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Joint Advanced Student School 2006. Jeff Hillyard Technische Universität München. Magnetic Bearings. Overview Magnetic Bearings. Introduction Magnetism Review Active Magnetic Bearings Passive Magnetic Bearings Industry Applications. Introduction Magnetic Bearing Types. - PowerPoint PPT Presentation
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Joint Advanced Student School2006
Jeff Hillyard
Technische Universität München
Magnetic Bearings
Overview Magnetic Bearings
• Introduction• Magnetism Review• Active Magnetic Bearings• Passive Magnetic Bearings• Industry Applications
Introduction Magnetic Bearing Types
• Active/passive magnetic bearings– electrically controlled– no control system
• Radial/axial magnetic bearings
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
Introduction Survey of Magnetic Bearings
Source: Schweitzer
Magnetism Magnetic Field
north polesouth pole
magnetic field line
iron filings
Pole Transition
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
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
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
Magnetism Lorentz Force
f = force
Q = electric charge
E = electric field
V = velocity of charge Q
B = magnetic flux density
BvEQf
Magnetism Lorentz Force
Simplification:
BvQf
Source: MIT Physics Dept. website
BvEQf
BvE
Magnetism Lorentz Force
Further simplification:
Bif
BvQf
vQi
force perpendicular to flux!
f
i
B
Analogous Wire
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
Aa
slFe 2
Magnetism Reluctance Force
V
BHdVU2
1
Basic equation:
sAHBVHBU aaaaaaa 22
1
2
1
Energy contained within airgap:
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
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!
Active Magnetic Bearings Elements of System
• Electromagnet• Rotor• Sensor• Controller• Amplifier
Active Magnetic Bearings Force Behavior
Distance
fs
For
ce
Distance
fm
For
ce
2
1~
sx
Magnetic Force Spring Force
xs xs
Active Magnetic Bearings Force Linearization
Magnetic Force Spring Force
fsfm2
1~
sx
xs xs
mg
0x
mg
0x
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
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)
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
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
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!
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
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...
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
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
Radial Bearing Axial Bearing
Active Magnetic Bearings Bearing Geometry
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
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
Active Magnetic Bearings Sensors
“Sensorless“ Bearing- calculate position- less equipment- lower cost
Source: Hoffmann
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
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:
Active Magnetic Bearings Control Equations of Motion
Block diagram with voltage control:
fxm
xkdt
diLRiu u
ikxkixf is ),(
Source: Schweitzer
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
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
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
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!
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
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
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
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
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)
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
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
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
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%)
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
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
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
Applications Maglev Trains
Noise Reduction
by FrequencyNoise Reduction
by Speed
Source: Moon
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/>.
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 >.
Questions?
Applications Crystal Growing System