EKT 103 KT 103 CHAPTER CHAPTER 5 5 DC Machine Contents - - PowerPoint PPT Presentation

EKT 103 KT 103

CHAPTER CHAPTER 5 5

DC Machine

Contents Contents

O er ie

• f Direct C rrent Machines

– Overview of Direct Current Machines – Construction P i i l f O ti – Principle of Operation – Types of DC Machine – Power Flow Diagram – Speed Control

LEARNING OBJECTIVES LEARNING OBJECTIVES

• Upon completion of the chapter the student

p p p should be able to:

– State the principle by which machines convert mechanical energy to electrical energy mechanical energy to electrical energy. – Discuss the operating differences between different types of generators – Understand the principle of DC generator as it represents a logical behavior of dc motors.

Overview of Direct Current Machines Machines

• Direct-current (DC) machines are divided into dc generators and dc

motors. motors.

• Most DC machines are similar to AC machines: i.e. they have AC

voltages and current within them. DC hi h DC t t j t b th h

• DC machines have DC outputs just because they have a

mechanism converting AC voltages to DC voltages at their terminals.

• This mechanism is called a commutator; therefore, DC machines

are also called commutating machines.

• DC generators are not as common as they used to be, because

g y , direct current, when required, is mainly produced by electronic rectifiers.

• While dc motors are widely used, such automobile, aircraft, and

y , , , portable electronics, in speed control applications…

DC Generator DC Generator

• A dc generator is a machine that converts

h i l i l i l mechanical energy into electrical energy (dc voltage and current) by using the principle of magnetic induction.

• In this example, the ends of the wire loop

have been connected to two slip rings mounted on the shaft, while brushes are , used to carry the current from the loop to the outside of the circuit.

Principle of magnetic induction in DC machine

DC Motor

• DC motors are everywhere! In a house, almost every mechanical

movement that you see around you is caused by an DC (direct current) motor current) motor.

• An dc motor is a machine that converts electrical energy into

h i l b l i d ( lt d t) mechanical energy by supplying a dc power (voltage and current).

• An advantage of DC motors is that it is easy to control their speed in

a wide diapason.

Construction of DC machine

Cutaway view of a dc motor Stator with poles visible.

Construction of DC machine

segments

R t f d t Rotor of a dc motor.

brushes

Construction of DC machine

Rotor is the rotating part - armature Stator is the stationary part - field Armature coil Brushes Brushes Stator: non-moving coil Brushes Brushes g Rotor: rotating part

ARMATURE

• More loops of wire = higher rectified voltage
• In practical, loops are generally placed in slots of an iron core
• The iron acts as a magnetic conductor by providing a low-reluctance path for

ti li f fl t i th i d t f th l d id magnetic lines of flux to increase the inductance of the loops and provide a higher induced voltage.

• The commutator is connected to the slotted iron core.

The entire assembly of iron core commutator and windings is called the

• The entire assembly of iron core, commutator, and windings is called the

armature.

• The windings of armatures are connected in different ways depending on the

requirements of the machine. requirements of the machine.

Loops of wire are wound around slot in a metal core DC machine armature

ARMATURE WINDINGS ARMATURE WINDINGS

• Lap Wound Armatures

are used in machines designed for low voltage and high current – are used in machines designed for low voltage and high current – armatures are constructed with large wire because of high current – Eg: - are used is in the starter motor of almost all automobiles The windings of a lap wound armature are connected in parallel – The windings of a lap wound armature are connected in parallel. This permits the current capacity of each winding to be added and provides a higher operating current – No of current path, C=2p ; p=no of poles No of current path, C 2p ; p no of poles

ARMATURE WINDINGS (Cont) ARMATURE WINDINGS (Cont)

• Wave Wound Armatures

– are used in machines designed for high voltage and low current – are used in machines designed for high voltage and low current – their windings connected in series – When the windings are connected in series, the voltage of each winding adds but the current capacity remains the same winding adds, but the current capacity remains the same – are used is in the small generator in hand-cranked megohmmeters – No of current path, C=2

ARMATURE WINDINGS (Cont) ARMATURE WINDINGS (Cont)

F l W d A t

• Frogleg Wound Armatures

– the most used in practical nowadays – designed for use with moderate current and moderate g armatures voltage – the windings are connected in series parallel. – Most large DC machines use frogleg wound armatures Most large DC machines use frogleg wound armatures.

