Download - Joint Advanced Student School 2006
![Page 1: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/1.jpg)
Joint Advanced Student School2006
Jeff Hillyard
Technische Universität München
Magnetic Bearings
![Page 2: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/2.jpg)
Overview Magnetic Bearings
• Introduction• Magnetism Review• Active Magnetic Bearings• Passive Magnetic Bearings• Industry Applications
![Page 3: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/3.jpg)
Introduction Magnetic Bearing Types
• Active/passive magnetic bearings– electrically controlled– no control system
• Radial/axial magnetic bearings
![Page 4: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/4.jpg)
Introduction Motivations
Advantages of magnetic bearings: contact-free no lubricant (no) maintenance tolerable against heat, cold, vacuum, chemicals low losses very high rotational speeds
Disadvantages: complexity high initial cost
Minimum Equipment for AMB
Source: Betschon
![Page 5: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/5.jpg)
Introduction Survey of Magnetic Bearings
Source: Schweitzer
![Page 6: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/6.jpg)
Magnetism Magnetic Field
north polesouth pole
magnetic field line
iron filings
Pole Transition
![Page 7: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/7.jpg)
Magnetism Magnetic Field
Magnetic field, H, is found around a magnet or a current carrying body.
r
iH
2
idsH
(for one current loop)
H
i
![Page 8: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/8.jpg)
Magnetism Magnetic Flux Density
B = magnetic flux density = magnetic permeability
H = magnetic field
HB
r 00 = permeability of free space
r = relative permeability
1
1
diamagnetic
paramagnetic
ferromagnetic
r
niH
2
multiple loops of wire, n
1
Meissner-Ochsenfeld Effect
![Page 9: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/9.jpg)
Magnetism B-H Diagram
H
B
area within loop represents hysteresis loss
magnetic saturation
Ferromagnetic: a material that can be magnetized
HB
Coercivity, Hc
Remanence, Br
![Page 10: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/10.jpg)
Magnetism Lorentz Force
f = force
Q = electric charge
E = electric field
V = velocity of charge Q
B = magnetic flux density
BvEQf
![Page 11: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/11.jpg)
Magnetism Lorentz Force
Simplification:
BvQf
Source: MIT Physics Dept. website
BvEQf
BvE
![Page 12: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/12.jpg)
Magnetism Lorentz Force
Further simplification:
Bif
BvQf
vQi
force perpendicular to flux!
f
i
B
Analogous Wire
![Page 13: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/13.jpg)
Magnetism Reluctance Force
V
BHdVU2
1
The energy in a magnetic field with linear materials is given by:
Force resulting from a difference between magnetic permeabilities in the presence of a magnetic field.
force perpendicular to surface!
2
2ABf
U = energy
V = volume
l
Uf
![Page 14: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/14.jpg)
Aa
slFe 2
Magnetism Reluctance Force
V
BHdVU2
1
Basic equation:
sAHBVHBU aaaaaaa 22
1
2
1
Energy contained within airgap:
![Page 15: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/15.jpg)
Magnetism Reluctance Force
Evaluating the magnetic circuit for a simple system:
nisHHlHds aFeFe 2
NIniB
sB
lr
Fe 00
2
s
l
NIB
r
Fe 20
aaFeFe ABAB
BBB aFe
Assumption:
Aa
slFe 2
![Page 16: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/16.jpg)
Magnetism Reluctance Force
Principle of virtual displacement:
0B
H a
aaa ABHl
Uf
cos2
2
0 arFe
Asl
nif
2
2
s
ikf
0
quadratic!
inversely quadratic!
