Joint Advanced Student School 2006

1
Joint Advanced Student School2006
Magnetic Bearings

• Jeff Hillyard
• Technische Universität München

2
Overview Magnetic Bearings

• Introduction
• Magnetism Review
• Active Magnetic Bearings
• Passive Magnetic Bearings
• Industry Applications

3
Introduction Magnetic Bearing Types

• Active/passive magnetic bearings
• electrically controlled
• no control system
• Radial/axial magnetic bearings

4
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
5
Introduction Survey of Magnetic Bearings
Source Schweitzer
6
Magnetism Magnetic Field
south pole
north pole
magnetic field line
iron filings
Pole Transition
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Magnetism Magnetic Field

• Magnetic field, H, is found around a magnet or a
  current carrying body.

(for one current loop)
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Magnetism Magnetic Flux Density
multiple loops of wire, n

• B magnetic flux density
• magnetic permeability
• H magnetic field

Meissner-Ochsenfeld Effect

• m0 permeability of free space
• mr relative permeability

diamagnetic paramagnetic ferromagnetic
9
Magnetism B-H Diagram
Ferromagnetic a material that can be magnetized
Remanence, Br
magnetic saturation
B
Coercivity, Hc

• H

area within loop represents hysteresis loss
10
Magnetism Lorentz Force

• f force
• Q electric charge
• E electric field
• V velocity of charge Q
• B magnetic flux density

11
Magnetism Lorentz Force

• Simplification

Source MIT Physics Dept. website
12
Magnetism Lorentz Force
Analogous Wire

• Further simplification

B
i
f
force perpendicular to flux!
13
Magnetism Reluctance Force
Force resulting from a difference between
magnetic permeabilities in the presence of a
magnetic field. ? force perpendicular to surface!
The energy in a magnetic field with linear
materials is given by
U energy V volume
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Magnetism Reluctance Force
Basic equation
Energy contained within airgap
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Magnetism Reluctance Force

• Evaluating the magnetic circuit for a simple
  system

?
16
Magnetism Reluctance Force

• Principle of virtual displacement

quadratic!
0
inversely quadratic!
17
Active Magnetic Bearings Elements of System

• Electromagnet
• Rotor
• Sensor
• Controller
• Amplifier

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Active Magnetic Bearings Force Behavior

• Magnetic Force

Spring Force
fs
fm
Force
Force
xs
xs
Distance
Distance
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Active Magnetic Bearings Force Linearization

• Magnetic Force

Spring Force
fs
fm
xs
xs
20
Active Magnetic Bearings Force Linearization

• Operating Point (constant current)

Redefining distance
fm
xs
ks force-displacement factor
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Active Magnetic Bearings Force Linearization
Operating Point (constant position)
ki force-current factor
22
Active Magnetic Bearings Force Linearization
im

• Linearized equation

x

• Not valid for
• rotor-bearing contact
• magnetic saturation
• small currents

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Active Magnetic Bearings Closed Control Loop

• Open Loop Equation

Basic System
Controller function? - Provide force,
f Controller signals? - Input position, x -
Output current, i ? i i(x)
Artifical damping and stiffness
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Active Magnetic Bearings Closed Control Loop

• Solving for controller function

Basic System
To model position of rotor
Just like for the spring system!
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Active Magnetic Bearings Closed Control Loop

• System characteristics
• ?
• with

General solution for position
Eigenfrequency
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Active Magnetic Bearings Closed Control Loop

• Controller Abilities
• k, d can be varied in controller
• air gap can be varied in controller
• specify position for different loads
• rotor balancing, vibrations, monitoring...

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Active Magnetic Bearings Closed Control Loop
Differential driving mode

• Linearization

magnetic force was determined to be
?
where
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Active Magnetic Bearings Closed Control Loop
Differential driving mode

• Linearization

linearized for differential driving mode
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Active Magnetic Bearings Bearing Geometry

• Radial Bearing

Axial Bearing
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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
31
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

other concerns observability placement cost
32
Active Magnetic Bearings Sensors

• Sensorless Bearing
• - calculate position
• - less equipment
• - lower cost

Source Hoffmann
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Active Magnetic Bearings Amplifier

• Converts control signals to control currents.

Analog Amplifier - simple structure - low power
applications Plt0.6 kVA
Switching Amplifier - lower losses - high power
applications - remagnetization loss
34
Active Magnetic Bearings Electrical Response

• There is an inherent delay in the electrical
  system
• ? inductance
• voltage drops and

Total voltage drop
velocity within magnetic field induces a voltage
ku voltage-velocity coefficient
35
Active Magnetic Bearings Control Equations of
Motion

• Block diagram with voltage control

Source Schweitzer
36
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

37
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

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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

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Active Magnetic Bearings Copper Losses

• For differential driving mode

An slot area Kn bulk factor r specific
resistance lm average length of turn
limit of permissible mmf!
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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
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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
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Active Magnetic Bearings Rotor Stresses

• Radial
• Tangential

Source Schweizer
largest stress is at inside radius of disc with
hole!
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Active Magnetic Bearings Rotor Stresses

• Implications of max stress
• ? max velocity (full disc)!