Frogleg wound armatures

FIELD WINDINGS FIELD WINDINGS

• Most DC machines use wound electromagnets to

g provide the magnetic field.

• Two types of field windings are used :

– series field shunt field – shunt field

FIELD WINDINGS (Cont) FIELD WINDINGS (Cont)

• Series field windings

– are so named because they are connected in series with the – are so named because they are connected in series with the armature – are made with relatively few windings turns of very large wire and have a very low resistance have a very low resistance – usually found in large horsepower machines wound with square or rectangular wire. The use of square wire permits the windings to be laid closer – The use of square wire permits the windings to be laid closer together, which increases the number of turns that can be wound in a particular space

FIELD WINDINGS (Cont) FIELD WINDINGS (Cont)

– Square and rectangular wire can also be made physically smaller than round wire and still contain the same surface area round wire and still contain the same surface area

Square wire contains more surface than round wire Square wire permits more turns than round wire in the same area

FIELD WINDINGS (Cont) FIELD WINDINGS (Cont)

• Shunt field windings

– is constructed with relatively many turns of small wire, thus, it has a much higher resistance than the series field. – is intended to be connected in parallel with, or shunt, the p , , armature. – high resistance is used to limit current flow through the field.

FIELD WINDINGS (Cont) FIELD WINDINGS (Cont)

• When a DC machine uses both series and shunt fields, each pole

piece will contain both windings. piece will contain both windings.

• The windings are wound on the pole pieces in such a manner that

when current flows through the winding it will produce alternate when current flows through the winding it will produce alternate magnetic polarities.

MACHINE WINDINGS OVERVIEW

Winding Separately Self excited armature field Lap C=2p Wave C=2 Separately Excited Frogleg Self excited series shunt compound

Principle operation of Generator Principle operation of Generator

• Whenever a conductor is moved within a

Whenever a conductor is moved within a magnetic field in such a way that the conductor cuts across magnetic lines of flux, voltage is t d i th d t generated in the conductor.

• The AMOUNT of voltage generated depends on:

i. the strength of the magnetic field, i. the strength of the magnetic field, ii. the angle at which the conductor cuts the magnetic field, iii the speed at which the conductor is moved and

• iii. the speed at which the conductor is moved, and
• iv. the length of the conductor within the magnetic field

Principle of operation (Cont) Principle of operation (Cont)

Fleming’s Right hand rule (G R l ) (Generator Rule)

• Use: To determine the direction of the induced emf/current of a

conductor moving in a magnetic field.

• The POLARITY of the voltage depends on the direction of the

magnetic lines of flux and the direction of movement of the conductor.

THE ELEMENTARY GENERATOR

• The simplest elementary generator that can be

built is an ac generator.

• Basic generating principles are most easily

easily explained explained through the use of the elementary ac generator generator.

• For this reason, the ac generator will be

discussed first. The dc generator will be discussed later.

• An elementary generator consists of a wire loop

consists of a wire loop mounted on the shaft, so that it can be rotated in mounted on the shaft, so that it can be rotated in a stationary magnetic field a stationary magnetic field.

• This will produce an induced

produce an induced emf emf in the loop in the loop.

• Sliding contacts (brushes) connect the loop to an

(brushes) connect the loop to an external circuit load in order to pick up or use the external circuit load in order to pick up or use the induced induced emf emf

Elementary Generator

induced induced emf emf. .

THE ELEMENTARY GENERATOR (Cont)

• The pole pieces (marked N and S) provide the magnetic field

provide the magnetic field. The l i h d d iti d h t t t th

THE ELEMENTARY GENERATOR (Cont)

pole pieces are shaped and positioned as shown to concentrate the magnetic field as close as possible to the wire loop.

• The loop of wire that rotates through the field is called the

The loop of wire that rotates through the field is called the ARMATURE

• ARMATURE. The ends of the armature loop are connected to rings

The ends of the armature loop are connected to rings called SLIP RINGS called SLIP RINGS. They rotate with the armature.

• The brushes, usually made of carbon, with wires attached to them,

ride against the rings. The generated voltage appears across these The generated voltage appears across these

• brushes. (
• brushes. (These brushes transfer power from the battery to the

These brushes transfer power from the battery to the commutator commutator as the motor spins as the motor spins – – discussed later in dc elementary discussed later in dc elementary generator generator). ).

THE ELEMENTARY GENERATOR (A) THE ELEMENTARY GENERATOR (A)

• An end view of the shaft and wire

loop is shown.

