electrical machines and energy conversion unit 1 deck 1 magnetism basics

Electrical Machines and

Energy Conversion

Unit 1 Deck 1Magnetism Basics

Unit 10Unit 10

Electronics FundamentalsCircuits, Devices and Applications - Floyd © Copyright 2009 Pearson

Magnetic fields are described by drawing flux lines that represent the magnetic field.

Summary

Where lines are close together, the flux density is higher.

Where lines are further apart, the flux density is lower.

Magnetic Quantities

Unit 10Unit 10


The unit of flux is the weber. The unit of flux density is the weber/square meter, which defines the unit tesla, (T), a very large unit.

Summary

Flux density is given by the equationwhere

B = flux density (T) = flux (Wb)

A = area (m2)

B=A

F lu x l in e s (

A rea (m )2

Magnetic Quantities

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Example: What is the flux density in a rectangular core that is 8 mm by 10 mm if the flux is 4 mWb?

Summary

B=A

3

2-3 -3

4 10 Wb50 Wb/m = 50 T

8 10 m 10 10 mB

Magnetic Quantities

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• Magnetic flux lines surround a current carrying wire.

Summary

• The field lines are concentric circles.

Magnetic Quantities

• As in the case of bar magnets, the effects of electrical current can be visualized with iron filings around the wire – the current must be large to see this effect.

Current-carrying wire

Iron filings

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Summary

• Permeability () defines the ease with which a magnetic field can be established in a given material. It is measured in units of the weber per ampere-turn meter.

Magnetic Quantities

• Relative Permeability (r) is the ratio of the absolute permeability to the permeability of a vacuum.

• The permeability of a vacuum (0) is 4 x 10-7 weber per ampere-turn meter, which is used as a reference.

0 r

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Summary

• Reluctance (R) is the opposition to the establishment of a magnetic field in a material.

R= reluctance in A-t/Wbl = length of the path = permeability (Wb/A-t m).A = area in m2

Magnetic Quantities

A

l

R

Unit 10Unit 10


Fm = NI

• Recall that magnetic flux lines surround a current-carrying wire. A coil reinforces and intensifies these flux lines.

Summary

• The cause of magnetic flux is called magnetomotive force (mmf), which is related to the current and number of turns of the coil.

Fm = magnetomotive force (A-t)

N = number of turns of wire in a coil I = current (A)

Magnetic Quantities

Unit 10Unit 10


Summary

• Ohm’s law for magnetic circuits is

Magnetic Quantities

• flux () is analogous to current• magnetomotive force (Fm) is analogous to voltage• reluctance (R) is analogous to resistance.

What flux is in a core that is wrapped with a 300 turn coil with a current of 100 mA if the reluctance of the core is 1.5 x 107 A-t/Wb? 2.0 Wb

RmF

Unit 10Unit 10


Summary

• The magnetomotive force (mmf) is not a true force in the physics sense, but can be thought of as a cause of flux in a core or other material.

Current in the coil causes flux in the iron core.

What is the mmf if a 250 turn coil has 3 A of current?

750 A-t

Magnetic Quantities

Iron core

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Summary

• Magnetic field intensity is the magnetomotive force per unit length of a magnetic path.

H= Magnetic field intensity (Wb/A-t m)Fm = magnetomotive force (A-t)

l = average length of the path (m)N = number of turns I = current (A)

H =

F m

l H = NI

lor

• Magnetic field intensity represents the effort that a given current must put into establishing a certain flux density in a material.

Unit 10Unit 10


Summary

• This relation between B and H is valid up to saturation, when further increase in H has no affect on B.

• If a material is permeable, then a greater flux density will occur for a given magnetic field intensity. The relation between B (flux density) and H (the effort to establish the field) is

B = H

= permeability (Wb/A-t m).H= Magnetic field intensity (Wb/A-t m)

Magnetic Quantities

Unit 10Unit 10


Summary

• As the graph shows, the flux density depends on both the material and the magnetic field intensity.

M a g n e tic F ie ld In te n s ity, , (A t/m )H

Flux

den

sity

, ,

(Wb/

/m)

B2

S a tu ra tio n b e g in s

M a g n e tic m a te r ia l

N o n -m a g n e t ic m a te r ia l

Unit 10Unit 10


SummaryAs H is varied, the magnetic hysteresis curve is developed.

(d )(c )

B

H

(b )

B

H

(a )

B

H

(f )

B

H

(g )

B

H

(e )

0 H sa t

Sa tura tio n

0

B sa t B R

H = 0 H

H sa t

B sa t

Sa tura tio n B

H C

0

H0 0

H = 0

B R

B

H sa t

B sa t

H C

H

B

H C

Unit 10Unit 10


Summary

A B-H curve is referred to as a magnetization curve for the case where the material is initially unmagnetized. The B-H curve differs for different materials; magnetic materials have in common much larger flux density for a given magnetic field intensity, such as the annealed iron shown here.

Magnetization Curve

M agn etic F ield In tensity, H , (A -t/m )200 400 600 800 1000 1200 16001400 1800 2000

0

0 .5

1 .0

1 .5

2 .0

0

Flu

x D

ensi

ty, B

, (T

)

M agn etic F ield In tensity, H , (A -t/m )200 400 600 800 1000 1200 16001400 1800 2000

0

0 .5

1 .0

1 .5

2 .0

0

Flu

x D

ensi

ty, B

, (T

)

Annealed iron

Unit 10Unit 10


Relative motion

When a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field.