![Page 17: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/17.jpg)
Active Magnetic Bearings Elements of System
• Electromagnet• Rotor• Sensor• Controller• Amplifier
![Page 18: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/18.jpg)
Active Magnetic Bearings Force Behavior
Distance
fs
For
ce
Distance
fm
For
ce
2
1~
sx
Magnetic Force Spring Force
xs xs
![Page 19: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/19.jpg)
Active Magnetic Bearings Force Linearization
Magnetic Force Spring Force
fsfm2
1~
sx
xs xs
mg
0x
mg
0x
![Page 20: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/20.jpg)
Active Magnetic Bearings Force Linearization
Operating Point (constant current)
xs
fm
xkf s
x
0x
f
xkf siismm
0
,
x
Redefining distance:
0xxx s
ks = force-displacement factor
![Page 21: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/21.jpg)
Active Magnetic Bearings Force Linearization
ikf ixxims
0
,im
fm
im0i
2~ mi
mg
fm
im0i
ikf i
i
0iii m
ki = force-current factor
Operating Point (constant position)
![Page 22: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/22.jpg)
Active Magnetic Bearings Force Linearization
Linearized equation:
00
,,,xximiism
sm
ffixf
ikf ixxims
0
,
x
im
xkf siismm
0
,
0iii m
0xxx s
ikxkixf is ,
Not valid for:- rotor-bearing contact- magnetic saturation- small currents
![Page 23: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/23.jpg)
Active Magnetic Bearings Closed Control Loop
Open Loop Equation: Basic System
ikxkixf is ,
Controller function?
- Provide force, f
Controller signals?
- Input: position, x
- Output: current, i
i = i(x)
x
i
x
Artifical damping and stiffness:
xdkxf x
k d
![Page 24: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/24.jpg)
Active Magnetic Bearings Closed Control Loop
Solving for controller function:Basic System
xdkxikxk is
x
i
x
To model position of rotor:
i
s
k
xdxkkxi
xmf
ikxkixf is ,
ikxkxm is
0 kxxdxm
Just like for the spring system!
![Page 25: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/25.jpg)
Active Magnetic Bearings Closed Control Loop
System characteristics:
with
02 kdm x(t)
ttCe
j
2
2
4m
d
m
k
m
d
2
General solution for position:
tCetx t cos
Eigenfrequency:
mk 220
![Page 26: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/26.jpg)
Active Magnetic Bearings Closed Control Loop
Controller Abilities:1) k, d can be varied in controller
2) air gap can be varied in controller
3) specify position for different loads
4) rotor balancing, vibrations, monitoring...
![Page 27: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/27.jpg)
Active Magnetic Bearings Closed Control Loop
Linearization:
cos4
12
20
s
iAnf a
cos20
20
20
20
xs
ii
xs
iikfff xx
x
xss 0
xss 0cos
2
2
s
ikf aAnk 2
04
1
magnetic force was determined to be
where
Differential driving mode
![Page 28: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/28.jpg)
Active Magnetic Bearings Closed Control Loop
Linearization:
xx
fi
i
ff
x
xx
xx
xx
00
xs
kii
s
kif xx
cos
4cos
430
20
20
0
ik sk
xkikf sxix
linearized for differential driving mode
Differential driving mode
![Page 29: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/29.jpg)
Radial Bearing Axial Bearing
Active Magnetic Bearings Bearing Geometry
![Page 30: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/30.jpg)
B circumferential to rotor axis
B parallel to rotor axis
- similar to electromotors
- rotor requires lamination- hysteresis loss low
- lamination avoided
Orientation:
magnet pole pairs are often lined up with the principle coordinate axes x and y (vertical and horizontal)
control equations are simplified
Active Magnetic Bearings Bearing Geometry
![Page 31: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/31.jpg)
Active Magnetic Bearings Sensors
Position Sensor• contact-free• measure rotating surface
– surface quality– homogeneity of surface material– various values
Other Sensors• speed• current• flux density• temperature• …
+ sensor
…other concerns:observabilityplacementcost
![Page 32: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/32.jpg)
Active Magnetic Bearings Sensors
“Sensorless“ Bearing- calculate position- less equipment- lower cost
Source: Hoffmann
![Page 33: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/33.jpg)
Active Magnetic Bearings Amplifier
Converts control signals to control currents.
