EE-260 : Electro-Mechanical Systems(EMS)EE-260 : Electro-Mechanical Systems(EMS)Lecture#17,18Lecture#17,18

4.1 A SIMPLE LOOP IN A UNIFORM MAGNETIC FIELD (Page 230) The torque induced in a current-carrying loop (Page

234)4.5 INDUCED TORQUE IN AC MACHINES (Page 255)

4.2 The rotating Magnetic Field (Page 238)

Text Book: Chapter 04 (Stephen J. Chapman 4th Ed)

Instructor: Miss Neelma NazClass: BEE 4 C/D

School of Electrical Engineering and Computer Science

Department of Electrical Engineering

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4. The Motor Action

4.1: A Current-Carrying Loop in a Uniform Magnetic FieldThe torque induced in a current-carrying loop

4.5: Induced Torque in an AC Machine

Production of Induced Force on a Current Carrying Wire

ilBSinFBliF

)(The force induced on the conductor is:

“If the index finger of right hand points in the direction of the vector l and the middle finger points in the direction of flux density vector B, then the thumb points in the direction of the resultant force F on the wire.”

The thumb, forefinger, and middle finger of the right hand are extended at right angles to each other.

Fleming’s Right Hand Rule:Direction of l defined to be in the direction of current flow

REVIEW

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1. The Torque Induced in a Current-Carrying Loop (1/8)

To determine the magnitude and direction of torque, first the force on each segment of the loop is calculated:

Assume that the rotor loop is at some arbitrary angle θ with respect to the magnetic field, and current is flowing in the loop

Torque will be induced on the wire loop

sinrF

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1. The Torque Induced in a Current-Carrying Loop (2/8)

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down)(

ilBFBliF

page into)(

ilBFBliF

clockwisesin)sin(

ab

ab

rilBrF

0)sin(

bcrF

Segment ab: The direction of current is into the page, while the magnetic field B points to the right, the vector lxB points down. The induced force and torque are:

Segment bc: The direction of current is in the plan of the page, while the magnetic field B points to the right. The vector lxB points into the page. The the induced force and torque are:

1. The Torque Induced in a Current-Carrying Loop (3/8)

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up)(

ilBFBliF

page ofout )(

ilBFBliF

clockwisecd

cd

rilBrF

sin)sin(

0)sin(

bcrF

Segment cd: The direction of current is out of the page, while the magnetic field B points to the right, the vector lxB points up. The induced force and torque are:

Segment da: The direction of current is in the plan of the page, while the magnetic field B points to the right. The quantity lxB points out the page. Thus the induced force and torque are:

1. The Torque Induced in a Current-Carrying Loop (4/8)

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• The resulting torque is shown as a function of angle

• The torque is maximum when the plane of the loop is parallel to the magnetic field

• The torque is zero when the plane of the loop is perpendicular to the magnetic field

cdabind

dacdbcabind

rilBrilB

sinsin cdab

sin2rilBind

The total induced torque on the loop is the sum of the torques on each of its side.

1. The Torque Induced in a Current-Carrying Loop (5/8)

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1. The Torque Induced in a Current-Carrying Loop (6/8)

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G depends upon the geometry of the loop

( ) loopGi B

sin

sin

2

s

( )

in

ind loop S

ind loop S

ind loop S

Grl

GA

B B

B B

B Bk

sin2sin2 Sind rilBrilB The equation can be alternatively expressed in terms of the flux density produced due to current in the loopIf the current in the loop is as shown in the figure , it will produce magnetic flux density Bloop.

The magnitude of the flux density will be:

loopNiB Hl

loopiBl

Loop area is equal to 2rl

1. The Torque Induced in a Current-Carrying Loop (7/8)

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The torque induced in the loop and also in general the torque in any real ac machine depends on four factors:

1)The strength of the rotor magnetic field

2)The strength of the external magnetic field

3)The angle between the two magnetic fields

4)A constant representing the construction of the machine (geometry).

ind loop SkB B

sinSloopind BkB

k depends upon construction of the machine, Bs is the stator magnetic field

The torque eq. can be expressed as a cross product

1. The Torque Induced in a Current-Carrying Loop (8/8)

In ac machines, there are two magnetic fields:- magnetic field from the rotor circuit (BR)

- magnetic field from the stator circuit (BS)

The interaction of the two magnetic fields produces torque in the machine, just as two permanent magnets near each other will experience a torque which causes them to line up

A simplified ac machine with a sinusoidal stator flux distributionthat peaks in the upward direction and a single coil of wire mounted on the rotor

2: Induced Torque in an AC Machine (1/4)

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2: Induced Torque in an AC Machine (2/4)

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Induced force and torque on conductor 1 are:

in

1

d

s

,1

F l×B si

τ = r×F =

n

sins

si

rilB

ilB

Induced force and torque on conductor 2 are:

in

2

d

s

,2

F l× B si

τ = r ×F =

n

sins

si

rilB

ilB

The resultant torque is:

ind ind,1 ind,2τ = τ τ = 2 sinsrilB

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• The induced torque can be expressed as:

sin ccwind R SkB B

• The current i flowing in the rotor coil produces a magnetic field of its own. Direction of the peak of this magnetic field is given by the right-hand rule

• The angle between the peak of the stator flux density Bs and the peak of the rotor magnetic filed BR is

ind R Sτ = B ×Bccwsin ind R S

kkB B

180

& sin sin(180 ) sin

o

o

2: Induced Torque in an AC Machine (3/4)

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The induced torque is a cross product of BR and Bnet.

Where is the angle between BR and Bnet

ind R netτ = (B ×B ) k

ind R net R Rτ (B × B ) - (B × B )k k

ind R net Rτ = B ×(B - B )k

net R s

S net R

B = B + BB = B - B

ind R Sτ = B ×Bk

sinind R netkB B

Alternative expression in terms of BR and Bnet

2: Induced Torque in an AC Machine (4/4)

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3: The Rotating Magnetic Field (1/7)A rotating magnetic field induces three phase set of voltages in the three-phase windings of a stator

What happens if three-phase set of voltages are applied to the three windings of the stator?

Fundamental principle of ac machine operation

http://www.teslasociety.com/magnetic.htm

How the stator magnetic field be made to rotate?

The fundamental principle of ac machine operation is that:

IF a 3-phase set of currents, each of equal magnitude and differing in phase by 1200, flows in a 3-phase winding, then it will produce a rotating magnetic field of constant magnitude (1.5 times the peak value).

3: The Rotating Magnetic Field (2/7)

Conclusion

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•A SIMPLE LOOP IN A UNIFORM MAGNETIC FIELD (Page 230)•The torque induced in a current- carrying loop (Page 234)•Induced Torque in an AC Machine (Page 255)•The rotating magnetic field (Page 238)