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Magnetism

Content of the presentation

- Maxwell's general equations on magnetism- Hysteresis curve- Inductance- Magnetic circuit modelling- Eddy currents and hysteresis losses- Force / torque / power

1990 - 1995 M.sc.EE Student at IET, Aalborg University. 1995 - 1999 Ph.D. Student at IET, Aalborg University. 1999 - 2002 Assistant Professor at IET, Aalborg University.2002 - Associate Professor at IET, Aalborg University.

Few words and mini CV of my self

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Maxwell

James Clerk Maxwell 1831 - 1879

Unified theory of the connection between electricity and magnetism

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Maxwells equations in free space

Not easy to understand in this form.Practical engineers tend to forget the definition of divergence, curl, surface and line integral

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1c

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Ørsted

H.C Ørsted 1777-1851

Ørsteds discovery was a deflection of a Compass needle when it is close to a current carrying conductor.But he was not able to describe the physicsor mathematics behind the phenomena

1820

{f = Bxil / 90° : f=Bil}

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Amperé

André-Marie Ampére 1775 – 1836

Just one week after Ørsteds discovery Ampere showed that two current carrying wires attract or repulse each other, and was ableto show that :

Thus, for two parallel wires carrying a current of 1 A, and spaced apart by 1 m in vacuum,the force on each wire per unit length is exactly 2 × 10-7 N/m.

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I IF

l r

I2

I1r

l

It was first in 1826 he published the circuit law in Maxwell’s equation

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Faraday

Michael Faraday 1791-1867

{e = Bxlv / 90° : e =Blv}

Induction by movement”generator”

Induction by alternating current”transformer”

The Induction law 1821

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Gauss

Carl Friedrich Gauss 1777 – 1855

Basically the magnetic induction can’t escape.The equation says that we don’t have a monopole.There will always be a north and a south pole

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Relations in Maxwell’s equations

Simplified analogies and the relations in Maxwell’s equations

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Permeability

Return

μ = μr μ0 Where μr typically is 1000-100000in magnetic cores

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Analogies

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Faraday’s law

Faraday’s law (again)

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Some of the first electrical machines

Not useful because it makes AC

Improved to a DC machinewhere Ampere proposed Pixii to use a mechanical commutator

Alternator by Pixii 1832

Note it is made with electromagnets(Henry 1828)

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Letz’s law

Letz’s law (consequence of Maxwell’s equation)

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Amperé’s law

Ampere’s law (again)

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Inductor example

Example : Inductor

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Inductor example

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Inductor example

No saturation and hysteresis

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Magnetic circuit model

Magnetic circuit model

Ohm’s law in magnetic circuits

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Magnetic circuit model

What about Kirchoff’s current law (KCL)

Gauss law

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Magnetic circuit model

What about Kirchoff’s voltage law (KVL)

Ampere law is similar to Kirchoff’s voltage law

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Magnetic circuit model (Steel and air-gap)

Magnetic circuit model (Steel and air-gap)

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Magnetic circuit model (Steel and air-gap)

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Core losses

Hysteresis losses

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Hysteresis losses

Hysteresis losses

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Hysteresis losses

Hysteresis curve at various H-fields

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Eddy current losses

Eddy current losses

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Eddy current losses

How do we reduce Eddy current losses

LAMINATED

SOLID

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Eddy current losses

Eddy current losses

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Eddy current losses in windings

Eddy current losses in windings

Can be a problem with thick wires- Low voltage machines- High speed machines

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Force, torque and power

Universal modeling of terminal characteristic of electro-magnetic devicesbased on energy balance

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Force, torque and power

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Simplified machines

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Simplified machines

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Electromagnetic gearing

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2

2

1{

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2

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2

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C

J

m

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E CU Capacitor Energy

E J Rotational Energy

E Mv translational Ener

E LI Inductor Energ

g

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2 0A

g

AL N

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2 0 uU

gu

AL N

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Lgu larger than Lg ≈ ∞

2 2 21 1 1

2 2 2A U AE L I L I L I

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2ALEI

Δθ=90

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Electromagnetic gearing

Same winding but now enclosing two poles : LA is the same (if end winding is neglected the Resistance is also the same)

Δθ=45

Torque doubling

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Normal/radial forces

Normal forces

Ex. Changing the air gap from 0.3 mm to 0.15 mmGives a doubling of inductanceThe Δx is very small i.e a large Force

In electrical machines the normal forces versus the tangential force (torque) is typically a factor 10.