• At this particular instant, the loop of

wire (the black and white conductors

• f the loop) is parallel to the

magnetic lines of flux, and no cutting action is taking place.

• Since the lines of flux are not being

cut by the loop, no emf is induced in the conductors, and the meter at this iti i di t position indicates zero.

• This position is called the NEUTRAL

PLANE.

00 Position (Neutral Plane) 00 Position (Neutral Plane)

THE ELEMENTARY GENERATOR (B)

• The

The shaft has been turned 90 shaft has been turned 900

0 clockwise,

clockwise, the the conductors cut through more and more lines of conductors cut through more and more lines of fl d fl d lt i i d d i th d t lt i i d d i th d t flux, and flux, and voltage is induced in the conductor. voltage is induced in the conductor.

• at a continually

at a continually increasing angle increasing angle , the induced , the induced emf emf in the conductors builds up from zero to a in the conductors builds up from zero to a maximum value or peak value maximum value or peak value maximum value or peak value. maximum value or peak value.

• Observe that from 0

Observe that from 00 to 90 to 900, the black , the black conductor cuts DOWN through the field. conductor cuts DOWN through the field.

• At the same time the white conductor cuts UP

At the same time the white conductor cuts UP At the same time the white conductor cuts UP At the same time the white conductor cuts UP through the field. through the field.

• The induced

The induced emfs emfs in the conductors are series in the conductors are series-

• adding.

adding.

• This means the resultant voltage across the

This means the resultant voltage across the brushes (the terminal voltage) is the sum of the brushes (the terminal voltage) is the sum of the two induced voltages. two induced voltages. Th t t iti B d i l Th t t iti B d i l

900 Position

• The meter at position B reads maximum value.

The meter at position B reads maximum value.

THE ELEMENTARY GENERATOR (C) THE ELEMENTARY GENERATOR (C)

• After another 900 of rotation, the loop

After another 90 of rotation, the loop has completed 1800 of rotation and is again parallel to the lines of flux.

• As the loop was turned, the voltage

As the loop was turned, the voltage decreased until it again reached zero.

• Note that : From 00 to 1800 the

conductors of the armature loop have conductors of the armature loop have been moving in the same direction through the magnetic field.

• Therefore, the polarity of the induced

e e o e, t e po a ty o t e duced voltage has remained the same

1800 Position

THE ELEMENTARY GENERATOR (D) THE ELEMENTARY GENERATOR (D)

• As the loop continues to turn, the

conductors again cut the lines of magnetic fl flux.

• This time, however, the conductor that

previously cut through the flux lines of the south magnetic field is cutting the lines of south magnetic field is cutting the lines of the north magnetic field, and vice-versa.

• Since the conductors are cutting the flux

lines of opposite magnetic polarity, the polarity of the induced voltage reverses.

• After 270' of rotation, the loop has rotated to

the position shown, and the maximum t i l lt ill b th it terminal voltage will be the same as it was from A to C except that the polarity is reversed.

2700 Position

THE ELEMENTARY GENERATOR (A) THE ELEMENTARY GENERATOR (A)

• After another 900 of rotation, the loop

h l t d t ti f 3600 has completed one rotation of 3600 and returned to its starting position.

• The voltage decreased from its

ti k b k t negative peak back to zero.

• Notice that the voltage produced in the

armature is an alternating polarity. The lt d d i ll t ti voltage produced in all rotating armatures is alternating voltage.

3600 Position

Elementary Generator (Conclusion)

• Observes

– The meter direction – The conductors of the armature loop The conductors of the armature loop – Direction of the current flow

THE ELEMENTARY DC GENERATOR THE ELEMENTARY DC GENERATOR

• Since DC generators must produce DC current

instead of AC current, a device must be used to change the AC voltage produced in the armature windings into DC voltage.

• This job is performed by the commutator

commutator

• This job is performed by the commutator

commutator.

• The commutator is constructed from a copper

ring split into segments with insulating material between the segments (See next page). g ( p g )

• Brushes riding against the commutator

segments carry the power to the outside circuit.

• The commutator in a dc generator replaces the

slip rings of the ac generator. This is the main difference in their construction.

• The commutator mechanically reverses the

armature loop connections to the external circuit armature loop connections to the external circuit.

THE ELEMENTARY DC GENERATOR (A t ) (Armature)

• The armature has an axle and the commutator
• The armature has an axle, and the commutator

is attached to the axle.

