1 magnetism content of the presentation - maxwell's general equations on magnetism - hysteresis...
TRANSCRIPT
![Page 1: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/1.jpg)
1
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
![Page 2: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/2.jpg)
2
Maxwell
James Clerk Maxwell 1831 - 1879
Unified theory of the connection between electricity and magnetism
![Page 3: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/3.jpg)
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
![Page 4: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/4.jpg)
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}
![Page 5: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/5.jpg)
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
![Page 6: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/6.jpg)
6
Faraday
Michael Faraday 1791-1867
{e = Bxlv / 90° : e =Blv}
Induction by movement”generator”
Induction by alternating current”transformer”
The Induction law 1821
![Page 7: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/7.jpg)
7
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
![Page 8: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/8.jpg)
8
Relations in Maxwell’s equations
Simplified analogies and the relations in Maxwell’s equations
![Page 9: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/9.jpg)
9
Permeability
Return
μ = μr μ0 Where μr typically is 1000-100000in magnetic cores
![Page 10: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/10.jpg)
10
Analogies
![Page 11: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/11.jpg)
11
Faraday’s law
Faraday’s law (again)
![Page 12: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/12.jpg)
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)
![Page 13: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/13.jpg)
13
Letz’s law
Letz’s law (consequence of Maxwell’s equation)
![Page 14: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/14.jpg)
14
Amperé’s law
Ampere’s law (again)
![Page 15: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/15.jpg)
15
Inductor example
Example : Inductor
![Page 16: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/16.jpg)
16
Inductor example
![Page 17: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/17.jpg)
17
Inductor example
No saturation and hysteresis
![Page 18: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/18.jpg)
18
Magnetic circuit model
Magnetic circuit model
Ohm’s law in magnetic circuits
![Page 19: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/19.jpg)
19
Magnetic circuit model
What about Kirchoff’s current law (KCL)
Gauss law
![Page 20: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/20.jpg)
20
Magnetic circuit model
What about Kirchoff’s voltage law (KVL)
Ampere law is similar to Kirchoff’s voltage law
![Page 21: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/21.jpg)
21
Magnetic circuit model (Steel and air-gap)
Magnetic circuit model (Steel and air-gap)
![Page 22: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/22.jpg)
22
Magnetic circuit model (Steel and air-gap)
![Page 23: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/23.jpg)
23
Core losses
Hysteresis losses
![Page 24: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/24.jpg)
24
Hysteresis losses
Hysteresis losses
![Page 25: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/25.jpg)
25
Hysteresis losses
Hysteresis curve at various H-fields
![Page 26: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/26.jpg)
26 Hysteresis losses
![Page 27: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/27.jpg)
27
Eddy current losses
Eddy current losses
![Page 28: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/28.jpg)
28
Eddy current losses
How do we reduce Eddy current losses
LAMINATED
SOLID
![Page 29: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/29.jpg)
29
Eddy current losses
Eddy current losses
![Page 30: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/30.jpg)
30
Eddy current losses in windings
Eddy current losses in windings
Can be a problem with thick wires- Low voltage machines- High speed machines
![Page 31: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/31.jpg)
31
Force, torque and power
Universal modeling of terminal characteristic of electro-magnetic devicesbased on energy balance
![Page 32: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/32.jpg)
32
Force, torque and power
![Page 33: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/33.jpg)
33
Force, torque and power
![Page 34: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/34.jpg)
34
Force, torque and power
![Page 35: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/35.jpg)
35
Force, torque and power
![Page 36: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/36.jpg)
36
Force, torque and power
![Page 37: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/37.jpg)
37
Force, torque and power
![Page 38: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/38.jpg)
38
Force, torque and power
![Page 39: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/39.jpg)
39
Force, torque and power
![Page 40: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/40.jpg)
40
Force, torque and power
![Page 41: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/41.jpg)
41
Simplified machines
![Page 42: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/42.jpg)
42
Simplified machines
![Page 43: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/43.jpg)
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
![Page 44: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/44.jpg)
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
![Page 45: 1 Magnetism Content of the presentation - Maxwell's general equations on magnetism - Hysteresis curve - Inductance - Magnetic circuit modelling - Eddy](https://reader035.vdocuments.net/reader035/viewer/2022062421/56649cb75503460f9497c7d0/html5/thumbnails/45.jpg)
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.