When a magnetic field is moved past a stationary wire, there is also relative motion.

NS

NS

In either case, the relative motion results in an induced voltage in the wire.

Unit 10Unit 10


The induced voltage due to the relative motion between the conductor and the magnetic field when the motion is perpendicular to the field is dependent on three factors:

Summary

Induced voltage

• the flux density

• the length of the conductor in the magnetic field

• the relative velocity (motion is perpendicular)

Unit 10Unit 10


Faraday experimented with generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:

Summary

Faraday’s law

1. The rate of change of the magnetic flux with respect to the coil.

NS

V- +Voltage is indicated only when magnet is moving.

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Faraday also experimented generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:

Summary

1. The rate of change of the magnetic flux with respect to the coil.

2. The number of turns of wire in the coil.

NS

V- +

Faraday’s law

Voltage is indicated only when magnet is moving.

Unit 10Unit 10


Just as a moving magnetic field induces a voltage, current in a coil causes a magnetic field. The coil acts as an electromagnet, with a north and south pole as in the case of a permanent magnet.

Summary

Magnetic field around a coil

No rthSo uth

Unit 10Unit 10


Summary

A dc generator includes a rotating coil,

DC GeneratorMechanical drive turns the shaft

which is driven by an external mechanical force (the coil is shown as a loop in this simplified view). As the coil rotates in a magnetic field, a pulsating voltage is generated.

Brushes

Commutator

To external circuit

Unit 10Unit 10


Magnetic flux densityFlux

Magnetizing force

Magnetomotive force

Permeability

Tesla

Weber

Weber/ampere-turn-meter

Ampere-turn/Weber

Ampere-turn

Ampere-turn/meter

B

RFm

H

Reluctance

It is useful to review the key magnetic units from this chapter:

Quantity SI Unit Symbol

Magnetic units

Unit 10Unit 10


Magnetic field

Magnetic flux

Weber (Wb)

Permeability

Reluctance

The lines of force between the north pole and south pole of a permanent magnet or an electromagnet.The SI unit of magnetic flux, which represents 108 lines.

A force field radiating from the north pole to the south pole of a magnet.

Selected Key Terms

The measure of ease with which a magnetic field can be established in a material.

The opposition to the establishment of a magnetic field in a material.

Unit 10Unit 10


Magnetomotive force (mmf)

Solenoid

Hysteresis

Retentivity

An electromagnetically controlled device in which the mechanical movement of a shaft or plunger is activated by a magnetizing current.

A characteristic of a magnetic material whereby a change in magnetism lags the application of the magnetic field intensity.

The cause of a magnetic field, measured in ampere-turns.

Selected Key Terms

The ability of a material, once magnetized, to maintain a magnetized state without the presence of a magnetizing current.

Unit 10Unit 10


Induced voltage (vind)

Faraday’s law

Lenz’s law

A law stating that the voltage induced across a coil of wire equals the number of turns in the coil times the rate of change of the magnetic flux.

Voltage produced as a result of a changing magnetic field.

Selected Key Terms

A law stating that when the current through a coil changes, the polarity of the induced voltage created by the changing magnetic field is such that it always opposes the change in the current that caused it. The current cannot change instantaneously.

Unit 10Unit 10


Quiz

1. A unit of flux density that is the same as a Wb/m2 is the

a. ampere-turn

b. ampere-turn/weber

c. ampere-turn/meter

d. tesla

Unit 10Unit 10


Quiz

2. If one magnetic circuit has a larger flux than a second magnetic circuit, then the first circuit has

a. a higher flux density

b. the same flux density

c. a lower flux density

d. answer depends on the particular circuit.

Unit 10Unit 10


Quiz

3. The cause of magnetic flux is

a. magnetomotive force

b. induced voltage

c. induced current

d. hysteresis

Unit 10Unit 10


Quiz

4. The measurement unit for permeability is

a. weber/ampere-turn


c. weber/ampere-turn-meter

d. dimensionless

Unit 10Unit 10


Quiz

5. The measurement unit for relative permeability is

a. weber/ampere-turn


c. weber/ampere-turn meter

d. dimensionless

Unit 10Unit 10


Quiz

6. The property of a magnetic material to behave as if it had a memory is called

a. remembrance

b. hysteresis

c. reluctance

d. permittivity

Unit 10Unit 10


Quiz

7. Ohm’s law for a magnetic circuit is

a.

b.

c.

d.

Fm = NI

B = H

A

l

R

RmF

Unit 10Unit 10


Quiz

8. The control voltage for a relay is applied to the

a. normally-open contacts

b. normally-closed contacts

c. coil

d. armature

Unit 10Unit 10


Quiz

9. A partial hysteresis curve is shown. At the point indicated, magnetic flux

a. is zero

b. exists with no magnetizing force

c. is maximum

d. is proportional to the current

B

H

BR

Unit 10Unit 10


Quiz

10. When the current through a coil changes, the induced voltage across the coil will

a. oppose the change in the current that caused it

b. add to the change in the current that caused it

c. be zero

d. be equal to the source voltage

Unit 10Unit 10


Quiz

Answers:

1. d

2. d

3. a

4. c

5. d

6. b

7. c

8. c

9. b

10. a

Unit 10Unit 10


Electrical Machines

and Energy Conversion

Unit 1 Deck 1Magnetism Basics

Electrical Machines and Energy Conversion

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electrical machines and energy conversion unit 1 deck 1 magnetism basics

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