1 Institute of Mechatronics and Information Systems Electric Machines

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Institute of Mechatronics and Information Systems

Electric Machines

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Witold Kubiak, Ph.D., M.Sc.,

Eng.e-mail: [email protected]

www: www.kubiak.imsi.pl

phone: 42 631 25 70

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Fundamentals of electromagnetic phenomena in electro-mechanic energy conversion

1. Basic electrical quantities and dependencies2. Basic magnetic quantities and properties3. Basic mechanical quantities4. Power conversion5. Fundamental principles of electromagnetism

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Basic electrical quantities

E - electromotive force (EMF) – [V] (volt)

U - voltage (potential difference) – [V] (volt)

I - current – [A] (ampere)

DC – direct current:

(Ohm’s law)

where:

R - resistance – [Ω] (ohm)

RU

I

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AC – alternating current

- instantaneous value

where:- angular frequency - [rad/s]

tsinUtu peak

f2

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AC – alternating current- instantaneous value

where:- angular frequency - [rad/s]

Upeak , (Um) - peak (maximum) value

URMS , (U) - root mean square value

Uav - rectified average value

tsinUtu peak

f2

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Ohm’s law:

where impedance Z :

ZU

I

jXRZ

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AC – alternating currentReactance X depends on the type of reactive element.

Inductive reactance:

Capacitive reactance:

LjXL

Cj1

XC

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Reactance introduces a phase shift between the current and voltage.

Voltage lagging current

Voltage leading current

LjXL

Cj1

XC

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Basic electrical circuits dependencies

Kirchoff’s circuit laws:

0In

1kk

0Un

1kk

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Basic magnetic quantities

F - magnetomotive force (MMF) – [A] (ampere)

H - magnetic field strenght – [a/m] (ampere per metre)

B - magnetic flux density – [T] (tesla)

- magnetic flux – [Wb] (weber)

(Hopkinson’s law)

where:

R - reluctance – [1/h] (1/henry)

RF

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Basic magnetic properties

Magnetisation curve in ferromagnetic materials

μ0 - permeability of vacuum [H/m] (henry per metre)

μr - relative permeability [-]

HB r0

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Basic magnetic propertiesHysteresis in ferromagnetic materials

BR - remanence HC - coercivity

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Basic magnetic dependencies

- magnetomotive force

- magnetic flux

- analogy to Kirchoff’s law

Sm ds B

dl H F

0n

1kk

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Basic mechanical quantities

Linear movementF - force – [N] (newton)

x - position – [m] (metre)]

- velocity – [m/s] (metre per second)

- acceleration – [m/s2] (metre per second square)

(Newton’s law)

dtdx

v

dtdv

a

maF

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Basic mechanical quantitiesRotational movement

- torque – [Nm] (newton metre)

α - angular position – [rad] (radian)]

- angular velocity – [rad/s] (radian per second)

- angular acceleration – [rad/s2] (radian per second

square) (analogy to Newton’s law)

dtd

dtd

FrM

IM

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Energy conversion (transformation)

akoutin WWW

http://en.wikipedia.org/wiki/File:EnergyTransformation.gif

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Power conversion

Efficiency

in

L

in

out

P

P1

PP

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Electric power

DC – direct current

AC – alternating current, single phase

apparent power:

real power:

reactive power:

RU

RIUIP2

2

cosUIP

UIS

sinUIQ

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Electric power

AC – alternating current, three phase system

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Electric power

AC – alternating current, three phase system

apparent power:

Delta connection (Δ, D, d) Star connection ( , Y, y)

3I

Iph

UI3IU3S phph

3U

Uph

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Mechanical power

Linear movement:

Rotational movement:

FvP

MP

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Fundamental principles of electromagnetism

Ampere’s circuital law:

k

kkSCNidS J dl H

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Ampere’s circuital law:

k

kkCNidl H F

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Faraday’s law of induction:

dtd

dS B dtd

es

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Faraday’s law of induction:

dtd

Ne

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Ampere’s force

r2II

F 210

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Lorentz (Laplace) force

lBIF

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Thank You for Your attention

Documents

1 Institute of Mechatronics and Information Systems Electric Machines