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Transcript of 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis...
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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
2
Maxwell
James Clerk Maxwell 1831 - 1879
Unified theory of the connection between electricity and magnetism
3
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
0 0
1c
4
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}
5
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.
0 1 2·
2
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
8
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
10
Analogies
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Faraday’s law
Faraday’s law (again)
12
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)
13
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
20
Magnetic circuit model
What about Kirchoff’s voltage law (KVL)
Ampere law is similar to Kirchoff’s voltage law
21
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)
23
Core losses
Hysteresis losses
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Hysteresis losses
Hysteresis losses
25
Hysteresis losses
Hysteresis curve at various H-fields
26 Hysteresis losses
27
Eddy current losses
Eddy current losses
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Eddy current losses
How do we reduce Eddy current losses
LAMINATED
SOLID
29
Eddy current losses
Eddy current losses
30
Eddy current losses in windings
Eddy current losses in windings
Can be a problem with thick wires- Low voltage machines- High speed machines
31
Force, torque and power
Universal modeling of terminal characteristic of electro-magnetic devicesbased on energy balance
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Force, torque and power
33
Force, torque and power
34
Force, torque and power
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Force, torque and power
36
Force, torque and power
37
Force, torque and power
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Force, torque and power
39
Force, torque and power
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Force, torque and power
41
Simplified machines
42
Simplified machines
43
Electromagnetic gearing
2
2
2
2
1{
2
1{
2
2
1
2
1
{
{
C
J
m
L
E CU Capacitor Energy
E J Rotational Energy
E Mv translational Ener
E LI Inductor Energ
g
y
y
2 0A
g
AL N
l
2 0 uU
gu
AL N
l
Lgu larger than Lg ≈ ∞
2 2 21 1 1
2 2 2A U AE L I L I L I
21
2ALEI
Δθ=90
44
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
45
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.