• In the diagram to the right, you can see three

different views of the same armature: front, front, , side and end side and end-

• on.
• n.
• In the end-on view, the winding is eliminated to

make the commutator more obvious.

• We can see that the commutator is simply a

simply a pair of plates attached to the axle pair of plates attached to the axle. Th l t id th t ti f Th l t id th t ti f

• These plates provide the two connections for

These plates provide the two connections for the coil of the electromagnet. the coil of the electromagnet.

Armature with commutator view

THE ELEMENTARY DC GENERATOR (C t t & B h k t th ) (Commutator & Brushes work together)

• The diagram at the right shows how the

how the commutator commutator and and

• The diagram at the right shows how the

how the commutator commutator and and brushes work together to let current flow to the brushes work together to let current flow to the electromagnet electromagnet, and also to flip the direction that the electrons are flowing at just the right moment.

• The contacts of the

The contacts of the commutator commutator are attached to the axle are attached to the axle

• f the electromagnet, so they spin with the magnet.
• f the electromagnet, so they spin with the magnet.
• The brushes are just two pieces of springy metal or

The brushes are just two pieces of springy metal or b th t k t t ith th t t f th b th t k t t ith th t t f th carbon that make contact with the contacts of the carbon that make contact with the contacts of the commutator commutator. .

• Through this process the commutator changes the

generated ac voltage to a pulsating dc voltage which also generated ac voltage to a pulsating dc voltage which also known as commutation process.

Brushes and commutator Brushes and commutator

THE ELEMENTARY DC GENERATOR

• The loop is parallel to the magnetic

lines of flux, and no voltage is induced in the loop induced in the loop

• Note that the brushes make

contact with both of the commutator segments at this time commutator segments at this time. The position is called neutral plane.

00 Position (DC Neutral Plane)

THE ELEMENTARY DC GENERATOR

A th l t t th d t

• As the loop rotates, the conductors

begin to cut through the magnetic lines

• f flux.

Th d t tti th h th

• The conductor cutting through the

south magnetic field is connected to the positive brush, and the conductor cutting through the north magnetic field cutting through the north magnetic field is connected to the negative brush.

• Since the loop is cutting lines of flux, a

voltage is induced into the loop voltage is induced into the loop.

• After 900 of rotation, the voltage

reaches its most positive point.

900 Position (DC)

THE ELEMENTARY DC GENERATOR

• As the loop continues to rotate,

the voltage decreases to zero.

• After 1800 of rotation, the

conductors are again parallel to the lines of flux, and no voltage is induced in the loop.

• Note that the brushes again make

g contact with both segments of the commutator at the time when there is no induced voltage in the

1800 Position (DC)

conductors

1800 Position (DC)

THE ELEMENTARY DC GENERATOR GENERATOR

• During the next 900 of rotation, the conductors

again cut through the magnetic lines of flux.

• This time, however, the conductor that previously

cut through the south magnetic field is now cutting the flux lines of the north field, and vice-versa. .

• Since these conductors are cutting the lines of flux
• Since these conductors are cutting the lines of flux
• f opposite magnetic polarities, the polarity of

induced voltage is different for each of the

• conductors. The commutator, however, maintains

the correct polarity to each brush.

• The conductor cutting through the north magnetic

field will always be connected to the negative brush, d th d t tti th h th th fi ld and the conductor cutting through the south field will always be connected to the positive brush.

• Since the polarity at the brushes has remained

Since the polarity at the brushes has remained constant, the voltage will increase to its peak value constant, the voltage will increase to its peak value

2700 Position (DC)

constant, the voltage will increase to its peak value constant, the voltage will increase to its peak value in the same direction. in the same direction.

THE ELEMENTARY DC GENERATOR GENERATOR

• As the loop continues to rotate, the

As the loop continues to rotate, the induced voltage again decreases to zero when the conductors become parallel to the magnetic lines of flux.

• Notice that during this 3600 rotation of the

loop the polarity of voltage remained the loop the polarity of voltage remained the same for both halves of the waveform. This is called rectified DC voltage.

• The voltage is pulsating. It does turn on

and off, but it never reverses polarity. Since the polarity for each brush remains

00 Position (DC Neutral Plane)

p y constant, the output voltage is DC.

THE ELEMENTARY DC GENERATOR GENERATOR

• Observes

– The meter direction Th d f h l – The conductors of the armature loop – Direction of the current flow

Effects of additional turns

• To increase the amount of output voltage, it is

common practice to increase the number of common practice to increase the number of turns of wire for each loop.