Analog Amplifier:
- simple structure
- low power applications
P<0.6 kVA
Switching Amplifier:
- lower losses
- high power applications
- remagnetization loss
![Page 34: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/34.jpg)
Active Magnetic Bearings Electrical Response
There is an inherent delay in the electrical system
inductance
voltage drops: and
velocity within magnetic field induces a voltage
dt
diLuL RiuR
xkdt
diLRiu u
ku = voltage-velocity coefficient
Total voltage drop:
![Page 35: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/35.jpg)
Active Magnetic Bearings Control Equations of Motion
Block diagram with voltage control:
fxm
xkdt
diLRiu u
ikxkixf is ),(
Source: Schweitzer
![Page 36: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/36.jpg)
Active Magnetic Bearings Current vs. Voltage Control
Voltage Control:- more accurate model- better stability- low stiffness easier to realize- voltage amplifier often more convenient- possible to avoid using position sensor
Current Control:- simple control plant description- simple PD or PID control
Flux Control:- very uncommon
![Page 37: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/37.jpg)
Active Magnetic Bearings Addressing of Assumptions
Uncertainties in bearing model- leakage flux outside of air gap- air gap is bigger than assumed- iron cross section is non-uniform
![Page 38: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/38.jpg)
Active Magnetic Bearings Types of Losses
Air Losses
- air friction divide shaft into sections
Copper Losses (Stator)
- wire resistance
Iron Losses (Rotor)
- hysteresis (higher w/ switching amplifier)
- eddy currents
2iRP CuCu
![Page 39: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/39.jpg)
Active Magnetic Bearings Copper Losses
For differential driving mode:
2maxmax, 2 iRP CuCu
nAKA dnn
m
nnCu l
KAPNI
2max,max
n = slot area
Kn = bulk factor
= specific resistance
lm = average length of turn
limit of permissible mmf!
![Page 40: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/40.jpg)
Active Magnetic Bearings Rotor Dynamics
Areas of Consideration• natural vibrations• forward/backward whirl (natural vibrations)• critical speeds• nutation• precession (change in rotation axis)
Source: Wikipedia
![Page 41: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/41.jpg)
Active Magnetic Bearings Rotor Dynamics
rotor touch-down in retainer bearings- maintenance
- sudden system shutoff
- during system shutdown
very difficult to simulate
cylindrical motion conical motion Source: Schweizer
![Page 42: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/42.jpg)
Active Magnetic Bearings Rotor Stresses
Radial
Tangential
2
2
222223
8
1r
r
rrrr aiair
2
2
22222 3133
8
1r
r
rrrr aiait
largest stress is at inside radius of disc with hole!
Source: Schweizer
![Page 43: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/43.jpg)
Active Magnetic Bearings Rotor Stresses
Implications of max stress:
max velocity (full disc)!
3
8max
Sarv
s = max tensile strength
Material vmax (m/s)
steel 576
brass 376
bronze 434
aluminium 593
titanium 695soft ferro. sheets 565
Actual reached speeds (length 600 mm, dia. 45 mm):
smv 300max rpm000,120max
Source: Schweizer
![Page 44: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/44.jpg)
Passive Magnetic Bearings Permanent Magnets
Common Materials:1) neodymium, iron, boron (Nd Fe B)
2) samarium, cobalt, boron(Sm Co, Sm Co B)
3) ferrite
4) aluminium, nickel, cobalt (Al Ni, Al Ni Co)
Relative Sizes
Issues:- material brittleness
- varying space requirements (B-H)
- operating temperatures(equal H at 10 mm)
![Page 45: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/45.jpg)
Passive Magnetic Bearings Permanent Magnets
at least one degree of freedom unstable!
increase in stiffness with multiple rings
caution: misalignment!
reluctance bearings:
- non-rotating magnets
- resistance to radial displacement
![Page 46: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/46.jpg)
Passive Magnetic Bearings Permanent Magnets
High Potential- economical
- reliable
- practical
already replacing some active magnetic bearings- smaller size equipment and systems
- systems with large air gaps
Source: Boden
![Page 47: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/47.jpg)
Applications Turbomolecular Pump
École Polytechnique Fédérale de Lausanne, Switzerland- eliminates complicated lubrication system- high temperature resistance- reduction of pollution- vibrations, noise, stresses avoided- improved monitoring (unbalances, defects, etc.)
Status: suboptimal design overheating at load (> 550°C) increase life span optimize fill factor reduce cost simplify manufacturing
![Page 48: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/48.jpg)
Applications Flywheel (‘97)
New Energy and Industrial Technology Development Organization (NEDO) – Japan‘s Ministry of International Trade and Industry (MITI)
• T=½J2 speed has larger influence than mass (better energy density)
• fiber-reinforced plastics for high strength
• fracture into small pieces upon failure above ground
• combination of superconductor and permanent magnet bearings (sys = 84%)
![Page 49: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/49.jpg)
Applications Flywheel (‘97)
Current Development Goals (NEDO)• increase load force
• reduce amount load force decrease with time (magnetic flux creep)
• reduce rotational loss
• increase size of bearings for larger systems
![Page 50: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/50.jpg)
Applications Maglev Trains
Maglev = Magnetic Levitation• 150 mm levitation over guideway track
undisturbed from small obstacles (snow, debris, etc.)