Material vmax (m/s) steel 576 brass 376 bronze
434 aluminium 593 titanium 695 soft ferro.
sheets 565
ss max tensile strength
Actual reached speeds (length 600 mm, dia. 45
mm) ?
Source Schweizer
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Passive Magnetic Bearings Permanent Magnets
Relative Sizes

• Common Materials
• neodymium, iron, boron (Nd Fe B)
• samarium, cobalt, boron
• (Sm Co, Sm Co B)
• ferrite
• aluminium, nickel, cobalt
• (Al Ni, Al Ni Co)

Issues - material brittleness - varying space
requirements (B-H) - operating temperatures
(equal H at 10 mm)
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Passive Magnetic Bearings Permanent Magnets

• at least one degree of freedom unstable!

reluctance bearings - non-rotating magnets -
resistance to radial displacement
increase in stiffness with multiple
rings caution misalignment!
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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
47
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 (gt 550C)
• increase life span
• optimize fill factor
• reduce cost
• simplify manufacturing

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Applications Flywheel (97)

• New Energy and Industrial Technology Development
  Organization (NEDO) Japans Ministry of
  International Trade and Industry (MITI)
• T½Jw2 ? 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 (hsys 84)

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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

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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
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Applications Maglev Trainsx

• Maglev in Shanghai
• - complete in 2004
• - airport to financial district (30 km)
• - worlds fastest maglev in commercial operation
  (501 km/h)
• - service speed of 430 km/h

Source www.monorails.org
52
Applications Maglev Trains
Noise Reduction by Frequency
Noise Reduction by Speed
Source Moon
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Magnetic Bearings References

• Betschon, F. Design Principles of Integrated
  Magnetic Bearings, Diss. ETH. Nr. 13643, ETH
  Zürich, 2000.
• 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.
• Electricity and Magnetism. Hyperphysics. Georgia
  State University, Dept. of Physics and
  Astronomy. 1 Apr. 2006 lthttp//hyperphysics.phy-a
  str.gsu.edu/Hbase/hph.htmlgt.
• Fremery, J.K. Permanentmagnetische Lager.
  Forshungszentrum Jülich, Zentralabteilung
  Technologie, 2000.
• Hoffmann, K.J. Integrierte aktive Magnetlager,
  Diss. TU Darmstadt. Herdecke GCA-Verlag 1999.
• Lösch, F. Identification and Automated Controller
  Design for Active Magnetic Bearing Systems,
  Diss. ETH. Nr. 14474, ETH Zürich, 2002.
• Maglev Monorails of the World Shanghai, China.
  The Monorail Society Website. 1 Apr. 2006
  lthttp//www.monorails.org/tMspages/MagShang.htmlgt
  .
• Maglev Train Explained, DiscoveryChannel.ca. Bell
  Globemedia 2005 lthttp//discoverychannel.ca/inter
  actives/japan/maglev/maglev.htmlgt.
• 9. Magnetic Bearings High Speed Motors, S2M. 1
  Apr. 2006 lthttp//www.s2m.fr/chap3/gt.

54
Magnetic Bearings References

• Moon, F.C. Superconducting Levitation
  Applications to Bearings and Magnetic
  Transportation. New York John Wiley Sons,
  1994.
• Research and Development for Superconducting
  Bearing Technology for Flywheel Electric Energy
  Storage System. New Energy and Industrial
  Technology Development Organization (NEDO). 1
  Apr. 2006 lthttp//www.nedo.go.jp/english/activiti
  es/2_sinenergy/1/p04033e.htmlgt.
• Schwall, R. Power Systems Other Applications
  Flywheels. Power Applications of
  Superconductivity in Japan and Germany. WTEC
  Hyper-Librarian 1997 lthttp//www.wtec.org/loyola/
  scpa/04_02.htmgt.
• 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
• lthttp//www.machinedesign.com/ASP/strArticleID/5
  7263/strSite/MDSite/viewSelectedArticle.aspgt.
• 15. Wikipedia contributors (2006). Hysteresis.
  Wikipedia, The Free Encyclopedia. April 1, 2006
• lthttp//en.wikipedia.org/w/index.php?titleHyste
  resisoldid45621877gt.
• 16. Wikipedia contributors (2006). Magnetic
  field. Wikipedia, The Free Encyclopedia. April 1,
  2006 lthttp//en.wikipedia.org/w/index.php?titleM
  agnetic_fieldoldid46010831 gt.

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Questions?
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Applications Crystal Growing System