• If a loop contains 20 turns of wire, the induced

voltage will be 20 times greater than that for a voltage will be 20 times greater than that for a single-loop conductor.

• The reason for this is that each loop is

connected in series with the other loops. Since the loops form a series path, the voltage induced in the loops will add.

• In this example, if each loop has an induced

voltage of 2V the total voltage for this winding voltage of 2V, the total voltage for this winding would be 40V (2V x 20 loops = 40 V).

Effects of additional turns

Effects of additional coils Effects of additional coils

• When more than one loop is used, the average
• utput voltage is higher and there is less
• utput voltage is higher and there is less

pulsation of the rectified voltage.

• Since there are four segments in the

commutator, a new segment passes each brush every 900 instead of every 1800.

• Since there are now four commutator

segments in the commutator and only two brushes the voltage cannot fall any lower brushes, the voltage cannot fall any lower than at point A.

• Therefore, the ripple is limited to the rise and

fall between points A and B on the graph. By fall between points A and B on the graph. By adding more armature coils, the ripple effect can be further reduced. Decreasing ripple in this way increases the effective voltage of the o tp t the output.

Effects of additional coils

The Practical DC Generator The Practical DC Generator

• The actual construction and operation of a practical

dc generator differs somewhat from our elementary dc generator differs somewhat from our elementary generators

• Nearly all practical generators use electromagnetic

poles instead of the permanent magnets used in our poles instead of the permanent magnets used in our elementary generator

• The main advantages of using electromagnetic

poles are: (1) increased field strength and (2) possible to control the strength of the

• fields. By varying the input voltage, the

fi ld t th i i d B i th fi ld field strength is varied. By varying the field strength, the output voltage of the generator can be controlled.

Four-pole generator (without armature)

DC Motor Operation DC Motor Operation

• In a dc motor, the stator

, poles are supplied by dc excitation current, which produces a dc magnetic produces a dc magnetic field.

• The rotor is supplied by dc

t th h th current through the brushes, commutator and coils.

• The interaction of the

magnetic field and rotor current generates a force current generates a force that drives the motor

DC Motor Operation

• The magnetic field lines enter

into the rotor from the north l ( ) d i d h

B v

a

pole (N) and exit toward the south pole (S).

• The poles generate a

Vdc

30

N S

v

b 1 2

magnetic field that is perpendicular to the current carrying conductors.

(a) Rotor current flow from segment 1 to 2 (slot a to b)

v

Ir_dc

B

• The interaction between the

field and the current produces a Lorentz force,

30

N S Vdc

a 2

B v v

• The force is perpendicular to

both the magnetic field and conductor

dc

b 1

Ir_dc

(b) Rotor current flow from segment 2 to 1 (slot b to a)

DC Motor Operation

• The generated force turns the

rotor until the coil reaches the

N S

B v

a

neutral point between the poles.

• At this point, the magnetic field

becomes practically zero together

Vdc

30

N S

v

b 1 2

with the force.

• However, inertia drives the motor

beyond the neutral zone where the

(a) Rotor current flow from segment 1 to 2 (slot a to b)

Ir_dc

B

direction of the magnetic field reverses.

• To avoid the reversal of the force

30

N S Vdc

a 1 2

B v v

direction, the commutator changes the current direction, which maintains the counterclockwise t ti

b 1

Ir_dc

rotation.

(b) Rotor current flow from segment 2 to 1 (slot b to a)

DC Motor Operation

• Before reaching the neutral zone,

the current enters in segment 1

B v

a

g and exits from segment 2,

• Therefore, current enters the coil

end at slot a and exits from slot

Vdc

30

N S

v

b 1 2

b during this stage.

• After passing the neutral zone,

the current enters segment 2 and

(a) Rotor current flow from segment 1 to 2 (slot a to b)

v

Ir_dc

B

g exits from segment 1,

• This reverses the current

direction through the rotor coil,

30

N S Vdc

a 2

B v v

when the coil passes the neutral zone.

• The result of this current reversal

dc

b 1

v v

Ir dc

is the maintenance of the rotation.

(b) Rotor current flow from segment 2 to 1 (slot b to a)

r_dc

DC Machine Equivalent Circuit q

DC Machine Equivalent Circuit DC Machine Equivalent Circuit

• The magnetic field produced by the stator poles induces a

The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated.