• typical ave. speed of 350 km/h (max 500 km/h)what if? Paris-Moscow in 7 hr 10 min (2495 km)!
• stator: track, rotor: magnets on train
Source: DiscoveryChannel.com
![Page 51: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/51.jpg)
Applications Maglev Trainsx
Maglev in Shanghai
- complete in 2004
- airport to financial district (30 km)
- world‘s fastest maglev in commercial operation (501 km/h)
- service speed of 430 km/h
Source: www.monorails.org
![Page 52: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/52.jpg)
Applications Maglev Trains
Noise Reduction
by FrequencyNoise Reduction
by Speed
Source: Moon
![Page 53: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/53.jpg)
Magnetic Bearings References
1. Betschon, F. Design Principles of Integrated Magnetic Bearings, Diss. ETH. Nr. 13643, ETH Zürich, 2000.
2. Boden, K. & Fremerey, J.K. Industrial Realization of the “SYSTEM KFA-JÜLICH“ Permanent Magnet Bearing Lines, Proceedings of MAG ‘92 Magnetic Bearings, Magnetic Drives and Dry Gas Seals Conference & Exhibition. Lancaster: Technomic Publishing, 1998.
3. Electricity and Magnetism. Hyperphysics. Georgia State University, Dept. of Physics and Astronomy. 1 Apr. 2006 <http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html>.
4. Fremery, J.K. Permanentmagnetische Lager. Forshungszentrum Jülich, Zentralabteilung Technologie, 2000.
5. Hoffmann, K.J. Integrierte aktive Magnetlager, Diss. TU Darmstadt. Herdecke: GCA-Verlag 1999.
6. Lösch, F. Identification and Automated Controller Design for Active Magnetic Bearing Systems, Diss. ETH. Nr. 14474, ETH Zürich, 2002.
7. Maglev Monorails of the World: Shanghai, China. The Monorail Society Website. 1 Apr. 2006 <http://www.monorails.org/tMspages/MagShang.html>.
8. Maglev Train Explained, DiscoveryChannel.ca. Bell Globemedia 2005 <http://discoverychannel.ca/interactives/japan/maglev/maglev.html>.
9. Magnetic Bearings & High Speed Motors, S2M. 1 Apr. 2006 <http://www.s2m.fr/chap3/>.
![Page 54: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/54.jpg)
Magnetic Bearings References
10. Moon, F.C. Superconducting Levitation: Applications to Bearings and Magnetic Transportation. New York: John Wiley & Sons, 1994.
11. Research and Development for Superconducting Bearing Technology for Flywheel Electric Energy Storage System. New Energy and Industrial Technology Development Organization (NEDO). 1 Apr. 2006 <http://www.nedo.go.jp/english/activities/2_sinenergy/1/p04033e.html>.
12. Schwall, R. Power Systems – Other Applications: Flywheels. Power Applications of Superconductivity in Japan and Germany. WTEC Hyper-Librarian 1997 <http://www.wtec.org/loyola/scpa/04_02.htm>.
13. Schweizer, G., Bleuler, H., & Traxler, A. Active Magnetic Bearings: Basics, Properties and Applications of Active Magnetic Bearings. Zürich: Hochschulverlag AG an der ETH, 1994.
14. Widbro, L. Magnetic Bearings Come of Age. Revolve Magnetic Bearings Inc. 2004. MachineDesign.com. 1 Apr. 2006
<http://www.machinedesign.com/ASP/strArticleID/57263/strSite/MDSite/viewSelectedArticle.asp>.
15. Wikipedia contributors (2006). Hysteresis. Wikipedia, The Free Encyclopedia. April 1, 2006 <http://en.wikipedia.org/w/index.php?title=Hysteresis&oldid=45621877>.
16. Wikipedia contributors (2006). Magnetic field. Wikipedia, The Free Encyclopedia. April 1, 2006 <http://en.wikipedia.org/w/index.php?title=Magnetic_field&oldid=46010831 >.
![Page 55: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/55.jpg)
Questions?
![Page 56: Joint Advanced Student School 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062720/5681358b550346895d9cf2ad/html5/thumbnails/56.jpg)
Applications Crystal Growing System