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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


Simplification:

BvQf

Source: MIT Physics Dept. website

BvEQf

BvE


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


V

BHdVU2

1

Basic equation:

sAHBVHBU aaaaaaa 22

1

2

1

Energy contained within airgap:


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


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


Operating Point (constant current)

xs

fm

xkf s

x

0x

f

xkf siismm

0

,

x

Redefining distance:

0xxx s

ks = force-displacement factor


ikf ixxims

0

,im

fm

im0i

2~ mi

mg

fm

im0i

ikf i

i

0iii m

ki = force-current factor

Operating Point (constant position)


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


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!


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


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...


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


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)


at least one degree of freedom unstable!

increase in stiffness with multiple rings

caution: misalignment!

reluctance bearings:

- non-rotating magnets

- resistance to radial displacement


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