• This induced voltage is represented by a voltage source.
• The stator coil has resistance, which is connected in

series series.

• The pole flux is produced by the DC excitation/field

current, which is magnetically coupled to the rotor

• The field circuit has resistance and a source
• The voltage drop on the brushes represented by a battery

DC Machine Equivalent Circuit q

1. Permanent magnet 2. Separately excited 2. Separately excited 3. Self-excited

DC Machine Equivalent Circuit q

1. Permanent magnet

• The poles are made of permanent magnets.

N fi ld i di i d

• No field winding required.
• Small size.
• Disadvantage is low flux density, so low torque.

DC Machine Equivalent Circuit

2. Separately excited

The field flux is derived from a separate power source independent of the generator itself.

B

Field winding Armature winding g

DC Machine Equivalent Circuit q

3. Self-excited

Sh nt machine

• Shunt machine

The field flux is derived by connecting the field directly across the terminals of the t generator. B

DC Machine Equivalent Circuit q

3. Self-excited

Series machine

• field are connected in

series with armature

B

DC Machine Equivalent Circuit q

3. Self-excited

C m lati el compo nded

• Cumulatively compounded

B B B

• Differentially compounded

B B

DC Machine Equivalent Circuit q

3. Self-excited Compounded dc generator

• both a shunt and a series field are

present present

DC Machine Equivalent Circuit DC Machine Equivalent Circuit

3. Self-excited Compounded dc motor

• both a shunt and a series

fi ld t field are present

Equivalent circuit of a DC motor motor

The armature circuit (the entire ( rotor structure) is represented by an ideal voltage source EA and a resistor RA. A battery Vbrush in the

• pposite to a current flow in the
• pposite to a current flow in the

machine direction indicates brush voltage drop. The field coils producing the magnetic flux are represented by inductor LF and resistor RF. The resistor Radj represents an external variable resistor external variable resistor (sometimes lumped together with the field coil resistance) used to control the amount of current in th fi ld i it the field circuit.

DC Motor Equivalent Circuit.

The armature is represented by an ideal voltage source EA and a

resistor RA.

The brush voltage drop is represented by a small battery Vbrush

• pposing the direction of the current flow in the machine.

The field coils, which produce the magnetic flux, are represented

b i d t L d R by inductor LF and RF.

The separate resistor Radj represents an external variable resistor

used to control the amount of current in the field circuit. Equivalent Circuit of a DC Motor.

The brush drop voltage is often only a very tiny fraction of the

generated voltage in the motor.

Therefore, in cases where it is not critical, the brush drop voltage

may be left out or approximately included in the value of RA.

Also, the internal resistance of the filed coils is sometimes lumped

h i h h i bl i d h l i ll d R Fi together with the variable resistor, and the total is called RF , Figure below.

A Simplified Equivalent Circuit eliminating the Brush Voltage Drop and Combining Radj with the Field Resistance .

Motor types: Separately Excited DC motors.

Separately excited DC motor: a field circuit is supplied from a separate constant voltage power

Th E i l Ci i f S l E i d d M

separate constant voltage power source.

The Equivalent Circuit of Separately Excited dc Motor.

From the above figure,

V

F F F

R V I =

A A A T

R I E V + =

A L

I I =

Motor types: Shunt DC motors.

Shunt DC motor: a field circuit gets its power from the armature terminals of the motor.

The Equivalent Circuit of a Shunt dc Motor.

From the above figure,

F F F

R V I =

F A A A T

R I E V + =

F A L

I I I + =

Motor types: The permanent-magnet DC motor DC motor

A permanent magnet DC (PMDC) motor is a motor whose poles are d t f t t made out of permanent magnets.

Advantages:

• 1. Since no external field circuit is needed, there are no field circuit copper

losses;

• 2. Since no field windings are needed, these motors can be considerable

smaller. Disadvantages:

• 1. Since permanent magnets produces weaker flux

densities then externally supported shunt fields, such motors have lower induced torque such motors have lower induced torque.

• 2. There is always a risk of demagnetization from

extensive heating or from armature reaction effects (via armature mmf). ( )

Motor types: The series DC motor motor

A series DC motor is a DC motor whose field windings consists of a relatively few turns connected in series with armature circuit. Therefore:

( )

R R I E V + + =

( )

S A A A T

R R I E V + + =

Motor types: Compounded DC motor motor

A compounded DC motor is a motor with both a shunt and a series field.

