1200 rpm? What must be the speed at which it is to be driven to produce the
same e.m.f. if it is wave- wound?

1. If the armature is lap-wound 𝒂 = 𝟐𝒑 = 𝟖

𝒁 ∗ 𝟐𝑷 𝟓𝟎𝟎 ∗ 𝟖
𝑲𝒂 = = = 𝟕𝟗. 𝟓𝟕
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟖
𝟐𝝅 ∗ 𝟏𝟐𝟎𝟎
𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎 𝑬𝒂 = 𝟕𝟗. 𝟓𝟕 ∗ 𝟎. 𝟎𝟓 ∗ = 𝟓𝟎𝟎 𝑽
𝟔𝟎

2. If the armature is wave-wound 𝒂=𝟐

𝒁 ∗ 𝟐𝑷 𝟓𝟎𝟎 ∗ 𝟖
𝑲𝒂 = = = 𝟑𝟏𝟖. 𝟑
𝟐𝝅𝒂 𝟐𝝅 ∗ 𝟐

𝟐𝝅 ∗ 𝒏
𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎 𝟓𝟎𝟎 = 𝟑𝟏𝟖. 𝟑 ∗ 𝟎. 𝟎𝟓 ∗ 𝒏 = 𝟑𝟎𝟎 𝒓𝒑𝒎
𝟔𝟎
 Magnetization Curve of DC Machine
➢ It is the relation between armature generated voltage 𝑬𝒂 and field current 𝑰𝒇 at constant speed in DC machine

𝑬𝒂 = 𝑲𝒂 ∗ ∅ ∗ 𝝎

𝑨𝒕 𝒘 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑬𝒂 ∝ ∅

∅ ∝ 𝑰𝒇 𝑬 𝒂 ∝ 𝑰𝒇

➢ This curve is also called:

• No load Characteristics

• Open Circuit Characteristics (O.C.C)

• Saturation Curve
 Magnetization Curve of DC Machine
Saturation
❑ Notes on magnetization curve region
Linear
▪ In linear region:
region
As field current increases, flux increases, and the induced voltage Knee
increases with the same amount point
𝑰𝒇 ∅ 𝑬𝒂
▪ In Saturation region:

For further increase in the field current, the poles get saturated, and the
flux becomes practically constant. Thus, Ea also remains constant.

𝑰𝒇 ∅ ≅ 𝒄𝒐𝒏𝒔𝒕 𝑬𝒂 ≅ 𝒄𝒐𝒏𝒔𝒕

▪ To get the maximum possible power, DC machines are designed to operate near
the saturation point on the magnetization curve (at the knee of the curve).

▪ This allows a linear relationship between the Voltage and the field current,
which facilitates the dc machine control.
 Magnetization Curve of DC Machine
Saturation
region
❑ Notes on magnetization curve
Linear
▪ At initial point region
➢ When the field current is zero, some amount of emf is generated
➢ This initially induced emf is due to residual magnetism in the field
poles. Therefore, a small initial emf is induced in the armature.

𝑰𝒇 = 𝟎 ∅ = ∅𝒓𝒆𝒔 𝑬𝒂 = 𝑬𝒓𝒆𝒔 𝑬𝒓𝒆𝒔

▪ For different speeds

 DC Machines Classifications
➢ A DC machine has two distinct circuits, a field circuit and an armature circuit.

➢ A simple schematic representation of the DC machine is shown below:

➢ The field circuit and the armature circuit can be interconnected in various ways to
provide a wide variety of performance characteristics.

➢ DC machines are usually classified according to the way in which their field circuits are excited.
 DC Machines Classifications
1. Separately excited

• DC machines are those whose field circuit is energized

from an independent external source of DC current.

• Field and armature circuits are separate from each others

2. Self excited
• DC machines whose field magnets are energized by the
current produced by the machines themselves.

• There are three types of self-excited generators named according to the

manner in which the field circuit is connected to the armature.

• For compound machines, Field poles are excited from 2 windings:

shunt field winding and series field winding