Current flowing into a dotted end of a coil (shunt or series) produces a positive Long-shunt connection mmf. If current flows into the dotted ends of both coils, the dotted ends of both coils, the resulting mmfs add to produce a larger total mmf – cumulative compounding. Short-shunt connection If current flows into the dotted end of

• ne coil and out of the dotted end of

another coil, the resulting mmfs subtract – differential compounding.

Motor types: Compounded DC motor motor

The Kirchhoff’s voltage law equation for a compounded DC motor is The currents in a compounded DC motor are

(5.85.1)

( )

S A A A T

R R I E V + + = V

(5.85.2) (5.85.3)

F L A

I I I − =

F T F

R V I =

The mmf of a compounded DC motor:

Cumulatively compounded (5.85.4)

AR SE F net

F F F F − ± =

Differentially compounded

The effective shunt field current in a compounded DC motor:

AR SE F net

F N

Number of turns (5.85.5)

F AR A F SE F F

N F I N N I I − + =

*

Torque Equation Torque Equation

A A I

k T φ =

T = torque of armature (N-m) k = geometry constant kA = geometry constant φ= flux/pole (Wb) IA = armature current (A) IA armature current (A)

Geometry Constant Geometry Constant

) ( 60 ), / ( 2

'

rpm M pN k s rad M pN k

A A

= = π

p = number of field poles N = number of active conductors on armature M = number of parallel paths in armature winding (=p for lap winding, =2 for wave winding)

Power Equation Power Equation

ω T EI P = =

P=power (W) not counting losses

ω T EI P

A =

=

P=power (W) – not counting losses E = EMF induced in armature (back EMF) IA = armature current (A) T = torque of armature (N-m) ω = speed of rotation (rad/s) Note that Pin = VLIL which will be higher than P Note that Pin VLIL which will be higher than P because of loss in the field and armature windings as well as rotational (friction) losses.

EMF Equation EMF Equation

n k k E φ φω

'

= =

ω 60 n

n k k E

A A

φ φω = =

π 2 = n E = EMF induced in armature (V) kA = geometry constant φ= flux/pole (Wb) ω = speed of rotation (rad/s) d f t ti f t ( ) n = speed of rotation of armature (rpm)

Terminal Voltage Equation Terminal Voltage Equation

RA E VT + +

A A T

R I E V + =

• VT = voltage at motor terminals

E = EMF induced in armature (V) IA = armature current (A) RA = armature resistance

Speed Equation Speed Equation

A A T

R I V − φ

' A A A T

k R I V n =

(applies to shunt connected motor only) Note that φ can also be written as kfIf where kf is φ/If (normally a constant ratio)

f

Ratio Equation

1 2 1 2

E E n n =

Speed-Torque Speed Torque

Speed p

Differential Compound Shunt Cumulative Compound

Torque

Series

Power flow and losses in DC machines machines

Unfortunately, not all electrical power is converted to mechanical power by a motor and not all mechanical power is converted to electrical power by a generator… The efficiency of a DC machine is:

% 100 x P P

• ut

= η

• r

% 100 x P P

loss in −

= η

P

in

% 100 x P

in

= η

The losses in DC machines

There are five categories of losses occurring in DC machines.

• 1. Electrical or copper losses – the resistive losses in the armature and field

windings of the machine.

2

Armature loss: Field loss:

A A A

R I P

2

=

R I P

2

=

e d oss Where IA and IF are armature and field currents and RA and RF are armature and field (winding) resistances usually measured at normal operating temperature F F F

R I P =

field (winding) resistances usually measured at normal operating temperature.

The losses in DC machines

• 2. Brush (drop) losses – the power lost across the contact potential at the
• 2. Brush (drop) losses

the power lost across the contact potential at the brushes of the machine. A BD BD

I V P =

Where IA is the armature current and VBD is the brush voltage drop. The voltage drop across the set of brushes is approximately constant over a large range of armature currents and it is usually assumed to be about 2 V. Other losses are exactly the same as in AC machines…

The losses in DC machines

• 3. Core losses – hysteresis losses and eddy current losses. They vary as B2

(square of flux density) and as n1.5 (speed of rotation of the magnetic field).

• 4. Mechanical losses – losses associated with mechanical effects: friction

(friction of the bearings) and windage (friction between the moving parts of the machine and the air inside the casing). These losses vary as the cube of rotation speed n3 speed n3.

• 5. Stray (Miscellaneous) losses – losses that cannot be classified in any of the

previous categories They are usually due to inaccuracies in modeling For many previous categories. They are usually due to inaccuracies in modeling. For many machines, stray losses are assumed as 1% of full load.

The power-flow diagram g

On of the most convenient technique to account for power losses in a machine is the power flow diagram machine is the power-flow diagram.

For a DC motor: motor: Electrical power is input to the machine, and the electrical and brush losses must be subtracted The remaining power is ideally converted from electrical to mechanical

• subtracted. The remaining power is ideally converted from electrical to mechanical

form at the point labeled as Pconv.

The power-flow diagram g

The electrical power that is converted is

A A conv

I E P =

And the resulting mechanical power is

P ω τ =

After the power is converted to mechanical form, the stray losses, mechanical losses and core losses are subtracted and the remaining mechanical power is

m ind conv

P ω τ =

losses, and core losses are subtracted, and the remaining mechanical power is

• utput to the load.

Example 1 Example 1

A 6 pole, 3.0 hp 120V DC lap-wound shunt motor has 960 conductors in the armature. It takes 25.0 A from the supply at full load. Armature resistance is 0.75Ω, flux/pole=10.0 mWb, field winding current is 1.20A. Find the speed and torque.

( )(

)

s rad V E K E

A

/ 9 . 66 102

3 =

= = = ω φω

( )

kW W hp P 24 . 2 746 3 = ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ = A A A I I I

F L A

8 . 23 2 . 1 25 = − = − =

( )(

)

x K A 10 10 153

3 −

φ rpm n 638 2 60 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = π ω

( )

hp p ⎟ ⎟ ⎠ ⎜ ⎜ ⎝

( )( )

V A V R I V E

A A T

102 75 . 8 . 23 120 = Ω − = − =

( )( ) ( )( )

153 6 2 960 6 2 = = = π πM pN K A 2 ⎠ ⎝ π m N s rad kW P T ⋅ = = = 5 . 33 / 9 . 66 24 . 2 ω

( )( )

6 2 2 π πM

Example 2 Example 2

A 10hp, 115V Dc series motor takes 40A at its full load speed of

• 1800rpm. What is the torque at 30A?

( )

s rad n / 188 60 1800 2 60 2 = = = π π ω

( )

kW W h P 46 7 746 10 ⎟ ⎞ ⎜ ⎛

A F F A A A

I I K K I K T = = φ

A F

I I =

2

( )

kW hp W hp P 46 . 7 7 10 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = T P = ω

2 A F A

I K K T =

( )

025 . 40 6 . 39

2 2

= ⋅ = = A m N I T K K

A F A

m N s rad kW P T ⋅ = = = 6 . 39 / 188 46 . 7 ω

( )( )

m N A I K K T

new

A F A new

⋅ = = = 2 . 22 30 025 .

2 2

Example 3 (a) Example 3 (a)

A 220V DC shunt motor draws 10A at 1800rpm. The armature resistance is 0.2Ω and field winding resistance is 440Ω. (a) What is the torque?

A V R V I

F T F

5 . 440 220 = Ω = =

( )

n 1800 2 2 π π

F

A A A I I I

F L A

5 . 9 5 . 10 = − = − =

( )

s rad n / 188 60 1800 2 60 2 = = = π π ω m N s rad kW P T ⋅ = = = . 11 / 188 07 . 2 ω

( )( )

V A V R I V E

A A T

218 2 . 5 . 9 220 = Ω − = − =

( )( )

kW A V EI P

A

07 . 2 5 . 9 218 = = = s rad / 188 ω

( )( )

A

Example 3 (b) Example 3 (b)

A 220V DC shunt motor draws 10A at 1800rpm. The armature resistance is 0.2Ω and field winding resistance is 440Ω. (b) What will be the speed and line current at a torque of 20 N-m (if field current is constant)?

= K E

Aφω

A A A I I I

F A L

8 . 17 5 . 3 . 17 = + = + =

( )( )

16 . 1 / 188 218 = = = s rad V E K A ω φ I K T

A A

= φ

( )( )

V V R I V E

A A T

217 2 . 3 . 17 220 = Ω − = − = s rad V K E

A

/ 187 16 . 1 217 = = = φ ω A m N K T I

A A A A

3 . 17 16 . 1 20 = ⋅ = = φ φ rpm x n

A 3

10 79 . 1 2 60 = = π ω φ

(shunt is constant speed)